From 15efe30de6a2fe933fdf2d43b562732d55d941ce Mon Sep 17 00:00:00 2001 From: stefan-woerner Date: Thu, 20 Dec 2018 18:46:31 +0100 Subject: [PATCH 001/116] switch from BasicAer to LegacySimulators --- .../european_call_option_pricing.ipynb | 54 ++++++++++--------- .../aqua/finance/fixed_income_pricing.ipynb | 12 ++--- .../aqua/finance/portfolio_optimization.ipynb | 16 +++--- 3 files changed, 45 insertions(+), 37 deletions(-) diff --git a/qiskit/aqua/finance/european_call_option_pricing.ipynb b/qiskit/aqua/finance/european_call_option_pricing.ipynb index 6ccf50564..4ef0c1a31 100644 --- a/qiskit/aqua/finance/european_call_option_pricing.ipynb +++ b/qiskit/aqua/finance/european_call_option_pricing.ipynb @@ -53,15 +53,13 @@ { "cell_type": "code", "execution_count": 1, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "import numpy as np\n", - "from qiskit import BasicAer\n", + "from qiskit import LegacySimulators\n", "from qiskit_aqua.algorithms import AmplitudeEstimation\n", "from qiskit_aqua.components.uncertainty_problems import EuropeanCallExpectedValue, EuropeanCallDelta\n", "from qiskit_aqua.components.random_distributions import LogNormalDistribution" @@ -120,12 +118,14 @@ "outputs": [ { "data": { - "image/png": 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+tZdNx2Z1TwMeAN4MnJz93D+3/9cD1wBXAF8G3gGcJWl+RFzYzHM2M7P+0eplsoeAx0lT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\nYII=\n", 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\n", 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kdTSzj4GjJG0DbGNZVjd0zjk++ABOOAG+9z24/35o2RJOOokZ06dz0EEHxZ3O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\nnHOuTv4faiZuMWvWF98AAAAASUVORK5CYII=\n", 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\n", "text/plain": [ "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -269,13 +271,11 @@ { "cell_type": "code", "execution_count": 8, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ - "# result = ae.run(quantum_instance=BasicAer.get_backend('qasm_simulator'), shots=100)\n", - "result = ae.run(quantum_instance=BasicAer.get_backend('statevector_simulator'))" + "# result = ae.run(quantum_instance=LegacySimulators.get_backend('qasm_simulator'), shots=100)\n", + "result = ae.run(quantum_instance=LegacySimulators.get_backend('statevector_simulator'))" ] }, { @@ -306,22 +306,26 @@ "outputs": [ { "data": { - "image/png": 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N3yfSNIofR0R+hZFHSTd9/Cvgo6TpF/MkHdJEXXtRV3+bPGigvo1qsdGNVLNt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\nMyuFA46ZmZXCAcfMzErx/wEcoM5WrinEjAAAAABJRU5ErkJggg==\n", 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\n", 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\n", 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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -396,8 +400,8 @@ }, "outputs": [], "source": [ - "# result_delta = ae_delta.run(quantum_instance=BasicAer.get_backend('qasm_simulator'), shots=100)\n", - "result_delta = ae_delta.run(quantum_instance=BasicAer.get_backend('statevector_simulator'))" + "# result_delta = ae_delta.run(quantum_instance=LegacySimulators.get_backend('qasm_simulator'), shots=100)\n", + "result_delta = ae_delta.run(quantum_instance=LegacySimulators.get_backend('statevector_simulator'))" ] }, { @@ -428,12 +432,14 @@ "outputs": [ { "data": { - "image/png": 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WA8NrpA8Dnm+wjA8DAn7cV8aIWA1cB/jG8WZmJSs64Cyi6lyNpJ2ALak6t1PHscDtEfFY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\nBxwzMyuEA46ZmRX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cglYqa9ZxvZxDHX3atXUPW/r1IzpRG7OOKrqHcwnwCnC1pEOyE/bTgQsjN1Va0hJJ36tx/LHAWuCq6h2Shkn6uaRpkg6WNAmYC+wIfK0DbTEzsyYU2sOJiOWSDga+DfyMdN7mIlLQqa5XreVujgVuiYhlNfa9AiwjrVgwEngZuAM4KCLmt6UBZmbWssIX74yI+4H39JFndC/p76hzzMvAUf2qnFnRxmYz+xd41NcGP68WbVamhQvLroFZYXwDNjMzK4QDjpmZFcIBx8zMCuGAY2ZmhXDAMTOzQniWmlmZpkwpuwZmhXHAMStT5RbTZl3AQ2pmZlaIpgKOpFrLzZhZqxYs8CoD1jWaHVJ7QtIVwGUR8UAnKmTWVcZlN0os8M67ZmVpdkhtBnAM8FtJv5Q0VdLWHaiXmZkNMk0FnIg4KyJ2BQ4FFgMXAk9J+qGkQzpRQTMzGxxamjQQEbdGxMeB7YHPAW8DbpS0VNJ0SX/RzkqamdnGr7+z1MYB7ybdNno58HPgBGCJpI/1s2wzMxtEmg44knaRdJakh4BbgB2Avwf+IiL+DtiFdK7ngrbW1MzMNmpNzVKTdCupR/M4cDlpttoj+TwR8aqkHwGfb1clzcxs49fstOhngInAzRF153HeDby55VqZdYv5vvu5dY9mA863gYW1go2kocDeEXFbRKwBHtngaDNbX+UW02ZdoNlzOHOBPXrZ97Zsv5mZ2QaaDTiqs28osKofdTHrPlOnps2sC/Q5pCbp3cD4XNIJkt5XlW0L4Ajg3vZVzawLXHppevSq0dYFGjmHsx/p4k6AAD4ErK3K8ydgEXBK+6pmZmaDSZ8BJyIuILumRtLDwAcj4u5OV8zMzAaXpmapRYSnOpuZWUsaOYczEbg9IlZkP9cVEde1pWZmZjaoNNLDuQbYH/hV9nPQ+2y1AHyTNjMz20AjAefNwFO5n82sXfbeu+wamBWmkUkDj9T62czawLeXti7SyDmcNzRTYET44k8zM9tAI0NqK0nnZhrlczhmZraBRgLO39NcwDGzRimbf1N38XWzwaGRcziXF1APMzMb5Pp7i2kzM7OGNDJp4FfA5Ii4X9Jd9DG8FhH7tqtyZmY2eDRyDuc+YHXuZw82m5lZ0xo5h/PJ3M+TO1obMzMbtFo+h6NkO0n1bspmZmYGNLlaNPx5Mc8zgbHZ8WslLQC+GhHXtrl+ZoPbjBll18CsME0FHEnTgO8AtwCfB/4IjASOAv5b0mciwn9BZo3y7aWtizTbwzkDmBkRn65Kv0TSJcAXAQccMzPbQLPncN4IXN3Lvp8A2/RVgKQ9JN0iaZWkJyWdI6nucjiSRkuKGtusGnmPlHSvpJcl3S9pUkMtMyvDzJlpM+sCzfZw5gIHATfX2HcQcFu9gyWNAOYA9wNHArsB3yQFvjMbeP2TgV/knj9TVf6BpMD3HeBEYCJwpaTlEXFTA+WbFWvatPTooTXrAo1c+LlH7um/AN+V9EZgNq+dw/kgcDhwQh/FfQoYAhwVESuAmyVtDUyXdH6WVs/iiLizzv4vAbdFxInZ87mS9gS+DDjgmJmVqJEezm9Z/2JPAdOyrfrunzdQf7Xow4EbqwLLLOA8Ug/pZw3UpyZJrwcmkHo2ebOAyyQNi4gXWi3fzMz6p5GAM6GNrzcGuDWfEBGPSlqV7esr4FwmaRtSz+pK4IsRUVkFYTdgc2BR1TEPkIbsdgfu6l/1zcysVY2sNDCvja83Ani+RvrybF9vXgH+lTQstgIYD5xKCjJH5sqmRvnLq/avR9JUYCrAqFGj6OnpqVf/hq1cubJtZQ10bmvrxmeP1WWetNfauscV9X77sx2cympr0xd+VkjaBNiiOr2BO37WWotNvaRXynwK+IdcUo+kp4HvSHpHRNxdp3z1kl4peyYwE2DcuHExfvz4+rVvUE9PD+0qa6BzW/uvuszJp9W/hnrpR9tfh1r82Q5OZbW1qWnR2XI2p0paAqwBXqyx1bMcGF4jfRi1ez71XJU97p0rmxrlV543W76ZmbVRs9fhnAicBnyP1HP4KnAO8CCwlGxoqo5FpHM1fyZpJ2BLNjz30peoenyIFATHVOUbA6zL6mg2sET4bp/WNZoNOFOAs4Dzs+ezI+JsYE9SwHhrH8dfD7xX0la5tEmk2x80e67omOxxAUBEvEK6TuhDVfkmAXd4hpqZWbmaPYfzZuDuiHhV0hqy4aqIWCfpO8B3ST2g3lxC6iVdLek8YFdgOnBhfqp0NmQ3LyKOz55PB7YiXfS5Ang3cApwdUT8Jlf+uaTzOxeTrhOamG3va7KdZmbWZs32cJ4FhmY/Pwq8M7dvBOmizl5FxHLgYNK1Oj8DzgYuIvWa8jZj/et5FpGu07kMuA44Drgge8yXfzup53MIcCPwt8BxXmXABqyxY9Nm1gWa7eH8AtiH9KX/I9IKAdsAfwI+S1pFuq6IuB94Tx95Rlc9n0W6gLNPETGb1LsxG/gWLiy7BmaFaTbgTAd2zH7+GmlIbTKpZ3Mz8Ll2VczMzAaXpgJORCwGFmc/v0K6J87nO1AvMzMbZPpz4eebgB2AJyPiifZVyczMBqNmJw0g6dOSHgMeAX4JPCrpcUmfaXvtzMxs0Gh2pYEvA98mXU9zBDAue7we+Jdsv5mZ2QaaHVL7LPC1iPhSVfoN2dpmnyWtPGBmjZgypewamBWm2YAzhN7v6jkPz1Iza45vL21dpNlzOLOBo3rZdzRwTf+qY2Zmg1Ujt5iemHt6PXC+pNFseIvpPYEvtL+KZoPYggXp0asNWBdoZEjtGja8lfSOwHtr5P0B6U6cZtaIcePSo1eMti7QSMB5c8drYWZmg14jt5h+pIiKmJnZ4Nb0SgOSNiNNEDgQ2AZ4Dvg56VYB9W/EbmZmXaupgCNpJHAT8HbSHT6fBg4gXX9zj6TDImJZuytpZmYbv2anRV8IvBHYLyJ2jYgDImJXYL8s/cJ2V9DMzAaHZgPORODUiLgrn5g9P520zI2ZmdkGmj2H83rgxV72vQi8rn/VMesy8+eXXQOzwjQbcO4ETpV0a0S8VEmUtCVwarbfzBrlCz6tizQbcE4C5gKPSbqJNGlgJOkiUAHj21o7MzMbNJo6hxMRdwNvBWYC2wGHkgLOJcBbI+KettfQbDCbOjVtZl2g4R6OpM2BfYGHI+K0zlXJrItceml69KrR1gWa6eG8CtwK/GWH6mJmZoNYwwEnItYBvwNGda46ZmY2WDV7Hc4XgS9L2qsTlTEzs8Gr2VlqZ5JWFLhb0hOkWWrrraseEfu2qW5mZjaINBtwfpttZmZmTWko4EgaQlrW5rfAH4A5EfF0Jytm1hX23rvsGpgVppFbTO8KzAFG55JXSPpwRNzUqYqZdYXKLabNukAjkwbOB9YBfwO8AdgT+DUwo4P1MjOzQaaRgHMAcGZE/CIiXo6IB4BpwM6Sduhs9czMbLBoJODsAPy+Ku0h0tpp27e9RmbdREqbWRdo9Dqc6DuLmZlZ7xqdFn2jpLU10m+pTo+Ikf2vlpmZDTaNBJyzO14LMzMb9PoMOBHhgGNmZv3W7FpqZmZmLXHAMTOzQjS7lpqZtdMMXz9t3cMBx6xMvr20dREPqZmZWSEccMzKNHNm2sy6QOEBR9Iekm6RtErSk5LOkbRpH8fsI+kySUuy4xZLOkvSFlX5pkuKGtv7OtsqsxZNm5Y2sy5Q6DkcSSNItzq4HzgS2A34JinwnVnn0ElZ3vOA3wFvB87NHo+uyvsCUB1gHuhv3c3MrH+KnjTwKWAIcFRErABulrQ1MF3S+VlaLedFxLLc8x5JLwMzJO0SEY/k9q2NiDs7U30zM2tV0UNqhwM3VgWWWaQgdFBvB1UFm4pfZ49eu83MbCNQdMAZAyzKJ0TEo8CqbF8z3kW6MdziqvThkp6RtEbSryUd1XJtzcysbRRR3J0HJK0BTomIi6vSHweuiIgzGixne+A3wHURMTmX/jFSj+duYCjpRnETgaMj4upeypoKTAUYNWrU2FmzZjXbrJpWrlzJ0KFD21LWQOe2tm78hAkA9Mydu176vU+8UPe4vXYc1rY61OPPdnBqZ1snTJiwICLGNZK3jIBzckT8c1X6E8DlEfHFBsp4HWniwZuAsRGxvE5eAf8DDImId/RV9rhx42L+/Pl9ZWtIT08P48ePb0tZA53b2g+Vm69V/R2OPu3auoct/foR7atDHf5sB6d2tlVSwwGn6CG15cDwGunDgOf7OjgLIFcAewIT6wUbgEjR9Grg7X1NvTYrRcQGwcZssCp6ltoiqs7VSNoJ2JKqczu9uIg0nfrQiGgkf4X/os3MSlZ0D+d64L2StsqlTQJWA/PqHSjpdOBzwMci4vZGXizrEX0QuCciXm2tymZm1g5F93AuAU4ErpZ0HrArMB24MD9VWtISYF5EHJ89Pw74GnA58ISk/XNlPlSZNi1pHvATUm9pS2AKsD/wgc42y6xFY8emxwULyq2HWQEKDTgRsVzSwcC3gZ+RzttcRAo61fXKn3M5LHucnG15nyQFIoAlwD8CO5CmTC8EjoiI69tRf7O2W7iw7BqYFabw2xNExP3Ae/rIM7rq+WQ2DDS1jju+H1UzM7MO8mrRZmZWCAccMzMrhAOOmZkVwgHHzMwKUfikATPLmTKl7BqYFcYBx6xMvr20dREPqZmZWSEccMzKtGCBVxmwruEhNbMyjctWdfeK0dYF3MMxM7NCOOCYmVkhHHDMzKwQDjhmZlYIBxwzMyuEA46ZmRXC06LNyjR/ftk1MCuMA45ZH0afdu2ffz5pr7VMzj0HWPr1I1ovvHKLabMu4CE1MzMrhAOOWZmmTk2bWRdwwDEr06WXps2sCzjgmJlZIRxwzMysEA44ZmZWCAccMzMrhAOOmZkVwhd+mpVp773LroFZYRxwzMrk20tbF/GQmpmZFcIBx8zMCuGAY1YmKW1mXcABx8zMCuGAY2ZmhXDAMTOzQjjgmJlZIRxwzMysEA44ZmZWCK80YFamGTPKroFZYRxwzMrk20tbF3HAMTNGn3ZtzfST9lrL5Gzf0q8fUWSVbBDyORyzMs2cmTazLuAejlmZpk1Ljx5asy7ggGMbnd6Gf/I8/GM28BQ+pCZpD0m3SFol6UlJ50jatIHjhkm6TNJySS9I+qGkN9bId6SkeyW9LOl+SZM60xIzM2tGoQFH0ghgDhDAkcA5wEnA2Q0c/mNgPHACMBnYB5hdVf6BwE+AucDhwLXAlZIOa0sDzMysZUUPqX0KGAIcFRErgJslbQ1Ml3R+lrYBSQcA7wUOiojbsrQngF9KOiQi5mRZvwTcFhEnZs/nStoT+DJwU+eaZWbN8LBodyo64BwO3FgVWGYB5wEHAT+rc9zTlWADEBG/kvRwtm+OpNcDE4ATq46dBVwmaVhEvNCmdmzUOvXH7i8RG2j6+p3072Oxig44Y4Bb8wkR8aikVdm+3gLOGGBRjfQHsn0AuwGb18j3AGnocHfgrtaq3bfqX+z89QutqPWH4D8es4Ghnf9ctfJ33cjr13PSXmsZ368SWqOIKO7FpDXAKRFxcVX648AVEXFGL8fdDLwUER+oSv8BsGtEvEvSXwO3A++MiLtzed4C/A54b0RsMKwmaSpQmZP6NmBxyw1c37bAM20qa6BzWwevbmqv29qaXSJiu0YyljEtulaEUy/prRxX/Vy9pKfEiJlA26+8kzQ/Isa1u9yByG0dvLqpvW5r5xU9LXo5MLxG+jDg+RaOG547bnkurToPfZRvZmYdVnTAWcRr51wAkLQTsCW1z9H0elwmf27nIWBNjXxjgHXAgy3U18zM2qTogHM98F5JW+XSJgGrgXl9HLd9dp0NAJLGAbtm+4iIV0jX33yo6thJwB0lzFDrpgWy3NbBq5va67Z2WNGTBkYA9wO/JU2F3hW4ELg4Is7M5VsCzIuI43NpN5Bmmp1M6rGcB/wxIv4ml+dAoAf4Numi0IlZ/vfVmjBgZmbFKbSHExHLgYOBTUlToM8GLgLOqsq6WZYn71hSL+j7wBXAAuCDVeXfDhwDHALcCPwtcJyDjZlZ+Qrt4ZiZWffy/XCa1OnFRweSVtoqaZ+snUuy4xZLOkvSFkXVu1Wtfra54zeRtEBSSHp/J+vaX/1pq6SjJN1LdR/BAAAEwklEQVQlabWkZyXdIGnLTte5Vf34mx0n6aasjc9JmiNpvyLq3CpJb5E0Q9I9kl6V1NPgcYV8P/n2BE3ILT56P2nx0d2Ab5IC95l1DoW0+OjbSIuPVs5BzQb+pt5BZelHWydlec8jXXD7duDc7PHoDla5X/r52VacAOzYkQq2UX/aKukE0jnS84FTgBHAexig3yWttjWbPTsHWAh8PEs+BbhJ0tsj4pFO1rsf9iSdu74TeF0TxxXz/RQR3hrcgNNJ1/tsnUv7ArAqn1bjuANIF56+O5e2b5Z2SNntanNbt6uRNjVr6y5lt6vd7c3lHQEsA47P2vr+stvUgc92W+BFYErZbSigrZ8CXgWGV33GrwKfLrtddeq9Se7nq4CeBo4p7PvJQ2rN6W3x0SGkxUfrHbfB4qNAZfHRgailtkbEshrJv84eR7avem3X6mdbcS7wC+CWDtSt3Vpt64ezx3/vVMU6oNW2bg6sBVbm0lZmaap5xAAQEetaOKyw7ycHnOZssIhoRDxK+m+p1oWpvR6XyS8+OtC02tZa3kXqprdrnbpOaLm9kt4OfJI0BX9j0Gpb9yN9hsdLelzSGkm/lPSuzlW131pt60+yPN+UNFLSSNKM2uXAf3aormUp7PvJAac5I6i9RM7ybF+7jytTW+osaXvgi8D/j17udzRA9Ke93wL+NSKWtL1WndFqW7cnjfOfCZwK/F/gJeAGSaPaXck2aamtEfEk6XYnRwNPZ9tRpEWAa/XiN2aFfT854DSv04uPDiT9qrOk1wH/QRqK+Kc21qtTmm6vpGNJX8Jf6VSlOqSVz3YTYChwfET8MCJuAD5AOq/xD+2vYtu08rnuQDoHsoA0rHR49vO1knbuRCVLVsj3kwNOczq5+OhA02pbAZAk0gW6ewITI130O5A13V5JmwMXkGb0bCJpOLB1tnvLqiWcBpJWP9vnsseeSkLWa10A7NGuyrVZq209hTTz7piIuCELrkeTguvGMnTaqMK+nxxwmtPJxUcHmlbbWnERaRrqkRExUNuY10p7twTeRFqeaXm23ZPtm8VrkyUGmlY/2wdI//FWnzQX6RzdQNRqW8cA90XEmkpCRPwJuI80tXowKez7yQGnOR1bfHQAarWtSDod+BzwsUjLDW0MWmnvStI4f377SLbvDOCjnalqv7X62V5DCi4TKgmShgFjeS3QDjSttvUR4K+yYWEAlG5j/1fA0g7Us0zFfT+VPW98Y9pIJ9CeAm4mrdc2lfSl85WqfEuA71Wl3QD8nnTi8QOk2T4/L7tN7W4rcBzpv+DLgP2rtg2u0RkoW38+26r9oxn41+H05/d4dnbsJ4AjSF/ay4ARZbernW0lBdE1wLVZO99P+vJdA/yfsttVp71vIK0neQxwB6lHVnn+hjqfayHfT6W/QRvbRhqrvpX0H9JTpOsvNq3KsxS4vCptePYl/DywAvgRsG3Z7Wl3W4HLsy/cWtvkstvUic+2av+ADzj9aStp0sC/Ac9mx84B9iq7PR1q68HAbaRzV8+Rguv4stvTR1srv3+1ttF12lrI95MX7zQzs0L4HI6ZmRXCAcfMzArhgGNmZoVwwDEzs0I44JiZWSEccMzMrBAOOGZmVggHHDMzK8T/ArLcU/xD9Gw7AAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -462,9 +468,9 @@ ], "metadata": { "kernelspec": { - "display_name": "qiskit_wor", + "display_name": "qiskit_stable", "language": "python", - "name": "qiskit_wor" + "name": "qiskit_stable" }, "language_info": { "codemirror_mode": { @@ -476,7 +482,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.6" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/qiskit/aqua/finance/fixed_income_pricing.ipynb b/qiskit/aqua/finance/fixed_income_pricing.ipynb index 0b01e19b5..41387bf22 100644 --- a/qiskit/aqua/finance/fixed_income_pricing.ipynb +++ b/qiskit/aqua/finance/fixed_income_pricing.ipynb @@ -50,7 +50,7 @@ "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "import numpy as np\n", - "from qiskit import BasicAer\n", + "from qiskit import LegacySimulators\n", "from qiskit_aqua.algorithms import AmplitudeEstimation\n", "from qiskit_aqua.components.random_distributions import MultivariateNormalDistribution\n", "from qiskit_aqua.components.uncertainty_problems import FixedIncomeExpectedValue" @@ -237,8 +237,8 @@ }, "outputs": [], "source": [ - "# result = ae.run(quantum_instance=BasicAer.get_backend('qasm_simulator'), shots=100)\n", - "result = ae.run(quantum_instance=BasicAer.get_backend('statevector_simulator'))" + "# result = ae.run(quantum_instance=LegacySimulators.get_backend('qasm_simulator'), shots=100)\n", + "result = ae.run(quantum_instance=LegacySimulators.get_backend('statevector_simulator'))" ] }, { @@ -324,9 +324,9 @@ ], "metadata": { "kernelspec": { - "display_name": "qiskit_wor", + "display_name": "qiskit_stable", "language": "python", - "name": "qiskit_wor" + "name": "qiskit_stable" }, "language_info": { "codemirror_mode": { @@ -338,7 +338,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.6" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/qiskit/aqua/finance/portfolio_optimization.ipynb b/qiskit/aqua/finance/portfolio_optimization.ipynb index f3e186db1..36dbe2be7 100644 --- a/qiskit/aqua/finance/portfolio_optimization.ipynb +++ b/qiskit/aqua/finance/portfolio_optimization.ipynb @@ -57,10 +57,12 @@ { "cell_type": "code", "execution_count": 1, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ - "from qiskit import BasicAer\n", + "from qiskit import LegacySimulators\n", "from qiskit_aqua import QuantumInstance\n", "from qiskit_aqua import Operator, run_algorithm\n", "from qiskit_aqua.input import EnergyInput\n", @@ -264,7 +266,7 @@ } ], "source": [ - "backend = BasicAer.get_backend('statevector_simulator')\n", + "backend = LegacySimulators.get_backend('statevector_simulator')\n", "seed = 50\n", "\n", "cobyla = COBYLA()\n", @@ -348,7 +350,7 @@ } ], "source": [ - "backend = BasicAer.get_backend('statevector_simulator')\n", + "backend = LegacySimulators.get_backend('statevector_simulator')\n", "seed = 50\n", "\n", "cobyla = COBYLA()\n", @@ -394,9 +396,9 @@ ], "metadata": { "kernelspec": { - "display_name": "qiskit_wor", + "display_name": "qiskit_stable", "language": "python", - "name": "qiskit_wor" + "name": "qiskit_stable" }, "language_info": { "codemirror_mode": { @@ -408,7 +410,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.6" + "version": "3.6.1" } }, "nbformat": 4, From ef583e8dc3c4fc886cdb14345c4ea653c94702c5 Mon Sep 17 00:00:00 2001 From: Manoel Marques Date: Tue, 12 Feb 2019 10:51:52 -0500 Subject: [PATCH 002/116] Eliminate paulis_grouping --- community/aqua/chemistry/h2_qpe.ipynb | 47 +++++++++---------- .../aqua/chemistry/input_files/iqpe_h2.txt | 1 - .../aqua/chemistry/input_files/qpe_h2.txt | 1 - community/aqua/general/input_files/eoh.json | 3 +- community/aqua/general/vqe2iqpe.ipynb | 45 ++++++++---------- 5 files changed, 43 insertions(+), 54 deletions(-) diff --git a/community/aqua/chemistry/h2_qpe.ipynb b/community/aqua/chemistry/h2_qpe.ipynb index 8a11cca5c..40f36c613 100644 --- a/community/aqua/chemistry/h2_qpe.ipynb +++ b/community/aqua/chemistry/h2_qpe.ipynb @@ -25,21 +25,21 @@ "outputs": [], "source": [ "from collections import OrderedDict\n", - "from qiskit import LegacySimulators\n", + "from qiskit import BasicAer\n", + "from qiskit.qobj import RunConfig\n", "from qiskit.transpiler import PassManager\n", - "from qiskit_aqua import AquaError\n", - "from qiskit_aqua import QuantumInstance\n", - "from qiskit_aqua.algorithms import ExactEigensolver\n", - "from qiskit_aqua.algorithms import QPE\n", - "from qiskit_aqua.components.iqfts import Standard\n", - "from qiskit_chemistry import FermionicOperator\n", - "from qiskit_chemistry import QiskitChemistry\n", - "from qiskit_chemistry.drivers import ConfigurationManager\n", - "from qiskit_chemistry.aqua_extensions.components.initial_states import HartreeFock\n", + "from qiskit.aqua import AquaError\n", + "from qiskit.aqua import QuantumInstance\n", + "from qiskit.aqua.algorithms import ExactEigensolver\n", + "from qiskit.aqua.algorithms import QPE\n", + "from qiskit.aqua.components.iqfts import Standard\n", + "from qiskit.chemistry import FermionicOperator\n", + "from qiskit.chemistry import QiskitChemistry\n", + "from qiskit.chemistry.drivers import get_driver_class\n", + "from qiskit.chemistry.aqua_extensions.components.initial_states import HartreeFock\n", "import time\n", "\n", "distance = 0.735\n", - "cfg_mgr = ConfigurationManager()\n", "pyscf_cfg = OrderedDict([\n", " ('atom', 'H .0 .0 .0; H .0 .0 {}'.format(distance)),\n", " ('unit', 'Angstrom'),\n", @@ -47,14 +47,12 @@ " ('spin', 0),\n", " ('basis', 'sto3g')\n", "])\n", - "section = {}\n", - "section['properties'] = pyscf_cfg\n", "try:\n", - " driver = cfg_mgr.get_driver_instance('PYSCF')\n", + " driver = get_driver_class('PYSCF').init_from_input(pyscf_cfg)\n", "except ModuleNotFoundError:\n", " raise AquaError('PYSCF driver does not appear to be installed')\n", "\n", - "molecule = driver.run(section)\n", + "molecule = driver.run()\n", "qubit_mapping = 'parity'\n", "fer_op = FermionicOperator(h1=molecule.one_body_integrals, h2=molecule.two_body_integrals)\n", "qubit_op = fer_op.mapping(map_type=qubit_mapping,threshold=1e-10).two_qubit_reduced_operator(2)" @@ -76,7 +74,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "The exact ground state energy is: -1.857275030202382\n" + "The exact ground state energy is: -1.8572750302023824\n" ] } ], @@ -103,7 +101,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "The ground state energy as computed by QPE is: -1.8571368753258874\n" + "The ground state energy as computed by QPE is: -1.857136875325887\n" ] } ], @@ -120,10 +118,11 @@ "iqft = Standard(n_ancillae)\n", "\n", "qpe = QPE(qubit_op, state_in, iqft, num_time_slices, n_ancillae,\n", - " paulis_grouping='random', expansion_mode='suzuki',\n", + " expansion_mode='suzuki',\n", " expansion_order=2, shallow_circuit_concat=True)\n", - "backend = LegacySimulators.get_backend('qasm_simulator')\n", - "quantum_instance = QuantumInstance(backend, shots=100, pass_manager=PassManager())\n", + "backend = BasicAer.get_backend('qasm_simulator')\n", + "run_config = RunConfig(shots=100, max_credits=10, memory=False)\n", + "quantum_instance = QuantumInstance(backend, run_config, pass_manager=PassManager())\n", "result_qpe = qpe.run(quantum_instance)\n", "print('The ground state energy as computed by QPE is: {}'.format(result_qpe['energy']))" ] @@ -190,7 +189,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "The groundtruth total ground state energy is -1.8572750302023797.\n", + "The groundtruth total ground state energy is -1.8572750302023806.\n", "The total ground state energy as computed by QPE is -1.857136875325887.\n", "In comparison, the Hartree-Fock ground state energy is -1.8369679912029842.\n" ] @@ -214,9 +213,9 @@ ], "metadata": { "kernelspec": { - "display_name": "Quantum py37", + "display_name": "Python 3", "language": "python", - "name": "quantum-dev-37" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -228,7 +227,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.6.7" } }, "nbformat": 4, diff --git a/community/aqua/chemistry/input_files/iqpe_h2.txt b/community/aqua/chemistry/input_files/iqpe_h2.txt index 9fe87ca4d..3043ead2a 100644 --- a/community/aqua/chemistry/input_files/iqpe_h2.txt +++ b/community/aqua/chemistry/input_files/iqpe_h2.txt @@ -34,7 +34,6 @@ &algorithm name=IQPE num_time_slices=200 - paulis_grouping=random expansion_mode=suzuki expansion_order=2 num_iterations=9 diff --git a/community/aqua/chemistry/input_files/qpe_h2.txt b/community/aqua/chemistry/input_files/qpe_h2.txt index 1b032fc96..b72c0b228 100644 --- a/community/aqua/chemistry/input_files/qpe_h2.txt +++ b/community/aqua/chemistry/input_files/qpe_h2.txt @@ -34,7 +34,6 @@ &algorithm name=QPE num_time_slices=50 - paulis_grouping=random expansion_mode=suzuki expansion_order=2 num_ancillae=9 diff --git a/community/aqua/general/input_files/eoh.json b/community/aqua/general/input_files/eoh.json index d76d4c3ee..2b6d0014d 100644 --- a/community/aqua/general/input_files/eoh.json +++ b/community/aqua/general/input_files/eoh.json @@ -5,8 +5,7 @@ "expansion_order": 1, "name": "EOH", "num_time_slices": 1, - "operator_mode": "paulis", - "paulis_grouping": "default" + "operator_mode": "paulis" }, "backend": { "provider": "qiskit.BasicAer", diff --git a/community/aqua/general/vqe2iqpe.ipynb b/community/aqua/general/vqe2iqpe.ipynb index 8557c8381..3d559f5b6 100644 --- a/community/aqua/general/vqe2iqpe.ipynb +++ b/community/aqua/general/vqe2iqpe.ipynb @@ -18,15 +18,16 @@ "outputs": [], "source": [ "import numpy as np\n", - "from qiskit import LegacySimulators\n", + "from qiskit import BasicAer\n", + "from qiskit.qobj import RunConfig\n", "from qiskit.transpiler import PassManager\n", - "from qiskit_aqua import Operator, QuantumInstance, run_algorithm\n", - "from qiskit_aqua.input import EnergyInput\n", - "from qiskit_aqua.algorithms import VQE\n", - "from qiskit_aqua.algorithms import IQPE\n", - "from qiskit_aqua.components.variational_forms import RYRZ\n", - "from qiskit_aqua.components.optimizers import SPSA\n", - "from qiskit_aqua.components.initial_states.varformbased import VarFormBased" + "from qiskit.aqua import Operator, QuantumInstance, run_algorithm\n", + "from qiskit.aqua.input import EnergyInput\n", + "from qiskit.aqua.algorithms import VQE\n", + "from qiskit.aqua.algorithms import IQPE\n", + "from qiskit.aqua.components.variational_forms import RYRZ\n", + "from qiskit.aqua.components.optimizers import SPSA\n", + "from qiskit.aqua.components.initial_states.varformbased import VarFormBased" ] }, { @@ -70,7 +71,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "The reference ground energy level is -1.8572750302023788.\n" + "The reference ground energy level is -1.8572750302023793.\n" ] } ], @@ -105,14 +106,14 @@ "name": "stdout", "output_type": "stream", "text": [ - "VQE estimated the ground energy to be -1.7687172105530888.\n" + "VQE estimated the ground energy to be -1.6715595657632292.\n" ] } ], "source": [ "random_seed = 0\n", "np.random.seed(random_seed)\n", - "backend = LegacySimulators.get_backend('qasm_simulator')\n", + "backend = BasicAer.get_backend('qasm_simulator')\n", "\n", "var_form_depth = 3\n", "var_form = RYRZ(algo_input.qubit_op.num_qubits, var_form_depth)\n", @@ -137,7 +138,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -153,26 +154,18 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Continuing with VQE's result, IQPE estimated the ground energy to be -1.8551442391935626.\n" - ] - } - ], + "outputs": [], "source": [ "num_time_slices = 50\n", "num_iterations = 11\n", "\n", "iqpe = IQPE(algo_input.qubit_op, state_in, num_time_slices, num_iterations,\n", - " paulis_grouping='random', expansion_mode='suzuki', expansion_order=2,\n", + " expansion_mode='suzuki', expansion_order=2,\n", " shallow_circuit_concat=True)\n", - "quantum_instance = QuantumInstance(backend, shots=100, pass_manager=PassManager(),\n", - " seed=random_seed, seed_mapper=random_seed)\n", + "run_config = RunConfig(shots=100, max_credits=10, memory=False, seed=random_seed)\n", + "quantum_instance = QuantumInstance(backend, run_config, pass_manager=PassManager(), seed_mapper=random_seed)\n", "result_iqpe = iqpe.run(quantum_instance)\n", "print(\"Continuing with VQE's result, IQPE estimated the ground energy to be {}.\".format(\n", " result_iqpe['energy']))" @@ -202,7 +195,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.5" + "version": "3.6.7" } }, "nbformat": 4, From 5e1f6661c6b038de1a9ec419582299d405d67950 Mon Sep 17 00:00:00 2001 From: Richard Chen Date: Tue, 12 Feb 2019 11:35:36 -0500 Subject: [PATCH 003/116] update the tutorial to register a component/algorithm --- ...ild_a_pluggable_algorithm_components.ipynb | 66 +++++++++++++------ .../evolutionfidelity/evolutionfidelity.py | 26 ++++---- .../aqua/general/evolutionfidelity/setup.py | 47 +++---------- 3 files changed, 68 insertions(+), 71 deletions(-) diff --git a/qiskit/aqua/general/Aqua_howto_build_a_pluggable_algorithm_components.ipynb b/qiskit/aqua/general/Aqua_howto_build_a_pluggable_algorithm_components.ipynb index 870977486..57fbef38e 100644 --- a/qiskit/aqua/general/Aqua_howto_build_a_pluggable_algorithm_components.ipynb +++ b/qiskit/aqua/general/Aqua_howto_build_a_pluggable_algorithm_components.ipynb @@ -45,7 +45,7 @@ "\n", "\n", "#### Register it permentally\n", - "If you complete the pluggable algorithm/components as a Python package, you can refer to this [instruction](https://qiskit.org/documentation/aqua/extending.html#extending-aqua) to prepare the `setup.py` file to register the pluggable algorithm/component, which will be discovered in Aqua/Aqua-chemistry UI. We prepare a [setup.py](evolutionfidelity/setup.py) file for this tutorial. \n", + "If you complete the pluggable algorithm/components as a Python package, you can refer to this [instruction](https://qiskit.org/documentation/aqua/extending.html#extending-aqua) to prepare the `setup.py` file to register the pluggable algorithm/component, which will be discovered in Qiskit-Aqua. We prepare a [setup.py](evolutionfidelity/setup.py) example for this tutorial. \n", "\n", "Go to the `qiskit/aqua/general/evolutionfidelity` folder, and then do `python3 setup.py install` to install the package.\n", "\n", @@ -57,17 +57,9 @@ "cell_type": "code", "execution_count": 1, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\"Could not register class is already registered\"\n" - ] - } - ], + "outputs": [], "source": [ - "from qiskit_aqua import register_pluggable\n", + "from qiskit.aqua import register_pluggable\n", "from evolutionfidelity.evolutionfidelity import EvolutionFidelity\n", "try:\n", " register_pluggable(EvolutionFidelity)\n", @@ -83,7 +75,32 @@ "source": [ "from qiskit import Aer\n", "import numpy as np\n", - "from qiskit_aqua.operator import Operator" + "from qiskit.aqua.operator import Operator\n", + "from qiskit.aqua import local_pluggables, PluggableType" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "List all registered algorithms, and we will find `EvolutionFidelity` in the list if you registered." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "['QAOA.Variational', 'QSVM.Variational', 'VQE', 'ExactEigensolver', 'SVM', 'EOH', 'QSVM.Kernel', 'AmplitudeEstimation', 'BernsteinVazirani', 'DeutschJozsa', 'Grover', 'IQPE', 'QPE', 'Simon', 'EvolutionFidelity']\n" + ] + } + ], + "source": [ + "print(local_pluggables(PluggableType.ALGORITHM))" ] }, { @@ -96,21 +113,21 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "0.9818615150811041\n" + "0.9234907613356655\n" ] } ], "source": [ "from evolutionfidelity.evolutionfidelity import EvolutionFidelity\n", - "from qiskit_aqua.components.initial_states import Zero\n", - "from qiskit_aqua import QuantumInstance\n", + "from qiskit.aqua.components.initial_states import Zero\n", + "from qiskit.aqua import QuantumInstance\n", "num_qubits = 2\n", "temp = np.random.random((2 ** num_qubits, 2 ** num_qubits))\n", "qubit_op = Operator(matrix=temp + temp.T)\n", @@ -136,12 +153,12 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ - "from qiskit_aqua.input import EnergyInput\n", - "from qiskit_aqua import run_algorithm\n", + "from qiskit.aqua.input import EnergyInput\n", + "from qiskit.aqua import run_algorithm\n", "\n", "params = {\n", " 'problem': {\n", @@ -161,14 +178,14 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "0.9818615150811041\n" + "0.9234907613356655\n" ] } ], @@ -176,6 +193,13 @@ "result = run_algorithm(params, algo_input, backend=backend)\n", "print(result['score'])" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { diff --git a/qiskit/aqua/general/evolutionfidelity/evolutionfidelity/evolutionfidelity.py b/qiskit/aqua/general/evolutionfidelity/evolutionfidelity/evolutionfidelity.py index 7daec6166..3834e9560 100644 --- a/qiskit/aqua/general/evolutionfidelity/evolutionfidelity/evolutionfidelity.py +++ b/qiskit/aqua/general/evolutionfidelity/evolutionfidelity/evolutionfidelity.py @@ -31,8 +31,8 @@ from qiskit import QuantumRegister from qiskit.quantum_info import state_fidelity -from qiskit_aqua.algorithms import QuantumAlgorithm -from qiskit_aqua import AquaError, PluggableType, get_pluggable_class +from qiskit.aqua.algorithms import QuantumAlgorithm +from qiskit.aqua import AquaError, Pluggable, PluggableType, get_pluggable_class logger = logging.getLogger(__name__) @@ -74,18 +74,21 @@ class EvolutionFidelity(QuantumAlgorithm): 'additionalProperties': False }, 'problems': ['eoh'], - 'depends': ['initial_state'], - 'defaults': { - 'initial_state': { - 'name': 'ZERO' - } - } + 'depends': [ + { + 'pluggable_type': 'initial_state', + 'default': { + 'name': 'ZERO', + } + }, + ] } """ If directly use these objects programmatically then the constructor is more convenient to call than init_params. init_params itself uses this to do the actual object initialization. """ + def __init__(self, operator, initial_state, expansion_order=1): self.validate(locals()) super().__init__() @@ -113,14 +116,14 @@ def init_params(cls, params, algo_input): operator = algo_input.qubit_op - evolution_fidelity_params = params.get(QuantumAlgorithm.SECTION_KEY_ALGORITHM) + evolution_fidelity_params = params.get(Pluggable.SECTION_KEY_ALGORITHM) expansion_order = evolution_fidelity_params.get(EvolutionFidelity.PROP_EXPANSION_ORDER) # Set up initial state, we need to add computed num qubits to params - initial_state_params = params.get(QuantumAlgorithm.SECTION_KEY_INITIAL_STATE) + initial_state_params = params.get(Pluggable.SECTION_KEY_INITIAL_STATE) initial_state_params['num_qubits'] = operator.num_qubits initial_state = get_pluggable_class(PluggableType.INITIAL_STATE, - initial_state_params['name']).init_params(initial_state_params) + initial_state_params['name']).init_params(params) return cls(operator, initial_state, expansion_order) @@ -130,6 +133,7 @@ def init_params(cls, params, algo_input): E.g., the `_run` method is required to be implemented for an algorithm. """ + def _run(self): evo_time = 1 # get the groundtruth via simple matrix * vector diff --git a/qiskit/aqua/general/evolutionfidelity/setup.py b/qiskit/aqua/general/evolutionfidelity/setup.py index 439a66a78..541fac6ab 100644 --- a/qiskit/aqua/general/evolutionfidelity/setup.py +++ b/qiskit/aqua/general/evolutionfidelity/setup.py @@ -5,48 +5,17 @@ # ============================================================================= import setuptools -from setuptools.command.install import install -from setuptools.command.develop import develop -from setuptools.command.egg_info import egg_info -import atexit long_description = """An example to install a pluggable algorithm/component.""" requirements = [ - "qiskit-aqua>=0.4.0", - "qiskit-terra>=0.7,<0.8", - "numpy>=1.13" + "qiskit-aqua>=0.5", + "numpy>=1.13,<1.16" ] - -def _post_install(): - from qiskit_aqua_cmd.preferences import Preferences - preferences = Preferences() - preferences.add_package('evolutionfidelity') - preferences.save() - - -class CustomInstallCommand(install): - def run(self): - atexit.register(_post_install) - install.run(self) - - -class CustomDevelopCommand(develop): - def run(self): - atexit.register(_post_install) - develop.run(self) - - -class CustomEggInfoCommand(egg_info): - def run(self): - atexit.register(_post_install) - egg_info.run(self) - - setuptools.setup( name='evolutionfidelity', - version="0.4.0", # this should match __init__.__version__ + version="0.1.0", # this should match __init__.__version__ description='Example', long_description=long_description, long_description_content_type="text/markdown", @@ -70,9 +39,9 @@ def run(self): install_requires=requirements, include_package_data=True, python_requires=">=3.5", - cmdclass={ - 'install': CustomInstallCommand, - 'develop': CustomDevelopCommand, - 'egg_info': CustomEggInfoCommand - } + entry_points={ + 'qiskit.aqua.pluggables': [ + 'EvolutionFidelity = evolutionfidelity:EvolutionFidelity' + ], + }, ) From a45b41b3ffdb5f8a46c4a9addd57d70274950769 Mon Sep 17 00:00:00 2001 From: Manoel Marques Date: Tue, 12 Feb 2019 12:09:02 -0500 Subject: [PATCH 004/116] Fix grover input file --- community/aqua/optimization/input_files/grover.json | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/community/aqua/optimization/input_files/grover.json b/community/aqua/optimization/input_files/grover.json index e8837bd55..d8a3bb5ea 100644 --- a/community/aqua/optimization/input_files/grover.json +++ b/community/aqua/optimization/input_files/grover.json @@ -7,7 +7,7 @@ "name": "qasm_simulator" }, "oracle": { - "cnf": "c This is an example DIMACS 3-sat file with 3 satisfying solutions: 1 -2 3 0, -1 -2 -3 0, 1 2 -3 0\np cnf 3 5\n-1 -2 -3 0\n1 -2 3 0\n1 2 -3 0\n1 -2 -3 0\n-1 2 3 0", + "dimacs_cnf": "c This is an example DIMACS 3-sat file with 3 satisfying solutions: 1 -2 3 0, -1 -2 -3 0, 1 2 -3 0\np cnf 3 5\n-1 -2 -3 0\n1 -2 3 0\n1 2 -3 0\n1 -2 -3 0\n-1 2 3 0", "name": "SAT" }, "problem": { From c1236aaced0f7e2a3db6f45b7ce8466c332a7274 Mon Sep 17 00:00:00 2001 From: Manoel Marques Date: Tue, 12 Feb 2019 12:30:11 -0500 Subject: [PATCH 005/116] Change from qiskit_aqua to qiskit.aqua and from qiskit_chemistry to qiskit.chemistry --- .../qsvm_kernel_directly.ipynb | 10 +++++----- .../qsvm_kernel_multiclass.ipynb | 4 ++-- .../qsvm_variational.ipynb | 14 +++++++------- .../artificial_intelligence/svm_classical.ipynb | 6 +++--- .../svm_classical_multiclass.ipynb | 6 +++--- .../LiH_with_qubit_tapering_and_uccsd.ipynb | 16 ++++++++-------- .../aqua/chemistry/ParticleHole_example.ipynb | 14 +++++++------- community/aqua/chemistry/PySCF_end2end.ipynb | 14 +++++++------- community/aqua/chemistry/Pyquante_end2end.ipynb | 14 +++++++------- community/aqua/chemistry/beh2_reductions.ipynb | 2 +- community/aqua/chemistry/dictinput.py | 4 ++-- community/aqua/chemistry/energyplot.ipynb | 2 +- community/aqua/chemistry/h2_basis_sets.ipynb | 2 +- community/aqua/chemistry/h2_excited_states.ipynb | 2 +- community/aqua/chemistry/h2_iqpe.ipynb | 2 +- community/aqua/chemistry/h2_mappings.ipynb | 2 +- community/aqua/chemistry/h2_particle_hole.ipynb | 2 +- community/aqua/chemistry/h2_qpe.ipynb | 2 +- community/aqua/chemistry/h2_swaprz.ipynb | 2 +- community/aqua/chemistry/h2_uccsd.ipynb | 2 +- community/aqua/chemistry/h2_var_forms.ipynb | 2 +- .../aqua/chemistry/h2_vqe_initial_point.ipynb | 2 +- community/aqua/chemistry/h2_vqe_spsa.ipynb | 4 ++-- community/aqua/chemistry/h2o.ipynb | 2 +- community/aqua/chemistry/lih_dissoc.ipynb | 4 ++-- community/aqua/chemistry/lih_uccsd.ipynb | 2 +- community/aqua/chemistry/nah_uccsd.ipynb | 2 +- community/aqua/general/eoh.ipynb | 10 +++++----- community/aqua/general/evolution.ipynb | 4 ++-- community/aqua/general/vqe.ipynb | 4 ++-- community/aqua/optimization/clique.ipynb | 8 ++++---- community/aqua/optimization/exact_cover.ipynb | 8 ++++---- .../aqua/optimization/graph_partition.ipynb | 8 ++++---- community/aqua/optimization/grover.ipynb | 10 +++++----- community/aqua/optimization/maxcut.ipynb | 8 ++++---- community/aqua/optimization/partition.ipynb | 8 ++++---- community/aqua/optimization/set_packing.ipynb | 8 ++++---- community/aqua/optimization/stableset.ipynb | 8 ++++---- community/aqua/optimization/vertex_cover.ipynb | 8 ++++---- .../exercises/w8_01.ipynb | 4 ++-- .../exercises/w8_02.ipynb | 8 ++++---- .../exercises/w8_03.ipynb | 8 ++++---- .../exercises/w8_04.ipynb | 8 ++++---- .../exercises/w8_05.ipynb | 12 ++++++------ .../latex/main.tex | 4 ++-- .../qml_mooc/00_Course_Introduction.ipynb | 2 +- .../qml_mooc/07_Variational Circuits.ipynb | 4 ++-- .../qml_mooc/08_Sampling a Thermal State.ipynb | 10 +++++----- ...rete Optimization and Ensemble Learning.ipynb | 8 ++++---- ... Optimization and Unsupervised Learning.ipynb | 8 ++++---- .../qsvm_kernel_classification.ipynb | 12 ++++++------ qiskit/aqua/chemistry/declarative_approach.ipynb | 4 ++-- .../dissociation_profile_of_molecule.ipynb | 6 +++--- .../aqua/chemistry/programmatic_approach.ipynb | 14 +++++++------- .../finance/european_call_option_pricing.ipynb | 6 +++--- qiskit/aqua/finance/fixed_income_pricing.ipynb | 6 +++--- qiskit/aqua/finance/portfolio_optimization.ipynb | 14 +++++++------- qiskit/aqua/general/amplitude_estimation.ipynb | 8 ++++---- .../evolutionfidelity/evolutionfidelity.py | 2 +- qiskit/aqua/optimization/maxcut_and_tsp.ipynb | 16 ++++++++-------- 60 files changed, 198 insertions(+), 198 deletions(-) diff --git a/community/aqua/artificial_intelligence/qsvm_kernel_directly.ipynb b/community/aqua/artificial_intelligence/qsvm_kernel_directly.ipynb index 77421c01b..6eb74b102 100644 --- a/community/aqua/artificial_intelligence/qsvm_kernel_directly.ipynb +++ b/community/aqua/artificial_intelligence/qsvm_kernel_directly.ipynb @@ -29,11 +29,11 @@ "source": [ "from datasets import *\n", "from qiskit import Aer\n", - "from qiskit_aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name\n", - "from qiskit_aqua import run_algorithm, QuantumInstance\n", - "from qiskit_aqua.input import SVMInput\n", - "from qiskit_aqua.components.feature_maps import SecondOrderExpansion\n", - "from qiskit_aqua.algorithms import QSVMKernel" + "from qiskit.aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name\n", + "from qiskit.aqua import run_algorithm, QuantumInstance\n", + "from qiskit.aqua.input import SVMInput\n", + "from qiskit.aqua.components.feature_maps import SecondOrderExpansion\n", + "from qiskit.aqua.algorithms import QSVMKernel" ] }, { diff --git a/community/aqua/artificial_intelligence/qsvm_kernel_multiclass.ipynb b/community/aqua/artificial_intelligence/qsvm_kernel_multiclass.ipynb index f3205feb9..3284add29 100644 --- a/community/aqua/artificial_intelligence/qsvm_kernel_multiclass.ipynb +++ b/community/aqua/artificial_intelligence/qsvm_kernel_multiclass.ipynb @@ -25,8 +25,8 @@ "source": [ "from datasets import *\n", "from qiskit import Aer\n", - "from qiskit_aqua.input import SVMInput\n", - "from qiskit_aqua import run_algorithm\n", + "from qiskit.aqua.input import SVMInput\n", + "from qiskit.aqua import run_algorithm\n", "import numpy as np" ] }, diff --git a/community/aqua/artificial_intelligence/qsvm_variational.ipynb b/community/aqua/artificial_intelligence/qsvm_variational.ipynb index cbe9fc7b4..c0c500634 100644 --- a/community/aqua/artificial_intelligence/qsvm_variational.ipynb +++ b/community/aqua/artificial_intelligence/qsvm_variational.ipynb @@ -31,14 +31,14 @@ "outputs": [], "source": [ "from datasets import *\n", - "from qiskit_aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name\n", + "from qiskit.aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name\n", "from qiskit import Aer\n", - "from qiskit_aqua.input import SVMInput\n", - "from qiskit_aqua import run_algorithm, QuantumInstance\n", - "from qiskit_aqua.algorithms import QSVMVariational\n", - "from qiskit_aqua.components.optimizers import SPSA\n", - "from qiskit_aqua.components.feature_maps import SecondOrderExpansion\n", - "from qiskit_aqua.components.variational_forms import RYRZ" + "from qiskit.aqua.input import SVMInput\n", + "from qiskit.aqua import run_algorithm, QuantumInstance\n", + "from qiskit.aqua.algorithms import QSVMVariational\n", + "from qiskit.aqua.components.optimizers import SPSA\n", + "from qiskit.aqua.components.feature_maps import SecondOrderExpansion\n", + "from qiskit.aqua.components.variational_forms import RYRZ" ] }, { diff --git a/community/aqua/artificial_intelligence/svm_classical.ipynb b/community/aqua/artificial_intelligence/svm_classical.ipynb index b833e7c36..3e5e40ed2 100644 --- a/community/aqua/artificial_intelligence/svm_classical.ipynb +++ b/community/aqua/artificial_intelligence/svm_classical.ipynb @@ -18,9 +18,9 @@ "outputs": [], "source": [ "from datasets import *\n", - "from qiskit_aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name\n", - "from qiskit_aqua.input import SVMInput\n", - "from qiskit_aqua import run_algorithm" + "from qiskit.aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name\n", + "from qiskit.aqua.input import SVMInput\n", + "from qiskit.aqua import run_algorithm" ] }, { diff --git a/community/aqua/artificial_intelligence/svm_classical_multiclass.ipynb b/community/aqua/artificial_intelligence/svm_classical_multiclass.ipynb index 9f2c0f362..717ea81e1 100644 --- a/community/aqua/artificial_intelligence/svm_classical_multiclass.ipynb +++ b/community/aqua/artificial_intelligence/svm_classical_multiclass.ipynb @@ -24,9 +24,9 @@ "outputs": [], "source": [ "from datasets import *\n", - "from qiskit_aqua.utils import split_dataset_to_data_and_labels\n", - "from qiskit_aqua.input import SVMInput\n", - "from qiskit_aqua import run_algorithm\n", + "from qiskit.aqua.utils import split_dataset_to_data_and_labels\n", + "from qiskit.aqua.input import SVMInput\n", + "from qiskit.aqua import run_algorithm\n", "import numpy as np" ] }, diff --git a/community/aqua/chemistry/LiH_with_qubit_tapering_and_uccsd.ipynb b/community/aqua/chemistry/LiH_with_qubit_tapering_and_uccsd.ipynb index c0ce12fb2..6238a76c9 100644 --- a/community/aqua/chemistry/LiH_with_qubit_tapering_and_uccsd.ipynb +++ b/community/aqua/chemistry/LiH_with_qubit_tapering_and_uccsd.ipynb @@ -14,15 +14,15 @@ "\n", "from qiskit import Aer\n", "\n", - "from qiskit_aqua import Operator, set_aqua_logging, QuantumInstance\n", - "from qiskit_aqua.algorithms.adaptive import VQE\n", - "from qiskit_aqua.algorithms.classical import ExactEigensolver\n", - "from qiskit_aqua.components.optimizers import COBYLA\n", + "from qiskit.aqua import Operator, set_aqua_logging, QuantumInstance\n", + "from qiskit.aqua.algorithms.adaptive import VQE\n", + "from qiskit.aqua.algorithms.classical import ExactEigensolver\n", + "from qiskit.aqua.components.optimizers import COBYLA\n", "\n", - "from qiskit_chemistry.drivers import PySCFDriver, UnitsType\n", - "from qiskit_chemistry.core import Hamiltonian, TransformationType, QubitMappingType \n", - "from qiskit_chemistry.aqua_extensions.components.variational_forms import UCCSD\n", - "from qiskit_chemistry.aqua_extensions.components.initial_states import HartreeFock\n", + "from qiskit.chemistry.drivers import PySCFDriver, UnitsType\n", + "from qiskit.chemistry.core import Hamiltonian, TransformationType, QubitMappingType \n", + "from qiskit.chemistry.aqua_extensions.components.variational_forms import UCCSD\n", + "from qiskit.chemistry.aqua_extensions.components.initial_states import HartreeFock\n", "\n", "# set_aqua_logging(logging.INFO)" ] diff --git a/community/aqua/chemistry/ParticleHole_example.ipynb b/community/aqua/chemistry/ParticleHole_example.ipynb index 848af7262..a6980de2e 100644 --- a/community/aqua/chemistry/ParticleHole_example.ipynb +++ b/community/aqua/chemistry/ParticleHole_example.ipynb @@ -10,14 +10,14 @@ "from qiskit import Aer\n", "from qiskit.transpiler import PassManager\n", "\n", - "from qiskit_aqua import Operator, QuantumInstance\n", - "from qiskit_aqua.algorithms.adaptive import VQE\n", - "from qiskit_aqua.algorithms.classical import ExactEigensolver\n", - "from qiskit_aqua.components.optimizers import L_BFGS_B\n", - "from qiskit_aqua.components.variational_forms import RY\n", + "from qiskit.aqua import Operator, QuantumInstance\n", + "from qiskit.aqua.algorithms.adaptive import VQE\n", + "from qiskit.aqua.algorithms.classical import ExactEigensolver\n", + "from qiskit.aqua.components.optimizers import L_BFGS_B\n", + "from qiskit.aqua.components.variational_forms import RY\n", "\n", - "from qiskit_chemistry import FermionicOperator\n", - "from qiskit_chemistry.drivers import PySCFDriver, UnitsType" + "from qiskit.chemistry import FermionicOperator\n", + "from qiskit.chemistry.drivers import PySCFDriver, UnitsType" ] }, { diff --git a/community/aqua/chemistry/PySCF_end2end.ipynb b/community/aqua/chemistry/PySCF_end2end.ipynb index ccf81a511..e98113091 100644 --- a/community/aqua/chemistry/PySCF_end2end.ipynb +++ b/community/aqua/chemistry/PySCF_end2end.ipynb @@ -10,14 +10,14 @@ "from qiskit import Aer\n", "from qiskit.transpiler import PassManager\n", "\n", - "from qiskit_aqua import Operator, QuantumInstance\n", - "from qiskit_aqua.algorithms.adaptive import VQE\n", - "from qiskit_aqua.algorithms.classical import ExactEigensolver\n", - "from qiskit_aqua.components.optimizers import L_BFGS_B\n", - "from qiskit_aqua.components.variational_forms import RYRZ\n", + "from qiskit.aqua import Operator, QuantumInstance\n", + "from qiskit.aqua.algorithms.adaptive import VQE\n", + "from qiskit.aqua.algorithms.classical import ExactEigensolver\n", + "from qiskit.aqua.components.optimizers import L_BFGS_B\n", + "from qiskit.aqua.components.variational_forms import RYRZ\n", "\n", - "from qiskit_chemistry import FermionicOperator\n", - "from qiskit_chemistry.drivers import PySCFDriver, UnitsType" + "from qiskit.chemistry import FermionicOperator\n", + "from qiskit.chemistry.drivers import PySCFDriver, UnitsType" ] }, { diff --git a/community/aqua/chemistry/Pyquante_end2end.ipynb b/community/aqua/chemistry/Pyquante_end2end.ipynb index dee663931..33037430f 100644 --- a/community/aqua/chemistry/Pyquante_end2end.ipynb +++ b/community/aqua/chemistry/Pyquante_end2end.ipynb @@ -10,14 +10,14 @@ "from qiskit import Aer\n", "from qiskit.transpiler import PassManager\n", "\n", - "from qiskit_aqua import Operator, QuantumInstance\n", - "from qiskit_aqua.algorithms.adaptive import VQE\n", - "from qiskit_aqua.algorithms.classical import ExactEigensolver\n", - "from qiskit_aqua.components.optimizers import L_BFGS_B\n", - "from qiskit_aqua.components.variational_forms import RY\n", + "from qiskit.aqua import Operator, QuantumInstance\n", + "from qiskit.aqua.algorithms.adaptive import VQE\n", + "from qiskit.aqua.algorithms.classical import ExactEigensolver\n", + "from qiskit.aqua.components.optimizers import L_BFGS_B\n", + "from qiskit.aqua.components.variational_forms import RY\n", "\n", - "from qiskit_chemistry import FermionicOperator\n", - "from qiskit_chemistry.drivers import PyQuanteDriver, UnitsType, BasisType" + "from qiskit.chemistry import FermionicOperator\n", + "from qiskit.chemistry.drivers import PyQuanteDriver, UnitsType, BasisType" ] }, { diff --git a/community/aqua/chemistry/beh2_reductions.ipynb b/community/aqua/chemistry/beh2_reductions.ipynb index af7bc06d4..b2f247456 100644 --- a/community/aqua/chemistry/beh2_reductions.ipynb +++ b/community/aqua/chemistry/beh2_reductions.ipynb @@ -73,7 +73,7 @@ "source": [ "import numpy as np\n", "import pylab\n", - "from qiskit_chemistry import QiskitChemistry\n", + "from qiskit.chemistry import QiskitChemistry\n", "\n", "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", "qiskit_chemistry_dict = {\n", diff --git a/community/aqua/chemistry/dictinput.py b/community/aqua/chemistry/dictinput.py index 03c2668bd..f3f84bc5e 100644 --- a/community/aqua/chemistry/dictinput.py +++ b/community/aqua/chemistry/dictinput.py @@ -15,7 +15,7 @@ # limitations under the License. # ============================================================================= -import qiskit_chemistry +import qiskit.chemistry # An example of using a loop to vary inter-atomic distance. A dictionary is # created outside the loop, but inside the loop the 'atom' value is updated @@ -35,6 +35,6 @@ for i in range(21): d = (0.5 + i * 0.5 / 20) / 2 input_dict['PYSCF']['atom'] = molecule.format(d) - solver = qiskit_chemistry.QiskitChemistry() + solver = qiskit.chemistry.QiskitChemistry() result = solver.run(input_dict) print('{:.4f} : {}'.format(d * 2, result['energy'])) diff --git a/community/aqua/chemistry/energyplot.ipynb b/community/aqua/chemistry/energyplot.ipynb index 1e2e2dbf2..9e3042680 100644 --- a/community/aqua/chemistry/energyplot.ipynb +++ b/community/aqua/chemistry/energyplot.ipynb @@ -42,7 +42,7 @@ "source": [ "import numpy as np\n", "import pylab\n", - "from qiskit_chemistry import QiskitChemistry\n", + "from qiskit.chemistry import QiskitChemistry\n", "\n", "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", "# Note: In order to allow this to run reasonably quickly it takes advantage\n", diff --git a/community/aqua/chemistry/h2_basis_sets.ipynb b/community/aqua/chemistry/h2_basis_sets.ipynb index 1aa7ff17a..10a097850 100644 --- a/community/aqua/chemistry/h2_basis_sets.ipynb +++ b/community/aqua/chemistry/h2_basis_sets.ipynb @@ -45,7 +45,7 @@ "source": [ "import numpy as np\n", "import pylab\n", - "from qiskit_chemistry import QiskitChemistry\n", + "from qiskit.chemistry import QiskitChemistry\n", "\n", "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", "qiskit_chemistry_dict = {\n", diff --git a/community/aqua/chemistry/h2_excited_states.ipynb b/community/aqua/chemistry/h2_excited_states.ipynb index 909333717..7bd30e4c6 100644 --- a/community/aqua/chemistry/h2_excited_states.ipynb +++ b/community/aqua/chemistry/h2_excited_states.ipynb @@ -49,7 +49,7 @@ "source": [ "import numpy as np\n", "import pylab\n", - "from qiskit_chemistry import QiskitChemistry\n", + "from qiskit.chemistry import QiskitChemistry\n", "\n", "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", "qiskit_chemistry_dict = {\n", diff --git a/community/aqua/chemistry/h2_iqpe.ipynb b/community/aqua/chemistry/h2_iqpe.ipynb index d055c03b6..ca2857eac 100644 --- a/community/aqua/chemistry/h2_iqpe.ipynb +++ b/community/aqua/chemistry/h2_iqpe.ipynb @@ -22,7 +22,7 @@ "import numpy as np\n", "import pylab\n", "from qiskit import LegacySimulators\n", - "from qiskit_chemistry import QiskitChemistry\n", + "from qiskit.chemistry import QiskitChemistry\n", "import time\n", "\n", "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", diff --git a/community/aqua/chemistry/h2_mappings.ipynb b/community/aqua/chemistry/h2_mappings.ipynb index f2ce9eb2c..9d4db6934 100644 --- a/community/aqua/chemistry/h2_mappings.ipynb +++ b/community/aqua/chemistry/h2_mappings.ipynb @@ -69,7 +69,7 @@ "source": [ "import numpy as np\n", "import pylab\n", - "from qiskit_chemistry import QiskitChemistry\n", + "from qiskit.chemistry import QiskitChemistry\n", "\n", "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", "qiskit_chemistry_dict = {\n", diff --git a/community/aqua/chemistry/h2_particle_hole.ipynb b/community/aqua/chemistry/h2_particle_hole.ipynb index e7fa24fdd..b7b44864e 100644 --- a/community/aqua/chemistry/h2_particle_hole.ipynb +++ b/community/aqua/chemistry/h2_particle_hole.ipynb @@ -62,7 +62,7 @@ "source": [ "import numpy as np\n", "import pylab\n", - "from qiskit_chemistry import QiskitChemistry\n", + "from qiskit.chemistry import QiskitChemistry\n", "\n", "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", "qiskit_chemistry_dict = {\n", diff --git a/community/aqua/chemistry/h2_qpe.ipynb b/community/aqua/chemistry/h2_qpe.ipynb index 40f36c613..f7e9bdc2e 100644 --- a/community/aqua/chemistry/h2_qpe.ipynb +++ b/community/aqua/chemistry/h2_qpe.ipynb @@ -133,7 +133,7 @@ "source": [ "As can be easily seen, the QPE computed energy is quite close to the groundtruth value we computed earlier.\n", "\n", - "Next we demonstrate how the same computation can be carried out using json dictionaries to drive the qiskit_chemistry stack. Such a dictionary can of course also be manipulated programmatically. An sibling notebook `h2_iqpe` is also provided, which showcases how the ground state energies over a range of inter-atomic distances can be computed and then plotted as well." + "Next we demonstrate how the same computation can be carried out using json dictionaries to drive the qiskit.chemistry stack. Such a dictionary can of course also be manipulated programmatically. An sibling notebook `h2_iqpe` is also provided, which showcases how the ground state energies over a range of inter-atomic distances can be computed and then plotted as well." ] }, { diff --git a/community/aqua/chemistry/h2_swaprz.ipynb b/community/aqua/chemistry/h2_swaprz.ipynb index e83b87076..8bbd7eccd 100644 --- a/community/aqua/chemistry/h2_swaprz.ipynb +++ b/community/aqua/chemistry/h2_swaprz.ipynb @@ -47,7 +47,7 @@ "source": [ "import numpy as np\n", "import pylab\n", - "from qiskit_chemistry import QiskitChemistry\n", + "from qiskit.chemistry import QiskitChemistry\n", "\n", "# Input dictionary to configure qiskit chemistry for the chemistry problem.\n", "qiskit_chemistry_dict = {\n", diff --git a/community/aqua/chemistry/h2_uccsd.ipynb b/community/aqua/chemistry/h2_uccsd.ipynb index d4d5c47f7..ccad2fe26 100644 --- a/community/aqua/chemistry/h2_uccsd.ipynb +++ b/community/aqua/chemistry/h2_uccsd.ipynb @@ -47,7 +47,7 @@ "source": [ "import numpy as np\n", "import pylab\n", - "from qiskit_chemistry import QiskitChemistry\n", + "from qiskit.chemistry import QiskitChemistry\n", "\n", "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", "qiskit_chemistry_dict = {\n", diff --git a/community/aqua/chemistry/h2_var_forms.ipynb b/community/aqua/chemistry/h2_var_forms.ipynb index 845277bc7..0d87d7d13 100644 --- a/community/aqua/chemistry/h2_var_forms.ipynb +++ b/community/aqua/chemistry/h2_var_forms.ipynb @@ -30,7 +30,7 @@ "source": [ "import numpy as np\n", "import pylab\n", - "from qiskit_chemistry import QiskitChemistry\n", + "from qiskit.chemistry import QiskitChemistry\n", "\n", "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", "qiskit_chemistry_dict = {\n", diff --git a/community/aqua/chemistry/h2_vqe_initial_point.ipynb b/community/aqua/chemistry/h2_vqe_initial_point.ipynb index ef3d7c1a1..ebb1d1f6a 100644 --- a/community/aqua/chemistry/h2_vqe_initial_point.ipynb +++ b/community/aqua/chemistry/h2_vqe_initial_point.ipynb @@ -55,7 +55,7 @@ "source": [ "import numpy as np\n", "import pylab\n", - "from qiskit_chemistry import QiskitChemistry\n", + "from qiskit.chemistry import QiskitChemistry\n", "\n", "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", "qiskit_chemistry_dict = {\n", diff --git a/community/aqua/chemistry/h2_vqe_spsa.ipynb b/community/aqua/chemistry/h2_vqe_spsa.ipynb index 699abd2d4..880884406 100644 --- a/community/aqua/chemistry/h2_vqe_spsa.ipynb +++ b/community/aqua/chemistry/h2_vqe_spsa.ipynb @@ -8,7 +8,7 @@ "\n", "This notebook demonstrates using Qiskit Chemistry to plot graphs of the ground state energy of the Hydrogen (H2) molecule over a range of inter-atomic distances using VQE with SPSA optimizer. It is compared to the same energies as computed by the ExactEigensolver. SPSA is designed to work well with probabalistic/noisy measurements. And with RYRZ variational form makes this a suitable configuration to run on a near term device.\n", "\n", - "This notebook populates a dictionary, that is a progammatic representation of an input file, in order to drive the qiskit_chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here where we alter the molecule supplied to the driver in each loop.\n", + "This notebook populates a dictionary, that is a progammatic representation of an input file, in order to drive the qiskit.chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here where we alter the molecule supplied to the driver in each loop.\n", "\n", "This notebook has been written to use the PYSCF chemistry driver. See the PYSCF chemistry driver readme if you need to install the external PySCF library that this driver requires." ] @@ -43,7 +43,7 @@ "source": [ "import numpy as np\n", "import pylab\n", - "from qiskit_chemistry import QiskitChemistry\n", + "from qiskit.chemistry import QiskitChemistry\n", "\n", "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", "qiskit_chemistry_dict = {\n", diff --git a/community/aqua/chemistry/h2o.ipynb b/community/aqua/chemistry/h2o.ipynb index 07efda166..c2c25e0d1 100644 --- a/community/aqua/chemistry/h2o.ipynb +++ b/community/aqua/chemistry/h2o.ipynb @@ -17,7 +17,7 @@ "metadata": {}, "outputs": [], "source": [ - "from qiskit_chemistry import QiskitChemistry\n", + "from qiskit.chemistry import QiskitChemistry\n", "\n", "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", "qiskit_chemistry_dict = {\n", diff --git a/community/aqua/chemistry/lih_dissoc.ipynb b/community/aqua/chemistry/lih_dissoc.ipynb index 8450bb21a..45b6c4804 100644 --- a/community/aqua/chemistry/lih_dissoc.ipynb +++ b/community/aqua/chemistry/lih_dissoc.ipynb @@ -10,7 +10,7 @@ "\n", "This notebook demonstrates using Qiskit Chemistry to plot graphs of the ground state energy and dipole moments of a Lithium Hydride (LiH) molecule over a range of inter-atomic distances.\n", "\n", - "This notebook populates a dictionary, which is a progammatic representation of an input file, in order to drive the qiskit_chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here where we alter the molecule supplied to the driver in each loop.\n", + "This notebook populates a dictionary, which is a progammatic representation of an input file, in order to drive the qiskit.chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here where we alter the molecule supplied to the driver in each loop.\n", " \n", "This notebook has been written to use the PYSCF chemistry driver. See the PYSCF chemistry driver readme if you need to install the external PySCF library that this driver requires.\n", " " @@ -24,7 +24,7 @@ "source": [ "import numpy as np\n", "import pylab\n", - "from qiskit_chemistry import QiskitChemistry" + "from qiskit.chemistry import QiskitChemistry" ] }, { diff --git a/community/aqua/chemistry/lih_uccsd.ipynb b/community/aqua/chemistry/lih_uccsd.ipynb index dd4087ad8..c72f282fe 100644 --- a/community/aqua/chemistry/lih_uccsd.ipynb +++ b/community/aqua/chemistry/lih_uccsd.ipynb @@ -47,7 +47,7 @@ "source": [ "import numpy as np\n", "import pylab\n", - "from qiskit_chemistry import QiskitChemistry\n", + "from qiskit.chemistry import QiskitChemistry\n", "\n", "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", "qiskit_chemistry_dict = {\n", diff --git a/community/aqua/chemistry/nah_uccsd.ipynb b/community/aqua/chemistry/nah_uccsd.ipynb index b4b2bbbaf..8195f5fd2 100644 --- a/community/aqua/chemistry/nah_uccsd.ipynb +++ b/community/aqua/chemistry/nah_uccsd.ipynb @@ -59,7 +59,7 @@ "source": [ "import numpy as np\n", "import pylab\n", - "from qiskit_chemistry import QiskitChemistry\n", + "from qiskit.chemistry import QiskitChemistry\n", "\n", "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", "qiskit_chemistry_dict = {\n", diff --git a/community/aqua/general/eoh.ipynb b/community/aqua/general/eoh.ipynb index 4a8108d03..36855a14a 100644 --- a/community/aqua/general/eoh.ipynb +++ b/community/aqua/general/eoh.ipynb @@ -22,11 +22,11 @@ "import numpy as np\n", "from qiskit import LegacySimulators\n", "from qiskit.transpiler import PassManager\n", - "from qiskit_aqua import run_algorithm\n", - "from qiskit_aqua.operator import Operator, QuantumInstance\n", - "from qiskit_aqua.algorithms import EOH\n", - "from qiskit_aqua.components.initial_states import Custom\n", - "from qiskit_aqua.input import EnergyInput\n", + "from qiskit.aqua import run_algorithm\n", + "from qiskit.aqua.operator import Operator, QuantumInstance\n", + "from qiskit.aqua.algorithms import EOH\n", + "from qiskit.aqua.components.initial_states import Custom\n", + "from qiskit.aqua.input import EnergyInput\n", "\n", "num_qubits = 2\n", "temp = np.random.random((2 ** num_qubits, 2 ** num_qubits))\n", diff --git a/community/aqua/general/evolution.ipynb b/community/aqua/general/evolution.ipynb index bf8e5e28c..98b67cb12 100644 --- a/community/aqua/general/evolution.ipynb +++ b/community/aqua/general/evolution.ipynb @@ -25,8 +25,8 @@ "from qiskit import execute as q_execute\n", "from qiskit import QuantumCircuit, QuantumRegister\n", "from qiskit.quantum_info import state_fidelity\n", - "from qiskit_aqua.operator import Operator\n", - "from qiskit_aqua.components.initial_states import Custom\n", + "from qiskit.aqua.operator import Operator\n", + "from qiskit.aqua.components.initial_states import Custom\n", "\n", "num_qubits = 2\n", "evo_time = 1\n", diff --git a/community/aqua/general/vqe.ipynb b/community/aqua/general/vqe.ipynb index 2dd432820..98257da86 100644 --- a/community/aqua/general/vqe.ipynb +++ b/community/aqua/general/vqe.ipynb @@ -21,8 +21,8 @@ }, "outputs": [], "source": [ - "from qiskit_aqua import Operator, run_algorithm\n", - "from qiskit_aqua.input import get_input_instance" + "from qiskit.aqua import Operator, run_algorithm\n", + "from qiskit.aqua.input import get_input_instance" ] }, { diff --git a/community/aqua/optimization/clique.ipynb b/community/aqua/optimization/clique.ipynb index d050cd8e8..e43a53568 100644 --- a/community/aqua/optimization/clique.ipynb +++ b/community/aqua/optimization/clique.ipynb @@ -33,10 +33,10 @@ "\n", "from qiskit import Aer\n", "\n", - "from qiskit_aqua import run_algorithm\n", - "from qiskit_aqua.input import EnergyInput\n", - "from qiskit_aqua.translators.ising import clique\n", - "from qiskit_aqua.algorithms import ExactEigensolver" + "from qiskit.aqua import run_algorithm\n", + "from qiskit.aqua.input import EnergyInput\n", + "from qiskit.aqua.translators.ising import clique\n", + "from qiskit.aqua.algorithms import ExactEigensolver" ] }, { diff --git a/community/aqua/optimization/exact_cover.ipynb b/community/aqua/optimization/exact_cover.ipynb index 4ade3a565..aa8b5b169 100644 --- a/community/aqua/optimization/exact_cover.ipynb +++ b/community/aqua/optimization/exact_cover.ipynb @@ -44,10 +44,10 @@ "import numpy as np\n", "import json\n", "from qiskit import Aer\n", - "from qiskit_aqua import run_algorithm\n", - "from qiskit_aqua.input import EnergyInput\n", - "from qiskit_aqua.translators.ising import exactcover\n", - "from qiskit_aqua.algorithms import ExactEigensolver\n", + "from qiskit.aqua import run_algorithm\n", + "from qiskit.aqua.input import EnergyInput\n", + "from qiskit.aqua.translators.ising import exactcover\n", + "from qiskit.aqua.algorithms import ExactEigensolver\n", "\n", "input_file = 'sample.exactcover'\n", "with open(input_file) as f:\n", diff --git a/community/aqua/optimization/graph_partition.ipynb b/community/aqua/optimization/graph_partition.ipynb index f7b024103..9fe476ba5 100644 --- a/community/aqua/optimization/graph_partition.ipynb +++ b/community/aqua/optimization/graph_partition.ipynb @@ -50,10 +50,10 @@ "source": [ "import numpy as np\n", "from qiskit import Aer\n", - "from qiskit_aqua import run_algorithm\n", - "from qiskit_aqua.input import EnergyInput\n", - "from qiskit_aqua.translators.ising import graphpartition\n", - "from qiskit_aqua.algorithms import ExactEigensolver\n", + "from qiskit.aqua import run_algorithm\n", + "from qiskit.aqua.input import EnergyInput\n", + "from qiskit.aqua.translators.ising import graphpartition\n", + "from qiskit.aqua.algorithms import ExactEigensolver\n", "\n", "np.random.seed(100)\n", "num_nodes = 4\n", diff --git a/community/aqua/optimization/grover.ipynb b/community/aqua/optimization/grover.ipynb index 116853c44..fa938b875 100644 --- a/community/aqua/optimization/grover.ipynb +++ b/community/aqua/optimization/grover.ipynb @@ -10,7 +10,7 @@ "\n", "This notebook demonstrates how to use the `Qiskit Aqua` library Grover algorithm and process the result.\n", "\n", - "Further information is available for the algorithms in the github repo qiskit_aqua/readme.md" + "Further information is available for the algorithms in the github repo qiskit/aqua/readme.md" ] }, { @@ -23,10 +23,10 @@ "import numpy as np\n", "from qiskit import LegacySimulators\n", "from qiskit.tools.visualization import plot_histogram\n", - "from qiskit_aqua import QuantumInstance\n", - "from qiskit_aqua import run_algorithm\n", - "from qiskit_aqua.algorithms import Grover\n", - "from qiskit_aqua.components.oracles import SAT" + "from qiskit.aqua import QuantumInstance\n", + "from qiskit.aqua import run_algorithm\n", + "from qiskit.aqua.algorithms import Grover\n", + "from qiskit.aqua.components.oracles import SAT" ] }, { diff --git a/community/aqua/optimization/maxcut.ipynb b/community/aqua/optimization/maxcut.ipynb index a3696c362..daa003ba2 100644 --- a/community/aqua/optimization/maxcut.ipynb +++ b/community/aqua/optimization/maxcut.ipynb @@ -23,10 +23,10 @@ "source": [ "import numpy as np\n", "\n", - "from qiskit_aqua import Operator, run_algorithm\n", - "from qiskit_aqua.input import EnergyInput\n", - "from qiskit_aqua.translators.ising import maxcut\n", - "from qiskit_aqua.algorithms.classical.cplex.cplex_ising import CPLEX_Ising\n", + "from qiskit.aqua import Operator, run_algorithm\n", + "from qiskit.aqua.input import EnergyInput\n", + "from qiskit.aqua.translators.ising import maxcut\n", + "from qiskit.aqua.algorithms.classical.cplex.cplex_ising import CPLEX_Ising\n", "from qiskit import Aer" ] }, diff --git a/community/aqua/optimization/partition.ipynb b/community/aqua/optimization/partition.ipynb index 7a6cffb59..c619277a4 100644 --- a/community/aqua/optimization/partition.ipynb +++ b/community/aqua/optimization/partition.ipynb @@ -22,11 +22,11 @@ "outputs": [], "source": [ "import numpy as np\n", - "from qiskit_aqua import Operator, run_algorithm\n", - "from qiskit_aqua.input import EnergyInput\n", - "from qiskit_aqua.translators.ising import partition\n", + "from qiskit.aqua import Operator, run_algorithm\n", + "from qiskit.aqua.input import EnergyInput\n", + "from qiskit.aqua.translators.ising import partition\n", "from qiskit import Aer\n", - "from qiskit_aqua.algorithms.classical.cplex.cplex_ising import CPLEX_Ising" + "from qiskit.aqua.algorithms.classical.cplex.cplex_ising import CPLEX_Ising" ] }, { diff --git a/community/aqua/optimization/set_packing.ipynb b/community/aqua/optimization/set_packing.ipynb index 214f15125..b2d539e74 100644 --- a/community/aqua/optimization/set_packing.ipynb +++ b/community/aqua/optimization/set_packing.ipynb @@ -46,10 +46,10 @@ "\n", "from qiskit import Aer\n", "\n", - "from qiskit_aqua import run_algorithm\n", - "from qiskit_aqua.input import EnergyInput\n", - "from qiskit_aqua.translators.ising import setpacking\n", - "from qiskit_aqua.algorithms import ExactEigensolver\n", + "from qiskit.aqua import run_algorithm\n", + "from qiskit.aqua.input import EnergyInput\n", + "from qiskit.aqua.translators.ising import setpacking\n", + "from qiskit.aqua.algorithms import ExactEigensolver\n", "\n", "\n", "input_file = 'sample.setpacking'\n", diff --git a/community/aqua/optimization/stableset.ipynb b/community/aqua/optimization/stableset.ipynb index bf998e045..c2229f33a 100644 --- a/community/aqua/optimization/stableset.ipynb +++ b/community/aqua/optimization/stableset.ipynb @@ -23,10 +23,10 @@ "source": [ "import numpy as np\n", "\n", - "from qiskit_aqua import Operator, run_algorithm\n", - "from qiskit_aqua.translators.ising import stableset\n", - "from qiskit_aqua.input import EnergyInput\n", - "from qiskit_aqua.algorithms.classical.cplex.cplex_ising import CPLEX_Ising\n", + "from qiskit.aqua import Operator, run_algorithm\n", + "from qiskit.aqua.translators.ising import stableset\n", + "from qiskit.aqua.input import EnergyInput\n", + "from qiskit.aqua.algorithms.classical.cplex.cplex_ising import CPLEX_Ising\n", "from qiskit import Aer" ] }, diff --git a/community/aqua/optimization/vertex_cover.ipynb b/community/aqua/optimization/vertex_cover.ipynb index e081d322f..31e0869cd 100644 --- a/community/aqua/optimization/vertex_cover.ipynb +++ b/community/aqua/optimization/vertex_cover.ipynb @@ -45,10 +45,10 @@ "source": [ "import numpy as np\n", "from qiskit import Aer\n", - "from qiskit_aqua import run_algorithm\n", - "from qiskit_aqua.input import EnergyInput\n", - "from qiskit_aqua.translators.ising import vertexcover\n", - "from qiskit_aqua.algorithms import ExactEigensolver\n", + "from qiskit.aqua import run_algorithm\n", + "from qiskit.aqua.input import EnergyInput\n", + "from qiskit.aqua.translators.ising import vertexcover\n", + "from qiskit.aqua.algorithms import ExactEigensolver\n", "\n", "np.random.seed(100)\n", "num_nodes = 3\n", diff --git a/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_01.ipynb b/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_01.ipynb index 8199a579d..f15a5137a 100755 --- a/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_01.ipynb +++ b/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_01.ipynb @@ -29,8 +29,8 @@ "outputs": [], "source": [ "import pylab\n", - "from qiskit_aqua import run_algorithm\n", - "from qiskit_aqua.input import get_input_instance\n", + "from qiskit.aqua import run_algorithm\n", + "from qiskit.aqua.input import get_input_instance\n", "from qiskit.tools.visualization import matplotlib_circuit_drawer as draw\n", "from qiskit.tools.visualization import plot_histogram" ] diff --git a/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_02.ipynb b/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_02.ipynb index 130a6383a..73058409b 100755 --- a/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_02.ipynb +++ b/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_02.ipynb @@ -42,13 +42,13 @@ "outputs": [], "source": [ "from qsvm_datasets import *\n", - "from qiskit_aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name\n", - "from qiskit_aqua.input import get_input_instance\n", - "from qiskit_aqua import run_algorithm\n", + "from qiskit.aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name\n", + "from qiskit.aqua.input import get_input_instance\n", + "from qiskit.aqua import run_algorithm\n", "\n", "# setup aqua logging\n", "import logging\n", - "from qiskit_aqua._logging import set_logging_config, build_logging_config\n", + "from qiskit.aqua._logging import set_logging_config, build_logging_config\n", "# set_logging_config(build_logging_config(logging.DEBUG)) # choose INFO, DEBUG to see the log" ] }, diff --git a/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_03.ipynb b/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_03.ipynb index c627a92e1..6c6b8ba22 100755 --- a/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_03.ipynb +++ b/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_03.ipynb @@ -107,13 +107,13 @@ "import networkx as nx\n", "\n", "from qiskit.tools.visualization import plot_histogram\n", - "from qiskit_aqua import Operator, run_algorithm, get_algorithm_instance\n", - "from qiskit_aqua.input import get_input_instance\n", - "from qiskit_aqua.translators.ising import maxcut, tsp\n", + "from qiskit.aqua import Operator, run_algorithm, get_algorithm_instance\n", + "from qiskit.aqua.input import get_input_instance\n", + "from qiskit.aqua.translators.ising import maxcut, tsp\n", "\n", "# setup aqua logging\n", "import logging\n", - "from qiskit_aqua._logging import set_logging_config, build_logging_config\n", + "from qiskit.aqua._logging import set_logging_config, build_logging_config\n", "# set_logging_config(build_logging_config(logging.DEBUG)) # choose INFO, DEBUG to see the log\n", "\n", "# ignoring deprecation errors on matplotlib\n", diff --git a/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_04.ipynb b/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_04.ipynb index 3ca4d85a4..f687a4973 100755 --- a/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_04.ipynb +++ b/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_04.ipynb @@ -107,13 +107,13 @@ "import networkx as nx\n", "\n", "from qiskit.tools.visualization import plot_histogram\n", - "from qiskit_aqua import Operator, run_algorithm, get_algorithm_instance\n", - "from qiskit_aqua.input import get_input_instance\n", - "from qiskit_aqua.translators.ising import maxcut, tsp\n", + "from qiskit.aqua import Operator, run_algorithm, get_algorithm_instance\n", + "from qiskit.aqua.input import get_input_instance\n", + "from qiskit.aqua.translators.ising import maxcut, tsp\n", "\n", "# setup aqua logging\n", "import logging\n", - "from qiskit_aqua._logging import set_logging_config, build_logging_config\n", + "from qiskit.aqua._logging import set_logging_config, build_logging_config\n", "# set_logging_config(build_logging_config(logging.DEBUG)) # choose INFO, DEBUG to see the log\n", "\n", "# ignoring deprecation errors on matplotlib\n", diff --git a/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_05.ipynb b/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_05.ipynb index 92efc3255..6ce9607ae 100755 --- a/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_05.ipynb +++ b/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_05.ipynb @@ -32,7 +32,7 @@ "\n", "This notebook has been written to use the HDF5 chemistry driver. This driver uses molecular data that has been saved from a prior computation so that this notebook can be run with no additional driver installation requirements. See the HDF5 chemistry driver readme for more detail.\n", "\n", - "First we import AquaChemistry, which is the object that will carry out the computation for us" + "First we import QiskitChemistry, which is the object that will carry out the computation for us" ] }, { @@ -41,7 +41,7 @@ "metadata": {}, "outputs": [], "source": [ - "from qiskit_aqua_chemistry import AquaChemistry" + "from qiskit.chemistry import QiskitChemistry" ] }, { @@ -82,7 +82,7 @@ "outputs": [], "source": [ "# Input dictionary to configure Qiskit AQUA Chemistry for the chemistry problem.\n", - "aqua_chemistry_dict = {\n", + "qiskit_chemistry_dict = {\n", " 'driver': {'name': 'HDF5'},\n", " 'HDF5': {'hdf5_input': '0.7_sto-3g.hdf5'},\n", " 'operator': {'name': 'hamiltonian'},\n", @@ -98,7 +98,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We can now create a AquaChemistry object and call run on it passing in the problem dictionary to get a result. This may take a short time and it will use a local quantum simulator to carry out the quantum computation that the VQE algorithm uses." + "We can now create a QiskitChemistry object and call run on it passing in the problem dictionary to get a result. This may take a short time and it will use a local quantum simulator to carry out the quantum computation that the VQE algorithm uses." ] }, { @@ -107,8 +107,8 @@ "metadata": {}, "outputs": [], "source": [ - "solver = AquaChemistry()\n", - "result = solver.run(aqua_chemistry_dict)" + "solver = QiskitChemistry()\n", + "result = solver.run(qiskit_chemistry_dict)" ] }, { diff --git a/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/latex/main.tex b/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/latex/main.tex index f8b3d435b..b5b20e31a 100755 --- a/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/latex/main.tex +++ b/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/latex/main.tex @@ -137,7 +137,7 @@ \section{Troubleshooting \qka} \section{\gvsa in \qka} \begin{frame}[fragile]{\gvsa in \qka} Go ahead and run the following code, while trying to understand it:\begin{minted}{python} -from qiskit_aqua import run_algorithm +from qiskit.aqua import run_algorithm # problem in DIMACS CNF format: sat_cnf = """ p cnf 3 5 @@ -223,7 +223,7 @@ \section{Chemistry in \qka} \small{We will not go much deeper into explaining the typical approaches, as this should be done by those students that truly benefit from it. However, here is an example of how such problems may be configured (the input comes from \href{https://support.hdfgroup.org/HDF5/whatishdf5.html}{HDF5} files):}\begin{minted}{python} # Input dictionary to configure Qiskit aqua Chemistry # for the chemistry problem. -aqua_chemistry_dict = { +qiskit_chemistry_dict = { 'driver': {'name': 'HDF5'}, 'HDF5': {'hdf5_input': 'H2/0.7_sto-3g.hdf5'}, 'operator': {'name': 'hamiltonian'}, diff --git a/community/awards/teach_me_quantum_2018/qml_mooc/00_Course_Introduction.ipynb b/community/awards/teach_me_quantum_2018/qml_mooc/00_Course_Introduction.ipynb index 64a6243b0..c61e5622e 100644 --- a/community/awards/teach_me_quantum_2018/qml_mooc/00_Course_Introduction.ipynb +++ b/community/awards/teach_me_quantum_2018/qml_mooc/00_Course_Introduction.ipynb @@ -69,7 +69,7 @@ "import dimod\n", "import minorminer\n", "import qiskit\n", - "import qiskit_aqua" + "import qiskit.aqua" ] } ], diff --git a/community/awards/teach_me_quantum_2018/qml_mooc/07_Variational Circuits.ipynb b/community/awards/teach_me_quantum_2018/qml_mooc/07_Variational Circuits.ipynb index a68a074b8..55b98a5f4 100644 --- a/community/awards/teach_me_quantum_2018/qml_mooc/07_Variational Circuits.ipynb +++ b/community/awards/teach_me_quantum_2018/qml_mooc/07_Variational Circuits.ipynb @@ -59,8 +59,8 @@ "from functools import partial, reduce\n", "from qiskit import BasicAer, QuantumRegister, execute\n", "from qiskit.quantum_info import Pauli\n", - "from qiskit_aqua import Operator, get_aer_backend\n", - "from qiskit_aqua.components.initial_states import Custom\n", + "from qiskit.aqua import Operator, get_aer_backend\n", + "from qiskit.aqua.components.initial_states import Custom\n", "from scipy.optimize import minimize\n", "np.set_printoptions(precision=3, suppress=True)" ] diff --git a/community/awards/teach_me_quantum_2018/qml_mooc/08_Sampling a Thermal State.ipynb b/community/awards/teach_me_quantum_2018/qml_mooc/08_Sampling a Thermal State.ipynb index b71b4ba06..bf4c1c5c8 100644 --- a/community/awards/teach_me_quantum_2018/qml_mooc/08_Sampling a Thermal State.ipynb +++ b/community/awards/teach_me_quantum_2018/qml_mooc/08_Sampling a Thermal State.ipynb @@ -196,11 +196,11 @@ "from qiskit import BasicAer, QuantumRegister, QuantumCircuit, ClassicalRegister\n", "from qiskit import execute\n", "from qiskit.quantum_info import Pauli\n", - "from qiskit_aqua import get_aer_backend, QuantumInstance\n", - "from qiskit_aqua.operator import Operator\n", - "from qiskit_aqua.components.optimizers import COBYLA\n", - "from qiskit_aqua.algorithms import VQE\n", - "from qiskit_aqua.algorithms.adaptive.qaoa.varform import QAOAVarForm" + "from qiskit.aqua import get_aer_backend, QuantumInstance\n", + "from qiskit.aqua.operator import Operator\n", + "from qiskit.aqua.components.optimizers import COBYLA\n", + "from qiskit.aqua.algorithms import VQE\n", + "from qiskit.aqua.algorithms.adaptive.qaoa.varform import QAOAVarForm" ] }, { diff --git a/community/awards/teach_me_quantum_2018/qml_mooc/09_Discrete Optimization and Ensemble Learning.ipynb b/community/awards/teach_me_quantum_2018/qml_mooc/09_Discrete Optimization and Ensemble Learning.ipynb index e95d85884..55616d3e4 100644 --- a/community/awards/teach_me_quantum_2018/qml_mooc/09_Discrete Optimization and Ensemble Learning.ipynb +++ b/community/awards/teach_me_quantum_2018/qml_mooc/09_Discrete Optimization and Ensemble Learning.ipynb @@ -499,7 +499,7 @@ ], "source": [ "from qiskit.quantum_info import Pauli\n", - "from qiskit_aqua import Operator\n", + "from qiskit.aqua import Operator\n", "\n", "num_nodes = w.shape[0]\n", "pauli_list = []\n", @@ -536,9 +536,9 @@ }, "outputs": [], "source": [ - "from qiskit_aqua import get_aer_backend, QuantumInstance\n", - "from qiskit_aqua.algorithms import QAOA\n", - "from qiskit_aqua.components.optimizers import COBYLA\n", + "from qiskit.aqua import get_aer_backend, QuantumInstance\n", + "from qiskit.aqua.algorithms import QAOA\n", + "from qiskit.aqua.components.optimizers import COBYLA\n", "p = 1\n", "optimizer = COBYLA()\n", "qaoa = QAOA(ising_model, optimizer, p, operator_mode='matrix')\n", diff --git a/community/awards/teach_me_quantum_2018/qml_mooc/10_Discrete Optimization and Unsupervised Learning.ipynb b/community/awards/teach_me_quantum_2018/qml_mooc/10_Discrete Optimization and Unsupervised Learning.ipynb index fcb304192..544d87440 100644 --- a/community/awards/teach_me_quantum_2018/qml_mooc/10_Discrete Optimization and Unsupervised Learning.ipynb +++ b/community/awards/teach_me_quantum_2018/qml_mooc/10_Discrete Optimization and Unsupervised Learning.ipynb @@ -126,10 +126,10 @@ } ], "source": [ - "from qiskit_aqua import get_aer_backend, QuantumInstance\n", - "from qiskit_aqua.algorithms import QAOA\n", - "from qiskit_aqua.components.optimizers import COBYLA\n", - "from qiskit_aqua.translators.ising import maxcut" + "from qiskit.aqua import get_aer_backend, QuantumInstance\n", + "from qiskit.aqua.algorithms import QAOA\n", + "from qiskit.aqua.components.optimizers import COBYLA\n", + "from qiskit.aqua.translators.ising import maxcut" ] }, { diff --git a/qiskit/aqua/artificial_intelligence/qsvm_kernel_classification.ipynb b/qiskit/aqua/artificial_intelligence/qsvm_kernel_classification.ipynb index 2cc61161b..093c21f96 100644 --- a/qiskit/aqua/artificial_intelligence/qsvm_kernel_classification.ipynb +++ b/qiskit/aqua/artificial_intelligence/qsvm_kernel_classification.ipynb @@ -47,15 +47,15 @@ "from qsvm_datasets import *\n", "\n", "from qiskit import Aer\n", - "from qiskit_aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name\n", - "from qiskit_aqua.input import SVMInput\n", - "from qiskit_aqua import run_algorithm, QuantumInstance\n", - "from qiskit_aqua.algorithms import QSVMKernel\n", - "from qiskit_aqua.components.feature_maps import SecondOrderExpansion\n", + "from qiskit.aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name\n", + "from qiskit.aqua.input import SVMInput\n", + "from qiskit.aqua import run_algorithm, QuantumInstance\n", + "from qiskit.aqua.algorithms import QSVMKernel\n", + "from qiskit.aqua.components.feature_maps import SecondOrderExpansion\n", "\n", "# setup aqua logging\n", "import logging\n", - "from qiskit_aqua import set_aqua_logging\n", + "from qiskit.aqua import set_aqua_logging\n", "# set_aqua_logging(logging.DEBUG) # choose INFO, DEBUG to see the log" ] }, diff --git a/qiskit/aqua/chemistry/declarative_approach.ipynb b/qiskit/aqua/chemistry/declarative_approach.ipynb index 0011b3998..a00573e48 100644 --- a/qiskit/aqua/chemistry/declarative_approach.ipynb +++ b/qiskit/aqua/chemistry/declarative_approach.ipynb @@ -33,7 +33,7 @@ "source": [ "### Introduction\n", "\n", - "This notebook demonstrates how to use Qiskit Chemistry to compute the ground state energy of molecular Hydrogen (H$_2$) using the Variational Quantum Eigensolver (VQE) algorithm and the Unitary Coupled Cluster Singles and Doubles (UCCSD) variational form. This notebook uses the so called *declarative approach*: a Python dictionary automatically generated via the Qiskit Chemistry GUI wizard summarizes the entire experiment declaratively. That dictionary is simply then passed as a paramter to the `run` method of the `AquaChemistry` solver to get the result of the experiment, also in the form of a Python dictionary.\n", + "This notebook demonstrates how to use Qiskit Chemistry to compute the ground state energy of molecular Hydrogen (H$_2$) using the Variational Quantum Eigensolver (VQE) algorithm and the Unitary Coupled Cluster Singles and Doubles (UCCSD) variational form. This notebook uses the so called *declarative approach*: a Python dictionary automatically generated via the Qiskit Chemistry GUI wizard summarizes the entire experiment declaratively. That dictionary is simply then passed as a paramter to the `run` method of the `QiskitChemistry` solver to get the result of the experiment, also in the form of a Python dictionary.\n", "\n", "Users who are more interested in learning the Qiskit Aqua and Qiskit Chemistry APIs and/or in contributing new algorithmic components can look at the same experiment executed [programmatically](https://github.com/Qiskit/qiskit-tutorials/blob/master/qiskit/aqua/chemistry/programmatic_approach.ipynb).\n", "\n", @@ -48,7 +48,7 @@ "metadata": {}, "outputs": [], "source": [ - "from qiskit_chemistry import QiskitChemistry\n", + "from qiskit.chemistry import QiskitChemistry\n", "from qiskit import Aer" ] }, diff --git a/qiskit/aqua/chemistry/dissociation_profile_of_molecule.ipynb b/qiskit/aqua/chemistry/dissociation_profile_of_molecule.ipynb index 231637f09..b2d1831a2 100644 --- a/qiskit/aqua/chemistry/dissociation_profile_of_molecule.ipynb +++ b/qiskit/aqua/chemistry/dissociation_profile_of_molecule.ipynb @@ -116,13 +116,13 @@ "%matplotlib inline\n", "import numpy as np\n", "from qiskit import Aer\n", - "from qiskit_chemistry import QiskitChemistry\n", + "from qiskit.chemistry import QiskitChemistry\n", "import warnings\n", "warnings.filterwarnings('ignore')\n", "\n", - "# setup qiskit_chemistry logging\n", + "# setup qiskit.chemistry logging\n", "import logging\n", - "from qiskit_chemistry import set_qiskit_chemistry_logging\n", + "from qiskit.chemistry import set_qiskit_chemistry_logging\n", "set_qiskit_chemistry_logging(logging.ERROR) # choose among DEBUG, INFO, WARNING, ERROR, CRITICAL and NOTSET" ] }, diff --git a/qiskit/aqua/chemistry/programmatic_approach.ipynb b/qiskit/aqua/chemistry/programmatic_approach.ipynb index 3e3ce1f4f..2b0a47d06 100644 --- a/qiskit/aqua/chemistry/programmatic_approach.ipynb +++ b/qiskit/aqua/chemistry/programmatic_approach.ipynb @@ -48,15 +48,15 @@ "from qiskit import Aer\n", "\n", "# lib from Qiskit Aqua\n", - "from qiskit_aqua import Operator, QuantumInstance\n", - "from qiskit_aqua.algorithms import VQE, ExactEigensolver\n", - "from qiskit_aqua.components.optimizers import COBYLA\n", + "from qiskit.aqua import Operator, QuantumInstance\n", + "from qiskit.aqua.algorithms import VQE, ExactEigensolver\n", + "from qiskit.aqua.components.optimizers import COBYLA\n", "\n", "# lib from Qiskit Aqua Chemistry\n", - "from qiskit_chemistry import FermionicOperator\n", - "from qiskit_chemistry.drivers import PySCFDriver, UnitsType\n", - "from qiskit_chemistry.aqua_extensions.components.variational_forms import UCCSD\n", - "from qiskit_chemistry.aqua_extensions.components.initial_states import HartreeFock" + "from qiskit.chemistry import FermionicOperator\n", + "from qiskit.chemistry.drivers import PySCFDriver, UnitsType\n", + "from qiskit.chemistry.aqua_extensions.components.variational_forms import UCCSD\n", + "from qiskit.chemistry.aqua_extensions.components.initial_states import HartreeFock" ] }, { diff --git a/qiskit/aqua/finance/european_call_option_pricing.ipynb b/qiskit/aqua/finance/european_call_option_pricing.ipynb index 6ccf50564..70a5e1485 100644 --- a/qiskit/aqua/finance/european_call_option_pricing.ipynb +++ b/qiskit/aqua/finance/european_call_option_pricing.ipynb @@ -62,9 +62,9 @@ "%matplotlib inline\n", "import numpy as np\n", "from qiskit import BasicAer\n", - "from qiskit_aqua.algorithms import AmplitudeEstimation\n", - "from qiskit_aqua.components.uncertainty_problems import EuropeanCallExpectedValue, EuropeanCallDelta\n", - "from qiskit_aqua.components.random_distributions import LogNormalDistribution" + "from qiskit.aqua.algorithms import AmplitudeEstimation\n", + "from qiskit.aqua.components.uncertainty_problems import EuropeanCallExpectedValue, EuropeanCallDelta\n", + "from qiskit.aqua.components.random_distributions import LogNormalDistribution" ] }, { diff --git a/qiskit/aqua/finance/fixed_income_pricing.ipynb b/qiskit/aqua/finance/fixed_income_pricing.ipynb index 0b01e19b5..f5db68337 100644 --- a/qiskit/aqua/finance/fixed_income_pricing.ipynb +++ b/qiskit/aqua/finance/fixed_income_pricing.ipynb @@ -51,9 +51,9 @@ "%matplotlib inline\n", "import numpy as np\n", "from qiskit import BasicAer\n", - "from qiskit_aqua.algorithms import AmplitudeEstimation\n", - "from qiskit_aqua.components.random_distributions import MultivariateNormalDistribution\n", - "from qiskit_aqua.components.uncertainty_problems import FixedIncomeExpectedValue" + "from qiskit.aqua.algorithms import AmplitudeEstimation\n", + "from qiskit.aqua.components.random_distributions import MultivariateNormalDistribution\n", + "from qiskit.aqua.components.uncertainty_problems import FixedIncomeExpectedValue" ] }, { diff --git a/qiskit/aqua/finance/portfolio_optimization.ipynb b/qiskit/aqua/finance/portfolio_optimization.ipynb index f3e186db1..5eaaf712c 100644 --- a/qiskit/aqua/finance/portfolio_optimization.ipynb +++ b/qiskit/aqua/finance/portfolio_optimization.ipynb @@ -61,13 +61,13 @@ "outputs": [], "source": [ "from qiskit import BasicAer\n", - "from qiskit_aqua import QuantumInstance\n", - "from qiskit_aqua import Operator, run_algorithm\n", - "from qiskit_aqua.input import EnergyInput\n", - "from qiskit_aqua.translators.ising import portfolio\n", - "from qiskit_aqua.algorithms import VQE, QAOA, ExactEigensolver\n", - "from qiskit_aqua.components.optimizers import COBYLA\n", - "from qiskit_aqua.components.variational_forms import RY\n", + "from qiskit.aqua import QuantumInstance\n", + "from qiskit.aqua import Operator, run_algorithm\n", + "from qiskit.aqua.input import EnergyInput\n", + "from qiskit.aqua.translators.ising import portfolio\n", + "from qiskit.aqua.algorithms import VQE, QAOA, ExactEigensolver\n", + "from qiskit.aqua.components.optimizers import COBYLA\n", + "from qiskit.aqua.components.variational_forms import RY\n", "import numpy as np" ] }, diff --git a/qiskit/aqua/general/amplitude_estimation.ipynb b/qiskit/aqua/general/amplitude_estimation.ipynb index ca1743c51..43d45dcef 100644 --- a/qiskit/aqua/general/amplitude_estimation.ipynb +++ b/qiskit/aqua/general/amplitude_estimation.ipynb @@ -57,10 +57,10 @@ "import numpy as np\n", "from qiskit.tools.visualization import plot_bloch_vector\n", "from qiskit import BasicAer\n", - "from qiskit_aqua.algorithms import AmplitudeEstimation\n", - "from qiskit_aqua.algorithms.single_sample.ae.q_factory import QFactory\n", - "from qiskit_aqua.components.uncertainty_problems import UncertaintyProblem\n", - "from qiskit_aqua.utils.circuit_utils import cry" + "from qiskit.aqua.algorithms import AmplitudeEstimation\n", + "from qiskit.aqua.algorithms.single_sample.ae.q_factory import QFactory\n", + "from qiskit.aqua.components.uncertainty_problems import UncertaintyProblem\n", + "from qiskit.aqua.utils.circuit_utils import cry" ] }, { diff --git a/qiskit/aqua/general/evolutionfidelity/evolutionfidelity/evolutionfidelity.py b/qiskit/aqua/general/evolutionfidelity/evolutionfidelity/evolutionfidelity.py index 3834e9560..11de1a484 100644 --- a/qiskit/aqua/general/evolutionfidelity/evolutionfidelity/evolutionfidelity.py +++ b/qiskit/aqua/general/evolutionfidelity/evolutionfidelity/evolutionfidelity.py @@ -19,7 +19,7 @@ This is a simple tutorial example to show how to build an algorithm to extend Qiskit Aqua library. Algorithms are designed to be dynamically discovered within Qiskit Aqua. For this the entire parent directory 'evolutionfidelity' should -be moved under the 'qiskit_aqua' directory. The current demonstration notebook +be moved under the 'qiskit/aqua' directory. The current demonstration notebook shows how to explicitly register the algorithm and works without re-locating this code. The former automatic discovery does however allow the algorithm to be found and seen in the UI browser, and selected from the GUI when choosing an algorithm. diff --git a/qiskit/aqua/optimization/maxcut_and_tsp.ipynb b/qiskit/aqua/optimization/maxcut_and_tsp.ipynb index 0766edcba..d39a81c0a 100644 --- a/qiskit/aqua/optimization/maxcut_and_tsp.ipynb +++ b/qiskit/aqua/optimization/maxcut_and_tsp.ipynb @@ -110,17 +110,17 @@ "\n", "from qiskit import Aer\n", "from qiskit.tools.visualization import plot_histogram\n", - "from qiskit_aqua import Operator, run_algorithm\n", - "from qiskit_aqua.input import EnergyInput\n", - "from qiskit_aqua.translators.ising import maxcut, tsp\n", - "from qiskit_aqua.algorithms import VQE, ExactEigensolver\n", - "from qiskit_aqua.components.optimizers import SPSA\n", - "from qiskit_aqua.components.variational_forms import RY\n", - "from qiskit_aqua import QuantumInstance\n", + "from qiskit.aqua import Operator, run_algorithm\n", + "from qiskit.aqua.input import EnergyInput\n", + "from qiskit.aqua.translators.ising import maxcut, tsp\n", + "from qiskit.aqua.algorithms import VQE, ExactEigensolver\n", + "from qiskit.aqua.components.optimizers import SPSA\n", + "from qiskit.aqua.components.variational_forms import RY\n", + "from qiskit.aqua import QuantumInstance\n", "\n", "# setup aqua logging\n", "import logging\n", - "from qiskit_aqua import set_aqua_logging\n", + "from qiskit.aqua import set_aqua_logging\n", "# set_aqua_logging(logging.DEBUG) # choose INFO, DEBUG to see the log" ] }, From c5e2a9f876550572a0d09ea49bc9e248d075674c Mon Sep 17 00:00:00 2001 From: Manoel Marques Date: Tue, 12 Feb 2019 15:27:27 -0500 Subject: [PATCH 006/116] Add run_config to some notebooks --- .../qsvm_kernel_directly.ipynb | 12 +- .../qsvm_kernel_multiclass.ipynb | 19 +-- .../qsvm_variational.ipynb | 12 +- community/aqua/general/eoh.ipynb | 55 ++++----- community/aqua/optimization/grover.ipynb | 44 +++---- ...e Optimization and Ensemble Learning.ipynb | 27 ++-- .../qsvm_kernel_classification.ipynb | 19 +-- qiskit/aqua/optimization/maxcut_and_tsp.ipynb | 115 ++++++++---------- 8 files changed, 129 insertions(+), 174 deletions(-) diff --git a/community/aqua/artificial_intelligence/qsvm_kernel_directly.ipynb b/community/aqua/artificial_intelligence/qsvm_kernel_directly.ipynb index 6eb74b102..08b9e25c0 100644 --- a/community/aqua/artificial_intelligence/qsvm_kernel_directly.ipynb +++ b/community/aqua/artificial_intelligence/qsvm_kernel_directly.ipynb @@ -29,6 +29,7 @@ "source": [ "from datasets import *\n", "from qiskit import Aer\n", + "from qiskit.qobj import RunConfig\n", "from qiskit.aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name\n", "from qiskit.aqua import run_algorithm, QuantumInstance\n", "from qiskit.aqua.input import SVMInput\n", @@ -139,7 +140,7 @@ }, { "data": { - "image/png": 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+ "image/png": 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\n", 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" ] @@ -195,7 +196,8 @@ "feature_map = SecondOrderExpansion(num_qubits=feature_dim, depth=2, entangler_map={0: [1]})\n", "svm = QSVMKernel(feature_map, training_input, test_input, None)# the data for prediction can be feeded later.\n", "svm.random_seed = random_seed\n", - "quantum_instance = QuantumInstance(backend, shots=shots, seed=random_seed, seed_mapper=random_seed)\n", + "run_config = RunConfig(shots=shots, max_credits=10, memory=False, seed=random_seed)\n", + "quantum_instance = QuantumInstance(backend, run_config, seed_mapper=random_seed)\n", "result = svm.run(quantum_instance)" ] }, @@ -220,7 +222,7 @@ }, { "data": { - "image/png": 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+ "image/png": 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\n", "text/plain": [ "
" ] @@ -283,9 +285,9 @@ ], "metadata": { "kernelspec": { - "display_name": "mykernel", + "display_name": "Python 3", "language": "python", - "name": "mykernel" + "name": "python3" }, "language_info": { "codemirror_mode": { diff --git a/community/aqua/artificial_intelligence/qsvm_kernel_multiclass.ipynb b/community/aqua/artificial_intelligence/qsvm_kernel_multiclass.ipynb index 3284add29..901bd98f9 100644 --- a/community/aqua/artificial_intelligence/qsvm_kernel_multiclass.ipynb +++ b/community/aqua/artificial_intelligence/qsvm_kernel_multiclass.ipynb @@ -39,7 +39,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": {}, "outputs": [ { @@ -78,20 +78,9 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "'testing_accuracy' : 0.8695652173913043\n", - "'test_success_ratio' : 0.8695652173913043\n", - "'predicted_labels' : [0 0 0 0 0 0 1 0 0 0 1 2 1 1 1 0 1 1 1 1 2 2 2]\n", - "'predicted_classes' : ['A', 'A', 'A', 'A', 'A', 'A', 'B', 'A', 'A', 'A', 'B', 'C', 'B', 'B', 'B', 'A', 'B', 'B', 'B', 'B', 'C', 'C', 'C']\n" - ] - } - ], + "outputs": [], "source": [ "aqua_dict = {\n", " 'problem': {'name': 'svm_classification', 'random_seed': 10598},\n", @@ -127,7 +116,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.6.7" } }, "nbformat": 4, diff --git a/community/aqua/artificial_intelligence/qsvm_variational.ipynb b/community/aqua/artificial_intelligence/qsvm_variational.ipynb index c0c500634..9d62d274e 100644 --- a/community/aqua/artificial_intelligence/qsvm_variational.ipynb +++ b/community/aqua/artificial_intelligence/qsvm_variational.ipynb @@ -33,6 +33,7 @@ "from datasets import *\n", "from qiskit.aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name\n", "from qiskit import Aer\n", + "from qiskit.qobj import RunConfig\n", "from qiskit.aqua.input import SVMInput\n", "from qiskit.aqua import run_algorithm, QuantumInstance\n", "from qiskit.aqua.algorithms import QSVMVariational\n", @@ -57,7 +58,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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L778qC3egBRhxox3OnFz6eOSbGjACR4sw4kY7DG1a+T5zs9nIHEgcwY122HlQGiywQcFyI3MgIQQ3muPoaNaLXk1P+uq90nW3SkObJVnyMpsZFBmZAw1HjxvNUMaskKv3nrvv4seTshH5zoPl1QzUhBE3mmG5WSGr7UkvHoEPbc5uc2ESLcCIG82wXO95LT3phSNwoEUYcaMZlus905MGXoTgRjMsNSuEnjSwJIIbzUBPGiiMHjeag540UAgjbgBIDMENAIkhuAEgMQQ3ACSG4AaAxBDcAJAYgnut1rKiHbASXl9YAvO414J9DlElXl9YRrIj7rHJKe245QFdccN92nHLAxqbnOp/EWWvaAcs1ObXF2cSa5LkiHtsckoHDh/T7Fy2n+DUzKwOHD4mSdq9faR/hVSxoh0wr62vL84k1mzFEbftzbY/a/sx21+x/a5+FHYhh44cfyG0583OndWhI8f7Wwgr2qFKbX19tflMok+KtEqel/QbEXGlpH8l6VdtX1ltWRd2ama2p+OVYUU7VKmtr6+2nkn00YrBHRHfjIgv5V9/W9LjkvrYj3ixjcNLbwq73PHKsKIdqtTW11dbzyT6qKcet+0tkrZLeqiKYorav2vreT1uSeoMDmj/rq39L4YV7VClNr6+dh5kP9A1KjyrxPYlku6S9O6IeHaJ7++zPW57fHp6uswaX2T39hHdvGebRoY7sqSR4Y5u3rOtvxcmAazO4jOJzqXSRR3p8D5mmBTkiFj5TvagpHslHYmI9610/263G+Pj4yWUB6DVFs8wkbLRdxtaQj2yPRER3SL3LTKrxJLukPR4kdAGgMKYYbIqRVolOyS9TdLrbT+Sf/ybiusCsB4ww2RVVrw4GREPSnIfagGw3gxtyt6As9RxLCvZt7wDaIG2zlWvWJJveV8vxiandOjIcZ2amdXG4Y7279rKzBm0y/wFyPtvytojQ5uy0F5nFyZ7RXA3VGPWYwGq1sa56hWjVdJQjVmPBUDjENwN1Zj1WAA0DsHdUI1ZjwVA4xDcDbV/11Z1BgfOO1bbeiwAGoWLkw01fwGSWSUAFiO4G2z39hGCGsCLENxATZinj9UiuIEaME8fa9H64GZUgya60Dx9Xp9YSauDm1ENmop5+liLVk8H5N2HaCrm6WMtWh3cjGrQVMzTx1q0ulWycbijqSVCusioht44qsQ8faxFq4N7tbvB0xtHPzBPH6vV6lbJaneDpzdek6Oj2S7fNw6z2zdwAa0ecUurG9XQG6/B4t2+z5zIbkus1Qws0uoR92pxxb8G7PYNFEZwL4Er/jVgt2+gsNa3SlaDK/41YLdvoDCCexlc8e+znQfP73FL7PYNLGPFVontD9g+bfvRfhSEderqvdJ1t0pDmyU5+3zdrVyYBJZQZMT9QUl/IOnD1ZaCdY/dvoFCVhxxR8TnJT3dh1oAAAUwqwQAElNacNveZ3vc9vj09HRZDwsAWKS04I6I2yKiGxHdDRs2lPWwAIBFaJUAQGKKTAf8mKQvSNpq+6Ttf199WQCA5aw4HTAifqEfhQAAiqFVAgCJIbgBIDEENwAkhuAGgMQQ3ACQGIIbABJDcANAYghuAEgMwQ0AiSG4ASAxBDcAJIbgBoDEENwAkJgimwWjj8Ymp3ToyHGdmpnVxuGO9u/aqt3bR+ouC+vN0VHp/pukMyeloU3SzoNs5NwgBHeDjE1O6cDhY5qdOytJmpqZ1YHDxySJ8Eb/HB2V7rlempvNbp85kd2WCO+GoFXSIIeOHH8htOfNzp3VoSPHa6oI69L9N50L7Xlzs9lxNALB3SCnZmZ7Og5U4szJ3o6j7wjuBtk43OnpOFCJoU29HUffEdwNsn/XVnUGB8471hkc0P5dW2uqCOvSzoPS4KLBwmAnO45G4OJkg8xfgGRWCWo1fwGSWSWN5Ygo/UG73W6Mj4+X/rgA0Fa2JyKiW+S+jLgBJIH3OJxDcANoPN7jcL5CFydtv8H2cdtftX1D1UUBwEK8x+F8Kwa37QFJfyjpjZKulPQLtq+sujAAmMd7HM5XZMR9jaSvRsTXI+K7kj4u6WerLQsAzuE9DucrEtwjkk4suH0yP3Ye2/tsj9sen56eLqs+AOA9DouU9gaciLgtIroR0d2wYUNZDwsA2r19RDfv2aaR4Y4saWS4o5v3bFuXFyalYrNKpiRtXnB7U34MAPpm9/aRdRvUixUZcf+VpB+yfYXt75H0Fkl/Vm1ZAIDlrDjijojnbf+apCOSBiR9ICK+UnllAIAlFXoDTkR8UtInK64FAFAAqwMCQGIIbgBIDMENAImpZFlX29OSvlH6A/fHZZK+VXcRJeM5pYHn1HxVPp9XRkShN8FUEtwpsz1edE3cVPCc0sBzar6mPB9aJQCQGIIbABJDcL/YbXUXUAGeUxp4Ts3XiOdDjxsAEsOIGwASQ3ADQGII7pztD9g+bfvRumspi+3Ntj9r+zHbX7H9rrprWgvb32f7Ydtfzp/Pe+uuqSy2B2xP2r637lrKYPtJ28dsP2J7vO56ymB72PYnbD9h+3HbP1ZbLfS4M7ZfJ+k5SR+OiKvqrqcMti+XdHlEfMn2SyVNSNodEY/VXNqq2LakiyPiOduDkh6U9K6I+GLNpa2Z7f8sqSvp+yPi2rrrWSvbT0rqRkRr3nxj+0OS/jIibs+XuH5JRMzUUQsj7lxEfF7S03XXUaaI+GZEfCn/+tuSHtcS286lIjLP5TcH84/kRx62N0l6k6Tb664FS7M9JOl1ku6QpIj4bl2hLRHc64btLZK2S3qo3krWJm8pPCLptKTPRETSzyf3e5LeI+kf6i6kRCHp07YnbO+ru5gSXCFpWtKdeUvrdtsX11UMwb0O2L5E0l2S3h0Rz9Zdz1pExNmIeLWyLfSusZ10W8v2tZJOR8RE3bWU7LUR8RpJb5T0q3krMmUXSXqNpP8ZEdsl/Z2kG+oqhuBuubwXfJekj0bE4brrKUt+mvpZSW+ou5Y12iHpzXlP+OOSXm/7I/WWtHYRMZV/Pi3pbknX1FvRmp2UdHLBGd4nlAV5LQjuFssv5t0h6fGIeF/d9ayV7Q22h/OvO5J+WtIT9Va1NhFxICI2RcQWZfu5PhARv1RzWWti++L8YrjydsLPSEp6tlZEPCXphO2t+aGdkmq7yF9o67L1wPbHJP2kpMtsn5T0XyPijnqrWrMdkt4m6VjeF5ak38y3okvR5ZI+ZHtA2aBjNCJaMX2uZV4h6e5s3KCLJP1JRHyq3pJK8euSPprPKPm6pHfWVQjTAQEgMbRKACAxBDcAJIbgBoDEENwAkBiCGwASQ3ADQGIIbgBIzD8CW32kBECtJ7IAAAAASUVORK5CYII=\n", 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\n", 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" ] @@ -195,7 +196,8 @@ "feature_map = SecondOrderExpansion(num_qubits=feature_dim, depth=2)\n", "var_form = RYRZ(num_qubits=feature_dim, depth=3)\n", "svm = QSVMVariational(optimizer, feature_map, var_form, training_input, test_input)\n", - "quantum_instance = QuantumInstance(backend, shots=shots, seed=random_seed, seed_mapper=random_seed)" + "run_config = RunConfig(shots=shots, max_credits=10, memory=False, seed=random_seed)\n", + "quantum_instance = QuantumInstance(backend, run_config, seed_mapper=random_seed)" ] }, { @@ -254,9 +256,9 @@ ], "metadata": { "kernelspec": { - "display_name": "mykernel", + "display_name": "Python 3", "language": "python", - "name": "mykernel" + "name": "python3" }, "language_info": { "codemirror_mode": { diff --git a/community/aqua/general/eoh.ipynb b/community/aqua/general/eoh.ipynb index 36855a14a..82511a425 100644 --- a/community/aqua/general/eoh.ipynb +++ b/community/aqua/general/eoh.ipynb @@ -17,13 +17,26 @@ "cell_type": "code", "execution_count": 1, "metadata": {}, - "outputs": [], + "outputs": [ + { + "ename": "ImportError", + "evalue": "cannot import name 'QuantumInstance'", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mImportError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtranspiler\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mPassManager\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0maqua\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mrun_algorithm\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0maqua\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0moperator\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mOperator\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mQuantumInstance\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 7\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0maqua\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0malgorithms\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mEOH\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0maqua\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcomponents\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minitial_states\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mCustom\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mImportError\u001b[0m: cannot import name 'QuantumInstance'" + ] + } + ], "source": [ "import numpy as np\n", - "from qiskit import LegacySimulators\n", + "from qiskit import BasicAer\n", + "from qiskit.qobj import RunConfig\n", "from qiskit.transpiler import PassManager\n", - "from qiskit.aqua import run_algorithm\n", - "from qiskit.aqua.operator import Operator, QuantumInstance\n", + "from qiskit.aqua import run_algorithm, QuantumInstance\n", + "from qiskit.aqua.operator import Operator\n", "from qiskit.aqua.algorithms import EOH\n", "from qiskit.aqua.components.initial_states import Custom\n", "from qiskit.aqua.input import EnergyInput\n", @@ -44,7 +57,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -63,20 +76,11 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The result is\n", - "{'avg': (2.722036822009398-5.381265357255164e-17j), 'std_dev': 0.0}\n" - ] - } - ], + "outputs": [], "source": [ - "backend = LegacySimulators.get_backend('statevector_simulator')\n", + "backend = BasicAer.get_backend('statevector_simulator')\n", "quantum_instance = QuantumInstance(backend, pass_manager=PassManager())\n", "\n", "ret = eoh.run(quantum_instance)\n", @@ -92,7 +96,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -122,18 +126,9 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The result is\n", - "{'avg': (2.722036822009398-5.381265357255164e-17j), 'std_dev': 0.0}\n" - ] - } - ], + "outputs": [], "source": [ "ret = run_algorithm(params, algo_input, backend=backend)\n", "print('The result is\\n{}'.format(ret))" @@ -156,7 +151,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.5" + "version": "3.6.7" } }, "nbformat": 4, diff --git a/community/aqua/optimization/grover.ipynb b/community/aqua/optimization/grover.ipynb index fa938b875..e4248107e 100644 --- a/community/aqua/optimization/grover.ipynb +++ b/community/aqua/optimization/grover.ipynb @@ -21,7 +21,8 @@ "source": [ "import pylab\n", "import numpy as np\n", - "from qiskit import LegacySimulators\n", + "from qiskit import BasicAer\n", + "from qiskit.qobj import RunConfig\n", "from qiskit.tools.visualization import plot_histogram\n", "from qiskit.aqua import QuantumInstance\n", "from qiskit.aqua import run_algorithm\n", @@ -115,8 +116,9 @@ } ], "source": [ - "backend = LegacySimulators.get_backend('qasm_simulator')\n", - "quantum_instance = QuantumInstance(backend, shots=100)\n", + "backend = BasicAer.get_backend('qasm_simulator')\n", + "run_config = RunConfig(shots=100, max_credits=10, memory=False)\n", + "quantum_instance = QuantumInstance(backend, run_config)\n", "result = grover.run(quantum_instance)\n", "print(result['result'])" ] @@ -136,15 +138,15 @@ "metadata": {}, "outputs": [ { - "data": { - "image/png": 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\n", 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" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" + "ename": "KeyError", + "evalue": "'measurements'", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mKeyError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mplot_histogram\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'measurements'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;31mKeyError\u001b[0m: 'measurements'" + ] } ], "source": [ @@ -160,23 +162,11 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": null, "metadata": { "scrolled": true }, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "execution_count": 7, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ "params = {\n", " 'problem': {'name': 'search'},\n", @@ -213,7 +203,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.5" + "version": "3.6.7" } }, "nbformat": 4, diff --git a/community/awards/teach_me_quantum_2018/qml_mooc/09_Discrete Optimization and Ensemble Learning.ipynb b/community/awards/teach_me_quantum_2018/qml_mooc/09_Discrete Optimization and Ensemble Learning.ipynb index 55616d3e4..dbdcedd52 100644 --- a/community/awards/teach_me_quantum_2018/qml_mooc/09_Discrete Optimization and Ensemble Learning.ipynb +++ b/community/awards/teach_me_quantum_2018/qml_mooc/09_Discrete Optimization and Ensemble Learning.ipynb @@ -122,7 +122,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "/home/pwittek/.anaconda3/envs/qiskit/lib/python3.7/site-packages/sklearn/linear_model/stochastic_gradient.py:144: FutureWarning: max_iter and tol parameters have been added in Perceptron in 0.19. If both are left unset, they default to max_iter=5 and tol=None. If tol is not None, max_iter defaults to max_iter=1000. From 0.21, default max_iter will be 1000, and default tol will be 1e-3.\n", + "/Users/manoel/anaconda3/envs/QISKitenv/lib/python3.6/site-packages/sklearn/linear_model/stochastic_gradient.py:144: FutureWarning: max_iter and tol parameters have been added in Perceptron in 0.19. If both are left unset, they default to max_iter=5 and tol=None. If tol is not None, max_iter defaults to max_iter=1000. From 0.21, default max_iter will be 1000, and default tol will be 1e-3.\n", " FutureWarning)\n" ] } @@ -164,7 +164,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "/home/pwittek/.anaconda3/envs/qiskit/lib/python3.7/site-packages/sklearn/svm/base.py:196: FutureWarning: The default value of gamma will change from 'auto' to 'scale' in version 0.22 to account better for unscaled features. Set gamma explicitly to 'auto' or 'scale' to avoid this warning.\n", + "/Users/manoel/anaconda3/envs/QISKitenv/lib/python3.6/site-packages/sklearn/svm/base.py:196: FutureWarning: The default value of gamma will change from 'auto' to 'scale' in version 0.22 to account better for unscaled features. Set gamma explicitly to 'auto' or 'scale' to avoid this warning.\n", " \"avoid this warning.\", FutureWarning)\n" ] } @@ -487,16 +487,7 @@ "start_time": "2018-11-19T20:10:18.767740Z" } }, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/home/pwittek/.anaconda3/envs/qiskit/lib/python3.7/site-packages/marshmallow/schema.py:364: ChangedInMarshmallow3Warning: strict=False is not recommended. In marshmallow 3.0, schemas will always be strict. See https://marshmallow.readthedocs.io/en/latest/upgrading.html#schemas-are-always-strict\n", - " ChangedInMarshmallow3Warning\n" - ] - } - ], + "outputs": [], "source": [ "from qiskit.quantum_info import Pauli\n", "from qiskit.aqua import Operator\n", @@ -537,13 +528,15 @@ "outputs": [], "source": [ "from qiskit.aqua import get_aer_backend, QuantumInstance\n", + "from qiskit.qobj import RunConfig\n", "from qiskit.aqua.algorithms import QAOA\n", "from qiskit.aqua.components.optimizers import COBYLA\n", "p = 1\n", "optimizer = COBYLA()\n", "qaoa = QAOA(ising_model, optimizer, p, operator_mode='matrix')\n", "backend = get_aer_backend('statevector_simulator')\n", - "quantum_instance = QuantumInstance(backend, shots=100)\n", + "run_config = RunConfig(shots=100)\n", + "quantum_instance = QuantumInstance(backend, run_config)\n", "result = qaoa.run(quantum_instance)" ] }, @@ -592,7 +585,7 @@ { "data": { "text/plain": [ - "array([1., 0., 0.])" + "array([0., 1., 1.])" ] }, "execution_count": 17, @@ -625,8 +618,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "accuracy (train): 0.55\n", - "accuracy (test): 0.41\n" + "accuracy (train): 0.64\n", + "accuracy (test): 0.29\n" ] } ], @@ -661,7 +654,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.6.7" } }, "nbformat": 4, diff --git a/qiskit/aqua/artificial_intelligence/qsvm_kernel_classification.ipynb b/qiskit/aqua/artificial_intelligence/qsvm_kernel_classification.ipynb index 093c21f96..94ea0b51e 100644 --- a/qiskit/aqua/artificial_intelligence/qsvm_kernel_classification.ipynb +++ b/qiskit/aqua/artificial_intelligence/qsvm_kernel_classification.ipynb @@ -47,6 +47,7 @@ "from qsvm_datasets import *\n", "\n", "from qiskit import Aer\n", + "from qiskit.qobj import RunConfig\n", "from qiskit.aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name\n", "from qiskit.aqua.input import SVMInput\n", "from qiskit.aqua import run_algorithm, QuantumInstance\n", @@ -95,7 +96,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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\n", 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\n", 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" ] @@ -175,7 +176,8 @@ "qsvm = QSVMKernel(feature_map, training_input, test_input, datapoints[0])\n", "\n", "backend = Aer.get_backend('qasm_simulator')\n", - "quantum_instance = QuantumInstance(backend, shots=1024, seed=seed, seed_mapper=seed)\n", + "run_config = RunConfig(shots=1024, max_credits=10, memory=False, seed=seed)\n", + "quantum_instance = QuantumInstance(backend, run_config, seed_mapper=seed)\n", "\n", "result = qsvm.run(quantum_instance)\n", "\n", @@ -212,7 +214,7 @@ }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -283,7 +285,8 @@ "qsvm = QSVMKernel(feature_map, training_input, test_input)\n", "\n", "backend = Aer.get_backend('qasm_simulator')\n", - "quantum_instance = QuantumInstance(backend, shots=1024, seed=seed, seed_mapper=seed)\n", + "run_config = RunConfig(shots=1024, max_credits=10, memory=False, seed=seed)\n", + "quantum_instance = QuantumInstance(backend, run_config, seed_mapper=seed)\n", "\n", "result = qsvm.run(quantum_instance)\n", "\n", @@ -329,9 +332,9 @@ ], "metadata": { "kernelspec": { - "display_name": "Quantum py37", + "display_name": "Python 3", "language": "python", - "name": "quantum-dev-37" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -343,7 +346,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.6.7" } }, "nbformat": 4, diff --git a/qiskit/aqua/optimization/maxcut_and_tsp.ipynb b/qiskit/aqua/optimization/maxcut_and_tsp.ipynb index d39a81c0a..d5cf1f79c 100644 --- a/qiskit/aqua/optimization/maxcut_and_tsp.ipynb +++ b/qiskit/aqua/optimization/maxcut_and_tsp.ipynb @@ -109,6 +109,7 @@ "import networkx as nx\n", "\n", "from qiskit import Aer\n", + "from qiskit.qobj import RunConfig\n", "from qiskit.tools.visualization import plot_histogram\n", "from qiskit.aqua import Operator, run_algorithm\n", "from qiskit.aqua.input import EnergyInput\n", @@ -160,13 +161,13 @@ "name": "stderr", "output_type": "stream", "text": [ - "/usr/local/Cellar/python/3.7.1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages/networkx/drawing/nx_pylab.py:611: MatplotlibDeprecationWarning: isinstance(..., numbers.Number)\n", + "/Users/manoel/anaconda3/envs/QISKitenv/lib/python3.6/site-packages/networkx/drawing/nx_pylab.py:611: MatplotlibDeprecationWarning: isinstance(..., numbers.Number)\n", " if cb.is_numlike(alpha):\n" ] }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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\n", 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cffWff6QzMzPLwmLnzp0sW7aMnJwcunTpYnfO4s032+LrW5PxIwu+vi2Ijl6Jr28Lzp79LydOTKd9+3fw86v4IgsvL3j7bQkGT+SSoaRztvcGMrTWjevzUFKpnTt3snz5ct588038/PzMLkc0YFlZWSQmJpYNRf3223527nyRoCALjRr5ExDQiICAAPz9/YDqwyIpaSDNmo0iNLTi//EsFsjPh99/r92lr8J5XDmU9B3QSSnVHuOqo4HA4HOKidJap9hu3g3E277+BJivlGpiu30LMMMBNbmNm266iffff5+1a9cyYsQIs8sRDVhYWBhXXHEFV1xhjPTu3w933GHBx6eAgoJ8zp49Q2pqKhZLCf7+ATRqFEBAQAABAY3OC4uSkgyKio7h79+h0v15exvzG5KTwUMO8oVNnYNBa12ilBqH8UfeG3hNa/2bUmoOsFdrvQ2YoJS6GygBMoCHbc/NUEr9CyNcAOZorTPqWpM7UUoxbdo0hgwZwi233OIxw2Ci/svOBh8fb4KCguxWvbNaLeTnl4bFWdLS0igpKcHPz5/g4GCaNQvj5Mknadz4Tvz921W5Dy8v4wS38Cwywc1F3nrrLb788kuWL18ucxuEW9i7F4YOhZqshFpcXMSRI0cpKSnCz28Vvr4W2rR5DqWq/t/y7FljPoO0D3MPNR1KkpE/Fxk4cCB5eXls377d7FKEACA83BjqqU5JSTHHjx8nNDSE4OB3yM09SYsW86sNBTDOMzRpUu1mws1IMLiIl5cXcXFxLFu2jMzMKufvCeESbdsany2WyrcpPVIIDW2M1boai+U4zZsv4o8/sqp9/ZISY35EixYOKli4jASDC8XExHDbbbexZMkSs0sRAm9vo3VFXl7FjxcWFnLkyFGaNg2nceNisrK2UFCwn8zMoaSl3cfvv19NdvZHlb5+Xh706OGY2dTCtSQYXGz06NHs27ePb7/91uxShOChhyoeTiooyOfo0aNERkbSpEk4vr5RxMbuJSZmNzExX9Gp0xf4+a0hJKTqli8PPuikwoVTSTC4WGBgINOmTWPBggUUFhaaXY5o4G691ViRrfyPYl5eLseOHadlyygaV9JVLygoiMDAQFJT0yp8vKDAmE19443OqFo4mwSDCa699lpiYmJYtWqV2aWIBi4gAOLijIloWsPZs2dITj5Bq1atCA4OqfK5zZs3Jzs7m4KCArv7tTZe76mnHNt/SbiOBINJpkyZwpYtWzh48KDZpYgGrn9/Y/3mlJRcTp5MoU2bNnbzGirj7e1D8+aRpKSkYDRHNmRlwfXXw913O7Fo4VQSDCZp1qwZY8eOZf78+Vhrcs2gEE7i5QW33vo+BQWHadKkHY1q0Q61cePGeHkpMjIyy9ptt29vtPGWk86eS4LBRPfddx8AmzdvNrkS0ZCtXbuWzZtXsmtXOJ07+5GZaVxqWjOKqKgoUlPTSU8voXNn2LhR1n32dBIMJvLy8uLJJ59k+fLlpKamml2OaGC01rz00kts376dVatW0b17S7ZvhxEjjCU+MzOrnuMARoDk5voTGBhJ+/YfsnWrMXFOeDYJBpN16NCB+++/n2eeecbsUkQDYrVaWbRoEd988w2vvvoqkZGRgHEyesYM2L7dWAM6L89oa5GRYfRWyskxPmdkGPcXFMCAAbBrVyOaNHmD//3vS5O/M+EI0ivJDRQWFjJw4EAmT57M9ddfb3Y5op4rKSlh9uzZnD59miVLllR5ojknB3780Wid/dtvxmWtAQFw8cXGR7duEGK7eOn777/nn//8J++++y6BgYEu+m5EbbhsaU8z1LdgANizZw9z5sxh48aN8kslnKaoqIjp06djsVh4+umn8ff3d+jrz549m5CQEB5//HGHvq5wDGmi52F69erF5ZdfzvLly80uRdRTeXl5TJgwgYCAAJ599lmHhwLApEmT+Pjjj4mPj69+Y+G2JBjcyOTJk+WXSjhFTk4OY8eOJTo6mrlz5+LrpJlnjRs3ZuLEicybNw9LdWeuhduSYHAjYWFhTJgwgblz58ovlXCYtLQ0Ro4cyeWXX86MGTPwcvI6m7fffjshISFs2LDBqfsRziPB4GbuuOMOQkNDeeedd8wuRdQDJ0+eZMSIEfTt25fx48e7ZJEopRQzZsxg9erVnD592un7E44nweBmSn+pXnvtNU6ePGl2OcKDJSUlMWLECIYMGcLf//53l64cGB0dzaBBg1i0aBGeeIFLQyfB4Iaio6MZMmSI/FKJC/b7778zZswYxo0bR79+/Uyp4aGHHuLYsWN88cUXpuxfXDiHBINSqq9SKlEpdVApNb2Cxx9XSv2ulPpZKbVTKdW23GMWpdSPto9tjqinPhg6dCgpKSl89tlnZpciPMwPP/zAxIkTiYuL4/bbbzetDj8/P2bOnMkzzzxDbm6uaXWI2qtzMCilvIGXgNuArsAgpdS5S3/vA3pqrS8FNgFPl3ssX2vd3fYh/RhtfH19iYuLY/HixZw5c8bscoSH+Prrr5k2bRrz5s3jhhtuMLscevTowVVXXcXLL79sdimiFhxxxNALOKi1TtJaFwHvAPeU30Br/bnWunQBwW+A1g7Yb73XrVs3rr/+el588UWzSxEe4NNPP2XOnDksWbKEXr16mV1OmYkTJ7Jjxw5+//13s0sRNeSIYGgFHC93O9l2X2WGA+UXig1QSu1VSn2jlLrXAfXUK+PHj+err77ip59+MrsU4cY2b97MkiVLePnll7nkkkvMLsdOaGgokyZNksuwPYhLTz4rpR4EegLlO8a1tU3RHgwsVUpdVMlzR9kCZG9D6kRa2l5g3rx5FBcXm12OcENr167ljTfeYOXKlXTs2NHscip02223ERYWJpdhewhHBMMJoE25261t99lRSt0MxAF3a63LVpjVWp+wfU4CvgAuq2gnWuuVWuueWuueERERDijbc9x8881ERUWxbt06s0sRbkRrzcsvv8y2bdtYtWoVbdq0qf5JJil/Gbax4ptwZ44Ihu+ATkqp9kopP2AgYHd1kVLqMmAFRij8Ue7+Jkopf9vXzYBrABmIPIdSiunTp/Pmm29y7Ngxs8sRbsBqtfL000+ze/duu7bZ7qxNmzZyGbaHqHMwaK1LgHHAJ0A8sFFr/ZtSao5SqvQqo2eAYODdcy5LjQX2KqV+Aj4HFmqtJRgqEBUVxSOPPML8+fPll6qBKykpYdasWRw8eJDly5fTpEkTs0uqsaFDh3Ly5Ek+//xzs0sRVZC22x7EYrEwbNgwBg4cyJ133ml2OcIEpW2zS0pKePrppwkICDC7pFr78ccfmTlzJhs3biQ4ONjschoUabtdD3l7exMXF8cLL7xAVlaW2eUIF8vLy2PixIkEBASwePFijwwFgO7du3PNNdfI3AY3JsHgYWJjY+nbty9LliwxuxThQjk5OTz66KO0bt3aqW2zXWX8+PHs2rWLX3/91exSRAUkGDzQmDFj+P7779mzZ4/ZpQgXKG2bfdlllzFz5kynt812hdDQUCZPnsy8efMoKSkxuxxxDs//CWuAAgMDmTp1KgsWLKCwsLD6JwiPVdo2+9Zbb2XChAku7ZDqbLfccgtNmzblrbfeMrsUcQ4JBg91/fXX06lTJ1avXm12KcJJDh8+zIgRIxg8eDCPPPJIvQoF+PMy7DVr1kiLeTcjweDB/vGPf7B582aSkpLMLkU4WHx8fFnb7P79+5tdjtO0bt2aBx98UOY2uBkJBg8WERHBmDFjmDt3Llar1exyhIP88MMPTJgwgRkzZpjaNttVhg4dyqlTp6TFvBuRYPBw999/PwBbtmwxuRLhCP/973/L2mb37t3b7HJcwsfHh7i4OJ577jlpMe8mJBg8nJeXF3FxcbzyyiukpaWZXY6og08//ZTZs2fz3HPPuVXbbFe49NJLue6663jppZfMLkUgwVAvXHTRRdx33308++yzZpciLtCWLVtYsmQJL730En/5y1/MLscU48eP54svvuDnn382u5QGT4KhnhgxYgQJCQl8/fXXZpciamnt2rW8/vrrrFy5kk6dOpldjmnKt5iXuQ3mkmCoJ/z9/Zk5cyaLFi0iLy+v+icI03lS22xX+etf/0rz5s158803zS6lQZNgqEd69erFZZddxooVK8wuRVTDE9tmu0Lp3Ia1a9dy4sR5y7oIF5FgqGcmT57MRx99REJCgtmliEp4cttsV2jZsiXDhg1j4cKFMrfBJBIM9UyTJk0YP3488+bNk/V13VBRURFTp04lKyuLF198UdpOV2Lw4MGkpqayY8cOs0tpkCQY6qE777yToKAgNmzYYHYpopz60jbbFcrPbcjJyTG7nAZHgqEeUkoxc+ZMVq9ezalTp8wuR1D/2ma7wl/+8hduvPFGli1bZnYpDY4EQz0VHR3NoEGDpAeNG6iPbbNd5bHHHuOrr77ip59+MruUBkV+QuuxYcOGkZyczK5du8wupcGqz22zXSE4OJgnnniCefPmUVxcbHY5DYYEQz3m6+tLXFwczz77LGfPnjW7nAanvrfNdpU+ffrQsmVL1q9fb3YpDYZDgkEp1VcplaiUOqiUml7B4/5KqQ22x79VSrUr99gM2/2JSqlbHVGP+FP37t259tprZZzWxRpK22xXUEoxdepU1q9fT3JystnlNAh1DgallDfwEnAb0BUYpJTqes5mw4FMrXVHYAmwyPbcrsBA4GKgL/Cy7fWEA0kPGtdqaG2zXaFly5Y8/PDDLFiwQM6ZuYAjjhh6AQe11kla6yLgHeCec7a5B1hj+3oT0EcZx9X3AO9orQu11oeBg7bXEw4UGhoqPWhcpCG2zXaVQYMGkZmZySeffGJ2KfWeI4KhFXC83O1k230VbqO1LgGygaY1fC4ASqlRSqm9Sqm9qampDii7YSntQbNu3TqzS6m3GnLbbFconduwZMkSmdvgZB5z8llrvVJr3VNr3TMiIsLscjxOaQ+a9evXc/z48eqfIGpF2ma7xsUXX0yfPn144YUXzC6lXnNEMJwAyreFbG27r8JtlFI+QGMgvYbPFQ4i47TOsW7dOmmb7UKPPfYYu3fvZt++fWaXUm85Ihi+AzoppdorpfwwTiZvO2ebbcAw29cPALu08ZdpGzDQdtVSe6ATsMcBNYlKDB48mKysLD766COzS/F4pW2z33vvPWmb7UJBQUFMmTKF+fPny9wGJ6lzMNjOGYwDPgHigY1a69+UUnOUUnfbNlsNNFVKHQQeB6bbnvsbsBH4HfgYeExrLZ3fnMjb25snn3ySpUuXkpWVZXY5HstqtfLMM89I22yT3HjjjbRp04a1a9eaXUq9pDxxSKFnz5567969Zpfh0Z599llyc3N56qmnzC7F41gsFmbPnk1KSgpLliyRDqkmOXXqFEOGDOH1118nOjra7HI8glLqe611z+q285iTz8KxHn30Ufbs2YMEbO1I22z30aJFC4YPHy7rNjiBBEMDFRgYyLRp05g/fz5FRUVml+MRSttm+/n5SdtsNzFgwACys7PlnJmDSTA0YNdffz0dO3bktddeM7sUt1faNrtVq1bMmzdP2ma7CW9vb+Li4li6dCnZ2dlml1NvSDA0cFOmTGHTpk0kJSWZXYrbSk9PZ9SoUXTv3p24uDhpm+1munbtyi233MLzzz9vdin1hvyEN3CRkZGMGjWKefPmYbVazS7H7ZS2zb7llluYOHGidEh1U48++ijffPMNP/zwg9ml1AsSDIIHHngAi8XC1q1bzS7FrRw+fJiRI0cyaNAgaZvt5gIDA5k6dSrz5s2Tc2YOIMEg8PLyIi4ujpdffpn09HSzy3ELCQkJjBkzhkcffVTaZnuI3r17065dO9asWVP9xqJKEgwCgE6dOnHPPfewePFis0sx3b59+xg/fjwzZszgjjvuMLscUQtTp05lw4YNHDt2zOxSPJoEgygzcuRIfvvtN3bv3m12KabZvXs3//jHP6Rttodq3rw5w4cPZ/78+TK3oQ4kGESZgIAAZsyYwcKFC8nPzze7HJfbsWMHs2bNkrbZHm7AgAHk5ubywQcfmF2Kx5JgEHauvPJKunXrxsqVK80uxaW2bt3Kc889x0svvcSll15qdjmiDkrPmb3wwgvSD+wCSTCI80yePJkPPviA/ftWT0PVAAAan0lEQVT3m12KS6xfv57Vq1ezYsUKaZtdT8TExNC3b1+WLl1qdikeSYJBnCc8PJxx48Yxd+7cej23QWvNK6+8wpYtW1i1apU0YqtnxowZw3fffSf9wC6ABIOo0F133UVAQAAbNmwwuxSnKG2b/fXXX7Nq1SqaN29udknCwaQf2IWTYBAVUkoRFxfHqlWrOH36tNnlOJTFYmHWrFns37+fFStW0KRJE7NLEk5S2g/sjTfeMLsUjyLBICrVtm1bBgwYwKJFi+rNpX9FRUVMmzaNrKwsli1bJm2zG4ApU6awceNGjhw5YnYpHkOCQVTp4Ycf5tixY3z++edml1JneXl5TJo0CR8fH2mb3YBERkYycuRImdtQCxIMokp+fn7MnDmTZ599lrNnz5pdzgXLycnhscceIyoqivnz50vb7AamX79+FBQUsH37drNL8QgSDKJaPXr04Oqrr+bll182u5QLUto2u1u3bjz55JPSNrsB8vLy4sknn2TZsmVkZmaaXY7bq9NviFIqXCm1Qyl1wPb5vLN4SqnuSqn/KaV+U0r9rJQaUO6xN5RSh5VSP9o+utelHuE8EyZMYNeuXfzyyy9ml1IrKSkp0jZbANC5c2duv/12lixZYnYpbq+u/zpNB3ZqrTsBO223z5UHPKS1vhjoCyxVSoWVe/wfWuvuto8f61iPcJLQ0FAmT57MvHnzKCkpMbucGjly5AgjRoyQttmizKhRo9i3bx979uwxuxS3VtdguAco7XG7Brj33A201vu11gdsX58E/gAi6rhfYYJbbrmFiIgI1q9fb3Yp1UpISGD06NHSNlvYKV23YcGCBTK3oQp1DYbmWusU29engCpnCSmlegF+wKFyd8+zDTEtUUr5V/HcUUqpvUqpvampqXUsW1wIpRQzZsxg3bp1JCcnm11Opfbt28eECROkbbao0HXXXUfnzp1ZvXq12aW4rWqDQSn1mVLq1wo+7im/nTauA6v0WjClVBSwDvi71rq0z8IMIAb4PyAcmFbZ87XWK7XWPbXWPSMi5IDDLC1btmTYsGEsWLDALS/92717N1OnTmXu3LnSNltUasqUKfz73/+Wtc4rUW0waK1v1lpfUsHHe8Bp2x/80j/8f1T0GkqpUOADIE5r/U25107RhkLgdUB6HXuAwYMHk5GRwccff2x2KXY+++wzZs2axeLFi6VttqhSREQEo0ePZv78+fW6H9iFqutQ0jZgmO3rYcB7526glPIDtgBrtdabznmsNFQUxvmJX+tYj3ABHx8fnnzySZYuXUpOTo7Z5QDw3nvvsXjxYmmbLWrsb3/7GyUlJWzbts3sUtxOXYNhIfBXpdQB4GbbbZRSPZVSq2zb9AeuBx6u4LLUN5VSvwC/AM2AuXWsR7jIxRdfzM033+wWbY3ffPNNaZstas3Ly4uZM2fy0ksvkZGRYXY5bkW54zhxdXr27Kmlla75cnNz6devH3PnzqVHjx4u37/WmhUrVrBjxw5efvll6ZAqLsgLL7xAamoq//rXv8wuxemUUt9rrXtWt51MARUXLCgoiKlTpzJv3jyXX/pntVp59tln+eqrr6RttqiTkSNH8tNPP/Htt9+aXYrbkGAQddK7d2/at2/v0rbGFouF2bNnk5iYKG2zRZ01atSI6dOnM3/+fAoLC80uxy1IMIg6mzp1Khs2bODw4cNO31dp2+zMzExpmy0c5uqrr6Zr164yt8FGgkHUWWRkJKNGjXL6pX/SNls40xNPPMGWLVtkbgMSDMJB+vXrR1FRkdMu/ZO22cLZmjVrxpgxY+r9Wuc1IcEgHMLLy4u4uLgqL/3TGoqKwGKp3Wunp6czevRoLr30UmmbLZzqvvvuQ2vN1q1bzS7FVPIbJhymc+fO3HXXXSxevBgAqxW++gpmzIC//hU6doQuXeCii6B7dxg2DFatgqpaX6WkpDBy5EhuvvlmJk2aJB1ShVOV/oPzyiuvkJ6ebnY5ppF5DMKh8vPz6d9/IFdeuYjt22NITzeOEBo1An9/8PIyjhxKSiA/3wgPpeC222DmTGjR4s/XOnLkCOPGjWPo0KEMGDCg8p0K4WDLli3j5MmTzJ8/3+xSHErmMQhTZGc3orBwFfPnNyYnx0rjxhAebgRD6QiQUuDrC6GhEBYGwcHwwQfQpw/8+99GcCQmJjJmzBjGjh0roSBcbsSIEfz666/s3r3b7FJMIcEgHCYpCe66C5KSIggJsXL2bM3ao3t7Q5MmRnBMnQqTJ59g3LjxTJs2TdpmC1MEBAQwY8YMFi5cSEFBgdnluJwEg3CI06dhwADIzjaOAlq0aE5WVnatfqmMoaazrFih6N59BTfeeKMTKxaialdddRV/+ctfWLVqVfUb1zMSDKLOtIYpUyAjwxgeAqMDa2RkBCkpKVSxTIednJwcTp8+Sdu2YWzd2p6ff3ZezULUxOOPP857773HwYMHzS7FpSQYRJ1t3Qq7dxtHCuWFhYXh5aXIzMys9jWysrI4ffoU0dHRBAcHohRMnAjFxU4qWogaaNq0KWPHjmXevHkNam6DBIOoE6sVFi82hoHOv5JU0aJFFKmpqZSUVP4XPiMjnbS0VNq2bVs2mzk0FJKT4YsvnFa6EDVy77334uXlxZYtW8wuxWUkGESd7NljnF9o1Kjix/39/WnSJJxTp05hseSQnDyFhIRrOXjwTrKzPyI19Q8yMzNp27Ydfn72S34rBStXuuCbEKIK5ec2pKWlmV2OS0gwiDr55BNjnkJV886aNWtKYWEhx47NQSlfOnf+lJYt/8WxY3PIzv6dtm3bVdjiIiQEfvgB3GSRONGAdejQgfvvv79s8mZ9J8Eg6uS776C6XnZKedG8eRjZ2Z/RtOkovLwakZUVibf3/xES8hM+Pj6VPM+Y75CY6ITChail4cOHEx8fz3//+1+zS3E6CQZRJwcOGOcXquPjk46Xly9ZWQEkJydTUmIhMvJyioqOVPm84mJoYBeECDfl7+/PjBkzWLRoEfn5+WaX41QSDOKCaQ0FBX/OaK6K1ZpHQEAY2dk5nDlzlsDAQEpK/LBYzlb5PIvFaJ0hhDu44oor6NatG6+++qrZpThVnYJBKRWulNqhlDpg+1zhUlpKKYtS6kfbx7Zy97dXSn2rlDqolNqglPKrSz3CtZQyZi3XhJdXIFZrHh07XkTLllFYLCVkZ58iJ6eIgwcPkJycTFpaGrm5Z7FYSi5oH0K4wuTJk9m+fTv79+83uxSnqesRw3Rgp9a6E7DTdrsi+Vrr7raPu8vdvwhYorXuCGQCw+tYj3Cx5s2NVtrV8fOLBixYLCdp3DiM5s1bEBKSSYsWlxMdHU1oaAgWi4W0tHQOHjzIgQMHSE4+Tn5+FunpvzaYq0GE+wsPD2fcuHFOX5jKTHUNhnuANbav1wD31vSJyuiffBOw6UKeL9xD9+7GcFJ1vLwaERJyE6mpy7Fa88nL+4kzZ76kceM78fPzJzS0Mc2bN6dt27Z06dKFtm3bEhraGItFs2/f2/Tv35++ffsyadIkVqxYwZdffskff/yBJ3YHFp7vrrvuwtfXl02bNlW/sQeqU9ttpVSW1jrM9rUCMktvn7NdCfAjUAIs1FpvVUo1A76xHS2glGoDfKS1vqS6/Urbbffx9tvw//7f+bOeK2Kx5HDy5Gxyc7/F27sxkZHjady4b6XbFxYaVyXt3QtKaVJSUkhISCj7iI+PByAmJobY2FhiYmKIiYkhKipK1m0QTpeUlMSoUaN4++23iYiIMLucGqlp2+1qg0Ep9RnQooKH4oA15YNAKZWptT7vPINSqpXW+oRSqgOwC+gDZFOLYFBKjQJGAURHR19+9OjR6r434QI5OfB//2dMcKvkqtMLlpkJkyfDuHEVP661JjU1tSwkSj8XFRWVhURpaLRq1UpWfhMO98orr3DkyBEWLVpkdik14rBgqGYniUBvrXWKUioK+EJr3aWa57wBvA/8G0gFWmitS5RSVwGztNa3VrdfOWJwLzNmwMaNRutsRykuNoao/vMf4zxGbaSlpZ13ZJGbm0uXLl3sji6io6MlLESdFBUVMWDAAB5//HGuu+46s8uplquC4RkgXWu9UCk1HQjXWk89Z5smQJ7WutA2fPQ/4B6t9e9KqXeBf2ut31FKLQd+1lq/XN1+JRjcS0YG3HijsSpbZa0xakNryMoy1mYYPbrurweQmZl5XlhkZWXRuXNnu7Bo164d3nIZlKiFPXv2MGfOHDZu3EhgYKDZ5VTJVcHQFNgIRANHgf5a6wylVE9gjNZ6hFLqamAFYMU42b1Ua73a9vwOwDtAOLAPeFBrXVjdfiUY3M+nn8LYsUYbi7oOKWVlQWwsbNni+OGp8nJycuzCIiEhgT/++INOnTrZhUWHDh0qnZ0tBMA///lPwsPDmTRpktmlVMklwWAWCQb3tGIFLFpkhEMFrY+qpbWx0E/LlrB5MzRr5vgaq3P27Fn2799vd97i5MmTXHTRRXbnLTp27Iifn0y7EYbMzEwGDBjAiy++SJcuVY6mm0qCQZhi3TqYO9doxx0aWnVzvfKKiyE3Fy6+GFavNicUKpOXl8eBAwfswuL48eO0bdu27KgiNjaWTp064V+T/iCiXtq2bRubNm3ijTfecNtzVxIMwjQHDsCkSbB/v3EUEBpacdsMrY1LUgsKjCGjJ56ARx7xjJnOhYWF54XFkSNHaN269Xlh4e7jzsIxtNaMHj2aPn36MGDAALPLqZAEgzCV1Wqs6vbqq/D118bQksVi3A/G7ZISCA83wuCBB9zrKOFCFBUVcejQobKgSEhI4NChQ7Rs2dLu0tnOnTsTHBxsdrnCCY4cOcKIESN46623iIyMNLuc80gwCLdRWGgcPRw8CHl5xhFB8+bQtStERtZ8uMkTlZSUkJSUZHc11IEDB4iMjLQ7ZxETE0No6YLZwqOtXLmSAwcO8Mwzz5hdynkkGIRwUxaLhaNHj9pNytu/fz9hYWHnzeJu4sjJIcIlioqKGDhwIBMnTuSGG24wuxw7EgxCeBCr1cqxY8fsjiwSEhIIDg62C4vY2FiaNm1qdrmiGnv37uWpp57i3XffdatzTBIMQng4q9XKiRMn7IIiISEBPz8/u6OK2NhYIiIipD+Um5k9ezYhISE8/vjjZpdSRoJBiHpI68qbCZYPC2kmaL6srCz69+/P888/T2xsrNnlABIMQjQYNWkmWBoa0kzQtd5//33eeecd1qxZ4xatViQYhGjg0tLSSExMtAsLaSboWlprxo4dyw033MCgQYPMLkeCQQhxvqqaCZYfipJmgo5z7Ngx/v73v/PWW2/RvLatgh1MgkEIUSMVNRNMTU2lY8eOdmEhzQQv3KuvvkpCQgKLFy82tQ4JBiHEBcvNzSUxMbHKZoKxsbFcdNFF0kywBoqKihg8eDDjxo2jd+/eptUhwSCEcKjKmgm2a9fOLiykmWDFfvjhB5588kk2bdpk2twGCQYhhNNV1kywTZs254WFO030MsucOXMIDAxkypQppuxfgkEIYYqKmgkmJSURFRVldzVUly5dCAoKMrtcl8rOzqZfv34sXbqUrl27unz/EgxCCLchzQT/9OGHH/Lmm2+ydu1al1/5JcEghHBrVTUTPLflR1hYmNnlOozWmscee4xrrrmGIUOGnPsgpKdDZqbxdVgYREQ4rAWxBIMQwuNYrVaOHz9uFxaJiYkEBQWdFxae3EywdG7D+vXriYqIgC+/hLfegu+/hzNn/lwb12KBwEDo1g0GD4abboI6XAXmkmBQSoUDG4B2wBGgv9Y685xtbgSWlLsrBhiotd6qlHoDuAHItj32sNb6x+r2K8EgRMNRvplg+ZPc5ZsJln72pGaCq1etwrptGyNOnkRl2/4EBgYayxmWfg9aGyta5ef/+XhcHPztbxUvi1gNVwXD00CG1nqhUmo60ERrPa2K7cOBg0BrrXWeLRje11pvqs1+JRiEaNgqayaolDrvnIVbNhPMysIyeTKp775LcLNmBNd0+cLCQmO1qyuvhKVLjWGmWnBVMCQCvbXWKUqpKOALrXWXKrYfBdygtR5iu/0GEgxCCAeoTTPB1q1bmxcW6enQvz8cOUKenx8nTp6kw0UX4V3TIwCtISsLWrSATZsgKqrGu3ZVMGRprcNsXysgs/R2JdvvAp7TWr9vu/0GcBVQCOwEpmutC6vbrwSDEKKmqmomWH4oqk2bNs5vJlhYCPfeCwcOGCeWgZMpKXgpRYsWLWr3WllZ0Lo1fPAB1PCyX4cFg1LqM6CiiuOANeWDQCmVqbWucC1C2xHFz0BLrXVxuftOAX7ASuCQ1npOJc8fBYwCiI6Ovvzo0aPVfGtCCFGxzMzM88Li3GaCsbGxtG3b1rGXlD79NKxYYYSC7YjFYrFwKCmJNq1b06hRo9p+I8ZJ6X/9q0abu91QklJqInCx1npUJY/3BqZore+sbr9yxCCEcDSnNxNMSIC77jL+uz/n+dk5OaSnp9O+XbvaDXFZLMZVTBs3Qo8e1W5e02Coa6vEbcAwYKHt83tVbDsImFH+DqVUlC1UFHAv8Gsd6xFCiAsSGhpKr1696NWrV9l95ZsJfvfdd6xbt46UlBQ6dOhQ+2aCr75q/CGvIFRCQ0PJysoiIyODpQUF7MnLI99qpZmPDw81bcq9lc3jKD2aeeUV4/UdpK5HDE2BjUA0cBTjctUMpVRPYIzWeoRtu3bAf4E2WmtruefvAiIABfxoe87Z6vYrRwxCCLNU10yw9OjCrplgVhZccYVxuWklQ1NFRUUcPnIE3bIlHQID8fPy4khhIaOOHuX5Nm2IrWyYyWqFnBz4+mvjhHQVXHLEoLVOB/pUcP9eYES520eAVhVsd1Nd9i+EEK4WGBhIt27d6NatW9l95zYT3LJli10zwRssFq4qLMQvKIjKTm/7+fnRNDycvMxMfIODAeM/ZqUUycXFlQeDl5fxsWcP3H23Q75HWXVDCCHqyN/fn0suuYRLLrmk7L7yzQSLV68mJz2djLQ0fP38CAgIsPsovVQ1vGlTsg8fZvaRI+woKKBQa7oEBHCNLSgqVVwMP/4owSCEEO6sdGZ2bGwsfPQRREURERJCYWEhBQUFFBQUcCYnh4LCQnx8fMpCIiwsjMFpacR16sRvhYV8n5eHX3UnpP394VfHnaKVYBBCCGfLzwcvL5RSZQFQSgNFhYXk28KioKCAoqIiSoqK6B4YyIfZ2WzKzGRgeHjlr+/l9WfbDAeQYBBCCGfz9zdOEldAYQxF+fv7Q+PGgBEWpccIFiC5qKjq19fa2IeDOHmanxBCCGJijPMA1cgoKeHTnBzyrVasWvO/s2f5JDubXtXNbC4shC6VdiOqNTliEEIIZ7v00hq1y1bApsxM5qekYAWifH15onlzrg8JqfqJ3t5w+eUOKRUkGIQQwvl69DCGkqzWKttlN/HxYWXbtrV7bavVGErqWe30hBqToSQhhHC2iAjo08eYiOZoZ85Ar14QHe2wl5RgEEIIVxhlaxNXyUnoC1J6tDB2rONeEwkGIYRwjR49oF8/KF2tzRGys6FvX7juOse9JhIMQgjhOnFxRj8jR4RDTg40bQpzKlypoE4kGIQQwlWCg+Htt6FJE6Ox3oU0MdXaCJagIHjrLahq4tsFkmAQQghXio6GrVuha1cjHGowv6FMcbHxnPbtYcsW6NjRKSVKMAghhKu1bGn8YZ8+HYqKjD/2ubkVn5i2WiEvz9imoAAmTDCW82zXzmnlyTwGIYQwg7c3jBwJAwfC9u2wbp2xFrSPT9myn2htHCV06AAPPmisF21rm+FMEgxCCGGmkBBj3ebBg42jh4MHjaMDMEKgY0eH9kGqCQkGIYRwF35+xrkHk8k5BiGEEHYkGIQQQthR+kKuozWZUioVOOrAl2wGpDnw9eoreZ+qJ+9Rzcj7VD1nvEdttdYR1W3kkcHgaEqpvVprx7UmrKfkfaqevEc1I+9T9cx8j2QoSQghhB0JBiGEEHYkGAwrzS7AQ8j7VD15j2pG3qfqmfYeyTkGIYQQduSIQQghhJ0GGQxKqX5Kqd+UUlalVKVn/ZVSfZVSiUqpg0qp6a6s0R0opcKVUjuUUgdsn5tUsp1FKfWj7WObq+s0Q3U/G0opf6XUBtvj3yql2rm+SvPV4H16WCmVWu7nZ4QZdZpJKfWaUuoPpdSvlTyulFIv2N7Dn5VSPZxdU4MMBuBX4H7gP5VtoJTyBl4CbgO6AoOUUubPVXet6cBOrXUnYKftdkXytdbdbR93u648c9TwZ2M4kKm17ggsARa5tkrz1eJ3aEO5n59VLi3SPbwB9K3i8duATraPUcArzi6oQQaD1jpea51YzWa9gINa6yStdRHwDnCP86tzK/cAa2xfrwHuNbEWd1KTn43y790moI9SpS0zGwz5HaoBrfV/gIwqNrkHWKsN3wBhSqkoZ9bUIIOhhloBx8vdTrbd15A011qn2L4+BTSvZLsApdRepdQ3SqmGEB41+dko20ZrXQJkA01dUp37qOnv0N9sQySblFJtXFOaR3H536J6211VKfUZ0KKCh+K01u+5uh53VdX7VP6G1lorpSq7hK2t1vqEUqoDsEsp9YvW+pCjaxX10nbgba11oVJqNMZR1k0m19Tg1dtg0FrfXMeXOAGU/++lte2+eqWq90kpdVopFaW1TrEduv5RyWucsH1OUkp9AVwG1OdgqMnPRuk2yUopH6AxkO6a8txGte+T1rr8e7IKeNoFdXkal/8tkqGkyn0HdFJKtVdK+QEDgQZxxU0524Bhtq+HAecdaSmlmiil/G1fNwOuAX53WYXmqMnPRvn37gFgl254k4aqfZ/OGSu/G4h3YX2eYhvwkO3qpCuB7HJDvM6htW5wH8B9GON0hcBp4BPb/S2BD8ttdzuwH+O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\n", + "image/png": 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\n", 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" ] @@ -377,7 +378,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": null, "metadata": { "scrolled": true }, @@ -386,16 +387,16 @@ "name": "stdout", "output_type": "stream", "text": [ - "energy: -1.4999638236459272\n", - "time: 123.54426908493042\n", - "maxcut objective: -3.999963823645927\n", - "solution: [1. 0. 1. 0.]\n", + "energy: -1.4986779698866395\n", + "time: 28.347098112106323\n", + "maxcut objective: -3.9986779698866393\n", + "solution: [0. 1. 0. 1.]\n", "solution objective: 4.0\n" ] }, { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -414,7 +415,8 @@ "vqe = VQE(qubitOp, ry, spsa, 'matrix')\n", "\n", "backend = Aer.get_backend('statevector_simulator')\n", - "quantum_instance = QuantumInstance(backend=backend, seed=seed, seed_mapper=seed)\n", + "run_config = RunConfig(seed=seed)\n", + "quantum_instance = QuantumInstance(backend, run_config, seed_mapper=seed)\n", "\n", "result = vqe.run(quantum_instance)\n", "\n", @@ -459,7 +461,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": null, "metadata": {}, "outputs": [ { @@ -467,15 +469,15 @@ "output_type": "stream", "text": [ "energy: -1.5\n", - "time: 186.3367669582367\n", + "time: 63.78048515319824\n", "maxcut objective: -4.0\n", - "solution: [0 1 0 1]\n", + "solution: [1 0 1 0]\n", "solution objective: 4.0\n" ] }, { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "
" ] @@ -495,7 +497,8 @@ "vqe = VQE(qubitOp, ry, spsa, 'grouped_paulis')\n", "\n", "backend = Aer.get_backend('qasm_simulator')\n", - "quantum_instance = QuantumInstance(backend=backend, shots=1024, seed=seed, seed_mapper=seed)\n", + "run_config = RunConfig(shots=1024, seed=seed)\n", + "quantum_instance = QuantumInstance(backend, run_config, seed_mapper=seed)\n", "\n", "result = vqe.run(quantum_instance)\n", "\n", @@ -554,7 +557,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": null, "metadata": {}, "outputs": [ { @@ -562,14 +565,14 @@ "output_type": "stream", "text": [ "distance\n", - " [[ 0. 56. 39.]\n", - " [56. 0. 17.]\n", - " [39. 17. 0.]]\n" + " [[ 0. 18. 90.]\n", + " [18. 0. 93.]\n", + " [90. 93. 0.]]\n" ] }, { "data": { - "image/png": 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\n", + "image/png": 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rZ5nZWjPbZmYrzaym/OWKiEhf0vTQTwDz3H0OMBe4xswuB+4F7nf3c4GDwNLylSkiIvnkDXQP3k0Wq5MfB+YBq5L1zcCislQoIiKppBpDN7NKM9sI7AdWA78EDrl7Z7LJLmBqH/suM7MWM2tpa2srRc0iItKLVIHu7l3uPheYBlwKXJD2AO6+wt2b3L2psbGxyDJFRCSfgma5uPsh4AXgCmCsmVUlL00Ddpe4NhERKUCaWS6NZjY2eT4SuBrYTAj2m5LNlgBPlatIERHJryr/JkwGms2skvAL4HF3f8bMNgGPmdnXgA3Aw2WsU0RE8sgb6O7+/4GLe1n/BmE8XUREMkBnioqIREKBLiISCQW6iEgkFOgiIpFQoIuIREKBLiISCQW6iEgkFOgiIpFQoIuIREKBLiISCQW6iEgkFOgiIpFQoIuIREKBLiISCQW6iEgkFOgiIpFQoIuIREKBLiISiTQ3iZ5uZi+Y2SYze9XMbk/WjzOz1Wb2evJ4VvnLFRGRvqTpoXcC/8PdLwQuBz5nZhcCy4E17n4esCZZFhGRQZI30N19r7uvT54fATYDU4EbgeZks2ZgUbmKFBGR/AoaQzezmcDFwFpgorvvTV5qBSaWtDIRESlI6kA3s9HAPwJ3uPvh019zdwe8j/2WmVmLmbW0tbUNqFgREelbqkA3s2pCmH/f3Z9IVu8zs8nJ65OB/b3t6+4r3L3J3ZsaGxtLUbOIiPQizSwXAx4GNrv7/z7tpaeBJcnzJcBTpS9PRETSqkqxzZXAJ4F/N7ONybq7gHuAx81sKbADWFyeEkVEJI28ge7u/wZYHy/PL205IiJSLJ0pKiISCQW6iEgkFOgiIpFQoIuIREKBLiISCQW6iEgk0sxDFxGRtA4fhn/9V3jxRdi4Efbtg64uqKuD88+Hyy6DBQtgzhywvmaEF0eBLiJSCgcOwH33wRNPQGdnWDdyJNTXh+Du6oLNm2HDBnjoIfjAB+DOO+Hqq0sW7BpyEREZqOeeg3nzYOVKGDECxo4NP7W1UFERAruqCkaNgvHjYcwY2L0bPvtZ+OM/hnfeKUkZCnQRkWK5w9/8TQjlzk4466wQ3PmYhXBvaIDnn4cbboA9ewZcjgJdRKRY3/kO3H9/GFYZObLw/Ssqwi+B1lZYvHjAPXUFuohIMTZtgrvvDmGeplfen7FjYe9euOuu0OsvkgJdRKRQnZ1w++1h6KS6ujRtNjTA6tVhCKZICnQRkUL95CewfXvonZdKRQXU1MDXv150L13TFkVECrViReid9zPdsCOX457WVl4+dozDXV1Mq67mv519Nv9l9Oi+262rgx07wvz1iy8uuCz10EVECnH4MLS05O2ddwGTqqtZMWMGPz7/fD7b2Mjy3bvZ09HR905mYTjnueeKKk09dBGRQmzZEsbN85wMNLKigmWn3Uf5N+vrmVJdzZbjx5lSU9P3jiNGwNq1RZWmHrqISCG2bYOTJwve7Z3OTnZ2dHBObW3/G9bWwtatRZWmQBcRKcTRo+E0/gJ0uvO/9uxhYUMDM/MFemUlvPdeUaXlDXQz+z9mtt/MXjlt3TgzW21mryePZxV1dBGRoaaysqBrr+Tc+bM9e6gC7pw0Kf8O7uEYRUjTQ/8ucE2PdcuBNe5+HrAmWRYRid/EiWF6YQruzl/s3cuBzk6+Pm0aVWl+EZw8CWefXVRpeQPd3X8K9Dwf9UagOXneDCwq6ugiIkPNBz+YetO7W1t5s6OD+6dPp7Yi5Qj38eNFTVmE4me5THT3vcnzVmBiXxua2TJgGcCMGTOKPJyISEbMnBm+uOzo6LenvvfkSZ44dIgaMxa8/vr76++aNIlrGxr6bt8drrqqqNIGPG3R3d3M+jytyd1XACsAmpqair9IgYhIFlRUwCc+AQ8+2G+gT66upqWA3jwQ5qBXVsJ11xVXWlF7wT4zmwyQPO4vsh0RkaHnlltC8HbfyKJUjhyBRYvCdV2KUGygPw0sSZ4vAZ4qsh0RkaFn+nRYtiwE8ACujvgrjh8P10j/wheKbiLNtMVHgZeA2Wa2y8yWAvcAV5vZ68DHkmURkeHjttvgnHPCpQAGqrMzzD2/+26YMKHoZvKOobv7LX28NL/oo4qIDHU1NdDcHIZIDh4sepiEzs7wS+G22+D66wdUks4UFREp1pQp8OST4YbPBw8WNqbuHoL86FFYvjxcX32AzEs1/pPmYGZtwI4zdsDeTQDeHuQa0lKt5TOU6lWt5TNU6v2Auzfm2+iMBnoWmFmLuzcNdh1pqNbyGUr1qtbyGWr15qMhFxGRSCjQRUQiMRwDfcVgF1AA1Vo+Q6le1Vo+Q63efg27MXQRkVgNxx66iEiUog10MxthZi+b2S/M7FUz+0qyfpaZrTWzbWa20szSXdj4DDCzSjPbYGbPJMtZrnW7mf27mW00s5ZkXSZvfGJmY81slZltMbPNZnZFhmudnbyn3T+HzeyODNf7J8n/r1fM7NHk/10mP7dmdntS56tmdkeyLpPva7GiDXTgBDDP3ecAc4FrzOxy4F7gfnc/FzgILB3EGnu6Hdh82nKWawX4bXefe9q0r6ze+OQB4Fl3vwCYQ3iPM1mru29N3tO5wCXAMeBJMlivmU0FbgOa3P1DQCVwMxn83JrZh4BPA5cSPgMLzexcMvi+Doi7R/8D1AHrgcsIJxFUJeuvAJ4b7PqSWqYRPlDzgGcAy2qtST3bgQk91m0FJifPJwNbM1BnA/AmyfdFWa61l9p/B/hZVusFpgJvAeMIlxF5BliQxc8t8F+Bh09b/jJwZxbf14H8xNxD7x7C2Ei4vO9q4JfAIXfvPj93F+FDmQXfIHzAcsnyeLJbK4ADz5vZuuQmJlDAjU/OoFlAG/CdZDjrITMbRTZr7elm4NHkeebqdffdwF8BO4G9QDuwjmx+bl8BftPMxptZHXAdMJ0Mvq8DEXWgu3uXhz9dpxH+1LpgkEvqlZktBPa7+7rBrqUAV7n7h4Frgc+Z2UdOf9FDlycLU6iqgA8Df+fuFwNH6fFndYZqfV8y7nwD8IOer2Wl3mS8+UbCL80pwCj+8/2HM8HdNxOGgp4HngU2Al09tsnE+zoQUQd6N3c/BLxA+PNvrJl1X2VyGrB70Ao75UrgBjPbDjxGGHZ5gGzWCrzfO8Pd9xPGeC8lmzc+2QXscve1yfIqQsBnsdbTXQusd/d9yXIW6/0Y8Ka7t7n7SeAJwmc5k59bd3/Y3S9x948QxvZfI5vva9GiDXQzazSzscnzkcDVhC/DXgBuSjbLxM053P2L7j7N3WcS/sz+kbt/nAzWCmBmo8ysvvs5Yaz3FTJ44xN3bwXeMrPZyar5wCYyWGsPt3BquAWyWe9O4HIzqzMz49R7m9XP7dnJ4wzgd4FHyOb7WrRoTywys4uAZsI37xXA4+7+VTM7h9ALHgdsAD7h7icGr9JfZWa/Bfypuy/Maq1JXU8mi1XAI+7+l2Y2HngcmEG4quZid39nkMp8n5nNBR4CaoA3gE+RfCbIWK3w/i/JncA57t6erMvqe/sV4PeBTsJn9FbCmHkWP7cvEr6bOgl83t3XZPV9LVa0gS4iMtxEO+QiIjLcKNBFRCKhQBcRiYQCXUQkEgp0EZFIKNBFRCKhQBcRiYQCXUQkEv8BP2MHC9hYLwwAAAAASUVORK5CYII=\n", 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" ] @@ -603,20 +606,20 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": null, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "order = (0, 1, 2) Distance = 112.0\n", - "Best order from brute force = (0, 1, 2) with total distance = 112.0\n" + "order = (0, 1, 2) Distance = 201.0\n", + "Best order from brute force = (0, 1, 2) with total distance = 201.0\n" ] }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -671,7 +674,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -688,22 +691,22 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": null, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "energy: -600056.0\n", + "energy: -600100.5\n", "feasible: True\n", - "solution: [0, 1, 2]\n", - "solution objective: 112.0\n" + "solution: [1, 2, 0]\n", + "solution objective: 201.0\n" ] }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -750,23 +753,23 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": null, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "energy: -597781.6405056512\n", - "time: 255.34230828285217\n", + "energy: -594841.9262828702\n", + "time: 56.990293979644775\n", "feasible: True\n", "solution: [2, 0, 1]\n", - "solution objective: 112.0\n" + "solution objective: 201.0\n" ] }, { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -785,7 +788,8 @@ "vqe = VQE(qubitOp, ry, spsa, 'matrix')\n", "\n", "backend = Aer.get_backend('statevector_simulator')\n", - "quantum_instance = QuantumInstance(backend=backend, seed=seed, seed_mapper=seed)\n", + "run_config = RunConfig(seed=seed)\n", + "quantum_instance = QuantumInstance(backend, run_config, seed_mapper=seed)\n", "\n", "result = vqe.run(quantum_instance)\n", "\"\"\"\n", @@ -827,33 +831,9 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "energy: -582286.57421875\n", - "time: 2370.5845291614532\n", - "feasible: True\n", - "solution: [2, 1, 0]\n", - "solution objective: 112.0\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "# run quantum algorithm with shots\n", "\n", @@ -864,7 +844,8 @@ "vqe = VQE(qubitOp, ry, spsa, 'grouped_paulis', batch_mode=True)\n", "\n", "backend = Aer.get_backend('qasm_simulator')\n", - "quantum_instance = QuantumInstance(backend=backend, shots=1024, seed=seed, seed_mapper=seed)\n", + "run_config = RunConfig(shots=1024, seed=seed)\n", + "quantum_instance = QuantumInstance(backend, run_config, seed_mapper=seed)\n", "\n", "result = vqe.run(quantum_instance)\n", "\n", @@ -897,9 +878,9 @@ "metadata": { "anaconda-cloud": {}, "kernelspec": { - "display_name": "Quantum py37", + "display_name": "Python 3", "language": "python", - "name": "quantum-dev-37" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -911,7 +892,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.6.7" } }, "nbformat": 4, From 38ac4a9e69993e1c6754445643ce99ecca50783a Mon Sep 17 00:00:00 2001 From: Manoel Marques Date: Tue, 12 Feb 2019 15:41:30 -0500 Subject: [PATCH 007/116] Remove LegacySimulators --- community/aqua/chemistry/h2_iqpe.ipynb | 65 ++++------------------ community/aqua/general/evolution.ipynb | 76 +++++++++----------------- 2 files changed, 35 insertions(+), 106 deletions(-) diff --git a/community/aqua/chemistry/h2_iqpe.ipynb b/community/aqua/chemistry/h2_iqpe.ipynb index ca2857eac..75151fbee 100644 --- a/community/aqua/chemistry/h2_iqpe.ipynb +++ b/community/aqua/chemistry/h2_iqpe.ipynb @@ -21,7 +21,7 @@ "source": [ "import numpy as np\n", "import pylab\n", - "from qiskit import LegacySimulators\n", + "from qiskit import Aer\n", "from qiskit.chemistry import QiskitChemistry\n", "import time\n", "\n", @@ -48,7 +48,7 @@ "]\n", "\n", "backends = [\n", - " LegacySimulators.get_backend('qasm_simulator'),\n", + " Aer.get_backend('qasm_simulator'),\n", " None\n", "]\n", "\n", @@ -62,7 +62,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -80,32 +80,9 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - " --- complete\n", - "Distances: [0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.675 0.7 0.725 0.75 0.775\n", - " 0.8 0.825 0.85 0.875 0.9 0.925 0.95 0.975 1. ]\n", - "Energies: [[-1.05394029 -1.07537168 -1.09193522 -1.10534368 -1.11548918 -1.1232653\n", - " -1.12869848 -1.13338114 -1.13493551 -1.13632972 -1.1364747 -1.13529234\n", - " -1.13323618 -1.13012864 -1.12773585 -1.12335899 -1.11914159 -1.11450112\n", - " -1.10994671 -1.10478822 -1.09957597]\n", - " [-1.05515979 -1.07591366 -1.09262991 -1.10591805 -1.11628601 -1.12416092\n", - " -1.12990478 -1.13382622 -1.13618945 -1.13722138 -1.13711707 -1.13604436\n", - " -1.13414767 -1.13155121 -1.12836188 -1.12467175 -1.12056028 -1.11609624\n", - " -1.11133942 -1.10634211 -1.10115033]]\n", - "Hartree-Fock energies: [-1.04299627 -1.06306214 -1.07905074 -1.0915705 -1.10112824 -1.10814999\n", - " -1.11299655 -1.11597526 -1.11734903 -1.11734327 -1.11615145 -1.11393966\n", - " -1.1108504 -1.10700581 -1.10251055 -1.09745432 -1.09191404 -1.08595587\n", - " -1.07963693 -1.07300676 -1.06610865]\n", - "--- 517.6182761192322 seconds ---\n" - ] - } - ], + "outputs": [], "source": [ "start_time = time.time()\n", "max_workers = max(4, mp.cpu_count())\n", @@ -142,20 +119,9 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "pylab.plot(distances, hf_energies, label='Hartree-Fock')\n", "for j in range(len(algorithms)):\n", @@ -169,20 +135,9 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "pylab.plot(distances, np.subtract(hf_energies, energies[1]), label='Hartree-Fock')\n", "pylab.plot(distances, np.subtract(energies[0], energies[1]), label='IQPE')\n", @@ -210,7 +165,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.6.7" } }, "nbformat": 4, diff --git a/community/aqua/general/evolution.ipynb b/community/aqua/general/evolution.ipynb index 98b67cb12..07fea27c9 100644 --- a/community/aqua/general/evolution.ipynb +++ b/community/aqua/general/evolution.ipynb @@ -17,11 +17,23 @@ "cell_type": "code", "execution_count": 1, "metadata": {}, - "outputs": [], + "outputs": [ + { + "ename": "ImportError", + "evalue": "cannot import name 'LegacySimulators'", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mImportError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mnumpy\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mscipy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinalg\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mexpm\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mLegacySimulators\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 4\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mexecute\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mq_execute\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mQuantumCircuit\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mQuantumRegister\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mImportError\u001b[0m: cannot import name 'LegacySimulators'" + ] + } + ], "source": [ "import numpy as np\n", "from scipy.linalg import expm\n", - "from qiskit import LegacySimulators\n", + "from qiskit import BasicAer\n", "from qiskit import execute as q_execute\n", "from qiskit import QuantumCircuit, QuantumRegister\n", "from qiskit.quantum_info import state_fidelity\n", @@ -45,19 +57,9 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The directly computed groundtruth evolution result state is\n", - "[-0.35888043-0.10717084j -0.34485103+0.42765631j 0.05738265+0.48043469j\n", - " -0.28881915+0.49028597j].\n" - ] - } - ], + "outputs": [], "source": [ "state_in_vec = state_in.construct_circuit('vector')\n", "groundtruth = expm(-1.j * h1 * evo_time) @ state_in_vec\n", @@ -73,19 +75,9 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The groundtruth evolution result as computed by the Dynamics algorithm is\n", - "[-0.35888043-0.10717084j -0.34485103+0.42765631j 0.05738265+0.48043469j\n", - " -0.28881915+0.49028597j].\n" - ] - } - ], + "outputs": [], "source": [ "groundtruth_evolution = qubitOp.evolve(state_in_vec, evo_time, 'matrix', 0)\n", "print('The groundtruth evolution result as computed by the Dynamics algorithm is\\n{}.'.format(groundtruth_evolution))\n", @@ -101,7 +93,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -124,21 +116,11 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The evolution result state from executing the Dynamics circuit is\n", - "[-0.01000053+0.37433407j 0.5027273 +0.22166398j 0.4488905 -0.18050667j\n", - " 0.54861817+0.15111948j].\n" - ] - } - ], + "outputs": [], "source": [ - "backend = LegacySimulators.get_backend('statevector_simulator')\n", + "backend = BasicAer.get_backend('statevector_simulator')\n", "job = q_execute(circuit, backend)\n", "circuit_execution_result = np.asarray(job.result().get_statevector(circuit))\n", "print('The evolution result state from executing the Dynamics circuit is\\n{}.'.format(circuit_execution_result))" @@ -153,17 +135,9 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Fidelity between the groundtruth and the circuit result states is 0.9999999825657268.\n" - ] - } - ], + "outputs": [], "source": [ "print('Fidelity between the groundtruth and the circuit result states is {}.'.format(\n", " state_fidelity(groundtruth, circuit_execution_result)\n", @@ -194,7 +168,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.5" + "version": "3.6.7" } }, "nbformat": 4, From accfa516d0c517aacab216b122389b0981295a21 Mon Sep 17 00:00:00 2001 From: Manoel Marques Date: Tue, 12 Feb 2019 19:15:26 -0500 Subject: [PATCH 008/116] Remove get_aer_backend and arr run_config --- .../qml_mooc/07_Variational Circuits.ipynb | 53 +++------ ...e Optimization and Ensemble Learning.ipynb | 5 +- .../aqua/finance/portfolio_optimization.ipynb | 103 ++++++------------ 3 files changed, 53 insertions(+), 108 deletions(-) diff --git a/community/awards/teach_me_quantum_2018/qml_mooc/07_Variational Circuits.ipynb b/community/awards/teach_me_quantum_2018/qml_mooc/07_Variational Circuits.ipynb index 55b98a5f4..1f2140a81 100644 --- a/community/awards/teach_me_quantum_2018/qml_mooc/07_Variational Circuits.ipynb +++ b/community/awards/teach_me_quantum_2018/qml_mooc/07_Variational Circuits.ipynb @@ -43,23 +43,14 @@ "start_time": "2018-11-19T20:09:25.393410Z" } }, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/home/pwittek/.anaconda3/envs/qiskit/lib/python3.7/site-packages/marshmallow/schema.py:364: ChangedInMarshmallow3Warning: strict=False is not recommended. In marshmallow 3.0, schemas will always be strict. See https://marshmallow.readthedocs.io/en/latest/upgrading.html#schemas-are-always-strict\n", - " ChangedInMarshmallow3Warning\n" - ] - } - ], + "outputs": [], "source": [ "import itertools\n", "import numpy as np\n", "from functools import partial, reduce\n", - "from qiskit import BasicAer, QuantumRegister, execute\n", + "from qiskit import Aer, BasicAer, QuantumRegister, execute\n", "from qiskit.quantum_info import Pauli\n", - "from qiskit.aqua import Operator, get_aer_backend\n", + "from qiskit.aqua import Operator\n", "from qiskit.aqua.components.initial_states import Custom\n", "from scipy.optimize import minimize\n", "np.set_printoptions(precision=3, suppress=True)" @@ -290,7 +281,7 @@ "def evaluate_circuit(gamma_beta, qr, p):\n", " n = len(gamma_beta)//2\n", " circuit = create_circuit(qr, gamma_beta[:n], gamma_beta[n:], p)\n", - " return np.real(Hc.eval(\"matrix\", circuit, get_aer_backend('statevector_simulator'))[0])\n", + " return np.real(Hc.eval(\"matrix\", circuit, Aer.get_backend('statevector_simulator'))[0])\n", "evaluate = partial(evaluate_circuit, qr=qr, p=p)" ] }, @@ -311,34 +302,18 @@ } }, "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/home/pwittek/.anaconda3/envs/qiskit/lib/python3.7/site-packages/marshmallow/schema.py:364: ChangedInMarshmallow3Warning: strict=False is not recommended. In marshmallow 3.0, schemas will always be strict. See https://marshmallow.readthedocs.io/en/latest/upgrading.html#schemas-are-always-strict\n", - " ChangedInMarshmallow3Warning\n", - "/home/pwittek/.anaconda3/envs/qiskit/lib/python3.7/site-packages/marshmallow/schema.py:364: ChangedInMarshmallow3Warning: strict=False is not recommended. In marshmallow 3.0, schemas will always be strict. See https://marshmallow.readthedocs.io/en/latest/upgrading.html#schemas-are-always-strict\n", - " ChangedInMarshmallow3Warning\n", - "/home/pwittek/.anaconda3/envs/qiskit/lib/python3.7/site-packages/marshmallow/schema.py:364: ChangedInMarshmallow3Warning: strict=False is not recommended. In marshmallow 3.0, schemas will always be strict. See https://marshmallow.readthedocs.io/en/latest/upgrading.html#schemas-are-always-strict\n", - " ChangedInMarshmallow3Warning\n", - "/home/pwittek/.anaconda3/envs/qiskit/lib/python3.7/site-packages/marshmallow/schema.py:364: ChangedInMarshmallow3Warning: strict=False is not recommended. In marshmallow 3.0, schemas will always be strict. See https://marshmallow.readthedocs.io/en/latest/upgrading.html#schemas-are-always-strict\n", - " ChangedInMarshmallow3Warning\n", - "/home/pwittek/.anaconda3/envs/qiskit/lib/python3.7/site-packages/marshmallow/schema.py:364: ChangedInMarshmallow3Warning: strict=False is not recommended. In marshmallow 3.0, schemas will always be strict. See https://marshmallow.readthedocs.io/en/latest/upgrading.html#schemas-are-always-strict\n", - " ChangedInMarshmallow3Warning\n" - ] - }, { "data": { "text/plain": [ - " fun: -0.9999999999999905\n", + " fun: -0.9999999999999931\n", " hess_inv: <4x4 LbfgsInvHessProduct with dtype=float64>\n", " jac: array([-0., 0., 0., 0.])\n", " message: b'CONVERGENCE: NORM_OF_PROJECTED_GRADIENT_<=_PGTOL'\n", - " nfev: 60\n", - " nit: 7\n", + " nfev: 50\n", + " nit: 8\n", " status: 0\n", " success: True\n", - " x: array([ 0.785, 2.124, 1.519, -0.393])" + " x: array([3.927, 6.113, 0.455, 2.749])" ] }, "execution_count": 12, @@ -396,7 +371,7 @@ "output_type": "stream", "text": [ "[0.707 0. 0. 0.707]\n", - "[-0.785 -0.285 -0.285 -0.785]\n" + "[-0.785 0.172 0.172 -0.785]\n" ] } ], @@ -451,14 +426,14 @@ "name": "stdout", "output_type": "stream", "text": [ - "-5.495603971894525e-15\n", - "-5.495603971894525e-15\n" + "-1.7208456881689926e-15\n", + "-1.7208456881689926e-15\n" ] } ], "source": [ - "print(Z0.eval(\"matrix\", circuit, get_aer_backend('statevector_simulator'))[0])\n", - "print(Z1.eval(\"matrix\", circuit, get_aer_backend('statevector_simulator'))[0])" + "print(Z0.eval(\"matrix\", circuit, Aer.get_backend('statevector_simulator'))[0])\n", + "print(Z1.eval(\"matrix\", circuit, Aer.get_backend('statevector_simulator'))[0])" ] }, { @@ -485,7 +460,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.6.7" } }, "nbformat": 4, diff --git a/community/awards/teach_me_quantum_2018/qml_mooc/09_Discrete Optimization and Ensemble Learning.ipynb b/community/awards/teach_me_quantum_2018/qml_mooc/09_Discrete Optimization and Ensemble Learning.ipynb index dbdcedd52..1853fc0f8 100644 --- a/community/awards/teach_me_quantum_2018/qml_mooc/09_Discrete Optimization and Ensemble Learning.ipynb +++ b/community/awards/teach_me_quantum_2018/qml_mooc/09_Discrete Optimization and Ensemble Learning.ipynb @@ -527,14 +527,15 @@ }, "outputs": [], "source": [ - "from qiskit.aqua import get_aer_backend, QuantumInstance\n", + "from qiskit.aqua import QuantumInstance\n", + "from qiskit import Aer\n", "from qiskit.qobj import RunConfig\n", "from qiskit.aqua.algorithms import QAOA\n", "from qiskit.aqua.components.optimizers import COBYLA\n", "p = 1\n", "optimizer = COBYLA()\n", "qaoa = QAOA(ising_model, optimizer, p, operator_mode='matrix')\n", - "backend = get_aer_backend('statevector_simulator')\n", + "backend = Aer.get_backend('statevector_simulator')\n", "run_config = RunConfig(shots=100)\n", "quantum_instance = QuantumInstance(backend, run_config)\n", "result = qaoa.run(quantum_instance)" diff --git a/qiskit/aqua/finance/portfolio_optimization.ipynb b/qiskit/aqua/finance/portfolio_optimization.ipynb index 5eaaf712c..8ff3543c5 100644 --- a/qiskit/aqua/finance/portfolio_optimization.ipynb +++ b/qiskit/aqua/finance/portfolio_optimization.ipynb @@ -61,12 +61,14 @@ "outputs": [], "source": [ "from qiskit import BasicAer\n", + "from qiskit.qobj import RunConfig\n", "from qiskit.aqua import QuantumInstance\n", "from qiskit.aqua import Operator, run_algorithm\n", "from qiskit.aqua.input import EnergyInput\n", "from qiskit.aqua.translators.ising import portfolio\n", "from qiskit.aqua.algorithms import VQE, QAOA, ExactEigensolver\n", "from qiskit.aqua.components.optimizers import COBYLA\n", + "from qiskit.aqua.components.initial_states import Zero\n", "from qiskit.aqua.components.variational_forms import RY\n", "import numpy as np" ] @@ -83,7 +85,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -102,10 +104,8 @@ }, { "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": true - }, + "execution_count": 3, + "metadata": {}, "outputs": [], "source": [ "# set number of assets (= number of qubits)\n", @@ -130,10 +130,8 @@ }, { "cell_type": "code", - "execution_count": 3, - "metadata": { - "collapsed": true - }, + "execution_count": 4, + "metadata": {}, "outputs": [], "source": [ "def index_to_selection(i, num_assets):\n", @@ -170,7 +168,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -232,7 +230,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 6, "metadata": {}, "outputs": [ { @@ -244,22 +242,22 @@ "----------------- Full result ---------------------\n", "selection\tvalue\t\tprobability\n", "---------------------------------------------------\n", - " [0 0 1 1]\t-0.7012\t\t0.5104\n", - " [1 1 0 0]\t-0.5110\t\t0.2438\n", - " [1 0 0 1]\t-0.4158\t\t0.1839\n", - " [0 1 1 0]\t-0.5149\t\t0.0605\n", - " [1 0 1 1]\t3.0617\t\t0.0004\n", - " [0 1 0 0]\t4.5153\t\t0.0003\n", - " [0 0 1 0]\t3.4782\t\t0.0003\n", - " [0 1 0 1]\t2.1421\t\t0.0002\n", - " [1 1 1 1]\t15.6136\t\t0.0001\n", - " [1 1 0 1]\t4.6445\t\t0.0001\n", - " [1 1 1 0]\t2.6688\t\t0.0000\n", - " [0 0 0 1]\t4.0314\t\t0.0000\n", + " [0 0 1 1]\t-0.7012\t\t0.4800\n", + " [1 1 0 0]\t-0.5110\t\t0.2290\n", + " [1 0 0 1]\t-0.4158\t\t0.2173\n", + " [0 1 1 0]\t-0.5149\t\t0.0723\n", + " [1 0 1 1]\t3.0617\t\t0.0003\n", + " [0 0 1 0]\t3.4782\t\t0.0002\n", + " [1 1 0 1]\t4.6445\t\t0.0002\n", + " [0 1 0 0]\t4.5153\t\t0.0002\n", + " [1 1 1 0]\t2.6688\t\t0.0001\n", + " [0 0 0 1]\t4.0314\t\t0.0001\n", + " [0 1 0 1]\t2.1421\t\t0.0001\n", + " [1 1 1 1]\t15.6136\t\t0.0000\n", " [1 0 1 0]\t-0.2876\t\t0.0000\n", - " [0 1 1 1]\t4.9012\t\t0.0000\n", + " [0 0 0 0]\t16.0000\t\t0.0000\n", " [1 0 0 0]\t4.0242\t\t0.0000\n", - " [0 0 0 0]\t16.0000\t\t0.0000\n" + " [0 1 1 1]\t4.9012\t\t0.0000\n" ] } ], @@ -269,11 +267,12 @@ "\n", "cobyla = COBYLA()\n", "cobyla.set_options(maxiter=250)\n", - "ry = RY(qubitOp.num_qubits, depth=3, entanglement='full')\n", + "init_state = Zero(qubitOp.num_qubits)\n", + "ry = RY(qubitOp.num_qubits, depth=3, entanglement='full', initial_state=init_state)\n", "vqe = VQE(qubitOp, ry, cobyla, 'matrix')\n", "vqe.random_seed = seed\n", - "\n", - "quantum_instance = QuantumInstance(backend=backend, seed=seed, seed_mapper=seed)\n", + "run_config = RunConfig(seed=seed)\n", + "quantum_instance = QuantumInstance(backend, run_config, seed_mapper=seed)\n", "\n", "result = vqe.run(quantum_instance)\n", "\n", @@ -316,47 +315,19 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Optimal: selection [0 0 1 1], value -0.7012\n", - "\n", - "----------------- Full result ---------------------\n", - "selection\tvalue\t\tprobability\n", - "---------------------------------------------------\n", - " [0 0 1 1]\t-0.7012\t\t0.1831\n", - " [1 1 0 0]\t-0.5110\t\t0.1795\n", - " [0 1 1 0]\t-0.5149\t\t0.1767\n", - " [1 0 0 1]\t-0.4158\t\t0.1762\n", - " [1 0 1 0]\t-0.2876\t\t0.1518\n", - " [0 1 0 1]\t2.1421\t\t0.1196\n", - " [1 1 1 0]\t2.6688\t\t0.0053\n", - " [1 0 1 1]\t3.0617\t\t0.0023\n", - " [0 1 1 1]\t4.9012\t\t0.0017\n", - " [0 0 0 1]\t4.0314\t\t0.0014\n", - " [0 0 1 0]\t3.4782\t\t0.0007\n", - " [0 1 0 0]\t4.5153\t\t0.0005\n", - " [1 0 0 0]\t4.0242\t\t0.0005\n", - " [1 1 0 1]\t4.6445\t\t0.0005\n", - " [1 1 1 1]\t15.6136\t\t0.0002\n", - " [0 0 0 0]\t16.0000\t\t0.0000\n" - ] - } - ], + "outputs": [], "source": [ "backend = BasicAer.get_backend('statevector_simulator')\n", "seed = 50\n", "\n", "cobyla = COBYLA()\n", "cobyla.set_options(maxiter=250)\n", - "qaoa = QAOA(qubitOp, cobyla, 3, 'matrix')\n", + "qaoa = QAOA(qubitOp, cobyla, 3, operator_mode='matrix')\n", "qaoa.random_seed = seed\n", - "\n", - "quantum_instance = QuantumInstance(backend=backend, seed=seed, seed_mapper=seed)\n", + "run_config = RunConfig(seed=seed)\n", + "quantum_instance = QuantumInstance(backend, run_config, seed_mapper=seed)\n", "\n", "result = qaoa.run(quantum_instance)\n", "\n", @@ -385,18 +356,16 @@ { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { - "display_name": "qiskit_wor", + "display_name": "Python 3", "language": "python", - "name": "qiskit_wor" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -408,7 +377,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.6" + "version": "3.6.7" } }, "nbformat": 4, From 4c14d06306293db1d19d56ce58ffb5035566003d Mon Sep 17 00:00:00 2001 From: Manoel Marques Date: Tue, 12 Feb 2019 20:16:03 -0500 Subject: [PATCH 009/116] Remove get_aer_backend and add run_config --- .../08_Sampling a Thermal State.ipynb | 133 +++++------------- ...timization and Unsupervised Learning.ipynb | 11 +- 2 files changed, 43 insertions(+), 101 deletions(-) diff --git a/community/awards/teach_me_quantum_2018/qml_mooc/08_Sampling a Thermal State.ipynb b/community/awards/teach_me_quantum_2018/qml_mooc/08_Sampling a Thermal State.ipynb index bf4c1c5c8..030f36603 100644 --- a/community/awards/teach_me_quantum_2018/qml_mooc/08_Sampling a Thermal State.ipynb +++ b/community/awards/teach_me_quantum_2018/qml_mooc/08_Sampling a Thermal State.ipynb @@ -119,7 +119,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "
" ] @@ -179,24 +179,16 @@ "start_time": "2018-11-19T20:11:12.766644Z" } }, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/home/pwittek/.anaconda3/envs/qiskit/lib/python3.7/site-packages/marshmallow/schema.py:364: ChangedInMarshmallow3Warning: strict=False is not recommended. In marshmallow 3.0, schemas will always be strict. See https://marshmallow.readthedocs.io/en/latest/upgrading.html#schemas-are-always-strict\n", - " ChangedInMarshmallow3Warning\n" - ] - } - ], + "outputs": [], "source": [ "import itertools\n", "import numpy as np\n", "from functools import reduce\n", - "from qiskit import BasicAer, QuantumRegister, QuantumCircuit, ClassicalRegister\n", + "from qiskit import Aer, BasicAer, QuantumRegister, QuantumCircuit, ClassicalRegister\n", "from qiskit import execute\n", + "from qiskit.qobj import RunConfig\n", "from qiskit.quantum_info import Pauli\n", - "from qiskit.aqua import get_aer_backend, QuantumInstance\n", + "from qiskit.aqua import QuantumInstance\n", "from qiskit.aqua.operator import Operator\n", "from qiskit.aqua.components.optimizers import COBYLA\n", "from qiskit.aqua.algorithms import VQE\n", @@ -464,29 +456,26 @@ ] }, { - "name": "stderr", - "output_type": "stream", - "text": [ - "/home/pwittek/.anaconda3/envs/qiskit/lib/python3.7/site-packages/marshmallow/schema.py:364: ChangedInMarshmallow3Warning: strict=False is not recommended. In marshmallow 3.0, schemas will always be strict. See https://marshmallow.readthedocs.io/en/latest/upgrading.html#schemas-are-always-strict\n", - " ChangedInMarshmallow3Warning\n", - "/home/pwittek/.anaconda3/envs/qiskit/lib/python3.7/site-packages/marshmallow/schema.py:364: ChangedInMarshmallow3Warning: strict=False is not recommended. In marshmallow 3.0, schemas will always be strict. See https://marshmallow.readthedocs.io/en/latest/upgrading.html#schemas-are-always-strict\n", - " ChangedInMarshmallow3Warning\n", - "/home/pwittek/.anaconda3/envs/qiskit/lib/python3.7/site-packages/marshmallow/schema.py:364: ChangedInMarshmallow3Warning: strict=False is not recommended. In marshmallow 3.0, schemas will always be strict. See https://marshmallow.readthedocs.io/en/latest/upgrading.html#schemas-are-always-strict\n", - " ChangedInMarshmallow3Warning\n", - "/home/pwittek/.anaconda3/envs/qiskit/lib/python3.7/site-packages/marshmallow/schema.py:364: ChangedInMarshmallow3Warning: strict=False is not recommended. In marshmallow 3.0, schemas will always be strict. See https://marshmallow.readthedocs.io/en/latest/upgrading.html#schemas-are-always-strict\n", - " ChangedInMarshmallow3Warning\n", - "/home/pwittek/.anaconda3/envs/qiskit/lib/python3.7/site-packages/marshmallow/schema.py:364: ChangedInMarshmallow3Warning: strict=False is not recommended. In marshmallow 3.0, schemas will always be strict. See https://marshmallow.readthedocs.io/en/latest/upgrading.html#schemas-are-always-strict\n", - " ChangedInMarshmallow3Warning\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Results of QAOA {'eigvals': array([0.]), 'opt_params': array([ 1.898, -0.447]), 'eigvecs': array([[-0.177-0.438j, -0.076-0.058j, -0.076-0.058j, -0.075-0.055j,\n", - " -0.076-0.058j, 0.328+0.241j, -0.075-0.055j, 0.219-0.137j,\n", - " -0.076-0.058j, -0.075-0.055j, 0.328+0.241j, 0.219-0.137j,\n", - " -0.075-0.055j, 0.219-0.137j, 0.219-0.137j, 0.028+0.328j]]), 'energy': 0.0, 'eval_count': 28, 'eval_time': 11.246169090270996}\n" + "ename": "TypeError", + "evalue": "construct_circuit() missing 1 required positional argument: 'qr'", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in 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\u001b[0mQuantumInstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbackend\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrun_config\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mqaoa\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mquantum_instance\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 11\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Results of QAOA\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mresult\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 12\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/Documents/Quantum/qiskit-aqua/qiskit/aqua/algorithms/quantum_algorithm.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self, quantum_instance, **kwargs)\u001b[0m\n\u001b[1;32m 88\u001b[0m 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optimizer bounds={}\\ninitial point={}'\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbounds\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minitial_point\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 400\u001b[0m sol, opt, nfev = self._optimizer.optimize(self._var_form.num_parameters, self._energy_evaluation,\n\u001b[0;32m--> 401\u001b[0;31m variable_bounds=bounds, initial_point=initial_point)\n\u001b[0m\u001b[1;32m 402\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mnfev\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 403\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_eval_count\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_eval_count\u001b[0m \u001b[0;32mif\u001b[0m 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\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcircuit\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mqregs\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 56\u001b[0m \u001b[0mq\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mQuantumRegister\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_cost_operator\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnum_qubits\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'q'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mTypeError\u001b[0m: construct_circuit() missing 1 required positional argument: 'qr'" ] } ], @@ -496,9 +485,10 @@ " print(\"Begin QAOA...\")\n", " \n", " optimizer = COBYLA()\n", - " qaoa = MyQAOA(Hc, optimizer, initial_state, p, \"matrix\")\n", - " backend = get_aer_backend('statevector_simulator')\n", - " quantum_instance = QuantumInstance(backend, shots=100)\n", + " qaoa = MyQAOA(Hc, optimizer, initial_state, p, operator_mode=\"matrix\")\n", + " backend = Aer.get_backend('statevector_simulator')\n", + " run_config = RunConfig(shots=100)\n", + " quantum_instance = QuantumInstance(backend, run_config)\n", " result = qaoa.run(quantum_instance)\n", " print(\"Results of QAOA\", result)\n", " \n", @@ -515,27 +505,14 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": null, "metadata": { "ExecuteTime": { "end_time": "2018-11-19T20:11:44.601197Z", "start_time": "2018-11-19T20:11:14.085143Z" } }, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "var_form = MyQAOAVarForm(Hc, p, initial_state)\n", "thermal_state = var_form.construct_circuit(result['opt_params'], qr, cr)\n", @@ -572,21 +549,9 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Begin QAOA...\n", - "Results of QAOA {'eigvals': array([-0.973]), 'opt_params': array([0., 0.]), 'eigvecs': array([[ 0.993+0.j , -0. -0.j , -0. -0.j , -0. +0.j ,\n", - " -0. -0.j , 0. -0.082j, -0. +0.j , -0. +0.j ,\n", - " -0. -0.j , -0. +0.j , 0. -0.082j, -0. +0.j ,\n", - " -0. +0.j , -0. +0.j , -0. +0.j , -0.007-0.j ]]), 'energy': -0.973407734380529, 'eval_count': 27, 'eval_time': 12.175426006317139}\n" - ] - } - ], + "outputs": [], "source": [ "β = 5\n", "initial_state = InitialState(β, n_qubits)\n", @@ -595,35 +560,9 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(array([4.923, 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ,\n", - " 0.078]),\n", - " array([-1. , -0.8, -0.6, -0.4, -0.2, 0. , 0.2, 0.4, 0.6, 0.8, 1. ]),\n", - " )" - ] - }, - "execution_count": 17, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "var_form = MyQAOAVarForm(Hc, p, initial_state)\n", "thermal_state = var_form.construct_circuit(result['opt_params'], qr, cr)\n", @@ -673,7 +612,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.6.7" } }, "nbformat": 4, diff --git a/community/awards/teach_me_quantum_2018/qml_mooc/10_Discrete Optimization and Unsupervised Learning.ipynb b/community/awards/teach_me_quantum_2018/qml_mooc/10_Discrete Optimization and Unsupervised Learning.ipynb index 544d87440..12e444040 100644 --- a/community/awards/teach_me_quantum_2018/qml_mooc/10_Discrete Optimization and Unsupervised Learning.ipynb +++ b/community/awards/teach_me_quantum_2018/qml_mooc/10_Discrete Optimization and Unsupervised Learning.ipynb @@ -126,7 +126,9 @@ } ], "source": [ - "from qiskit.aqua import get_aer_backend, QuantumInstance\n", + "from qiskit import Aer\n", + "from qiskit.qobj import RunConfig\n", + "from qiskit.aqua import QuantumInstance\n", "from qiskit.aqua.algorithms import QAOA\n", "from qiskit.aqua.components.optimizers import COBYLA\n", "from qiskit.aqua.translators.ising import maxcut" @@ -174,8 +176,9 @@ }, "outputs": [], "source": [ - "backend = get_aer_backend('statevector_simulator')\n", - "quantum_instance = QuantumInstance(backend, shots=100)\n", + "backend = Aer.get_backend('statevector_simulator')\n", + "run_config = RunConfig(shots=100)\n", + "quantum_instance = QuantumInstance(backend, run_config)\n", "result = qaoa.run(quantum_instance)\n", "x = maxcut.sample_most_likely(result['eigvecs'][0])\n", "graph_solution = maxcut.get_graph_solution(x)\n", @@ -280,7 +283,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.6.7" } }, "nbformat": 4, From 41b6887f0506cb1778cbd356329738116e28140a Mon Sep 17 00:00:00 2001 From: Richard Chen Date: Fri, 15 Feb 2019 11:04:07 -0500 Subject: [PATCH 010/116] fix the format of entangler_map --- .../aqua/artificial_intelligence/qsvm_kernel_directly.ipynb | 2 +- .../aqua/artificial_intelligence/qsvm_kernel_multiclass.ipynb | 2 +- community/aqua/chemistry/ParticleHole_example.ipynb | 2 +- community/aqua/chemistry/PySCF_end2end.ipynb | 2 +- community/aqua/chemistry/Pyquante_end2end.ipynb | 2 +- 5 files changed, 5 insertions(+), 5 deletions(-) diff --git a/community/aqua/artificial_intelligence/qsvm_kernel_directly.ipynb b/community/aqua/artificial_intelligence/qsvm_kernel_directly.ipynb index 08b9e25c0..b3b4c830b 100644 --- a/community/aqua/artificial_intelligence/qsvm_kernel_directly.ipynb +++ b/community/aqua/artificial_intelligence/qsvm_kernel_directly.ipynb @@ -193,7 +193,7 @@ "outputs": [], "source": [ "backend = Aer.get_backend('qasm_simulator')\n", - "feature_map = SecondOrderExpansion(num_qubits=feature_dim, depth=2, entangler_map={0: [1]})\n", + "feature_map = SecondOrderExpansion(num_qubits=feature_dim, depth=2, entangler_map=[[0, 1]])\n", "svm = QSVMKernel(feature_map, training_input, test_input, None)# the data for prediction can be feeded later.\n", "svm.random_seed = random_seed\n", "run_config = RunConfig(shots=shots, max_credits=10, memory=False, seed=random_seed)\n", diff --git a/community/aqua/artificial_intelligence/qsvm_kernel_multiclass.ipynb b/community/aqua/artificial_intelligence/qsvm_kernel_multiclass.ipynb index 901bd98f9..2b7c41f3f 100644 --- a/community/aqua/artificial_intelligence/qsvm_kernel_multiclass.ipynb +++ b/community/aqua/artificial_intelligence/qsvm_kernel_multiclass.ipynb @@ -87,7 +87,7 @@ " 'algorithm': {\n", " 'name': 'QSVM.Kernel'\n", " },\n", - " 'feature_map': {'name': 'SecondOrderExpansion', 'depth': 2, 'entangler_map': {0: [1]}},\n", + " 'feature_map': {'name': 'SecondOrderExpansion', 'depth': 2, 'entangler_map': [[0, 1]]},\n", " 'multiclass_extension': {'name': 'AllPairs'},\n", " 'backend': {'shots': 1024}\n", "}\n", diff --git a/community/aqua/chemistry/ParticleHole_example.ipynb b/community/aqua/chemistry/ParticleHole_example.ipynb index a6980de2e..c1b1ba1f5 100644 --- a/community/aqua/chemistry/ParticleHole_example.ipynb +++ b/community/aqua/chemistry/ParticleHole_example.ipynb @@ -114,7 +114,7 @@ "lbfgs = L_BFGS_B(maxfun=1000, factr=10, iprint=10)\n", "\n", "# setup variational form generator (generate trial circuits for VQE)\n", - "var_form = RY(newqubitOp_jw.num_qubits, 5, entangler_map = {0: [1], 1:[2], 2:[3]})\n", + "var_form = RY(newqubitOp_jw.num_qubits, 5, entangler_map = [[0, 1], [1, 2], [2, 3]])\n", "\n", "# setup VQE with operator, variational form, and optimizer\n", "vqe_algorithm = VQE(newqubitOp_jw, var_form, lbfgs, 'matrix')\n", diff --git a/community/aqua/chemistry/PySCF_end2end.ipynb b/community/aqua/chemistry/PySCF_end2end.ipynb index e98113091..878d72ab5 100644 --- a/community/aqua/chemistry/PySCF_end2end.ipynb +++ b/community/aqua/chemistry/PySCF_end2end.ipynb @@ -105,7 +105,7 @@ "lbfgs = L_BFGS_B(maxfun=1000, factr=10, iprint=10)\n", "\n", "# setup variational form generator (generate trial circuits for VQE)\n", - "var_form = RYRZ(qubitOp.num_qubits, 5, entangler_map = {0: [1], 1:[2], 2:[3]})\n", + "var_form = RYRZ(qubitOp.num_qubits, 5, entangler_map = [[0, 1], [1, 2], [2, 3]])\n", "\n", "# setup VQE with operator, variational form, and optimizer\n", "vqe_algorithm = VQE(qubitOp, var_form, lbfgs, 'matrix')\n", diff --git a/community/aqua/chemistry/Pyquante_end2end.ipynb b/community/aqua/chemistry/Pyquante_end2end.ipynb index 33037430f..adada2985 100644 --- a/community/aqua/chemistry/Pyquante_end2end.ipynb +++ b/community/aqua/chemistry/Pyquante_end2end.ipynb @@ -118,7 +118,7 @@ "lbfgs = L_BFGS_B(maxfun=1000, factr=10, iprint=10)\n", "\n", "# setup variational form generator (generate trial circuits for VQE)\n", - "var_form = RY(qubitOp_jw.num_qubits, 5, entangler_map = {0: [1], 1:[2], 2:[3]})\n", + "var_form = RY(qubitOp_jw.num_qubits, 5, entangler_map = [[0, 1], [1, 2], [2, 3]])\n", "\n", "# setup VQE with operator, variational form, and optimizer\n", "vqe_algorithm = VQE(qubitOp_jw, var_form, lbfgs, 'matrix')\n", From e8cb5f4e0d7dd601df83cac9f74ce2fac83b6532 Mon Sep 17 00:00:00 2001 From: Manoel Marques Date: Fri, 22 Feb 2019 18:28:11 -0500 Subject: [PATCH 011/116] Update h2_uccsd to latest chemistry/aqua --- community/aqua/chemistry/h2_uccsd.ipynb | 54 +++++++++++++++---------- 1 file changed, 33 insertions(+), 21 deletions(-) diff --git a/community/aqua/chemistry/h2_uccsd.ipynb b/community/aqua/chemistry/h2_uccsd.ipynb index ccad2fe26..dbde1be85 100644 --- a/community/aqua/chemistry/h2_uccsd.ipynb +++ b/community/aqua/chemistry/h2_uccsd.ipynb @@ -27,10 +27,10 @@ "Processing step 20 --- complete\n", "Distances: [0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.675 0.7 0.725 0.75 0.775\n", " 0.8 0.825 0.85 0.875 0.9 0.925 0.95 0.975 1. ]\n", - "Energies: [[-1.05515973 -1.0759136 -1.09262986 -1.105918 -1.11628597 -1.12416088\n", - " -1.12990474 -1.13382618 -1.13618943 -1.13722134 -1.13711706 -1.13604435\n", - " -1.13414766 -1.13155119 -1.12836188 -1.12467173 -1.12056028 -1.11609624\n", - " -1.11133942 -1.1063421 -1.10115033]\n", + "Energies: [[-1.05515973 -1.0759136 -1.09262986 -1.105918 -1.11628597 -1.12416089\n", + " -1.12990475 -1.1338262 -1.13618942 -1.13722134 -1.13711706 -1.13604434\n", + " -1.13414766 -1.1315512 -1.12836186 -1.12467174 -1.12056028 -1.11609624\n", + " -1.11133942 -1.10634211 -1.10115033]\n", " [-1.05515974 -1.07591361 -1.09262987 -1.10591802 -1.11628599 -1.12416089\n", " -1.12990476 -1.1338262 -1.13618944 -1.13722136 -1.13711707 -1.13604436\n", " -1.13414767 -1.13155121 -1.12836188 -1.12467175 -1.12056028 -1.11609624\n", @@ -39,14 +39,15 @@ " -1.11299652 -1.11597525 -1.11734902 -1.11734325 -1.11615145 -1.11393966\n", " -1.1108504 -1.10700581 -1.10251056 -1.09745432 -1.09191405 -1.08595588\n", " -1.07963694 -1.07300677 -1.06610866]\n", - "VQE num evaluations: [49. 52. 50. 50. 43. 54. 47. 47. 52. 46. 42. 56. 45. 49. 44. 55. 47. 49.\n", - " 54. 58. 55.]\n" + "VQE num evaluations: [45. 52. 50. 50. 43. 50. 47. 47. 51. 46. 42. 57. 45. 47. 44. 54. 53. 49.\n", + " 51. 56. 55.]\n" ] } ], "source": [ "import numpy as np\n", "import pylab\n", + "import copy\n", "from qiskit.chemistry import QiskitChemistry\n", "\n", "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", @@ -77,9 +78,14 @@ " d = start + i*by/steps\n", " qiskit_chemistry_dict['PYQUANTE']['atoms'] = molecule.format(d/2) \n", " for j in range(len(algorithms)):\n", - " qiskit_chemistry_dict['algorithm']['name'] = algorithms[j] \n", + " dict = copy.deepcopy(qiskit_chemistry_dict)\n", + " dict['algorithm']['name'] = algorithms[j] \n", + " if algorithms[j] == 'ExactEigensolver':\n", + " del dict['optimizer']\n", + " del dict['variational_form']\n", + " del dict['initial_state']\n", " solver = QiskitChemistry()\n", - " result = solver.run(qiskit_chemistry_dict)\n", + " result = solver.run(dict)\n", " energies[j][i] = result['energy']\n", " hf_energies[i] = result['hf_energy']\n", " if algorithms[j] == 'VQE':\n", @@ -101,7 +107,7 @@ { "data": { "text/plain": [ - "" + "" ] }, "execution_count": 2, @@ -110,12 +116,14 @@ }, { "data": { - "image/png": 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yhCVLltyzbcmSJTzxxBP06dOH8ePHEx4ezpEjR9i3bx/ffvttWrn008kHBQXRoEGDvA6/SNAJJRf8vd05FXmHI5eirB2KphV6AwYMYP369SQmGhe6O3v2LJcvX+bkyZNpMwIDODs7M3PmTL788ktrhlsk6ckhc6Fn40pMWn2UlYcu4eVRytrhaFre2TAerhwx7zkrNoYen2W6u0yZMvj6+rJhwwb69u3LkiVLGDRoEEePHqV58+b3lK1VqxZ3797l9u3bwL3TyQPs2bMny9mHtYejayi54FrMns71y7P28GWSUwzWDkfTCr30zV5LlixhyJAhOTru/iYvnUwsQ9dQcsnf250NIVfYceI6HeuVt3Y4mpY3sqhJWFLfvn159dVXOXjwIHFxcTRv3pxDhw6xffv2e8qdPn2asmXLUqqUbjnIS7qGkkuPeJanlLO9nopF0/JAiRIl6NixI88++2xa7WTYsGHs3LmTrVu3AsZVHV955RUmT55szVCLJJ1QcsnBzobeXpXYHHqF2IRka4ejaYXekCFDOHz4cFpCKVasGGvWrGHKlCnUrVuXcuXK4efnx7Bhw9KOSV1DPvWxe/dua4VfqOnp683gwLmb9P9uD1MHNmFAcw+zn1/T8oOCMn39qlWreO211/j777+pVq2atcMpcPT09XkgOupCpvuaVS1NtbLOrDx0MQ8j0jQtI/369eP06dM6mViBTig5MGVpTwat6IkyZHwnl4jQr6k7u0/d4EpUfB5Hp2malj/ohJIDjdy8uGQLwaHLMi3Tz9sdpfRULJqmFV06oeRA5xbjcFCKgNAFmZapUa443lVL6bu9NE0rsnRCyYESLpXoYFuKTbFnSU7KvEnL39udY1diCIuIzsPoNE3T8gedUHKoR42e3LAV9h3+OdMyvb0qY2cjupaiaVqRpBNKDrVrPpoSBsWG439kWqZMcQce8XRjddAlUgxF53ZsTcsrtra294wn+ewz843YDwoKIiAgIO11ZtPeX758mQEDBpjtug/j7NmzNGrUyKoxZERPvZJDTsVK08mxAlsTrvB+fBSOTq4ZlvP39mBr2DX2nLpB2zrl8jhKTSvcihUrRlBQkEXOHRQURGBgID179kzbNnjwYGbOnPmfssuXL7dIDHktOTkZOzvzpQFdQ3kAPev4E2sj7DzwXaZlOtcvj4ujnW720rQ8EhUVhaenJ+Hh4YBxJP3cuXMBGD16ND4+PjRs2JBJkyalHbN//37atGlDkyZN8PX1JSoqiokTJ6aNqF+6dGmm10tfO4iLi2PQoEE0aNAAf39/WrZsSerg6c2bN9O6dWuaNWvGwIEDiY2NBaB69epMmjSJZs2a0bhxY44dOwbAP//8k1YT8vb2JiYmBqUUb775Jo0aNaJx48YZxtWqVSuOHj2a9vqRRx4hMDCQO3fu8Oyzz+Lr64u3tzerV68GjDWvPn360KlTJzp37vzQn3tGrFJDEZGBwAdAfcBXKZXh8HUR6Q58C9gCPyqlPjNtF+BjYCCQAnynlJpu6bhbNh1JmZDvWX96PZ39xmdYxsnelp6NK7Eu+DIf92tEMQdbS4elaXnu832fc+zmMbOes16Zerzt+3aWZe7evUvTpk3TXr/zzjtptYjhw4czbtw4bt26xfPPPw/AlClTKFOmDCkpKXTu3Jng4GDq1avH4MGDWbp0KS1atCA6OhpnZ2c+/PBDAgMD02ok8+bNy3Da+/Rmz55N6dKlCQ0NJSQkJC2269ev8/HHH7N161aKFy/O559/zrRp05g4cSIA5cqV4+DBg8yePZupU6fy448/MnXqVGbNmoWfnx+xsbE4OTnxxx9/EBQUxOHDh7l+/TotWrSgffv298QwePBgli1bxuTJk4mIiCAiIgIfHx/effddOnXqxM8//8zt27fx9fWlS5cuABw8eJDg4GDKlCnzMH+qTFmrySsEeBz4IbMCImILzAK6AheB/SKyRikVCgwHqgD1lFIGEcmTaX7t7J141LkqK+POExsTQQmXShmW82/mztLAC2wOvZK2VLCmabmXWZNX165d+f333xkzZgyHDx9O275s2TLmzJlDcnIyERERhIaGIiJUqlSJFi1aAFCyZMlMr5dZk1eqnTt3Mm7cOAAaNWqEl5cXAHv37iU0NBQ/Pz8AEhMTad26ddpxjz/+OADNmzfnjz+M/bJ+fn689tprDBs2jMcffxwPDw927tzJkCFDsLW1pUKFCnTo0IH9+/enXQdg0KBBPProo0yePJlly5al9e9s3ryZNWvWMHXqVADi4+M5f/582udl7mQCVkooSqkwMI4wz4IvcFIpddpUdgnQFwgFRgNDlVIG0/muWTTgdHo1GMaSg5/x1/4Z9On0SYZlfKuXwb1UMVYeuqQTilYoZVeTyGsGg4GwsDCcnZ25desWHh4enDlzhqlTp7J//35Kly7N8OHDiY/Pm5kslFJ07dqVxYsXZ7jf0dERMN5kkJxsnFR2/Pjx9OrVi4CAAPz8/Ni0aVOOruXu7k7ZsmUJDg5m6dKlfP/992kxrFixAk9Pz3vK//vvvxQvXvxh31qW8nMfijuQfgKti6ZtALWAwSISKCIbRKROZicRkVGmcoGRkZG5DqpJwyFUToGAC39mWsbGRujbtDI7TlwnMiYh19fUNC1rX3/9NfXr12fRokWMGDGCpKQkoqOjKV68OK6urly9epUNGzYA4OnpSUREBPv37wcgJiaG5ORkXFxciImJeaDr+vn5sWyZcQaN0NBQjhwxrmLZqlUrdu3axcmTJwG4c+cOx48fz/Jcp06donHjxrz99tu0aNGCY8eO0a5dO5YuXUpKSgqRkZFs374dX1/f/xw7ePBgvvjiC6KiotJqL926dWPGjBmkTgB86NChB3pvD8NiCUVEtopISAaPvmY4vSMQb5r9ci6Q6eAQpdQcpZSPUsrHzc0t1xcWGxt6uHqyV93h5s2TmZbz93YnxaBYe/hyrq+paZpRah9K6mP8+PGEh4fz448/8tVXX9GuXTvat2/Pxx9/TJMmTfD29qZevXoMHTo0rfnJwcGBpUuXMnbsWJo0aULXrl2Jj4+nY8eOhIaG3tMpn9209y+99BKRkZE0aNCA999/n4YNG+Lq6oqbmxvz5s1jyJAheHl50bp167TO98x88803ac1m9vb29OjRA39/f7y8vGjSpAmdOnXiiy++oGLFiv85dsCAAWlLIqeaMGECSUlJeHl50bBhQyZMmJDbjz9bVp2+XkS2AW9k1CkvIq2BD5RS3Uyv3wFQSn0qIseAHkqpM6YO+ttKqYzv403HXNPXh59Yz4Dd43mvwiM80X1GpuV6z9iBIKwd2zbX19Q0ayso09fnpZSUFJKSknBycuLUqVN06dKF8PBwHBwcrB3aQyus09fvB+qISA0RcQCeANaY9q0COpqedwCyrkuaWd1aPaidIgRcyXqRnn5N3TlyKYqT1x6sGq1pWsEQFxdH27ZtadKkCf7+/syePbtAJ5PcskpCERF/EbkItAbWi8gm0/bKIhIAoJRKBl4GNgFhwDKlVOrN1p8B/UXkCPApMDJP47exoUe5JhySRC5fzrzG06dpZWwEPSZF0wopFxcXAgMDOXz4MMHBwfTo0cPaIVmVVRKKUmqlUspDKeWolKqQ2qyllLqslOqZrlyAUqquUqqWUmpKuu23lVK9lFKNlVKtlVKHM7qOJfXwfgmADQdmZVqmvIsTbeu4serQZQx6KhatEChKK7wWRbn9++bnJq98rUqV1ngZ7Nhw/WCW5fo3c+fS7bv8cyL3d5hpmjU5OTlx48YNnVQKKaUUN27cwMnJ6aHPoefyyoWeFVvx2bWdnDq1hVq1umZYpkejSnxa8hg/7jhNR888GX+paRbh4eHBxYsXMcft91r+5OTkhIeHx0MfrxNKLnTzeYUv1u8gIPhHxmaSUBzsbBjhV51PNxwj5FIUjdyzvRlN0/Ile3t7atSoYe0wtHxMN3nlQjm3+viKMwG3QjNdbx5gSMuqlHC0Y+6O03kYnaZpWt7SCSWXerp34KIthIStyLRMSSd7nmhRhXXBEVy6fTcPo9M0Tcs7OqHkUucWr2CvFAFHf82y3Ii2xqaCX3aeyYuwNE3T0kRE5c0PWZ1QcqmkaxXa2bqyMfYMKcmJmZZzL1WM3l6VWLzvPFF3k/IwQk3TirK1hy/T4YttbA29avFr6YRiBj2rd+e6rRAYPC/Lcs+3q8mdxBSW7DufN4FpmlakLQu8wLglh2hapRQta5p/uvr76YRiBh18XsbZoAgI/z3Lco3cXfGrXZZfdp0lMTnzTnxN07TcmrfrDG8tD8avdjnmP+uLi5O9xa+pE4oZOBUrTWeH8myJjyAxIet5u55vV5Mr0fF6FmJN0yxm1t8n+WBtKN0aVuDHZ3zybOVYnVDMpEedfsRks948QIe6bnhWcGHujtN6xLGmaWallOKLjcf4clM4/ZpWZtbQZjja5d0y5DqhmEkr75GUNig2nF6XZTkRYWS7Ghy7EsOOE9fzKDpN0wo7g0ExeW0os7edYohvVaYNaoqdbd5+xeuEYib29s48WqwK25JuEheb9YrEfZpWpryLox7oqGmaWaQYFG+tCGbe7rOMbFuDT/wbYWOT5RLrFqETihn1rD+EeBvhr8DMF90CcLSzZbhfdXacuE7o5eg8ik7TtMIoMdnAK0sOsfzARcZ1rsN7vepjXHcw7+mEYkZNGw2lYooi4PyWbMsO862Gs4MtP+paiqZpDyk+KYXRCw6wPjiC93rW59Wuda2WTEAnFLOysbWjh2td9hhiuXXzVJZlXZ3teaJFVdYcvpxno1g1TSs87iQk8+y8/fwVfo2P+zXi+fY1rR2STijm1rPRcJJF2LJ/erZlR/hVRwG/7Dpr8bg0TSs8ou4m8dRP/7L39A2+GtiEJ1tVs3ZIgE4oZudZpzc1U4SAiF3Zlq1SxpmejSux6N/zRMfr6Vg0TcvejdgEhszZy5FLUcwe1ozHmz38+iXmphOKmYmNDT3KenFAErgScSjb8s+3q0FsQjJL913Ig+g0TSvIrkTFM3jOXk5FxjL3aR+6N6pk7ZDuoROKBfT0fhGAjVmsN5/Ky6MUrWqW4eddZ0hK0dOxaJqWsQs34xj4w24ibt9l/rO+PJIPV4DVCcUCqlZtSyODHQGRgTkqP6p9TSKi4lkfHGHhyDRNK4hOXotl4Pd7iL6bzMLnW9GqZllrh5QhnVAspGcFX8JsUjh95q9syz5Stzy1y5dgznY9HYumafcKunCbgd/vJtlgYMmoVjStUsraIWVKJxQL6dZ8LKIUG4LmZlvWxkYY1a4moRHR7D51Iw+i0zStINh+PJKhc/fi4mTPitFtqF+ppLVDypJOKBZSvkIjfKUYG26FZLnefKq+3pUpV8KRH7brgY6apsGaw5d5bv5+qpUtzvIXW1OtbHFrh5QtnVAsqEfl9pyzhdDwldmWdbSzZYRfdbYfjyQsQk/HomlF2fzdZxm35BDeVUuzZFQrypd0snZIOaITigV18R2HnVIEhGS93nyqYS2rUszelh936HXnNa0oUkoxbctxJq05Spf6Ffj1WV9ci1l+YSxz0QnFglxdq9LWpiQbY05lud58qlLODgxuUYU1hy9xJSo+DyLUNC2/SDEo3l8VwvQ/TzDIx4PvhjXDyT7v1jIxB51QLKx3jR5csxV25WBMCsCzfjVIMSjm7T5r2cA0Tcs3EpJTGLv4IAv/Pc/oR2rxeX+vPF/LxBwKXsQFTKdWr1M+RbHg2OIcla9a1pkejSqx8N9zxCYkWzg6TdOsLTYhmRG/7CfgyBXe71Wft7vXs+qMwbmhE4qF2ds7M7icN3u4y6lT2U9rD8aBjjHxySzdr6dj0bTC7LppXq5/z9xk2qAmjGxn/RmDc0MnlDwwoO0kHJRi4f6vclS+SZVS+NYow8879XQsmlZYXbgZx8Dv93DiWgxzn26eryZ5fFg6oeSBMmVq08uxImvvXiTq9tkcHTOqXU0u3b5LwBE9HYumFTbHrkTT/7vd3IhNYOHIlnSqV8HaIZmFTih5ZJjPq8TbCCt2fJij8p3qlaemW3Hm7tDTsWhaYRJ49iaDvt+DCPz+YhuaVytj7ZDMxmoJRUQGishRETEtduupAAAgAElEQVSIiE8W5bqLSLiInBSR8em2dxaRgyISJCI7RaR23kT+cDzr9KKFcmRx5D6Sk7K/JdjGRni+XU1CLkWz8+T1PIhQ0zRL+zPsKsN+/JdyJRxZMboNnhVdrB2SWVmzhhICPA5sz6yAiNgCs4AeQANgiIg0MO3+DhimlGoKLALet2y4ufdk3UFcsRX+2js1R+X9vd3xKF2MKevDSNZ9KZpWoP0eeIFRvx3As6ILv7/YGo/SztYOyeysllCUUmFKqfBsivkCJ5VSp5VSicASoG/qKYDUmdJcgcuWidR8Ovj+D/cUWHgq+6lYAJzsbXmvZ32OXYlhsb7jS9MKJKUU32w9zpvLg2ldsyyLnm9F2RKO1g7LIvJ7H4o7kP6b9KJpG8BIIEBELgJPAZ9ldAIRGSUigSISGBkZadFgs2Nr58DQiq05KImEHluVo2O6N6pIq5plmLY5nNtx2Y+21zQt/0hMNvDm8mC+2XqCAc09+Hl4C0o42lk7LIuxaEIRka0iEpLBo2/2R2frVaCnUsoD+AWYllEhpdQcpZSPUsrHzc3NDJfNHf+2k3A2KBYenJ6j8iLCxN4NibqbxDdbT1g4Ok3TzCU6PokR8/ax/MBFXu1Sly8HeOFgl99/w+eORVOlUqpLLk9xCaiS7rUHcElE3IAmSql/TduXAhtzea084VLSnb7O1Vh+9xyvXj9GuXL1sj2mQeWSDPGtym97zzG0ZVXqVihcHXmaVthcun2XEb/s43TkHaYObMKA5gV/jElO5Pd0uR+oIyI1RMQBeAJYA9wCXEWkrqlcVyDMSjE+sKEt3yJJhN935uwWYoDXH/WkuIMtH60L1bcRa1o+FnIpCv9Zu4i4Hc/8Z32LTDIB69427G/q/2gNrBeRTabtlUUkAEAplQy8DGzCmDCWKaWOmrY/D6wQkcMY+1DetMb7eBjVq3egnRRn6c1gEhNicnRMmeIOvNq1LjtOXGdr2DULR6hp2sP4O/wag37Yg52NsHx0G/xql7N2SHlKitKvXR8fHxUYGGjtMADYvX8WL4R+z5Qqj9Gn0yc5OiYpxUDPb3eQmGJg86vtcbQrWFNba1phtujf80xYHUK9ii78PLwFFQrIolg5ISIHlFKZjhdMlaMaioj8ISK9RCS/N5EVGK2bj6ZmirDgXECOlggGsLe1YeJjDTh3I46fd561bICapuWIwaD4fOMx3l15hPZ1yrHshdaFKpk8iJwmiNnAUOCEiHwmIp4WjKlIEBsbhrl3JMwmhUNHFuT4uHZ13OhSvwIz/zrBtWi9CJemWVNCcgrjlgbx3bZTDG1ZlblP+1C8EN8WnJ0cJRSl1Fal1DCgGXAW2Coiu0VkhIgUnPUp85ne7SZQ0qBYEDz3gY57v1d9ElMMfL4xu3GhmqZZyu24RJ76cR9rD19mfI96TOnXqEAuimVOOX73IlIWGI5xQOEh4FuMCSZni3xo/+HsXI7+JevyV8otIi4fyPFx1csV59m2NVhx8CJBF25bMEJN0zJy/kYcj3+3m6ALt5k+xJsXO9QqsItimVNO+1BWAjsAZ+AxpVQfpdRSpdRYoIQlAyzshrR+D4DFe6Y80HFjO9XBzcWRD9YcxWAoOjdWaJq1BV24jf/sXdyITWTByJb0aVLZ2iHlGzmtoUxXSjVQSn2qlLpngY6c9PxrmatUuTmdbEuzIvo4cXE5n1W4hKMdb3XzJOjCbVYFXbJghJqmpdp09ApPzNmDs6Mtf7zUBt8ahWfqeXPIaUIpLSKP3/foLCLlLRpdEfGk1/NE2wjrdn78QMf1b+ZBEw9XPttwjDt6/XlNsxilFLP+PsmLCw7gWbEkK1/yo5abbpy5X04TynPAj8Aw02Mu8DawS0SeslBsRYZ34yepb7Bl0cW/cnwLMRjXTJn4WEOuxSQwe9tJC0aoaUXX3cQUXlkSxJebwnnMqzJLR7WiXCGdLTi3cppQ7IH6Sqn+Sqn+GNcmUUBLjIlFywWxseHJaj05ZavYc/D7Bzq2ebXS+Hu7M3fHGc7fiLNQhJpWNEVE3WXQD3tYF3yZt7p78u0TTXGy1wOKM5PThOKhlLqa7vU1oIpS6iaQZP6wip7ufu9QNkWxMPS3Bz727e71sLMRpgSEWiAyTSuaDp6/RZ+ZuzgdGcvcp3x46ZHa+k6ubOQ0oWwTkXUi8oyIPAOsNm0rDuj7Vs3AwdGFQaUbs13Fcu7cjgc6tqKrE2M61mbT0avs0ssFa1quLT9wkSd+2Esxe1tWjvGjS4MK1g6pQMhpQhmDcc2RpqbHr8AYpdQdpVRHSwVX1AxqOxE7pVj07+cPfOxzbWvgUboYH64N1csFa9pDSjEopqwP5Y3fD9O8WmlWj/HTy0U8gGwTimld97+UUiuUUq+aHstVUZpVMo+Uc6tPT4fyrLpzlpjoB7sV2Mnelvd71Sf8agyL9p23UISaVnhF3U3i2Xn7mbvjDM+0rsavz/lSuriDtcMqULJNKEqpFMAgIq55EE+RN6zZK8TZCCt3Tn7gY7s1rEjrmmX5avNxbt3RywVrWk6diozFf9Yudp28zif+jZnctxH2RXwalYeR008sFjgiIj+JyPTUhyUDK6oa1OtHM+XAoit7SEl+sKQgIkzq04CY+CS+2XrcQhFqWuHyz/FI+s3axe27SSwc2ZKhLataO6QCK6cJ5Q9gArAdOJDuoVnAsFr+XLKFf/Z988DH1qtYkmEtq7Hg3/OEX8nZ4l2aVhQppfhxx2lG/LIP91LFWD3Gj5Y1y1o7rAItp7MNzweWAXuVUvNTH5YNrejq1OoNKqUoFh5f9lDHv9a1LiUc7Zi89qheLljTMpCQnMKby4P5eH0YXRtUYMXoNlQp42ztsAq8nE4O+RgQBGw0vW4qImssGVhRZmfvxBNuvuyTBMJPrH/g40sXd+C1rnXZfeoGG0OuWCBCTSu4rsXEM2TOXpYfuMgrnevw3bDmRXoNE3PKaZPXB4AvpjEnSqkgoKaFYtKA/u0m4mRQLAp88GYvgGEtq1K/UkneXXmEy7fvmjk6TSuYDpy7Rd+ZuwiNiGbW0Ga81rUuNjZ6sKK55DShJCmlou7bpgc7WJBrqeo8VsyD9fER3Lp56oGPt7O1YdZQbxKTDby86CBJemyKVoQppfh55xkG/7AHWxth+Ytt6OVVydphFTo5TShHRWQoYCsidURkBrDbgnFpwJMt3yRRYN7fbz3U8TXdSvD5AC8Onr/N5xuOmTk6TSsYYuKTeGnhQT5cF8ojnuVZP7Ydjdz1KAhLyGlCGQs0BBKAxUA08D9LBaUZ1azRmV72biyMDudKxKGHOkdvr8o807oaP+48o/tTtCInLCKaPjN3sTn0Ku/0qMfcp5vj6qxXLbeUnN7lFaeUek8p1UIp5WN6Hm/p4DQY2/FLDAIz/37zoc/xbq/6eHm48ubyw3pGYq3IWBZ4gX6zdnEnIZlFI1vygl6m1+JyepdXXRGZIyKbReSv1Ielg9OgcmUfhpWow5rEKxw/ueGhzuFoZ8usoc0Q4KVFB4hPSjFvkJqWj8QnpfDW8sO8tTyYZlVLs/6Vdnp8SR7JaZPX78Ah4H3gzXQPLQ+M7PotLgq+3vXg07GkqlLGma8GNSXkUjQfr9fT3GuF05nrd+g3axfLAi/ycsfaLBjZEjcXvRhWXslpQklWSn2nlNqnlDqQ+rBoZFoaV9eqPO/Wip3cYe+BHx76PF0bVOCF9jVZsPc8q/U69Fohs+FIBI/N2MmV6Hh+GdGCN7p5YqtvCc5TOU0oa0XkJRGpJCJlUh8WjUy7x5AuX1EpRTEt+DsMKQ+/fvwb3TzxqVaad/44wslrsWaMUNOsIzHZwIdrQxm98CC1ypdg/Svt6OhZ3tphFUk5TSjPYGzi2s3/z+MVaKmgtP9ydHJlbI1+hNmksHHnRw99HntbG2YM9cbJ3paXFh7gbqLuT9EKrsu37/LEnD38vOsMw9tU5/cXWuNeqpi1wyqycnqXV40MHnqkfB7r1f4D6hlsmH7qDxITHn7ix0quxfhmcFNOXItlwuoQM0aoaXnnn+OR9Jq+g/ArMcwc6s0HfRriYKennLemLD99EXkr3fOB9+37xFJBaRmzsbXj1cYvcMkWlvz5eq7O1b6uG2M71WH5gYss23/BTBFqmuWlGBTTthxn+C/7KO/ixJqxbentVdnaYWlkX0N5It3zd+7b193MsWg50MbnJdpQjDlXdxMdlbtEMK5zHfxql2XC6hDCIqLNFKGmWc6Fm3EM/mEP0/88wePeHqwa40cttxLWDkszyS6hSCbPM3qt5ZFXW71PtMBPW3M3WYGtjfDNYG9ci9nz0sKDxMQnmSlCTTMvpRTLAi/Q/ZvthF+JYdqgJkwd6EUxB1trh6alk11CUZk8z+i1lkfqefbhMYfyLIgJJ+Jy7u7ednNxZMYQb87duMM7fxzR66do+c6N2AReXHCAt5YH08jdlQ3/a8fjzTz0qPd8KLuE0kREokUkBvAyPU993fhhLyoiA0XkqIgYRMQni3I/i8g1EQm5b3sZEdkiIidM/y39sLEUVC8/8iUAM7c93MSR6bWsWZY3unmyLjiC3/aey/X5NM1c/jp2lW7f7ODvY5G827Mei55vhUdpvRBWfpVlQlFK2SqlSiqlXJRSdqbnqa9zM8NaCPA4xiWFszKPjPtqxgN/KqXqAH+aXhcplSo3Z1iJOqxNvEr48XW5Pt+L7WvRqV55PloXyuELt80QoaY9vLjEZN5beYRn5wVSroQDq1/2Y1T7WnqgYj5nlXvslFJhSqnwHJTbDtzMYFdfIHUJ4vlAPzOGV2A8lzoly56HH5eSysZG+GpgE8q7ODFm0UGi4nR/imYdh87fotf0nSzad55R7Wuyaowf9SuVtHZYWg4U1Ju2KyilIkzPrwAVMisoIqNEJFBEAiMjI/Mmujzi6lqVUeXbsIs49hz4PtfnK13cgZlDvbkaHc/rvx/W/SlankpKMfD1luMM+H4PickGFo1sxbs96+NkrzveCwqLJRQR2SoiIRk8+przOsr4rZfpN59Sao5pyn0fNzc3c146XxjS5Ssqp8DXwd/nakqWVN5VS/NOj/psDbvKd/88+EqRmvYwTkXGMuC73Xz75wn6NqnMhv+1o3UtPUOwOURHXeCzZY8RGxORfeFcslhCUUp1UUo1yuCx2gynvyoilQBM/71mhnMWSA6OLoytaZySJWDHw89GnN4Iv+r09qrEFxvD+WnnGbOcU9MyopTit73n6DV9B2dvxDFraDOmDW5KSSe9CJY5HDg8nwErerA07gyBRxdZ/HoFtclrDcb5xTD91xxJqsDq2W4S9Q22zDi9KldTsqQSEaYNakqPRhX5aF0os7edNEOUmnava9HxjJi3nwmrQmhRvQyb/tder/NuJklJccxYOZhnD32JPcJvvpN4pFXuZtfICaskFBHxF5GLQGtgvYhsMm2vLCIB6cotBvYAniJyUUSeM+36DOgqIieALqbXRZaNrR2veY3msi0s3mqefzQOdjbMGOJN36aV+WJjOF9vOa77VDSzUEqxOugS3b7Zzp5TN5jcpyG/PutLRVcna4dWKFy4sIfhC9oyJzqUxxwqsmzQFho1GJj9gWYgRelLwsfHRwUGFt5Jkl+c35IjhjsEPB6Aq2tVs5wzxaAYvyKY3w9c5MUOtXi7u6ceUKY9tLPX7zBhdQg7TlzHy8OVaYOaULu8i7XDKhSUwcC6fyYw5exqbICJtQbRvf1Es5xbRA4opTIdM5jKzixX0/KFV1tPYODu8fy0ZRyvDVhplnPa2gif9/fCwc6G7/85RUJyChN7N9BJRXsgCckpzPnnNDP+PomDrQ0fPNaAp1pX1+NKzCQm+hIfrRnKhpSbNBNHPnt0DpUqN8/zOHRCKUQ86/bmscCvWRh7giGXD5jtH5SNjfBxv0Y42tny864zJCYb+KhvI2z0l4GWA3tP3+C9lUc4FXmHXo0rMaF3A928ZUaHghcwPvBzrtooXi7tzcheP2Fr52CVWHRCKWTGdpzKxk1PMXPbm0wZ+pfZzisiTOhdH0d7G77bdoqEZAOf9/fSvzC1TN28k8iU9WGsOHgRj9LF+GV4CzrW0yspmktyUjxz1o3gh6gjVEaY7/M+TRo9kf2BFqQTSiFTsZI3w1zqMi/mOE+Fr6GeZx+znVtEeKubJ052tny99TiJyQamDWqCnW1BvVlQswSDQbH8wEU+2RBGbHwyLz1Si7Gd6uiZgc3o4sW9vLP1JYIkiT4O5XnnsYWUcLH+HXI6oRRCI7t8yx9/9ODrvR/zgxkTChiTyrgudXCws+HzjcdITDYwfYi3XilPA+D41RjeXxnCvrM3aVG9NFP8G1O3gu50N6d12yYw5Yyxj/TzGv3p2cE848/MQSeUQqikaxVGVWjDl5F72B04mzY+L5n9GqMfqYWjnQ0frgvlxQUHmD2smZ4iowi7m5jCjL9OMGf7aUo42fFFfy8GNPfQ/WxmFBsTwZQ1Q1mXfB1vceTTrt/h7u5r7bDuoW8bLqQSE2Lot7ANClg+aAvFS1S0yHUW7D3H+6tCaFenHHOe8tHNGkXQ3+HXmLg6hAs379K/mQfv9qxH2RKO1g6rUAk6spDx+z/jio3ihVJNeL7XT9jZ592NDTm9bVi3UxRSDo4uTPF5m8s2is/XPmmx6zzZqhpfDvBi58nrjJi3jzsJuZ9PTCsYrkbHM2bhQUb8sh8HWxsWP9+KrwY10cnEjBITYvhmxQCeOfApAPOav8PofgvzNJk8CJ1QCjFvryd5rmR9ViZe5c/dn1vsOgN9qvDN4KbsP3uLp3/eR7ReSrhQi7qbxBcbj9Hhy7/ZEnaV17vWJWCcnszR3MJPrGfIorb8FBuOv2NlVgzaQtPGw6wdVpZ0k1chl5Rwh2GL/IggmT96LcWtfEOLXWtjSARjFx+ifqWS/PqsL6WcrXMvvGYZdxNTmLf7LN9tO0lMQjJ9mlTm9a6eVC2rV1A0p5TkROZveJGZN/ZR0gCTGzxLh1avWTWmnDZ56YRSBJw+8yeDto2jhU0JZj+1G7GxXMX0z7CrjF5wkBrlijN9iDeeFfUdPgVdUoqBpfsvMP3PE1yLSaBTvfK88agnDSrrRa/M7cKFXbz35ysckkS62Lgyodc8ypSpbe2wdB+K9v9q1ujMa5U6sJM7LN08zqLX6ly/Ar+MaMH12AQem7GTWX+fJDnFYNFrapZhMBgncewy7R/eXxVC1TLO/P5ia34e3kInEzNTBgO/b36V/ltf4KRK4JOqfZk2bHu+SCYPQtdQighlMDD6t9YcMNxhWceZ1Kj+iEWvd/NOIhNXh7AuOAIvD1emDmyixyMUEEopth2P5IuN4YRFRFOvogtvdfeko2d5PYebBUReO8qkjc+xQ92hJU58/OgcKlbytnZY99BNXhkoygkF4NrVEB4PeAIP7Pjtyd3Y21u+7TvgSAQTVoUQE5/MuC51eKF9TT2yPh8LPHuTLzaGs+/sTaqWceb1R+vymFdlPZ7EQjbt+IiPTi4lHni1YjuGPDoDG9v8NzxQJ5QMFPWEArB156e8emoRo0o2YKz/0jy55o3YBCauPsr6IxE0MdVW6ujaSr4SFhHN1E3h/HnsGm4ujrzSuQ6DfaroGRAsJCrqPJ+ue4b1yddpaLDlk0emUbNGJ2uHlSmdUDKgE4rR+4u6sDbxCvObv5OntyGuD45gwuoQYuOT+V/XOoxqp2sr1nb+Rhxfbz3OqqBLlHC048UOtRjhVx1nh/z3K7mw2B04mwnBs7lhAy+U8mJkrx/zpLUgN3RCyYBOKEaxMREM+P1RBMuOos/I9dgEJq4OIeDIFV1bsRKlFHtO32D+7rNsCb2Kva0NI/xq8GKHmvpWbwu6G3eTr9c+xeL489RIET5tPYmG9ftbO6wc0QklAzqh/L+Dh39lxKEv6OdYiclDtuT59dcFX2bi6qPExifzate6PN+uhq6tWFhcYjIrD13i193nCL8aQ2lne57wrcrwNtWpUDJ/jrwuLAKD5jHp4Fect4UnnWswrvd8nIqVtnZYOaYTSgZ0QrnXtysG8GNsON/UeZLObd7O8+tfj01gwqoQNoRcoUmVUnw10EsvB2sB52/E8euesywLvEB0fDINKpVkeJvq9GlaWU/oaWF3Yq/w9fpnWRp/AfcU+NB7HL7eI60d1gPTCSUDOqHcK3UU/RWS+aP375Rzq5/nMSilWBccwcTVIdxJTOG1rnV5vl1NvXBXLiml2HHiOvN3n+Wv8GvYiNC9UUWGt6mOT7XS+vbfPLB7/yw+OPIdV2xgmHMNxvb+BWfnctYO66HohJIBnVD+Ky9H0WclMsZYW9l41FhbGduxNh3rldeJ5QHFJiSz4sBF5u85y+nIO5Qr4cAQ36oMa1lNL7ubR6KjLjA1YAQrE69SPUX4qMXb+X4OruzohJIBnVAytnDDS3x2bQfvV+zI4G7TrRaHUoq1wRF8vC6UazEJuJcqxtCWVRnkUwU3Fz2DbVZOR8by655zLD9wkdiEZJp4uPJMm+r08qqEo51u1sorf++Zysdh87hhA8Nd6jG61084OrlaO6xc0wklAzqhZMyQksxLC/zybBR9dpJSDGwJvcqCvefYfeoG9rZCt4YVebJVNVrWKKOba0wiYxL469hV1gVHsOPEdexthV6NK/FMm+p4Vy04Hb6Fwa2bp/hsw3MEJN+gjsGGj1pNLDB3cOWETigZ0Aklc9YYRZ8TpyJjWbj3PMsPGDuU65QvwbCWVXm8uQclneytHV6eUkpx4losW0KvsjXsKkEXbqMUuJcqxkAfD4a2rEp5F92slZeUwcDmXVP45ORSogVGlfJiZI+52DsWt3ZoZqUTSgZ0Qsnalp2f8NqpxbxQsiEv+y+xdjj3uJuYwtrgyyzce47DF6MoZm9LP+/KDGtZjUbuBb9JITNJKQb2n73J1tBrbA27yvmbcQB4ebjSpX4FutSvQP1KLrrWZgXXI8P4eONI/jRE09Bgy4ftPqVu7R7WDssidELJgE4o2XtvUWfWJV5lvs+7NG001NrhZCj44m0W7D3HmsOXiU8y0LRKKZ5sVY3eXpUKxW2w0fFJ/BMeydawq/x97BrR8ck42NngV6ssXRpUoHO9CrqD3YqUwcDabe/z+bk1xAuMKevL091n59tVFM1BJ5QM6ISSPWuOon9QUXFJrDh4kQX/nuN05B1KOdszoJkHHTzdaFCpZIFaivbCzTj+DLvK1rBr7D19g2SDokxxBzrVK0+X+hVoV6ccxR31dCjWdiXiEJM3j2Ynd2iq7PnwkWlW73PMCzqhZEAnlJw5cHg+Iw59SW/78kwZstVqtxLnVOpUIgv3nmfT0SskG4z/piuWdKJB5ZI0rFySBpVK0rCyK1XKFLNa85BSiuuxiZy4FsPJa7GcuBqb9vx6bCIANd2K07V+Bbo0qECzqqX1bdP5RHJSPIu3jGPm1V0oYFzFdjzR9Vts7YrGVDU6oWRAJ5Sc+27VUGZHHWFkCU/G9V9u7XByLCouiZDLUYRejubo5ShCI6I5eS0WU47BxdGO+mkJpiQNKpekTnkXs86qq5TiWkxCWsI4cS2Wk6bnt+KS0sq5ONpRp0IJ6pR3wbOiCx083ajlVsJscWjmEXx0KR/t+4RjNgbaUpx3O31NlSqtrR1WntIJJQM6oeScMhj4cFkPlidc5o1yrXmm1xxrh/TQ4pNSCL8Sw9HL0YRGRHH0cjTHImK4m5QCgL2tUKe8Cw0rl6RcBuNdMvpfRPHfjbfvJKUlkJj45LTtrsXsqVuhBLXLu1CnfAnqVChB3QoulHdx1J3p+VhU1HmmbxjF7/EXcTPA+LpD6dJmfL6vsVuCTigZ0AnlwaQkJ/Lm4s5sMdzm4yq96NvpM2uHZDYpBsWZ63cIjTDVZC5HExYRTfTd5P8WzuQ7//7NLk521C5vrHHUqVAi7Xm5Eg46cRQgymBg3T8TmXp2FVECQ4vXYkyPH/J1f6Kl6YSSAZ1QHlxiQgxjlnRmv4rja8/hdGz9hrVD0jSLOX3mL6b88xb7JAEvgx0T2kymnmcfa4dldTlNKEWv7qY9EAdHF77tv44Gyp43wuexP+hna4ekaWYXf/cW0/8YRP9/XiFMxTOhUmd+e3q/TiYPyCoJRUQGishRETGISKZZT0R+FpFrIhJy3/YvReSYiASLyEoRKWX5qIsu5xLlmdV3OR4GG145NI2w8NXWDknTzGb7v9/Sb3F75saE0cO+PGsf+4NBj36TL9d2z++sVUMJAR4HtmdTbh7QPYPtW4BGSikv4Djwjlmj0/6jdJla/NDzV1wUvLj7Pc6d22HtkDQtV65cCeK139oy5tiPOCD85DWOT4b9Rdlyda0dWoFllYSilApTSoXnoNx24GYG2zcrpVJ7T/cCHmYOUctAxYpN+aHTTBTwwp8vce1qSLbHaFp+k5wUz68Bo+i74Um2J9/mldLerBi2p0AufJXfFIY+lGeBDZntFJFRIhIoIoGRkZF5GFbhVKP6I3zXajK3RPFCwDCibp+1dkialmP7g37miQUt+TJyD81sSrCyy1ye7/NroZvM0VosllBEZKuIhGTw6GvGa7wHJAMLMyujlJqjlPJRSvm4ubmZ69JFWsP6/Zne5BXOSQpjVj5OXNx1a4ekaVk6f34n//vNj2cPf02USuGrmoOZ/dTuIjdA0dIs1uuklOpiqXMDiMhwoDfQWRWle5/ziZbNRvFF3A1eP7mQ137vxYwn/tK/8rR8JzrqAnM2j2XhnZPYKxhb1punu07HqZheL8YSCmSTl4h0B94C+iil4qwdT1HVpe07TPLozi7ieO/3nhhSMhgUqGlWkJwUz5KNY+n9Rw9+vXOSxxwrsr7XUkb1+U0nEwuy1m3D/iJyEWgNrBeRTabtlUUkIF25xcAewFNELorIc6ZdMwEXYIuIBInI93n8FjSTx7tM5dUyLdiQcpNPl/dBGXfBZ3EAABH4SURBVAzWDkkr4nbtn8mA33yZcnUbtcWJpa2n8OGQrbiVb2jt0Ao9PVJeM4uvlvsz785JXnJtzOh+i6wdjlYEnT7zJ19uf4+d3KFKCrxe70k6tXqzSM69ZW45HSmvR+5oZvHa4yu4veRRZkcdwXXjGIZ2n2XtkLQi4tbNU8zeMpbf757HWcEb5VszpMs0HBxdrB1akaMTimYWYmPDpIHriFrcmU+vbsd120R6PfKhtcPSCrGkhDss2voqP1zbTZzAgGJVeanrdMqUqW3t0IosXRfUzMbO3okvBwXgoxx59+wf/LLuOd2nopmdMhj4a/cX9FvYiqnX9+BlU5zl7abx/uAAnUysTCcUzawcnVyZNSCALnalmXZjH28s6kBc7DVrh6UVAspgYM+B73lqvg/jTvyGHcJ39Ufx/TP/UrvWo9YOT0MnFM0CnEuUZ+rQf3itrC9bk28xdFkXPfeXliv7D/3E8F9b/F979x4dVXnucfz7S4LcIchFQCDhZpEqIsrFGyICtdKKF2prFaXW2mN7vB1be1rb2uNx1QtrVY+ttWKPtVIFW9Qj1htgQS2FAAYIQaAiDfdLBKSAEJPZz/ljb+wQBxhgkp1Jns9as/Jm9p49zzszmV/23jPvy42lj7LFPuGnnUbw/Lj5nDvo5rhLc0n8U16uRs199zfcWfIrqoD7T76e84f8R9wluSxSvORpHl30CPNVQYeEcUPnYVxxwX1+wr2W+QRbKXigxGPDhvncPv1GluckuKnVKfzbJZN8aHB3SEtKp/Drd3/B39hL24RxQ6dzGTvsPv9SYkw8UFLwQInPvr07+O8XxzKtcivnqwU/H/NHWrXuGndZro5Ztvx5Hl0wgXdsD20C45sdzuLKCx6gabPj4y6tQfNAScEDJV4WBEyZfgsPbp5N50A8PHQCvXulmu7GNTQrVk7j0aL7mW27aB0Y49udydcveJBmLTrEXZrDAyUlD5S6oXjJ09zx7oPsEdzT80ouGvrTuEtyMXl/1es8NvdeZgQ7aRkY1x1/OlcPf5AWLTvFXZpL4oGSggdK3bF1Syl3vHYti1XJN5r34pYxk8lr1CTuslwt+fuq13hi3n28UbWd5gbj8k/lmuEP+mHQOsoDJQUPlLqlsmIPD7w4lucq1jOYJkz48hTaHN8z7rJcDQkSVbyz4BEmrZxMEftoGhjXtD6Z64ZPoHV+YdzluUPwQEnBA6VuevHNO7l33au0DeChs+/h830uj7skl0Ef797KS3+9h2c2vsWaXOiQML7efiBjz7vbgyRLeKCk4IFSdy1b/jy3zb2b7Tnwk66jGXPBfT5KbJbbvGkRz865h6m73mdXjjg1yGNcjzGMOPtOGjVqFnd57gh4oKTggVK3bd++ijtfvooi9jGYJtw++Ie+t5KFlpRO4Q+Lf82Mqu0YMCKvDeP638Rpfb/m/yRkKQ+UFDxQ6r6qyn08N/N2Ht/8DjtyxBdzj+fm839O167nxF2aO4Sqyn3MnPsAkz54iZKcSloGxhUte3PV2XfRufNh34dcHeeBkoIHSvbYvWsTv5t5G5M+Wkal4Mpmhdw4/Be0bXdS3KW5JDt3ruX5t3/G5PL5bM4V3RJwdeehXHru3f4dknrEAyUFD5TsU751GY/95Q5e2Leexgbj25zGdSMe8jerGAWJKoqX/oE/L3+WV/dtZG+OGGSNGdfnKoYOvNWH1amHPFBS8EDJXv8om80v3/kxM4KdtE0YN504nMuH3+8nd2vRqg+m88riibyycwWbckXTwBjVuCPXnHELfT53SdzluRrkgZKCB0r2W1I6hV8snECxPqEgAbf0/iojz/mRn+ytIVu3lPLawv/hz1vnsyInINeMs9SC0QUjGX7mzb6n2EB4oKTggVI/WBDw9vyHefi9p1iVa5wa5HH76TczsP/1cZdWL+zetYkZ8x/ilfWzmG97MYUf+R3dcQhfGHgr7dr1ibtEV8s8UFLwQKlfElWfMO2tH/PomlfZkivOU3NuO/tuTur1xbhLyzqVFXv4a/FjvPLBNGZXbqciR3RNwJfanMLoAd+hoOC8uEt0MfJAScEDpX7at3cHk9/8Hk+UF7FbMEhNGdnxLC4ccBPt2p8cd3l1VmXFHhYvf443VvyJ1/euY2eOaBMYFzUrYPTnx9Gv75V+KNEBHigpeaDUbzs/KuMPs37I6ztKKcsFmXE6jRl5wkBG9P82HTudHneJsQoSVaxc9QpF77/MvG1LKQ72sDdHNAmMCxq15Uu9L+esAd/yDzq4z/BAScEDpWGwIGDV6unMLH2a6TuWsSonAKBfkMfI9mcwov8NdOkyJOYqa54FAWvXzaFoxVTmbS1mQdUOPsoRAN0TYnDzLgzpMpQhp42neYuOMVfr6jIPlBQ8UBqmsrK3mFnyJNO3LWF5TgKAk4NcRrbtx4h+19O9cFi8BWbQ1i2lFL03haJN8yjat5nNuWGAdEwYg5t0ZHCnwQzq+1VOOKFfzJW6bOKBkoIHilu/fh4zF/+WGeXFlORUAtAryGFkfl9GnnodvXqMyprzBpUVe1i3sYgPNsxjwYY5FO1Zx+rc8O+5dWAMymvDkA4DGNxnLN26npM1/XJ1jwdKCh4oLtnmzYt5c9HjzNiygGL2YRKtA6OARnQ9Lp+C5p3omt+Tbu1PoeDEwbEMtR4kqti8ZTFlG+ez5sP3WPvPNZTtLWdNYg8bcoxA4R5I08AYkNOcIW1PZXDvL/O5XqP9G+suYzxQUvBAcQfzYflyZi2ayIrty1lbsZ21ib1syjEsesMGaBUY3WhEt+Na061ZJ7pFYdOt80Dy87sf0R6ABQGJxCcEQSVViQo+/vhD1m1cSFl5CWs+Ws2ajzdTVrWLdSSoyPlXDU0Do5A8Chq1oqB5Zwrye1HY4TT69LqYRo2bZ/QxcW4/D5QUPFDckfikYhfrN85n7ZbFrNm2knW71rGmYhvrEnvZWC1sWgZGW8shwEgAVRgBkBBUQdgGqhS1k25bXZ4ZXYMcCvJaUNjsBLq1KqSw/SkUdB5M+/Z9/dCVq3XpBorvEzt3EMc1bkmP7hfSo/uFn1kWhs0C1m5ZxNrtK1n7z3XsqNpNLjnkKZdc5SRdcv/1M2d/O++AduO8JnRr24fCTmfQqeMZ5DVqEkOPnTs2HijOHYUwbIbTo/vwuEtxrs7wfWfnnHMZEUugSPqKpGWSAkkHPS4n6UlJWyWVHmT5HZJMUruaq9Y551w64tpDKQUuB94+zHpPARelWiCpKzAKWJvRypxzzh2VWALFzJab2co01nsb2H6QxQ8BdwIN52NqzjlXh2XlORRJY4ANZrYkjXVvlLRQ0sLy8vJaqM455xqmGvuUl6SZQKoR5+4ys5eOYbvNgB8RHu46LDObCEyE8HsoR3u/zjnnDq3GAsXMRtTQpnsC3YElCr8c1gUoljTIzDbX0H0655w7jKz7HoqZLQU+nchaUhlwppl9GFtRzjnn4hl6RdJlwC+B9sBHwGIz+4KkzsBvzeziaL3JwDCgHbAFuNvM/rfatspIM1AklQNrjrLsdkBDCy3vc8PgfW4YjqXPBWbW/nArNaixvI6FpIXpjGVTn3ifGwbvc8NQG33Oyk95Oeecq3s8UJxzzmWEB0r6JsZdQAy8zw2D97lhqPE++zkU55xzGeF7KM455zLCA8U551xGeKBUI+kiSSslrZL0nymWj5dULmlxdLkhjjoz6XB9jta5UtJ70bQDz9Z2jZmWxvP8UNJz/HdJH8VRZyal0edukmZJWiSpRNLFcdSZKWn0t0DSm1FfZ0vqEkedmZTGlB+S9Ej0mJRIGpDRAszML9EFyAU+AHoAxwFLgL7V1hkP/CruWmu5z72BRUCb6PcOcddd032utv7NwJNx110Lz/NE4Kao3Rcoi7vuGu7vn4DrovZwYFLcdWeg30OBAUDpQZZfDLwGCBgCFGXy/n0P5UCDgFVmttrMPgGmAGNirqmmpdPnbwGPmtkOADPbWss1ZtqRPs9XAZNrpbKak06fDWgVtVsDG2uxvkxLp799gb9E7VkplmcdO/SUHxD28WkLzQPyJXXK1P17oBzoRGBd0u/ro+uquyLaXZwaTfSVzdLp80nASZLmSJonKeWkZ1kk3ecZSQWEg5H+JdXyLJJOn38GXCNpPfAq4Z5Ztkqnv0sIJ/oDuAxoKaltLdQWp7Rf+0fDA+XIvQwUmlk/YAbw+5jrqQ15hIe9hhH+t/6EpPxYK6o9XwOmmlki7kJqwVXAU2bWhfDQyCRJ9fk94nvA+ZIWAecDG4CG8DzXmPr8YjkaG4DkPY4u0XWfMrNtZlYR/fpb4Ixaqq2mHLbPhP/FTDOzSjP7B/B3woDJVun0eb+vkf2HuyC9Pn8T+COAmc0FmhAOKJiN0vlb3mhml5vZ6cBd0XVZ/+GLwziS1/4R80A50AKgt6Tuko4jfDOZlrxCteONlwDLa7G+mnDYPgP/R7h3gqR2hIfAVtdmkRmWTp+R1AdoA8yt5fpqQjp9XgtcCCDpZMJAydZpTtP5W26XtAf2Q+DJWq4xDtOAa6NPew0BdprZpkxtPOvmQ6lJZlYl6d+BNwg/JfKkmS2TdA+w0MymAbdIugSoIjz5NT62gjMgzT6/AYyS9B7hIYHvm9m2+Ko+Nmn2GcI3oSkWfTwmm6XZ5zsID2feTniCfny29j3N/g4D7pNkwNvAd2MrOEOSp/yIzoXdDTQCMLPfEJ4buxhYBXwMfCOj95+lrxfnnHN1jB/ycs45lxEeKM455zLCA8U551xGeKA455zLCA8U55xzGeGB4rKapN1prHObpGYZvM9LJfXN4Pb+dgy33R397Cxp6iHWy5f0naO9H+fS4YHiGoLbgCMKFEm5h1h8KeHAghlhZmdnYBsbzWzsIVbJBzxQXI3yQHH1gqRh0ZwWUyWtkPRM9G3gW4DOwCxJs6J1R0maK6lY0p8ktYiuL5P0gKRi4CuSviVpgaQlkp6X1EzS2YQjJEyI5krpKal/NGhmiaQXJbWJtjdb4bwqCyUtlzRQ0guS3pd0b1Ltu5PaP5C0NLrP+1P0s3tU+9Jq2yjcPweGpM9Lmh/VVyKpN3A/0DO6boKkFgrnAimOtjUmaTvLJT2hcO6b6ZKaRst6SZoZ1VYsqWd0/fejx6lE0n9l9Il12SXu8fv94pdjuQC7o5/DgJ2EYxPlEA6Xcm60rAxoF7XbEX4runn0+w+Anyatd2fSttsmte8Fbo7aTwFjk5aVAOdH7XuAh6P2bOCBqH0r4XDwnYDGhOOjta3Why8CfwOaRb8fn6K/04Bro/Z3k25bSDQHBvBL4OqofRzQNHl5dH0e0CrpMVlFOEdGIeEoEP2jZX8EronaRcBlUbsJ4V7fKMJ5VBQ97n8Ghsb9uvBLPBcfesXVJ/PNbD2ApMWEb45/rbbOEMLDVXMkQfiGmzxW13NJ7VOivYB8oAXhMB4HkNQayDezt6Krfk84cdN++4dxWQoss2jcJEmrCQfpSx7CZgTwOzP7GMDMUs1rcQ5wRdSeBDyQYp25wF0KZyB8wczej/p6QOnAzyUNBQLCIcxPiJb9w8wWR+13gUJJLYETzezFqLZ9UT9GEYbKomj9FoQDh76doi5Xz3mguPqkIqmdIPXrW8AMM7vqINvYk9R+CrjUzJZIGk80QOZR1hRUqy84SH3pOOR4SWb2rKQiYDTwqqRv89nBPK8G2gNnmFmlpDLCvY7kmiF8HJse4u4E3Gdmjx9B/a6e8nMoriHYBbSM2vOAcyT1ApDUXNJJB7ldS2CTpEaEb8Cf2Z6Z7QR2SDovWjYOeIujMwP4xv5PpEk6PsU6cwgHraRaTZ+S1ANYbWaPAC8B/TjwMYBwRsatUZhcABQcqjAz2wWsl3RpdB+NozrfAK5POg91oqQOafXW1TseKK4hmAi8LmmWmZUTjhA9WVIJ4eGhPge53U8IzxvMAVYkXT8F+L6kRdGJ6esIT9KXAP0Jz6McMTN7nfAQ2cLokN33Uqx2K/BdSUs5+Ex7VwKl0TZOIZzydRvhYb5SSROAZ4Azo+1cW61/BzOOcLTtEsJzPR3NbDrwLDA32tZUDgwu14D4aMPOOecywvdQnHPOZYQHinPOuYzwQHHOOZcRHijOOecywgPFOedcRnigOOecywgPFOeccxnx/8N/bkLxDnv5AAAAAElFTkSuQmCC\n", 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\n", 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\n", 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\n", 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Ny9i0xlNHICKHRORZEXlKRPambf/vIvKCiOwTkS95aYPBMBMZ2LmNg1s38dJ7FnNw66ai+mcbysvwU4+g1vgZInO50rTlFmLHDjLy3KPZd/aIUswIrlDV8x0pVBG5ArgO2KCq64G/KYENBsOMYWDnNk7cdZvdNU8Vq/soJ+66zTiDCmVoz9Qic7lQf+k1+ObMpb+M+kPlCA19DPiiqo4BqOrJMthgMJSN7nvvQMejE7bpeJTue+8ok0WGQlErxvATP6f+ordnFJnLBV8oQuMV72Noz3ZiPcdctjBHGzw+vgI7RORxEXGa1J8NvFlEfisivxSRjG5URG4Vkb0isrda9YQMsxOrpzOv7YaZS/SFx0gM9eWVNpqJxqs+CIk4Az+/1yXL8sNrR/AmVb0QeAfwcRG5HFvfaB5wCXAb8D3JsMKiqner6kZV3dja2uqxmQZD6Qg0t+W13TBzOS0y95aijhNatILaDW+h/6F70bjlknW546kjUNWjyd8ngQeAi4EjwDa1eQxIAC1e2mEwzCRabrwd/MEJ2yRUY283VAy2yNyOrCJzudK05Was3mOpxvelxDNHICJ1IjLHeQxsBp4Dfghckdx+NhACur2yw2CYaTRcfj11aXo0gZbFLNh6Jw2XX19Gqwz5Mv7aCzmLzOVC3UVXEWheRP/20lcaeylDvQB4IBn1CQD3qupPRSQE/IuIPAeMA7foTFBdMhhKSKDJDneGlpzN8i8/Ul5jDAWREpnbeJUrxxN/gMa3f4Ce++9k/NhBQotWunLcXPBsRqCqB1V1Q/Jnvap+Ibl9XFU/oKrnqOqFqvoLr2wwGGYq8X57Emz1lidLxFA8Q3u2EznrQgJzF7h2zMa33wj+AP07vu3aMXPBVBYbDGXA6rcz4RIjg8RHBstsjSFfYj3HGHvl6YKLyKYiMHcB9Zt+h/6H7ycxFs0+wCWMIzAYykC8vwcC9oKxSRutPIb32iJzdZs2u37spi03kxjqY3DXf7h+7KkwjsBgKAPx/i7C7WsAsMpURGQonKE9hYnM5ULNOZcRbOsoaaWxcQQGQ4lJjI+SGBkksvI8AFtqosqpJm2lRHSI6HO/pn7TlrxF5nLBaVoz+vITvPLR80vyN6vY5vUGQ6XiLBSHV5wDIsSqPDTkaCs5shqOthJQkSmzw08+jFrjrqWNZkJCNQDE+2wFHq//ZmZGYDCUmHh/DwCB5kX4m+ZXfWio2rSVhvZsxzdnLjWrN3p2jt5tXzljm5d/M+MIDIYS42QM+RtaCDa3YXVX94ygmrSVTovMXVWwyFwulPpvZhyBwVBinNBQoKmVQPOiirwg5kM1aStFn/8tieF+6ja6ny2UTqn/ZsYRGAwlJu7MCBqbCbS0EevppJqL61tuvD0V83aoVG0lt0TmslHqv5lZLDYYSozV34NE6vCFawk0t6GjIyRGBvDXNZbbNE9wFjdP3PXH6PgoEopUpLaSqjK0dwe1577ZFZG56XD+Nt333oHV00mguY2WG2/37G9mHIHBUGLifV0EGm3B3WDzIgCs7s6qdQRgX9j6/vOfGT3wJIGWtopzAgDjh5/HOvk6837vEyU5X8Pl15fs72RCQwZDiYn3d+FPOgIn5lvtmUNAKk02duI11IqV2Zr8GdqzHURcE5mbSRhHYDCUGKu/57QjaLEdQbXXEmhsnHjfSYLz2yFuETtxuNwm5c1pkbn55TbFdYwjMBhKTLy/KyVDHZi7AHy+6k8h7TsJqtSe92YAxo8eKLNF+RHr6WTs4DPUe5wtVC6MIzAYSojG48QHe/E32DMC8QcINC3A6q1yR5CU0Ug5gs5XymlO3gzvcUTmvKsmLifGERgMJSQ+dAoSCfxNp7uzBlqqv6jMCX2Flq7B39RacTOCob07CC5cQWjJWeU2xRM8dQQickhEnhWRp0Rk76TX/khEVERMv+IZQDWJgs1kUsVkjWmOYN6iql8jcBbDA82LCLWtqpgZwcDObRz8bxsZeeoR4v1dDP7qgXKb5AmlmBFcoarnq2pKmENElmL3MH6tBOc3ZMERBbO6j4JqSuDKOAP3ifc5xWStqW2BljasnmNVXVRmdXfiq52Dv3YOocUdFeEIUt+LpJNORIeq9ntRrtDQ/wE+DVTvJ7+CqDZRsJmMNWDPCPxpM4Jgcxs6FiUx1FcuszwnliyKAgi1dZAYPEV8oKfMVk3PbPpeeO0IFNghIo+LyK0AInIdcFRVn55uoIjcKiJ7RWRvV1eXx2bObqpJFGymE+/LEBpqcWoJqvfvbfUcI5AsngsuXgXM/AXj2fS98NoRvElVLwTeAXxcRC4H/gz4i2wDVfVuVd2oqhtbW1uz7W4ogmoSBZvpxPu7wR/Al1ZF7FwgY1VcVGZNmhHAzE8hnU3fC08dgaoeTf4+CTwAvAVYATwtIoeAJcATIrLQSzsM01NNomAzHStZVSy+01+9VHVxlWYOJWJjxPu6CCZnPsHWpUggNONnBC033p7qK+1Qrd8LzxyBiNSJyBznMfbi8B5Vna+qy1V1OXAEuFBVj3tlhyE7DZdfz4Ktd4LYH4dKFQWrBOL93QQamidsCzTNB5+/KkMOAPHeE4CdHQUgfj/BRStm/Iyg4fLriay6wP5eiBBoWVy13wsvRecWAA8ke3oGgHtV9acens9QBPVv+B34+wQA/qbWqvywzwSs/m78TRNDneL3E5i3oGr1hpzUWGctBCC0eBVjrz1fLpNyxurppP7i36Httq+X2xRP8cwRqOpBYEOWfZZ7dX5DfjhhidCSsxg/8jKJ6BC+mvoyW1V9xPu7CbWtOmN7oLmtamsJnM9WMN0RtHUwtGc7asWQSeGXmUKs6whW1xFqrrm13KZ4jqksNgCnC37qLrgSgLHXXiinOVWJqtqhoaYzayiruWWlE/IKzJvoCGzxuUNlsio70X27AKhdf2mZLfEe4wgMwOnpe92FbwOMI/ACHR1Gx0cn1BA4BJoXYfVWZ1FZrKcTX13jhGYuqRTSozN3wXhk/y589U2E2teW2xTPMY7AAJyevkfOvghfTT3jFRC/rTSsZFVxoPHMdOhAy2J0fJTEYG+pzfIcq7vzjJTLSkghje7fTc2aiydkeFUr1f8ODTlh9R7D39CML1xDaOlqxg6bGYHbODpDmWcEyb4EVRgesnpPF5M5+Osa8DfNn7EppLGeY8SOH5oVYSEwjsCQJNbdmcrqCC9by9hrL1RlmKKcWNM6gmTLyt7qyxyyujsnLBQ7hNpmruZQdL+9PlCzzjgCwyxiQuVn+xoSQ6eInzpRZquqi5TyaNOZoSHnQlltC8aJ8VHiAz0Zq3FDiztm7BpBdP9ufLVzCC9fX25TSoJxBAZgohZMOLk4ZhaM3SXen1QenVRQBkk1Un+g6lJIrV67VnRyaAgg1LbKvuGYgeJzI/t22esDfn+5TSkJxhEYSESHSQz3E0zetYXb1wAwdtgsGLuJ1deFr35uxrx58fkIzFtYdUVlqRqCDDOC4OKZuWBsnTpJrPMVatZdUm5TSoZxBIYzKj/9c+bin7eQcTMjcJV4fw+BxjNnAw7VWEtgZagqdgjNUBXS6PO7gdmzPgDGERhI+7Km3bWF29dUhARAJRHv75rQkGYydoOaanMEpzuTTSbYsgQJhmecIxjZtwuJ1BJZeW65TSkZxhEYMk7fw+1rGD/yMhq3ymVW1WH1d2fMGHIINC+quk5lsZ5OfPVz8YVrz3htporPRfftomb1phkrfeEFxhEY0iQATquBh9vXorExYsdfLZdZVcdU8hIOgeY21BqfkYunhWJ1HyXYcuZswGGmpZBa/T2MH3mJ2vVvLLcpJcU4AgOxnmP4m1qRYCi1LZRaMDbrBG6gsXESw/34G6Z2BNWYQmr1HJugMTSZUFsHseOH0dh4Ca2amtPrA7NnoRiMIzAwsYbAIbTkLPD5TeaQS6R6FWeoIXBwLpjVtE4Q6+nMuFDsEFq8ChJxYicPl9CqqYnu24WEIkQ6phVOrjqMIzDYlZ+THIEvFCHUttIsGLtEqphsmqwh54JZLbUEibEREoOnpm3tGJxhmkMj+3dTs3rjhNnxbMBTRyAih0TkWRF5SkT2JrfdKSIviMgzIvKAiDR5aUMhDOzcxsGtm3jpPYs5uHUTAzu3ldskT8mkBQN2eGimp5BWyv/KaVo/XdaQv6EZCYSqJjTkFJMFM3y2HE6Lz5V/nSA+eIrx156fVWmjDqWYEVyhquer6sbk858B56jqecBLwIxqADqwcxsn7roNq/soqGJ1H+XEXbfN2AtMscRHBkmMDGacvofb1xI7cZhEdLgMlmWnkv5XqdDQNFlD1VZU5ji06UJDM0l8Lvr8b0GVmlkiNJdOTo5ARDpEJJx8/FYR+UShd/KqukNVnZzE3dgN7GcM3ffegY5HJ2zT8Sjd995RJou8JVMNgUOqwvj1F0tqU65U0v8qPo0EdTrVVEsQm+azlU6orWNGhIZG9u9GgmEiq84vtyklJ9cZwQ+AuIisAu4GlgL35jBOgR0i8riIZOr39hHgJ5kGisitIrJXRPZ2dXXlaGbxTPUlrJYv52Scu89M0/fQMltzaKb2Jqik/1W8vxsJRZDImfn06VRTy8pUMVlaWnImQotXMd75StnrJ6L7dxE560J8oUhZ7SgHuTqCRPIu/veAr6rqbcDUgb/TvElVLwTeAXxcRC53XhCR/wlYwHczDVTVu1V1o6pubG2d/i7KTaa6e8l2V1OpWN1HAbsxymSCrUuRSO2MFZ+rpP+V07ReRKbdz+5UdhxNJEpkmXdY3Z34G+bhC9dMu1+orYPEUB/xgfI15YkPDzB2aB8162dX2qhDro4gJiI3ALcAP0puy1p2p6pHk79PAg8AFwOIyIeAa4CbtNy3AZNoufF2JDApY8Dnp+XGGbWU4Rqxnk4QITB3wRmvic9HeOmaGesIWm68HSZVf0qoZkb+r+L93QSmqSFwCDa3gRVLZRlVMpnSkjPhaA7FOssXHoq+8BgkEtTOwoViyN0RfBi4FPiCqr4qIiuAb083QETqRGSO8xjYDDwnIr8DfBq4VlVHCjfdGxouv55AWwf4fCCCROogEU9lN1QbVs8x/E3zpyyntzOHni/7tD0TDZdfT7jjdDzX1zCPBVvvpOHy68toVWbi/V34p6kqdnAWVmdieCtfYj2Zs9Emk1IhLeOCcXT/LggEiZx9YdlsKCc5OQJV3a+qn1DVf00+f1VV/3eWYQuAR0XkaeAx4Meq+lPga8Ac4GfJtNK7irDfdcZPHCb2+gvMe9f/4OzvH2XlPz6Ov2k+J+7+NBqPl9s818lUQ5BOuH0N8YHe1GLnTEJVifccpW7jVeAP0Pi2G2ekEwBbumC6jCEH58IZq4LMoVxnBCnxuTIuGEf37Say6vyMmkizgVyzhi4TkZ+JyEsiclBEXhWRg9ONUdWDqroh+bNeVb+Q3L5KVZcmU0rPV9WtbrwRt+jf8W0QH41vvwmw09vmf/hzjB18lr7t3yyvcR5gZan8DC9zmtTMvAVj6+TrWN2d1G54i91e85Wny21SRjSRsENDWTKGAALN9lqNs3ZTqSRGR0gM9WVsUTmZlPhcmWYEiegQowefmbVhIcg9NPTPwN8BbwI2ARuTv6uKRGyMgYfvo37j5glZNPVvvJbaDW+h51//d6pIphpQVVsCYJrpu5NCOhMLy0aSfWVr111KpGMDo688MyNDWInhPkjEc5oR+BvmIcFwxfcuni4tORN2Cml5HEH0hT2QiM/K+gGHXB1Bv6r+RFVPqmqP8+OpZWVgaNePiQ/00rjl5gnbRYT5H/1r1IrR9c3Plsc4D0iMDKCjI9N+Wf0Nzfib5s/IGUF0/y589XMJLV1NpGMDieF+YscPldusM7D6sheTOYiInTlU4dXFudYQOIQWryJ2ojzicyP7d4E/QM3qqru3zZlcHcHDSWmIS0XkQufHU8vKQN+ObxFcuILac998xmuhRSuYd/1/Z/A3DzL81COlN84DUn0Iskzfw+1rZqQKaXTfbmrWvcHObkqKhI2+8lSZrToTp1dxIAdHANVRS5BLVXE6obaOsonPRfftItKxAV+WGo9qJldH8AbscNBfA3+b/Pkbr4wqB2OHn2f0hT00bv4g4sv8Z5n7zo9jkcdjAAAgAElEQVQTbFvJya//GYmxaMZ9KonTBT/TZ3aEl61l/MhLM2qxPNZ9lNjJ11Jx3fDS1UgowuiBmbdO4KSCTqc8mk6gua3iZSZyLSZzSLWtLPGCcWJ0hNFXnp51stOTyTVr6IoMP1d6bVwp6dtxDxIM03jFe6fcxxcMs+CjdxA7fojeH36thNZ5w+RexVMRal+Djo8SO3GoBFblRnT/RN14CQQJL18/IxeMrb78ZgRBp6hsBjnefLF6OvE3tuALhnPaP1gm8bnoS3shbs3qhWLIPWuoUUT+zpF8EJG/FZFGr40rFYnoEAO//DfmvPFa/HPmTbtv7XlvZs6bfo9TD/zfGSGUVQxWdyf4fBmLydIJtzuZQzMnPDSybxe+2gbCy9altkU6NjD66rMz7gIaH+gBnx9f/dyc9g+0tEHcSoWUKpFYd26pow7+2jlJ8bnSzgii+3aDz0dkzexdH4DcQ0P/AgwC703+DADf8MqoUjOw8wfo6DCNW27Jaf/WWz6DhCKc/KfbZ2SWSq5YvZ0EmhYg/sC0+9lNanwzqklNdP9uatZejPj9qW2RVeejoyMlv5hkw+rrsiWmpwg5Tsa5gFZyLcFU0ubTEVq8qvQzgv27CK84F3/tnJKed6aRqyPoUNXPJGsDDqrq54CVXhpWKlSVvu33EF5xDpGzLshpTGDufFpuup2RZx9l8NEHPLbQO6zu6WsIHHzhGoILl8+YFFLr1Alixw6eoRufWjA+MLMWjONZmtZPxrmAVnJ1sdXdmVMNQTpO/+JS3VwlxqKMvvwktbN8fQBydwRREXmT80RELgMqf7UUGH1xD+OvPU/j5luyCoKl0/j2DxBedT5d3/ws8aE+Dy30jliOlZ9gh4dmSmhoZF+yfmBS3neorQOJ1DE6w9YJ7GKy3B1BpfcuTkSHSIwM5C3+F1q8qqTic6MvP4la47O6fsAhV0fwMeD/JjuOHcaWiZhRFcGF0rf9Hny1c2h48+/lNU78fhbc+kXig710/2s2tY2Zh6rajcVznL6H29cQO/4qidHyy0NF9+/GV1NPeMU5E7aLz0dk5XmMzbDMoXxnBL76uUgoUrEzAieklXdoKLlgXCrxuej+XSBCzdo3lOR8M5lcs4aeUtUNwHnAuap6garOrG9bAVj9PQzt+hENb3l3QTnEkZXn0fSOj9C/4x6iLz/pgYXekRjqQ8ei0+oMpRNqXwuqjB95yWPLshPdv4vImoszrm1EVm1g7PD+shQmTYXV30Ugx9RRcIrKKreWICVt3nymtPl0lDqFdGT/bsLL1uGvq5q8l4KZ1hGIyAeSvz8lIp8CPgp8NO15RTPw8H2oNU7j5puz7zwFze+7Df/cBZy8+0/QuJV9wAzByjF11CG8LNmtrMwLxlZ/N+NHXp4yrhvp2IDGxhh7fWaEsRKjI+hYFH/D1E3rMxFobqvY0JDz2cp3jSDQstgWnytBNl4iNsboS4+bsFCSbDOCuuTvORl+6j20y3M0kaD/Z9+hZt0lhJeuLvg4/to5zP/Q5xh79Tn6fvpN9wz0mFh3fhIAwfnLkFCk7OsEqfqBKb7A4WSbwZlSWGYlU0BzLSZzCLa0VazekNVzbMoeF9OREp8rwYxg7MBT6PjorGxUn4lp8wZV9R+TDx9S1V+nv5ZcMK5YRp7+JbETh2m+4U+KPlb9pddQe/4V9Nz3JeovuTpj28eZhpVnHFf8fkJLV5e9bWV0/y4kUktk5XkZXw/Ob8dXPze5YPzB0hqXgVRVcR5rBOB0KjuBxuMTUmQrgVhPJ/7GViQYyr7zJEJtqxg7vN8DqyYykryhqF1n1gcg98Xir+a4rWLo2/4t/I0tzHnD7xZ9LFuU7gto3KoYUTqrpxP8AQJN83MeE24vf7eykX27qTl745SNdESESMd5jM0QzaFcm9ZPJtDcBok4Vt8JL8zylFzTkjMRWtxREvG56L5dhNrXZi0gnS1kWyO4VET+CGh11gWSP58FKus2JY1Y1xGGn3iIxitvKOiuJROhhcuZd/0nGNr1Hww/+bArx/SSWHcngbkL8rrbDC9bR7y/G6tMbRTjAz2Mv/Z81rhuZNX5jL324ozQg7L6bZFef2OeawSpTmWVFx6yeo4RzKJfNRWhxasgEWf8hHfic2rFiL64h9pZ2p84E9lmBCHstYAAE9cHBoB3Zzt4Mt302WQnsr3JbfOSTW5eTv7Ore7eRfofuhdUadzsbuhg7nUfI9jWwbGvfoKDWzfy0nsWc3DrJgZ2bsv5GAM7t3Fw66aCxuZDIZWfqd4EZVowHnn+MYCsBUCRjvMgEWfs0L5SmDUtjkxEvqEhJ5urEheMszU7mo5SpJCOvvI0OhY16wNpZFsj+CXwSxH5pqoW6qKvUNX0W8g/BX6uql8UkT9NPi8+UJ8jGhun/+ffpe7CtxFsXeLqsX3BMPWX/C6ntn2VRHKb1X2UE3fdBpC1jeLAzm2cuOs2dDya99h8sbo7iaw8N68xoWWnNYdqzztTqttrovt3IaFIakF4Kpw+xqOvPE3N6o2lMG1K4v3d+GobchZfc6jU6uL48ACJ6FDexWQOp8XnvHME0WRDo9muOJrO9CIzpxkRkTuB9UDE2VigAul1wFuTj78FPEIJHcHQnp8S7+vKWVcoXwYz3MHreJQTd93G0GM/mXbs8BO/SDmB9LHd997hqiNQVXtGcPGWvMYFGlvwN7aUrUlNdN8uImdflPWiGpi3EH/T/BmROWTl2LR+Mr66RiRSW3F6Q06mU76zTQd/7Rz8cxd4mkI6sm83oSVn5VXtXe3k6gi+C9wPXINdUXwLkIs0ogI7RESBf1TVu4EFqup8uo9jN7k/AxG5FbgVoL29PUczs9O3/R4C85dSt+Gtrh0znanu4HQ8mvUuZ7ITyHbMQkkM9qLjowXdtZVrwTg+1MfY4f00vyd7+YqI2IVlB8vvCOL9PQQa8r/giAjBCqwlyLXZ0XR42bZS4xbRFx6j4fJ3eXL8SiVXR9Csqv8sIn+YFi7ak8O4N6nqURGZD/xMRCZcQVRVk07iDJJO426AjRs3uqJCNXbkZaL7fkPLTbd7lpJnFwKd2Xg80LKY5f9n+kXkg1s3ZR5b4DR7KvKtIUgn1L6W/oe+gyYSOatpukH0hcdANee4bqTjfIYff4hEdAhfTflKXuL9XYSWnF3Q2EDzoooLDRXz2XIILV7F4G8eRFXz0v/KhbFXn0NHh01YaBK5fpNjyd/HRORqEbkAyJp3papHk79PAg8AFwMnRGQRQPL3ybytLpD+HfdAIEjDlTd4do6WG29HQjUTtkmohpYbb/d0bD4UWvkJ9oxAx6LEPMzqyER03y4kEMpZITbSsQFUGX3lGY8tmx4rT52hdCqxU5nV21lQMVk6obYOz8TnphIsnO3k6gj+KtmI5o+APwa+DnxyugEiUicic5zHwGbgOeBB7NASyd//XoDdeZMYHWHgke8z55KrPY0NNlx+PQu23kmgZbH9hWhZzIKtd+YU43fG+pK5zf6m+TmPzYd8i8nSCS8rT5Oakf27iZx1Ab5wTfadSZOkLqMSqVoxEoOnCv68BVrasPpOVJZ0SXcn/rkLpqzzyAUvNYei+3cRXLSyKEdVjeQUGlLVHyUf9gNX5HjsBcADyaldALhXVX+aDCl9T0R+HziM3ejGcwZ//UMSIwM0bvZmkTidhsuvL/ji3XD59YRXrOfwJ6+g9YN/7roTgGSLykAQf55FTgChpWeDiF1h/IZ3uG5bJuIjg4y9+izzrv9EzmMCjc0EWpeUtZl9fMCpISjQEcxrg0QCq/e46xluXmH1dOYsZDgVE1JIXaz81Xic6POPUX/pNa4ds1rIyRGIyDewF34noKofmWqMqh4ENmTY3gO8LQ8bXaFv+z2Elq6mZu3FpT513oQWrYRA0LPsHKu7k8C8hQXF+H3hWoILljN2uHQzgtEX9kAikXdf2UjH+YyVMTRkpeQl8ne4kNaXoOdYBTmCY4SK0O6CNPE5l2cEY4f3kxgZMGGhDOR6JfgR8OPkz8+BBmDIK6PcZvTAU4wdfIamzTe7vvjkBRIIEl5ylmcX22IqP8HJHCpdCunI/l0QCBJZfVFe4yId5xE7cZj4YGkanUzG0RkK5FlV7HC6urgyFoxVNa9mR1Nhi8+tdD2FNCVYaBaKzyDXfgQ/SPv5LnY4p7yVOnnQt/1bSKSWOW/JWgw9Ywi1r/WsNWQxlZ8AoWXJJjUlknCI7t9NpGMDvnB+PSMijhJpmWYFKcG5PJVHHQJJZx2rkBTSxHA/OjpSVOqog9228qALVp1mZP8ugguWEWzJr0/CbKDQ/L+zgNzVyspIfKiPwV//Ow1vfldFNagOt6/B6j3mehtMTSSSnckK/7KG29dCIsH40ZddtCwzidERRl95Ou+wEEA4WTldrgVjq8+RlyjMEfjrGvDV1FeMHHUxSQiTCS1e5ar4nCYSRPf/1swGpiAnRyAigyIy4PwG/oMSVgMXgqPZ88qH1tnFUxV2FxBu9yY7Jz7Yi1rjRX1ZHc2hUmQORV/cA3GroAYi/rpGgm0ry+YI4gPdSDBcVB2D2w1qvNSycjqquVH3Elrc4Zr43MDObRz8bxeSGDrF0N4dnul3VTK5Zg1Vzq00Z2r2APT+4CsEW5d4koXjBaFlpwXesoms5YMblZ/BhSuQUKQk4nPR/bvB5y9YMyjScT7RZO54qYn32TUExaxLBZoXuday0mstK+ezVUzY0SGUpjkUXnJWwceZ/J4Tg6c80++qZLLJUF843U+pjMyX7nvvmFKzp1IIzFuEr67R9btuq6ewfrLpiN9PaMlZJWlbGd23i8jK8wq+q450bMDqPYZ1qvS6/sUUkzkEWtwrKvP6e2H1HAOfL68eF1MRdEmFtBquBaUg24zgb6d5TYFCROc8Z6osi0rJvgBba8aL7JyYS3HccPtahp96xAWLpiYxFmX0wFM0Xf37BR8jsup0YVn9xs1umZYT8f4uAnMXFnWMYHMb8b6TaGy86N4ZXn8vrB6nx0WuyjVT45b4XDVcC0rBtDMCVb1imp8Z6QRg6hil25o9XhNqX8P46y+i6orUEmBP3yUQyruZ+mRC7WuI951MFU15wejLT6DWeFG68eHl54DPx+iB0heWxft78m5IM5lA8yJQdWVG4/X3ItZdfOpoOqHFq4oWn6uWa4HX5Jw1JCLniMh7ReRm58dLw4qhVJo9XhNuX0tiZDCjEF2hWD2dBJoXFS0YV4oF45F9u8Dno2ZN4UWAvkgtoSWrS55CqqpYA90Fp446OBcsN+5gW268HfwTpR/c/F5YvS47grYOxjtfKepGqP6y687YVonXAq/JNWvoM9g9ir+KLTHxJeBaD+0qimL0fmYS4eSCsZuxeDt1tPj0vpTmkIfrBNF9uwgvX4+/rqGo4zg9jN2cWWUjMdwPVqwgCep0nGw3NxaMGy6/nmDbSvDZyru+mnrXvheqitXd6UoNgUNo8aqk+Fxhs87EWJTh3T/G1zS/4q8FXpNrMO/d2HIRT6rqh0VkAfAd78wqnmL0fmYKoaXJzKHXXoCNV7lyzFhPJzWrNxV9HH/TfHxz5no2I0iMjzL68hOuNBCKrDqfgYfvx+o+WjKphlSLygKa0qQTdDqVuZBCGh8eIHbsIHP/y61Ek7Idbn1HEkOnCu5xMRWnM4deKUi4r3fbV4mdOMySz3yP2nPf5Jpd1Uiu8YGoqiYAS0QasKWjl3pnlgHsgqJAy2LXFow1KWDmRnqfvZjtXfXz6IGn0NiYK7owEUeJtITrBKeb1hfnCHw19fhqG1zJHBp+8hdgxajftIXadZcy+srTJKLDRR8X3C0mcyimf/H40Zfp/ff/y5zL32WcQA7k6gj2ikgT8E/A48ATQHmSs2cZ4fa1roVf4v3dYMWK0hlKJ9y+hrHXX0ATiew750l03y4QoWZt8eqToWVrIRAsaWFZPFlVHCiwqjidQEubK6Gh4T3b8Tc0EznrIrtALxG3C/ZcwI2GNJMJtCy261XyFJ9TVU7805/hC9fSevNfuGZPNZOr1tAfqGqfqt4FXAXcoqof9tY0A9iFZeOdr7hSau8sOLoxIwBbD0lHR4h1ve7K8dKJ7t9FeNla/PVNRR/LFwwTXraupD2MUzpDLvS+CMxbVHRoSGPjDD/5MHUbr0L8fjs86POnhNiKpZhmR1Mhfj/BhSvyTiEd/NU2os/9mpYbbydQ5GL9bCHXxeIHReRGEalT1UOqWt62T7OIcPsaiFuuSPK6fdfmLBi7XWGssXGiL+4tKm10MpEOu4exF7OXTFj9XSCCf07WRn5ZCba0Fa03NPL8bhIjA9Rv2gKAr6aOSMcGW9nVBayeY+APFKyrNBX5ppDGh/ro+tbniJx1IY1XfcBVW6qZXENDfwu8CdgvIv8mIu8WkYiHdhmSuKk5ZLmoBQMQTurOu71gPPrK0+j4qOuOIDEySOz4q64dczri/T3458xzpTd2oLmNeF8XidhYwccY3rMdCUWoPe/NqW016y5h9MBTJMZGirYx1u0Uk7nbCzzU1kHs5Gs5v/fue79IfLCX+bd+saQ9tSudXENDv1TVPwBWAv+ILUOdU69hEfGLyJMi8qPk87eJyBMi8pSIPCoiqwo1fjYQausAf8CVBWOrpxMJRfA3FH+XCvZdZXDBMtern51wRa2L3alOLxiXJjxk9XcVXUPg4CzAWr3HCxqvqgzt2U7teZdPkPKuWX8pWDFGX3qiaBuLlTafCkd8LnY8u/hc9KUn6P/Zt2l6x+8TWXGO67ZUM/kUlNUA7wK2ApuAb+U49A+B9CvF/w/cpKrnA/cCf56rDbMRCYbs6bEbM4LuTgLzFrnanCfUvsb1zKGR/bsILV1ddPVzOqGlZyOhSMkWjON9XfiLrCFwCKR1KiuEsVefw+ruTIWFHGrWXAw+nyvhoWKbHU1FqC3ZvzjLOoHGLU7e/ScE5i6k5f23uW5HtZPrGsH3sC/mVwJfAzpU9b/nMG4JcDV2s3sHxe5wBtAIGNGPLLilORTrdaeYLJ1w+1rGOw8WFbZIR+MW0Rf2uK4bL/4A4RXnlKyHcXygh0CRNQQOTg/gQheMh/ZsBxHqJtWi+GvnEF5+DtF9xS0YqypW7zFPZgTBtpVA9hTSvp98g7FD+2j9yOeLkv2ereQ6I/hn7Iv/VlV9OFlTkAtfBj4NpO//UeA/ReQI8EHgi5kGisitIrJXRPZ2dXXleLrqJNy+Fqu7k/hwf1HHsVzWgoFk9XMizvgRd5rUjB58Fh0d9qSvbGTV+Yy9+hwat1w/9mSsvi5XMoYgXWaiMKmR4b07iKzemLEoq3b9pYy+/ASJ8dGC7YsP9LpeTObgr52Df97CaReMYz2ddN/3JeoufBv1b/hd122YDWSTof40gKpuB66f9NpfZxl7DXBSVR+f9NIngd9V1SXAN4C/yzReVe9W1Y2qurG1dXangIWc7JwiQjAaj2P1Hnc1vQ/sFFIozrZ0oskwRc1a9ztJRTrOR8eirjmtqUiMjaCjw67UEICtl+Srb0opx+ZDrOsIY68+d0ZYyKFm3SVobKyoYju3kxAm42gOTUXXNz4LiTitv/9XFdGTfCaSbUbw/rTHk1WafifL2MuAa0XkEHAfcKWI/BjYoKq/Te5zP/DGHG2dtbgh8Bbv74JE3PXQUGjRCiQYdm3BOLpvN8G2DgJz3e+EGuk4D/C+dWU8VVXs3hpHoZ3KhvbuAJhSgrtm7RtApKjmPV7UEKRjp5AeyKgVNfTEzxna/SPmvet/EFqwzJPzzwayOQKZ4nGm5xNQ1dtVdYmqLsd2KL8ArgMaReTs5G5XMXEh2ZCBQMtifLUNRTkCLyo/wY69hxavYuxw8TMCjceJvvBbT8JCAMFFK/HVzvHcEVipYjL3ZrLB5kUFKZAO79lOsK2D0OLMyXn++ibCy9amZmKFYHn02XIItXWQGO4/Q3wuMTZC19f/J6ElZzHv2q2enHu2kM0R6BSPMz3PiqpawH8FfiAiT2OvEZgl/iyICKH21UUVbnl51xZySXNo7PA+EiODBfUnzgXx+QivPM9zzaGU4JxLawSQnBHkGRqKD/czsm/XlGEhh5p1lxJ9cW/B1eux3mMQCLr6ftNJF59Lp3fbV4mdfI35H72j6KY9s51sjmCD07QeOC/52Hl+bq4nUdVHVPWa5OMHVPVcVd2gqm9V1YNF2D9rCLevZey1FwqWUvZCFMwhvGwNVu8x4kN9RR3HyV6pdbGQbDKRjg2MHd7vWpZTJhx5CTflDQItbcQHevJa1B1+8hcQt3JyBDo+WnBGlZ2WvNCzAi5nNpNeXT925GV6//0faHjLe6g9x0SXiyVbhzK/qjao6hxVDSQfO8+D0401uEu4fQ2JkYGCG5Q4xWS++rkuW+Ze9fPI/l0EF64gMK+49o7TEenYAFaMcRdCWVNh9SVDQy7WQaSKyvKYFQw/th1/YwuRs6ZvL+4U7o0UmEZq9XSmUly9wBGfc1JIVZWT/3Q7vkgdLTf/L8/OO5swNdgVQqjIi22s26789CKrIuQsZh/eX/AxNJEg+vxj1Kx3P1sonciq8wFvF4zjA922fHS4JvvOOZKqJcjREWhsnOGnTovMTYe/oZnQ0tUFrxO41exoKsTnI7hoZSo0NLjzB0T3/YaWm/6soD4FhjMxjqBCCLfbuj6FrhNYPZ0E5nlz1xaYtxBffVNR6wTjr71AYuiUp2EhgEDrEnxz5npaWBbv63JdfO10dXFuM8KR/btIjAxOmS00mZp1lxB9cQ9qxfKySxOJpCPwtgewk0IaHzxli8qdfRGNb7vR03POJowjqBD89U0EmhcVPCOwetxtI5jO4K8eQEdH6P/Zdzi4dRMDO7flNX5g5zZe/8y7AOj67l/nPT4fRIRIx/me9jC2XGhaPxknXBbLMYV0KIPI3HTUrn8jOjrC6MFn87IrPtCDWuOeVBWno/EYseOv8sqH1xMf6KHuoquMqJyLmL9kBRFKLhjni8YtrFMnPLlrG9i5jRN33YZadsaJ1X2UE3fdlvPF3BmfSFZNx3uP5zW+ECKrNjD++ouuqG5mIt7f5VoxmYMvXItvztyc5KhVleG9O6jd8JYJInPT4Uh65BseckJVQQ9DQwM7tzH8xM8nbOv9wVc8/YzMNnLtWWyYAYTb1zDy7K9QK4YEcl+rt/pOQiLhSRy3+9470PHohG06HuXE3Z9mZN9vso4f/PUPM47vvvcOz3pORzo2QCLO2Kv7qFlTfP/mycT7u/Gvudj14wab27C6s8tMjL36LFZ3J83v/eOcjx1oaiW0eJWt/PrOj+c8zpG9CDQvznlMvnTfewdMCll5/RmZbRhHUEGEl621M16OHUz1AsiFVMGPB9P3qWLWOjpipy9mQUcz35UXmh2VCylJ6leedt0RaNwiPthbdNP6TARyLCob2rMdfD7qLroq677p1Ky71HbM8XjOfQViHn62HKZ6z15+RmYbxhFUECmpicPP5+cInGIyD0JDgSnuUgMti1l5V/Z+uAe3bso83st0xHkL8c9b6ElhWXzwFKgScEmCOp1Ay2KiL02W7jqT4T3bqTl7I4E81ylq1l9C/8++zdihfSk5jmxYPceQQMiVTmxTMeVnzOMF6tmEWSOoIIKLV4HPn3d2jpfFZC033o6EJqZJSqiGlhsnS1N5M75QIh0bPEkhdZrWu9WUJp1gcxuJwVPTrm3Euo4wdmg/dZtyyxZKx8nYymedwOrpJNC8yNOF23J9RmYTxhFUEL5gmFBbR94Cb7HuTiRSi6+u0XWbGi6/ngVb7yTQshhECLQsZsHWO3OO3RY7vlAiHRuIdb5CfHjA1eNaA+41rZ9MLkVlQ3u2A2StJs54/HkLCS5cwUgeAnReSJtPplyfkdmECQ1VGOH2NUQPPJnXGKfy0yuJ3obLry/qS1ns+EJwCsvGXn2W2nMuc+248WRVsReFToG0ojJHf2cyw3u2E1q8asrXs1Gz/hKGfvsTNJHI6S4/1nuMmtXuL7hPphyfkdmEmRFUGKFla7FOvk58ZDDnMV5XflYikZW2VJbb6wTxfg9nBMkF2dgUi6Tx4X5G9u+mroDZgEPtuktJDPUxnsOsUxMJrN7jntcQGLzHOIIKw1kwzmedINbj/fS90vA3NBOc3+56YZnV3wWBoCdhOKeobKq+BMNP/DwnkbnpcOoJcgkPxfu7wIp5qjNkKA3GEVQY+Qq8qRUjfuqEuWvLQHjVBtelJuL9XQQaWjwJw/lCEfwNzVOuEQztyU1kbjqCrUsIzF9q1xNkwcskBENpMY6gwgi0LkEidTkvGFunTtjpjB7pDFUykY4NdphtUsOTYoj393hSQ+AQaGnLmD+fiI0x8mRSZK7IDJ7adZcSfX43mpi+NblXzY4MpcdzRyAifhF5UkR+lHwuIvIFEXlJRJ4XkU94bUM1IT4f4fY1OYeGvG4jWMk4GUOvfOTcgjSSMmH1deH3oIbAIdDcllFvKLpvF4noUFFhIYeadZcQH+hl/MhL0+5nPlvVQylmBH/IxHaUHwKWAmtUdS12P2NDHoSX5d6kphSVn5XIwM5t9P3o7tTzfDWSpiI+0O1qQ5rJBJoXZdQbGtqzHQnXUHtubiJz0+F0iMvWxzjV48LDYjJDafDUEYjIEuBq4Otpmz8GfF5VEwCqetJLG6qRUPsaEkN9WL3Hs+6biuPOM3HcdGyNpIndvhz9mkJRVeJ93a4rj6YTbG4jMdRHIk2aY6LIXPE9EILz2wk0L2IkyzqB3ZlskWdpyYbS4fWM4MvAp4H0YGMH8D4R2SsiPxGRszINFJFbk/vs7erq8tjMysJZMM4lPGT1dOKrqcdf1+C1WRWFF/o1iZFB1Bp3vRdBOqf7EpyWXBg7+CxWzzFXwkJgS3XXrH8j0f27pp11xno6zUyzSvDMEYjINcBJVZ0sjhIGRlV1I/BPwL9kGq+qd6vqRlXd2Nrq3RerEjGqBV4AABMCSURBVElpDuWwYFyKys9KZKq/STF/K6dpvZddsxz7YmmZQ0N7fmqLzF34dtfOU7vuEuL93an2kJmweo6ZmWaV4OWM4DLgWhE5hL0OcKWIfAc4AjiB2AeA3NStDCn8c+bin7eQsRz67sZ6TTFZJrzQr/GymMwh1bIybcF4aM+OgkTmpsNZJ5iqj7HG41i9x81CcZXgmSNQ1dtVdYmqLgfeD/xCVT8A/BC4IrnbW4DpUxMMGbEzh3KcEZgv6xlM0K8B8AeK1q+xSuAIUkVlyRBW7OTrjB/eX1Q1cSaCC1fgn7tgSgE6u8dF3Mw2q4Ry1BF8EXiXiDwL3AF8tAw2VDzh9jWMHz2Axq0p99HYOPH+LlP5OQUNl1/Pyrv20PqRv4S4RWTVhqKO58wIvMwakmAIf1NrKgkgJTJ3sbuOQESoXXcJI/t3Z1wnMMVk1UVJHIGqPqKq1yQf96nq1ap6rqpeqqruawHPAsLta9HYGOPHXp1yH6v3uF1MZhzBtDiLrM5FtVAsR4La43TK9FqCoT07CC05i9Cila6fp2bdpcR7jxM7fuiM10wNQXVhKosrlFBKc2jq8FDM3LXlRLB1CeHl64t2BPGBHnxz5ubVRrQQgs12dXF8qI/o/l2uh4UcUvUEGcJDlqkqriqMI6hQQkvOAp9/2gXjVD/ZFu/6yVYLdZu2MPri3lScvxDife43rc+E3bLyGMNP/AIScdfSRicTWrwKf2NLxgVjq/eYXUxW3+TJuQ2lxTiCCsUXihBatGLaFFLnri1oZgRZqd+0BVQZfvyhgo8R7+/2dKHYIdDSRmJkgIGdP8Df1Epk1QWenEdEqFl7ScYZQSyZhGCKyaoD4wgqmFD72mmLyqzeY/hqG/DV1JfQqsokvOIcAi1tRYWHrP5uT2sIHJxwzMhTD1N3UfEic9NRs/4SrO6jxE6+PmG70+zIUB0YR1DBhNvXEDtxmER0OOPrMZM6mjMiQt3GzYw8/ctpewJPR6lmBOlicMN7trsiljcVTh/jkUmzAsv0uKgqjCOoYMLLkhXGr7+Y8XXzZc2P+k1b0PFRRp75Vd5jE+OjJEYGPGlan87Azm2cevCu1PP4QI8rYnlTEVq6Gl/93AkCdBq3sE6dMJ+tKsI4ggomlNIcyrxOYPUcM+sDeVC77lJ8tXMKCg85PQ28lKAGb8TypkN8PmrWvWFCoxrr1AlIJMxss4owjqCCCc5vRyK1GbuVJWJjxPu7zV1bHkgwRN0FVzK892doPJ7X2FTTeg+b0oA3YnnZqF13KbETh4l1H02ey6QlVxvGEVQw4vMRXrI6oyNIfVnNXVte1G3aQnygh9GXn8hrnJUUnPN6jcALsbxsOH2MnVlBqpjM3GRUDcYRVDihZbbm0GQZAHPXVhh1F1wB/kDe4aGUvITHdQReiOVlI7xsHb66xlRDe9PsqPowjqDCCbevJT7QS7xvYs8Gc9dWGP66RmrXX1qAIyjNjGCCWJ4IgZbFRYvlZUP8fmrWXpw2IziGRGrx1ZoeF9VCoNwGGIoj1Zvg8H4Cc+enthsJgMKp27SFrn/+c8aPHiC0eFVOY6z+HvviGKn12DrbGXh54c9EzbpLGd77M6xTJ1I1BKaYrHowM4IKx8kcmrxOEOvpxFffVJILU7VRv3EzkJ8IXbyvi4DHGUPlJFVPsG+XaXZUhRhHUOEEGpvxN80/o8LY1BAUTrB1CeEV5zC0d0fOY+ID3Z7XEJST8Ir1+Grqie7fbZodVSHGEVQB4fY1Z2gOWd1GAqAY6vMUobP6uvE3eNe0vtyIP0BkzcWMPPso8VMnzEJxlWEcQRUQXraW8SMvT8h9t8xdW1HUbdxsi9Dt/VlO+8cHuj1tSDMTqF13CbFjB0HV3GRUGZ47AhHxi8iTIvKjSdv/XkSGvD7/bCDUvgYdHyV23G5SkxiLEh/oNXdtRWCL0C3OaZ1A43HiAz0l0RkqJ4nxsdTj7nv/t6caR4bSUooZwR8CE+IWIrIRmFuCc88KwpMWjK1eu4bA3LUVjohQv2kzI8/szCpCFx/qg0Siqh3BwM5tnPr3f0g9jw90e6pxZCgtnjoCEVkCXA18PW2bH7gT+LSX555N2E1qfKl1AlNM5g51jgjd0zun3c+pISiFBHW5sDWOohO2ealxZCgtXs8Ivox9wU+kbfv/gAdV9dh0A0XkVhHZKyJ7u7q6ptt11uML1xBcuJzxZLcyy1R+uoItQteQNXvIqSr2l6A7Wbkoh8aRoXR45ghE5BrgpKo+nratDXgP8NVs41X1blXdqKobW1ur9wvmFuH2tanQUCz55QzMMzOCYpBAkLoLs4vQlUpnqJyUQ+PIUDq8nBFcBlwrIoeA+4ArgX3AKuBAcnutiBzw0IZZg92k5hCJ0RGsnmP45szFF67JPtAwLXUbNydF6B6fcp94vy1B7bXyaDkph8aRoXR45ghU9XZVXaKqy4H3A79Q1bmqulBVlye3j6hqbjX8hmkJta8FVcaPvGRqCFyk7oIrIRCcNnso3tcFPj++uupt5F4OjSND6TBaQ1VCqlvZ4eeJ9XQSbF1cZouqA39dA7XrbBG61g/+r4z7WAN2i0ovewfPBMqhcWQoDSX55KrqI6p6TYbtpqu6SwTnL0NCEcZeewGr55iJ3bpI/aYtxDoPMn705Yyvx/u6qjpjyFD9VPctzCxC/H5CS1cz+vITJIZOmdCQi9RtckToMmcPxfurv5jMUN0YR1BFhNvXMHrgScCkjrpJsGUx4ZXnTrlOYPV3VXXqqKH6MY6gigi3r4WEXbJhUkfdpX7jZkZfehxrUgMgVbV7QzdWr+CcofoxjqCKCCUXjMHMCNymbtMWW4Tu8YkidDo6jI6PVrUEtaH6MY6gihjvPJh6fOSz7zY6MC4SXr6eQOuSM8JDzgzBrBEYKhnjCKqEgZ3b6L7nL1PPre5OIwrmIiJC/cbNjDzzKxKjp0XoStW03mDwEuMIqgQjCuY99Y4I3TOnReislM6QWSMwVC7GEVQJRhTMe2rWXYKvrnFCeGg2CM4Zqh/jCKoEIwrmPRIIUnfBlQw//lBKhC4lQV3FbSoN1Y9xBFWCEQUrDfWbkiJ0L+0F7NCQr74JCYbKbJnBUDjGEVQJRhSsNNROEqGLV3nTesPswIjOVRFGFMx7/LVzqF3/Rob27KDlg/9rVjStN1Q/ZkZgMORJ/aYtxI4dJNZ5AKuvC3+DqSEwVDbGERgMeZISoXtsO/GBHvxV3JDGMDswjsBgyJNgcxvhlecxuOtHJIb6jAS1oeIxjsBgKID6TZsZO/gMYGoIDJWP545ARPwi8qSI/Cj5/Lsi8qKIPCci/yIiQa9tMBhcx3c6z6L7vi8ZKQ9DRVOKGcEfAs+nPf8usAY4F6gBPloCGwwG1xjYuY3eH3wl9Twx0GN0nQwVjaeOQESWAFcDX3e2qep/ahLgMWCJlzYYDG5jdJ0M1YbXM4IvA58GEpNfSIaEPgj8NNNAEblVRPaKyN6urq5MuxgMZcHoOhmqDc8cgYhcA5xU1cen2OUfgJ2q+qtML6rq3aq6UVU3traaxTjDzMHoOhmqDS9nBJcB14rIIeA+4EoR+Q6AiHwGaAU+5eH5DQZPMLpOhmrDM0egqrer6hJVXQ68H/iFqn5ARD4KbAFuUNUzQkYGw0zH6DoZqo1yaA3dBRwGdokIwDZV/XwZ7DAYCsboOhmqiZI4AlV9BHgk+dgI3RkMBsMMwlQWGwwGwyzHOAKDwWCY5RhHYDAYDLMc4wgMBoNhliO20sPMRkS6sDONCqEF6HbRnErAvOfZgXnPs4Ni3vMyVc1akVsRjqAYRGSvqm4stx2lxLzn2YF5z7ODUrxnExoyGAyGWY5xBAaDwTDLmQ2O4O5yG1AGzHueHZj3PDv4f+2dfYwdZRWHn59AoaWFLV1RKNotpQ1WQiqoaUDb+pEGS0KLIKEByqIhRisfRioa4hchQtM/NKiJgqnFhpaPFXQ1SKm6pbFsC7Uf25Yi1NJogaRNxYZKRKDHP96zOL3sbmeXuXd67z1PMrln5n3vO78zM3fOzDtzz1t1nxv+GUEQBEEwMM1wRxAEQRAMQASCIAiCJqdhAoGkCyT9VdIOSd/oo7xd0l5Jm3yq+7GSD+ez17lM0tOStklaVmuNRZNjP/8gs4+flfSvMnQWSQ6f3y+pS9JGST2SZpWhsyhy+DtO0h/d11U+JG5dI2mxpD2StvZTLkl3+jbpkXROoQLMrO4n4Cjgb8DpwDBgMzC5ok478OOytdbY54nARmC0z59ctu5q+1xR/zpgcdm6a7Cf7wK+5PZkYFfZuqvs74PA1W5/Elhatu4C/J4GnANs7ad8FvB7QMBUYF2R62+UO4KPAjvMbKeZ/Zc0ItrskjVVmzw+Xwv8xMxeBjCzPTXWWDSD3c9zgeU1UVY98vhswAlunwjU8+DJefydDPzJ7a4+yusOM1sN/HOAKrOBX1piLdAi6ZSi1t8ogWAs8I/M/G5fVsklflvVIel9tZFWNfL4PAmYJGmNpLWSLqiZuuqQdz8jaRwwnv+fMOqVPD5/F7hS0m7gEdKdUL2Sx9/NQO+oQBcDoySNqYG2Msl97A+FRgkEefgt0GZmZwMrgXtK1lMLjiZ1D80gXR3fLamlVEW143Kgw8zeLFtIDZgLLDGz00hdCEslNfJv+yZguqSNwHTgBaAZ9nPVaJSD5QUge4V/mi97CzPbZ2av+ezPgXNrpK1aHNZn0lVDp5m9bmbPA8+SAkO9ksfnXi6n/ruFIJ/PXwAeADCzbuA4UqKyeiTPb/lFM/usmX0IuMWX1f1LAYdhMMf+oGmUQPAUMFHSeEnDSCeBzmyFiv60i4DtNdRXDQ7rM/Br0t0AklpJXUU7aymyYPL4jKQzgdFAd431VYM8Pv8d+BSApA+QAsHemqosjjy/5dbMHc83gcU11lgGncA8f3toKrDfzF4qqvGGGD/YzN6Q9BVgBemtg8Vmtk3SrcB6M+sErpd0EfAG6aFMe2mCCyCnzyuAmZKeJt06LzCzfeWpfmfk9BnSyeM+89ct6pmcPn+N1O33VdKD4/Z69T2nvzOA2yUZsBqYX5rggpC0nORXqz/r+Q5wDICZ/ZT07GcWsAN4Fbim0PXX6fESBEEQFESjdA0FQRAEQyQCQRAEQZMTgSAIgqDJiUAQBEHQ5EQgCIIgaHIiEASlIOlAjjo3ShpR4DrnSJpcYHtPvIPvHvDPUyV1DFCvRdKXh7qeIMhDBILgSOZGYFCBQNJRAxTPISUsKwQzO6+ANl40s0sHqNICRCAIqkoEgqBUJM3wnPIdkp6RdK//e/J64FSgS1KX150pqVvSBkkPShrpy3dJWihpA/A5SddKekrSZkm/kjRC0nmkf5Qv8rEKJkia4sn4eiQ9LGm0t7dKaVyD9ZK2S/qIpIckPSfptoz2Axn7ZklbfJ139OHneNe+paKNtt4c9JI+KOlJ19cjaSJwBzDBly2SNFIpF/8Gb2t2pp3tku5WGnviMUnDvewMSX9wbRskTfDlC3w79Uj6XqE7Nqgvys7DHVNzTsAB/5wB7CflTnkXKS3Ex7xsF9DqdivpX6TH+/zNwLcz9b6eaXtMxr4NuM7tJcClmbIeYLrbtwI/dHsVsNDtG0hpnU8BjiXlbxpT4cNngCeAET5/Uh/+dgLz3J6f+W4bnoMe+BFwhdvDgOHZcl9+NHBCZpvsIOWobyP9a36Klz0AXOn2OuBit48j3WXNJI1jIN/uvwOmlX1cxFTO1BApJoK650kz2w0gaRPppPbnijpTSd06ayRBOlFmcwndn7HP8qvuFmAkKV3BIUg6EWgxs8d90T2kAU966U1XsQXYZp7XRdJOUvKvbKqOTwO/MLNXAcysr7zy5wOXuL0UWNhHnW7gFqURtx4ys+fc10OkA9+XNA04SEpF/B4ve97MNrn9F6BN0ihgrJk97Nr+437MJAWDjV5/JCkh4eo+dAUNTgSC4EjgtYz9Jn0flwJWmtncftr4d8ZeAswxs82S2vHEe0PUdLBC38F+9OVhwHwuZrZM0jrgQuARSV/k7UkCrwDeDZxrZq9L2kW6ys9qhrQdhw+wOgG3m9nPBqE/aFDiGUFwJPMKMMrttcD5ks4AkHS8pEn9fG8U8JKkY0gnzre1Z2b7gZclfdzLrgIeZ2isBK7pfcNJ0kl91FlDSoZHhaa3kHQ6sNPM7gR+A5zNodsA0ghkezwIfAIYN5AwM3sF2C1pjq/jWNe5Avh85jnLWEkn5/I2aDgiEARHMncBj0rqMrO9pIyxyyX1kLpRzuzne98i9YuvAZ7JLL8PWKA0yPsE4GrSw+MeYArpOcGgMbNHSV1J671r66Y+qt0AzJe0hf5HlroM2OptnEUamnAfqTtsq6RFwL3Ah72deRX+9cdVpOy7PaRnGe81s8eAZUC3t9XBoQEnaCIi+2gQBEGTE3cEQRAETU4EgiAIgiYnAkEQBEGTE4EgCIKgyYlAEARB0OREIAiCIGhyIhAEQRA0Of8DiHmR8xihiWcAAAAASUVORK5CYII=\n", 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\n", "text/plain": [ - "" + "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -222,7 +234,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.6.7" } }, "nbformat": 4, From 9e7bc3e38cc45b34d53c1669d8898d41e4504eab Mon Sep 17 00:00:00 2001 From: Manoel Marques Date: Sat, 23 Feb 2019 11:09:04 -0500 Subject: [PATCH 012/116] Update ExactEigensolver valid dictionaries --- community/aqua/chemistry/h2_mappings.ipynb | 137 +++-------------- .../aqua/chemistry/h2_particle_hole.ipynb | 129 +++------------- community/aqua/chemistry/h2_swaprz.ipynb | 107 +++---------- community/aqua/chemistry/h2_var_forms.ipynb | 84 ++-------- .../aqua/chemistry/h2_vqe_initial_point.ipynb | 118 +++----------- community/aqua/chemistry/lih_uccsd.ipynb | 132 +++------------- community/aqua/chemistry/nah_uccsd.ipynb | 144 +++--------------- 7 files changed, 126 insertions(+), 725 deletions(-) diff --git a/community/aqua/chemistry/h2_mappings.ipynb b/community/aqua/chemistry/h2_mappings.ipynb index 9d4db6934..6a3a3ad6c 100644 --- a/community/aqua/chemistry/h2_mappings.ipynb +++ b/community/aqua/chemistry/h2_mappings.ipynb @@ -17,52 +17,14 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": null, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Processing step 20 --- complete\n", - "Distances: [0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.675 0.7 0.725 0.75 0.775\n", - " 0.8 0.825 0.85 0.875 0.9 0.925 0.95 0.975 1. ]\n", - "Energies: [[[-1.05500736 -1.07447588 -1.09246402 -1.10560676 -1.11617529\n", - " -1.12411244 -1.12989941 -1.13377935 -1.1361881 -1.13718163\n", - " -1.13692659 -1.11393966 -1.13359243 -1.10702389 -1.10251128\n", - " -1.09745562 -1.11702035 -1.08595587 -1.09201117 -1.10586236\n", - " -1.10113428]\n", - " [-1.05515979 -1.07591366 -1.09262991 -1.10591805 -1.11628601\n", - " -1.12416092 -1.12990478 -1.13382622 -1.13618945 -1.13722138\n", - " -1.13711707 -1.13604436 -1.13414767 -1.13155121 -1.12836188\n", - " -1.12467175 -1.12056028 -1.11609624 -1.11133942 -1.10634211\n", - " -1.10115033]]\n", - "\n", - " [[-1.05515979 -1.07591366 -1.09262991 -1.10591805 -1.11628601\n", - " -1.12416092 -1.12990478 -1.13382621 -1.13618944 -1.13720887\n", - " -1.13709532 -1.13602101 -1.13411462 -1.13150623 -1.12831803\n", - " -1.12464048 -1.12052035 -1.11605108 -1.11130129 -1.10631433\n", - " -1.10113126]\n", - " [-1.05515979 -1.07591366 -1.09262991 -1.10591805 -1.11628601\n", - " -1.12416092 -1.12990478 -1.13382622 -1.13618945 -1.13722138\n", - " -1.13711707 -1.13604436 -1.13414767 -1.13155121 -1.12836188\n", - " -1.12467175 -1.12056028 -1.11609624 -1.11133942 -1.10634211\n", - " -1.10115033]]\n", - "\n", - " [[-1.05456417 -1.07579293 -1.09245928 -1.10580546 -1.11600146\n", - " -1.1239087 -1.12915555 -1.13218011 -1.13590305 -1.13719849\n", - " -1.13674886 -1.13514256 -1.13334844 -1.13069428 -1.12796707\n", - " -1.12444893 -1.12027861 -1.11593003 -1.1113173 -1.10626115\n", - " -1.10100374]\n", - " [-1.05515979 -1.07591366 -1.09262991 -1.10591805 -1.11628601\n", - " -1.12416092 -1.12990478 -1.13382622 -1.13618945 -1.13722138\n", - " -1.13711707 -1.13604436 -1.13414767 -1.13155121 -1.12836188\n", - " -1.12467175 -1.12056028 -1.11609624 -1.11133942 -1.10634211\n", - " -1.10115033]]]\n", - "Hartree-Fock energies: [-1.04299627 -1.06306214 -1.07905074 -1.0915705 -1.10112824 -1.10814999\n", - " -1.11299655 -1.11597526 -1.11734903 -1.11734327 -1.11615145 -1.11393966\n", - " -1.1108504 -1.10700581 -1.10251055 -1.09745432 -1.09191404 -1.08595587\n", - " -1.07963693 -1.07300676 -1.06610865]\n" + "Processing step __\b\b 0" ] } ], @@ -77,9 +39,7 @@ " 'driver': {'name': 'PYSCF'},\n", " 'PYSCF': {'atom': '', 'basis': 'sto3g'},\n", " 'operator': {'name': 'hamiltonian', 'qubit_mapping': '', 'two_qubit_reduction': False},\n", - " 'algorithm': {'name': ''},\n", - " 'optimizer': {'name': 'L_BFGS_B', 'maxfun': 2500},\n", - " 'variational_form': {'name': 'RYRZ', 'depth': 5}\n", + " 'algorithm': {'name': ''}\n", "}\n", "molecule = 'H .0 .0 -{0}; H .0 .0 {0}'\n", "\n", @@ -99,6 +59,15 @@ " qiskit_chemistry_dict['PYSCF']['atom'] = molecule.format(d/2) \n", " for j in range(len(algorithms)):\n", " qiskit_chemistry_dict['algorithm']['name'] = algorithms[j] \n", + " if algorithms[j] == 'ExactEigensolver':\n", + " if 'optimizer' in qiskit_chemistry_dict:\n", + " del qiskit_chemistry_dict['optimizer']\n", + " if 'variational_form' in qiskit_chemistry_dict:\n", + " del qiskit_chemistry_dict['variational_form']\n", + " else:\n", + " qiskit_chemistry_dict['optimizer'] = {'name': 'L_BFGS_B', 'maxfun': 2500}\n", + " qiskit_chemistry_dict['variational_form'] = {'name': 'RYRZ', 'depth': 5}\n", + " \n", " for k in range(len(mappings)):\n", " qiskit_chemistry_dict['operator']['qubit_mapping'] = mappings[k] \n", " solver = QiskitChemistry()\n", @@ -115,20 +84,9 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "pylab.rcParams['figure.figsize'] = (6, 4)\n", "for k in range(len(mappings)):\n", @@ -256,7 +153,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.6.7" } }, "nbformat": 4, diff --git a/community/aqua/chemistry/h2_particle_hole.ipynb b/community/aqua/chemistry/h2_particle_hole.ipynb index b7b44864e..b130f635a 100644 --- a/community/aqua/chemistry/h2_particle_hole.ipynb +++ b/community/aqua/chemistry/h2_particle_hole.ipynb @@ -15,7 +15,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": null, "metadata": { "scrolled": true }, @@ -24,38 +24,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Processing step 20 --- complete\n", - "Distances: [0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.675 0.7 0.725 0.75 0.775\n", - " 0.8 0.825 0.85 0.875 0.9 0.925 0.95 0.975 1. ]\n", - "Energies: [[[-1.05515972 -1.0759136 -1.09262986 -1.105918 -1.11628597\n", - " -1.12416087 -1.12990475 -1.13382619 -1.13618942 -1.13722134\n", - " -1.13711706 -1.13604434 -1.13414766 -1.13155119 -1.12836187\n", - " -1.12467174 -1.12056027 -1.11609624 -1.11133942 -1.10634211\n", - " -1.10115033]\n", - " [-1.05515974 -1.07591361 -1.09262987 -1.10591802 -1.11628599\n", - " -1.12416089 -1.12990476 -1.1338262 -1.13618944 -1.13722136\n", - " -1.13711707 -1.13604436 -1.13414767 -1.13155121 -1.12836188\n", - " -1.12467175 -1.12056028 -1.11609624 -1.11133943 -1.10634212\n", - " -1.10115034]]\n", - "\n", - " [[-1.05515973 -1.07591359 -1.09262986 -1.105918 -1.11628597\n", - " -1.12416089 -1.12990475 -1.13382616 -1.13618942 -1.13722135\n", - " -1.13711706 -1.13604434 -1.13414766 -1.1315512 -1.12836188\n", - " -1.12467174 -1.12056028 -1.11609624 -1.11133942 -1.10634211\n", - " -1.10115033]\n", - " [-1.05515974 -1.07591361 -1.09262987 -1.10591802 -1.11628599\n", - " -1.12416089 -1.12990476 -1.1338262 -1.13618944 -1.13722136\n", - " -1.13711707 -1.13604436 -1.13414767 -1.13155121 -1.12836188\n", - " -1.12467175 -1.12056028 -1.11609624 -1.11133943 -1.10634212\n", - " -1.10115034]]]\n", - "Hartree-Fock energies: [-1.04299622 -1.0630621 -1.0790507 -1.09157046 -1.10112822 -1.10814997\n", - " -1.11299652 -1.11597525 -1.11734902 -1.11734325 -1.11615145 -1.11393966\n", - " -1.1108504 -1.10700581 -1.10251056 -1.09745432 -1.09191405 -1.08595588\n", - " -1.07963694 -1.07300677 -1.06610866]\n", - "VQE num evaluations: [[50. 53. 56. 50. 43. 52. 51. 45. 51. 46. 42. 57. 45. 49. 48. 50. 50. 52.\n", - " 51. 56. 60.]\n", - " [49. 49. 56. 50. 43. 51. 49. 45. 61. 46. 43. 57. 45. 47. 44. 50. 53. 49.\n", - " 54. 56. 55.]]\n" + "Processing step 9" ] } ], @@ -71,10 +40,7 @@ " 'PYQUANTE': {'atoms': '', 'basis': 'sto3g'},\n", " 'operator': {'name': 'hamiltonian', 'qubit_mapping': 'jordan_wigner',\n", " 'two_qubit_reduction': False},\n", - " 'algorithm': {'name': ''},\n", - " 'optimizer': {'name': 'COBYLA', 'maxiter': 10000 },\n", - " 'variational_form': {'name': 'UCCSD'},\n", - " 'initial_state': {'name': 'HartreeFock'}\n", + " 'algorithm': {'name': ''}\n", "}\n", "molecule = 'H .0 .0 -{0}; H .0 .0 {0}'\n", "algorithms = ['VQE', 'ExactEigensolver']\n", @@ -95,6 +61,18 @@ " qiskit_chemistry_dict['PYQUANTE']['atoms'] = molecule.format(d/2) \n", " for j in range(len(algorithms)):\n", " qiskit_chemistry_dict['algorithm']['name'] = algorithms[j] \n", + " if algorithms[j] == 'ExactEigensolver':\n", + " if 'optimizer' in qiskit_chemistry_dict:\n", + " del qiskit_chemistry_dict['optimizer']\n", + " if 'variational_form' in qiskit_chemistry_dict:\n", + " del qiskit_chemistry_dict['variational_form']\n", + " if 'initial_state' in qiskit_chemistry_dict:\n", + " del qiskit_chemistry_dict['initial_state']\n", + " else:\n", + " qiskit_chemistry_dict['optimizer'] = {'name': 'COBYLA', 'maxiter': 10000 }\n", + " qiskit_chemistry_dict['variational_form'] = {'name': 'UCCSD'}\n", + " qiskit_chemistry_dict['initial_state'] = {'name': 'HartreeFock'}\n", + " \n", " for k in range(len(transformations)):\n", " qiskit_chemistry_dict['operator']['transformation'] = transformations[k] \n", " solver = QiskitChemistry()\n", @@ -114,30 +92,9 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 2, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "pylab.plot(distances, hf_energies, label='Hartree-Fock')\n", "for j in range(len(algorithms)):\n", @@ -151,30 +108,9 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 18, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "pylab.plot(distances, np.subtract(hf_energies, energies[0][1]), label='Hartree-Fock')\n", "for k in range(len(transformations)):\n", @@ -187,30 +123,9 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 12, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "for k in range(len(transformations)):\n", " pylab.plot(distances, eval_counts[k], '-o', label='VQE + ' + transformations[k])\n", @@ -244,7 +159,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.6.7" } }, "nbformat": 4, diff --git a/community/aqua/chemistry/h2_swaprz.ipynb b/community/aqua/chemistry/h2_swaprz.ipynb index 8bbd7eccd..da46c7db6 100644 --- a/community/aqua/chemistry/h2_swaprz.ipynb +++ b/community/aqua/chemistry/h2_swaprz.ipynb @@ -15,7 +15,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": null, "metadata": { "scrolled": true }, @@ -24,29 +24,14 @@ "name": "stdout", "output_type": "stream", "text": [ - "Processing step 20 --- complete\n", - "Distances: [0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.675 0.7 0.725 0.75 0.775\n", - " 0.8 0.825 0.85 0.875 0.9 0.925 0.95 0.975 1. ]\n", - "Energies: [[-1.05515973 -1.07591361 -1.09262987 -1.10591801 -1.11628597 -1.12416089\n", - " -1.12990475 -1.1338262 -1.13618943 -1.13722136 -1.13711706 -1.13604435\n", - " -1.13414767 -1.1315512 -1.12836188 -1.12467173 -1.12056028 -1.11609624\n", - " -1.11133942 -1.10634211 -1.10115033]\n", - " [-1.05515974 -1.07591361 -1.09262987 -1.10591802 -1.11628599 -1.12416089\n", - " -1.12990476 -1.1338262 -1.13618944 -1.13722136 -1.13711707 -1.13604436\n", - " -1.13414767 -1.13155121 -1.12836188 -1.12467175 -1.12056028 -1.11609624\n", - " -1.11133943 -1.10634212 -1.10115034]]\n", - "Hartree-Fock energies: [-1.04299622 -1.0630621 -1.0790507 -1.09157046 -1.10112822 -1.10814997\n", - " -1.11299652 -1.11597525 -1.11734902 -1.11734325 -1.11615145 -1.11393966\n", - " -1.1108504 -1.10700581 -1.10251056 -1.09745432 -1.09191405 -1.08595588\n", - " -1.07963694 -1.07300677 -1.06610866]\n", - "VQE num evaluations: [ 685. 687. 707. 717. 666. 755. 828. 668. 750. 786. 645. 875.\n", - " 649. 788. 832. 2379. 938. 875. 816. 917. 757.]\n" + "Processing step __\b\b 0" ] } ], "source": [ "import numpy as np\n", "import pylab\n", + "import copy\n", "from qiskit.chemistry import QiskitChemistry\n", "\n", "# Input dictionary to configure qiskit chemistry for the chemistry problem.\n", @@ -78,9 +63,14 @@ " d = start + i*by/steps\n", " qiskit_chemistry_dict['PYQUANTE']['atoms'] = molecule.format(d/2) \n", " for j in range(len(algorithms)):\n", - " qiskit_chemistry_dict['algorithm']['name'] = algorithms[j] \n", + " dict = copy.deepcopy(qiskit_chemistry_dict)\n", + " dict['algorithm']['name'] = algorithms[j]\n", + " if algorithms[j] == 'ExactEigensolver':\n", + " del dict['optimizer']\n", + " del dict['variational_form']\n", + " del dict['initial_state']\n", " solver = QiskitChemistry()\n", - " result = solver.run(qiskit_chemistry_dict)\n", + " result = solver.run(dict)\n", " energies[j][i] = result['energy']\n", " hf_energies[i] = result['hf_energy']\n", " if algorithms[j] == 'VQE':\n", @@ -96,30 +86,9 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 2, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "pylab.plot(distances, hf_energies, label='Hartree-Fock')\n", "for j in range(len(algorithms)):\n", @@ -132,30 +101,9 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 3, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "pylab.plot(distances, np.subtract(hf_energies, energies[1]), label='Hartree-Fock')\n", "pylab.plot(distances, np.subtract(energies[0], energies[1]), label='VQE')\n", @@ -168,30 +116,9 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "pylab.plot(distances, eval_counts, '-o', color=[0.8500, 0.3250, 0.0980], label='VQE')\n", "pylab.xlabel('Interatomic distance')\n", @@ -224,7 +151,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.6.7" } }, "nbformat": 4, diff --git a/community/aqua/chemistry/h2_var_forms.ipynb b/community/aqua/chemistry/h2_var_forms.ipynb index 0d87d7d13..9f5aefd11 100644 --- a/community/aqua/chemistry/h2_var_forms.ipynb +++ b/community/aqua/chemistry/h2_var_forms.ipynb @@ -22,8 +22,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "Hartree-Fock energy: -1.1173432691225829\n", - "FCI energy: -1.1372213770723043\n" + "Hartree-Fock energy: -1.1173432691225826\n", + "FCI energy: -1.1372213770723034\n" ] } ], @@ -39,10 +39,7 @@ " 'PYSCF': {'atom': 'H .0 .0 -0.3625; H .0 .0 0.3625', 'basis': 'sto3g'},\n", " 'operator': {'name': 'hamiltonian', 'qubit_mapping': 'jordan_wigner',\n", " 'two_qubit_reduction': False},\n", - " 'algorithm': {'name': 'ExactEigensolver'},\n", - " 'optimizer': {'name': 'COBYLA', 'maxiter': 10000 },\n", - " 'variational_form': {'name': 'RYRZ', 'depth': 3, 'entanglement': 'full'},\n", - " 'initial_state': {'name': 'ZERO'}\n", + " 'algorithm': {'name': 'ExactEigensolver'}\n", "}\n", "var_forms = ['RYRZ', 'RY']\n", "entanglements = ['full', 'linear']\n", @@ -70,7 +67,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": { "scrolled": true }, @@ -79,27 +76,16 @@ "name": "stdout", "output_type": "stream", "text": [ - "Processing step 7 --- complete\n", - "Depths: [3, 4, 5, 6, 7, 8, 9, 10]\n", - "Energies: [[[-1.11734327 -1.13697842 -1.13720129 -1.13719983 -1.13722136\n", - " -1.13722136 -1.13722135 -1.13722137]\n", - " [-1.1372213 -1.13721845 -1.13722128 -1.13714447 -1.13715117\n", - " -1.13710957 -1.13721905 -1.13717202]]\n", - "\n", - " [[-1.13722043 -1.13722129 -1.13722093 -1.1372209 -1.13722136\n", - " -1.13722136 -1.13722137 -1.13722137]\n", - " [-1.13722134 -1.13722138 -1.13722136 -1.13722137 -1.13722137\n", - " -1.13722137 -1.13722137 -1.13722137]]]\n", - "Num evaluations: [[[ 770. 10000. 10000. 10000. 4018. 2982. 3503. 3571.]\n", - " [ 5668. 10000. 4820. 10000. 10000. 10000. 10000. 10000.]]\n", - "\n", - " [[ 7196. 2785. 4062. 5296. 1744. 2008. 1127. 1219.]\n", - " [ 1125. 380. 1105. 794. 952. 914. 706. 829.]]]\n" + "Processing step __\b\b 0" ] } ], "source": [ "qiskit_chemistry_dict['algorithm']['name'] = 'VQE' \n", + "qiskit_chemistry_dict['optimizer'] = {'name': 'COBYLA', 'maxiter': 10000 }\n", + "qiskit_chemistry_dict['variational_form'] = {'name': 'RYRZ', 'depth': 3, 'entanglement': 'full'}\n", + "qiskit_chemistry_dict['initial_state'] = {'name': 'ZERO'}\n", + " \n", "print('Processing step __', end='')\n", "for i, d in enumerate(depths):\n", " print('\\b\\b{:2d}'.format(i), end='', flush=True)\n", @@ -121,30 +107,9 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 3, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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rV1atWpWh/FyNaXEkQaPyBRnevjor9p3lq+UH3C2OwWBII1FRUQQHB1OsWDHOnDnDww8/fOtYiRIlaN68OYMGDbojTWhoKMHBwRQtWpTixYtTu3btW8fi4uLo1asXH3zwAcktMN61a9etcZBx48YxfPjwW/sRERHOOVE3kSlaHCLSEWgL5AEmKqX+cnaZve8ty67wS4xZeYjqJfLSumYxZxdpMHgd9rYMHE3CGMf169dp1aoVY8eO5YUXXrh13MfHBx+fO7+bE8Y4zp8/zwMPPMCCBQvo0KEDAB9++CHFixfnmWeeSbbMWrVqERISAugxjqCgIPr06WOXvH5+fsTHx9/a9/RV905vcYjIJBE5KyK7E4W3FpH9InJIRN5IKQ+l1Dyl1ABgIPC4M+W1kY8POtakTul8/G9WCAfPXHFFsQaDwYHkyJGDMWPG8PnnnxMbG2tXmkKFCjF69Gg++ugjADZu3MjkyZMZP9557uXLli3Lnj17uHHjBpGRkaxYscJpZTkCV3RVTQZa2waIiC8wFmgDVAd6iEh1EaklIosSbUVskr5jpXMJgf6+/NCrPtkD/BgwdSuXosxgucGQ2ahbty61a9dm5syZdqfp2LEj169fZ+3atbz77rtcv36dZs2a3TEtNzQ01GEyli5dmu7du1OzZk26d+9O3bp1HZa3M3CJrSoRCQIWKaVqWvv3ASOUUq2s/TcBlFIfJZNegNHAMqXU8tTKc7Stqq1hF+jx40YeqFiIiU/fg68ZLDcYkmXv3r1Uq1bN3WIYUiGp++TptqpKAsdt9sOtsOQYCrQEuorIwKQiiMizIrJVRLaeO3fOcZICDYIKMKJDDVbtP8fnf+13aN4Gg8GQ2cgUg+NKqTHAmFTijBeRU0D7gICA+o6WoWejsuw+cYnvVoVSo0Re2tYu7ugiDAaDIVPgrhbHCaC0zX4pK8yjGdGhBvXK5OPV2TvYd9qxc9MNBoMhs+AuxbEFqCQi5UQkAHgCWJDRTJ3tOjabny/jetUnd6Afz07dRuT1m04px2AwGDwZV0zHnQlsAKqISLiI9FNKxQJDgKXAXmCWUuo/B5SVISOH9lAkTyDjetfn9KVohs78l7h473OEZTAYDCnhdMWhlOqhlCqulPJXSpVSSk20whcrpSorpSoopUY6qCyntjgSqFcmP+8/VoO1B8/zydJ9Ti3LYDAYPA2vMjniihZHAk80LEOve8vww+rDLNhx0unlGQwG+8kMZtVtzaU/+uijREZGZig/V+JVisNVLY4EhrerwT1B+Xltzg6HG3IzGAzpJzOYVbdl8eLF5MuXL0PnnBL2rpq3F69SHK5scQAE+Pkwtmc98mUP4NlpW7lwzQyWGwyehieaVU9MgoOmsLAwqlWrxoABA6hRowaPPPLILSdPoaGhtG7dmvr169OkSRP27dPd5AsXLqRRo0bUrVuXli1bcuaMdkQ3YsQIevfuzQMPPJCkFeCMkCnWcdiLUmohsLBBgwYDXFVmkdyB/NC7Pt1+2MCQn7cztW9D/Hy9Sh8bDOlnyRtwelfq8dJCsVrQZrRdUT3VrHpKHDx4kJkzZ/Ljjz/SvXt35s6dS69evXj22WcZN24clSpVYtOmTQwePJiVK1fSuHFjNm7ciIgwYcIEPvnkEz7//HMA9uzZw7p16xzuKMqrFIe7qFM6HyM71uT/5uxk9JJ9vNOuurtFMhiyNAlm1U+cOEG1atWSNKtu6zgJbptVP3LkCG3btk2XWfUERXT69GkCAgL46quvAFixYgUFCxa0S/Zy5coRHBwMQP369QkLC+Pq1ausX7+ebt263Yp348YNAMLDw3n88cc5deoUN2/epFy5crfidOjQwSneBb1KcYhIe6B9cjfWmXRrUJr/Tl5mwroj1CiZh051S7lcBoPB47CzZeBoMptZdVuyZct267+vry9RUVHEx8eTL1++W/nbMnToUF555RU6dOjAqlWr7uhGy5kzZ5rLtwev6lNx9eB4Yt5uW41G5Qrwxtxd7D7hmnEWg8GQPJnFrHpq5MmTh3LlyjF79mwAlFLs2LEDgEuXLlGypDb1N2XKFJfI41WKw934++rB8oI5A3hu2jYirt5wt0gGQ5YnM5hVt4cZM2YwceJE6tSpQ40aNZg/fz6gWzfdunWjfv36FCpUyCWyuMSsuquw6aoacPDgQbfJsSv8El3HradumXxM69cIfzNYbshCGLPqmYPMaFbdKbi7qyqBWqXy8lHnWmw8fIGRf+x1qywGg8HgaLxqcNyT6FyvFLtPXGbSP0eoWTIvXeubwXKDweAdeFWLw9N469Gq3F+hIG/9vosdxzOPOQGDwWBICaM4nIifrw/fPlmPwrmy8dy0bZy7YgbLDQZD5serFIerTY7YQ4GcAYx/qj6RUTcZPGMbN2Pj3S2SwWAwZAivUhyeMjiemBol8vJxl9psCbvIB4v2uFscg8FgyBBepTg8mceCS/Lsg+WZtvEov2455m5xDAavJq1m1TPCuXPnbhkZXLt2bbLxRowYwWeffQZAnz59mDNnTobKdSdGcbiQ11pVoUmlQgyb9x/bj110tzgGg9eSHrPqSbFq1apUzYasWLGCWrVq8e+//9KkSRMHn4lnYhSHC/Hz9eGbHnUpmjcbg6Zv4+zlaHeLZDB4PWk1q54WQkJCeO2115g/fz7BwcFERUXd4adjzpw56bJX5emYdRwuJl+OAMb3bkDn79YzaMZ2Zg64lwA/o78N3snHmz9m3wXHuleuWqAqrzd83a646TGrnhaCg4N5//332bp1K99++22G8spMeHyNJSLVRGSciMwRkUHulscRVCueh0+71Wbb0YuMWPifu8UxGLyOBLPqxYoV48yZM0maVR80KPnqpFGjRgQHB9O/f38WLFhwyz7V0qVLXSG+x+PUFoeITALaAWeVUjVtwlsDXwO+wASlVLKdjEqpvcBAEfEBpgLfO1NmV9Gudgn+O3mZ71eFUqNEHno2KutukQwGh2Nvy8DRpMesui2bNm0C9BjH5MmT0+QGVkRu/Y+O9s7uaGe3OCYDrW0DRMQXGAu0AaoDPUSkuojUEpFFibYiVpoOwB/AYifL61JefaQKD1UuzIgF/7E17IK7xTEYvI70mFXPKEWLFmXv3r3Ex8fz+++/u6RMV+NUxaGUWgMkrhEbAoeUUoeVUjeBX4DHlFK7lFLtEm1nrXwWKKXaAD2TK0tEnhWRrSKy9dy5c846JYfi6yOMeaIuJfJlZ9CM7Zy+5J1fJwaDO0mPWfWMMHr0aNq1a8f9999P8eLFXVKmq3G6WXURCQIWJXRViUhXoLVSqr+13xtopJQakkz6pkBnIBuwUyk1NoWyPMKselo5cOYKHcf+Q+Wiufn1uXvJ5ufrbpEMhnRjzKpnDrzarLpSapVS6gWl1HMpKQ0rrkeuHE+NykVz80X3OoQcj2TYvN14k48Ug8HgfbhDcZwAStvsl7LCMown2qqyl9Y1izO0eUVmbQ1n+saj7hbHYDAYksUdimMLUElEyolIAPAEsMANcngcL7esTPOqRXhv4R42HzGD5QaDwTNxquIQkZnABqCKiISLSD+lVCwwBFgK7AVmKaUcspghs3ZVJeDjI3z5eDBlCuRg8IxtnIyMcrdIBoPBcBfOnlXVQylVXCnlr5QqpZSaaIUvVkpVVkpVUEqNdFR5mbmrKoG82f0Z/1R9omPiGTh9G9Exce4WyWAwGO7A4wfH00Jmb3EkULGIHizfGX6Jt383g+UGg8Gz8CrF4U08UqMYL7WsxNzt4UxeH+ZucQyGTIUrzarbmksfPnw4y5cvz1B+mQGvUhze0FVlywvNK/Fw9aJ8+MdeNoRGuFscgyHT4Eqz6ra8//77tGzZ0gFnkDSuWv2eGl6lOLylqyoBHx/hi+51CCqYg+d/3k74xevuFslgyHQ406x6YmwdNAUFBfHuu+9Sr149atWqxb592krwtWvX6Nu3Lw0bNqRu3brMnz8fgLCwMJo0aUK9evWoV68e69evB7TyatKkCR06dKB69eoOkzUjeJVZdZuV4+4WxWHkDvRn/FMN6PjtPzw3bRtzBt5P9gCzstyQOTg9ahQ39jrWrHq2alUp9tZbdsV1tln11ChUqBDbt2/nu+++47PPPmPChAmMHDmS5s2bM2nSJCIjI2nYsCEtW7akSJEiLFu2jMDAQA4ePEiPHj3YunUrANu3b2f37t2UK1fOqfLai2lxZAIqFM7F1z2C2XPqMm/+ttMMlhsMqeApZtU7d+4MQP369QkLCwPgr7/+YvTo0QQHB9O0aVOio6M5duwYMTExDBgwgFq1atGtWzf27NlzK5+GDRt6jNIAL2txeDPNqxbllZaV+XzZAWqWzEv/JuXdLZLBkCr2tgwcjTvNqtuSLVs2QA/WJ4xPKKWYO3cuVapUuSPuiBEjKFq0KDt27CA+Pp7AwMBbx3LmzJmu8p2FV7U4vJ3nm1WkdY1ijFq8l3UHz7tbHIPB43GHWfXUaNWqFd98882tnoN///0XgEuXLlG8eHF8fHyYNm0acXGeu4bLqxSHt82qSoyPj/BZ9zpUKJyLITO3c/yCGSw3GFLD1WbVU2PYsGHExMRQu3ZtatSowbBhwwAYPHgwU6ZMoU6dOuzbt8/jWhm2ON2sujto0KCBShhU8kbCzl+jw7frKJk/B7MH3keubKbH0eA5GLPqmQOvNqtuuJugQjkZ06Mu+09fpv036wg5HulukQwGQxbCKI5MStMqRfh5wL3ciImjy/fr+WbFQWLj4t0tlsFgyAKkqjhE00tEhlv7ZUSkofNFM6TGveULsuSlB2lbqzifLzvA4+M3cizCjHsY3I83doF7Exm9P/a0OL4D7gN6WPtXgBQ98bkLbx8cT4q82f0Z06MuXz8RzIHTV3h0zFrmbAs3L67BbQQGBhIREWGeQQ9FKUVERMQd033TSqqD4yKyXSlVT0T+VUrVtcJ2KKXqpLtUJ+Ptg+PJEX7xOq/M2sHmIxd4tFYxRnWqRb4cAe4Wy5DFiImJITw8nOjoaHeLYkiGwMBASpUqhb+//x3h9g6O2zMdJ0ZEfAFlZVwYMJ3pHkip/DmYOeBeflgTyhd/HWDb0Yt83i2YxpUKuVs0QxbC39/fo1Y5GxyPPV1VY4DfgSIiMhJYB4xyqlSGdOPrIwxuWpF5zz9Azmx+9Jq4iQ8X7TEOoQwGg8Owax2HiFQFWgACrFBK7XW2YBkhq3ZVJSbqZhyjFu9l2sajVC2Wm6+fqEuVYrndLZbBYPBQHLaOQ0TuBU4opcYqpb4FTohII0cIaS8iklNEtopIO1eWm9nJHuDLBx1r8lOfezh/9Qbtv13HpHVHiI83g5YGgyH92NNV9T1w1Wb/qhWWKiIySUTOisjuROGtRWS/iBwSkTfsyOp1YJY9ZRruplnVIvz50oM8WKkQ7y/aw9M/bebMZTNwaXAyMVFwbj8c+As2jYc/34JfesKU9nDyX3dLZ8gA9syqClFKBScK26mUqp1q5iIPohXNVKVUTSvMFzgAPAyEA1vQU319gY8SZdEXqAMUBAKB80qpRamVa7qqkkYpxc+bj/HBoj0E+vvyUadatKlV3N1iGTIr8fFw9TRcDLO2o7f/Rx6FK6fujO+fA/KVhesRoOKg719QyHt853gD9nZV2aM4fgNWcbuVMRhoppTqaKcgQcAiG8VxHzBCKdXK2n8TQCmVWGkkpB8J5ASqA1FAJ6XUXbO6RORZ4FmAMmXK1D969Kg94mVJQs9d5eVfQ9gZfolu9Uvxbocaxt6VIWmiL99WBIkVROQxiLthE1kgbynIH6QVRP4ga7P+5ywMIhARChMf0Yqk31LIU8Llp2VIGkcqjiLomVXN0VNyVwAvKaXO2ilIEHcqjq5Aa6VUf2u/N9BIKTUklXz6YFocDiMmLp6vlx/ku1WHKJU/B18+Hkz9so5zoWnIJMTFwKXwO1sKtgoi6sKd8QPz3lYIdyiHIMhbGvzsXDd08l+Y3E6neWYx5CjgsFMypB+HreOwFMQTDpEqAyilJqcWxxtdxzoLf18fXm1VhQcrF+blX0Po/sMGhjSryNDmFfHzNSbMOHcAYqPANxv4+oNftkT/A8AnE7jwVUp3Dd1SBmF3KohLJ3S3UQI+/pDC6vdyAAAgAElEQVSvtFYEJeomUhBlIbuDPi5K1IUnfoYZXWHmE9B7HgTkcEzeBqeTquKwFvwNAIJs4yul+qazzBNAaZv9UlaYwQ00LFeAJS81YcSC//h6xUFWHzjHV48HE1TIc30BOJ3Dq2DqY6nHE19LifhbSiVAf3H7WluCgrm1H5B0vMRxbfO8FS+R0koc7+bVu8cZEhTEzat3yp2ziFYEpRtB7aA7lUOeEq5TiOUfgs4/wuw+entihj4fg8djT1fVemAtsA249WmilJprVwF3d1X5oQfHW6AVxhbgSaXUf2kXP2lMV1X6WLTzJG/9tovYeMW77avTvUFpRMTdYrkWpWB8U7h2HtqMhribujsn9ob1/6b1P0b378fdhNib1v8MxFMOXKDpl/3u8YVb3UtlIMDDPgq2TIQ/XoE6PeCx7yAFl64G5+JIkyM5lFKvp1OImUBToJCIhAPvKqUmisgQYCl6JtUkRykN01WVMdrVLkH9svn536wdvD53Fyv3neWjzrUpkDML2bvaMx9OhegKrFp715UbH2ejSG4mUja2iiiZff8ct5VDwiB0ZuGefro77e+RkLMQPPKhuyUypII9LY4PgfVKqcWuESnjmBZHxoiPV0xcd4RPl+4nXw5/Pu1Wh4cqF3a3WM4nLha+awQ+fjBofeYYw/AWlIIlr8Hm8fDw+/DAi+6WKEviSA+ALwKLRCRaRC6LyBURuZxxER1PVjSr7gx8fIQBD5Zn3vMPkDe7P09P2syIBf95v72rkBkQcQiaDzNKw9WIQOuPoUZnWDYc/p3ubokyJ/GusT+bquJQSuVWSvkopQKVUnms/TyuEC6tKKUWKqWezZs3r7tF8Qqql8jDwqGN6XN/EJPXh9Hh23XsOemR3wwZJyYKVo2Gkg2galt3S5M18fGBTj9A+Waw4AXYl2k6OTyDkyHwQxO9TsbJpMUD4DBrv7SnegA0LQ7HE+jvy4gONZjStyEXr8fQcew/jF8T6n32rjb/CFdOQssRmWt8wNvwC4DHp0HxOjDnGTi63t0SZQ72/wk/PQpRkXrMy8mkxQPgk9b+VTzUA6BpcTiPhyoXZulLD9K0SmFGLd5HzwmbOBkZ5W6xHENUJKz9HCq0gHJN3C2NIVtu6DlbLw78+Qk4vTv1NFmZTePhlx5QqBIMWAFFqjm9SHsURyOl1PNANIBS6iKQhabZGBIokDOAH3rX5+MutdgRHknrr9awaOdJd4uVcdZ/A9GR0GK4uyUxJJCzEPT+TU8dnt5Fr0kx3El8HPz5Jiz5P6jUSq/Az13MJUXbozgyjQdA01XlfESEx+8pw+IXmlC+cC6G/Pwvr/wawpXoGHeLlj6unIGN3+lB2RLBqcc3uI58ZbTyiI2GaZ3g6jl3S+Q53LwGs57Sz26jgXrxpAvX53iVB0DTVeU6ggrlZPbA+3ixRSXmhZygzddr2RJ2IfWEnsaaT/V6iObvuFsSQ1IUqaa7rS6fghldtNHFrM6VMzC5Lez7Q89Ea/Oxy2cB2jOragbwGtrk+Smgo1JqtrMFM3g+/r4+vPxwZWYPvB8fER7/YQOfLd1PTJxHNkjv5sIR2PYT1HsKClZwtzSG5CjdUA+Yn/kPfnkSYrKwL5mze2FCS+3n5Imf4d6BbhEjRcUhIr4isk8ptS/BA6Anu401XVXuoX7Z/Cx+sQld6pXi278P0eX79YSeu5p6Qnfz9yi92O+hdBlGMLiSSg/r1fxha+G3Abp/P6txeBVMbKWtCjyzGKo+6jZRUlQcSqk4YL+IlHGRPBnCdFW5j1zZ/Pi0Wx2+71mPYxeu027MOmZsOoo9Pu3dwuldsGu27h/OY5xZZQrqPA6tRsHeBfDH//Rq86zCv9P1JIE8JaD/cm1d2I3YY6sqP/CfiGwGriUEKqU6OE0qQ6alTa3i1C2Tn1dn7+Dt33fz976zjO5Sm0K5srlbtDtZ8QEE5oHGL7lbEkNauO95uHYO1n2pbXI1f9vdEjkXpWDlh7D2M70wsvsU7RPFzdijOIY5XQqDV1EsbyBT+zZk8vowRv+5j9ZfreHTrnVoVrVIuvJTShEXr4iNV8TExRMbp4iJ17+2/2Pi4vVxm3ix8fHEWPFi4+O5GRtP/vNbaXlwKVsrvsD2LReIiYu4I25MXDy+PsKghyqQPysZeMwstHhXK481n+hpu42ec7dEziH2BswbDLvn6HG4tl94jNl5exw5rRaRskAlpdRyEcmBtmprMCSLj4/Qt3E57q9YkJd+CeGZyVtoVK4Afr5iVeQJFXxCJW9V8DZKIDb+tmJwXK+EYnbAKM5IPnrtrkv07n23joiAv48Pfr7C9ZtxxMUrhrWr7qiCDY5CBNp9DdcvwpLXIUdBqNXV3VI5lusX9ESAYxv0+qLGr3iURQN7rOMOQPvyLqCUqiAilYBxSqkWrhAwLdiYVR9w8OBBd4tjsIiOiePrFQdZf+g8fr4++PkI/r66gvb39cHfV/CzKuyEitvfiudnc9zf7/ZxP18f/BMd1+msuAnhicrLc3Q5hRc9zeWWnxJXtw/+freP+/rcfjFf+TWExbtP8c/rzSnoad1sBk1MlO73P74ZnvwVKnpclZQ+IkJhRjft0rfT91Czi8uKdqTP8RCgIbBJKVXXCtullKrlEEmdgDGrbkiS+DgY11gvKHt+c4rN/kNnr/Dwl2sY3LQC/9eqqguFNKSJ6EvwU1u4cBieXgil6rtbooxxbCPM7KH/95gJZe51afGONKt+Qyl1y2qW5cEvC01nMHgNu2bD2T16sV8qfcUVi+SmdY1iTF1/lEtRmXRVfFYgMC/0mqPHOmZ01b7iMyu758KUDtqve//lLlcaacEexbFaRN4CsovIw8BsYKFzxTIYHEzsDe1hrlhtqN7JriTPN6vIlRuxTNsQ5lTRDBkkdzHo/btePT2tE1w64W6J0oZS2sjmnL5Qsp5WGh6+INUexfEGcA7YBTwHLAaMfQZD5mLbZIg8Bi3ftdundc2SeWlWpTAT1x3h+s1Y58pnyBgFK0CvubrralonPbicGYiLgQVDYcX7ULMr9J4HOQq4W6pUSfYNEpEV1t+PlFI/KqW6KaW6Wv9d1lUlIk1FZK2IjBORpq4q1+BF3LgCqz+BoCbadHoaGNK8Ihevx/DzpmNOEs7gMIrX0eMCF4/Az921IUBPJvqSHgT/dxo0eRU6/wj+ge6Wyi5S+vQqLiL3Ax1EpK6I1LPd7MlcRCaJyFkR2Z0ovLWI7BeRQyLyRirZKLQPkEAg3J5yDYY72Pg9XD+v5/+ncUpj/bIFuLd8AcavOez9rnO9gXJNoMtEOLENZj2tv+g9kcjjMKm1NqHy2FhoMczulrAnkJKkw9GL/0oBXwCf22yf2Zn/ZKC1bYBlon0s0AaoDvQQkeoiUktEFiXaigBrlVJtgNeB9+w/NYMBuBYB/4yBqu2g9D3pymJo80qcvXKDOdvMd0umoHoHaPclHFoG8593mR9uuzn5L0xooafb9poLdXu5W6I0k9ICwFNKqTYiMlwp9X56MldKrRGRoETBDYFDSqnDACLyC/CYUuojoF0K2V0EzIR6Q9pY9wXEXMuQ2fT7KxQkuHQ+xq0O5fF7SuPvm3m+DLMs9fvAtfOw8gO9QLDVKM9YQLd/iR4Ez1EInprvEm99ziClN2CM9dvRwWWWBI7b7IdbYUkiIp1F5AdgGvBtCvGeFZGtIrL13Dnj8MWA7g7Y/CPU6ZGhF1REGNKsIuEXo5gf4gUeD7MKTf4HjQZpZ0frvnS3NLDpB70avHAVPXMqkyoNSLnFESMi44GSIjIm8UGl1AvOE+uOcn4DfrMj3ngROQW0DwgIyOSrgAwOYfVoQEHT1IbRUqdFtSJULZab71YdolPdknesMjd4KCK6pXH9PKx4T7c86j/tejni42Dp27Dpe6jSFrr86FJvfc4gpRZHO2Al2tf4tiS29HICKG2zX8oKMxgcx7n9EPIz3NNfuyDNICLCkOYVOXzuGn/uPu0AAQ0uwcdH+/Go0AIWvQR7F7m2/JvX4NdeWmncO1g7pMrkSgPsMzlSRym1I90F6DGORUqpmta+H3AAaIFWGFuAJ5VS/6W3jMQYkyMGfu0FoX/Dizv0qmIHEBevePjL1WTz82XxC40RT+gzN9jHzWt6VfbpXdqPeVBj55d55YyeFnx6p3bx2uhZ55eZQTJsckREXrP+9heRMYk3O4WYCWwAqohIuIj0U0rFAkOApcBeYJajlIbxAGgAIHwb7F0I9w91mNIAbpla33vqMiv3nXVYvgYXEJBT+y7PH6RtQZ3a6dzyzuzRM6fOH4AnZmYKpZEWkm1xiEh7pdRCEUmyU1ApNcWpkmUA0+LIwigFU9prm1Qv7oBsuR2afUxcPE0/XUWRPNn4bdD9ptWR2bgUDhMf0es7+i2FAuUdX0boSr2GxD+HttpbItjxZTiJDLc4lFILrd8pSW2OFNZRmBaHgcN/60VVD/6fw5UGgL+vDwObVuDfY5FsCI1weP4GJ5O3lLZrFR8D0zrr7iRHsn2qXg2etzQMWJGplEZaSKnFsZAUrOB6sutY0+LIosTHw4/NtJ2ioVvBzznLfqJj4njwk7+pWCQXPw/wXAumhhQI36pbpgUrQJ8/Mu6ONT5erxlZ9wVUaA7dpmjXxJkMR5hV/wy9SvwIEAX8aG1XgVBHCOloTIsji7N3PpwKgWZvOU1pAAT6+zKgSXnWh0aw7ehFp5VjcCKlGugZTmf3wswnISY6/XnFRMPcflpp1HsanpyVKZVGWrBnVtXWxBooqTBPwrQ4siBxMTC2EfgGwKB/tIltJ3LtRiwPfLySemXyM6lP+kyZGDyAnbPht/7aJE23KeCbqjftO7kWoRf1Hd8ILd+DB170jBXq6cSRjpxyisitESQRKQdk/onIBu/i3+lwIVT7Z3ay0gDImc2Pvg+UY+W+s/x30rRwMy21u+mpsvsWwR8vkybn9hGhMLGltj3VbTI0filTK420YI/ieBlYJSKrRGQ18DfwonPFSh+mqyqLcvM6rP4YSjWEKm1cVuzT9weRO5sf3/3tkT23Bnu5d6A2a759qh6nsIejG/R02+hL2mVtDfucg3kLqbbLlFJ/ikglIMHx8j6l1A3nipU+rJlgCxs0aDDA3bIYXMjm8XDllDan7cIvvrzZ/el9X1m+Xx3KobNXqFjE8bO4DC6i+Ttw7Zz2xJejENw3OPm4u+bAvEHaIkHP2c6Z0uvh2GXmUyl1Qym1w9o8UmlkSVznT8tzibqoByUrPgxBD7i8+H6Ny5HNz4fvVplWR6ZGRJtir9Yelr4JO2fdHUcpWPOZHggv2QD6LcuSSgPsVByZhSzVVXVkDXxWSfuayMr8M0Z3F7QY7pbiC+bKRo+GZZgfcpLjF667RQaDg/Dxhc4TtKfIeYPg4PLbx+JiYMEQ3ZVVqzs8lTlcvDoLr1IcSqmFSqln8+bN4JxsT+fYRvj5cW1/Z9kw+PujrNn6uHJae/er2RWK13abGM8+WB5fEcatNq2OTI9/IDzxMxSpDrN6w/EtEBUJ07voCRgPvgadxzt1undmIFXFISK/iUhbEfEqJZNpObENpneFPCVg6DYI7qnNhy8blvWUx+pP9ArgZm+5VYziebPTpX4pZm8N58zlDKwHMHgGgXm0Z75cReHnbjCpFRz9R1vZbf52lpk5lRL2KIPvgCeBgyIyWkSqOFkmQ3Kc2qnNJOQoAE8t0Mqjw7fadPj6b+CP/3mem0xnEREK26foBVcFK7hbGgY9VIE4pRi/5rC7RTE4glxFtGkS3wC4fAp6/QZ1e7pbKo/BnllVy4HlIpIX6GH9P45eRT5dKeWh3uC9jLN7YVpHCMilp//ltZwm+vjAo59pg2rrx0BMFHT4Ju0LmTIbf48CH3946LXU47qAMgVz0KFOCX7edIznm1WkQM4Ad4tkyCgFysHAdaDiIXcxd0vjUdjV/SQiBYE+QH/gX+BroB6wzGmSpQOvHRw/fwimPqYryqcXQP6ydx4XgYffh6Zvwo6f9UrYOC/W56d2wu45cO8gj3qhBzetQHRsHJPWHXG3KAZHkauIRz1jnoI9Yxy/A2uBHEB7pVQHpdSvSqmhQC5nC5gWvHJw/GIYTO2g3U8+NT/5bhkR7SL14Q/gv9/h194Zs7/jyax4HwLzafMOHkSlorlpXaMYU9aHcSnKixW3IctjT4tjjFKqulLqI6XUKdsDnmyvyiu4FK4teN68pqf/FamaepoHXtBdVweWwMwndFpvImwdHFoGjV+G7PncLc1dPN+sIlduxDJtQ5i7RTEYnIY9iiO/iHROtLUQkSJOly4rc+W0dnUZFakH6YrVsj9twwF6BsiR1XoaYfRl58npSpSC5e9B7uLQ0DM9qtUsmZemVQozcd0Rrt+Mdbc4BoNTsEdx9AMmAD2t7UfgdeAfEentRNmyLtfO6zGNK6eh5xwoWS/tedTtCV0mQPgWndf1C46X09XsXwLhm+Gh1yEgh7ulSZahzSty8XoMP2865m5RDAanYI/i8AeqKaW6KKW6ANXRDp4aoRWIwZFcvwBTO+qxjSd/hTKN0p9XzS7w+HQ4s1t3eV095zAxXU58nB7bKFAB6vZytzQpUr9sAe4tX4Af1x4mOibO3eIYDA7HHsVRSill61/xLFBaKXUBcPoIoIj4iMhIEfkmOf/nXkP0JZjeGc7v16tXyzXJeJ5V2mgFFBEKP7WByycznqc72DkLzu2FFsPA19/d0qTKkGaVOHP5BnO2hbtbFIPB4dijOFaJyCIRedqquOdbYTmByJQSisgkETkrIrsThbcWkf0ickhE3kil/MeAUmgl5b1v4Y2r2lfx6V3QfSpUbOG4vCs0h96/6a6vSa11ayYzEXtDr9soHgzVHnO3NHbxQMWC1Cmdj3GrQ4mJyyKLMg1ZBnsUx/PAT0CwtU0FnldKXVNKNUsl7WSgtW2AiPgCY4E26G6vHiJSXURqWQrKdisCVAHWK6VeAQal5eTSyqmrpwi7FObMIpLm5nU9Ayp8izYN7gyfEmXv19N5oyPhp0f12pDMwtZJcOkYtHxXL3jMBIgIQ5tVJPxiFAtCMmkrz2BIhhTfQquSX6mUmquUetna5qjU/M1aKKXWAIlHZRsCh5RSh5VSN4FfgMeUUruUUu0SbWfRrYwEx87JdhiLyLMislVEtp47l76+/I+3fEy3hd2YuW8m8cpFX4mxN+DXnnqaaacfoEZH55VVqj70+UOX+VMbOPOf88pyFDeuwJpPodyDUD617xTPokW1IlQtlpvvVh0iLj6L2REzeDUpKg6lVBwQb5kbcRQlgeM2++FWWHL8BrQSkW+ANclFUkqNB94DtgcEpM/cw5sN36R+0fqM2jSKgcsGcvra6XTlYzexN2HW0xC6UpsJqd3dueWBntb7zBJtQnpyWzix3fllZoQNY+F6BLQYkemMy4kIzzerSOi5a/y528nPksHgQuxp918FdonIRBEZk7A5W7AElFLXlVL9lFJDlVJjU4mboZXjRXMW5fuW3zPs3mGEnAuh8/zOLAxdiJ0NrLQRF6tNgxxYohfs1XPhzObClbXyyJZbT9U9ttF1ZaeFa+e18cZq7XVrKRPyaK3ilC+Uk2//PuSc58hgcAP2KI7fgGHor/1tNlt6OQGUttkvZYVlGEfYqhIRulfpzpz2c6iQrwJvrXuL/63+HxeiHbgOIj4O5g+GPfPhkZF6wZ6rKVBOK49cRWBaJzi8yvUypMbazyHmOjQf5m5J0o2vjzCoaQX2nrrM3/vPulscg8EhpKo4lFJTgFnARqXUlIQtA2VuASqJSDkRCQCeABZkID+nUCZPGSa3nszL9V9m1fFVdJrfib+P/Z3xjOPjYdFLsPNX7ef4/iEZzzO95C0FfRZD/iCY0R0OLHWfLImJPAZbJkDwk1A4c1vy71i3JCXzZefblabVYfAO7DFy2B4IAf609oNFxK6KXkRmAhuAKiISLiL9lFKxwBBgKbAXmKWUcsgoraONHPr6+NK3Zl9mtp1JoeyFeOHvFxj+z3Cu3ryaXgFhyWuwfSo8+H96cze5i+oB8yLV4Jcn4b957pZIs2o0IPBQarO1PR9/Xx8GPlSe7cci2XA4wt3iGAwZxp6uqhHomVCRAEqpEMAuD+1KqR5KqeJKKX+lVCml1EQrfLFSqrJSqoJSamQ6Zb8LZ5lVr1KgCr+0/YUBtQYwP3Q+XRZ0YcvpLWnLRCntpW/Lj3DfEGj2tkNlzBA5Cmhz7SXrw5xnYMcv7pXn7F7YMVN34eUrnXr8TEC3BqUpnDsb367MRNOgDYZksEdxxCilEtfEHrmiyZlm1f19/Xmh3gtMaT0FPx8/+i7tyydbPiE61k7T5X+P0gO99wyARz70vBlCgXm1McWgxvD7QL12wl2s/BD8c0LjV9wng4MJ9PdlQJNyrA+NYPuxi6knMBg8GHvcxP0nIk8CviJSCXgBWO9csdKH1a3WvmLFik4rI7hIMLPbz+aLbV8wbc80/jnxD6Maj6JGoRrJJ1rzGaz5BOo9BW0+8TylkUBATnhylp4ivOhl7U3wvuedXqxSilgVS1x8HLHHNxN7YDGxjV8ilhhir4QTp+KIjY/Vm4q99T8uPu6usNj42FvxY+Jj7kgbp+KIiY+xK62/jz/9a/WnfD67Gtd20bNRWb5bFcrYlYeY2Oceh+VrMLgaSW2wTkRyAG8DjwCCHpv4QCnlsV6CGjRooLZu3er0ctafWM+w9cOIiIrgudrP0b92f/x9EtlRWv8t/PU21OoOncbp9ROeTuxNPVV4z3xo9g48+GqGlN3OczuZtHsSu87v0hV24spfudb8uCD4+fjpTfSvr4/vHfvno87j6+PLuJbjqFmopsPKHrPiIF8sO8AfLzSmRgkvcjhm8ApEZJs9fpZSVRyZEVcpDoBLNy7x0eaP+OPwH9QoWINRjUfd/krd/CMsfhWqPwZdJmUuP+BxsTD/edj5i3aa1OLdNCkPpRQbTm1g4q6JbD69mTwBeWhauinZfLPpilp88ffxv11pix9+F8Pw2z4Nv2od8Cv30O3K3KZCT0h7KzyJyt9f/O9Ie0dZ4ouvHcr7+OXjDFg2gIvRF/mm+Tc0LN4wI1fzFpeux/DAxyt5qHJhxvZMh7l8g8GJOExxiEhl4FUgCJuuLaVU8wzK6HBsuqoGHDx40KVl/xX2Fx9s/ICo2CherPciPaMUPguHQuU28Pi0TGHR9S7i4+GPV2DbT9BoILT6KFVbUXHxcaw8vpIJuyawJ2IPRbIX4akaT9G1cldy+udMuazxD2lbWkO2gl82B59M2jl7/SzPLXuOY5eP8elDn9K8jGMe+Y//3Me41aEse/khKhbxKO/LhiyOIxXHDmAcetHfLVtRSqmMLAJ0Kq5scdhyPuo8I9aPYHX4au6JiubDHFUp8eQcj6gE041SsPRt2DgW6vaG9l8n2d0WExfDosOLmLR7EmGXwyiTuwzP1HyGDhU6EOBrhwmY3XNhTl9tr6vOE044kfQRGR3J4BWD2ROxh/fuf4/HKmbcOu/5qzdo/PFK2tYqwefd6zhASoPBMdirOOyZVRWrlPpeKbVZKbUtYXOAjF5HoeyF+KZYS94/f5H/ArPT2fcsvx9ZnLkXfYlAq5F6zcm/0+D35yDuthuW6zHXmbZnGm1+a8Pw9cMJ9Avk04c+ZUHHBXSt3NU+pREXo2dSFakOtbo58WTSTr7AfEx4ZAINijXgnX/eYfqe6RnOs1CubPRoWIZ5ISc4fuG6A6Q0GFyLPYpjoYgMFpHiIlIgYXO6ZJmR/UuQuf3olK86c9vPoWrBagxfP5wX/n6B81Hn3S1d+hHRq9xbvAu7ZsPsPly6dpbvd3xPq7mt+GTLJ5TKXYrvW37PrHazaB3U2q5xhFv8Ow0uHNb5e+DkgRz+OfiuxXe0LNOSj7d8zNiQsRn+GHj2wfL4CIxbHeogKQ0G12FPV9WRJIKVUspx8xQdhDvHODi0QvvUKFpD+70IzEu8imfanmmM2T6GnP45GX7fcFqWbelauRzMmbWfMfXfb5idNy9RKJqWakq/Wv0ILhKcvgxvXocxdbXZk75/eu5UZSA2Ppb3NrzHvEPzeLLqk7ze8HV8JP3+Qd78bSdzt51g7evNKJon0IGSGgzpw8yqcuUYR9g6mN4VClbUK7Bz3NkgC40M5c21b7L3wl7al2/PG43eIE9AHtfJ5wCOXj7KT7t/YkHoAuLjY2l99Sp9c1akco+52spueln3JSwfAc/8CWXvc5i8zkIpxWdbP2Pqnqm0K9+O9x94/+4p2HZyLOI6zT5fxTP3B/FOu+oOltRgSDsZHuMQkdds/ndLdGxUxsTzIo5t0gYC85eFp+bdpTQAKuSrwIy2MxhYZyCLjyym8/zObDi5wQ3Cpp29EXt5dfWrdJjXgYWhC+lcqTOLOi9mdJOPqXx0q7asG5WiB+HkibqoFUelVplCaYC2nvxqg1d5oe4LLDq8iJf/ftl+6wGJKFMwBx3qlGDGpmNcuHbTwZIaDM4jpXa27dSWNxMda41BO0Ga0VUbCnxqPuQslGxUfx9/ng9+numPTie7X3aeXfYsozaNIio2yoUC24dSii2ntzBw2UC6L+rOuhPr6FOjD0u7LuWde9+hVO5SULsbdJ8CJ0NgSjvtOyOtrPsKoi9Di+GOPwknIiIMqD2Adxq9w5rwNQxaPijdhi8HN61AVEwck9Yl1SNsMHgmKSkOSeZ/UvtZj9O79Nd29nzw9ELIXcyuZDUL1WR2+9n0qtaLmftm0n1hd3ae2+lkYe0jXsWz6vgqei/pTd+lfdl7YS8v1nuRv7r+xcv1X6ZQ9kSKsVp76PELnD+ovQleSYOXu8snYdM4PYuqmONWZruSx6s+zugmowk5G0LfpX3T5bOlUtHctK5RjCkbwrgcHZNqfIPBE0hJcahk/ie17xE4yzruXZzdB1M7attOTy/Ufi3SQJlcQ3IAACAASURBVKBfIK83fJ0Jj0zgRtwNei/pzZjtY4iJc0/FERsfy6LDi+iyoAtDVw7l3PVzvNXoLZZ2WUr/Wv1THo+p1BJ6zoHI4zCptfajYQ+rP4H4WGj2lmNOwk08Wv5Rvm7+NYcvHebpJU+ny93wkOYVuRIdy7QNR50gocHgeJIdHBeROOAaunWRHUiYcC5AoFLKY5dCO3VwPCIUfnoUUNoJUqGMGVS8cvMKH2/+mPmh86laoCqjGo+iUv5KjpE1FaJjo5l3aB6T/5vMiasnqJivIn1r9qV1udZpH/A9vgWmd9ED5U8vgIIVko8bEQrf3gMN+kLbzzJ2Eh7CtjPbGLJiCLkCcjH+4fGUy1suTen7/LSZneGXWPd6M3IEZCLTNAavIsOD40opX6VUHqVUbqWUn/U/Yd9jlYZTuXgUpnSA+Bg9ppFBpQGQOyA3Hzb+kK+bfc3Z62d5fNHj/LT7J+Li41JPnE6u3LzChF0TaD23NSM3jaRg9oKMaTaGuR3m0r5C+/TNEip9D/RZCLFRWrGe3Zd83JUf6tX0nuDIykHUL1qfSa0mcTPuJn3+7MOeiD1pSj+kWUUuXLvJzM3HnSShweA40j8JPatx6QRMaQ83r0DvedpjngNpXqY5v3X4jQdLPcgX276g79K+HL/i2ErkfNR5vt7+NY/MeYSvt39NlQJVmNRqEtPbTKdZmWYZWpMAQPE6uhWGgsmPwqkdd8c5GQL//Qb3DtaTCryIagWrMaX1FLL5ZqPf0n5sPW1/q7dBUAEalSvA+DWh3Ih13keDweAIjOKwhytnYGoHuH5BOzsqXtspxRTMXpAvm37JyMYjOXDxAF0WdGH2gdkZXqV84uoJPtz4Ia3ntmbironcX+J+fm33Kz88/AP3FLsHceSiuyJV4Zkl4J8DJrfXXVi2rHgfsueHB15wXJkeRFDeIKa2mUrhHIUZuHwga8LX2J12aPNKnLl8gznbwp0oocGQcTx+AaCINAF6oi3zVldK3Z9aGoeOcVyL0DOGIo9B79+gzL2OyTcVTl09xbD1w9h0ahONSzbm/fvfp3COwmnK49DFQ0zcPZElR5YgInSo0IFnajxDUN4g5whtS+Qx3a137ZyeeVWuCRxZo1ttD3/gtYojgQvRFxi0fBAHLhzgw8Yf0rZ821TTKKXo+N16Lly7wd//a4qfr/muM7gWRxo5zIgQk0TkrIjsThTeWkT2i8ghEXkjpTyUUmuVUgOBRcAUZ8p7F1EXYdpjcPEIPPmLy5QGQPFcxRn/8HjeaPgGW09vpdOCTvwZ9qddaXec28HQlUPptKATK46toGe1nizpvIT37n/PNUoDIF8ZbUIkbym91uXgclj+HuQuoX2JezkFAgsw8ZGJBBcJ5s21b/LLvtT9uIsIQ5pV5PiFKBbsOOkCKQ2G9OHUFoeIPAhcBaYqpWpaYb7AAeBhIBzYAvQAfIGPEmXRVyl11ko3C+inlLqSWrkOaXFEX4ZpHfV6jSdm6mmnbuLIpSO8ve5tdp3fRZugNrx979vkzXan9zilFOtPrmfCrglsPbOVvNny0rNqT3pU7UG+wHxukpz/b+/M46Oqzj7+fWbJZCYJScgKgQiKRVHLFqwLotVXRetaEW3V1qXSqmDxFYVWW7GruFVw16KgragvVWu1VUFFbbXKqoKKgrKEJQlZCMlkmeV5/7g3YRKSkIQkM5Oc7+dzP/feM/ee87tDuL8523OsiYFPnwc71wIKZ8+DsT+Onp4epjZYy03v3MSywmVMHTWVKd+e0mbTYDisnDnvPQKhMEtuOBGHw0yZMvQcMROrSkSGAK9EGMexwGxVPd0+/wWAqjY3jcg88oFfqWqrP1VFZAowBSA/P3/s5s0HMCa+vtoaWlq4HCY/DYed2fm8uohgOMj8T+fzyMePkJ6Yzm+O/w3j88YTCodYumUp8z+dz+dln5Pty+bHI37MpG9Nwuf2RVu2RU0FPHMRBKrh6mXxtRJiFxAIB/j1f37NK1+/wmUjLmNGwYw2ByK8/PF2rl+0mocuGcOZRw3oQaWGvk4sG8ckYKKq/sQ+vwz4jqpObSOP24HXVfX99pR5QDWOQA08M9kKXDjpCTji/M7l0018VvoZt/z7FjZUbOCMIWfwednnbKrcxJB+Q7jyyCs56+CzcMfiaoOq1oS/WNTWA4Q1zJyP5vDMF89w7iHnMvu42bgcLRtoKKz8z73v4Etw8sq08V07eMFgaIOY6OPoKlT1tvaYxgHPHA/WwXOXwTfvwXmPxJxpAIzIGMGzZz3L5UdczmubXsPr8nLPiffw0rkvcf6h58emaYAVLj1WtfUADnEw6+hZXDPyGv6+8e/MeGcGdaG6Fq91OoRrTjqEddsrWba+pIeVGgz7JxrGsQ0YHHE+yE6LPi9Pgw1LrOVRR14UbTWt4nF6uLHgRj665COeO+s5ThtyWscWTjJEBRHh2lHXMnPcTN7c8ibXLb2O6kB1i9eePzqPvDQv97/1VXyvIGnolUTDOJYDh4rIUBFJwIrC+3JXZKyq/1DVKampqfu/uCWOngJn/SluOm8TXYmmGSMOuXTEpfx+/O9ZUbSCn7z+Eypq9w1L73Y6+OmJB7NqSwUffF0aBZUGQ+t093DcRcAHwHARKRSRq1Q1CEwFXgc+B55X1XVdVN6BNVUNKrDiJxkM3cw5h5zDvSfdy5flX3L5a5dTVF20zzWTCwaTleLhwbc3REGhwdA6MT8BsDP0+AqABkMn+WjHR0x7axrpiek8dupj5PfLb/L5Y+9u5A///IIXrj2OMfnpUVJp6Cv0qs7x9tJjYdUNhi7i6AFH88TpT1AdqOZH//oR68vWN/n8ku8cRJrPzYNvmVqHIXboVcZxwH0cBkMUOCLzCBZOXIjT4eSK169gTfGaxs+SPC6uOG4ob35RzGfbK6Oo0mDYS68yDlPjMMQrB6cdzNNnPE26J52r37ia/2z7T+Nnlx83hGSPiweXmVqHITboVcZhahyGeGZg8kAWnrGQIalDmPrW1MbYZKk+N5cdexD//HQHG0s6t7a5wdCV9CrjOFA0HEaDwWjLMPRhMr2ZzD99Pt/O/DY3v3Mzi79cDMBV44ficTl4eNnGKCs0GHqZcRxoU9Wuhx9m65QpBMvLu1iZwdB++iX045FTH+H4vOO5/YPbmf/pfDKTPVw8Lp8XV29ja5l//5kYDN1IrzKOA22qcufm4l++gk0XTqZ2/fr932AwdBNel5d5353HxCETuW/Vfdy78l6mTBiKQ+DRd02twxBdepVxHChpF1zAQU8/hdbVseniH1D52uvRlmTow7idbu444Q4mf2syT659ksc+u5MLxgzk+RWFFFfWRlueoQ/Tq4yjK0ZVeUeNYsjfFpM4fDjbpk+n+E/3oSGzBrQhOjgdTm495lauPupq/vbV39idsoBgqJ7H3/s62tIMfZheZRxdNarKnZ1N/lMLSbvwQkoffZSt115LqNKMoTdEBxHh+jHXc+PYG/n3jjcZfPiz/OXDDZRV10dbmqGPYkKO7IfyZ59j5+9+R0JeHoMeehDPIYd0Sb4GQ2d44asXuP392wn4B3Hp0N/wy4ljoy0pJgiFlbpgiLpAmNrm+0CIuuC++ybHrVxTGwiR7ktgdH4ao/PTOWJgPxLdvTcSdcws5BQNujpWlX/lSgp/Ph2tqWHgnXNIOeWULsvbYOgoSzYv4cZlN6P1Wbw8aSFD02N/lUBVpbS6nh0VteysrMVfH6QuEKYuGKJ2P/umL/Jwo0FEXhMIHdh7zONy4HE5SHQ78bgdJLqsvcflZOfuWrZV1ACQ4HQwYmC/RiMZk59GXpq310SpNsbRxUEOAzt3Ujh1GrVr15I5dSqZ116DOHpVS58hjnjm46X8YdVMUhP689w5TzIoZVBU9dTUh9i+u4btFQ1brbXfvfe4LhhuMw8RGl/Yre09jXv7Jd+JvcflJLFZXvt78RdV1rJ6SwWrt5SzeksFn2yroDZgPU9WiocxjUaSzlF5qXgT4rNW0ieNQ0TOBs4eNmzY1V999VWX5x+uq2PnbbPZ/dJLJJ9yCgPn3IEzObnLyzEY2sOkJxaxnj+RmZzEb4//Lf0T++NxekhwJJDgtDaP00OCM6HVZWrbQzislFTVsa2idWNo3t8iAtkpHgamea0tNbHxOLdfIkke1z6/8N1OiZtf7oFQmC927GH11nJWbS5n9dYKNpda82tcDuHwAQ21kjTG5KeT398XF8/WJ42jge4Mq66qlD/9F4rmzCFhyBAGPXA/nqFDu6Usg6Etlm8q46InXyTr0IX4Q21PWnWIA4/Tg9vhbjSTBmNx4gJ1Ewo7CYacBIIO6uod1NY78NeDv1YIhV0QdqLqBnXicXpI8/ro7/ORmZREdnIS2SlJ5KakMDA1hQH9UkhK8DQpK8GR0KtXqiytqrNqJVvLWbW5go8LK/DXWyMyM5L29pOMHpzGyMFpJHk6b+bdhTGObl6Po/q/H7Jt+nQ0FCLv7rtIPvHEbi0v3qnbuJG69etxZWfjys3FlZ2NIyEh2rLinose/YBvyouY88P+KEHqw/XUh+qpC9VRH6qnJlBHeY2f0mo/FbV+dtfWsKe2hqr6WvyBWmoCdQQ1ABJEHEFrL0GczhAOZxCREEqAEAHgwN8VLnHhc/s4ZsAxnDbkNE7IOwGf23fgX0QMEgorXxbtYZXdvLVqSzlfl1hLBTsEvpWTwpiDLCMZc1A6QzOScDiiWysxxtEDCznVF26jcNo06r74gqzp08mYcnVcVEd7kuCuXZTMu5+KxYsh3LSN25mejisnB3dODq6cHFw52RHHVrqjXz/znbbBe1+VcNn8j7j6hKEMSvc16VPYXlFDUWUt4Wb/xdN8bgamWs1GeWl7m5AG2sfZKYk4m73AVJWgBqkP7TWmQChgGVQzs6oP1VMfbnoeeV1ZbRnLti6jrLYMr8vLCXkn9HoTaaDCX8/qrRWN/SVrtlawp9aKj5fqdVu1ksHpjM5PY1R+Gv0S3T2qzxhHD60AGK6pYcetv6Ly1VdJOf10Bv7h9ziSknqk7FgmXFdH2cKnKH30UcJ1daT/8AeknX8+wdIygkVFBIuLCOwsIlhURKC4iGBRMaHSfdfWlsREy1Cyc3Dl5uLOycaVbRtLrm0ymZmIK/aq/T2BqnL+Q++zZqu1bnmC09FoAANSmxuDZQ6+hOh/V6FwiFXFq3h90+ss2byk0UTG543n9CGn9wkTAav/aGNJVWOtZPWWCr4s3oOq1U80LCuZMfnpjc1ch2Ynd2utpNcYh4jkA/OAMuBLVb1jf/f09NKxqkrZkwsovvtuPMOGMejBB0gYPLjHyo8lVJU9//oXxXffQ2D7dpJPPpnsm2a0qx8oXF9PsLiEYLFtKEVFBHfaJlNUbBlOUREaCDS90eHAlZFhmUhujmUyDTWY3Fxc2Tm4c7J7raGXV9ezpczPwDQvGUkJUW/u6CiRJrJ081JKa0tJdCZywqAT+pSJNFBZG+CTrbttM7E63iv81t98isfFyMFpjaO4RuenkebruibfmDAOEXkCOAsoVtUjI9InAnMBJ/DntsxARL4HpKvqX0TkOVW9aH/lRmvN8ap//4dtN94IQN6995B8/PE9riGa1Hz8MUV/vIOaNWvwHHYYObNmknTMMV1ahqoSKi9vwVisWkuwaCeBomLCLcz0dyQnt9I0ltt47Ozf3wyzjiJtmchpQ05jQt6EPmUiYP3Nf7OrurGfZPWWCr7YWdnYBHlwZhKj7NFbo/PTGJ6TgsvZub/hWDGOCUAV8FSDcYiIE/gSOBUoBJYDP8AykT82y+JKIAQsxuqZe1pVn9xfudEyDoD6LVsovG4qdRs3kj1jBv2vuLzXt9EHtm+n+J57qXz1VZxZmWRPn07qeechzuiNoAn7/QSLi+2ays4IY2kwmSKCJSX79LvgduPKysSdnYMjORmHz2dvXhw+H+Lz4fD69kl3+HyI14vDl4QjyYfD60U8nl7/b9+dGBNpneq6IJ8U7m4cwbV6Szml9pDoBVeM46Th2Z3KNyaMwxYyBHglwjiOBWar6un2+S8AVLW5aTTcPwP4SFXfFZHFqjppf2VG0zgAwtXVbP/FL9nzxhv0O+ssBvz2Nzi83qjp6S5CVdWUPv44ZQsWAND/isvJ+MnVOJPjo0lIQyGCu0rt/padjcYSLC4iUFxMuNpP2F+N+msI+/2E/X60vgPxoRwOy1S8EabTsHm9Tcyn8bMGU0pqeo147TSfD0lIOGBD0lDIWrQsGEQjtqbnITQYiEjr3PnefO0yBRIPH4FvXAHuvLx2PYsxkbZRVbaW1bB6azknH5ZNSic71WPZOCYBE1X1J/b5ZcB3VHVqK/cfCcwGdgFVqjqjleumAFMA8vPzx27evLlrH6SDqCqljz5Gydy5eA4/jMH33487Ly+qmroKDYWoeOEFSubOI7RrF/3OPpvsG6bjHjgw2tK6HQ0GCdfsNZKw34/6/XvTqiOO/dVoS+k1NYT91fa9NQduSEk+xOlqhxHsPaen+zbdbsTlQlyWTq2xQni4cnPxjR2Lb1wBvoICEg45ZL9GYkyk++g1xtHBsrp15nhn2LNsGdtn3IS43eTddx9J3zk62pIOiOoPPqDojjnUrV+Pd/RocmbNxDtyZLRlxT1NDKnaT7jGNqQGo6n2NzGd5oakwWDjixmXE3G593PustOcdloL504X4na1fh6xEfHZPufNmiw1HKbuqw34V66gZsUK/MtXWM2GWEO0vWPH4CsowFcwjsTDhrc5Ys6YSNcSy8bRoaaqDpYVc8YBUPf1NxROnUr95s3kzJpF+qWXxF3bd93X31B8111Uvf027oEDyb5pBikTJ8bdcxhiD1UlsHUr/uUr8K9YgX/lSgJbtgDg8PnwjrGNZFwBiUcd1erE0QYTeWPTGyzZvMSYSCeIZeNwYXWOnwJsw+oc/6GqruuqMqPdx9ESoaoqtt88k6q33iL1/PPJnX0bDo8n2rL2S7C8nF0PPUz5okU4PB4yfvZT+v/oR3Gh3RC/BIqKLBNZsYKaFSups38ISkIC3m9/G++4AnxjC/COGtVin1qbJnLQaUwYZEykJWLCOERkEXASkAkUAbep6nwRORO4D2sk1ROq+vsuKi8maxwNaDjMrgcfYteDD5J41FEMun8e7tzcaMtqEa2vp3zRIkoeepjwnj2kXXghWdOm4srMjLY0Qx8kWF5OzapV+FesxL9iBbWffQahEDidJI4Y0dhP4h0zBld6epN7I01k6Zal7KrZZUykFWLCOKJFLNY4ItmzdCnbb56J+HwMmjcX35gx0ZbUiKpS9dZbFN95F/WbN5N03HFkz5xJ4vBvRVuawdBIqKqamjVrrH6S5Suo+eSTxgEGnkOH4S0osPtJCnDn5Oy9r5eZSLi2lmBJCcHi4sZ9vzPOwJWV1an8+qRxxHqNI5K6DRvYet11BLbvIPeWW0i/eL/zGrud2s8/p+iOOfg//JCEgw8mZ+bNJE2YYPoxDDFPuK6O2rVrG/tJalatIuy3wpy7Bw9uNBFfwVjc+fmICKFwiNXFq62O9RgzkbDfbxlBhCkEGs1hb3p4z5597s1/8gmSjj22U+X2SeNoINZrHA2EKivZNmMG1e++R9rkyeTcektUIsYGiospmTuX3S+8iDM1lcxpU0mfPBlx92yANYOhq9BgkNov1uNfsbyxnyRUYcXzcmVlWc1aBVY/iefQYYTRFk1kfN54xuWOI8eXQ5YviyxvFpneTNzOzv3fCFdXt2oCkUYRrqra515xu3FlZVkRprOymh5nZ+PKtvbO1NRORz/ok8YRTzWOBjQUomTuPEofewzv6NHkzb0Pd3bnZn12lHBNDWULFrDr8T+jgQD9L72UzGt+hrNfvx4p32DoKTQcpv7rr+0O95X4ly8nWFQEgCM11eojsftJ3MO/xZrytbyx2epY31Wza5/8+if2J8ub1WgmuZLKwJpEMv1O0vcoSZUBPBXVhEtKmxhDuLp6n7wkIaGpAexjCta5My2t22v/fdI4GoiXGkcklf/6F9t/eQvOlBQG3T+vW+dGaDhM5auvUnzPvQR37iTl1FPJvmkGCfn53VamwRBLqCqBbdv2jtxavoJ6e9Kw+Hz4Ro3EW1CAd+xYqlJclBdupHLHZvw7txEoLkJ3leEsrSSxwk9yZQBP/b7v0ToXVKY48ad5qE9LRjNScWRl4skZQPKAQaQOHErG4EPJyMrvdA2mqzHGEWfGAVC7fj2F100lWFRE7uzZpF3w/S4vw79qFUV3zKH2k09IHDGCnF/MwjduXJeXYzDEG8GSEvwrVzb2k9R9+WWLM+zF622sBbjtWoEjM5PaNB+VqU7KfEqRL0Cx7KG4poSSmhJK/CUU+4spqy1Dmy2I5RAHGYkZZPmyyPZmk+nLJNubbZ37shtrNume9G5fQbFPGkc8NlU1J1hezvYbb6T6/Q9Iv+QScmbN7JK+hvrCQorvvoc9r72GKzubrP+9gdRzzjGRYA2GVgjt3o1/1SrCVdVN+hEcSUmdbjIKhoOU1pRSUmMZSYnfNpZm52W1Zfvc6xQnGd6MRlNpMJQGc8n2ZZPpzSQ9MR2HmD6ODhOvNY4GNBik+J57KXvySXwFBeTNvQ9XRkan8grt2UPpo49StvApcDrJuOoqMq66EocvfoYcGgx9jUAoQGltaaOZFNdEmEzEeUVdxT73Pn7a4xwzoHPLGbTXOKK/FJhhH8TlImfmzSSOOJwdt/6KbyZdyKD778d75BHtzkODQSoWL6Zk3v2EyspIPe88sm6Y3mRMu8FgiE3cTje5SbnkJrU9Qbg+VM+uml2WwdimMixtWLfr61U1jt7QVNWcmnXrKJw6jVBZGQN+91tSzz57v/dUvfdviu+cQ91XG/AWjCVn1i86ZDoGg6FvYpqq4ripqjnB0lK2Tb8B//Ll9L/8crJn3NhixNC6DRsouvNOqt99D/fgwVYgwlNPNRP4DAZDuzBNVb0IV0YG+U/Mp2jOnZQtWEDt+i/Iu/fexpg8wbIydj3wAOXPPY/D5yP75ptJv/SSqEwmNBgMvR9jHHGCuN3k3noLiYcfzs7Zs9k06ULy7vsT/o+Ws+uRRwj7/aRfdBGZU6/D1b9/tOUaDIZejDGOOCPtgu/jGXYIhdOuZ9OFkwFIOnECOTfdhGdY93eKGQwGQ68yjojO8WhL6Va8I0cy9G+L2fXwIySffDLJ44+PtiSDwdCHMJ3jBoPBYADa3zlupg0bDAaDoUMY4zAYDAZDhzDGYTAYDIYOYYzDYDAYDB0i5o1DREaIyPMi8rCITIq2HoPBYOjrdKtxiMgTIlIsImubpU8UkfUiskFEZu0nmzOA+1X1GuBH3SbWYDAYDO2iu+dxLAAeAJ5qSBARJ/AgcCpQCCwXkZcBJ/DHZvdfCTwN3CYi5wCdiy1uMBgMhi6jW41DVd8VkSHNko8GNqjq1wAi8ixwrqr+ETirlayusw3nhdbKEpEpwBSAfLMEqsFgMHQb0Zg5ngdsjTgvBL7T2sW28fwSSALuau06VX1MRHYAZ2/ZsuVQEelsXPVMYN/V6WOXeNIbT1ohvvTGk1aIL719SetB7bko5kOOqOom7JpEO679B/CP9l7fEiKyoj0zJ2OFeNIbT1ohvvTGk1aIL71G675EY1TVNmBwxPkgO81gMBgMcUA0jGM5cKiIDBWRBOBi4OUo6DAYDAZDJ+ju4biLgA+A4SJSKCJXqWoQmAq8DnwOPK+q67pTRwd5LNoCOkg86Y0nrRBfeuNJK8SXXqO1Gb0yOq7BYDAYuo+YnzluMBgMhtjCGIfBYDAYOoQxDhsRSRSRj0TkYxFZJyK3R1vT/hARp4isFpFXoq1lf4jIJhH5VETWiEhMr7IlImkislhEvhCRz0Xk2Ghrag0RGW5/pw1bpYhMj7au1hCRG+z/X2tFZJGIJEZbU2uIyM9tneti8TttKaSTiPQXkSUi8pW9T++Oso1x7KUOOFlVRwKjgIkickyUNe2Pn2MNMIgXvquqo+JgTPxc4DVVPQwYSQx/x6q63v5ORwFjAT/wYpRltYiI5AHXAwWqeiRWmKGLo6uqZUTkSOBqrEgXI4GzRCTW1qReAExsljYLeFNVDwXetM+7HGMcNmpRZZ+67S1mRw6IyCDge8Cfo62lNyEiqcAEYD6AqtarakV0VbWbU4CNqro52kLawAV4RcQF+IDtUdbTGocDH6qq3x4J+g7w/ShraoKqvguUNUs+F1hoHy8EzuuOso1xRGA3/awBioElqvphtDW1wX3AzUA42kLaiQJviMhKO65YrDIUKAGetJsB/ywiSdEW1U4uBhZFW0RrqOo24G5gC7AD2K2qb0RXVausBU4QkQwR8QFn0nTicqySo6o77OOdQE53FGKMIwJVDdlV/kHA0XZ1NeYQkbOAYlVdGW0tHWC8qo7BCpN/nYhMiLagVnABY4CHVXU0UE03Vfe7Ensy7TnA/0VbS2vY7e3nYpnzQCBJRC6NrqqWUdXPgTnAG8BrwBogFFVRHUStuRbd0mpijKMF7KaJt9m3/TBWOB44R0Q2Ac8CJ4vIX6IrqW3sX5uoajFWG/zR0VXUKoVAYURtczGWkcQ6ZwCrVLUo2kLa4H+Ab1S1RFUDWNGuj4uyplZR1fmqOlZVJwDlwJfR1tQOikRkAIC9L+6OQoxx2IhIloik2cderPVCvoiuqpZR1V+o6iBVHYLVPPGWqsbkLzcAEUkSkZSGY+A0rKaAmENVdwJbRWS4nXQK8FkUJbWXHxDDzVQ2W4BjRMQnIoL13cbswAMRybb3+Vj9G89EV1G7eBn4sX38Y+Dv3VFIzEfH7UEGAAvtdT8cWKFQYn6Ya5yQA7xovStwAc+o6mvRldQm04C/2s0/XwNXRFlPm9hmfCrw02hraQtV/VBEFgOrgCCwmtgO5/E3EckAAsB1sTZIwg7pdBKQKSKFwG3AHcDzInIVQPKF9wAABJdJREFUsBmY3C1lm5AjBoPBYOgIpqnKYDAYDB3CGIfBYDAYOoQxDoPBYDB0CGMcBoPBYOgQxjgMBoPB0CGMcRhiChF5W0ROb5Y2XUQe7mA+/2yYl9PGNb9sdv5+R8pop44FIjKphfTD7Gi2q0XkkK4ut6N62nnvSSJyXMR5p/MyxDfGOAyxxiL2jZja7hhMYuFQ1TPbMe6+iXGoak/OYj4PWKyqo1V14/4ubniuHtDVFicRwzO9DT1HtP8QDYbmLAa+Z0++Q0SGYMU1ek9EkkXkTRFZZa/tcW7DNSKyXkSewpqRPthe/yPT/vwlO7jiuoYAiyJyB1aU1jUi8lc7rcrei4jcZa/F8KmIXGSnnyQiy2TvWh1/tWdAIyK/FpHl9j2PNaS3hIicCUwHrhGRt+20/7XvXSv22g+tPFeVrW2diCwVkaNtTV+LyDktlCUi8oCdz1IgO+KzsSLyjv3dvB4RqmKZiMy1v5u1dhlDgJ8BN9jpJ9jZTBCR9+3yTe2jr6CqZjNbTG3AK8C59vEs4G772AX0s48zgQ2AAEOwogQfE5HHJiDTPu5v771YL+AM+7yqWblV9v4CYAnWehE5WKEyBmD94t6NFQTTAXyAFbyxsQz7+GngbPt4ATCphWecDcywj8cCnwJJQDKwDhjdynMpcIZ9/CJWED431poRa1oo5/sRzzIQqAAm2fe8D2TZ110EPGEfLwMet48nAGuba454tv+zv4sRwIZo/+2YrWc2U+MwxCKRzVWRzVQC/EFEPgGWAnnsDRu9WVX/20p+14vIx8B/sUJjH7qf8scDi9SKllyEtRbDOPuzj1S1UFXDWBFTh9jp3xWRD0XkU+Bk4Ij2PWpjeS+qarVaa8K8ADT8om/+XPVY0VrBMpt31AoY+GmElkgmRDzLduAtO304cCSwRKylBG7FMsQGFkHjmg/92ugveklVw6r6Gd0UwtsQe5hYVYZY5O/An0RkDODTveHjLwGygLGqGhArOnDD0qPVLWUkIidhRWU9VlX9IrIs4p7OUBdxHAJcYi1/+hDWynZbRWT2AZYRSfPnCqhqQ5ygcIMeVQ2LtThSexFgnaq2tixu81hErcUmivw+Wm2eM/QuTI3DEHPYv7rfBp6gaad4KtY6JAER+S5wUDuySwXKbdM4DIhcDjggIu4W7nkPuEishb2ysH61f9RGGQ0msUtEkrGagjrCe8B5YkWNTQLOt9O6gnfZ+ywDgO/a6euBLLHXUxcRt4hE1pIa+nXGYy24tBvYA6R0kS5DHGNqHIZYZRFWG37kCKu/Av+wm4NW0L6w968BPxORz7FelpHNPo8Bn4jIKlW9JCL9ReBY4GOsX9o3q+pO23j2QVUrRORxrP6TncDy9jxgxP2rRGQBe83pz6q62u6QPlBexGo6+wyrr+YDu8x6uzN7nljL5bqwVpVcZ99XKyKrsfpCrrTT/gEstgclTOsCbYY4xUTHNRgMTbCb82ao6opoazHEJqapymAwGAwdwtQ4DAaDwdAhTI3DYDAYDB3CGIfBYDAYOoQxDoPBYDB0CGMcBoPBYOgQxjgMBoPB0CH+H3CXQ7Xn5M38AAAAAElFTkSuQmCC\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "for k in range(len(var_forms)):\n", " for j in range(len(entanglements)):\n", @@ -158,30 +123,9 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "for k in range(len(var_forms)):\n", " for j in range(len(entanglements)):\n", @@ -216,7 +160,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.6.7" } }, "nbformat": 4, diff --git a/community/aqua/chemistry/h2_vqe_initial_point.ipynb b/community/aqua/chemistry/h2_vqe_initial_point.ipynb index ebb1d1f6a..e74286c0b 100644 --- a/community/aqua/chemistry/h2_vqe_initial_point.ipynb +++ b/community/aqua/chemistry/h2_vqe_initial_point.ipynb @@ -15,7 +15,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": null, "metadata": { "scrolled": true }, @@ -24,37 +24,14 @@ "name": "stdout", "output_type": "stream", "text": [ - "Processing step 20 --- complete\n", - "Distances: [0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.675 0.7 0.725 0.75 0.775\n", - " 0.8 0.825 0.85 0.875 0.9 0.925 0.95 0.975 1. ]\n", - "Energies: [[-1.05515974 -1.07591361 -1.09262987 -1.10591801 -1.11628598 -1.12416089\n", - " -1.12990476 -1.1338262 -1.13618944 -1.13722136 -1.13711706 -1.13604436\n", - " -1.13414767 -1.1315512 -1.12836188 -1.12467175 -1.12056028 -1.11609624\n", - " -1.11133943 -1.10634211 -1.10115033]\n", - " [-1.05515974 -1.07591361 -1.09262987 -1.10591801 -1.11628598 -1.12416089\n", - " -1.12990476 -1.1338262 -1.13618944 -1.13722136 -1.13711706 -1.13604436\n", - " -1.13414767 -1.1315512 -1.12836188 -1.12467175 -1.12056028 -1.11609624\n", - " -1.11133942 -1.10634211 -1.10115033]\n", - " [-1.05515974 -1.07591361 -1.09262987 -1.10591802 -1.11628599 -1.12416089\n", - " -1.12990476 -1.1338262 -1.13618944 -1.13722136 -1.13711707 -1.13604436\n", - " -1.13414767 -1.13155121 -1.12836188 -1.12467175 -1.12056028 -1.11609624\n", - " -1.11133943 -1.10634212 -1.10115034]]\n", - "Hartree-Fock energies: [-1.04299622 -1.0630621 -1.0790507 -1.09157046 -1.10112822 -1.10814997\n", - " -1.11299652 -1.11597525 -1.11734902 -1.11734325 -1.11615145 -1.11393966\n", - " -1.1108504 -1.10700581 -1.10251056 -1.09745432 -1.09191405 -1.08595588\n", - " -1.07963694 -1.07300677 -1.06610866]\n", - "VQE num evaluations: [[383 375 379 364 382 389 376 382 377 345 365 320 341 391 370 340 343 389\n", - " 352 381 331]\n", - " [383 291 280 281 260 263 268 290 294 281 319 297 258 297 283 295 272 319\n", - " 317 312 297]\n", - " [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n", - " 0 0 0]]\n" + "Processing step 16" ] } ], "source": [ "import numpy as np\n", "import pylab\n", + "import copy\n", "from qiskit.chemistry import QiskitChemistry\n", "\n", "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", @@ -66,7 +43,7 @@ " 'two_qubit_reduction': True},\n", " 'algorithm': {'name': ''},\n", " 'optimizer': {'name': 'COBYLA', 'maxiter': 10000 },\n", - " 'variational_form': {'name': 'RYRZ', 'depth': '5', 'entanglement': 'linear'}\n", + " 'variational_form': {'name': 'RYRZ', 'depth': 5, 'entanglement': 'linear'}\n", "}\n", "molecule = 'H .0 .0 -{0}; H .0 .0 {0}'\n", "algorithms = [{'name': 'VQE'},\n", @@ -88,15 +65,19 @@ " d = start + i*by/steps\n", " qiskit_chemistry_dict['PYQUANTE']['atoms'] = molecule.format(d/2) \n", " for j in range(len(algorithms)):\n", - " qiskit_chemistry_dict['algorithm'] = algorithms[j] \n", + " dict = copy.deepcopy(qiskit_chemistry_dict)\n", + " dict['algorithm'] = algorithms[j] \n", + " if algorithms[j]['name'] == 'ExactEigensolver':\n", + " del dict['optimizer']\n", + " del dict['variational_form']\n", " solver = QiskitChemistry()\n", - " result = solver.run(qiskit_chemistry_dict)\n", + " result = solver.run(dict)\n", " energies[j][i] = result['energy']\n", " hf_energies[i] = result['hf_energy']\n", " if algorithms[j]['name'] == 'VQE':\n", " eval_counts[j][i] = result['algorithm_retvals']['eval_count']\n", " if j == 1:\n", - " algorithms[j]['initial_point'] = result['algorithm_retvals']['opt_params']\n", + " algorithms[j]['initial_point'] = result['algorithm_retvals']['opt_params'].tolist()\n", " distances[i] = d\n", "print(' --- complete')\n", "\n", @@ -108,30 +89,9 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 2, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "pylab.plot(distances, hf_energies, label='Hartree-Fock')\n", "for j in range(len(algorithms)):\n", @@ -144,30 +104,9 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 3, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "for i in range(2):\n", " pylab.plot(distances, np.subtract(energies[i], energies[2]), label=titles[i])\n", @@ -180,30 +119,9 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "for i in range(2):\n", " pylab.plot(distances, eval_counts[i], '-o', label=titles[i])\n", @@ -237,7 +155,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.6.7" } }, "nbformat": 4, diff --git a/community/aqua/chemistry/lih_uccsd.ipynb b/community/aqua/chemistry/lih_uccsd.ipynb index c72f282fe..66b200343 100644 --- a/community/aqua/chemistry/lih_uccsd.ipynb +++ b/community/aqua/chemistry/lih_uccsd.ipynb @@ -15,7 +15,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": null, "metadata": { "scrolled": true }, @@ -24,29 +24,14 @@ "name": "stdout", "output_type": "stream", "text": [ - "Processing step 22 --- complete\n", - "Distances: [0.6 0.7 0.8 0.9 1. 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9\n", - " 2. 2.25 2.5 2.75 3. 3.25 3.5 3.75 4. ]\n", - "Energies: [[-7.3133458 -7.50092208 -7.63097824 -7.72081237 -7.78224239 -7.82359926\n", - " -7.85069836 -7.86756328 -7.87700148 -7.8810157 -7.88107204 -7.87826816\n", - " -7.87344027 -7.86723396 -7.8601532 -7.8410427 -7.82307661 -7.80861236\n", - " -7.79836339 -7.79175315 -7.78771692 -7.78531925 -7.78391762]\n", - " [-7.31334583 -7.50092209 -7.63097825 -7.72081241 -7.7822424 -7.82359928\n", - " -7.85069838 -7.86756329 -7.87700149 -7.88101572 -7.88107204 -7.87826817\n", - " -7.87344029 -7.86723396 -7.86015321 -7.84104271 -7.82307664 -7.8086124\n", - " -7.79836343 -7.79175325 -7.78771697 -7.78531972 -7.78391847]]\n", - "Hartree-Fock energies: [-7.29954105 -7.48594487 -7.61577016 -7.70575334 -7.76736214 -7.80874318\n", - " -7.83561583 -7.85195386 -7.86053866 -7.86335762 -7.86186477 -7.85714496\n", - " -7.8500187 -7.84111204 -7.83090558 -7.80193896 -7.77087367 -7.74000074\n", - " -7.7108299 -7.68437642 -7.6612016 -7.64145387 -7.62497563]\n", - "VQE num evaluations: [ 217. 180. 201. 188. 191. 144. 190. 159. 182. 175. 195. 184.\n", - " 168. 196. 209. 179. 231. 211. 268. 569. 216. 948. 1032.]\n" + "Processing step __\b\b 0" ] } ], "source": [ "import numpy as np\n", "import pylab\n", + "import copy\n", "from qiskit.chemistry import QiskitChemistry\n", "\n", "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", @@ -77,9 +62,14 @@ " print('\\b\\b{:2d}'.format(i), end='', flush=True)\n", " qiskit_chemistry_dict['PYSCF']['atom'] = molecule.format(d/2) \n", " for j in range(len(algorithms)):\n", - " qiskit_chemistry_dict['algorithm']['name'] = algorithms[j] \n", + " dict = copy.deepcopy(qiskit_chemistry_dict)\n", + " dict['algorithm']['name'] = algorithms[j] \n", + " if algorithms[j] == 'ExactEigensolver':\n", + " del dict['optimizer']\n", + " del dict['variational_form']\n", + " del dict['initial_state']\n", " solver = QiskitChemistry()\n", - " result = solver.run(qiskit_chemistry_dict)\n", + " result = solver.run(dict)\n", " energies[j][i] = result['energy']\n", " hf_energies[i] = result['hf_energy']\n", " dipoles[j][i] = result['total_dipole_moment'] / 0.393430307\n", @@ -96,32 +86,11 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": { "scrolled": true }, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 2, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "pylab.plot(distances, hf_energies, label='Hartree-Fock')\n", "for j in range(len(algorithms)):\n", @@ -134,30 +103,9 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 3, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "pylab.plot(distances, np.subtract(hf_energies, energies[1]), label='Hartree-Fock')\n", "pylab.plot(distances, np.subtract(energies[0], energies[1]), label='VQE')\n", @@ -169,30 +117,9 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "for j in reversed(range(len(algorithms))):\n", " pylab.plot(distances, dipoles[j], label=algorithms[j])\n", @@ -204,30 +131,9 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "pylab.plot(distances, eval_counts, '-o', color=[0.8500, 0.3250, 0.0980], label='VQE')\n", "pylab.xlabel('Interatomic distance')\n", @@ -260,7 +166,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.6.7" } }, "nbformat": 4, diff --git a/community/aqua/chemistry/nah_uccsd.ipynb b/community/aqua/chemistry/nah_uccsd.ipynb index 8195f5fd2..ce3c7da82 100644 --- a/community/aqua/chemistry/nah_uccsd.ipynb +++ b/community/aqua/chemistry/nah_uccsd.ipynb @@ -15,7 +15,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": null, "metadata": { "scrolled": false }, @@ -24,41 +24,14 @@ "name": "stdout", "output_type": "stream", "text": [ - "Processing step 23 --- complete\n", - "Distances: [1. 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2. 2.1 2.2 2.3\n", - " 2.4 2.5 2.75 3. 3.25 3.5 3.75 4. 4.25 4.5 ]\n", - "Energies: [[-160.0584908 -160.15699853 -160.22568738 -160.27202157 -160.30172257\n", - " -160.31895195 -160.32675454 -160.32741543 -160.32269884 -160.31400293\n", - " -160.30245857 -160.2889906 -160.27435549 -160.25916613 -160.24391108\n", - " -160.22897215 -160.19475712 -160.16708738 -160.14746324 -160.13627081\n", - " -160.1312006 -160.12966451 -160.12935288 -160.1272386 ]\n", - " [-160.05849084 -160.15699856 -160.22568741 -160.2720216 -160.30172261\n", - " -160.31895199 -160.32675458 -160.32741545 -160.32269886 -160.31400297\n", - " -160.30245861 -160.28899063 -160.27435552 -160.25916618 -160.24391112\n", - " -160.22897222 -160.19475719 -160.16708762 -160.14746354 -160.13627173\n", - " -160.13150727 -160.12988489 -160.12941537 -160.12738873]]\n", - "Hartree-Fock energies: [-160.04320295 -160.14360744 -160.21336733 -160.26022033 -160.29007462\n", - " -160.30721237 -160.31476208 -160.31507193 -160.30995602 -160.30085169\n", - " -160.28891892 -160.2751014 -160.26016389 -160.24471683 -160.2292359\n", - " -160.21408033 -160.17913095 -160.14978812 -160.12634274 -160.10810649\n", - " -160.09400858 -160.08298959 -160.07419396 -160.0607817 ]\n", - "Dipoles: [[2.97283503 3.47766098 3.89571273 4.26007211 4.59366828 4.91064169\n", - " 5.21881014 5.52062327 5.82225205 6.12073518 6.41351277 6.70026841\n", - " 6.97550548 7.22874789 7.45326529 7.64302302 7.80687793 7.21426635\n", - " 5.34909309 2.7107585 1.0689969 0.21149191 0.05667558 0.03530844]\n", - " [2.97335246 3.47789485 3.89561999 4.26006188 4.59374084 4.91025573\n", - " 5.21772576 5.52078168 5.82151088 6.11992744 6.41423476 6.70095324\n", - " 6.97491033 7.22906568 7.45413201 7.63797444 7.80073442 7.19343854\n", - " 5.31627389 2.65735429 0.91782197 0.26885135 0.07470177 0.0219034 ]]\n", - "VQE num evaluations: [ 542. 570. 598. 579. 511. 546. 545. 519. 544. 555.\n", - " 562. 610. 591. 642. 695. 758. 982. 1400. 2393. 5254.\n", - " 10000. 10000. 3549. 10000.]\n" + "Processing step __\b\b 0" ] } ], "source": [ "import numpy as np\n", "import pylab\n", + "import copy\n", "from qiskit.chemistry import QiskitChemistry\n", "\n", "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", @@ -89,9 +62,14 @@ " print('\\b\\b{:2d}'.format(i), end='', flush=True)\n", " qiskit_chemistry_dict['PYSCF']['atom'] = molecule.format(d/2) \n", " for j in range(len(algorithms)):\n", - " qiskit_chemistry_dict['algorithm']['name'] = algorithms[j] \n", + " dict = copy.deepcopy(qiskit_chemistry_dict)\n", + " dict['algorithm']['name'] = algorithms[j] \n", + " if algorithms[j] == 'ExactEigensolver':\n", + " del dict['optimizer']\n", + " del dict['variational_form']\n", + " del dict['initial_state']\n", " solver = QiskitChemistry()\n", - " result = solver.run(qiskit_chemistry_dict)\n", + " result = solver.run(dict)\n", " energies[j][i] = result['energy']\n", " hf_energies[i] = result['hf_energy']\n", " dipoles[j][i] = result['total_dipole_moment'] / 0.393430307\n", @@ -109,30 +87,9 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 2, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "pylab.plot(distances, hf_energies, label='Hartree-Fock')\n", "for j in range(len(algorithms)):\n", @@ -145,30 +102,9 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 3, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "pylab.plot(distances, np.subtract(hf_energies, energies[1]), label='Hartree-Fock')\n", "pylab.plot(distances, np.subtract(energies[0], energies[1]), label='VQE')\n", @@ -180,30 +116,9 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "for j in reversed(range(len(algorithms))):\n", " pylab.plot(distances, dipoles[j], label=algorithms[j])\n", @@ -215,30 +130,9 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "pylab.plot(distances, eval_counts, '-o', color=[0.8500, 0.3250, 0.0980], label='VQE')\n", "pylab.xlabel('Interatomic distance')\n", @@ -271,7 +165,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.6.7" } }, "nbformat": 4, From c19b78d2df0b6d46bbb6d58503a80b95ffecad2b Mon Sep 17 00:00:00 2001 From: Manoel Marques Date: Mon, 25 Feb 2019 17:36:30 -0500 Subject: [PATCH 013/116] Shots defaults for statevector_simulator --- community/aqua/general/input_files/H2-0.735.json | 1 - community/aqua/general/input_files/eoh.json | 1 - community/aqua/general/input_files/vqe.json | 1 - community/aqua/optimization/input_files/maxcut.json | 1 - 4 files changed, 4 deletions(-) diff --git a/community/aqua/general/input_files/H2-0.735.json b/community/aqua/general/input_files/H2-0.735.json index f93007ca8..560f20117 100644 --- a/community/aqua/general/input_files/H2-0.735.json +++ b/community/aqua/general/input_files/H2-0.735.json @@ -7,7 +7,6 @@ "backend": { "provider": "qiskit.BasicAer", "name": "statevector_simulator", - "shots": 1, "skip_transpiler": false }, "initial_state": { diff --git a/community/aqua/general/input_files/eoh.json b/community/aqua/general/input_files/eoh.json index 2b6d0014d..11e2cd71c 100644 --- a/community/aqua/general/input_files/eoh.json +++ b/community/aqua/general/input_files/eoh.json @@ -10,7 +10,6 @@ "backend": { "provider": "qiskit.BasicAer", "name": "statevector_simulator", - "shots": 1024, "skip_transpiler": false }, "initial_state": { diff --git a/community/aqua/general/input_files/vqe.json b/community/aqua/general/input_files/vqe.json index c9e792e9e..ffdf3968f 100644 --- a/community/aqua/general/input_files/vqe.json +++ b/community/aqua/general/input_files/vqe.json @@ -7,7 +7,6 @@ "backend": { "provider": "qiskit.BasicAer", "name": "statevector_simulator", - "shots": 1024, "skip_transpiler": false }, "initial_state": { diff --git a/community/aqua/optimization/input_files/maxcut.json b/community/aqua/optimization/input_files/maxcut.json index 9ca120f25..f14958c22 100644 --- a/community/aqua/optimization/input_files/maxcut.json +++ b/community/aqua/optimization/input_files/maxcut.json @@ -7,7 +7,6 @@ "backend": { "provider": "qiskit.BasicAer", "name": "statevector_simulator", - "shots": 1024, "skip_transpiler": false }, "initial_state": { From 00df8c39a11be257d50d0f1c3ac355d00545dcc2 Mon Sep 17 00:00:00 2001 From: Shaohan Hu Date: Tue, 26 Feb 2019 11:24:17 -0500 Subject: [PATCH 014/116] add example: 3-Coloring oracle by reduction to SAT --- ...Coloring Oracle via Reduction to SAT.ipynb | 225 ++++++++++++++++++ 1 file changed, 225 insertions(+) create mode 100644 community/aqua/optimization/3-Coloring Oracle via Reduction to SAT.ipynb diff --git a/community/aqua/optimization/3-Coloring Oracle via Reduction to SAT.ipynb b/community/aqua/optimization/3-Coloring Oracle via Reduction to SAT.ipynb new file mode 100644 index 000000000..8b041dc44 --- /dev/null +++ b/community/aqua/optimization/3-Coloring Oracle via Reduction to SAT.ipynb @@ -0,0 +1,225 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Constructing Quantum Oracles for 3-Coloring Problems via NP-Reduction\n", + "\n", + "In this notebook, we demonstrate how to easily construct quantum oracles for [3-Coloring problems](https://en.wikipedia.org/wiki/Graph_coloring) using Qiskit Aqua via simple NP-Reduction to [SAT problems](https://en.wikipedia.org/wiki/Boolean_satisfiability_problem).\n", + "\n", + "3-Coloring is the decision problem of determining whether a graph's vertices can be colored using only 3 different colors s.t. no neighboring vertices have the same color. SAT is also a decision problem where we want to see if an \n", + "given conjunctive normal form (CNF) can have a satisfying assignment.\n", + "\n", + "Aqua already provides an `LogicExpressionOracle` class capable of building Quantum Oracle circuits from arbitrary logic expressions, with support for the [DIMACS CNF format](https://www.satcompetition.org/2009/format-benchmarks2009.html). So, to take advantage of that, we in this notebook aim to reduce 3-coloring problems to SAT problems, and then directly use the `LogicExpressionOracle` class to build the Oracle circuit.\n", + "\n", + "For 3-coloring problem instances, we work with the [DIMACS graph coloring format](https://mat.tepper.cmu.edu/COLOR/instances.html), which basically indicates the number of vertices and edges on the `'p edge'` line, followed by the `'e'` lines listing all edges (vertex pairs). For example we can have the following toy instance, and easily parse it." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The input 3-coloring instance has 3 vertices and 3 edges: [[1, 2], [1, 3], [2, 3]].\n" + ] + } + ], + "source": [ + "three_coloring_instance = '''\n", + "c This is an example DIMACS 3-coloring file\n", + "p edge 3 3\n", + "e 1 2\n", + "e 1 3\n", + "e 2 3\n", + "'''\n", + "\n", + "import itertools\n", + "\n", + "def parse_3_coloring_instance(instance):\n", + " ls = [\n", + " l.strip() for l in instance.split('\\n')\n", + " if len(l) > 0 and not l.strip()[0] == 'c'\n", + " ]\n", + " headers = [l for l in ls if l[0] == 'p']\n", + " if len(headers) == 1:\n", + " p, sig, nv, ne = headers[0].split()\n", + " assert p == 'p' and sig == 'edge'\n", + " elif len(headers) > 1:\n", + " raise RuntimeError('Invalid input format for 3-Coloring.')\n", + " h_nv, h_ne = int(nv), int(ne)\n", + " edges = [[int(v) for v in l.split()[1:]] for l in ls if l[0] == 'e']\n", + " nv = len(set(list(itertools.chain.from_iterable(edges))))\n", + " ne = len(edges)\n", + " if not h_nv == nv:\n", + " print((\n", + " 'Warning: inaccurate vertex count {} in header. '\n", + " 'Actual vertex count is {}.'\n", + " ).format(h_nv, nv))\n", + " if not h_ne == ne:\n", + " print((\n", + " 'Warning: inaccurate edge count {} in header. '\n", + " 'Actual edge count is {}.'\n", + " ).format(h_ne, ne))\n", + "\n", + " return nv, ne, edges\n", + "\n", + "nv, ne, edges = parse_3_coloring_instance(three_coloring_instance)\n", + "\n", + "print('The input 3-coloring instance has {} vertices and {} edges: {}.'.format(nv, ne, edges))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For any 3-coloring problem instance, we can use the following simple strategy to reduce it to a SAT problem:\n", + "\n", + "- For each vertex $v$, we create three boolean variables $v_r$, $v_g$, and $v_b$, corresponding to the vertex $v$ being of color red, green, and blue, respectively.\n", + "- For each vertex $v$, we then have the constraint that it needs to be of one and only one color. Therefore, $v_r \\vee v_g \\vee v_b = True$, and $v_i \\wedge v_j = False$ for $i,j \\in \\{r,g,b\\}, i \\ne j$.\n", + "- For each edge $(v, t)$, we have constraint that they cannot both be of the same color. Therefore, $v_i \\wedge t_i = False$ for $i \\in \\{r, g, b\\}$.\n", + "\n", + "With this simple strategy and the help of the [De Morgan's Law](https://en.wikipedia.org/wiki/De_Morgan%27s_laws), we can carry out the reduction as follows." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The input 3-Coloring instance can be reduced to the following SAT instance:\n", + "\n", + "p cnf 9 21\n", + "1 2 3 0\n", + "-1 -2 0\n", + "-1 -3 0\n", + "-2 -3 0\n", + "4 5 6 0\n", + "-4 -5 0\n", + "-4 -6 0\n", + "-5 -6 0\n", + "7 8 9 0\n", + "-7 -8 0\n", + "-7 -9 0\n", + "-8 -9 0\n", + "-1 -4 0\n", + "-2 -5 0\n", + "-3 -6 0\n", + "-1 -7 0\n", + "-2 -8 0\n", + "-3 -9 0\n", + "-4 -7 0\n", + "-5 -8 0\n", + "-6 -9 0.\n" + ] + } + ], + "source": [ + "def reduce_to_three_sat(nv, ne, edges):\n", + "\n", + " def _get_vertex_rgb(v):\n", + " return 3 * v - 2, 3 * v - 1, 3 * v\n", + "\n", + " def _get_vertex_constraints(v):\n", + " r, g, b = _get_vertex_rgb(v)\n", + " return [\n", + " '{0} {1} {2} 0'.format(r, g, b),\n", + " '{} {} 0'.format(-r, -g),\n", + " '{} {} 0'.format(-r, -b),\n", + " '{} {} 0'.format(-g, -b)\n", + " ]\n", + "\n", + " def _get_edge_constraints(v1, v2):\n", + " r1, g1, b1 = _get_vertex_rgb(v1)\n", + " r2, g2, b2 = _get_vertex_rgb(v2)\n", + " return [\n", + " '{0} {1} 0'.format(-r1, -r2),\n", + " '{0} {1} 0'.format(-g1, -g2),\n", + " '{0} {1} 0'.format(-b1, -b2)\n", + " ]\n", + "\n", + " buf = list()\n", + " buf.append('p cnf {0} {1}'.format(nv * 3, nv * 4 + ne * 3))\n", + " buf.extend(itertools.chain.from_iterable([\n", + " _get_vertex_constraints(v)\n", + " for v in range(1, nv + 1)])\n", + " )\n", + " buf.extend(itertools.chain.from_iterable([\n", + " _get_edge_constraints(v1, v2)\n", + " for v1, v2 in edges])\n", + " )\n", + " return '\\n'.join(buf)\n", + "\n", + "sat_instance_cnf = reduce_to_three_sat(nv, ne, edges)\n", + "print('The input 3-Coloring instance can be reduced to the following SAT instance:\\n\\n{}.'.format(sat_instance_cnf))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we have successfully reduced the 3-Coloring problem instance to its equivalent SAT instance, we can go ahead using Aqua's `LogicExpressionOracle` to build the oracle and construct the quantum circuit." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from qiskit.aqua.components.oracles import LogicExpressionOracle\n", + "\n", + "oracle = LogicExpressionOracle(expression=sat_instance_cnf)\n", + "oracle.circuit.draw(output='mpl', scale=0.3)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From 7b66e9f6c8a88af72daa241f84fd3d4ce6f12346 Mon Sep 17 00:00:00 2001 From: Shaohan Hu Date: Wed, 27 Feb 2019 09:35:40 -0500 Subject: [PATCH 015/116] minor edits --- .../3-Coloring Oracle via Reduction to SAT.ipynb | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/community/aqua/optimization/3-Coloring Oracle via Reduction to SAT.ipynb b/community/aqua/optimization/3-Coloring Oracle via Reduction to SAT.ipynb index 8b041dc44..2f72efc93 100644 --- a/community/aqua/optimization/3-Coloring Oracle via Reduction to SAT.ipynb +++ b/community/aqua/optimization/3-Coloring Oracle via Reduction to SAT.ipynb @@ -8,8 +8,8 @@ "\n", "In this notebook, we demonstrate how to easily construct quantum oracles for [3-Coloring problems](https://en.wikipedia.org/wiki/Graph_coloring) using Qiskit Aqua via simple NP-Reduction to [SAT problems](https://en.wikipedia.org/wiki/Boolean_satisfiability_problem).\n", "\n", - "3-Coloring is the decision problem of determining whether a graph's vertices can be colored using only 3 different colors s.t. no neighboring vertices have the same color. SAT is also a decision problem where we want to see if an \n", - "given conjunctive normal form (CNF) can have a satisfying assignment.\n", + "3-Coloring is the decision problem of determining whether a graph's vertices can be colored using only 3 different colors s.t. no neighboring vertices share the same color. SAT is also a decision problem where we want to see if an \n", + "given conjunctive normal form (CNF) has a satisfying assignment.\n", "\n", "Aqua already provides an `LogicExpressionOracle` class capable of building Quantum Oracle circuits from arbitrary logic expressions, with support for the [DIMACS CNF format](https://www.satcompetition.org/2009/format-benchmarks2009.html). So, to take advantage of that, we in this notebook aim to reduce 3-coloring problems to SAT problems, and then directly use the `LogicExpressionOracle` class to build the Oracle circuit.\n", "\n", @@ -81,7 +81,7 @@ "\n", "- For each vertex $v$, we create three boolean variables $v_r$, $v_g$, and $v_b$, corresponding to the vertex $v$ being of color red, green, and blue, respectively.\n", "- For each vertex $v$, we then have the constraint that it needs to be of one and only one color. Therefore, $v_r \\vee v_g \\vee v_b = True$, and $v_i \\wedge v_j = False$ for $i,j \\in \\{r,g,b\\}, i \\ne j$.\n", - "- For each edge $(v, t)$, we have constraint that they cannot both be of the same color. Therefore, $v_i \\wedge t_i = False$ for $i \\in \\{r, g, b\\}$.\n", + "- For each edge $(v, t)$, we have the constraint that they cannot both be of the same color. Therefore, $v_i \\wedge t_i = False$ for $i \\in \\{r, g, b\\}$.\n", "\n", "With this simple strategy and the help of the [De Morgan's Law](https://en.wikipedia.org/wiki/De_Morgan%27s_laws), we can carry out the reduction as follows." ] @@ -123,7 +123,7 @@ } ], "source": [ - "def reduce_to_three_sat(nv, ne, edges):\n", + "def reduce_to_sat(nv, ne, edges):\n", "\n", " def _get_vertex_rgb(v):\n", " return 3 * v - 2, 3 * v - 1, 3 * v\n", @@ -158,7 +158,7 @@ " )\n", " return '\\n'.join(buf)\n", "\n", - "sat_instance_cnf = reduce_to_three_sat(nv, ne, edges)\n", + "sat_instance_cnf = reduce_to_sat(nv, ne, edges)\n", "print('The input 3-Coloring instance can be reduced to the following SAT instance:\\n\\n{}.'.format(sat_instance_cnf))" ] }, From e6bc7dd1ccd28aaff2200ff70bec3fea3831c1be Mon Sep 17 00:00:00 2001 From: Shaohan Hu Date: Wed, 27 Feb 2019 09:41:36 -0500 Subject: [PATCH 016/116] remove period --- .../optimization/3-Coloring Oracle via Reduction to SAT.ipynb | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/community/aqua/optimization/3-Coloring Oracle via Reduction to SAT.ipynb b/community/aqua/optimization/3-Coloring Oracle via Reduction to SAT.ipynb index 2f72efc93..3ff37dcf9 100644 --- a/community/aqua/optimization/3-Coloring Oracle via Reduction to SAT.ipynb +++ b/community/aqua/optimization/3-Coloring Oracle via Reduction to SAT.ipynb @@ -118,7 +118,7 @@ "-3 -9 0\n", "-4 -7 0\n", "-5 -8 0\n", - "-6 -9 0.\n" + "-6 -9 0\n" ] } ], @@ -159,7 +159,7 @@ " return '\\n'.join(buf)\n", "\n", "sat_instance_cnf = reduce_to_sat(nv, ne, edges)\n", - "print('The input 3-Coloring instance can be reduced to the following SAT instance:\\n\\n{}.'.format(sat_instance_cnf))" + "print('The input 3-Coloring instance can be reduced to the following SAT instance:\\n\\n{}'.format(sat_instance_cnf))" ] }, { From 7f33fa66c13f3bf1c79c90bb910e84284d8e3c6b Mon Sep 17 00:00:00 2001 From: Manoel Marques Date: Thu, 28 Feb 2019 22:57:55 -0500 Subject: [PATCH 017/116] Remove RunConfig from QuantumInstance parameters --- .../qsvm_kernel_directly.ipynb | 10 +-- .../qsvm_variational.ipynb | 51 +++--------- community/aqua/chemistry/h2_qpe.ipynb | 18 +---- community/aqua/general/eoh.ipynb | 45 ++++++----- community/aqua/general/vqe2iqpe.ipynb | 4 +- community/aqua/optimization/grover.ipynb | 4 +- .../08_Sampling a Thermal State.ipynb | 10 +-- ...e Optimization and Ensemble Learning.ipynb | 4 +- ...timization and Unsupervised Learning.ipynb | 39 ++------- .../qsvm_kernel_classification.ipynb | 51 +++--------- .../aqua/finance/portfolio_optimization.ipynb | 11 +-- qiskit/aqua/optimization/maxcut_and_tsp.ipynb | 79 +++++++++---------- 12 files changed, 108 insertions(+), 218 deletions(-) diff --git a/community/aqua/artificial_intelligence/qsvm_kernel_directly.ipynb b/community/aqua/artificial_intelligence/qsvm_kernel_directly.ipynb index b3b4c830b..601c0fc37 100644 --- a/community/aqua/artificial_intelligence/qsvm_kernel_directly.ipynb +++ b/community/aqua/artificial_intelligence/qsvm_kernel_directly.ipynb @@ -29,7 +29,6 @@ "source": [ "from datasets import *\n", "from qiskit import Aer\n", - "from qiskit.qobj import RunConfig\n", "from qiskit.aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name\n", "from qiskit.aqua import run_algorithm, QuantumInstance\n", "from qiskit.aqua.input import SVMInput\n", @@ -140,7 +139,7 @@ }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -194,10 +193,9 @@ "source": [ "backend = Aer.get_backend('qasm_simulator')\n", "feature_map = SecondOrderExpansion(num_qubits=feature_dim, depth=2, entangler_map=[[0, 1]])\n", - "svm = QSVMKernel(feature_map, training_input, test_input, None)# the data for prediction can be feeded later.\n", + "svm = QSVMKernel(feature_map, training_input, test_input, None)# the data for prediction can be fed later.\n", "svm.random_seed = random_seed\n", - "run_config = RunConfig(shots=shots, max_credits=10, memory=False, seed=random_seed)\n", - "quantum_instance = QuantumInstance(backend, run_config, seed_mapper=random_seed)\n", + "quantum_instance = QuantumInstance(backend, shots=shots, seed=random_seed, seed_mapper=random_seed)\n", "result = svm.run(quantum_instance)" ] }, @@ -222,7 +220,7 @@ }, { "data": { - "image/png": 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\n", + "image/png": 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4FE1+RXEpmvyK4lI0+RXFpZTquK4qVYLQJba/l1YrnI9d+uBF2co7svH7NLbvgCFC+2nVIhrbPjZWaDt/k8YhAB+hNWrMMKExIw6At+xeffPVNHZov1uEduON99HYAYNuElpuDm//jEuQx7Ynk4+qerCnrFS/9+XXQjtxTLaqAkBV4og7c6wcFwYA138u269nf7uYRAKBtQKFFtE4nMY2CJF3frbulXdCdm/ldyxq1akptBHP3ktjU8h5nDBvIY015I7F0IfvpLHjv/1JaCGRfOFsxl7vuwDZOdyJmqFXfkVxKZr8iuJSNPkVxaVo8iuKSynVgl85n3KoVMW7KHTiuHQqBYDg4Aih7Ung7Z+tW5/rL+q8Zj1hXZzQ/P35DPnExHVC8ykn1807ueyy9fhOLbusuDdv3uc09h3zitBOnpAOtwAwY9xkoT34uixaAkDnzrIAdfTQUaE5zYrfECcdhAeM4EWttUlJQivI5y7KB/ceFJqfvx+NrUH8C1hx70i6g9k0aXc/1oq/RxP37hOa07k5mSd9IPYf4fvQrVNr+VwOjslpSd4jzpzOIUOv/IriUjT5FcWlaPIrikvR5FcUl1IcD78JxpgMY8yWs7RXjTH7jDEbPf/4ImZFUS5bzmvmYYzpDOAYgC/OmtX3KoBj1tr3/pcnC4uoZx97cbSX9sPEGTT24TeeFFpwDe4EW7embMlclcBn17E2y6jaV9JYZtwxjhg7sNl5AHfZ7XRbJxrbPlrOBWT7CgAxEfJOyDOvjqOx77z8qNCmLllKY+uFhQqtdpA0NFmfnEK3r0Rmzzk51Fb2k9X6OtX565uYLivd6xJk6zUArPlxjdA63S7PefcW0XR7NvNw27odNJYZqAx9bhCNXbB8vdCc7tDc31deS8dN5G3Sg+70vtN1Uc08HMZ1KYpSxinJZ/7HjTFxno8F8vKgKMplzYUm/8cA6gOIAZAGYIxT4Nmz+o4fK/5AAUVR/lguKPmttQestaestacBfAag3e/E/ndWX+UA3kmnKErpUyz3XmNMJIDZZxX8Qs9M6TXGPAWgvbW2v/NPKKJmcG17W//HvDSn549oKotav8zka6U79LpWaEPuvpnG9uku200HPvUIjW3aooF8rgZSY0UigBfmPp34HY0NCpXFLqeCEGt3HfMqHxM1aaFcI+/kX1A/RroCD+wiz+3xfNmqCvCC324H7wC27t6JXPJ8H03/nsY+dKd83cuR8ldlv4p0+/wC2R7b9/anaez4KaOF5le++B3zD9//GtVjYqVj8iMDpd8DAFzh7+/1uF3btli3bl2xCn7n3VPPuK4uAGoYY1IB/BVAF2NMDIqm86YAeKg4T6YoyuXDhY7r4itOFEUpM2iHn6K4FE1+RXEpmvyK4lJKdVZf4+bN7aTvvKvd5X18aOziZbIdMn55PI0tLCgUWodbOtDY3OzjQkvazOe+bV33m9Duf/0xoSXH8e273Sj3wel8M5fdyW99QmOXr/hWaE4tu/d2vV5oA+5+gcYyZ2HmZtu8Th26/ba0NKH1aS2NKQBgXpw0VckvlK8jwCvoTrFdGjcW2oodsj33tMPrEEgciNvU5e7M2XnSxXjjbu4KzM7ZqdOnaexX/5Ez/O7rx5fP/BznbSTz8v33IWnbNp3VpyiKM5r8iuJSNPkVxaVo8iuKSynVgl/T6Gg7bfZsLy0pI4PGsoLMgmm8vbcqGedUv0U9GnuqUBZZrmkpx2oBQAEpKk2f8qPQfHx50bLLTdcI7XpSkAKA79ZJp+A8B2fjcqRf1alld9dGqX819S0aO+3XX4XWs0ULofmU49cMtkY/+aBsRQaA6gHS5fZkIXeereovi3BTF/ECZ6doOQasXi05Eq6cg1cCY2E8LzS3JO3b+7OyaGydINm+7fRzU3ftF9odN3amsX6+3sXQG67rgo2//aYFP0VRnNHkVxSXosmvKC5Fk19RXIomv6K4lFKt9tesFWb79PN2k60WzO3/Pn3vr0Ib+f4/aexnb74jte+n0thfl24QmtP8vN3bZdvuR5OlgUPCflmdBYCIGnJW37odO2nsgz1l+yabnQcAL48bIbRdqbK1FuCz9mqSll0AuOsaeXfirc++Etr+nfx465E7LPO+kHdHAGA8uePw7ruTaGw+mXPHWpEBoHx5eedl+1rZ3rsvUc7ZA/i5efHZv9DYGYuWCc0w5xAAW1cmCG3Es/fS2Lg9e4S26hfZag4A+bne52bCP95AWmqKVvsVRXFGk19RXIomv6K4lOKM66pjjFlsjNlqjIk3xgzz6EHGmPnGmETPV/XuV5QyRHGsRgsBPGOt3WCMqQJgvTFmPoB7ASy01r5tjHkewPMAZCXqLGqFVMeTzw/20ioSx1cACG8SLrTbu/JRV1dGyXFbh4/LdfsAMPD2G4X2+RfcCTZz/yGhsf3t2pS3B4+fNVdo/bpLN1wAeO/Lr4XGinUAH6F1dVQUjZ25Ro6v6kFadgFe3HvhAWnhOPKd8XT7uCWbhPbQaO7tev9dw4UWHy8LaAAQGdlcaK27c5+Ao8fkOVv6w89C27KFP1dEhGwPHjykN409kiFbeedO4e+lvsMGCi0+lReab2gujzfzKJ95MbBTR6oXh+KM60qz1m7wfJ8DIAFAGIBbAEz2hE0G0OeC90JRlFLnf/rM7/HvbwlgNYDgM979ANIBBF/UPVMU5Q+l2MlvjAkAMBPAk9Zar7+tbFGzAG0YOHtc15HDOu9TUS4XipX8xhhfFCX+l9baMwZyB4wxoZ7/DwVA1+aePa6rGlnWqCjKpaE4E3sMioZ0JFhrx571X98DGAzgbc/XWef7WcdPnMDKLdu8tC3Lt9DYQ/tkse2eXl1pbM1AOQN+x7YUGstGSsX25GafIXXlSKkD2dlC23VAzo8HgFbRDYW2IYUbPJ44Js0gAwLlmncAWJ+cIrRqlXksM450Wo/POvdYce/NEQ/S7VvGdBMaK4oBwD8myU7Jd177jMbOnilnxCyYyv0aCvLliDM/P3+htWghjU0BwBh5brbt592TC6fPE9qQUQ/T2Ed6yTFir306gcbWJ/4DY4fx0V7PvDrO6/HUT9+lcYziVPs7AhgEYLMxZqNHG4mipJ9hjLkPwG4A/Yr9rIqiXHKKM65rOQCnXmF+KVYU5bJHO/wUxaVo8iuKS9HkVxSXUpyC30UjwN8f1zT3dq/NTM2ksWyd/+Fjx2hsgxBZld+9m1dorwoNFdqU6XzNed7RXKEFXSfXkReeOkW3Z14JrSMjaWxVMiZqQ9x2GsvuWDAN4CO0GoeF0Vi2Hp+17LKqPgD8tlGOmWrdsQuNnfLlHKE1bCvvjgDAhpX1hRZ7VyyNnTdRtlQfPLhXaNWr83OwebN0BW5d930ay1pbrm3ciEZGRbUSWucOMTQ2jdxRyszkrcA5h73bfk+d4iPAGHrlVxSXosmvKC5Fk19RXIomv6K4lFIt+GVl5+D7n7zXUaenpNPY3fGyDfae/j1p7Mw5S4TWvBUvHmXnyiJe3WaRNLZq1SpCY62xex0WLLERTfM383bmmWNnCm3ACG7gGVxVtjPvzuSF0z6t5bp3pxFazGyTrcd3atllxb1/ffgSjWWvwxc/8nFssb3lavHYdrxYtmmxLFDeOvRWoaU6GHg2ipFr6UOqynFwABDVTBb3LF/fhtq15fuxpUPx9/2p3wotPFz6DADAtXd4+0PMnzeZxjH0yq8oLkWTX1Fciia/orgUTX5FcSma/IriUkp1XFer1q3tsl9XeGnZudLEAgB8feTYpcLTvHVxD6l0t6pbl8cekiYhP69cT2MP7JYmHUOH3CG04/lynBQAJGVIc6M29fh+Hc07IbS1SUk09irSztzoSulgDAA/btwotGuuuorG5uTJ14K57DIjDoC37A5/TLrWAryd+aX3/kVjq4XIVu+QSHkOnJg7Qbb8Vqoinx8A/Cr5Ce32e/hdpoM50lF39dy1NPa+++UdhywHh2n2Pk8+QI2yMOcT73M+b+4kHD6UpuO6FEVxRpNfUVyKJr+iuJSSjOt61Rizzxiz0fNPzphWFOWypSTjugDgfWvte8V9sqzcXHy/wXvOeDeHUVdjP5Kjo0YPf4DGzlq6SmgLFq6msT1ukDPoA2vx9s0EMlN9e7psR3Yqmm6O3yk03/L8lM/+drHQCvILaGzXEfdRnZFfWCi0k4X857777iShsRFaTi67bD2+U8suK+6NfvZ+Gsucdm+6S44RA4CoVnJsWZEBtTdzZvI22M6xtwktoGJFGrs9WfoELPlBFj0BILS+9JFo2IQXf7uTcV2HHLws5s/7wuvx0WxZ0HaiOAaeaQDSPN/nGGPOjOtSFKUMU5JxXQDwuDEmzhgzQaf0KkrZoiTjuj4GUB9ADIr+MhjjsN1/x3XlHDlyEXZZUZSLwQWP67LWHrDWnrLWngbwGYB2bNuzx3VVqaZ/HCjK5UJxqv10XNeZOX0ebgXAF6orinJZUpJxXQOMMTEosjBNASBdH4rBtB9llRsA0pNkVT2/gFepA6rJOXWnCrmjblqWNKLIPijdUgEgP0+27UaROWq5J+V8OADIayzdcH1I5RngdxwO7uWmG4npsu2YtfwCgB+5u1DVn7e2suONjJSVZzY7D3Bw2SVGHABQu2FtoTnNz9u0Sb5HmrfsSGOzDsrX95cF0iglN5e/5it+kSMn+xzoTWMXTV0ktN738rsQU/72kdCGvDiUxp4md8Amvj6FxkZENPN6nJcn73w5UZJxXdzvWlGUMoF2+CmKS9HkVxSXosmvKC6lVNfzh0XUs4+OfN1L863gS2Pzc2XxaVC/HjR26ZatQtu7XbZeAsC+HdK1dczbT9HYBfHyBkYhGYfEXHoBoCFZYz99sWyXBYArqkmn4PQUWdgDgMqBlYWWdYD3UNRvKltIDx/ixS5TTpZ2Ck7IIuuCqXIsF8BHaDm57K5PShZa/Ip4GrsnYY/Qpjp4Cizdtk1oEz/4Wmi1G/Am1YbtpCPvmKGjaOyoz98W2vI5vOBWnrzPp308jsau3CjfIyt27KCx6Xu91/m/M/xJ7NmZqOv5FUVxRpNfUVyKJr+iuBRNfkVxKZr8iuJSSnVWn6+fL0LreZsaLPs3r37HxMoqcZhDVb1bTLTQQrp0prGJxIxj6z4+t+2Kiv5CY86qberJNl4A6N37CaHdOlSaRQBAA9KeW6OKvAMAAF9/KltQx7z7NI0tPCXbnDOOHqWxq7fJivLRYzK2IJ+3M8+bKF1y2ew8AOjcV74+zIgD4C27rKoPAJ0byWr9oCEvC+2kg1HKv16Wbbgz502lsVEh8m5OgYNRyjUdZIvwzyt/prHs9Xl58DAae8/T3i3Cpx3a2hl65VcUl6LJryguRZNfUVyKJr+iuJRSLfj5+JRDlSu8W1NZYQ8ADu2XI7jSyVp8APhp5TqhNawfTmMziQtqcsJuGrt9zXahvf7G40I75TBGbOBIOaoqKjiYxm7dmyq03Vv5fnW6vZPQSGcuAN4WemO0LJACwBdTZgtt6Q+yKOXnJwuhAHDwoGypvnWoHFMF8BFazGUX4Ovx847xMW+suDdlwutCa9pUnkMAOH5ctj5vSOGvQ987nxXajFW8vTcoSBYHl27i7cz3dOsitGbRfH9XzFrq9fhYFnf5ZeiVX1Fciia/orgUTX5FcSnFMfCsaIxZY4zZ5BnXNcqj1zXGrDbG7DTGfG2MqfDH766iKBeL4hT88gHEWmuPeSy8lxtjfgLwNIrGdU03xnwC4D4Uefk7P1m5cggK8DbbDGwmTR8BYM5mOZvevwL//eLjKw9jBxmlBAAdW0hzxB0b5VgtAMjcJ4uO1chcedZF50RQgFyLD/Di3pF0vkZ/yJ03Ca2yHx8pdZr4NZRzKKztS5Sdjlu2yA5MJ6PN6tXlGvlU8jMBoFIVeR6dRmgxs02n9fisc48V9+Ljl9Ptw8ObCK0+MW0FgIgmsqi8YCofT1YrTI7rujKkBo1l49TqteBdpB++OdLrcW4u795knPfKb4s4U0L09fyzAGIBfOPRJwPgNq2KolyWFHdoh4/HtjsDwHwAuwBkWWvPTIFMhc7vU5QyRbGS3zOZJwZAbRRN5pGrJxw4e1xXlo7rUpTLhv+p2m+tzQKwGEAHAIHy2b4fAAALa0lEQVTGmDMftmsDoB/uzh7XFajjuhTlsqE41f6axphAz/f+ALoDSEDRL4E7PGGDAch1poqiXLYUp9ofCmCyMcYHRb8sZlhrZxtjtgKYbowZDeA3FM3zOy/n1plXLJKtuQDATIVTDx+msTVryr8onNbC+/lKF9X0ZLnGHwAqV+WV+XPJLyyk+rHs48XaHgBq1akpRQdn5eXbZdtx71ataGwguTvhRE2yDxERsvptDL9mbN68VGiNYuS4LwDwq+QntM6x3OuAjdBiLrsAX4/PWnZZVR8A9uyRTtANQnhL9vKfpIvx0x+8QGPHPTdWaI2JuzMA5BfI99OSWXxAVqNGV3s93rp1BY1jFGdcVxyAlkRPgsNkXkVRLn+0w09RXIomv6K4FE1+RXEppTquK+TKcHv3Q8O9tOAIXky57lpZwDpE1uIDQMvISKEtczB4/M9H3wttzD+Gk0ggpGpVof2SkCA0J2NR1vb7yUczaOyIZ+8V2rETJ2js9JnzhbZ23hoe++/3hLbcYfRTu/qy1Tr18CGhbdufRrdvXTdSaCFVA2ns2iTZvh1Qkbco7zogx5a99Yhctw9ws022Ht+pZZcV9wKIkSsAJBDj12UOa/Qj68j23p4xopQGANi+X/7cqv58Hw5kexcz+/Xqhfi4OB3XpSiKM5r8iuJSNPkVxaVo8iuKS9HkVxSXUurjukIivaupy77l47qOH5WtscMfGsBj8/OFdlvbtjS2/BM+QltHKs8AbwVmVdfw6tXp9v3ueEZo3QZ1p7EpmdI4JHEvN8JI3SGdfsdPGU1js/Oky23LiAgaO2ORfC2OZEjH5IXT59Hti2wevIlqxttwuw6IFdp2BwOWRVMXCW3U52/TWDZCi7nsMiMOgLfssqo+ADQOk6vYnYxd2ra+UWirE/ldlwLSLn5Na3m+AOCBkd53qrJzit9Srld+RXEpmvyK4lI0+RXFpWjyK4pLKdWCX41qVXF/X2/n2Uf7y7nlALAiMVFoTuOcZv0qW1vTdvEW1GFD7hCaU8Fv1Qo5W75iZdmCWugwrmvEe08IrV097sI6YZ50fQ0IDCCRwNDnBgnNrzx/KVftlM7EVzo4Khky82vuFNkOPWTUw3T7axvL4p4lRUAA+PiTb4S25Ic5NLb3vbLQu3wOH4tVQJxv2QgtJ5ddth7fqWWXFffK+8iCMgBs3C1bjBcsXUtjH+13s9DiE/jx9v6/R7we5xy+iO69iqL8OdHkVxSXosmvKC5Fk19RXEpJZvVNMsYkG2M2ev7F/PG7qyjKxaIks/oA4DlrrSzbOnA0Lw8Ltmzx0qa++SWNDW8kW1DbvsIr5eFh3BCEEU9aNZ2q9Y1bXSW0yn7SddbH4S4Ea61dn5xMY9mdjJN5sm0ZABYsXy+0e27uRmOb16kjtEoOMw8nrZRGJX2HDRTaI71kNRoAoqKkAUvt2g1p7JjPXhFaaH1peAEAU/4mHXl7DuhHY6/pIO8eBQXJll82Ow/gLrsv/vNFGstadllVHwBiSEv1lKW8tX1XhjQv6diUuzOP+uQzr8dbtstWaCeK495rAbBZfYqilGEuaFaftXa157/eMMbEGWPeN8bISyK8x3UdzZKLRBRFuTRc0Kw+Y0wzAC+gaGZfWwBBAEY4bPvfcV1XBHI/N0VRSp8LndXXw1qb5hnfnQ9gInSAh6KUKc7r3muMqQmgwFqb5ZnV9zOAdwCst9ammaJK1fsATlhrn/+9nxVaO8L+5Qnv4klQCG81jW4lW0V9HVonG4bK4s289Rtp7IIvpPPteFJ8AoAK5eV6fuYKXN1hNBhb+//p59/S2KEP3ym0/Q5TjRf9IkecrZvHx569O+45oa3ZtYvGXttInvP4VOkdsGmjHBcGAJ07yBs+zFkZ4C3VTu7MSTvlOv8xz/Ei3M8rfxbaUtKee2VIDbo9G6EVFcrHarH1+EtWbKCxzKV6UOdraeyONNmafsqhKH3ue+SRfv2wPT6+WO69JZnVt8jzi8EA2AiAN3wrinJZUpJZfdxaRFGUMoF2+CmKS9HkVxSXosmvKC6lVGf1NWvRws6cO9dLY5V6ANh7SM6IW5+SQmPXLpQV1rvu6kljt5Dq9a1t2tDYNNKUFFFDVomP5/OZegay6OpkSDL+25+E1q1TaxrLzDg+mSZNN5yez68S7cdC0+ZRQruheXOhpRw8SLdPO2duHACs+JXfdelwdbTQ2KxAADhNKt1HcnNpbMZRaWbBKvgniekHAOQXSOdcp+diLrvs/QHwll0/cjcJAK4iObGKmNsAQKu6db0eX92+PdavW6ez+hRFcUaTX1Fciia/orgUTX5FcSml6t57srAQyecUi5554DUa27BNE6ENfZyP66rbv6bQnFpF25Oi0uT5i2ksc8/deUAWbpyqK6xQ1MihwHnuGDMASCTPBQAz/yPXbA8lrsQAL0qdKODFrolfSffczKM5Qhs7jL9mmZmymBoeLl9HAAipGyI0p9ds4utThHb3yLto7MuDhwmtWXQnodVrwb0hlsz6UWiz53PPCTZCy8lll63HX50g3aEBXty7ukEDGjt50RKvx4dz5OvlhF75FcWlaPIrikvR5FcUl6LJryguRZNfUVxKqVb7fcqVQ9VKlby0v08YRWNnzJKz1KpVrkxjlyVIgw3WEgoAdaoHCS0zNZPGzvt8rtDGfCJnuVWpKOf3AcC0ufIuQqtI6eIKABl7M4SWlpROYx8Y0kdoVxDjEAD4asWvQuse3YzG5udKt+CBnToK7ZlXx9Htcw7LSvO1d3DDijmfyDsL8+d9QWMjIuT+ppPzBQD3PD1UaCtmLRXah2+OpNs3anS10A6QtmUAeGDkcKGdOzvvDOe67ALOZi3MVOXcqv4ZBsd2oXpx0Cu/orgUTX5FcSma/IriUjT5FcWllOp6fmPMQQBn5hnVAMArbWUbPa6yx5/p2CKstbLfnVCqye/1xMass9ZyF40yjB5X2ePPfGy/h/7ZryguRZNfUVzKpUz+8Zfwuf9I9LjKHn/mY3Pkkn3mVxTl0qJ/9iuKSyn15DfG9DDGbDfG7DTG/O5gz8sdY8wEY0yGMWbLWVqQMWa+MSbR85VPIr2MMcbUMcYsNsZsNcbEG2OGefQyfWzGmIrGmDXGmE2e4xrl0esaY1Z73pNfG2MqXOp9LQ1KNfk9wz4/BNATQBMAA4wx3OepbDAJQI9ztOcBLLTWNgCw0PO4rFEI4BlrbRMAVwN4zPM6lfVjywcQa61tASAGQA9jzNUomjr9vrU2CsARAPddwn0sNUr7yt8OwE5rbZK19iSA6QBuKeV9uGhYa5cCOHyOfAuAyZ7vJwOQS/Auc6y1adbaDZ7vcwAkAAhDGT82W8QZo0Bfzz8LIBbANx69zB3XhVLayR8G4Oxh66ke7c9EsLX2zID1dADSmbMMYYyJRNGU5tX4ExybMcbHGLMRQAaA+QB2Aciy1p5xOv0zvicpWvD7A7FFt1LK7O0UY0wAgJkAnrTWes3BKqvHZq09Za2NAVAbRX+JysXzLqG0k38fgDpnPa7t0f5MHDDGhAKA5yt3nbjMMcb4oijxv7TWfuuR/xTHBgDW2iwAiwF0ABBojDljbPNnfE9SSjv51wJo4KmuVgDQHwCfMFl2+R7AYM/3gwHMuoT7ckGYoumenwNIsNaOPeu/yvSxGWNqGmMCPd/7A+iOonrGYgBnBh+UueO6UEq9yccY0wvABwB8AEyw1r5RqjtwETHGfAWgC4pWhR0A8FcA/wEwA0A4ilYw9rPWnlsUvKwxxnQCsAzAZgBn/NBGouhzf5k9NmNMNIoKej4ouvDNsNa+Zoyph6LicxCA3wDcba2VnmZ/MrTDT1Fcihb8FMWlaPIrikvR5FcUl6LJryguRZNfUVyKJr+iuBRNfkVxKZr8iuJS/h/l3KikFmmUawAAAABJRU5ErkJggg==\n", 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" ] diff --git a/community/aqua/artificial_intelligence/qsvm_variational.ipynb b/community/aqua/artificial_intelligence/qsvm_variational.ipynb index 9d62d274e..ed80f5fc3 100644 --- a/community/aqua/artificial_intelligence/qsvm_variational.ipynb +++ b/community/aqua/artificial_intelligence/qsvm_variational.ipynb @@ -33,7 +33,6 @@ "from datasets import *\n", "from qiskit.aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name\n", "from qiskit import Aer\n", - "from qiskit.qobj import RunConfig\n", "from qiskit.aqua.input import SVMInput\n", "from qiskit.aqua import run_algorithm, QuantumInstance\n", "from qiskit.aqua.algorithms import QSVMVariational\n", @@ -53,12 +52,12 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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\n", 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\n", "text/plain": [ "
" ] @@ -117,7 +116,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -147,18 +146,9 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "testing success ratio: 1.0\n", - "predicted classes: ['A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B']\n" - ] - } - ], + "outputs": [], "source": [ "result = run_algorithm(params, svm_input, backend=backend)\n", "print(\"testing success ratio: \", result['testing_accuracy'])\n", @@ -186,7 +176,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -196,8 +186,7 @@ "feature_map = SecondOrderExpansion(num_qubits=feature_dim, depth=2)\n", "var_form = RYRZ(num_qubits=feature_dim, depth=3)\n", "svm = QSVMVariational(optimizer, feature_map, var_form, training_input, test_input)\n", - "run_config = RunConfig(shots=shots, max_credits=10, memory=False, seed=random_seed)\n", - "quantum_instance = QuantumInstance(backend, run_config, seed_mapper=random_seed)" + "quantum_instance = QuantumInstance(backend, shots=shots, seed=random_seed, seed_mapper=random_seed)" ] }, { @@ -209,17 +198,9 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "testing success ratio: 1.0\n" - ] - } - ], + "outputs": [], "source": [ "result = svm.run(quantum_instance)\n", "print(\"testing success ratio: \", result['testing_accuracy'])" @@ -236,17 +217,9 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "prediction: [0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1]\n" - ] - } - ], + "outputs": [], "source": [ "predicted_probs, predicted_labels = svm.predict(datapoints[0])\n", "predicted_classes = map_label_to_class_name(predicted_labels, svm.label_to_class)\n", diff --git a/community/aqua/chemistry/h2_qpe.ipynb b/community/aqua/chemistry/h2_qpe.ipynb index f7e9bdc2e..ff7148d0c 100644 --- a/community/aqua/chemistry/h2_qpe.ipynb +++ b/community/aqua/chemistry/h2_qpe.ipynb @@ -26,7 +26,6 @@ "source": [ "from collections import OrderedDict\n", "from qiskit import BasicAer\n", - "from qiskit.qobj import RunConfig\n", "from qiskit.transpiler import PassManager\n", "from qiskit.aqua import AquaError\n", "from qiskit.aqua import QuantumInstance\n", @@ -121,8 +120,7 @@ " expansion_mode='suzuki',\n", " expansion_order=2, shallow_circuit_concat=True)\n", "backend = BasicAer.get_backend('qasm_simulator')\n", - "run_config = RunConfig(shots=100, max_credits=10, memory=False)\n", - "quantum_instance = QuantumInstance(backend, run_config, pass_manager=PassManager())\n", + "quantum_instance = QuantumInstance(backend, shots=100, pass_manager=PassManager())\n", "result_qpe = qpe.run(quantum_instance)\n", "print('The ground state energy as computed by QPE is: {}'.format(result_qpe['energy']))" ] @@ -182,19 +180,9 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The groundtruth total ground state energy is -1.8572750302023806.\n", - "The total ground state energy as computed by QPE is -1.857136875325887.\n", - "In comparison, the Hartree-Fock ground state energy is -1.8369679912029842.\n" - ] - } - ], + "outputs": [], "source": [ "result_qpe = QiskitChemistry().run(qiskit_chemistry_qpe_dict, backend=backend)\n", "result_ees = QiskitChemistry().run(qiskit_chemistry_ees_dict)\n", diff --git a/community/aqua/general/eoh.ipynb b/community/aqua/general/eoh.ipynb index 82511a425..54dace550 100644 --- a/community/aqua/general/eoh.ipynb +++ b/community/aqua/general/eoh.ipynb @@ -17,23 +17,10 @@ "cell_type": "code", "execution_count": 1, "metadata": {}, - "outputs": [ - { - "ename": "ImportError", - "evalue": "cannot import name 'QuantumInstance'", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mImportError\u001b[0m Traceback (most recent call last)", - "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtranspiler\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mPassManager\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0maqua\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mrun_algorithm\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0maqua\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0moperator\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mOperator\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mQuantumInstance\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 7\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0maqua\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0malgorithms\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mEOH\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0maqua\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcomponents\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minitial_states\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mCustom\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;31mImportError\u001b[0m: cannot import name 'QuantumInstance'" - ] - } - ], + "outputs": [], "source": [ "import numpy as np\n", "from qiskit import BasicAer\n", - "from qiskit.qobj import RunConfig\n", "from qiskit.transpiler import PassManager\n", "from qiskit.aqua import run_algorithm, QuantumInstance\n", "from qiskit.aqua.operator import Operator\n", @@ -57,7 +44,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -76,9 +63,18 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The result is\n", + "{'avg': (0.36883301800844187+2.342013271062652e-17j), 'std_dev': 0.0}\n" + ] + } + ], "source": [ "backend = BasicAer.get_backend('statevector_simulator')\n", "quantum_instance = QuantumInstance(backend, pass_manager=PassManager())\n", @@ -96,7 +92,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -126,9 +122,18 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The result is\n", + "{'avg': (0.36883301800844187+2.342013271062652e-17j), 'std_dev': 0.0}\n" + ] + } + ], "source": [ "ret = run_algorithm(params, algo_input, backend=backend)\n", "print('The result is\\n{}'.format(ret))" diff --git a/community/aqua/general/vqe2iqpe.ipynb b/community/aqua/general/vqe2iqpe.ipynb index 3d559f5b6..48fd89215 100644 --- a/community/aqua/general/vqe2iqpe.ipynb +++ b/community/aqua/general/vqe2iqpe.ipynb @@ -19,7 +19,6 @@ "source": [ "import numpy as np\n", "from qiskit import BasicAer\n", - "from qiskit.qobj import RunConfig\n", "from qiskit.transpiler import PassManager\n", "from qiskit.aqua import Operator, QuantumInstance, run_algorithm\n", "from qiskit.aqua.input import EnergyInput\n", @@ -164,8 +163,7 @@ "iqpe = IQPE(algo_input.qubit_op, state_in, num_time_slices, num_iterations,\n", " expansion_mode='suzuki', expansion_order=2,\n", " shallow_circuit_concat=True)\n", - "run_config = RunConfig(shots=100, max_credits=10, memory=False, seed=random_seed)\n", - "quantum_instance = QuantumInstance(backend, run_config, pass_manager=PassManager(), seed_mapper=random_seed)\n", + "quantum_instance = QuantumInstance(backend, shots=100, seed=random_seed, pass_manager=PassManager(), seed_mapper=random_seed)\n", "result_iqpe = iqpe.run(quantum_instance)\n", "print(\"Continuing with VQE's result, IQPE estimated the ground energy to be {}.\".format(\n", " result_iqpe['energy']))" diff --git a/community/aqua/optimization/grover.ipynb b/community/aqua/optimization/grover.ipynb index e4248107e..63cda2b44 100644 --- a/community/aqua/optimization/grover.ipynb +++ b/community/aqua/optimization/grover.ipynb @@ -22,7 +22,6 @@ "import pylab\n", "import numpy as np\n", "from qiskit import BasicAer\n", - "from qiskit.qobj import RunConfig\n", "from qiskit.tools.visualization import plot_histogram\n", "from qiskit.aqua import QuantumInstance\n", "from qiskit.aqua import run_algorithm\n", @@ -117,8 +116,7 @@ ], "source": [ "backend = BasicAer.get_backend('qasm_simulator')\n", - "run_config = RunConfig(shots=100, max_credits=10, memory=False)\n", - "quantum_instance = QuantumInstance(backend, run_config)\n", + "quantum_instance = QuantumInstance(backend, shots=100)\n", "result = grover.run(quantum_instance)\n", "print(result['result'])" ] diff --git a/community/awards/teach_me_quantum_2018/qml_mooc/08_Sampling a Thermal State.ipynb b/community/awards/teach_me_quantum_2018/qml_mooc/08_Sampling a Thermal State.ipynb index 030f36603..b6a57fc5d 100644 --- a/community/awards/teach_me_quantum_2018/qml_mooc/08_Sampling a Thermal State.ipynb +++ b/community/awards/teach_me_quantum_2018/qml_mooc/08_Sampling a Thermal State.ipynb @@ -119,7 +119,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -186,7 +186,6 @@ "from functools import reduce\n", "from qiskit import Aer, BasicAer, QuantumRegister, QuantumCircuit, ClassicalRegister\n", "from qiskit import execute\n", - "from qiskit.qobj import RunConfig\n", "from qiskit.quantum_info import Pauli\n", "from qiskit.aqua import QuantumInstance\n", "from qiskit.aqua.operator import Operator\n", @@ -462,8 +461,8 @@ "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", - "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 12\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 13\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mresult\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 14\u001b[0;31m \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_thermal_state\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mweights\u001b[0m\u001b[0;34m,\u001b[0m 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a/community/awards/teach_me_quantum_2018/qml_mooc/09_Discrete Optimization and Ensemble Learning.ipynb b/community/awards/teach_me_quantum_2018/qml_mooc/09_Discrete Optimization and Ensemble Learning.ipynb index 1853fc0f8..d86ef9342 100644 --- a/community/awards/teach_me_quantum_2018/qml_mooc/09_Discrete Optimization and Ensemble Learning.ipynb +++ b/community/awards/teach_me_quantum_2018/qml_mooc/09_Discrete Optimization and Ensemble Learning.ipynb @@ -529,15 +529,13 @@ "source": [ "from qiskit.aqua import QuantumInstance\n", "from qiskit import Aer\n", - "from qiskit.qobj import RunConfig\n", "from qiskit.aqua.algorithms import QAOA\n", "from qiskit.aqua.components.optimizers import COBYLA\n", "p = 1\n", "optimizer = COBYLA()\n", "qaoa = QAOA(ising_model, optimizer, p, operator_mode='matrix')\n", "backend = Aer.get_backend('statevector_simulator')\n", - "run_config = RunConfig(shots=100)\n", - "quantum_instance = QuantumInstance(backend, run_config)\n", + "quantum_instance = QuantumInstance(backend, shots=100)\n", "result = qaoa.run(quantum_instance)" ] }, diff --git a/community/awards/teach_me_quantum_2018/qml_mooc/10_Discrete Optimization and Unsupervised Learning.ipynb b/community/awards/teach_me_quantum_2018/qml_mooc/10_Discrete Optimization and Unsupervised Learning.ipynb index 12e444040..f19f08a76 100644 --- a/community/awards/teach_me_quantum_2018/qml_mooc/10_Discrete Optimization and Unsupervised Learning.ipynb +++ b/community/awards/teach_me_quantum_2018/qml_mooc/10_Discrete Optimization and Unsupervised Learning.ipynb @@ -23,7 +23,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -115,19 +115,9 @@ "start_time": "2018-11-19T20:10:21.412811Z" } }, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/home/pwittek/.anaconda3/envs/qiskit/lib/python3.7/site-packages/marshmallow/schema.py:364: ChangedInMarshmallow3Warning: strict=False is not recommended. In marshmallow 3.0, schemas will always be strict. See https://marshmallow.readthedocs.io/en/latest/upgrading.html#schemas-are-always-strict\n", - " ChangedInMarshmallow3Warning\n" - ] - } - ], + "outputs": [], "source": [ "from qiskit import Aer\n", - "from qiskit.qobj import RunConfig\n", "from qiskit.aqua import QuantumInstance\n", "from qiskit.aqua.algorithms import QAOA\n", "from qiskit.aqua.components.optimizers import COBYLA\n", @@ -177,8 +167,7 @@ "outputs": [], "source": [ "backend = Aer.get_backend('statevector_simulator')\n", - "run_config = RunConfig(shots=100)\n", - "quantum_instance = QuantumInstance(backend, run_config)\n", + "quantum_instance = QuantumInstance(backend, shots=100)\n", "result = qaoa.run(quantum_instance)\n", "x = maxcut.sample_most_likely(result['eigvecs'][0])\n", "graph_solution = maxcut.get_graph_solution(x)\n", @@ -206,7 +195,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": null, "metadata": { "ExecuteTime": { "end_time": "2018-11-19T20:12:37.587621Z", @@ -214,25 +203,7 @@ }, "scrolled": true }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Energy of samples:\n", - "Energy: -13.331477071582572 Sample: {0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: -1, 6: -1, 7: -1, 8: -1, 9: -1}\n", - "Energy: -13.331477071582572 Sample: {0: -1, 1: -1, 2: -1, 3: -1, 4: -1, 5: 1, 6: 1, 7: 1, 8: 1, 9: 1}\n", - "Energy: -13.331477071582572 Sample: {0: -1, 1: -1, 2: -1, 3: -1, 4: -1, 5: 1, 6: 1, 7: 1, 8: 1, 9: 1}\n", - "Energy: -13.331477071582572 Sample: {0: -1, 1: -1, 2: -1, 3: -1, 4: -1, 5: 1, 6: 1, 7: 1, 8: 1, 9: 1}\n", - "Energy: -13.331477071582572 Sample: {0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: -1, 6: -1, 7: -1, 8: -1, 9: -1}\n", - "Energy: -13.331477071582572 Sample: {0: -1, 1: -1, 2: -1, 3: -1, 4: -1, 5: 1, 6: 1, 7: 1, 8: 1, 9: 1}\n", - "Energy: -13.331477071582572 Sample: {0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: -1, 6: -1, 7: -1, 8: -1, 9: -1}\n", - "Energy: -13.331477071582572 Sample: {0: -1, 1: -1, 2: -1, 3: -1, 4: -1, 5: 1, 6: 1, 7: 1, 8: 1, 9: 1}\n", - "Energy: -13.331477071582572 Sample: {0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: -1, 6: -1, 7: -1, 8: -1, 9: -1}\n", - "Energy: -13.331477071582572 Sample: {0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: -1, 6: -1, 7: -1, 8: -1, 9: -1}\n" - ] - } - ], + "outputs": [], "source": [ "import dimod\n", "\n", diff --git a/qiskit/aqua/artificial_intelligence/qsvm_kernel_classification.ipynb b/qiskit/aqua/artificial_intelligence/qsvm_kernel_classification.ipynb index 94ea0b51e..85d27cca5 100644 --- a/qiskit/aqua/artificial_intelligence/qsvm_kernel_classification.ipynb +++ b/qiskit/aqua/artificial_intelligence/qsvm_kernel_classification.ipynb @@ -47,7 +47,6 @@ "from qsvm_datasets import *\n", "\n", "from qiskit import Aer\n", - "from qiskit.qobj import RunConfig\n", "from qiskit.aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name\n", "from qiskit.aqua.input import SVMInput\n", "from qiskit.aqua import run_algorithm, QuantumInstance\n", @@ -96,7 +95,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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IQclrUmfKcyNV7D2Uc82o4IQUDDs4IQUTZJpsz845PXxw38T/C7HQZCjTHl2mmSyfqU/5k57VYppsEkNIuMV2yV3qlMcHEzLjBEmyzc/PYfHQfvOXQELhOg1nuc/cpPuN2mGRSMypjodKrKmvUG1FBSekYILE4As3XKsrJ+986+fQI5dvDOezj5vlSyFNdvR5Rp8XLpqea5ZicQsFn1RfFt97xuCEzDhRFHyUEKO/1cifi5L72mKx+COmgs+KclvH2VRwQmac6Ao+TqjTSnwIFbtOI1SM5oLPc1jlVkpT8NDKXUMFJ2TGSa7gNX3UIPTIH0vJU8yP1ozbb73BRKq2m0SXtQUWnljotqOCEzLjsIMTUjBBXzbJcWfQtqOIm+i7EMW1HlIk23xc9Joc31H3TdLm3mbck40QEnZHlz47ofgobBe6vA5ZM2nEr0frpgSOaz2M/n/9mRxfzolFn73IY9VTLK/FNxnpcvjgCRG5ICLPet2JEBKd1hhcRG4BsAHgq6q616nQal/0SaNP6hgv1j7jvjaEeqGjxnKhTo1VffmcbNKnfvrE4r7P2mf6cNSWhcV7sXLmFf8YXFUfB/CbtusIIflhFoOLyBKApdHfTYpLfeLy8TJCE+q+LnUQKxcxfj+rMvrY7WODdewdegdd19ja1w6zDq6qywCWAfujiwgh/cjmdNEuxFa38fuOEnojRctnjbk8tIvdbSqV4zx7aKw8CM6DE1IwLln0bwD4IIB5AP8F4LCqHm/5zGWFWm+UME7seK+rDW2bOvbJqsfKFlvhc8Za6Pnvul5Sz/CM0maLaxa91UVX1ds62EUIyQi66IQUzCCTbOP4Ts9Y2tDFnaxdw9DTZildc5/7hG5L66SjZdjR9v9ra+tO96GCE1Iw0c8mm0bMpFfoe0+7f5fliV2WSMbeDTYWXdrQJ+mYog58vRO+LkoIKSMGJ90pRbn7kEq5U+SHqOCEFEwUBU+hFqmWs47ff9SGaZs3dHkpZ9JzTSs3x/3GU5KqPlwWQYWyjQpOSMEUH4O7KHmfV1hDMKrAIUb01M+XCz5z8j5z3Sm23aKCE1Iw7OCEFEwUF33UVUnlJqZMuvncO4fwwedNsNT4hjo+bZbyAM0aKjghBRNEwV9a28Adx0977RHehUmjbKxESij6TJ9YqsEQkpJN+O7o66rcfU82iTVlRwUnpGCCKPju+R04fHCfyWkfffGJtUPb1ue0kliqOdT9zywUscuzW7/004XFQ/tx9MmzTtdSwQkpmKBZdJcRy0KZQm340MW2WMqXk8IOIRa3brs+i1cslbsrVHBCCiabpapWahBivjulUoV+GcECq/rJyTtpI6dMeRNUcEIKJoiCz8/PYfHQfq9VQJPIOdbLiT6qb6GeOaxY7EKfZ7Z+YcRiz/wmqOCEFAw7OCEF4+Sii8gBAPcA2ALgmKr+U1CrptAlmRMy2eZqQ27EtH8IU2hd6OKau4RGPq7+yWOn7fZFF5EtAI4C+CsA7wVwm4i8t7d1hJBouCj4TQB+oaovAoCIfBPAQQDPhzSsidBK7rJ/+bgNLvcJvaOHy15vNUOakkqB9eGOfcv0bSeXGPw9AH458vP56neEkMxxOT744wAOqOqh6ufbAfypqn5m7LolAEvVj3sBPGtvbmfmAaylNqIiF1tysQOgLZNwtWO3qu5su8jFRX8ZwHUjP++qfncZqroMYBkARGRFVRccyg5KLnYA+diSix0AbYlhh4uL/mMAfyQi14vI2wB8AsC/WxlACAlHq4Kr6hsi8hkA/4HNabITqvpccMsIId44zYOr6ncBfLdDucv9zDEnFzuAfGzJxQ6AtkzC1I4gxwcTQvKAS1UJKRjTDi4iB0Tk5yLyCxH5gmXZHe04ISIXRCTpVJ2IXCcij4nI8yLynIjcndCWbSLyIxH5aWXLkVS2VPZsEZGfiMh3EttxTkR+JiLPiMhKYluuFpEHROQFETkjIn/mXaaVi14taT0L4C+xuRjmxwBuU9XoK95E5BYAGwC+qqp7Y99/xI5rAFyjqk+LyByAVQB/nahOBMB2Vd0Qka0AngBwt6r+MLYtlT2fA7AA4B2qemsKGyo7zgFYUNXkc+Aich+AH6jqsWrG6u2q+qpPmZYK/taSVlV9HUC9pDU6qvo4gN+kuPeYHb9S1aerf68DOINEqwB1k43qx63VnyQJGBHZBeCjAI6luH+OiMg7AdwC4DgAqOrrvp0bsO3gXNLagIjsAfB+AE8ltGGLiDwD4AKAR1U1lS1fAfB5AL9PdP9RFMAjIrJarcZMxfUALgI4WYUux0Rku2+hTLJFQER2AHgQwGdV9bep7FDVN1X1fdhcjXiTiEQPX0TkVgAXVHU19r2n8AFVvRGbb0t+ugrvUnAlgBsB/Kuqvh/A/wDwzmNZdnCnJa2zRhXvPgjgflX9dmp7AKBy/R4DcCDB7W8G8LEq9v0mgA+JyNcS2AEAUNWXq78vAHgIm6FmCs4DOD/iVT2AzQ7vhWUH55LWMarE1nEAZ1T1y4lt2SkiV1f/vgqbydAXYtuhql9U1V2qugeb35HvqeonY9sBACKyvUp+onKHP4xEL0mp6q8B/FJE/rj61V/A4JVss00Xc1rSKiLfAPBBAPMich7AYVU9nsCUmwHcDuBnVewLAH9frQyMzTUA7qtmO64A8C1VTTpFlQHvBvDQ5jiMKwF8XVUfTmjPXQDurwTyRQCLvgVyJRshBcMkGyEFww5OSMGwgxNSMOzghBQMOzghBcMOTkjBsIMTUjDs4IQUzP8CS1BH043ZwoQAAAAASUVORK5CYII=\n", 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\n", 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\n", 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" ] @@ -176,8 +175,7 @@ "qsvm = QSVMKernel(feature_map, training_input, test_input, datapoints[0])\n", "\n", "backend = Aer.get_backend('qasm_simulator')\n", - "run_config = RunConfig(shots=1024, max_credits=10, memory=False, seed=seed)\n", - "quantum_instance = QuantumInstance(backend, run_config, seed_mapper=seed)\n", + "quantum_instance = QuantumInstance(backend, shots=1024, seed=seed, seed_mapper=seed)\n", "\n", "result = qsvm.run(quantum_instance)\n", "\n", @@ -187,7 +185,7 @@ " 'algorithm': {\n", " 'name': 'QSVM.Kernel'\n", " },\n", - " 'backend': {'name': 'qasm_simulator', 'shots': 1024},\n", + " 'backend': {'provider': 'qiskit.Aer', 'name': 'qasm_simulator', 'shots': 1024},\n", " 'feature_map': {'name': 'SecondOrderExpansion', 'depth': 2, 'entanglement': 'linear'}\n", "}\n", "algo_input = SVMInput(training_input, test_input, datapoints[0])\n", @@ -214,7 +212,7 @@ }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -267,17 +265,9 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "testing success ratio: 0.9\n" - ] - } - ], + "outputs": [], "source": [ "seed = 10598\n", "\n", @@ -285,8 +275,7 @@ "qsvm = QSVMKernel(feature_map, training_input, test_input)\n", "\n", "backend = Aer.get_backend('qasm_simulator')\n", - "run_config = RunConfig(shots=1024, max_credits=10, memory=False, seed=seed)\n", - "quantum_instance = QuantumInstance(backend, run_config, seed_mapper=seed)\n", + "quantum_instance = QuantumInstance(backend, shots=1024, seed=seed, seed_mapper=seed)\n", "\n", "result = qsvm.run(quantum_instance)\n", "\n", @@ -299,29 +288,9 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "kernel matrix during the training:\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "print(\"kernel matrix during the training:\")\n", "kernel_matrix = result['kernel_matrix_training']\n", diff --git a/qiskit/aqua/finance/portfolio_optimization.ipynb b/qiskit/aqua/finance/portfolio_optimization.ipynb index 8ff3543c5..3858359da 100644 --- a/qiskit/aqua/finance/portfolio_optimization.ipynb +++ b/qiskit/aqua/finance/portfolio_optimization.ipynb @@ -61,7 +61,6 @@ "outputs": [], "source": [ "from qiskit import BasicAer\n", - "from qiskit.qobj import RunConfig\n", "from qiskit.aqua import QuantumInstance\n", "from qiskit.aqua import Operator, run_algorithm\n", "from qiskit.aqua.input import EnergyInput\n", @@ -168,7 +167,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": null, "metadata": {}, "outputs": [ { @@ -230,7 +229,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": null, "metadata": {}, "outputs": [ { @@ -271,8 +270,7 @@ "ry = RY(qubitOp.num_qubits, depth=3, entanglement='full', initial_state=init_state)\n", "vqe = VQE(qubitOp, ry, cobyla, 'matrix')\n", "vqe.random_seed = seed\n", - "run_config = RunConfig(seed=seed)\n", - "quantum_instance = QuantumInstance(backend, run_config, seed_mapper=seed)\n", + "quantum_instance = QuantumInstance(backend, seed=seed, seed_mapper=seed)\n", "\n", "result = vqe.run(quantum_instance)\n", "\n", @@ -326,8 +324,7 @@ "cobyla.set_options(maxiter=250)\n", "qaoa = QAOA(qubitOp, cobyla, 3, operator_mode='matrix')\n", "qaoa.random_seed = seed\n", - "run_config = RunConfig(seed=seed)\n", - "quantum_instance = QuantumInstance(backend, run_config, seed_mapper=seed)\n", + "quantum_instance = QuantumInstance(backend, seed=seed, seed_mapper=seed)\n", "\n", "result = qaoa.run(quantum_instance)\n", "\n", diff --git a/qiskit/aqua/optimization/maxcut_and_tsp.ipynb b/qiskit/aqua/optimization/maxcut_and_tsp.ipynb index d5cf1f79c..17522c9fb 100644 --- a/qiskit/aqua/optimization/maxcut_and_tsp.ipynb +++ b/qiskit/aqua/optimization/maxcut_and_tsp.ipynb @@ -109,7 +109,6 @@ "import networkx as nx\n", "\n", "from qiskit import Aer\n", - "from qiskit.qobj import RunConfig\n", "from qiskit.tools.visualization import plot_histogram\n", "from qiskit.aqua import Operator, run_algorithm\n", "from qiskit.aqua.input import EnergyInput\n", @@ -167,7 +166,7 @@ }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -232,7 +231,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": null, "metadata": {}, "outputs": [ { @@ -261,7 +260,7 @@ }, { "data": { - "image/png": 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+ "image/png": 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\n", 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" ] @@ -299,7 +298,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -316,7 +315,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": null, "metadata": {}, "outputs": [ { @@ -331,7 +330,7 @@ }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -387,16 +386,16 @@ "name": "stdout", "output_type": "stream", "text": [ - "energy: -1.4986779698866395\n", - "time: 28.347098112106323\n", - "maxcut objective: -3.9986779698866393\n", - "solution: [0. 1. 0. 1.]\n", + "energy: -1.4991857466693328\n", + "time: 35.49838590621948\n", + "maxcut objective: -3.999185746669333\n", + "solution: [1. 0. 1. 0.]\n", "solution objective: 4.0\n" ] }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -415,12 +414,11 @@ "vqe = VQE(qubitOp, ry, spsa, 'matrix')\n", "\n", "backend = Aer.get_backend('statevector_simulator')\n", - "run_config = RunConfig(seed=seed)\n", - "quantum_instance = QuantumInstance(backend, run_config, seed_mapper=seed)\n", + "quantum_instance = QuantumInstance(backend, seed=seed, seed_mapper=seed)\n", "\n", "result = vqe.run(quantum_instance)\n", "\n", - "\"\"\"declarative apporach\n", + "\"\"\"declarative approach\n", "algorithm_cfg = {\n", " 'name': 'VQE',\n", " 'operator_mode': 'matrix'\n", @@ -442,7 +440,7 @@ " 'algorithm': algorithm_cfg,\n", " 'optimizer': optimizer_cfg,\n", " 'variational_form': var_form_cfg,\n", - " 'backend': {'name': 'statevector_simulator'}\n", + " 'backend': {provider': 'qiskit.Aer', 'name': 'statevector_simulator'}\n", "}\n", "\n", "result = run_algorithm(params, algo_input)\n", @@ -469,15 +467,15 @@ "output_type": "stream", "text": [ "energy: -1.5\n", - "time: 63.78048515319824\n", + "time: 41.23837685585022\n", "maxcut objective: -4.0\n", - "solution: [1 0 1 0]\n", + "solution: [0 1 0 1]\n", "solution objective: 4.0\n" ] }, { "data": { - "image/png": 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+ "image/png": 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\n", "text/plain": [ "
" ] @@ -497,13 +495,13 @@ "vqe = VQE(qubitOp, ry, spsa, 'grouped_paulis')\n", "\n", "backend = Aer.get_backend('qasm_simulator')\n", - "run_config = RunConfig(shots=1024, seed=seed)\n", - "quantum_instance = QuantumInstance(backend, run_config, seed_mapper=seed)\n", + "quantum_instance = QuantumInstance(backend, shots=1024, seed=seed, seed_mapper=seed)\n", "\n", "result = vqe.run(quantum_instance)\n", "\n", "\"\"\"declarative approach, update the param from the previous cell.\n", "params['algorithm']['operator_mode'] = 'grouped_paulis'\n", + "params['backend']['provider'] = 'qiskit.Aer'\n", "params['backend']['name'] = 'qasm_simulator'\n", "params['backend']['shots'] = 1024\n", "result = run_algorithm(params, algo_input)\n", @@ -565,14 +563,14 @@ "output_type": "stream", "text": [ "distance\n", - " [[ 0. 18. 90.]\n", - " [18. 0. 93.]\n", - " [90. 93. 0.]]\n" + " [[ 0. 11. 23.]\n", + " [11. 0. 33.]\n", + " [23. 33. 0.]]\n" ] }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -613,13 +611,13 @@ "name": "stdout", "output_type": "stream", "text": [ - "order = (0, 1, 2) Distance = 201.0\n", - "Best order from brute force = (0, 1, 2) with total distance = 201.0\n" + "order = (0, 1, 2) Distance = 67.0\n", + "Best order from brute force = (0, 1, 2) with total distance = 67.0\n" ] }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -698,15 +696,15 @@ "name": "stdout", "output_type": "stream", "text": [ - "energy: -600100.5\n", + "energy: -600033.5\n", "feasible: True\n", "solution: [1, 2, 0]\n", - "solution objective: 201.0\n" + "solution objective: 67.0\n" ] }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -760,16 +758,16 @@ "name": "stdout", "output_type": "stream", "text": [ - "energy: -594841.9262828702\n", - "time: 56.990293979644775\n", + "energy: -595242.8232593088\n", + "time: 66.49582099914551\n", "feasible: True\n", - "solution: [2, 0, 1]\n", - "solution objective: 201.0\n" + "solution: [1, 0, 2]\n", + "solution objective: 67.0\n" ] }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -788,8 +786,7 @@ "vqe = VQE(qubitOp, ry, spsa, 'matrix')\n", "\n", "backend = Aer.get_backend('statevector_simulator')\n", - "run_config = RunConfig(seed=seed)\n", - "quantum_instance = QuantumInstance(backend, run_config, seed_mapper=seed)\n", + "quantum_instance = QuantumInstance(backend, seed=seed, seed_mapper=seed)\n", "\n", "result = vqe.run(quantum_instance)\n", "\"\"\"\n", @@ -814,7 +811,7 @@ " 'algorithm': algorithm_cfg,\n", " 'optimizer': optimizer_cfg,\n", " 'variational_form': var_form_cfg,\n", - " 'backend': {'name': 'statevector_simulator'}\n", + " 'backend': {'provider': 'qiskit.Aer', 'name': 'statevector_simulator'}\n", "}\n", "result = run_algorithm(parahms,algo_input)\n", "\"\"\"\n", @@ -844,13 +841,13 @@ "vqe = VQE(qubitOp, ry, spsa, 'grouped_paulis', batch_mode=True)\n", "\n", "backend = Aer.get_backend('qasm_simulator')\n", - "run_config = RunConfig(shots=1024, seed=seed)\n", - "quantum_instance = QuantumInstance(backend, run_config, seed_mapper=seed)\n", + "quantum_instance = QuantumInstance(backend, shots=1024, seed=seed, seed_mapper=seed)\n", "\n", "result = vqe.run(quantum_instance)\n", "\n", "\"\"\"update params in the previous cell\n", "params['algorithm']['operator_mode'] = 'grouped_paulis'\n", + "params['backend']['provider'] = 'qiskit.Aer'\n", "params['backend']['name'] = 'qasm_simulator'\n", "params['backend']['shots'] = 1024\n", "result = run_algorithm(params,algo_input)\n", From 2f60a373de7d60d495ea396063dc7668ee78ec52 Mon Sep 17 00:00:00 2001 From: Shaohan Hu Date: Fri, 1 Mar 2019 11:23:32 -0500 Subject: [PATCH 018/116] remove cnf - its str content will be used directly --- community/aqua/optimization/3sat3-5.cnf | 7 ------- 1 file changed, 7 deletions(-) delete mode 100644 community/aqua/optimization/3sat3-5.cnf diff --git a/community/aqua/optimization/3sat3-5.cnf b/community/aqua/optimization/3sat3-5.cnf deleted file mode 100644 index 99ec81eec..000000000 --- a/community/aqua/optimization/3sat3-5.cnf +++ /dev/null @@ -1,7 +0,0 @@ -c This is an example DIMACS 3-sat file with 3 satisfying solutions: 1 -2 3 0, -1 -2 -3 0, 1 2 -3 0 -p cnf 3 5 --1 -2 -3 0 -1 -2 3 0 -1 2 -3 0 -1 -2 -3 0 --1 2 3 0 From af5418774bd4bd633150160cdf3a71cd37cfeb7e Mon Sep 17 00:00:00 2001 From: Shaohan Hu Date: Fri, 1 Mar 2019 11:26:26 -0500 Subject: [PATCH 019/116] Update grover.ipynb --- community/aqua/optimization/grover.ipynb | 115 ++++++++++++++--------- 1 file changed, 69 insertions(+), 46 deletions(-) diff --git a/community/aqua/optimization/grover.ipynb b/community/aqua/optimization/grover.ipynb index 63cda2b44..b225f72a5 100644 --- a/community/aqua/optimization/grover.ipynb +++ b/community/aqua/optimization/grover.ipynb @@ -6,9 +6,9 @@ "collapsed": true }, "source": [ - "## _*Using Grover Search for 3SAT problems*_\n", + "## _*Using Grover's Search to Find a Solution to a SAT problem*_\n", "\n", - "This notebook demonstrates how to use the `Qiskit Aqua` library Grover algorithm and process the result.\n", + "This notebook demonstrates how to use the `Qiskit Aqua` library `Grover` search algorithm and process the result.\n", "\n", "Further information is available for the algorithms in the github repo qiskit/aqua/readme.md" ] @@ -26,47 +26,51 @@ "from qiskit.aqua import QuantumInstance\n", "from qiskit.aqua import run_algorithm\n", "from qiskit.aqua.algorithms import Grover\n", - "from qiskit.aqua.components.oracles import SAT" + "from qiskit.aqua.components.oracles import LogicExpressionOracle" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "We have a SAT problem to which we want to find solutions using Grover and SAT oracle combination. The SAT problem is specified in the DIMACS CNF format. We read one of the sample cnf files to load the problem." + "Suppose we have a [Satisfiability (SAT) problem](https://en.wikipedia.org/wiki/Boolean_satisfiability_problem), for which we would like to use `Grover` search algorithm to find a satisfying solution. SAT problems are usually expressed in [Conjunctive Normal Forms (CNF)](https://en.wikipedia.org/wiki/Conjunctive_normal_form) and written in the [DIMACS-CNF](https://www.satcompetition.org/2009/format-benchmarks2009.html) format. For example:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "c This is an example DIMACS 3-sat file with 3 satisfying solutions: 1 -2 3 0, -1 -2 -3 0, 1 2 -3 0\n", - "p cnf 3 5\n", - "-1 -2 -3 0\n", - "1 -2 3 0\n", - "1 2 -3 0\n", - "1 -2 -3 0\n", - "-1 2 3 0\n", - "\n" - ] - } - ], + "outputs": [], "source": [ - "with open('3sat3-5.cnf', 'r') as f:\n", - " sat_cnf = f.read()\n", - "print(sat_cnf)" + "sat_instance = '''\n", + "c example DIMACS-CNF SAT\n", + "p cnf 3 5\n", + "-1 -2 -3 0\n", + "1 -2 3 0\n", + "1 2 -3 0\n", + "1 -2 -3 0\n", + "-1 2 3 0\n", + "'''" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "With this problem input, we create the corresponding `oracle` component:" + "The CNF of this SAT instance contains 3 variables and 5 clauses:\n", + "\n", + "$(\\neg v_1 \\vee \\neg v_2 \\vee \\neg v_3) \\wedge (v_1 \\vee \\neg v_2 \\vee v_3) \\wedge (v_1 \\vee v_2 \\vee \\neg v_3) \\wedge (v_1 \\vee \\neg v_2 \\vee \\neg v_3) \\wedge (\\neg v_1 \\vee v_2 \\vee v_3)$\n", + "\n", + "It can be verified that this SAT problem instance has three satisfying solutions:\n", + "\n", + "$(v_1, v_2, v_3) = (T, F, T)$ or $(F, F, F)$ or $(T, T, F)$\n", + "\n", + "Or, expressed using the DIMACS notation:\n", + "\n", + "`1 -2 3`, or `-1 -2 -3`, or `1 2 -3`.\n", + "\n", + "\n", + "With this example problem input, we then create the corresponding `oracle` for our `Grover` search. In particular, we use the `LogicExpressionOracle` component provided by Aqua, which supports parsing DIMACS-CNF format strings and constructing the corresponding oracle circuit." ] }, { @@ -75,7 +79,7 @@ "metadata": {}, "outputs": [], "source": [ - "sat_oracle = SAT(sat_cnf)" + "oracle = LogicExpressionOracle(sat_instance)" ] }, { @@ -91,7 +95,7 @@ "metadata": {}, "outputs": [], "source": [ - "grover = Grover(sat_oracle)" + "grover = Grover(oracle)" ] }, { @@ -116,7 +120,7 @@ ], "source": [ "backend = BasicAer.get_backend('qasm_simulator')\n", - "quantum_instance = QuantumInstance(backend, shots=100)\n", + "quantum_instance = QuantumInstance(backend, shots=1024)\n", "result = grover.run(quantum_instance)\n", "print(result['result'])" ] @@ -125,9 +129,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "As seen above, a satisfying solution to the specified sample SAT problem is obtained, with the absolute values indicating the variable indices, and the signs the `True/False` assignments, similar to the DIMACS format.\n", + "As seen above, a satisfying solution to the specified SAT problem is obtained. And it is indeed one of the three satisfying solutions.\n", "\n", - "A measurements result is also returned where it can be seen, below in the plot, that `result['result']` was the highest probability. But the other solutions were very close in probability too." + "Since we used the `'qasm_simulator'`, the complete measurement result is also returned, as shown in the plot below, where it can be seen that the binary strings `000`, `011`, and `101` (note the bit order in each string), corresponding to the three satisfying solutions all have high probabilities associated with them." ] }, { @@ -136,19 +140,19 @@ "metadata": {}, "outputs": [ { - "ename": "KeyError", - "evalue": "'measurements'", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mKeyError\u001b[0m Traceback (most recent call last)", - "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mplot_histogram\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'measurements'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", - "\u001b[0;31mKeyError\u001b[0m: 'measurements'" - ] + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ - "plot_histogram(result['measurements'])" + "plot_histogram(result['measurement'])" ] }, { @@ -160,11 +164,23 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "metadata": { "scrolled": true }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "params = {\n", " 'problem': {'name': 'search'},\n", @@ -172,17 +188,24 @@ " 'name': 'Grover'\n", " },\n", " 'oracle': {\n", - " 'name': 'SAT',\n", - " 'cnf': sat_cnf\n", + " 'name': 'LogicExpression',\n", + " 'expression': sat_instance\n", " },\n", " 'backend': {\n", - " 'shots': 100\n", + " 'shots': 1000\n", " }\n", "}\n", "\n", "result_dict = run_algorithm(params, backend=backend)\n", - "plot_histogram(result_dict['measurements'])" + "plot_histogram(result_dict['measurement'])" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { @@ -201,7 +224,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.7" + "version": "3.7.2" } }, "nbformat": 4, From 5682d9dbd55d6df7f1c50a6f6b78f40eece513e3 Mon Sep 17 00:00:00 2001 From: Shaohan Hu Date: Fri, 1 Mar 2019 11:29:06 -0500 Subject: [PATCH 020/116] minor edit --- community/aqua/optimization/grover.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/community/aqua/optimization/grover.ipynb b/community/aqua/optimization/grover.ipynb index b225f72a5..86dbe67d8 100644 --- a/community/aqua/optimization/grover.ipynb +++ b/community/aqua/optimization/grover.ipynb @@ -188,7 +188,7 @@ " 'name': 'Grover'\n", " },\n", " 'oracle': {\n", - " 'name': 'LogicExpression',\n", + " 'name': 'LogicExpressionOracle',\n", " 'expression': sat_instance\n", " },\n", " 'backend': {\n", From e280ae479336b1842ab825a3122cd69fd68841c7 Mon Sep 17 00:00:00 2001 From: Manoel Marques Date: Wed, 6 Mar 2019 14:26:21 -0500 Subject: [PATCH 021/116] Change get_input_instance to get_pluggable_class --- community/aqua/general/vqe.ipynb | 62 +++++++++++++++----------------- 1 file changed, 28 insertions(+), 34 deletions(-) diff --git a/community/aqua/general/vqe.ipynb b/community/aqua/general/vqe.ipynb index 98257da86..ba86e3fc8 100644 --- a/community/aqua/general/vqe.ipynb +++ b/community/aqua/general/vqe.ipynb @@ -16,13 +16,19 @@ { "cell_type": "code", "execution_count": 1, - "metadata": { - "collapsed": true - }, - "outputs": [], + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/manoel/Documents/Quantum/qiskit-terra/qiskit/tools/qcvv/__init__.py:13: DeprecationWarning: The qiskit.tools.qcvv package is deprecated. Please use qiskit-ignis available on PIP for similar functionality and more.\n", + " 'functionality and more.', DeprecationWarning)\n" + ] + } + ], "source": [ - "from qiskit.aqua import Operator, run_algorithm\n", - "from qiskit.aqua.input import get_input_instance" + "from qiskit.aqua import Operator, run_algorithm, PluggableType, get_pluggable_class" ] }, { @@ -35,9 +41,7 @@ { "cell_type": "code", "execution_count": 2, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "pauli_dict = {\n", @@ -65,12 +69,15 @@ "metadata": {}, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "{'eigvals': array([-1.85727503-7.00389617e-17j]), 'eigvecs': array([[-1.38777878e-16+2.45029691e-17j, 7.22856695e-01+6.81936898e-01j,\n", - " -8.11307233e-02-7.65380388e-02j, -2.22044605e-16+5.55111512e-17j]]), 'energy': -1.857275030202382, 'wavefunction': array([[-1.38777878e-16+2.45029691e-17j, 7.22856695e-01+6.81936898e-01j,\n", - " -8.11307233e-02-7.65380388e-02j, -2.22044605e-16+5.55111512e-17j]]), 'energies': array([-1.85727503])}\n" + "ename": "AquaError", + "evalue": "'PluggableType.INITIAL_STATE EnergyInput not registered'", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mAquaError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0;34m'algorithm'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0malgorithm_cfg\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 7\u001b[0m }\n\u001b[0;32m----> 8\u001b[0;31m \u001b[0malgo_input\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_pluggable_class\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mPluggableType\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mINITIAL_STATE\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'EnergyInput'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mqubitOp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 9\u001b[0m \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrun_algorithm\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0malgo_input\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 10\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/Documents/Quantum/qiskit-aqua/qiskit/aqua/_discover.py\u001b[0m in \u001b[0;36mget_pluggable_class\u001b[0;34m(pluggable_type, pluggable_name)\u001b[0m\n\u001b[1;32m 356\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mpluggable_name\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32min\u001b[0m \u001b[0m_REGISTERED_PLUGGABLES\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mpluggable_type\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 357\u001b[0m raise AquaError('{} {} not registered'.format(\n\u001b[0;32m--> 358\u001b[0;31m pluggable_type, pluggable_name))\n\u001b[0m\u001b[1;32m 359\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 360\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0m_REGISTERED_PLUGGABLES\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mpluggable_type\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mpluggable_name\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcls\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mAquaError\u001b[0m: 'PluggableType.INITIAL_STATE EnergyInput not registered'" ] } ], @@ -82,8 +89,7 @@ "params = {\n", " 'algorithm': algorithm_cfg\n", "}\n", - "algo_input = get_input_instance('EnergyInput')\n", - "algo_input.qubit_op = qubitOp\n", + "algo_input = get_pluggable_class(PluggableType.INPUT, 'EnergyInput')(qubitOp)\n", "result = run_algorithm(params,algo_input)\n", "print(result)" ] @@ -97,23 +103,11 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": null, "metadata": { "scrolled": true }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{'eigvals': array([-1.85727503]), 'opt_params': array([ 3.14152283, -1.86138772, 2.14320588, 2.93799407, -0.28074829,\n", - " -2.77067919, -1.20632283, 0.59925957, 3.14159265, 0.82165996,\n", - " 1.00013921, -1.75350817, 2.9702609 , -1.17088041, 0.32988214,\n", - " -2.99356035]), 'eigvecs': array([[-1.98163691e-06-7.88682378e-06j, -8.93429639e-01-4.35136014e-01j,\n", - " 1.00272726e-01+4.88416830e-02j, 2.96950529e-06-1.76810183e-06j]]), 'energy': -1.8572750301062404, 'eval_count': 374, 'eval_time': 18.833309173583984}\n" - ] - } - ], + "outputs": [], "source": [ "algorithm_cfg = {\n", " 'name': 'VQE',\n", @@ -145,9 +139,9 @@ ], "metadata": { "kernelspec": { - "display_name": "Quantum", + "display_name": "Python 3", "language": "python", - "name": "quantum" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -159,7 +153,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.3" + "version": "3.6.7" } }, "nbformat": 4, From f5f6bf2d88666ee754b7c61f99beaf8c2c08e27c Mon Sep 17 00:00:00 2001 From: Manoel Marques Date: Tue, 12 Mar 2019 10:11:54 -0400 Subject: [PATCH 022/116] Change set_aqua_logging to set_qiskit_aqua_logging --- .../LiH_with_qubit_tapering_and_uccsd.ipynb | 47 ++++---- .../qsvm_kernel_classification.ipynb | 31 +++-- qiskit/aqua/optimization/maxcut_and_tsp.ipynb | 107 ++++++++---------- 3 files changed, 85 insertions(+), 100 deletions(-) diff --git a/community/aqua/chemistry/LiH_with_qubit_tapering_and_uccsd.ipynb b/community/aqua/chemistry/LiH_with_qubit_tapering_and_uccsd.ipynb index 6238a76c9..2e08a8734 100644 --- a/community/aqua/chemistry/LiH_with_qubit_tapering_and_uccsd.ipynb +++ b/community/aqua/chemistry/LiH_with_qubit_tapering_and_uccsd.ipynb @@ -4,7 +4,16 @@ "cell_type": "code", "execution_count": 1, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/manoel/Documents/Quantum/qiskit-terra/qiskit/tools/qcvv/__init__.py:13: DeprecationWarning: The qiskit.tools.qcvv package is deprecated. Please use qiskit-ignis available on PIP for similar functionality and more.\n", + " 'functionality and more.', DeprecationWarning)\n" + ] + } + ], "source": [ "# import common packages\n", "import itertools\n", @@ -12,9 +21,9 @@ "\n", "import numpy as np\n", "\n", - "from qiskit import Aer\n", + "from qiskit import BasicAer\n", "\n", - "from qiskit.aqua import Operator, set_aqua_logging, QuantumInstance\n", + "from qiskit.aqua import Operator, set_qiskit_aqua_logging, QuantumInstance\n", "from qiskit.aqua.algorithms.adaptive import VQE\n", "from qiskit.aqua.algorithms.classical import ExactEigensolver\n", "from qiskit.aqua.components.optimizers import COBYLA\n", @@ -24,7 +33,7 @@ "from qiskit.chemistry.aqua_extensions.components.variational_forms import UCCSD\n", "from qiskit.chemistry.aqua_extensions.components.initial_states import HartreeFock\n", "\n", - "# set_aqua_logging(logging.INFO)" + "# set_qiskit_aqua_logging(logging.INFO)" ] }, { @@ -227,7 +236,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -252,13 +261,13 @@ "algo = VQE(the_tapered_op, var_form, optimizer, 'matrix')\n", "\n", "# setup backend\n", - "backend = Aer.get_backend('statevector_simulator')\n", + "backend = BasicAer.get_backend('statevector_simulator')\n", "quantum_instance = QuantumInstance(backend=backend)" ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -267,27 +276,9 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "=== GROUND STATE ENERGY ===\n", - " \n", - "* Electronic ground state energy (Hartree): -8.874303856889\n", - " - computed part: -1.078084288118\n", - " - frozen energy part: -7.796219568771\n", - " - particle hole part: 0.0\n", - "~ Nuclear repulsion energy (Hartree): 0.992207270475\n", - "> Total ground state energy (Hartree): -7.882096586414\n", - "The parameters for UCCSD are:\n", - "[ 0.03815735 0.00366554 0.03827111 0.00369737 -0.03604811 0.0594364\n", - " -0.02741369 -0.02735108 0.05956488 -0.11497243]\n" - ] - } - ], + "outputs": [], "source": [ "result = core.process_algorithm_result(algo_result)\n", "for line in result[0]:\n", @@ -320,7 +311,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.1" + "version": "3.6.7" } }, "nbformat": 4, diff --git a/qiskit/aqua/artificial_intelligence/qsvm_kernel_classification.ipynb b/qiskit/aqua/artificial_intelligence/qsvm_kernel_classification.ipynb index 85d27cca5..df5c71642 100644 --- a/qiskit/aqua/artificial_intelligence/qsvm_kernel_classification.ipynb +++ b/qiskit/aqua/artificial_intelligence/qsvm_kernel_classification.ipynb @@ -42,11 +42,20 @@ "cell_type": "code", "execution_count": 1, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/manoel/Documents/Quantum/qiskit-terra/qiskit/tools/qcvv/__init__.py:13: DeprecationWarning: The qiskit.tools.qcvv package is deprecated. Please use qiskit-ignis available on PIP for similar functionality and more.\n", + " 'functionality and more.', DeprecationWarning)\n" + ] + } + ], "source": [ "from qsvm_datasets import *\n", "\n", - "from qiskit import Aer\n", + "from qiskit import BasicAer\n", "from qiskit.aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name\n", "from qiskit.aqua.input import SVMInput\n", "from qiskit.aqua import run_algorithm, QuantumInstance\n", @@ -55,8 +64,8 @@ "\n", "# setup aqua logging\n", "import logging\n", - "from qiskit.aqua import set_aqua_logging\n", - "# set_aqua_logging(logging.DEBUG) # choose INFO, DEBUG to see the log" + "from qiskit.aqua import set_qiskit_aqua_logging\n", + "# set_qiskit_aqua_logging(logging.DEBUG) # choose INFO, DEBUG to see the log" ] }, { @@ -76,7 +85,7 @@ "outputs": [], "source": [ "from qiskit import IBMQ\n", - "IBMQ.load_accounts()" + "# IBMQ.load_accounts()" ] }, { @@ -95,7 +104,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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\n", 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" ] @@ -174,7 +183,7 @@ "feature_map = SecondOrderExpansion(num_qubits=feature_dim, depth=2, entanglement='linear')\n", "qsvm = QSVMKernel(feature_map, training_input, test_input, datapoints[0])\n", "\n", - "backend = Aer.get_backend('qasm_simulator')\n", + "backend = BasicAer.get_backend('qasm_simulator')\n", "quantum_instance = QuantumInstance(backend, shots=1024, seed=seed, seed_mapper=seed)\n", "\n", "result = qsvm.run(quantum_instance)\n", @@ -185,7 +194,7 @@ " 'algorithm': {\n", " 'name': 'QSVM.Kernel'\n", " },\n", - " 'backend': {'provider': 'qiskit.Aer', 'name': 'qasm_simulator', 'shots': 1024},\n", + " 'backend': {'provider': 'qiskit.BasicAer', 'name': 'qasm_simulator', 'shots': 1024},\n", " 'feature_map': {'name': 'SecondOrderExpansion', 'depth': 2, 'entanglement': 'linear'}\n", "}\n", "algo_input = SVMInput(training_input, test_input, datapoints[0])\n", @@ -212,7 +221,7 @@ }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -274,7 +283,7 @@ "feature_map = SecondOrderExpansion(num_qubits=feature_dim, depth=2, entanglement='linear')\n", "qsvm = QSVMKernel(feature_map, training_input, test_input)\n", "\n", - "backend = Aer.get_backend('qasm_simulator')\n", + "backend = BasicAer.get_backend('qasm_simulator')\n", "quantum_instance = QuantumInstance(backend, shots=1024, seed=seed, seed_mapper=seed)\n", "\n", "result = qsvm.run(quantum_instance)\n", diff --git a/qiskit/aqua/optimization/maxcut_and_tsp.ipynb b/qiskit/aqua/optimization/maxcut_and_tsp.ipynb index 17522c9fb..dbd9f213f 100644 --- a/qiskit/aqua/optimization/maxcut_and_tsp.ipynb +++ b/qiskit/aqua/optimization/maxcut_and_tsp.ipynb @@ -99,7 +99,16 @@ "cell_type": "code", "execution_count": 1, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/manoel/Documents/Quantum/qiskit-terra/qiskit/tools/qcvv/__init__.py:13: DeprecationWarning: The qiskit.tools.qcvv package is deprecated. Please use qiskit-ignis available on PIP for similar functionality and more.\n", + " 'functionality and more.', DeprecationWarning)\n" + ] + } + ], "source": [ "# useful additional packages \n", "import matplotlib.pyplot as plt\n", @@ -108,7 +117,7 @@ "import numpy as np\n", "import networkx as nx\n", "\n", - "from qiskit import Aer\n", + "from qiskit import BasicAer\n", "from qiskit.tools.visualization import plot_histogram\n", "from qiskit.aqua import Operator, run_algorithm\n", "from qiskit.aqua.input import EnergyInput\n", @@ -120,8 +129,8 @@ "\n", "# setup aqua logging\n", "import logging\n", - "from qiskit.aqua import set_aqua_logging\n", - "# set_aqua_logging(logging.DEBUG) # choose INFO, DEBUG to see the log" + "from qiskit.aqua import set_qiskit_aqua_logging\n", + "# set_qiskit_aqua_logging(logging.DEBUG) # choose INFO, DEBUG to see the log" ] }, { @@ -141,7 +150,7 @@ "outputs": [], "source": [ "from qiskit import IBMQ\n", - "IBMQ.load_accounts()" + "# IBMQ.load_accounts()" ] }, { @@ -166,7 +175,7 @@ }, { "data": { - "image/png": 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sbgTe0FoXKKX+BKwGBl66kdb6ZeBlMMs+LopNOFlhYSFbt27FMAzOnDnDmDFjiI+PJzQ01OrQRANw2WWXER8fT3x8PGvXrpXfqxpyRvJPA0ovwBFZ8txFWuszpR6+Cix2wueKeub06dMXSzsdOnRg/Pjx9OvXT+7OFE43dOhQ9uzZw+zZs1mxYoWUD2vAGf8rvwQ6KaWilVJ+QByQUnoDpVTp9jzDgZ+d8LmiHtBa89133/Hoo48yZswYzpw5w4svvsgLL7zAjTfeKIlf1JmpU6eilGLFihVWh+KWan3mr7UuUkpNBbYA3sBKrfWPSql5wC6tdQrwoFJqOFAEZAD31PZzhbXsdjvvv/8+CQkJZGdnY7PZmD17tszBFi7j7e3NggULLg4ADxs2zOqQ3Iqs7SOq5eTJkyQnJ7NhwwY6d+5MXFwc119/vZzhC8scOHCAP/3pT6xYsYLLL7/c6nAsJ2v7CKfRWvPtt99iGAaff/45Q4cO5ZVXXqF9+/ZWhyYEHTp0YM6cOcyYMYM1a9bIciBVJMlflKugoIAtW7aQkJBAfn4+sbGxzJ07l0aNGlkdmhC/MnDgwIsDwC+88ILcIV4FUvYRv3HixAmSkpJISUmha9eu2Gw2rrvuOintiHrN4XAwffp0WrVqxcyZM60OxzJS9hHVorXm66+/xjAMdu3axR/+8Adee+01udlOuA0vLy+efvppxo0bx1tvvcWIESOsDqlek+Tv4fLz83nnnXdITEykuLiY2NhYnnzySWmdJ9xScHAwy5cvZ+LEicTExHDllVdaHVK9JcnfQ6Wnp18s7Vx11VVMmzaN3/3ud9IHV7i99u3b8/jjjzNr1ixWr15Ns2bNrA6pXpLk70G01nz55ZckJCTw7bffctttt7FmzRratGljdWhCOFW/fv3Yt28fM2fO5KWXXsLPz8/qkOodGfD1ALm5uRdLOwBxcXEMGzaMwMBAiyMTou5orZk1axYhISHMnTvXY65qqzrgK8m/AUtNTSUpKYlNmzbRs2dPbDYbPXv29Jj/BELk5uYyfvx47rjjDsaMGWN1OC4hs308lMPh4PPPPychIYEff/yRESNG8O9//5tWrVpV/sNCNDBBQUEsW7aMCRMm0KFDB6655hqrQ6o3JPk3EDk5OWzatAnDMAgICMBms7F48WL8/f2tDk0IS0VGRvL000/zyCOPsHr1alq2bGl1SPWCJH83d/ToUQzD4N1336V379489thjXH311VLaEaKUa6+9lrvvvpv4+Hhee+01OSlCkr9bcjgcfPrppxiGwZ49exg5ciQJCQk0b97c6tCEqLfuuusudu/ezfz585k3b57HnyDJgK8bOXfuHBs3biQxMZGQkBBsNhu///3vZRqbEFWUn5/Pvffeyy233MJdd91ldTh1QgZ8G5CDBw+SmJjIli1b6NOnD/PmzePKK6/0+DMXIaorICCAZcuWMW7cODp16kTv3r2tDskykvzrKYfDwX/+8x8Mw+DAgQOMGjWKxMREuVtRiFpq2bIlCxYsYPbs2fzrX//y2JscJfnXM9nZ2bz11lskJSURERGBzWZj0KBBUtoRwomuueYaJk6cyPTp01m5cqVHrmUlNf96Yv/+/RiGwdatW+nXrx82m40rrrjC6rCEaLC01jz99NPk5OSwcOHCBlNGlTt83UBxcTEfffQRhmFw5MgRRo8ezahRo2jSpInVoQnhEex2O5MnT6Z///5MmDDB6nCcQgZ867GzZ8+yYcMGkpOTad68OXFxcQwYMABfX1+rQxPCo/j5+bFkyRLGjRtH586d6du3r9UhuYxnJX+t4fvv4b33YOdO2LMH8vJAKWjRAnr0gH79YOhQCA11+sfv3buXhIQEPvzwQ2666SaWLl3KZZdd5vTPEUJUXbNmzVi4cCHTp0/n1Vdf9Zje1J5R9tEatm2DxYvh4EEoKgJ/fwgIgAutCe12yM83v/fxgVGjYPp0qGUJpqioiA8//BDDMEhPT+eOO+7g9ttvJyIiopY7JYRwpg0bNrB27VpWr15NcHCw1eHUmNT8L8jMhLlzYfNm8PWFRo3MM/2KFBXBuXMQHAyLFplXAtWUkZFxsbTTpk0b4uLiuOmmm/D29q7hjggh6tqiRYv45ZdfWLp0qdv2rJbkD5CeDnFxkJYGYWH/O8uvqrw882rgL3+BqVMrP2gAP/30E4ZhsGPHDgYOHIjNZqNz58413AEhhCsVFhYyZcoUevbsyX333Wd1ODUiA76ZmWbiT0+HmpZYAgPNq4W//Q2CguDee8vcrLCwkG3btmEYBidPnmTMmDFMmzaNsLCwWuyAEMLVfH19WbRoEWPHjqVz584MHDjQ6pDqTMNM/lrDo4+aZ/y1ra37+EBICCxcCH36QNeuF186c+YM69atY/369URFRXH33XfTv39/Ke0I4cYaN27MkiVLeOCBB2jfvj0dOnSwOqQ60TCT/7ZtsGWLWepxBl9fs+Tz4IOweTM/7N5NQkICn3zyCYMHD+b5559vsL8gQniiyy+/nGnTpjF9+nTWrFlDaB3M/rNaw6v5aw1DhsDRo+aArZM4HA5yT5zg+a5d+SQoiNjYWIYPH94gfymEEKa//e1vHDhwgOeee85tBoA9d8D322/hjjvMefoVDNDaHQ4WnjjBF7m5ZBcXE+nry9Tmzbn+kgNGYVERmZmZnM3MJMzLC6+rr6bJtm1u84sghKi54uJiHnjgAS677DIefPBBq8Opkqom/4aXwd57z5yqWcnMnGKgpa8vL7drx/bOnflzs2bMTksj3W5HA7l5eRxLS+PgwYMUFxfTvn17WnToQLPUVLzOn3fJrgghrOXt7c2CBQvYunUrW7ZssTocp2p4Nf+dO80buCoR6OXF5FLLI/cLCaGVry+7zpyhW34+DoeDiIgIWrVqhXfps3xfX9i9Gzx4HXAhPElYWBjLli3jz3/+M1FRUXTp0sXqkJyi4Z3579lj3rlbDYWFhew5fpx9WVk0KSigebNmdOjQgSaNG/868Zsbw759TgxYCFHfderUidmzZxMfH09mZqbV4ThFw0v+ubnVupnr9JkzfPfjjzx16hSDg4Lo1KgR+QUFnD17luzsbM7n5JCXl0eB3U5hURGOwkK0lH2E8DiDBg1i6NChzJ49m6KiIqvDqbWGN+DbqZM5L7+KB4CMs2eZfeQIBAUxv3FjlNY4iospdjjK/DPYbudfrVvzYUwMwcHBhISEEBwc/JvvL/269DVZwVMI9+NwOHj44Ydp27Yt8fHxVodTJs+9w7d5c8jOrlLdX2vNitxc8gMCmOPjQ9PGjfGqbAmH7GxmLlzIn2+6ifPnz3P+/HnOnTv3m+/T09PLfe38+fP4+vpWePCo7EDSqFEjmXEkhIt5eXkxf/58xo0bR0pKCsOHD7c6pBpreMm/Rw/zBq8qJP8FJ05wyG7nxU6dyExP58SJE7Rq1YoK079S+HbvTuPGjWncuHGNQtRak5eXd/FAcOnXhYPEqVOnyj145OXlERAQUOEBo7KDSWBgYIPpXiSEq4SEhLBs2TImT55MTEwM3bp1szqkGml4yb9vX3MFz0ocLyxk/dmz+CnF0H370FpTUFDADIeD2PIaOtvt5myf6OhahaiUIigoiKCgIJo3b16j93A4HOTk5JR5YLjwlZWVxbFjx8q9QiksLKywPFWV76W3sPBE0dHRPPbYY8ycOZO1a9dW3H2voADOnzennwcHQz35P+OUmr9Saijwd8AbeFVrvfCS1/2BNUBP4Axg01ofrug9a1zzz8oyp2EGBprr8lSDvbCQw4cO0SYykkZlNXTOzIRJk2D27OrHVQ8VFRVVWLoq74qk9GMvL68qjXNUdBUiayEJd/XKK6/w2Wef8c9//vN/J0IOhznlfP16+PJLSE2FC7/jWpsnj9ddZ96M2r17lVYLrg6X3eGrlPIG9gKDgWPAl8AftdY/ldpmCtBda32fUioOuF1rbavofWu1pPPs2ZCUVKNF3XJyckhLSyMqOhq/0oOyRUXmTKKtW6Fdu5rF1cBorbHb7RUePMo7kFx4LScnB39//0rHOioqaQUFBcn4h7CEw+Fg1qxZREREMOeRR8ybTJ9+Gn75xTwIBAaaJegLCd7hMK8E8vLMA0JMjLm9E+8bcmXy7wM8qbUeUvL4EQCt9YJS22wp2eYzpZQPcAJopiv48Fol/9OnYeBAKC42//Kr6UxGBllZWUS1b/+/pJKZCX/6E8ycWbOYRJkujH9U9eBR1sEkPz+foKCgGs++CgkJwd/fX8Y/RI3k5uYy5c47eSw/nw7795tlncDAys/otTbLQcXFcOedMGdOte9RKosrZ/u0AVJLPT4GXFveNlrrIqVUFtAEOO2Ez/+tpk3NJZgfeMCs0Vez/NO4cWMK8vNJP36cNm3aoLKyzLP9hx6qk3A9WenxjxYtWtToPYqLiysc/zh37hwZGRkcPXq03ANLcXFxpQePyq5KZPquZwrKzeWfp0+T8dVX5EZFEVRWybgsSpnT0ouL4f/9P3PlgFWrzN4hLlCvBnyVUpOByQDtaltaueUW2LsXVqww/4KrcQBQQMtWrThy+DDZqamEtW8Pa9dWaQaRcD1vb29CQ0NrtcLqhfJVRWMdx48fr/AKxcfHp8ozrso7kEj5ys3k5sKddxJw4gShUVEcS08nOjoa3+qccHp7myXqr76CyZNhzZrqdx2sAWck/zSgbanHkSXPlbXNsZKyTxjmwO+vaK1fBl4Gs+xT68geesg8ii5Z8r+jbBUv7b2Ki2kbEsKP585RMHs2vSMjax2OqL/8/PxqPX03Pz+/0rGO06dPl7tNbm4uAQEBtZp9JdN3XWzpUjhwAMLDCVaKxo0bcyw1lfZRUZXfM1SaUhAeDp99Zib/e+6ps5AvfqQTav4+mAO+N2Mm+S+BO7XWP5ba5n7gylIDvqO01rEVva/TGrgD/PCD2YglNbXyg0BhoVmH8/KCSZP4fuBApj3yCK+++irt27d3TjxClMHhcJCbm1vtQfPS39vt9mrPvipr+q4cQKrgm29gzBhz+mbJbB4NpKWloZSidevWFd8zVBa73RwQ/uADqOEJp0vX81dK3QI8iznVc6XW+hml1Dxgl9Y6RSkVAKwFegAZQJzW+mBF7+nU5A9mUv/wQ3j5Zfjvf82xALvdrLcpZQ7SKGU+f9dd5gBMSbLfsGEDa9euZfXq1QQHO69BjBDOVlRURE5OTo1nX50vWbeqNrOvgoOD8anmOJtbmjTJzCnh4b962qE1hw8fJiwsjCaNG5NdXMy848fZef484T4+TG3WjKEVdRnMzDT7hc+ZU6OwPLeZS1WcPWsOruzbBzk55nhA8+Zmf97o6P/NyS1l8eLFpKens3z5cqnLigbNbrdXecZVeQcTPz+/Ws2+qvfTd0+cMG8oDQ0tsz5vLyzk8OHDtGndmmfOnkUDj7Vqxd78fB5KTeVfUVHElDeGWFhoTi3ftatGsxUl+TtZUVERU6ZM4eqrr2bKlClWhyNEvXXp8iVVPXiU/j4/P5/AwMBqL1lS+vmAgIC6K1+tXw+zZlXYJzwnN5cDqalMcjhI6tCBdiU3gT2enk4zHx8eqOju/vPnYfVquPbSiZOV89yF3eqIj48PixYtYuzYsXTu3JlBgwZZHZIQ9ZKzli+prDyVmZnJ0aNHyz3IFBUV0ahRo2oPmpf+Knf5kq+/NkvGFWgUFEReWBhFv/xCZKkyWCd/f77Oza34L6CwEH78sUbJv6ok+VdDREQES5cu5f7776ddu3Z07tzZ6pCEaJC8vLxqPX23sLCw0vLUiRMnKrwq8fb2LvOqYkJKCk1zcnA4HHh7eeHl7V3mn74hIQSfOvW/e4aAYC8vchyOioNXCr7/vsb7XhWS/KupS5cuzJgxg/j4eNasWUP4JYM9Qoj6wdfXl4iICCJqsMwLcHGxx7IOCuGbN+Pl40NxyRIn5fX/OF5URHZREadPnaJF8+b4+vqS43DQqLLxDC8vOHeuRnFXlST/GhgyZAh79+5l9uzZ/OMf//CMmQ1CeBilFAEBAQQEBNC0adNfv/jss2Zpppy7cYsdDs6ePYv9zBkoLES1bo1PyR3gewsKyh/svUDrOr+ptB4Pp9dv999/P35+fjz77LOsIdMDAAAXkElEQVRWhyKEcLWYGHOq+CXyCwo4fvw4+/ftIz8vjw6RkQxt1gyjsJB8h4Nvc3P56Nw5/lDRVE8wZ/t06lRHwZsk+deQl5cXzzzzDJ9++ikpKSlWhyOEcKXevc2zc8wbu7LPnePIkSMcPXoUHx8fYjp0oE2bNgQFBvJIy5YUOBwM3ruXOWlpPNKyZeVn/v7+5nLPdUjqFbVwoaPPpEmTiI6O5sorr7Q6JCGEK/TqRTGQefo0mWfP4uPjQ+PGjQkJCfnNsg6h3t4sa9u27Pcpi8NhziSq4+QvZ/61FB0dzeOPP86sWbM4deqU1eEIIerY3r17mZeUxFeZmejz54mMjCQ6Koqw0NDqredTnuxsc0n6S8cZnEySvxP079+f0aNHM3PmTOxl1AGFEO6tqKiI999/n4kTJ/KXv/yFyLZtufy552gWFkagMwdmL0wBnTTJee9ZDin7OMmECRPYs2cPCxcu5LHHHpOFsYRoADIyMli/fj3r1q2jbdu2xMXFcdNNN5kz/BwOSEkxb/hy1pTvrCwYORJ6VXqDbq3J8g5OlJuby4QJExg1ahSxsRUuWiqEqMd++uknEhIS+M9//sPNN99MbGxs2Td1pqbCsGFmjb5Ro9p9aHa2eRDZutVcM6iGZHkHCwQFBbFs2TLGjx9PTEwMvVxw9BZCOIfdbmfr1q0kJiZy5swZxowZQ3x8fMV3Gbdta3bfuvtucz2emq76m5Vl/uwbb9Qq8VeHnPnXgS+++IK5c+eyatUqWrdubXU4QogKnDp1inXr1rF+/Xo6duyIzWajX79+1VtV9JtvzDp9Roa52FtVf7aoyLyTt107WLnSXFW4lmRVT4u9/vrrbNq0iddee43AGizLKoSoO1prvvvuOwzD4LPPPmPIkCHExsYSExNT8zc9dw7mzzdX/HQ4zDKQr+9vG0dpbTZsycszl4+fNMlsNuWkgWNJ/hbTWvPUU09RUFDAX//6VxkAFqIesNvtbN68GcMwyMnJITY2lttuu42QkBDnfciRI/D662AYZinIx8dM+Fqbyb6wEJo0MUtFsbFmLxEnkuRfD9jtdiZOnMiAAQMYP3681eEI4bFOnDhBcnIyb731Fpdffjk2m40+ffrUbcMYreHkSdizx6zpKwWNG8Nll5l/1hEZ8K0H/Pz8WLp0KePGjaNTp0707dvX6pCE8Bhaa77++msMw2DXrl3ccsstvPbaa7Rr1841ASgFLVqYX/WQnPm7wHfffcf06dOlCbwQLpCXl8e7775LYmIiRUVFxMbGcuuttxJUzgqcDY2c+dcj3bt35/7772fatGnSBF6IOpKWlkZSUhIbN27kqquu4uGHH6Z3794y3lYOSf4uMnLkSPbs2cPcuXOlCbwQTqK15osvvsAwDL799luGDx/OmjVraNOmjdWh1XtS9nEhaQIvhHPk5uayadMmEhMT8fHxwWazMWzYMAICAqwOzXJS9qmHpAm8ELVz9OhREhMTeeedd+jVqxdz5syhR48eUtqpAUn+LiZN4IWoHofDwWeffYZhGPz888+MHDmSN954gxb1dBaNu5DkbwFpAi9E5c6dO8fGjRtJTEwkODgYm83G0qVL8fPzszq0BkGSv0WkCbwQZTt48CCGYfDee+/Rp08f5s2bx5VXXimlHSeTAV8LORwO/vKXv9CuXTvi4+OtDkcIyzgcDnbs2IFhGBw8eJBRo0YxatQomjVrZnVobkcGfN3AhSbw48aNIyUlheHDh1sdkhAulZWVxVtvvUVSUhJNmjTBZrMxaNAgfH19rQ6twZPkb7ELTeAnT55MTEwM3bp1szokIerc3r17MQyDbdu20a9fPxYtWkTXrl2tDsujSPKvB6Kjo3nssceYOXMmq1evlktd0SAVFRWxfft2DMMgLS2N0aNHs27dOhrX4SJnonyS/OuJ/v37s2/fPmbOnMlLL70kMxpEg5GRkcGGDRtITk6mdevW2Gw2BgwYIJMcLCYDvvWI1ppZs2YRHBwsTeCF2/vpp58wDIMdO3YwcOBAbDab3NfiArKev5uSJvDCnRUWFvLBBx9gGAanT59mzJgxjBgxgrCwMKtD8xgy28dNSRN44Y5Onz7N+vXrWbduHTExMYwbN47+/fvLAob1mCT/eqhNmzbMnz+fOXPmSBN4UW9prfn+++8xDINPP/2U3//+97z44ou164MrXEbKPvWYNIEX9ZHdbmfLli0YhsH58+frpg+uqDEp+zQAf/zjH9m7dy/z5s2TJvDCcidPniQ5OZkNGzbQpUsX7rvvPq6//nop7bgp+Verx5RSzJkzh7S0NFatWmV1OMIDXeiDO2vWLOLi4sjJyeGVV15hxYoV9O3bVxK/G6vVmb9SqjFgAFHAYSBWa51ZxnbFwPclD49qrWUdgyqSJvDCCvn5+Rf74Nrtdmw2G0888YTH9MH1BLWq+SulFgMZWuuFSqnZQITWelYZ253XWlerca3U/H9NmsALV0hPTycpKYmUlBS6d++OzWajd+/ecobvRlwyz18ptQe4SWt9XCnVCtiute5SxnaS/J1gw4YNrF27VprAC6fSWvPll1+SkJDAN998w2233UZsbKz0wXVTrkr+Z7XW4SXfKyDzwuNLtisCvgGKgIVa6w2Vvbck/7ItWrSI48ePSxN4UWu5ubm8/fbbJCYm4uXldbEPrswsc29OS/5Kqa1AyzJeehRYXTrZK6UytdYRZbxHG611mlIqBtgG3Ky1PlDGdpOByQDt2rXreeTIkcri9zjSBF7U1tGjR0lKSuLtt9+mV69e2Gw2rrnmGplN1kA4baqn1rrcLuNKqV+UUq1KlX1OlvMeaSV/HlRKbQd6AL9J/lrrl4GXwTzzryw2TyRN4EVNOBwOdu7cSUJCAj///DMjRozg9ddfp2XLss7rhCeo7Tz/FGAcsLDkz7cu3UApFQHkaq0LlFJNgRuAxbX8XI8mTeBFVZ0/f56NGzeSlJREYGAgNpuNJUuW4O/vb3VowmK1rfk3ARKBdsARzKmeGUqpXsB9WuuJSqnrgZcAB+Z9Bc9qrV+r7L2l5l+5LVu28Pzzz0sTePEbhw4dIjExkS1btnDddddhs9no3r27lHY8gKzq6SFWrFjBjz/+KE3gBQ6Hg48//piEhAT279/PqFGjGD16tDQH8jCS/D2ENIEX2dnZF/vgRkREXOyDKw2BPJOs7eMhpAm859q3bx+JiYls3bqVfv36sWDBAq644gqrwxJuQpJ/AyBN4D1HcXHxxT64qamp0gdX1Jgk/wZCmsA3bJmZmbz55pvSB1c4jfzmNCDSBL7h+fnnnzEMg48++ogBAwbwt7/9jS5dfrOCihDVJgO+DYw0gXd/hYWFbNu2DcMwOHnyJGPGjGHkyJHSB1dUiQz4eiilFE8++SQTJkwgKSlJmsC7kTNnzrBu3TrWr19PVFQUd999N/3798fb29vq0EQDJMm/AZIm8O5Da80PP/yAYRh88sknDB48mOeff54OHTpYHZpo4CT5N1DSBL5+s9vtvP/++xiGQVZWFrGxscycOZPQ0FCrQxMeQpJ/A9a7d2/uuece4uPjpQl8PVG6D27nzp2ZNGkSN9xwgyzPLVxOkn8Dd6EJ/NNPP80zzzwjA8AW0FrzzTffYBgGX3zxBUOHDuWVV16RjmzCUjLbxwPY7XYmTpzIwIEDueeee6wOx2MUFBSwefNmDMMgPz8fm83GrbfeSqNGjawOTTRgMttHXFS6CXzHjh2lCXwdS09PJzk5mZSUFLp168YDDzzAtddeK6UdUa9I8vcQzZs3Z9GiRdIEvo5c6INrGAb//e9/ufXWW1m1ahWRkZFWhyZEmaTs42GkCbxz5ebm8s4775CYmAhAXFyc9MEVlpKyjyjTyJEj2bNnD3PnzpUm8LWQmppKUlISmzZtomfPnsycOZOePXvKgLpwG/I/3wNNnz6d3Nxc/vnPf1odiltxOBx8+umnPPTQQ4wfPx5fX1/+/e9/s2TJEnr16iWJX7gVOfP3QNIEvnpycnLYuHEjiYmJBAQEEBcXx+LFi6UPrnBrkvw9lDSBr9zhw4dJTExk8+bNXHvttTz++ONcddVVcoYvGgRJ/h6sS5cuzJgxg/j4eGkCX+JCH1zDMNi3bx+33347CQkJNG/e3OrQhHAqSf4ebsiQIezZs4fZs2d7dBP47OxsUlJSSExMJDw8nLi4OOmDKxo0meopPLoJ/P79+0lMTOT999+nb9++2Gw2aYMp3JpM9RRV5mlN4IuLi/noo48wDIMjR44wevRokpOTadKkidWhCeEykvwF4BlN4M+ePcuGDRtITk6mRYsWF/vg+vr6Wh2aEC4nyV9c1FCbwO/evRvDMNi+fTsDBgxg6dKlXHbZZVaHJYSlJPmLX2koTeCLioou9sE9ceIEY8aM4c0335QZTUKUkOQvfmPChAns2bOHhQsXul0T+IyMjIt9cNu1a8ddd93FjTfeKH1whbiEzPYRZcrNzWXChAmMGjXKLZrAX+iD+/HHHzN48GBiY2Pp2LGj1WEJ4XIy20fUSukm8B06dKBnz57lb1xcDNnZ5p9BQeaXC9jtdrZu3UpCQgJnz54lNjaWGTNmSB9cIapAkr8o14Um8I888shvm8AfOgTJybBjB+zdCw6H+XxxMbRoAT16wMiRMGAAOHk2zcmTJ1m3bh1vvvkmnTp1YuLEifTt21dWKBWiGqTsIyr1+uuvs2nTJrMJfHo6PPYYfPGFmfD9/SEgAC7U1LUGux3y8sDLy7wKePhhuPtu83ENaa359ttvMQyDzz//nKFDhxIbG0tUVJRzdlKIBqKqZR9J/qJSWmvmPfkk3b/4gpEHDqAcDggLg6oMBBcUQG4uXHUV/P3v0LZttT67oKCALVu2kJCQQH5+PrGxsdx2223SB1eIckjNXziN0pq52dmc+fhjMsLDadKiRdV/2N8f/Pzgu+9gxAhISIAqrCB6/Pjxi31wu3btytSpU7nuuuuktCOEk0jyF5WbPx/vlBQioqM5dOQIfo0aEVKdFpBKQXi4OSgcFwebNkHp8YMSWmu++uorDMPgq6++4tZbb2XlypW0rebVghCicpL8RcU++QRWr4bQUHy9vYmMjORYaip+UVH4V/cGsNBQOHsWZsyAtWsvjgHk5eXx7rvvYhgGWmtsNhtPPfUUQS6aNSSEJ5LkL8qXl2cO1vr5XRzQDQoMpFnz5qSmphIdHY13dcswYWGwcyds2EDatdeSmJjIpk2b6NGjB/Hx8dIOUQgXkeQvyvfOO5CZaSbsUiLCw8nPzyctLY22bdvyeFoaX+Tmkudw0NTHh7FNmjCynGUUtFLkORwcf+AB7rvsMm4bMYK1a9f+ehqpEKLOSfIXZdMaXnoJymnu0rJFC44cPcqpU6cY37Qpj/n64uflxeGCAiYfOUIXf38uDwy8uH2xw0FWVhYZGRl4KUWLgAA2PfEE/v37u2qPhBCl1GrqhFJqjFLqR6WUQylV7tQipdRQpdQepdR+pdTs2nymcJFTp+DgwXLv1lVKEdmmDVlZWTQtKMCvpPyjSl47VlgIQIHdzokTJ9i/fz+5ubm0btWK6JgYgv398f/kE1ftjRDiErU98/8BGAW8VN4GSilv4HlgMHAM+FIplaK1/qmWny3q0u7d5ll/BfV3Hx8f2kZGcuToUf6elcXmnBwKtKZLQADdgaNHj5Kfn094RAQxMTH4lr6KCAiAzz+v+/0QQpSpVslfa/0zUNkAXW9gv9b6YMm2CcAIQJJ/fXbggHmDViVTOgMCAmjZsiVxJ08yIzqanRkZfJaZSfbp0zRr0oTItm3xKuv3w98f9u+vo+CFEJVxxR0zbYDUUo+PlTwn6rPc3P+t11OJsNBQwsLCSD16lE4OB/bgYHaFhxMeFlZ24gdzmmdBgRMDFkJUR6Vn/kqprUDLMl56VGv9ljODUUpNBiYDtGvXzplvLarLz69qyzeUaN6sGc2aNUMBXsePk2a3V/wDWv9vPSAhhMtVmvy11oNq+RlpQOlbNCNLnivrs14GXgZzbZ9afq6ojTZtzNJMJTKKitiVm0vf4GAClGJnTg5bsrL4a5tKLu7sdvMzhBCWcMVUzy+BTkqpaMykHwfc6YLPFbVx+eVV2kwByZmZ/PX4cRxAK19fprdoQf+QkIp/MD8felW69pQQoo7UKvkrpW4HVgDNgLeVUt9orYcopVoDr2qtb9FaFymlpgJbAG9gpdb6x1pHLupW+/bmNM+CggqvACJ8fHi5ffvqv7+XF/TtW4sAhRC1UasBX631m1rrSK21v9a6hdZ6SMnz6VrrW0pt947WurPWuoPW+pnaBi1cwMsL7rnHHPh1NrvdPKAMHuz89xZCVImsjyvKZ7OZc/1LbthymtxcGDvWnOsvhLCEJH9RvpYtYfp0OH/enJ3jDOfPQ9OmcP/9znk/IUSNSPIXFbv3XrjySsjKqv172e1mj9+//x2kE5cQlpLkLyrm7Q0rV5oDwGfP1vwKID8fcnJg0SK49lrnxiiEqDZJ/qJyjRtDUhL07GkeACq7gas0rc2fcTjgH/+AUaPqLk4hRJVJ8hdV07gxvPEGzJsHRUVmQs/NLf9KoKjI7AWQnQ19+sAHH8CwYa6NWQhRLlnPX1SdlxfcdRfcdhukpJjloCNHwNfXPAhobS4JcWHphlGjzOmiXbtWa6kIIUTdk+Qvqi80FP7v/8yvc+fM5Z9PnjQHcxs1gk6dIDLyYo9eIUT9I8lf1E5ICPzud1ZHIYSoJjk1E0IID6S0s27ecTKl1CngiNVx1FBT4LTVQbiQp+0vyD57Anfd3/Za62aVbVRvk787U0rt0lp7zJKVnra/IPvsCRr6/krZRwghPJAkfyGE8ECS/OvGy1YH4GKetr8g++wJGvT+Ss1fCCE8kJz5CyGEB5Lk7wRKqcZKqfeVUvtK/oyoYNtQpdQxpdQ/XBmjM1Vlf5VSVyulPlNK/aiU+k4pZbMi1tpSSg1VSu1RSu1XSs0u43V/pZRR8vrnSqko10fpPFXY32lKqZ9K/k0/UErVoIdn/VLZPpfabrRSSiulGsQMIEn+zjEb+EBr3Qn4oORxeZ4GdrgkqrpTlf3NBcZqra8AhgLPKqXCXRhjrSmlvIHngWFAV+CPSqmul2x2L5Cpte4I/A1Y5NoonaeK+/tfoJfWujuQDCx2bZTOVcV9RikVAjwEfO7aCOuOJH/nGAGsLvl+NTCyrI2UUj2BFsB7LoqrrlS6v1rrvVrrfSXfpwMngUpvPKlnegP7tdYHtdZ2IAFz30sr/XeRDNyslNuuYlfp/mqtP9RaX2jsvBOIdHGMzlaVf2MwT9oWAfmuDK4uSfJ3jhZa6+Ml35/ATPC/opTyApYB8a4MrI5Uur+lKaV6A37AgboOzMnaAKmlHh8rea7MbbTWRUAW0MQl0TlfVfa3tHuBd+s0orpX6T4rpa4B2mqt33ZlYHVNFnarIqXUVqBlGS89WvqB1lorpcqaQjUFeEdrfcwdTgydsL8X3qcVsBYYp7V2ODdKYRWl1P8BvYAbrY6lLpWctC0H7rE4FKeT5F9FWutB5b2mlPpFKdVKa328JNmdLGOzPkA/pdQUIBjwU0qd11pXND5gGSfsL0qpUOBt4FGt9c46CrUupQFtSz2OLHmurG2OKaV8gDDgjGvCc7qq7C9KqUGYJwE3aq0LXBRbXalsn0OAbsD2kpO2lkCKUmq41nqXy6KsA1L2cY4UYFzJ9+OAty7dQGt9l9a6ndY6CrP0s6a+Jv4qqHR/lVJ+wJuY+5nswtic6Uugk1IqumR/4jD3vbTSfxd3ANu0+948U+n+KqV6AC8Bw7XWZR703UyF+6y1ztJaN9VaR5X8392Jue9unfhBkr+zLAQGK6X2AYNKHqOU6qWUetXSyOpGVfY3FugP3KOU+qbk62prwq2Zkhr+VGAL8DOQqLX+USk1Tyk1vGSz14AmSqn9wDQqnulVr1Vxf5dgXrkmlfybXnowdCtV3OcGSe7wFUIIDyRn/kII4YEk+QshhAeS5C+EEB5Ikr8QQnggSf5CCOGBJPkLIYQHkuQvhBAeSJK/EEJ4oP8PYLwVDsB/KS4AAAAASUVORK5CYII=\n", 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\n", 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" ] @@ -231,7 +240,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -260,7 +269,7 @@ }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -298,7 +307,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": {}, "outputs": [], "source": [ @@ -315,7 +324,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "metadata": {}, "outputs": [ { @@ -330,7 +339,7 @@ }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -386,16 +395,16 @@ "name": "stdout", "output_type": "stream", "text": [ - "energy: -1.4991857466693328\n", - "time: 35.49838590621948\n", - "maxcut objective: -3.999185746669333\n", + "energy: -1.4999670167944144\n", + "time: 26.714055061340332\n", + "maxcut objective: -3.9999670167944146\n", "solution: [1. 0. 1. 0.]\n", "solution objective: 4.0\n" ] }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -413,7 +422,7 @@ "ry = RY(qubitOp.num_qubits, depth=5, entanglement='linear')\n", "vqe = VQE(qubitOp, ry, spsa, 'matrix')\n", "\n", - "backend = Aer.get_backend('statevector_simulator')\n", + "backend = BasicAer.get_backend('statevector_simulator')\n", "quantum_instance = QuantumInstance(backend, seed=seed, seed_mapper=seed)\n", "\n", "result = vqe.run(quantum_instance)\n", @@ -440,7 +449,7 @@ " 'algorithm': algorithm_cfg,\n", " 'optimizer': optimizer_cfg,\n", " 'variational_form': var_form_cfg,\n", - " 'backend': {provider': 'qiskit.Aer', 'name': 'statevector_simulator'}\n", + " 'backend': {provider': 'qiskit.BasicAer', 'name': 'statevector_simulator'}\n", "}\n", "\n", "result = run_algorithm(params, algo_input)\n", @@ -467,15 +476,15 @@ "output_type": "stream", "text": [ "energy: -1.5\n", - "time: 41.23837685585022\n", + "time: 34.49035096168518\n", "maxcut objective: -4.0\n", - "solution: [0 1 0 1]\n", + "solution: [1 0 1 0]\n", "solution objective: 4.0\n" ] }, { "data": { - 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0bdtWfpdqoK4Kq5uAN7TW+UqpPwFrgIGXb6S1fgV4BcyyTx3FJpysoKCAbdu2YRgGZ8+eZcyYMcTFxREcHGx1aKIBuOKKK4iLiyMuLo5169bJ71U1OSP5pwIlF+CIKH7uEq312RIPXwMWO2G/op45c+bMpdJO+/btGT9+PP369ZO7M4XTDR06lL179zJ79mxWrFgh5cNqcMb/yi+AjkqpKKWUDxALJJfcQClVsj3PcOAnJ+xX1ANaa7799lsee+wxxowZw9mzZ3nppZd48cUXuemmmyTxi1ozdepUlFKsWLHC6lBcUo2v/LXWhUqpqcBWwBNYpbX+QSk1D9ittU4GHlJKDQcKgXTg3pruV1jLbrfz/vvvEx8fT1ZWFjabjdmzZ8scbFFnPD09WbBgwaUB4GHDhlkdkkuRtX1ElZw6dYqkpCQ2btxIp06diI2N5YYbbpArfGGZgwcP8qc//YkVK1Zw5ZVXWh2O5WRtH+E0Wmu++eYbDMPgs88+Y+jQobz66qu0a9fO6tCEoH379syZM4cZM2awdu1aWQ6kkiT5izLl5+ezdetW4uPjycvLIyYmhrlz59KoUSOrQxPiVwYOHHhpAPjFF1+UO8QrQco+4jdOnjxJYmIiycnJdOnSBZvNxvXXXy+lHVGvORwOpk+fTsuWLZk5c6bV4VhGyj6iSrTWfPXVVxiGwe7du/nDH/7AypUr5WY74TI8PDx45plnGDduHG+99RYjRoywOqR6TZK/m8vLy+Odd94hISGBoqIiYmJieOqpp6R1nnBJgYGBLF++nIkTJxIdHc3VV19tdUj1liR/N5WWlnaptHPNNdcwbdo0fve730kfXOHy2rVrxxNPPMGsWbNYs2YNTZs2tTqkekmSvxvRWvPFF18QHx/PN998w+23387atWtp3bq11aEJ4VT9+vVj//79zJw5k5dffhkfHx+rQ6p3ZMDXDeTk5Fwq7QDExsYybNgw/P39LY5MiNqjtWbWrFkEBQUxd+5ct/lUW9kBX0n+DVhKSgqJiYls3ryZHj16YLPZ6NGjh9v8JxAiJyeH8ePHc+eddzJmzBirw6kTMtvHTTkcDj777DPi4+P54YcfGDFiBP/+979p2bJlxT8sRAMTEBDAsmXLmDBhAu3bt+e6666zOqR6Q5J/A5Gdnc3mzZsxDAM/Pz9sNhuLFy/G19fX6tCEsFRERATPPPMMjz76KGvWrKFFixZWh1QvSPJ3cceOHcMwDN5991169erF448/zrXXXiulHSFK6N27N/fccw9xcXGsXLlSLoqQ5O+SHA4Hn3zyCYZhsHfvXkaOHEl8fDzNmjWzOjQh6q27776bPXv2MH/+fObNm+f2F0gy4OtCzp8/z6ZNm0hISCAoKAibzcbvf/97mcYmRCXl5eVx3333ceutt3L33XdbHU6tkAHfBuTQoUMkJCSwdetW+vTpw7x587j66qvd/spFiKry8/Nj2bJljBs3jo4dO9KrVy+rQ7KMJP96yuFw8N///hfDMDh48CCjRo0iISFB7lYUooZatGjBggULmD17Nv/617/c9iZHSf71TFZWFm+99RaJiYmEhYVhs9kYNGiQlHaEcKLrrruOiRMnMn36dFatWuWWa1lJzb+eOHDgAIZhsG3bNvr164fNZuOqq66yOiwhGiytNc888wzZ2dksXLiwwZRR5Q5fF1BUVMSHH36IYRgcPXqU0aNHM2rUKBo3bmx1aEK4BbvdzuTJk+nfvz8TJkywOhynkAHfeuzcuXNs3LiRpKQkmjVrRmxsLAMGDMDb29vq0IRwKz4+PixZsoRx48bRqVMn+vbta3VIdca9kr/W8N138N57sGsX7N0LubmgFDRvDt27Q79+MHQoBAc7fff79u0jPj6e//znP9x8880sXbqUK664wun7EUJUXtOmTVm4cCHTp0/ntddec5ve1O5R9tEatm+HxYvh0CEoLARfX/Dzg4utCe12yMszv/fyglGjYPp0qGEJprCwkP/85z8YhkFaWhp33nknd9xxB2FhYTU8KCGEM23cuJF169axZs0aAgMDrQ6n2qTmf1FGBsydC1u2gLc3NGpkXumXp7AQzp+HwEBYtMj8JFBF6enpl0o7rVu3JjY2lptvvhlPT89qHogQorYtWrSIn3/+maVLl7psz2pJ/gBpaRAbC6mpEBLyy1V+ZeXmmp8G/vIXmDq14pMG8OOPP2IYBjt37mTgwIHYbDY6depUzQMQQtSlgoICpkyZQo8ePbj//vutDqdaZMA3I8NM/GlpUN0Si7+/+Wnhb3+DgAC4775SNysoKGD79u0YhsGpU6cYM2YM06ZNIyQkpAYHIISoa97e3ixatIixY8fSqVMnBg4caHVItaZhJn+t4bHHzCv+mtbWvbwgKAgWLoQ+faBLl0svnT17lvXr17NhwwYiIyO555576N+/v5R2hHBh4eHhLFmyhAcffJB27drRvn17q0OqFQ0z+W/fDlu3mqUeZ/D2Nks+Dz0EW7bw/Z49xMfH8/HHHzN48GBeeOGFBvsLIoQ7uvLKK5k2bRrTp09n7dq1BNfC7D+rNbyav9YwZAgcO2YO2DqJw+Eg5+RJXujShY8DAoiJiWH48OEN8pdCCGH629/+xsGDB3n++eddZgDYfQd8v/kG7rzTnKdfzgCt3eFg4cmTfJ6TQ1ZRERHe3kxt1owbLjthFBQWkpGRwbmMDEI8PPC49loab9/uMr8IQojqKyoq4sEHH+SKK67goYcesjqcSqls8m94Gey998ypmhXMzCkCWnh780rbtuzo1Ik/N23K7NRU0ux2NJCTm8vx1FQOHTpEUVER7dq1o3n79jRNScHjwoU6ORQhhLU8PT1ZsGAB27ZtY+vWrVaH41QNr+a/a5d5A1cF/D08mFxieeR+QUG09PZm99mzdM3Lw+FwEBYWRsuWLfEseZXv7Q179oAbrwMuhDsJCQlh2bJl/PnPfyYyMpLOnTtbHZJTNLwr/717zTt3q6CgoIC9J06wPzOTxvn5NGvalPbt29M4PPzXid/cGPbvd2LAQoj6rmPHjsyePZu4uDgyMjKsDscpGl7yz8mp0s1cZ86e5dsffuDp06cZHBBAx0aNyMvP59y5c2RlZXEhO5vc3Fzy7XYKCgtxFBSgpewjhNsZNGgQQ4cOZfbs2RQWFlodTo01vAHfjh3NefmVPAGknzvH7KNHISCA+eHhKK1xFBVR5HCU+meg3c6/WrXiP9HRBAYGEhQURGBg4G++v/zr8tdkBU8hXI/D4eCRRx6hTZs2xMXFWR1Oqdz3Dt9mzSArq1J1f601K3JyyPPzY46XF03Cw/GoaAmHrCxmLlzIn2++mQsXLnDhwgXOnz//m+/T0tLKfO3ChQt4e3uXe/Ko6ETSqFEjmXEkRB3z8PBg/vz5jBs3juTkZIYPH251SNXW8JJ/9+7mDV6VSP4LTp7ksN3OSx07kpGWxsmTJ2nZsiXlpn+l8O7WjfDwcMLDw6sVotaa3NzcSyeCy78uniROnz5d5skjNzcXPz+/ck8YFZ1M/P39G0z3IiHqSlBQEMuWLWPy5MlER0fTtWtXq0OqloaX/Pv2NVfwrMCJggI2nDuHj1IM3b8frTX5+fnMcDiIKauhs91uzvaJiqpRiEopAgICCAgIoFmzZtV6D4fDQXZ2dqknhotfmZmZHD9+vMxPKAUFBeWWpyrzvfQWFu4oKiqKxx9/nJkzZ7Ju3bryu+/l58OFC+b088BAqCf/Z5xS81dKDQX+DngCr2mtF172ui+wFugBnAVsWusj5b1ntWv+mZnmNEx/f3NdniqwFxRw5PBhWkdE0Ki0hs4ZGTBpEsyeXfW46qHCwsJyS1dlfSIp+djDw6NS4xzlfQqRtZCEq3r11Vf59NNP+ec///nLhZDDYU4537ABvvgCUlLg4u+41ubF4/XXmzejdutWqdWCq6LO7vBVSnkC+4DBwHHgC+CPWusfS2wzBeimtb5fKRUL3KG1tpX3vjVa0nn2bEhMrNaibtnZ2aSmphIZFYVPyUHZwkJzJtG2bdC2bfXiamC01tjt9nJPHmWdSC6+lp2dja+vb4VjHeWVtAICAmT8Q1jC4XAwa9YswsLCmPPoo+ZNps88Az//bJ4E/P3NEvTFBO9wmJ8EcnPNE0J0tLm9E+8bqsvk3wd4Sms9pPjxowBa6wUlttlavM2nSikv4CTQVJez8xol/zNnYOBAKCoy//Kr6Gx6OpmZmUS2a/dLUsnIgD/9CWbOrF5MolQXxz8qe/Io7WSSl5dHQEBAtWdfBQUF4evrK+MfolpycnKYctddPJ6XR/sDB8yyjr9/xVf0WpvloKIiuOsumDOnyvcolaYuZ/u0BlJKPD4O9C5rG611oVIqE2gMnHHC/n+rSRNzCeYHHzRr9FUs/4SHh5Ofl0faiRO0bt0alZlpXu0//HCthOvOSo5/NG/evFrvUVRUVO74x/nz50lPT+fYsWNlnliKiooqPHlU9KlEpu+6p4CcHP555gzpX35JTmQkAaWVjEujlDktvagI/t//M1cOWL3a7B1SB+rVgK9SajIwGaBtTUsrt94K+/bBihXmX3AVTgAKaNGyJUePHCErJYWQdu1g3bpKzSASdc/T05Pg4OAarbB6sXxV3ljHiRMnyv2E4uXlVekZV2WdSKR85WJycuCuu/A7eZLgyEiOp6URFRWFd1UuOD09zRL1l1/C5Mmwdm3Vuw5WgzOSfyrQpsTjiOLnStvmeHHZJwRz4PdXtNavAK+AWfapcWQPP2yeRZcs+eUsW8mP9h5FRbQJCuKH8+fJnz2bXhERNQ5H1F8+Pj41nr6bl5dX4VjHmTNnytwmJycHPz+/Gs2+kum7dWzpUjh4EEJDCVSK8PBwjqek0C4ysuJ7hkpSCkJD4dNPzeR/7721FvKlXTqh5u+FOeB7C2aS/wK4S2v9Q4ltHgCuLjHgO0prHVPe+zqtgTvA99+bjVhSUio+CRQUmHU4Dw+YNInvBg5k2qOP8tprr9GuXTvnxCNEKRwOBzk5OVUeNC/5vd1ur/Lsq9Km78oJpBK+/hrGjDGnbxbP5tFAamoqSilatWpV/j1DpbHbzQHhDz6Aal5w1ul6/kqpW4HnMKd6rtJaP6uUmgfs1lonK6X8gHVAdyAdiNVaHyrvPZ2a/MFM6v/5D7zyCvzvf+ZYgN1u1tuUMgdplDKfv/tucwCmONlv3LiRdevWsWbNGgIDndcgRghnKywsJDs7u9qzry4Ur1tVk9lXgYGBeFVxnM0lTZpk5pTQ0F897dCaI0eOEBISQuPwcLKKiph34gS7Llwg1MuLqU2bMrS8LoMZGWa/8DlzqhWW+zZzqYxz58zBlf37ITvbHA9o1szszxsV9cuc3BIWL15MWloay5cvl7qsaNDsdnulZ1yVdTLx8fGp0eyrej999+RJ84bS4OBS6/P2ggKOHDlC61atePbcOTTweMuW7MvL4+GUFP4VGUl0WWOIBQXm1PLdu6s1W1GSv5MVFhYyZcoUrr32WqZMmWJ1OELUW5cvX1LZk0fJ7/Py8vD396/ykiUln/fz86u98tWGDTBrVrl9wrNzcjiYksIkh4PE9u1pW3wT2BNpaTT18uLB8u7uv3AB1qyB3pdPnKyY+y7sVku8vLxYtGgRY8eOpVOnTgwaNMjqkISol5y1fElF5amMjAyOHTtW5kmmsLCQRo0aVXnQvORXmcuXfPWVWTIuR6OAAHJDQij8+WciSpTBOvr68lVOTvl/AQUF8MMP1Ur+lSXJvwrCwsJYunQpDzzwAG3btqVTp05WhyREg+Th4VHj6bsFBQUVlqdOnjxZ7qcST0/PUj9VTEhOpkl2Ng6HA08PDzw8PUv90zsoiMDTp3+5ZwgI9PAg2+EoP3il4Lvvqn3slSHJv4o6d+7MjBkziIuLY+3atYReNtgjhKgfvL29CQsLI6way7wAlxZ7LO2kELplCx5eXhQVL3FSVv+PE4WFZBUWcub0aZo3a4a3tzfZDgeNKhrP8PCA8+erFXdlSfKvhiFDhrBv3z5mz57NP/7xD/eY2SCEm1FK4efnh5+fH02aNPn1i889Z5Zmyrgbt8jh4Ny5c9jPnoWCAlSrVngV3wG+Lz+/7MHei7Su9ZtK6/Fwev32wANGw3bOAAAXoUlEQVQP4OPjw3PPPWd1KEKIuhYdbU4Vv0xefj4nTpzgwP795OXm0j4igqFNm2IUFJDncPBNTg4fnj/PH8qb6gnmbJ+OHWspeJMk/2ry8PDg2Wef5ZNPPiE5OdnqcIQQdalXL/PqHPPGrqzz5zl69CjHjh3Dy8uL6Pbtad26NQH+/jzaogX5DgeD9+1jTmoqj7ZoUfGVv6+vudxzLZJ6RQ1c7OgzadIkoqKiuPrqq60OSQhRF3r2pAjIOHOGjHPn8PLyIjw8nKCgoN8s6xDs6cmyNm1Kf5/SOBzmTKJaTv5y5V9DUVFRPPHEE8yaNYvTp09bHY4Qopbt27ePeYmJfJmRgb5wgYiICKIiIwkJDq7aej5lycoyl6S/fJzByST5O0H//v0ZPXo0M2fOxF5KHVAI4doKCwt5//33mThxIn/5y1+IaNOGK59/nqYhIfg7c2D24hTQSZOc955lkLKPk0yYMIG9e/eycOFCHn/8cVkYS4gGID09nQ0bNrB+/XratGlDbGwsN998sznDz+GA5GTzhi9nTfnOzISRI6FnhTfo1pgs7+BEOTk5TJgwgVGjRhETU+6ipUKIeuzHH38kPj6e//73v9xyyy3ExMSUflNnSgoMG2bW6Bs1qtlOs7LMk8i2beaaQdUkyztYICAggGXLljF+/Hiio6PpWQdnbyGEc9jtdrZt20ZCQgJnz55lzJgxxMXFlX+XcZs2Zvete+4x1+Op7qq/mZnmz77xRo0Sf1XIlX8t+Pzzz5k7dy6rV6+mVatWVocjhCjH6dOnWb9+PRs2bKBDhw7YbDb69etXtVVFv/7arNOnp5uLvVX2ZwsLzTt527aFVavMVYVrSFb1tNjrr7/O5s2bWblyJf7VWJZVCFF7tNZ8++23GIbBp59+ypAhQ4iJiSE6Orr6b3r+PMyfb6746XCYZSBv7982jtLabNiSm2suHz9pktlsykkDx5L8Laa15umnnyY/P5+//vWvMgAsRD1gt9vZsmULhmGQnZ1NTEwMt99+O0FBQc7bydGj8PrrYBhmKcjLy0z4WpvJvqAAGjc2S0UxMWYvESeS5F8P2O12Jk6cyIABAxg/frzV4Qjhtk6ePElSUhJvvfUWV155JTabjT59+tRuwxit4dQp2LvXrOkrBeHhcMUV5p+1RAZ86wEfHx+WLl3KuHHj6NixI3379rU6JCHchtaar776CsMw2L17N7feeisrV66kbdu2dROAUtC8uflVD8mVfx349ttvmT59ujSBF6IO5Obm8u6775KQkEBhYSExMTHcdtttBJSxAmdDI1f+9Ui3bt144IEHmDZtmjSBF6KWpKamkpiYyKZNm7jmmmt45JFH6NWrl4y3lUGSfx0ZOXIke/fuZe7cudIEXggn0Vrz+eefYxgG33zzDcOHD2ft2rW0bt3a6tDqPSn71CFpAi+Ec+Tk5LB582YSEhLw8vLCZrMxbNgw/Pz8rA7NclL2qYekCbwQNXPs2DESEhJ455136NmzJ3PmzKF79+5S2qkGSf51TJrAC1E1DoeDTz/9FMMw+Omnnxg5ciRvvPEGzevpLBpXIcnfAtIEXoiKnT9/nk2bNpGQkEBgYCA2m42lS5fi4+NjdWgNgiR/i0gTeCFKd+jQIQzD4L333qNPnz7MmzePq6++Wko7TiYDvhZyOBz85S9/oW3btsTFxVkdjhCWcTgc7Ny5E8MwOHToEKNGjWLUqFE0bdrU6tBcjgz4uoCLTeDHjRtHcnIyw4cPtzokIepUZmYmb731FomJiTRu3BibzcagQYPw9va2OrQGT5K/xS42gZ88eTLR0dF07drV6pCEqHX79u3DMAy2b99Ov379WLRoEV26dLE6LLciyb8eiIqK4vHHH2fmzJmsWbNGPuqKBqmwsJAdO3ZgGAapqamMHj2a9evXE16Li5yJsknyryf69+/P/v37mTlzJi+//LLMaBANRnp6Ohs3biQpKYlWrVphs9kYMGCATHKwmAz41iNaa2bNmkVgYKA0gRcu78cff8QwDHbu3MnAgQOx2WxyX0sdkPX8XZQ0gReurKCggA8++ADDMDhz5gxjxoxhxIgRhISEWB2a25DZPi5KmsALV3TmzBk2bNjA+vXriY6OZty4cfTv318WMKzHJPnXQ61bt2b+/PnMmTNHmsCLektrzXfffYdhGHzyySf8/ve/56WXXqpZH1xRZ6TsU49JE3hRH9ntdrZu3YphGFy4cKF2+uCKapOyTwPwxz/+kX379jFv3jxpAi8sd+rUKZKSkti4cSOdO3fm/vvv54YbbpDSjouSf7V6TCnFnDlzSE1NZfXq1VaHI9zQxT64s2bNIjY2luzsbF599VVWrFhB3759JfG7sBpd+SulwgEDiASOADFa64xStisCvit+eExrLesYVJI0gRdWyMvLu9QH1263Y7PZePLJJ92mD647qFHNXym1GEjXWi9USs0GwrTWs0rZ7oLWukqNa6Xm/2vSBF7UhbS0NBITE0lOTqZbt27YbDZ69eolV/gupE7m+Sul9gI3a61PKKVaAju01p1L2U6SvxNs3LiRdevWSRN44VRaa7744gvi4+P5+uuvuf3224mJiZE+uC6qrpL/Oa11aPH3Csi4+Piy7QqBr4FCYKHWemNF7y3Jv3SLFi3ixIkT0gRe1FhOTg5vv/02CQkJeHh4XOqDKzPLXJvTkr9SahvQopSXHgPWlEz2SqkMrXVYKe/RWmudqpSKBrYDt2itD5ay3WRgMkDbtm17HD16tKL43Y40gRc1dezYMRITE3n77bfp2bMnNpuN6667TmaTNRBOm+qptS6zy7hS6melVMsSZZ9TZbxHavGfh5RSO4DuwG+Sv9b6FeAVMK/8K4rNHUkTeFEdDoeDXbt2ER8fz08//cSIESN4/fXXadGitOs64Q5qOs8/GRgHLCz+863LN1BKhQE5Wut8pVQT4EZgcQ3369akCbyorAsXLrBp0yYSExPx9/fHZrOxZMkSfH19rQ5NWKymNf/GQALQFjiKOdUzXSnVE7hfaz1RKXUD8DLgwLyv4Dmt9cqK3ltq/hXbunUrL7zwgjSBF79x+PBhEhIS2Lp1K9dffz02m41u3bpJaccNyKqebmLFihX88MMP0gRe4HA4+Oijj4iPj+fAgQOMGjWK0aNHS3MgNyPJ301IE3iRlZV1qQ9uWFjYpT640hDIPcnaPm5CmsC7r/3795OQkMC2bdvo168fCxYs4KqrrrI6LOEiJPk3ANIE3n0UFRVd6oObkpIifXBFtUnybyCkCXzDlpGRwZtvvil9cIXTyG9OAyJN4Buen376CcMw+PDDDxkwYAB/+9vf6Nz5NyuoCFFlMuDbwEgTeNdXUFDA9u3bMQyDU6dOMWbMGEaOHCl9cEWlyICvm1JK8dRTTzFhwgQSExOlCbwLOXv2LOvXr2fDhg1ERkZyzz330L9/fzw9Pa0OTTRAkvwbIGkC7zq01nz//fcYhsHHH3/M4MGDeeGFF2jfvr3VoYkGTpJ/AyVN4Os3u93O+++/j2EYZGZmEhMTw8yZMwkODrY6NOEmJPk3YL169eLee+8lLi5OmsDXEyX74Hbq1IlJkyZx4403yvLcos5J8m/gLjaBf+aZZ3j22WdlANgCWmu+/vprDMPg888/Z+jQobz66qvSkU1YSmb7uAG73c7EiRMZOHAg9957r9XhuI38/Hy2bNmCYRjk5eVhs9m47bbbaNSokdWhiQZMZvuIS0o2ge/QoYM0ga9laWlpJCUlkZycTNeuXXnwwQfp3bu3lHZEvSLJ3000a9aMRYsWSRP4WnKxD65hGPzvf//jtttuY/Xq1URERFgdmhClkrKPm5Em8M6Vk5PDO++8Q0JCAgCxsbHSB1dYSso+olQjR45k7969zJ07V5rA10BKSgqJiYls3ryZHj16MHPmTHr06CED6sJlyP98NzR9+nRycnL45z//aXUoLsXhcPDJJ5/w8MMPM378eLy9vfn3v//NkiVL6NmzpyR+4VLkyt8NSRP4qsnOzmbTpk0kJCTg5+dHbGwsixcvlj64wqVJ8ndT0gS+YkeOHCEhIYEtW7bQu3dvnnjiCa655hq5whcNgiR/N9a5c2dmzJhBXFycNIEvdrEPrmEY7N+/nzvuuIP4+HiaNWtmdWhCOJUkfzc3ZMgQ9u7dy+zZs926CXxWVhbJyckkJCQQGhpKbGys9MEVDZpM9RRu3QT+wIEDJCQk8P7779O3b19sNpu0wRQuTaZ6ikpztybwRUVFfPjhhxiGwdGjRxk9ejRJSUk0btzY6tCEqDOS/AXgHk3gz507x8aNG0lKSqJ58+aX+uB6e3tbHZoQdU6Sv7ikoTaB37NnD4ZhsGPHDgYMGMDSpUu54oorrA5LCEtJ8he/0lCawBcWFl7qg3vy5EnGjBnDm2++KTOahCgmyV/8xoQJE9i7dy8LFy50uSbw6enpl/rgtm3blrvvvpubbrpJ+uAKcRmZ7SNKlZOTw4QJExg1apRLNIG/2Af3o48+YvDgwcTExNChQwerwxKizslsH1EjJZvAt2/fnh49epS5bVERZGWZfwYEmF91wW63s23bNuLj4zl37hwxMTHMmDFD+uAKUQmS/EWZLjaBf/TRR3/TBP7wYUhKgp07Yd8+cDjM54uKoHlz6N4dRo6EAQPA2ZNpTp06xfr163nzzTfp2LEjEydOpG/fvrJCqRBVIGUfUaHXX3+dzZs3s3LlStLS/Hn8cfj8czPh+/qCnx9cLKlrDXY75OaCh4f5KeCRR+Cee8zH1aW15ptvvsEwDD777DOGDh1KTEwMkZGRTjlGIRqKypZ9JPmLCmmteeqpeXz+eTcOHhyJw6EICYHKjAPn50NODlxzDfz979CmTdX2nZ+fz9atW4mPjycvL4+YmBhuv/126YMrRBmk5i+cRmtFVtZcPvroLKGh6TRvXvk7YX19wccHvv0WRoyA+HiozAKiJ06cuNQHt0uXLkydOpXrr79eSjtCOIkkf1Gh+fMhOdmTqKgwjh49TKNGPgQGBlX655WC0FBzUDg2FjZvhhLDB5dorfnyyy8xDIMvv/yS2267jVWrVtGmqh8XhBAVkuQvyvXxx7BmDQQHg6enNxEREaSkHCcy0gcfn6o1MwkOhnPnYMYMWLfulzGA3Nxc3n33XQzDQGuNzWbj6aefJqCupg0J4YYk+Ysy5eaag7U+Pr8M6Pr7B9CsWVNSUlKIiorCw6NqN0+FhMCuXbBxI/TunUpCQgKbN2+me/fuxMXFSTtEIeqIJH9RpnfegYwMM2GXFBoaRl5eHqmpqbRp04bU1CfIyfkchyMXL68mNG48ltDQkaW+p1IahyOXBx88wRVX3M+IEbezbt26X00jFULUPkn+olRaw8svQ1m9XZo3b8GxY0c5ffo0TZqMx9v7cTw8fMjPP8LRo5Px9e2Mv/+Vl7Z3OIrIzMwkPT0dpTzw82vOk09upn9/6YMrhBVqNHVCKTVGKfWDUsqhlCpzapFSaqhSaq9S6oBSanZN9inqxunTcOhQ2XfrKqVo3TqCzMxM8vOb4OFxcQE4hVKKgoLjANjt+Zw8eZIDBw6Qk5NDy5atiI6Owtc3kI8/lsQvhFVqeuX/PTAKeLmsDZRSnsALwGDgOPCFUipZa/1jDfctatGePeZVf3nldy8vLyIi2nDs2FEyM/9OdvYWtM7Hz68z0I1jx46Rl5dHWFgo0dHReHn9cquvnx989lntH4cQonQ1Sv5a65+AigboegEHtNaHireNB0YAkvzrsYMHzRu0AgPL387Pz48WLVpw6lQsUVEzSE/fRUbGp5w5k0Xjxk1p0yYCpX77AdPXFw4cqKXghRAVqos7ZloDKSUeHy9+TtRjOTm/rNdTkeDgEEJCQjh2LAWHoyOBgXZCQ3cTEhJaauIHc5pnfr4TAxZCVEmFV/5KqW1Ai1Jeekxr/ZYzg1FKTQYmA7Rt29aZby2qyMencss3XNS0abPizl+KEyc8sNtTy91e61+mjwoh6l6FyV9rPaiG+0gFSt6iGVH8XGn7egV4Bcy1fWq4X1EDrVubpZmKFBamk5Ozm8DAvijlR3b2LjIzt9K69V/L/Tm73dyHEMIadTHV8wugo1IqCjPpxwJ31cF+RQ1ceWXF25gUGRlJnDjxV8CBt3dLmjefTlBQ/3J/Ki8Pela49JQQorbUKPkrpe4AVgBNgbeVUl9rrYcopVoBr2mtb9VaFyqlpgJbAU9gldb6hxpHLmpVu3bmNM/8/PI/AXh5hdGu3StVfn8PD+jbtwYBCiFqpEYDvlrrN7XWEVprX611c631kOLn07TWt5bY7h2tdSetdXut9bM1DVrUPg8PuPdec+DX2ex284QyeLDz31sIUTmyPq4ok81mzvUvKHDu++bkwNix5lx/IYQ1JPmLMrVoAdOnw4UL5uwcZ7hwAZo0gQcecM77CSGqR5K/KNd998HVV0NmZs3fy243e/z+/e8gjbiEsJYkf1EuT09YtcocAD53rvqfAPLyIDsbFi2C3r2dG6MQouok+YsKhYdDYiL06GGeAOz2yv+s1ubPOBzwj3/AqFG1F6cQovIk+YtKCQ+HN96AefOgsNBM6Dk5ZX8SKCw0ewFkZUGfPvDBBzBsWN3GLIQom6znLyrNwwPuvhtuvx2Sk81y0NGj4O1tngS0NpeEuLh0w6hR5nTRLl2qtlSEEKL2SfIXVRYcDP/3f+bX+fPm8s+nTpmDuY0aQceOEBHxS49eIUT9I8lf1EhQEPzud1ZHIYSoKrk2E0IIN6S0s+7ecTKl1GngqNVxVFMT4IzVQdQhdztekGN2B656vO201k0r2qjeJn9XppTarbV2mzUr3e14QY7ZHTT045WyjxBCuCFJ/kII4YYk+deOqi9w79rc7XhBjtkdNOjjlZq/EEK4IbnyF0IINyTJ3wmUUuFKqfeVUvuL/wwrZ9tgpdRxpdQ/6jJGZ6rM8SqlrlVKfaqU+kEp9a1SymZFrDWllBqqlNqrlDqglJpdyuu+Simj+PXPlFKRdR+l81TieKcppX4s/jf9QCnVzoo4namiYy6x3WillFZKNYgZQJL8nWM28IHWuiPwQfHjsjwD7KyTqGpPZY43Bxirtb4KGAo8p5QKrcMYa0wp5Qm8AAwDugB/VEp1uWyz+4AMrXUH4G/AorqN0nkqebz/A3pqrbsBScDiuo3SuSp5zCilgoCHgc/qNsLaI8nfOUYAa4q/XwOMLG0jpVQPoDnwXh3FVVsqPF6t9T6t9f7i79OAU0CFN57UM72AA1rrQ1prOxCPeewllfy7SAJuUcpll7Gr8Hi11v/RWl/s7LwLiKjjGJ2tMv/GYF60LQLy6jK42iTJ3zmaa61PFH9/EjPB/4pSygNYBsTVZWC1pMLjLUkp1QvwAQ7WdmBO1hpIKfH4ePFzpW6jtS4EMoHGdRKd81XmeEu6D3i3ViOqfRUes1LqOqCN1vrtugystsnCbpWklNoGtCjlpcdKPtBaa6VUaVOopgDvaK2Pu8KFoROO9+L7tATWAeO01g7nRimsopT6P6AncJPVsdSm4ou25cC9FofidJL8K0lrPais15RSPyulWmqtTxQnu1OlbNYH6KeUmgIEAj5KqQta6/LGByzjhONFKRUMvA08prXeVUuh1qZUoE2JxxHFz5W2zXGllBcQApytm/CcrjLHi1JqEOZFwE1a6/w6iq22VHTMQUBXYEfxRVsLIFkpNVxrvbvOoqwFUvZxjmRgXPH344C3Lt9Aa3231rqt1joSs/Sztr4m/kqo8HiVUj7Am5jHmVSHsTnTF0BHpVRU8fHEYh57SSX/Lu4EtmvXvXmmwuNVSnUHXgaGa61LPem7mHKPWWudqbVuorWOLP6/uwvz2F068YMkf2dZCAxWSu0HBhU/RinVUyn1mqWR1Y7KHG8M0B+4Vyn1dfHXtdaEWz3FNfypwFbgJyBBa/2DUmqeUmp48WYrgcZKqQPANMqf6VWvVfJ4l2B+ck0s/je9/GToUip5zA2S3OErhBBuSK78hRDCDUnyF0IINyTJXwgh3JAkfyGEcEOS/IUQwg1J8hdCCDckyV8IIdyQJH8hhHBD/x/PAxUO8owGIwAAAABJRU5ErkJggg==\n", + "image/png": 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\n", 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" ] @@ -494,14 +503,14 @@ "ry = RY(qubitOp.num_qubits, depth=5, entanglement='linear')\n", "vqe = VQE(qubitOp, ry, spsa, 'grouped_paulis')\n", "\n", - "backend = Aer.get_backend('qasm_simulator')\n", + "backend = BasicAer.get_backend('qasm_simulator')\n", "quantum_instance = QuantumInstance(backend, shots=1024, seed=seed, seed_mapper=seed)\n", "\n", "result = vqe.run(quantum_instance)\n", "\n", "\"\"\"declarative approach, update the param from the previous cell.\n", "params['algorithm']['operator_mode'] = 'grouped_paulis'\n", - "params['backend']['provider'] = 'qiskit.Aer'\n", + "params['backend']['provider'] = 'qiskit.BasicAer'\n", "params['backend']['name'] = 'qasm_simulator'\n", "params['backend']['shots'] = 1024\n", "result = run_algorithm(params, algo_input)\n", @@ -563,14 +572,14 @@ "output_type": "stream", "text": [ "distance\n", - " [[ 0. 11. 23.]\n", - " [11. 0. 33.]\n", - " [23. 33. 0.]]\n" + " [[ 0. 54. 74.]\n", + " [54. 0. 34.]\n", + " [74. 34. 0.]]\n" ] }, { "data": { - 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\n", + "image/png": 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\n", 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" ] @@ -611,13 +620,13 @@ "name": "stdout", "output_type": "stream", "text": [ - "order = (0, 1, 2) Distance = 67.0\n", - "Best order from brute force = (0, 1, 2) with total distance = 67.0\n" + "order = (0, 1, 2) Distance = 162.0\n", + "Best order from brute force = (0, 1, 2) with total distance = 162.0\n" ] }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -696,15 +705,15 @@ "name": "stdout", "output_type": "stream", "text": [ - "energy: -600033.5\n", + "energy: -600081.0\n", "feasible: True\n", "solution: [1, 2, 0]\n", - "solution objective: 67.0\n" + "solution objective: 162.0\n" ] }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -753,31 +762,7 @@ "cell_type": "code", "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "energy: -595242.8232593088\n", - "time: 66.49582099914551\n", - "feasible: True\n", - "solution: [1, 0, 2]\n", - "solution objective: 67.0\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "seed = 10598\n", "\n", @@ -785,7 +770,7 @@ "ry = RY(qubitOp.num_qubits, depth=5, entanglement='linear')\n", "vqe = VQE(qubitOp, ry, spsa, 'matrix')\n", "\n", - "backend = Aer.get_backend('statevector_simulator')\n", + "backend = BasicAer.get_backend('statevector_simulator')\n", "quantum_instance = QuantumInstance(backend, seed=seed, seed_mapper=seed)\n", "\n", "result = vqe.run(quantum_instance)\n", @@ -811,7 +796,7 @@ " 'algorithm': algorithm_cfg,\n", " 'optimizer': optimizer_cfg,\n", " 'variational_form': var_form_cfg,\n", - " 'backend': {'provider': 'qiskit.Aer', 'name': 'statevector_simulator'}\n", + " 'backend': {'provider': 'qiskit.BasicAer', 'name': 'statevector_simulator'}\n", "}\n", "result = run_algorithm(parahms,algo_input)\n", "\"\"\"\n", @@ -840,14 +825,14 @@ "ry = RY(qubitOp.num_qubits, depth=5, entanglement='linear')\n", "vqe = VQE(qubitOp, ry, spsa, 'grouped_paulis', batch_mode=True)\n", "\n", - "backend = Aer.get_backend('qasm_simulator')\n", + "backend = BasicAer.get_backend('qasm_simulator')\n", "quantum_instance = QuantumInstance(backend, shots=1024, seed=seed, seed_mapper=seed)\n", "\n", "result = vqe.run(quantum_instance)\n", "\n", "\"\"\"update params in the previous cell\n", "params['algorithm']['operator_mode'] = 'grouped_paulis'\n", - "params['backend']['provider'] = 'qiskit.Aer'\n", + "params['backend']['provider'] = 'qiskit.BasicAer'\n", "params['backend']['name'] = 'qasm_simulator'\n", "params['backend']['shots'] = 1024\n", "result = run_algorithm(params,algo_input)\n", From 128e8329c59d3c7598deab0eeccfe0da58e4ae64 Mon Sep 17 00:00:00 2001 From: Manoel Marques Date: Tue, 12 Mar 2019 11:34:49 -0400 Subject: [PATCH 023/116] Fixed grover input file --- community/aqua/optimization/input_files/grover.json | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/community/aqua/optimization/input_files/grover.json b/community/aqua/optimization/input_files/grover.json index d8a3bb5ea..bbf409359 100644 --- a/community/aqua/optimization/input_files/grover.json +++ b/community/aqua/optimization/input_files/grover.json @@ -7,8 +7,8 @@ "name": "qasm_simulator" }, "oracle": { - "dimacs_cnf": "c This is an example DIMACS 3-sat file with 3 satisfying solutions: 1 -2 3 0, -1 -2 -3 0, 1 2 -3 0\np cnf 3 5\n-1 -2 -3 0\n1 -2 3 0\n1 2 -3 0\n1 -2 -3 0\n-1 2 3 0", - "name": "SAT" + "expression": "p cnf 3 5 \n -1 -2 -3 0 \n 1 -2 3 0 \n 1 2 -3 0 \n 1 -2 -3 0 \n -1 2 3 0", + "name": "LogicExpressionOracle" }, "problem": { "name": "search" From 332936fb030457921d88b5e89f7451409be3e03f Mon Sep 17 00:00:00 2001 From: Albert Frisch Date: Wed, 13 Mar 2019 16:49:28 +0100 Subject: [PATCH 024/116] Add Aqua tutorial solving linear systems of equation with HHL --- .../general/linear_systems_of_equations.ipynb | 559 ++++++++++++++++++ 1 file changed, 559 insertions(+) create mode 100644 qiskit/aqua/general/linear_systems_of_equations.ipynb diff --git a/qiskit/aqua/general/linear_systems_of_equations.ipynb b/qiskit/aqua/general/linear_systems_of_equations.ipynb new file mode 100644 index 000000000..b9ad0233d --- /dev/null +++ b/qiskit/aqua/general/linear_systems_of_equations.ipynb @@ -0,0 +1,559 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# _*Qiskit Aqua: Solving linear systems of equations with the HHL algorithm*_\n", + "\n", + "***\n", + "### Contributors\n", + "David Bucher[1], Jan Mueggenburg[1], Gawel Kus[1], Isabel Haide[1], Shubha Deutschle[1], Harry Barowski[1], Dominik Steenken[1], and Albert Frisch[1]\n", + "### Affiliation\n", + "- [1]IBMQ" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The HHL algorithm (after the author’s surnames Harrow-Hassidim-Lloyd) [1] is a quantum algorithm to solve systems of linear equations $A \\vec{x} = \\vec{b}$. To perform this calculation quantum mechanically, we need in general 4 main steps requiring three qubit registers:\n", + "
    \n", + "
  1. First, we have to express the vector $\\vec{b}$ as a quantum state $|b\\rangle$ on a quantum register.
    2. \n", + "
  2. Now, we have to decompose $\\vec{b}$ into a superposition of eigenvectors of A remembering on the linear combination of the vector $\\vec{b}$. We achieve this using the Quantum Phase Estimation algorithm (Quantum Phase Estimation (QPE)). Since the matrix is hereby diagonalized wherefore $A$ is easily invertible.
    3. \n", + "
  3. The inversion of the eigenvector base of $A$ is achieved by rotating an ancillary qubit by an angle $\\arcsin \\left( \\frac{C}{\\lambda _{\\text{i}}} \\right)$ around the y-axis where $\\lambda_{\\text{i}}$ are the eigenvalues of $A$. Now, we obtain the state $A^{-1}|b\\rangle = |x \\rangle$.
    4. \n", + "
  4. We need to uncompute the register storing the eigenvalues using the inverse QPE. We measure the ancillary qubit whereby the measurement of 1 indicates that the matrix inversion was successful. The inverse QPE leaves the system in a state proportional to the solution vector $|x\\rangle$. In many cases one is not interested in the single vector elements of $|x\\rangle$ but only on certain properties. These are accessible by applying a problem-specific operator $M$ to the state $|x\\rangle$. Another use-case of the HHL algorithm is the implementation in a larger quantum program.
    5. \n", + "
\n", + "Currently only hermitian matrices with a dimension of $2^n$ are supported.\n", + "\n", + "Take into account that in the general case, the entries of $\\vec{x}$ can not be efficiently read out because we would need to know all coefficients describing the quantum state.\n", + "In the following examples, we ignore this constraint and show for our small linear system as a proof of principle that $\\vec{x}$ is calculated correctly.\n", + "\n", + "References:\n", + "- A. W. Harrow, A. Hassidim, and S. Lloyd, Phys. Rev. Lett. 103, 150502 (2009), e-print arXiv 0811.3171\n", + "- S. Barz, I. Kassal, M. Ringbauer, Y. Ole Lipp, B. Dakić, A. Aspuru-Guzik, and P. Walther, Sci Rep. 4: 6115 (2014), e-print arXiv 1302.1210" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit.aqua import run_algorithm\n", + "from qiskit.aqua.input import LinearSystemInput\n", + "import numpy as np" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "params = {\n", + " 'problem': {\n", + " 'name': 'linear_system'\n", + " },\n", + " 'algorithm': {\n", + " 'name': 'HHL'\n", + " },\n", + " 'eigs': {\n", + " 'expansion_mode': 'suzuki',\n", + " 'expansion_order': 2,\n", + " 'name': 'EigsQPE',\n", + " 'num_ancillae': 3,\n", + " 'num_time_slices': 50\n", + " },\n", + " 'reciprocal': {\n", + " 'name': 'Lookup'\n", + " },\n", + " 'backend': {\n", + " 'name': 'statevector_simulator'\n", + " }\n", + "}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2x2 diagonal matrix" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First, we show an example for running the HHL algorithm with Qiskit Aqua on a diagonal matrix as input\n", + "$$\n", + "A=\n", + "\\begin{bmatrix}\n", + "1 & 0 \\\\\n", + "0 & 2\n", + "\\end{bmatrix}$$ with the vector $$\\vec{b}= \\left( \\begin{array}{c}1 \\\\ 4 \\end{array} \\right)$$\n", + "The `result` dictionary contains several return values. The HHL solution for $\\vec{x}$ is accessible by the key `'solution_hhl'`. For comparison, also the classical solution of the linear system of equations is calculated using standard linear algebra functions in numpy. The fidelity between the HHL solution and the classical solution is also given in the output. Furthermore, the probability is shown with which HHL was running successfully, i.e. the HHL ancillary qubit has been measured to be $|1\\rangle$." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "matrix = [[1, 0], [0, 2]]\n", + "vector = [1, 4]\n", + "params['input'] = {\n", + " 'name': 'LinearSystemInput',\n", + " 'matrix': matrix,\n", + " 'vector': vector\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "hhl solution [1.05859-0.j 1.99245-0.j]\n", + "classical solution [1. 2.]\n", + "fidelity 0.999389\n", + "probability 0.024630\n" + ] + } + ], + "source": [ + "result = run_algorithm(params)\n", + "\n", + "print(\"hhl solution \", np.round(result['solution_hhl'], 5))\n", + "print(\"classical solution \", np.round(result['solution_classical'], 5))\n", + "print(\"fidelity %f\" % result['fidelity_hhl_to_classical'])\n", + "print(\"probability %f\" % result['probability_result'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The probabilty that HHL runs successfully depends on the constant $C$ (see step 3. in the introduction). In the HHL algorithm, $C$ can be given as the parameter `scale` $\\in [0,1]$. In the above example `scale` is not defined in the `params` dictionary and the HHL algorithm initializes it to the smallest possible eigenvalue before execution. Alternatively, we can set `scale` to 0.5 and see how the results are influenced thereby." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "hhl solution [0.84664-0.j 2.01762-0.j]\n", + "classical solution [1. 2.]\n", + "fidelity 0.995605\n", + "probability 0.361437\n" + ] + } + ], + "source": [ + "params2 = params\n", + "params2['reciprocal'] = { \n", + " 'scale': 0.5\n", + "}\n", + "\n", + "result = run_algorithm(params2)\n", + "\n", + "print(\"hhl solution \", np.round(result['solution_hhl'], 5))\n", + "print(\"classical solution \", np.round(result['solution_classical'], 5))\n", + "print(\"fidelity %f\" % result['fidelity_hhl_to_classical'])\n", + "print(\"probability %f\" % result['probability_result'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you want to know how many qubits are required (circuit width) or how large the maximum number of gates applied to a single qubit (circuit depth) is, you can print it out by" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "circuit_depth 12255\n", + "circuit_width 7\n" + ] + } + ], + "source": [ + "print(\"circuit_depth\", result['circuit_depth'])\n", + "print(\"circuit_width\", result['circuit_width'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2x2 non-diagonal matrix" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we show an example for running the HHL algorithm with Qiskit Aqua on a non-diagonal matrix as input\n", + "$$\n", + "A=\n", + "\\begin{bmatrix}\n", + "1 & 3 \\\\\n", + "3 & 2\n", + "\\end{bmatrix}$$ with the vector $$\\vec{b}= \\left( \\begin{array}{c}1 \\\\ 1 \\end{array} \\right)$$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "matrix = [[1, 3], [3, 2]]\n", + "vector = [1, 1]\n", + "params['input'] = {\n", + " 'name': 'LinearSystemInput',\n", + " 'matrix': matrix,\n", + " 'vector': vector\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "hhl solution [0.22147+0.j 0.22034-0.j]\n", + "classical solution [0.14286 0.28571]\n", + "fidelity 0.898454\n", + "probability 0.424639\n" + ] + } + ], + "source": [ + "result = run_algorithm(params)\n", + "\n", + "print(\"hhl solution \", np.round(result['solution_hhl'], 5))\n", + "print(\"classical solution \", np.round(result['solution_classical'], 5))\n", + "print(\"fidelity %f\" % result['fidelity_hhl_to_classical'])\n", + "print(\"probability %f\" % result['probability_result'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Compared to the the first example, the circuit depth is increased approximately by a factor 2,5" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "circuit_depth 30253\n", + "circuit_width 7\n" + ] + } + ], + "source": [ + "print(\"circuit_depth\", result['circuit_depth'])\n", + "print(\"circuit_width\", result['circuit_width'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 8x8 non-diagonal matrix" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For simplicity, we show a HHL execution of a linear systom of equations defined by the following 8x8 dimensional matrix\n", + "$$\n", + "A=\n", + "\\begin{bmatrix}\n", + "4 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\\\\n", + "0 & 3 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", + "0 & 0 & 8 & 0 & 0 & 0 & 0 & 0 \\\\\n", + "0 & 0 & 0 & 5 & 0 & 0 & 0 & 0 \\\\\n", + "0 & 0 & 0 & 0 & 2 & 1 & 0 & 0 \\\\\n", + "0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\\\\n", + "0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\\\\n", + "1 & 0 & 0 & 0 & 0 & 0 & 0 & 5\n", + "\\end{bmatrix}$$ and the vector $$\\vec{b}= \\left( \\begin{array}{c}1 \\\\ 0 \\\\ 0 \\\\ 0 \\\\ 0 \\\\ 0 \\\\ 0 \\\\ 1 \\end{array} \\right)$$" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "matrix = [[4, 0, 0, 0, 0, 0, 0, 1],\n", + " [0, 3, 0, 0, 0, 0, 0, 0],\n", + " [0, 0, 8, 0, 0, 0, 0, 0],\n", + " [0, 0, 0, 5, 0, 0, 0, 0],\n", + " [0, 0, 0, 0, 2, 1, 0, 0],\n", + " [0, 0, 0, 0, 1, 1, 0, 0],\n", + " [0, 0, 0, 0, 0, 0, 1, 0],\n", + " [1, 0, 0, 0, 0, 0, 0, 5]]\n", + "vector = [1, 0, 0, 0, 0, 0, 0, 1]\n", + "params['input'] = {\n", + " 'name': 'LinearSystemInput',\n", + " 'matrix': matrix,\n", + " 'vector': vector\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "hhl solution [ 0.18195-0.j 0. -0.j -0. -0.j -0. +0.j 0. +0.j\n", + " 0. +0.j -0. -0.j 0.18041+0.j]\n", + "classical solution [0.21053 0. 0. 0. 0. 0. 0. 0.15789]\n", + "fidelity 0.981173\n", + "probability 0.935566\n" + ] + } + ], + "source": [ + "result = run_algorithm(params)\n", + "\n", + "print(\"hhl solution \", np.round(result['solution_hhl'], 5))\n", + "print(\"classical solution \", np.round(result['solution_classical'], 5))\n", + "print(\"fidelity %f\" % result['fidelity_hhl_to_classical'])\n", + "print(\"probability %f\" % result['probability_result'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Considering the circuit depth, it is increased approximately by a factor 10 compared to the two dimensional matrices. The circuit width is increased by two additional qubits" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "circuit_depth 315268\n", + "circuit_width 9\n" + ] + } + ], + "source": [ + "print(\"circuit_depth\", result['circuit_depth'])\n", + "print(\"circuit_width\", result['circuit_width'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 4x4 randomly-generated matrix" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, we show the application of HHL on a randomly-generated 4x4 matrix. We use the function `random_hermitian` to generate a random hermitian matrix and initialize the random seed to achieve reproducibility of the HHL run. Since the matrix can have negative eigenvalues, the `params` dictionary has to be modified by `\"negative_evals\": True` in `\"eigs\"` and `\"reciprocal\"`, respectively. We choose $$\\vec{b}= \\left( \\begin{array}{c}1 \\\\ 2 \\\\ 3 \\\\ 1 \\end{array} \\right)$$" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit import Aer\n", + "from qiskit.aqua import QuantumInstance\n", + "from qiskit.aqua.algorithms.single_sample import HHL\n", + "from qiskit.aqua.utils import random_hermitian" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is needed for this example to define the \"initial_state\", the \"qft\" and the \"iqft\" additionally:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "params3 = params\n", + "params3[\"reciprocal\"] = {\n", + " \"name\": \"Lookup\",\n", + " \"negative_evals\": True\n", + "}\n", + "params3[\"eigs\"] = {\n", + " \"expansion_mode\": \"suzuki\",\n", + " \"expansion_order\": 2,\n", + " \"name\": \"EigsQPE\",\n", + " \"negative_evals\": True,\n", + " \"num_ancillae\": 6,\n", + " \"num_time_slices\": 70\n", + "}\n", + "params3[\"initial_state\"] = {\n", + " \"name\": \"CUSTOM\"\n", + "}\n", + "params3[\"iqft\"] = {\n", + " \"name\": \"STANDARD\"\n", + "}\n", + "params3[\"qft\"] = {\n", + " \"name\": \"STANDARD\"\n", + "}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this example, we create an instance of the `HHL` class and run the algorithm with an input that is created programatically. To get the same pseudo-random matrix for every run, we set the random seed by using `np.random.seed(1)`." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "random matrix:\n", + "[[ 0.284+0.j -0.257-0.051j -0.124+0.033j 0.038+0.023j]\n", + " [-0.257+0.051j 0.404+0.j 0.067-0.079j 0.054+0.055j]\n", + " [-0.124-0.033j 0.067+0.079j 0.282-0.j 0.043+0.004j]\n", + " [ 0.038-0.023j 0.054-0.055j 0.043-0.004j 0.206+0.j ]]\n", + "HHL results:\n", + "hhl solution [ 79.9768 +4.52073j 60.28272 +3.09211j 37.51853 -9.5858j\n", + " -35.02324+26.46894j]\n", + "classical solution [ 76.1399 +1.92451j 57.30622 +1.20141j 35.96381-10.07775j\n", + " -32.03837+25.90593j]\n", + "fidelity 0.999946\n", + "probability 0.256771\n" + ] + } + ], + "source": [ + "# set the random seed to get the same pseudo-random matrix for every run\n", + "np.random.seed(1)\n", + "matrix = random_hermitian(4)\n", + "vector = [1, 2, 3, 1]\n", + "\n", + "print(\"random matrix:\")\n", + "m = np.array(matrix)\n", + "print(np.round(m, 3))\n", + "\n", + "algo_input = LinearSystemInput(matrix=matrix, vector=vector)\n", + "hhl = HHL.init_params(params3, algo_input)\n", + "backend = Aer.get_backend('statevector_simulator')\n", + "quantum_instance = QuantumInstance(backend=backend)\n", + "result_hhl = hhl.run(quantum_instance)\n", + "\n", + "print(\"HHL results:\")\n", + "print(\"hhl solution \", np.round(result_hhl['solution_hhl'], 5))\n", + "print(\"classical solution \", np.round(result_hhl['solution_classical'], 5))\n", + "print(\"fidelity %f\" % result_hhl['fidelity_hhl_to_classical'])\n", + "print(\"probability %f\" % result_hhl['probability_result'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The circuit depth and width are" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "circuit_depth 973532\n", + "circuit_width 12\n" + ] + } + ], + "source": [ + "print(\"circuit_depth\", result_hhl['circuit_depth'])\n", + "print(\"circuit_width\", result_hhl['circuit_width'])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From 9204369a5b7a0e49d370d26aa29d4f8d36cd25c7 Mon Sep 17 00:00:00 2001 From: Manoel Marques Date: Fri, 22 Mar 2019 16:29:50 -0400 Subject: [PATCH 025/116] Fix Hamiltonian run return values --- .../LiH_with_qubit_tapering_and_uccsd.ipynb | 29 +++++++++++++++---- 1 file changed, 23 insertions(+), 6 deletions(-) diff --git a/community/aqua/chemistry/LiH_with_qubit_tapering_and_uccsd.ipynb b/community/aqua/chemistry/LiH_with_qubit_tapering_and_uccsd.ipynb index 2e08a8734..d4d685ed4 100644 --- a/community/aqua/chemistry/LiH_with_qubit_tapering_and_uccsd.ipynb +++ b/community/aqua/chemistry/LiH_with_qubit_tapering_and_uccsd.ipynb @@ -65,8 +65,7 @@ "source": [ "core = Hamiltonian(transformation=TransformationType.FULL, qubit_mapping=QubitMappingType.PARITY, \n", " two_qubit_reduction=True, freeze_core=True)\n", - "algo_input = core.run(molecule)\n", - "qubit_op = algo_input.qubit_op\n", + "qubit_op, _ = core.run(molecule)\n", "\n", "print(\"Originally requires {} qubits\".format(qubit_op.num_qubits))\n", "print(qubit_op)" @@ -236,7 +235,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 8, "metadata": {}, "outputs": [], "source": [ @@ -267,7 +266,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, "metadata": {}, "outputs": [], "source": [ @@ -276,9 +275,27 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 10, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "=== GROUND STATE ENERGY ===\n", + " \n", + "* Electronic ground state energy (Hartree): -8.874303856889\n", + " - computed part: -1.078084288118\n", + " - frozen energy part: -7.796219568771\n", + " - particle hole part: 0.0\n", + "~ Nuclear repulsion energy (Hartree): 0.992207270475\n", + "> Total ground state energy (Hartree): -7.882096586414\n", + "The parameters for UCCSD are:\n", + "[ 0.03815735 0.00366554 0.03827111 0.00369737 -0.03604811 0.0594364\n", + " -0.02741369 -0.02735108 0.05956488 -0.11497243]\n" + ] + } + ], "source": [ "result = core.process_algorithm_result(algo_result)\n", "for line in result[0]:\n", From 7b082e29b47c8e35c6213a33d2842ff64c53f9fc Mon Sep 17 00:00:00 2001 From: woodsp Date: Sun, 31 Mar 2019 10:58:52 -0400 Subject: [PATCH 026/116] random_distributions was renamed to uncertainty_models --- qiskit/aqua/finance/european_call_option_pricing.ipynb | 8 ++++---- qiskit/aqua/finance/fixed_income_pricing.ipynb | 10 +++++----- 2 files changed, 9 insertions(+), 9 deletions(-) diff --git a/qiskit/aqua/finance/european_call_option_pricing.ipynb b/qiskit/aqua/finance/european_call_option_pricing.ipynb index 70a5e1485..f14bf4def 100644 --- a/qiskit/aqua/finance/european_call_option_pricing.ipynb +++ b/qiskit/aqua/finance/european_call_option_pricing.ipynb @@ -64,7 +64,7 @@ "from qiskit import BasicAer\n", "from qiskit.aqua.algorithms import AmplitudeEstimation\n", "from qiskit.aqua.components.uncertainty_problems import EuropeanCallExpectedValue, EuropeanCallDelta\n", - "from qiskit.aqua.components.random_distributions import LogNormalDistribution" + "from qiskit.aqua.components.uncertainty_models import LogNormalDistribution" ] }, { @@ -462,9 +462,9 @@ ], "metadata": { "kernelspec": { - "display_name": "qiskit_wor", + "display_name": "Python 3", "language": "python", - "name": "qiskit_wor" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -476,7 +476,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.6" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/qiskit/aqua/finance/fixed_income_pricing.ipynb b/qiskit/aqua/finance/fixed_income_pricing.ipynb index f5db68337..ca6a1a64c 100644 --- a/qiskit/aqua/finance/fixed_income_pricing.ipynb +++ b/qiskit/aqua/finance/fixed_income_pricing.ipynb @@ -52,8 +52,8 @@ "import numpy as np\n", "from qiskit import BasicAer\n", "from qiskit.aqua.algorithms import AmplitudeEstimation\n", - "from qiskit.aqua.components.random_distributions import MultivariateNormalDistribution\n", - "from qiskit.aqua.components.uncertainty_problems import FixedIncomeExpectedValue" + "from qiskit.aqua.components.uncertainty_problems import FixedIncomeExpectedValue\n", + "from qiskit.aqua.components.uncertainty_models import MultivariateNormalDistribution" ] }, { @@ -324,9 +324,9 @@ ], "metadata": { "kernelspec": { - "display_name": "qiskit_wor", + "display_name": "Python 3", "language": "python", - "name": "qiskit_wor" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -338,7 +338,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.6" + "version": "3.6.1" } }, "nbformat": 4, From 26cd630d86c506218dad3a08e6b4eb3289741ea5 Mon Sep 17 00:00:00 2001 From: Shaohan Hu Date: Tue, 2 Apr 2019 11:52:15 -0400 Subject: [PATCH 027/116] add arbitrary logic expr and truth table examples --- community/aqua/optimization/grover.ipynb | 135 ++++++++++++++++++++--- 1 file changed, 118 insertions(+), 17 deletions(-) diff --git a/community/aqua/optimization/grover.ipynb b/community/aqua/optimization/grover.ipynb index 86dbe67d8..e89608c2b 100644 --- a/community/aqua/optimization/grover.ipynb +++ b/community/aqua/optimization/grover.ipynb @@ -6,11 +6,9 @@ "collapsed": true }, "source": [ - "## _*Using Grover's Search to Find a Solution to a SAT problem*_\n", + "# _*Using Grover's Algorithm to Perform Quantum Search*_\n", "\n", - "This notebook demonstrates how to use the `Qiskit Aqua` library `Grover` search algorithm and process the result.\n", - "\n", - "Further information is available for the algorithms in the github repo qiskit/aqua/readme.md" + "This notebook demonstrates how to use the `Qiskit Aqua` library `Grover` search algorithm and process the result." ] }, { @@ -26,14 +24,16 @@ "from qiskit.aqua import QuantumInstance\n", "from qiskit.aqua import run_algorithm\n", "from qiskit.aqua.algorithms import Grover\n", - "from qiskit.aqua.components.oracles import LogicExpressionOracle" + "from qiskit.aqua.components.oracles import LogicExpressionOracle, TruthTableOracle" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Suppose we have a [Satisfiability (SAT) problem](https://en.wikipedia.org/wiki/Boolean_satisfiability_problem), for which we would like to use `Grover` search algorithm to find a satisfying solution. SAT problems are usually expressed in [Conjunctive Normal Forms (CNF)](https://en.wikipedia.org/wiki/Conjunctive_normal_form) and written in the [DIMACS-CNF](https://www.satcompetition.org/2009/format-benchmarks2009.html) format. For example:" + "## Use Quantum Search to Find Solutions to SATisfiability Problems\n", + "\n", + "Let's look at an example 3-Satisfiability (3-SAT) problem and walkthrough how we can use Quantum Search to find its satisfying solutions. 3-SAT problems are usually expressed in [Conjunctive Normal Forms (CNF)](https://en.wikipedia.org/wiki/Conjunctive_normal_form) and written in the [DIMACS-CNF](https://www.satcompetition.org/2009/format-benchmarks2009.html) format. For example:" ] }, { @@ -57,11 +57,11 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The CNF of this SAT instance contains 3 variables and 5 clauses:\n", + "The CNF of this 3-SAT instance contains 3 variables and 5 clauses:\n", "\n", "$(\\neg v_1 \\vee \\neg v_2 \\vee \\neg v_3) \\wedge (v_1 \\vee \\neg v_2 \\vee v_3) \\wedge (v_1 \\vee v_2 \\vee \\neg v_3) \\wedge (v_1 \\vee \\neg v_2 \\vee \\neg v_3) \\wedge (\\neg v_1 \\vee v_2 \\vee v_3)$\n", "\n", - "It can be verified that this SAT problem instance has three satisfying solutions:\n", + "It can be verified that this 3-SAT problem instance has three satisfying solutions:\n", "\n", "$(v_1, v_2, v_3) = (T, F, T)$ or $(F, F, F)$ or $(T, T, F)$\n", "\n", @@ -69,7 +69,6 @@ "\n", "`1 -2 3`, or `-1 -2 -3`, or `1 2 -3`.\n", "\n", - "\n", "With this example problem input, we then create the corresponding `oracle` for our `Grover` search. In particular, we use the `LogicExpressionOracle` component provided by Aqua, which supports parsing DIMACS-CNF format strings and constructing the corresponding oracle circuit." ] }, @@ -114,13 +113,13 @@ "name": "stdout", "output_type": "stream", "text": [ - "[1, 2, -3]\n" + "[1, -2, 3]\n" ] } ], "source": [ "backend = BasicAer.get_backend('qasm_simulator')\n", - "quantum_instance = QuantumInstance(backend, shots=1024)\n", + "quantum_instance = QuantumInstance(backend, shots=1024, circuit_caching=False)\n", "result = grover.run(quantum_instance)\n", "print(result['result'])" ] @@ -129,7 +128,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "As seen above, a satisfying solution to the specified SAT problem is obtained. And it is indeed one of the three satisfying solutions.\n", + "As seen above, a satisfying solution to the specified 3-SAT problem is obtained. And it is indeed one of the three satisfying solutions.\n", "\n", "Since we used the `'qasm_simulator'`, the complete measurement result is also returned, as shown in the plot below, where it can be seen that the binary strings `000`, `011`, and `101` (note the bit order in each string), corresponding to the three satisfying solutions all have high probabilities associated with them." ] @@ -141,7 +140,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -171,7 +170,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -183,7 +182,10 @@ ], "source": [ "params = {\n", - " 'problem': {'name': 'search'},\n", + " 'problem': {\n", + " 'name': 'search',\n", + " 'circuit_caching': False\n", + " },\n", " 'algorithm': {\n", " 'name': 'Grover'\n", " },\n", @@ -192,14 +194,113 @@ " 'expression': sat_instance\n", " },\n", " 'backend': {\n", - " 'shots': 1000\n", - " }\n", + " 'shots': 1000,\n", + " },\n", "}\n", "\n", "result_dict = run_algorithm(params, backend=backend)\n", "plot_histogram(result_dict['measurement'])" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Quantum Search with Arbitrary Boolean Logic Expressions\n", + "\n", + "Aqua's `Grover` can also be used to perform Quantum Search on `Oracle` constructed from means in addition to DIMACS. For example, the `LogicExpressionOracle` can actually be configured using arbitrary Boolean logic expressions, as demonstrated below." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "expression = '(w ^ x) & ~(y ^ z) & (x & y & z)'\n", + "oracle = LogicExpressionOracle(expression)\n", + "grover = Grover(oracle)\n", + "result = grover.run(QuantumInstance(BasicAer.get_backend('qasm_simulator'), shots=1024, circuit_caching=False))\n", + "plot_histogram(result['measurement'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the example above, the input Boolean logic expression `'(w ^ x) & ~(y ^ z) & (x & y & z)'` should be quite self-explanatory, where `^`, `~`, and `&` represent the Boolean logic XOR, NOT, and AND operators, respectively. It should be quite easy to figure out the satisfying solution by examining its parts: `w ^ x` calls for `w` and `x` taking different values; `~(y ^ z)` requires `y` and `z` be the same; `x & y & z` dictates all three to be `True`. Putting these together, we get the satisfying solution `(w, x, y, z) = (False, True, True, True)`, which our `Grover`'s result agrees with." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Quantum Search with Oracles from TruthTable\n", + "\n", + "With Aqua, `Oracle`s can also be constructed from truth tables, meaning we can also perform Quantum Search on truth tables. Even though this might seem like a moo point as we would be essentially searching for entries of a truth table with the $1$ value, it'd a good example for demonstrative purpose." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "truthtable = '1000000000000001'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As shown, the `truthtable` is specified with a bitstring containing values of all entries in the table. It has length $16$, so the corresponding truth table is of $4$ input bits. Since the very first and last values are $1$, the corresponding truth table target entries are `0000` and `1111`.\n", + "\n", + "Next, we can setup the `Oracle` and `Grover` objects to perform Quantum Search as usual." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "oracle = TruthTableOracle(truthtable)\n", + "grover = Grover(oracle)\n", + "result = grover.run(QuantumInstance(BasicAer.get_backend('qasm_simulator'), shots=1024, circuit_caching=False))\n", + "plot_histogram(result['measurement'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As shown, the search result coincides with our expectation." + ] + }, { "cell_type": "code", "execution_count": null, From 335f9cb85dce134bd5fa06da30a6a7d30765a094 Mon Sep 17 00:00:00 2001 From: Shaohan Hu Date: Wed, 3 Apr 2019 11:24:59 -0400 Subject: [PATCH 028/116] LogicExpressionOracle -> LogicalExpressionOracle --- community/aqua/optimization/grover.ipynb | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/community/aqua/optimization/grover.ipynb b/community/aqua/optimization/grover.ipynb index e89608c2b..484e398c0 100644 --- a/community/aqua/optimization/grover.ipynb +++ b/community/aqua/optimization/grover.ipynb @@ -24,7 +24,7 @@ "from qiskit.aqua import QuantumInstance\n", "from qiskit.aqua import run_algorithm\n", "from qiskit.aqua.algorithms import Grover\n", - "from qiskit.aqua.components.oracles import LogicExpressionOracle, TruthTableOracle" + "from qiskit.aqua.components.oracles import LogicalExpressionOracle, TruthTableOracle" ] }, { @@ -69,7 +69,7 @@ "\n", "`1 -2 3`, or `-1 -2 -3`, or `1 2 -3`.\n", "\n", - "With this example problem input, we then create the corresponding `oracle` for our `Grover` search. In particular, we use the `LogicExpressionOracle` component provided by Aqua, which supports parsing DIMACS-CNF format strings and constructing the corresponding oracle circuit." + "With this example problem input, we then create the corresponding `oracle` for our `Grover` search. In particular, we use the `LogicalExpressionOracle` component provided by Aqua, which supports parsing DIMACS-CNF format strings and constructing the corresponding oracle circuit." ] }, { @@ -78,7 +78,7 @@ "metadata": {}, "outputs": [], "source": [ - "oracle = LogicExpressionOracle(sat_instance)" + "oracle = LogicalExpressionOracle(sat_instance)" ] }, { @@ -190,7 +190,7 @@ " 'name': 'Grover'\n", " },\n", " 'oracle': {\n", - " 'name': 'LogicExpressionOracle',\n", + " 'name': 'LogicalExpressionOracle',\n", " 'expression': sat_instance\n", " },\n", " 'backend': {\n", @@ -208,7 +208,7 @@ "source": [ "## Quantum Search with Arbitrary Boolean Logic Expressions\n", "\n", - "Aqua's `Grover` can also be used to perform Quantum Search on `Oracle` constructed from means in addition to DIMACS. For example, the `LogicExpressionOracle` can actually be configured using arbitrary Boolean logic expressions, as demonstrated below." + "Aqua's `Grover` can also be used to perform Quantum Search on `Oracle` constructed from means in addition to DIMACS. For example, the `LogicalExpressionOracle` can actually be configured using arbitrary Boolean logic expressions, as demonstrated below." ] }, { @@ -230,7 +230,7 @@ ], "source": [ "expression = '(w ^ x) & ~(y ^ z) & (x & y & z)'\n", - "oracle = LogicExpressionOracle(expression)\n", + "oracle = LogicalExpressionOracle(expression)\n", "grover = Grover(oracle)\n", "result = grover.run(QuantumInstance(BasicAer.get_backend('qasm_simulator'), shots=1024, circuit_caching=False))\n", "plot_histogram(result['measurement'])" From abcc683bbb6ddb8e4eb01a4e6be7ef34ba2a40b0 Mon Sep 17 00:00:00 2001 From: Shaohan Hu Date: Wed, 3 Apr 2019 12:08:41 -0400 Subject: [PATCH 029/116] moo -> moot --- community/aqua/optimization/grover.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/community/aqua/optimization/grover.ipynb b/community/aqua/optimization/grover.ipynb index 484e398c0..aa26f955a 100644 --- a/community/aqua/optimization/grover.ipynb +++ b/community/aqua/optimization/grover.ipynb @@ -249,7 +249,7 @@ "source": [ "## Quantum Search with Oracles from TruthTable\n", "\n", - "With Aqua, `Oracle`s can also be constructed from truth tables, meaning we can also perform Quantum Search on truth tables. Even though this might seem like a moo point as we would be essentially searching for entries of a truth table with the $1$ value, it'd a good example for demonstrative purpose." + "With Aqua, `Oracle`s can also be constructed from truth tables, meaning we can also perform Quantum Search on truth tables. Even though this might seem like a moot point as we would be essentially searching for entries of a truth table with the $1$ value, it'd a good example for demonstrative purpose." ] }, { From 569ed81340fadcb12eda643b0ae79a50ac374fcb Mon Sep 17 00:00:00 2001 From: woodsp Date: Wed, 3 Apr 2019 14:13:56 -0400 Subject: [PATCH 030/116] Tutorial for variational algo optimization callback --- community/aqua/general/vqe_convergence.ipynb | 247 +++++++++++++++++++ 1 file changed, 247 insertions(+) create mode 100644 community/aqua/general/vqe_convergence.ipynb diff --git a/community/aqua/general/vqe_convergence.ipynb b/community/aqua/general/vqe_convergence.ipynb new file mode 100644 index 000000000..1f720d96a --- /dev/null +++ b/community/aqua/general/vqe_convergence.ipynb @@ -0,0 +1,247 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## _*VQE; using its callback to monitor optimization progress*_\n", + "\n", + "This notebook demonstrates using Qiskit Aqua's VQE algorithm to plot graphs of the convergence path to ground state energy with different optimizers.\n", + "\n", + "This notebook uses the callback capability of VQE to capture information at each objective functional evaluation where it is computing the energy using the parameterized variational form. While the params themselves are also part of the callback we are only interested in the energy value here to plot the convergence. \n", + "\n", + "Note: other variational algorithms such as QAOA and QSVM have similar callbacks." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pylab\n", + "\n", + "from qiskit import BasicAer\n", + "from qiskit.aqua import Operator, QuantumInstance, aqua_globals\n", + "from qiskit.aqua.algorithms.adaptive import VQE\n", + "from qiskit.aqua.algorithms.classical import ExactEigensolver\n", + "from qiskit.aqua.components.initial_states import Zero\n", + "from qiskit.aqua.components.optimizers import COBYLA, L_BFGS_B, SLSQP\n", + "from qiskit.aqua.components.variational_forms import RY" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First we create a qubit operator for VQE. Here we have taken a set of paulis that were originally computed by qiskit-chemistry for an H2 molecule." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "pauli_dict = {\n", + " 'paulis': [{\"coeff\": {\"imag\": 0.0, \"real\": -1.052373245772859}, \"label\": \"II\"},\n", + " {\"coeff\": {\"imag\": 0.0, \"real\": 0.39793742484318045}, \"label\": \"ZI\"},\n", + " {\"coeff\": {\"imag\": 0.0, \"real\": -0.39793742484318045}, \"label\": \"IZ\"},\n", + " {\"coeff\": {\"imag\": 0.0, \"real\": -0.01128010425623538}, \"label\": \"ZZ\"},\n", + " {\"coeff\": {\"imag\": 0.0, \"real\": 0.18093119978423156}, \"label\": \"XX\"}\n", + " ]\n", + "}\n", + "\n", + "qubit_op = Operator.load_from_dict(pauli_dict)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we loop over the set of optimizers. The defaults for maxiters/evals for the respective optimizers is more than sufficient to converge the above H2 problem so we do not need to add any logic to set accordingly." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Optimization complete \n" + ] + } + ], + "source": [ + "optimizers = [COBYLA, L_BFGS_B, SLSQP]\n", + "converge_cnts = np.empty([len(optimizers)], dtype=object)\n", + "converge_vals = np.empty([len(optimizers)], dtype=object)\n", + "num_qubits = qubit_op.num_qubits\n", + "\n", + "for i in range(len(optimizers)):\n", + " aqua_globals.random_seed = 250\n", + " optimizer = optimizers[i]()\n", + " print('\\rOptimizer: {} '.format(type(optimizer).__name__), end='')\n", + " init_state = Zero(num_qubits)\n", + " var_form = RY(num_qubits, initial_state=init_state)\n", + "\n", + " counts = []\n", + " values = []\n", + " def store_intermediate_result(eval_count, parameters, mean, std):\n", + " counts.append(eval_count)\n", + " values.append(mean)\n", + " \n", + " algo = VQE(qubit_op, var_form, optimizer, 'matrix', callback=store_intermediate_result)\n", + " backend = BasicAer.get_backend('statevector_simulator')\n", + " quantum_instance = QuantumInstance(backend=backend) \n", + " algo_result = algo.run(quantum_instance)\n", + " converge_cnts[i] = np.asarray(counts)\n", + " converge_vals[i] = np.asarray(values)\n", + "print('\\rOptimization complete ');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now from the callback data we stored we can plot the energy value at each objective function call each optimzer makes. An optimizer using a finite difference method for computing gradient has that characteristic step like plot where for a number of evaluations it is computing the value for close by points to establish a gradient (the close by points having very similiar values whose difference cannot be seen on the scale of the graph here)." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pylab.rcParams['figure.figsize'] = (12, 8)\n", + "for i in range(len(optimizers)):\n", + " pylab.plot(converge_cnts[i], converge_vals[i], label=optimizers[i].__name__)\n", + "pylab.xlabel('Eval count')\n", + "pylab.ylabel('Energy')\n", + "pylab.title('Energy convergence for various optimizers')\n", + "pylab.legend(loc='upper right')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally since the above problem is still easily tractable classically we can use ExactEigensolver to compute a reference value for the solution. We can now plot the difference from the resultant exact solution as the energy converges with VQE towards the minimum value which should be that exact classical solution." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Reference value: -1.85727503020238\n" + ] + } + ], + "source": [ + "ee = ExactEigensolver(qubit_op)\n", + "result = ee.run()\n", + "ref = result['energy']\n", + "print('Reference value: {}'.format(ref))" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pylab.rcParams['figure.figsize'] = (12, 8)\n", + "for i in range(len(optimizers)):\n", + " pylab.plot(converge_cnts[i], abs(ref - converge_vals[i]), label=optimizers[i].__name__)\n", + "pylab.xlabel('Eval count')\n", + "pylab.ylabel('Energy difference from solution reference value')\n", + "pylab.title('Energy convergence for various optimizers')\n", + "pylab.yscale('log')\n", + "pylab.legend(loc='upper right')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From f24934938451ab3d3eea5bbdc00ea191781f9b5e Mon Sep 17 00:00:00 2001 From: Shaohan Hu Date: Wed, 3 Apr 2019 18:07:50 -0400 Subject: [PATCH 031/116] remove circuit_caching=False flags --- community/aqua/optimization/grover.ipynb | 7 +++---- 1 file changed, 3 insertions(+), 4 deletions(-) diff --git a/community/aqua/optimization/grover.ipynb b/community/aqua/optimization/grover.ipynb index aa26f955a..30d78fd57 100644 --- a/community/aqua/optimization/grover.ipynb +++ b/community/aqua/optimization/grover.ipynb @@ -119,7 +119,7 @@ ], "source": [ "backend = BasicAer.get_backend('qasm_simulator')\n", - "quantum_instance = QuantumInstance(backend, shots=1024, circuit_caching=False)\n", + "quantum_instance = QuantumInstance(backend, shots=1024)\n", "result = grover.run(quantum_instance)\n", "print(result['result'])" ] @@ -184,7 +184,6 @@ "params = {\n", " 'problem': {\n", " 'name': 'search',\n", - " 'circuit_caching': False\n", " },\n", " 'algorithm': {\n", " 'name': 'Grover'\n", @@ -232,7 +231,7 @@ "expression = '(w ^ x) & ~(y ^ z) & (x & y & z)'\n", "oracle = LogicalExpressionOracle(expression)\n", "grover = Grover(oracle)\n", - "result = grover.run(QuantumInstance(BasicAer.get_backend('qasm_simulator'), shots=1024, circuit_caching=False))\n", + "result = grover.run(QuantumInstance(BasicAer.get_backend('qasm_simulator'), shots=1024))\n", "plot_histogram(result['measurement'])" ] }, @@ -290,7 +289,7 @@ "source": [ "oracle = TruthTableOracle(truthtable)\n", "grover = Grover(oracle)\n", - "result = grover.run(QuantumInstance(BasicAer.get_backend('qasm_simulator'), shots=1024, circuit_caching=False))\n", + "result = grover.run(QuantumInstance(BasicAer.get_backend('qasm_simulator'), shots=1024))\n", "plot_histogram(result['measurement'])" ] }, From 1ce67939022176c3980ceea3ffa950344be0fff2 Mon Sep 17 00:00:00 2001 From: Shaohan Hu Date: Thu, 4 Apr 2019 09:28:00 -0400 Subject: [PATCH 032/116] minor edits --- community/aqua/optimization/grover.ipynb | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/community/aqua/optimization/grover.ipynb b/community/aqua/optimization/grover.ipynb index 30d78fd57..b7f0accf2 100644 --- a/community/aqua/optimization/grover.ipynb +++ b/community/aqua/optimization/grover.ipynb @@ -31,7 +31,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Use Quantum Search to Find Solutions to SATisfiability Problems\n", + "## Use Quantum Search to Find Solutions to 3-SAT Problems\n", "\n", "Let's look at an example 3-Satisfiability (3-SAT) problem and walkthrough how we can use Quantum Search to find its satisfying solutions. 3-SAT problems are usually expressed in [Conjunctive Normal Forms (CNF)](https://en.wikipedia.org/wiki/Conjunctive_normal_form) and written in the [DIMACS-CNF](https://www.satcompetition.org/2009/format-benchmarks2009.html) format. For example:" ] @@ -42,7 +42,7 @@ "metadata": {}, "outputs": [], "source": [ - "sat_instance = '''\n", + "input_3sat_instance = '''\n", "c example DIMACS-CNF SAT\n", "p cnf 3 5\n", "-1 -2 -3 0\n", @@ -78,7 +78,7 @@ "metadata": {}, "outputs": [], "source": [ - "oracle = LogicalExpressionOracle(sat_instance)" + "oracle = LogicalExpressionOracle(input_3sat_instance)" ] }, { @@ -190,7 +190,7 @@ " },\n", " 'oracle': {\n", " 'name': 'LogicalExpressionOracle',\n", - " 'expression': sat_instance\n", + " 'expression': input_3sat_instance\n", " },\n", " 'backend': {\n", " 'shots': 1000,\n", @@ -205,9 +205,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Quantum Search with Arbitrary Boolean Logic Expressions\n", + "## Quantum Search with Arbitrary Boolean Logical Expressions\n", "\n", - "Aqua's `Grover` can also be used to perform Quantum Search on `Oracle` constructed from means in addition to DIMACS. For example, the `LogicalExpressionOracle` can actually be configured using arbitrary Boolean logic expressions, as demonstrated below." + "Aqua's `Grover` can also be used to perform Quantum Search on `Oracle` constructed from means in addition to DIMACS. For example, the `LogicalExpressionOracle` can actually be configured using arbitrary Boolean logical expressions, as demonstrated below." ] }, { @@ -239,7 +239,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "In the example above, the input Boolean logic expression `'(w ^ x) & ~(y ^ z) & (x & y & z)'` should be quite self-explanatory, where `^`, `~`, and `&` represent the Boolean logic XOR, NOT, and AND operators, respectively. It should be quite easy to figure out the satisfying solution by examining its parts: `w ^ x` calls for `w` and `x` taking different values; `~(y ^ z)` requires `y` and `z` be the same; `x & y & z` dictates all three to be `True`. Putting these together, we get the satisfying solution `(w, x, y, z) = (False, True, True, True)`, which our `Grover`'s result agrees with." + "In the example above, the input Boolean logical expression `'(w ^ x) & ~(y ^ z) & (x & y & z)'` should be quite self-explanatory, where `^`, `~`, and `&` represent the Boolean logical XOR, NOT, and AND operators, respectively. It should be quite easy to figure out the satisfying solution by examining its parts: `w ^ x` calls for `w` and `x` taking different values; `~(y ^ z)` requires `y` and `z` be the same; `x & y & z` dictates all three to be `True`. Putting these together, we get the satisfying solution `(w, x, y, z) = (False, True, True, True)`, which our `Grover`'s result agrees with." ] }, { From 0cfa662c8ec40d721c976bb0daad5f289ab35c2e Mon Sep 17 00:00:00 2001 From: Shaohan Hu Date: Thu, 4 Apr 2019 09:28:47 -0400 Subject: [PATCH 033/116] minor edit --- community/aqua/optimization/grover.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/community/aqua/optimization/grover.ipynb b/community/aqua/optimization/grover.ipynb index b7f0accf2..0dba7d671 100644 --- a/community/aqua/optimization/grover.ipynb +++ b/community/aqua/optimization/grover.ipynb @@ -43,7 +43,7 @@ "outputs": [], "source": [ "input_3sat_instance = '''\n", - "c example DIMACS-CNF SAT\n", + "c example DIMACS-CNF 3-SAT\n", "p cnf 3 5\n", "-1 -2 -3 0\n", "1 -2 3 0\n", From 6ee210414d91111cdb7fe2ab0c28b968b7141113 Mon Sep 17 00:00:00 2001 From: woodsp Date: Thu, 4 Apr 2019 16:19:47 -0400 Subject: [PATCH 034/116] Update for latest hhl & ExactLPsolver --- .../general/linear_systems_of_equations.ipynb | 150 +++++++----------- 1 file changed, 55 insertions(+), 95 deletions(-) diff --git a/qiskit/aqua/general/linear_systems_of_equations.ipynb b/qiskit/aqua/general/linear_systems_of_equations.ipynb index b9ad0233d..d99261ada 100644 --- a/qiskit/aqua/general/linear_systems_of_equations.ipynb +++ b/qiskit/aqua/general/linear_systems_of_equations.ipynb @@ -42,6 +42,7 @@ "source": [ "from qiskit.aqua import run_algorithm\n", "from qiskit.aqua.input import LinearSystemInput\n", + "from qiskit.aqua.algorithms.classical import ExactLPsolver\n", "import numpy as np" ] }, @@ -69,6 +70,7 @@ " 'name': 'Lookup'\n", " },\n", " 'backend': {\n", + " 'provider': 'qiskit.BasicAer',\n", " 'name': 'statevector_simulator'\n", " }\n", "}" @@ -112,27 +114,24 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "hhl solution [1.05859-0.j 1.99245-0.j]\n", - "classical solution [1. 2.]\n", - "fidelity 0.999389\n", - "probability 0.024630\n" + "solution [1.05859+0.j 1.99245+0.j]\n", + "classical solution [1. 2.]\n" ] } ], "source": [ "result = run_algorithm(params)\n", + "print(\"solution \", np.round(result['solution'], 5))\n", "\n", - "print(\"hhl solution \", np.round(result['solution_hhl'], 5))\n", - "print(\"classical solution \", np.round(result['solution_classical'], 5))\n", - "print(\"fidelity %f\" % result['fidelity_hhl_to_classical'])\n", - "print(\"probability %f\" % result['probability_result'])" + "classical_result = ExactLPsolver(matrix, vector).run()\n", + "print(\"classical solution \", np.round(classical_result['solution'], 5))" ] }, { @@ -144,17 +143,15 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "hhl solution [0.84664-0.j 2.01762-0.j]\n", - "classical solution [1. 2.]\n", - "fidelity 0.995605\n", - "probability 0.361437\n" + "solution [0.84664+0.j 2.01762+0.j]\n", + "classical solution [1. 2.]\n" ] } ], @@ -165,11 +162,10 @@ "}\n", "\n", "result = run_algorithm(params2)\n", + "print(\"solution \", np.round(result['solution'], 5))\n", "\n", - "print(\"hhl solution \", np.round(result['solution_hhl'], 5))\n", - "print(\"classical solution \", np.round(result['solution_classical'], 5))\n", - "print(\"fidelity %f\" % result['fidelity_hhl_to_classical'])\n", - "print(\"probability %f\" % result['probability_result'])" + "classical_result = ExactLPsolver(matrix, vector).run()\n", + "print(\"classical solution \", np.round(classical_result['solution'], 5))" ] }, { @@ -181,21 +177,21 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "circuit_depth 12255\n", + "circuit_depth 12256\n", "circuit_width 7\n" ] } ], "source": [ - "print(\"circuit_depth\", result['circuit_depth'])\n", - "print(\"circuit_width\", result['circuit_width'])" + "print(\"circuit_depth\", result['circuit_info']['depth'])\n", + "print(\"circuit_width\", result['circuit_info']['width'])" ] }, { @@ -220,7 +216,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 8, "metadata": {}, "outputs": [], "source": [ @@ -235,27 +231,24 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "hhl solution [0.22147+0.j 0.22034-0.j]\n", - "classical solution [0.14286 0.28571]\n", - "fidelity 0.898454\n", - "probability 0.424639\n" + "solution [0.22147+0.j 0.22034-0.j]\n", + "classical solution [0.14286 0.28571]\n" ] } ], "source": [ "result = run_algorithm(params)\n", + "print(\"solution \", np.round(result['solution'], 5))\n", "\n", - "print(\"hhl solution \", np.round(result['solution_hhl'], 5))\n", - "print(\"classical solution \", np.round(result['solution_classical'], 5))\n", - "print(\"fidelity %f\" % result['fidelity_hhl_to_classical'])\n", - "print(\"probability %f\" % result['probability_result'])" + "classical_result = ExactLPsolver(matrix, vector).run()\n", + "print(\"classical solution \", np.round(classical_result['solution'], 5))" ] }, { @@ -267,21 +260,21 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "circuit_depth 30253\n", + "circuit_depth 30254\n", "circuit_width 7\n" ] } ], "source": [ - "print(\"circuit_depth\", result['circuit_depth'])\n", - "print(\"circuit_width\", result['circuit_width'])" + "print(\"circuit_depth\", result['circuit_info']['depth'])\n", + "print(\"circuit_width\", result['circuit_info']['width'])" ] }, { @@ -312,7 +305,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 11, "metadata": {}, "outputs": [], "source": [ @@ -334,28 +327,25 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "hhl solution [ 0.18195-0.j 0. -0.j -0. -0.j -0. +0.j 0. +0.j\n", - " 0. +0.j -0. -0.j 0.18041+0.j]\n", - "classical solution [0.21053 0. 0. 0. 0. 0. 0. 0.15789]\n", - "fidelity 0.981173\n", - "probability 0.935566\n" + "solution [ 0.18195-0.j 0. -0.j 0. -0.j -0. +0.j 0. +0.j\n", + " -0. +0.j -0. -0.j 0.18041+0.j]\n", + "classical solution [0.21053 0. 0. 0. 0. 0. 0. 0.15789]\n" ] } ], "source": [ "result = run_algorithm(params)\n", + "print(\"solution \", np.round(result['solution'], 5))\n", "\n", - "print(\"hhl solution \", np.round(result['solution_hhl'], 5))\n", - "print(\"classical solution \", np.round(result['solution_classical'], 5))\n", - "print(\"fidelity %f\" % result['fidelity_hhl_to_classical'])\n", - "print(\"probability %f\" % result['probability_result'])" + "classical_result = ExactLPsolver(matrix, vector).run()\n", + "print(\"classical solution \", np.round(classical_result['solution'], 5))" ] }, { @@ -367,21 +357,21 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "circuit_depth 315268\n", + "circuit_depth 315281\n", "circuit_width 9\n" ] } ], "source": [ - "print(\"circuit_depth\", result['circuit_depth'])\n", - "print(\"circuit_width\", result['circuit_width'])" + "print(\"circuit_depth\", result['circuit_info']['depth'])\n", + "print(\"circuit_width\", result['circuit_info']['width'])" ] }, { @@ -400,11 +390,11 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 14, "metadata": {}, "outputs": [], "source": [ - "from qiskit import Aer\n", + "from qiskit import BasicAer\n", "from qiskit.aqua import QuantumInstance\n", "from qiskit.aqua.algorithms.single_sample import HHL\n", "from qiskit.aqua.utils import random_hermitian" @@ -419,7 +409,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 15, "metadata": {}, "outputs": [], "source": [ @@ -456,28 +446,9 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "random matrix:\n", - "[[ 0.284+0.j -0.257-0.051j -0.124+0.033j 0.038+0.023j]\n", - " [-0.257+0.051j 0.404+0.j 0.067-0.079j 0.054+0.055j]\n", - " [-0.124-0.033j 0.067+0.079j 0.282-0.j 0.043+0.004j]\n", - " [ 0.038-0.023j 0.054-0.055j 0.043-0.004j 0.206+0.j ]]\n", - "HHL results:\n", - "hhl solution [ 79.9768 +4.52073j 60.28272 +3.09211j 37.51853 -9.5858j\n", - " -35.02324+26.46894j]\n", - "classical solution [ 76.1399 +1.92451j 57.30622 +1.20141j 35.96381-10.07775j\n", - " -32.03837+25.90593j]\n", - "fidelity 0.999946\n", - "probability 0.256771\n" - ] - } - ], + "outputs": [], "source": [ "# set the random seed to get the same pseudo-random matrix for every run\n", "np.random.seed(1)\n", @@ -490,15 +461,13 @@ "\n", "algo_input = LinearSystemInput(matrix=matrix, vector=vector)\n", "hhl = HHL.init_params(params3, algo_input)\n", - "backend = Aer.get_backend('statevector_simulator')\n", + "backend = BasicAer.get_backend('statevector_simulator')\n", "quantum_instance = QuantumInstance(backend=backend)\n", "result_hhl = hhl.run(quantum_instance)\n", + "print(\"solution \", np.round(result['solution'], 5))\n", "\n", - "print(\"HHL results:\")\n", - "print(\"hhl solution \", np.round(result_hhl['solution_hhl'], 5))\n", - "print(\"classical solution \", np.round(result_hhl['solution_classical'], 5))\n", - "print(\"fidelity %f\" % result_hhl['fidelity_hhl_to_classical'])\n", - "print(\"probability %f\" % result_hhl['probability_result'])" + "classical_result = ExactLPsolver(matrix, vector).run()\n", + "print(\"classical solution \", np.round(classical_result['solution'], 5))" ] }, { @@ -510,21 +479,12 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "circuit_depth 973532\n", - "circuit_width 12\n" - ] - } - ], + "outputs": [], "source": [ - "print(\"circuit_depth\", result_hhl['circuit_depth'])\n", - "print(\"circuit_width\", result_hhl['circuit_width'])" + "print(\"circuit_depth\", result_hhl['circuit_info']['depth'])\n", + "print(\"circuit_width\", result_hhl['circuit_info']['width']" ] }, { @@ -551,7 +511,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.6.1" } }, "nbformat": 4, From d467b4f26838810645b343f48e03b6ab5eb3cb3a Mon Sep 17 00:00:00 2001 From: woodsp Date: Fri, 5 Apr 2019 16:55:22 -0400 Subject: [PATCH 035/116] Update Aqua general tutorials --- .../algorithm_introduction_with_vqe.ipynb | 298 ++++++++++++++++++ community/aqua/general/eoh.ipynb | 27 +- community/aqua/general/evolution.ipynb | 79 +++-- 3 files changed, 373 insertions(+), 31 deletions(-) create mode 100644 community/aqua/general/algorithm_introduction_with_vqe.ipynb diff --git a/community/aqua/general/algorithm_introduction_with_vqe.ipynb b/community/aqua/general/algorithm_introduction_with_vqe.ipynb new file mode 100644 index 000000000..e74cbabe9 --- /dev/null +++ b/community/aqua/general/algorithm_introduction_with_vqe.ipynb @@ -0,0 +1,298 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## _*Using Qiskit Aqua algorithms, a how to guide*_\n", + "\n", + "This notebook demonstrates how to use the `Qiskit Aqua` library to invoke an algorithm and process the result.\n", + "\n", + "Further information may be found for the algorithms in the online [Aqua documentation](https://qiskit.org/documentation/aqua/algorithms.html).\n", + "\n", + "Algorithms in Aqua can be created and run as usual in Python by constructing instances and calling methods. There is also a high level `run_algorithm` method that takes a configuration dictionary with data describing which algorithm to use, which components etc along with an InputInstance type to supply data to the algorithm. This latter approach is what we call `declarative` with the former, the regular Python way, `programmatic`. This tutorial will show both approaches.\n", + "\n", + "Aqua has many `algorithms` for solving different problems. For some we also have classical algorithms, that take the exact same input data, to solve the problem. This can be useful in the near term as Quantum algorithms are developed since we are still at a stage where we can do classical comparison of the result.\n", + "\n", + "Aqua also has various `components` which are dependent objects used by algorithms, such as variational forms, qfts, initial states etc. We will see more on this below.\n", + "\n", + "Lastly for developers we also have a collections of `circuits` and gates which can be used to help build out new components and algorithms.\n", + "\n", + "Here we will choose to show some of the main aspects of Aqua by solving a ground state energy problem." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit.aqua import Operator" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As input, for an energy problem, we need a Hamiltonian and so we first create a suitable `Operator ` instance. In this case we have a paulis list, as below, from a previously computed Hamiltonian, that we saved, so as to focus this notebook on using the algorithms. We simply load these paulis to create the original Operator.\n", + "\n", + "This Hamiltonian was created originally using Qiskit Chemistry for an H2 molecule at 0.735A interatomic distance. Please refer to the chemistry tutorials here if you are interested in understanding more. Suffice to say at this level Aqua does not really care about the source of the Operator." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "pauli_dict = {\n", + " 'paulis': [{\"coeff\": {\"imag\": 0.0, \"real\": -1.052373245772859}, \"label\": \"II\"},\n", + " {\"coeff\": {\"imag\": 0.0, \"real\": 0.39793742484318045}, \"label\": \"ZI\"},\n", + " {\"coeff\": {\"imag\": 0.0, \"real\": -0.39793742484318045}, \"label\": \"IZ\"},\n", + " {\"coeff\": {\"imag\": 0.0, \"real\": -0.01128010425623538}, \"label\": \"ZZ\"},\n", + " {\"coeff\": {\"imag\": 0.0, \"real\": 0.18093119978423156}, \"label\": \"XX\"}\n", + " ]\n", + "}\n", + "\n", + "qubit_op = Operator.load_from_dict(pauli_dict)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Let's start with a classical algorithm\n", + "\n", + "We can now use the Operator without regard to how it was created. We chose to start this tutorial with a classical algorithm as it involves a little less setting up than the `VQE` quantum algorithm we will use later. Here we will use `ExactEigensolver` to compute the minimum eigenvalue of the Operator (Hamiltonian).\n", + "\n", + "#### First let's show the `programmatic` approach.\n", + "\n", + "We construct an `ExactEigensolver` instance, passing in the Operator, and then call `run()` on in order to compute the result. All Aqua algorithms have the run method (it is defined by a base class which all algorithms extend) and while no parameters are need for classical algorithms a quantum algorithm will require a backend (quantum simulator or real device) on which it will be run. The `result` object returned is a dictionary. While the results fields can be different for algorithms solving different problems, and even within a given problem type there may be algorithm specific data returned, for a given problem the fields core to that problem are common across algorithms in order that different algorithms can be chosen to solve the same problem in a consistent fashion." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-1.857275030202378\n" + ] + } + ], + "source": [ + "from qiskit.aqua.algorithms import ExactEigensolver\n", + "\n", + "ee = ExactEigensolver(qubit_op)\n", + "result = ee.run()\n", + "print(result['energy'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Now let's show the `declarative` approach. \n", + "\n", + "Here we need to prepare a configuration dictionary of parameters to define the algorithm. Again we we will use the ExactEigensolver and need to create an `algorithm` where it is named by `name`. The name comes from a `CONFIGURATION` dictionary in the algorithm and this name is registered to the Aqua discovery framework so we can load the corresponding class and run it during the exceution of `run_algorithm`. `run_algorithm` requires the configuration dictionary and input data passed via an InputInstance class. For an energy problem the data is supplied via an EnergyInput (extends InputInstance), other problem types have their own specific InputInstance. `run_algorithm` returns the same dictionary as above (internally it calls the run() method of the algorithm and passes back the result)\n", + "\n", + "Note: there are other fields such `problem` that could have been added below. This field defaults to `energy`, which is what we want so it has been omitted. Defaults are convenient in the declarative form too as algorithms can define for both their properties as well as defaults for dependent components." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-1.8572750302023808\n" + ] + } + ], + "source": [ + "from qiskit.aqua import run_algorithm\n", + "from qiskit.aqua.input import EnergyInput\n", + "\n", + "aqua_cfg_dict = {\n", + " 'algorithm': {\n", + " 'name': 'ExactEigensolver'\n", + " }\n", + "}\n", + "\n", + "algo_input = EnergyInput(qubit_op)\n", + "result = run_algorithm(aqua_cfg_dict, algo_input)\n", + "print(result['energy'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Lets switch now to using a Quantum algorithm.\n", + "\n", + "We will use the Variational Quantum Eigensolver (VQE) to solve the same problem as above. As its name implies its uses a variational approach. An ansatz (a variational form) is supplied and using a quantum/classical hybrid technique the energy resulting from evaluating the Operator with the variational form on a quantum backend is taken down to a minimum using a classical optimizer that varies the parameters of the variational form.\n", + "\n", + "#### Lets do the `declarative` approach first this time\n", + "\n", + "In the description above we talked about `VQE` a `variational form` and an `optimizer`. We can now set this up as a dictionary. While we can omit them from the dictionary, such that defaults are used, here we specify them explicitly so we can set their parameters as we desire.\n", + "\n", + "As this is a quantum algorithm we need to specify a backend. Here we use the `statevector_simpulator` from the `qiskit.BasicAer` provider from `Qiskit Terra`. As this is a variational algorithm going from quantum to classical and looping until it finds a minimum it takes a few seconds. The result here is very close to our classical result above." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-1.8572750302012253\n" + ] + } + ], + "source": [ + "aqua_cfg_dict = {\n", + " 'algorithm': {\n", + " 'name': 'VQE',\n", + " 'operator_mode': 'matrix'\n", + " },\n", + " 'variational_form': {\n", + " 'name': 'RYRZ',\n", + " 'depth': 3,\n", + " 'entanglement': 'linear'\n", + " },\n", + " 'optimizer': {\n", + " 'name': 'L_BFGS_B',\n", + " 'maxfun': 1000\n", + " },\n", + " 'backend': {\n", + " 'name': 'statevector_simulator',\n", + " 'provider': 'qiskit.BasicAer'\n", + " }\n", + "}\n", + "\n", + "algo_input = EnergyInput(qubit_op)\n", + "result = run_algorithm(aqua_cfg_dict, algo_input)\n", + "print(result['energy'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### And now `programmatic`\n", + " \n", + "Here we create the variational form and optimizer and then pass them to VQE along with the Operator. The backend is created and passed to the algorithm so it can be run there." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-1.8572750301886618\n" + ] + } + ], + "source": [ + "from qiskit import BasicAer\n", + "from qiskit.aqua.algorithms import VQE\n", + "from qiskit.aqua.components.variational_forms import RYRZ\n", + "from qiskit.aqua.components.optimizers import L_BFGS_B\n", + "\n", + "var_form = RYRZ(qubit_op.num_qubits, depth=3, entanglement='linear')\n", + "optimizer = L_BFGS_B(maxfun=1000)\n", + "vqe = VQE(qubit_op, var_form, optimizer)\n", + "backend = BasicAer.get_backend('statevector_simulator')\n", + "result = vqe.run(backend)\n", + "print(result['energy'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "While a backend can be passed directly to the quantum algorithm run(), internally it will be detected as such and wrapped as a QuantumInstance. However by doing this explicitly yourself, as below, various parameters governing the execution can be set, including in more advanced cases ability to set noise models, coupling maps etc. The following shows the above but using a QuantumInstance and setting up a default transpiler PassManager for circuit processing." + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-1.8572750302012366\n" + ] + } + ], + "source": [ + "from qiskit.aqua import QuantumInstance\n", + "from qiskit.transpiler import PassManager\n", + "\n", + "var_form = RYRZ(qubit_op.num_qubits, depth=3, entanglement='linear')\n", + "optimizer = L_BFGS_B(maxfun=1000)\n", + "vqe = VQE(qubit_op, var_form, optimizer)\n", + "backend = BasicAer.get_backend('statevector_simulator')\n", + "qi = QuantumInstance(backend=backend, pass_manager=PassManager())\n", + "result = vqe.run(qi)\n", + "print(result['energy'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Concluding\n", + "\n", + "This completes an introduction to programming and using Aqua algorithms. There are plenty of other tutorials showing Aqua being used to solve other problems, including AI, Finance, Optimization and Chemistry. We encourage you to explore these further and see that various capabilities and techniques employed." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/community/aqua/general/eoh.ipynb b/community/aqua/general/eoh.ipynb index 54dace550..bf8a6d61c 100644 --- a/community/aqua/general/eoh.ipynb +++ b/community/aqua/general/eoh.ipynb @@ -71,7 +71,7 @@ "output_type": "stream", "text": [ "The result is\n", - "{'avg': (0.36883301800844187+2.342013271062652e-17j), 'std_dev': 0.0}\n" + "{'avg': (3.469125838650009-1.002992831056778e-16j), 'std_dev': 0.0}\n" ] } ], @@ -87,12 +87,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The above programmatic approach can also be achieved via a declarative manner using json dictionary configuration:" + "The above programmatic approach can also be achieved via a declarative manner using a configuration configuration to specify the algorithm, components, backend etc. The operators, the main data for the algorithm, are supplied to it via an EnergyInput (an InputInstance type)." ] }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 7, "metadata": {}, "outputs": [], "source": [ @@ -107,6 +107,10 @@ " 'initial_state': {\n", " 'name': 'CUSTOM',\n", " 'state': 'uniform'\n", + " },\n", + " 'backend': {\n", + " 'name': 'statevector_simulator',\n", + " 'provider': 'qiskit.BasicAer'\n", " }\n", "}\n", "algo_input = EnergyInput(qubit_op)\n", @@ -117,12 +121,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "With all the necessary pieces prepared, we can then proceed to run the algorithm and examine the result." + "With all the necessary pieces prepared, we can then proceed to run the algorithm and examine the result. The run_algorithm takes the configuration dictionary and the input data." ] }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 9, "metadata": {}, "outputs": [ { @@ -130,14 +134,21 @@ "output_type": "stream", "text": [ "The result is\n", - "{'avg': (0.36883301800844187+2.342013271062652e-17j), 'std_dev': 0.0}\n" + "{'avg': (3.469125838650008-3.2364937588818136e-16j), 'std_dev': 0.0}\n" ] } ], "source": [ - "ret = run_algorithm(params, algo_input, backend=backend)\n", + "ret = run_algorithm(params, algo_input)\n", "print('The result is\\n{}'.format(ret))" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { @@ -156,7 +167,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.7" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/community/aqua/general/evolution.ipynb b/community/aqua/general/evolution.ipynb index 07fea27c9..ba41def4a 100644 --- a/community/aqua/general/evolution.ipynb +++ b/community/aqua/general/evolution.ipynb @@ -17,19 +17,7 @@ "cell_type": "code", "execution_count": 1, "metadata": {}, - "outputs": [ - { - "ename": "ImportError", - "evalue": "cannot import name 'LegacySimulators'", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mImportError\u001b[0m Traceback (most recent call last)", - "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mnumpy\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mscipy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinalg\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mexpm\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mLegacySimulators\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 4\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mexecute\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mq_execute\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mQuantumCircuit\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mQuantumRegister\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;31mImportError\u001b[0m: cannot import name 'LegacySimulators'" - ] - } - ], + "outputs": [], "source": [ "import numpy as np\n", "from scipy.linalg import expm\n", @@ -57,9 +45,19 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The directly computed groundtruth evolution result state is\n", + "[ 0.00056445+0.29350579j 0.18403341+0.58990254j -0.25317957+0.57786906j\n", + " 0.11563928+0.34726897j].\n" + ] + } + ], "source": [ "state_in_vec = state_in.construct_circuit('vector')\n", "groundtruth = expm(-1.j * h1 * evo_time) @ state_in_vec\n", @@ -75,9 +73,19 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The groundtruth evolution result as computed by the Dynamics algorithm is\n", + "[ 0.00056445+0.29350579j 0.18403341+0.58990254j -0.25317957+0.57786906j\n", + " 0.11563928+0.34726897j].\n" + ] + } + ], "source": [ "groundtruth_evolution = qubitOp.evolve(state_in_vec, evo_time, 'matrix', 0)\n", "print('The groundtruth evolution result as computed by the Dynamics algorithm is\\n{}.'.format(groundtruth_evolution))\n", @@ -93,7 +101,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -116,9 +124,19 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The evolution result state from executing the Dynamics circuit is\n", + "[0.15938927-0.24595785j 0.16958867-0.5942064j 0.52996414-0.3428456j\n", + " 0.09599811-0.35304037j].\n" + ] + } + ], "source": [ "backend = BasicAer.get_backend('statevector_simulator')\n", "job = q_execute(circuit, backend)\n", @@ -135,9 +153,17 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Fidelity between the groundtruth and the circuit result states is 0.9999922464923452.\n" + ] + } + ], "source": [ "print('Fidelity between the groundtruth and the circuit result states is {}.'.format(\n", " state_fidelity(groundtruth, circuit_execution_result)\n", @@ -150,6 +176,13 @@ "source": [ "As seen, the fidelity is very close to `1`, indicating that the quantum circuit produced is a good approximation of the intended evolution." ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { @@ -168,7 +201,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.7" + "version": "3.6.1" } }, "nbformat": 4, From d43ed8bf8893f98e006c43abcc6f106d0725cdc1 Mon Sep 17 00:00:00 2001 From: Steve Wood <40241007+woodsp-ibm@users.noreply.github.com> Date: Fri, 5 Apr 2019 17:17:39 -0400 Subject: [PATCH 036/116] Notebook was refactored/renamed --- community/aqua/general/vqe.ipynb | 161 ------------------------------- 1 file changed, 161 deletions(-) delete mode 100644 community/aqua/general/vqe.ipynb diff --git a/community/aqua/general/vqe.ipynb b/community/aqua/general/vqe.ipynb deleted file mode 100644 index ba86e3fc8..000000000 --- a/community/aqua/general/vqe.ipynb +++ /dev/null @@ -1,161 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": { - "collapsed": true - }, - "source": [ - "## _*Using Qiskit Aqua algorithms, a how to guide*_\n", - "\n", - "This notebook demonstrates how to use the `Qiskit Aqua` library to invoke a specific algorithm and process the result.\n", - "\n", - "Further information is available for the algorithms in the github repo aqua/readme.md" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/Users/manoel/Documents/Quantum/qiskit-terra/qiskit/tools/qcvv/__init__.py:13: DeprecationWarning: The qiskit.tools.qcvv package is deprecated. Please use qiskit-ignis available on PIP for similar functionality and more.\n", - " 'functionality and more.', DeprecationWarning)\n" - ] - } - ], - "source": [ - "from qiskit.aqua import Operator, run_algorithm, PluggableType, get_pluggable_class" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here an Operator instance is created for our Hamiltonian. In this case the paulis are from a previously computed Hamiltonian for simplicity" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "pauli_dict = {\n", - " 'paulis': [{\"coeff\": {\"imag\": 0.0, \"real\": -1.052373245772859}, \"label\": \"II\"},\n", - " {\"coeff\": {\"imag\": 0.0, \"real\": 0.39793742484318045}, \"label\": \"ZI\"},\n", - " {\"coeff\": {\"imag\": 0.0, \"real\": -0.39793742484318045}, \"label\": \"IZ\"},\n", - " {\"coeff\": {\"imag\": 0.0, \"real\": -0.01128010425623538}, \"label\": \"ZZ\"},\n", - " {\"coeff\": {\"imag\": 0.0, \"real\": 0.18093119978423156}, \"label\": \"XX\"}\n", - " ]\n", - "}\n", - "\n", - "qubitOp = Operator.load_from_dict(pauli_dict)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can now use the Operator without regard to how it was created. First we need to prepare the configuration params to invoke the algorithm. Here we will use the ExactEigensolver first to return the smallest eigenvalue. Backend is not required since this is computed classically not using quantum computation. We then add in the qubitOp Operator in dictionary format. Now the complete params can be passed to the algorithm and run. The result is a dictionary." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "ename": "AquaError", - "evalue": "'PluggableType.INITIAL_STATE EnergyInput not registered'", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mAquaError\u001b[0m Traceback (most recent call last)", - "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0;34m'algorithm'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0malgorithm_cfg\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 7\u001b[0m }\n\u001b[0;32m----> 8\u001b[0;31m \u001b[0malgo_input\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_pluggable_class\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mPluggableType\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mINITIAL_STATE\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'EnergyInput'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mqubitOp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 9\u001b[0m \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrun_algorithm\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0malgo_input\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 10\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;32m~/Documents/Quantum/qiskit-aqua/qiskit/aqua/_discover.py\u001b[0m in \u001b[0;36mget_pluggable_class\u001b[0;34m(pluggable_type, pluggable_name)\u001b[0m\n\u001b[1;32m 356\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mpluggable_name\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32min\u001b[0m \u001b[0m_REGISTERED_PLUGGABLES\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mpluggable_type\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 357\u001b[0m raise AquaError('{} {} not registered'.format(\n\u001b[0;32m--> 358\u001b[0;31m pluggable_type, pluggable_name))\n\u001b[0m\u001b[1;32m 359\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 360\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0m_REGISTERED_PLUGGABLES\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mpluggable_type\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mpluggable_name\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcls\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;31mAquaError\u001b[0m: 'PluggableType.INITIAL_STATE EnergyInput not registered'" - ] - } - ], - "source": [ - "algorithm_cfg = {\n", - " 'name': 'ExactEigensolver',\n", - "}\n", - "\n", - "params = {\n", - " 'algorithm': algorithm_cfg\n", - "}\n", - "algo_input = get_pluggable_class(PluggableType.INPUT, 'EnergyInput')(qubitOp)\n", - "result = run_algorithm(params,algo_input)\n", - "print(result)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we want VQE and so change it and add its other configuration parameters. VQE also needs and optimizer and variational form. While we can omit them from the dictionary, such that defaults are used, here we specify them explicitly so we can set their parameters as we desire." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "scrolled": true - }, - "outputs": [], - "source": [ - "algorithm_cfg = {\n", - " 'name': 'VQE',\n", - " 'operator_mode': 'matrix'\n", - "}\n", - "\n", - "optimizer_cfg = {\n", - " 'name': 'L_BFGS_B',\n", - " 'maxfun': 1000\n", - "}\n", - "\n", - "var_form_cfg = {\n", - " 'name': 'RYRZ',\n", - " 'depth': 3,\n", - " 'entanglement': 'linear'\n", - "}\n", - "\n", - "params = {\n", - " 'algorithm': algorithm_cfg,\n", - " 'optimizer': optimizer_cfg,\n", - " 'variational_form': var_form_cfg,\n", - " 'backend': {'name': 'statevector_simulator'}\n", - "}\n", - "\n", - "result = run_algorithm(params,algo_input)\n", - "print(result)" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.7" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} From 3dc1dd384ac20b61cacd8bd21fa3af5390487cee Mon Sep 17 00:00:00 2001 From: stefan-woerner Date: Tue, 9 Apr 2019 14:35:21 +0200 Subject: [PATCH 037/116] initial commit for new qiskit finance folder structure --- qiskit/finance/data_providers/readme.txt | 0 qiskit/finance/machine_learning/readme.txt | 0 qiskit/finance/optimization/readme.txt | 0 qiskit/finance/simulation/readme.txt | 0 4 files changed, 0 insertions(+), 0 deletions(-) create mode 100644 qiskit/finance/data_providers/readme.txt create mode 100644 qiskit/finance/machine_learning/readme.txt create mode 100644 qiskit/finance/optimization/readme.txt create mode 100644 qiskit/finance/simulation/readme.txt diff --git a/qiskit/finance/data_providers/readme.txt b/qiskit/finance/data_providers/readme.txt new file mode 100644 index 000000000..e69de29bb diff --git a/qiskit/finance/machine_learning/readme.txt b/qiskit/finance/machine_learning/readme.txt new file mode 100644 index 000000000..e69de29bb diff --git a/qiskit/finance/optimization/readme.txt b/qiskit/finance/optimization/readme.txt new file mode 100644 index 000000000..e69de29bb diff --git a/qiskit/finance/simulation/readme.txt b/qiskit/finance/simulation/readme.txt new file mode 100644 index 000000000..e69de29bb From 1f46e5c268487c2299f190144b5625bf87d086e2 Mon Sep 17 00:00:00 2001 From: Albert Frisch Date: Wed, 10 Apr 2019 16:57:39 +0200 Subject: [PATCH 038/116] reintroduce fidelity and probability output --- .../general/linear_systems_of_equations.ipynb | 187 ++++++++++++------ 1 file changed, 127 insertions(+), 60 deletions(-) diff --git a/qiskit/aqua/general/linear_systems_of_equations.ipynb b/qiskit/aqua/general/linear_systems_of_equations.ipynb index d99261ada..58e2a5e06 100644 --- a/qiskit/aqua/general/linear_systems_of_equations.ipynb +++ b/qiskit/aqua/general/linear_systems_of_equations.ipynb @@ -38,10 +38,19 @@ "cell_type": "code", "execution_count": 1, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "qiskit.providers.ibmq.ibmqprovider\n" + ] + } + ], "source": [ "from qiskit.aqua import run_algorithm\n", "from qiskit.aqua.input import LinearSystemInput\n", + "from qiskit.quantum_info import state_fidelity\n", "from qiskit.aqua.algorithms.classical import ExactLPsolver\n", "import numpy as np" ] @@ -73,7 +82,13 @@ " 'provider': 'qiskit.BasicAer',\n", " 'name': 'statevector_simulator'\n", " }\n", - "}" + "}\n", + "\n", + "def fidelity(hhl, ref):\n", + " solution_hhl_normed = hhl / np.linalg.norm(hhl)\n", + " solution_ref_normed = ref / np.linalg.norm(ref)\n", + " fidelity = state_fidelity(solution_hhl_normed, solution_ref_normed)\n", + " print(\"fidelity %f\" % fidelity)" ] }, { @@ -94,7 +109,7 @@ "1 & 0 \\\\\n", "0 & 2\n", "\\end{bmatrix}$$ with the vector $$\\vec{b}= \\left( \\begin{array}{c}1 \\\\ 4 \\end{array} \\right)$$\n", - "The `result` dictionary contains several return values. The HHL solution for $\\vec{x}$ is accessible by the key `'solution_hhl'`. For comparison, also the classical solution of the linear system of equations is calculated using standard linear algebra functions in numpy. The fidelity between the HHL solution and the classical solution is also given in the output. Furthermore, the probability is shown with which HHL was running successfully, i.e. the HHL ancillary qubit has been measured to be $|1\\rangle$." + "The `result` dictionary contains several return values. The HHL solution for $\\vec{x}$ is accessible by the key `'solution'`. For comparison, also the classical solution of the linear system of equations is calculated using standard linear algebra functions in numpy. The fidelity between the HHL solution and the classical solution is also given in the output. Furthermore, the probability is shown with which HHL was running successfully, i.e. the HHL ancillary qubit has been measured to be $|1\\rangle$." ] }, { @@ -114,7 +129,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -122,7 +137,9 @@ "output_type": "stream", "text": [ "solution [1.05859+0.j 1.99245+0.j]\n", - "classical solution [1. 2.]\n" + "classical solution [1. 2.]\n", + "probability 0.024630\n", + "fidelity 0.999389\n" ] } ], @@ -130,8 +147,11 @@ "result = run_algorithm(params)\n", "print(\"solution \", np.round(result['solution'], 5))\n", "\n", - "classical_result = ExactLPsolver(matrix, vector).run()\n", - "print(\"classical solution \", np.round(classical_result['solution'], 5))" + "result_ref = ExactLPsolver(matrix, vector).run()\n", + "print(\"classical solution \", np.round(result_ref['solution'], 5))\n", + "\n", + "print(\"probability %f\" % result['probability_result'])\n", + "fidelity(result['solution'], result_ref['solution'])" ] }, { @@ -143,7 +163,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -151,7 +171,9 @@ "output_type": "stream", "text": [ "solution [0.84664+0.j 2.01762+0.j]\n", - "classical solution [1. 2.]\n" + "classical solution [1. 2.]\n", + "probability 0.361437\n", + "fidelity 0.995605\n" ] } ], @@ -164,8 +186,11 @@ "result = run_algorithm(params2)\n", "print(\"solution \", np.round(result['solution'], 5))\n", "\n", - "classical_result = ExactLPsolver(matrix, vector).run()\n", - "print(\"classical solution \", np.round(classical_result['solution'], 5))" + "result_ref = ExactLPsolver(matrix, vector).run()\n", + "print(\"classical solution \", np.round(result_ref['solution'], 5))\n", + "\n", + "print(\"probability %f\" % result['probability_result'])\n", + "fidelity(result['solution'], result_ref['solution'])" ] }, { @@ -177,21 +202,21 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "circuit_depth 12256\n", - "circuit_width 7\n" + "circuit_width 7\n", + "circuit_depth 12256\n" ] } ], "source": [ - "print(\"circuit_depth\", result['circuit_info']['depth'])\n", - "print(\"circuit_width\", result['circuit_info']['width'])" + "print(\"circuit_width\", result['circuit_info']['width'])\n", + "print(\"circuit_depth\", result['circuit_info']['depth'])" ] }, { @@ -216,13 +241,14 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "matrix = [[1, 3], [3, 2]]\n", "vector = [1, 1]\n", - "params['input'] = {\n", + "params3 = params\n", + "params3['input'] = {\n", " 'name': 'LinearSystemInput',\n", " 'matrix': matrix,\n", " 'vector': vector\n", @@ -231,7 +257,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 8, "metadata": {}, "outputs": [ { @@ -239,16 +265,21 @@ "output_type": "stream", "text": [ "solution [0.22147+0.j 0.22034-0.j]\n", - "classical solution [0.14286 0.28571]\n" + "classical solution [0.14286 0.28571]\n", + "probability 0.424639\n", + "fidelity 0.898454\n" ] } ], "source": [ - "result = run_algorithm(params)\n", + "result = run_algorithm(params3)\n", "print(\"solution \", np.round(result['solution'], 5))\n", "\n", - "classical_result = ExactLPsolver(matrix, vector).run()\n", - "print(\"classical solution \", np.round(classical_result['solution'], 5))" + "result_ref = ExactLPsolver(matrix, vector).run()\n", + "print(\"classical solution \", np.round(result_ref['solution'], 5))\n", + "\n", + "print(\"probability %f\" % result['probability_result'])\n", + "fidelity(result['solution'], result_ref['solution'])" ] }, { @@ -260,21 +291,21 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "circuit_depth 30254\n", - "circuit_width 7\n" + "circuit_width 7\n", + "circuit_depth 30254\n" ] } ], "source": [ - "print(\"circuit_depth\", result['circuit_info']['depth'])\n", - "print(\"circuit_width\", result['circuit_info']['width'])" + "print(\"circuit_width\", result['circuit_info']['width'])\n", + "print(\"circuit_depth\", result['circuit_info']['depth'])" ] }, { @@ -305,7 +336,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 10, "metadata": {}, "outputs": [], "source": [ @@ -318,7 +349,8 @@ " [0, 0, 0, 0, 0, 0, 1, 0],\n", " [1, 0, 0, 0, 0, 0, 0, 5]]\n", "vector = [1, 0, 0, 0, 0, 0, 0, 1]\n", - "params['input'] = {\n", + "params4 = params\n", + "params4['input'] = {\n", " 'name': 'LinearSystemInput',\n", " 'matrix': matrix,\n", " 'vector': vector\n", @@ -327,7 +359,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 11, "metadata": {}, "outputs": [ { @@ -336,16 +368,21 @@ "text": [ "solution [ 0.18195-0.j 0. -0.j 0. -0.j -0. +0.j 0. +0.j\n", " -0. +0.j -0. -0.j 0.18041+0.j]\n", - "classical solution [0.21053 0. 0. 0. 0. 0. 0. 0.15789]\n" + "classical solution [0.21053 0. 0. 0. 0. 0. 0. 0.15789]\n", + "probability 0.935566\n", + "fidelity 0.981173\n" ] } ], "source": [ - "result = run_algorithm(params)\n", + "result = run_algorithm(params4)\n", "print(\"solution \", np.round(result['solution'], 5))\n", "\n", - "classical_result = ExactLPsolver(matrix, vector).run()\n", - "print(\"classical solution \", np.round(classical_result['solution'], 5))" + "result_ref = ExactLPsolver(matrix, vector).run()\n", + "print(\"classical solution \", np.round(result_ref['solution'], 5))\n", + "\n", + "print(\"probability %f\" % result['probability_result'])\n", + "fidelity(result['solution'], result_ref['solution'])" ] }, { @@ -357,21 +394,21 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "circuit_depth 315281\n", - "circuit_width 9\n" + "circuit_width 9\n", + "circuit_depth 315281\n" ] } ], "source": [ - "print(\"circuit_depth\", result['circuit_info']['depth'])\n", - "print(\"circuit_width\", result['circuit_info']['width'])" + "print(\"circuit_width\", result['circuit_info']['width'])\n", + "print(\"circuit_depth\", result['circuit_info']['depth'])" ] }, { @@ -390,7 +427,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 13, "metadata": {}, "outputs": [], "source": [ @@ -409,16 +446,16 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 14, "metadata": {}, "outputs": [], "source": [ - "params3 = params\n", - "params3[\"reciprocal\"] = {\n", + "params5 = params\n", + "params5[\"reciprocal\"] = {\n", " \"name\": \"Lookup\",\n", " \"negative_evals\": True\n", "}\n", - "params3[\"eigs\"] = {\n", + "params5[\"eigs\"] = {\n", " \"expansion_mode\": \"suzuki\",\n", " \"expansion_order\": 2,\n", " \"name\": \"EigsQPE\",\n", @@ -426,13 +463,13 @@ " \"num_ancillae\": 6,\n", " \"num_time_slices\": 70\n", "}\n", - "params3[\"initial_state\"] = {\n", + "params5[\"initial_state\"] = {\n", " \"name\": \"CUSTOM\"\n", "}\n", - "params3[\"iqft\"] = {\n", + "params5[\"iqft\"] = {\n", " \"name\": \"STANDARD\"\n", "}\n", - "params3[\"qft\"] = {\n", + "params5[\"qft\"] = {\n", " \"name\": \"STANDARD\"\n", "}" ] @@ -446,9 +483,27 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 15, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "random matrix:\n", + "[[ 0.284-0.j -0.257-0.051j -0.124+0.033j 0.038+0.023j]\n", + " [-0.257+0.051j 0.404+0.j 0.067-0.079j 0.054+0.055j]\n", + " [-0.124-0.033j 0.067+0.079j 0.282-0.j 0.043+0.004j]\n", + " [ 0.038-0.023j 0.054-0.055j 0.043-0.004j 0.206-0.j ]]\n", + "solution [ 79.9768 +4.52073j 60.28272 +3.09211j 37.51853 -9.5858j\n", + " -35.02324+26.46894j]\n", + "classical solution [ 76.1399 +1.92451j 57.30622 +1.20141j 35.96381-10.07775j\n", + " -32.03837+25.90593j]\n", + "probability 0.256771\n", + "fidelity 0.999946\n" + ] + } + ], "source": [ "# set the random seed to get the same pseudo-random matrix for every run\n", "np.random.seed(1)\n", @@ -460,31 +515,43 @@ "print(np.round(m, 3))\n", "\n", "algo_input = LinearSystemInput(matrix=matrix, vector=vector)\n", - "hhl = HHL.init_params(params3, algo_input)\n", + "hhl = HHL.init_params(params5, algo_input)\n", "backend = BasicAer.get_backend('statevector_simulator')\n", "quantum_instance = QuantumInstance(backend=backend)\n", - "result_hhl = hhl.run(quantum_instance)\n", + "result = hhl.run(quantum_instance)\n", "print(\"solution \", np.round(result['solution'], 5))\n", "\n", - "classical_result = ExactLPsolver(matrix, vector).run()\n", - "print(\"classical solution \", np.round(classical_result['solution'], 5))" + "result_ref = ExactLPsolver(matrix, vector).run()\n", + "print(\"classical solution \", np.round(result_ref['solution'], 5))\n", + "\n", + "print(\"probability %f\" % result['probability_result'])\n", + "fidelity(result['solution'], result_ref['solution'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "The circuit depth and width are" + "The circuit width and depth are" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 16, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "circuit_width 12\n", + "circuit_depth 973537\n" + ] + } + ], "source": [ - "print(\"circuit_depth\", result_hhl['circuit_info']['depth'])\n", - "print(\"circuit_width\", result_hhl['circuit_info']['width']" + "print(\"circuit_width\", result['circuit_info']['width'])\n", + "print(\"circuit_depth\", result['circuit_info']['depth'])" ] }, { @@ -511,7 +578,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.1" + "version": "3.7.1" } }, "nbformat": 4, From dd970a72e8b5c851e2b90287dff6e80c36d1b1f8 Mon Sep 17 00:00:00 2001 From: Atsushi Matsuo Date: Thu, 11 Apr 2019 15:18:26 +0900 Subject: [PATCH 039/116] added docplex.ipynb and added docplex parts into an exisitng maxcut_and_tsp.ipynb --- qiskit/aqua/optimization/docplex.ipynb | 361 ++++++++++++++++++ qiskit/aqua/optimization/maxcut_and_tsp.ipynb | 276 ++++++++++--- 2 files changed, 585 insertions(+), 52 deletions(-) create mode 100644 qiskit/aqua/optimization/docplex.ipynb diff --git a/qiskit/aqua/optimization/docplex.ipynb b/qiskit/aqua/optimization/docplex.ipynb new file mode 100644 index 000000000..9f079ef0f --- /dev/null +++ b/qiskit/aqua/optimization/docplex.ipynb @@ -0,0 +1,361 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Introduction\n", + "There has been a growing interest in using quantum computers to find solutions of combinatorial problems. One of heuristic approach for finding solutions of combinatorial problems on quantum computers is a quantum variational approach, such as the Variational Quantum \n", + "Eigensolver (VQE) algorithm (see https://arxiv.org/abs/1802.00171 and the Quantum Approximate Optimization Algorithm (QAOA) (see https://arxiv.org/abs/1411.4028). In order to use a quantum variational approach on quantum computers, first, we need to map a combinatorial problem to an Ising Hamiltonians. However Ising Hamiltonians are complicated and unintuitive. Mapping a combinatorial problem to Ising Hamiltonians is difficult and time-consuming task, which requires specialized knowledge.\n", + "\n", + "In this tutorial, we introduce a translator to automatically generate Ising Hamiltonians from classical optimization models. We will explain about classical optimization models later. The translator dramatically simplifies the task of designing and implementing quantum-computing-based solutions for optimization problems by automatically generating Ising Hamiltoniansfor different optimization problems. With the translator, All a user has to do is to write optimization models using DOcplex (see https://cdn.rawgit.com/IBMDecisionOptimization/docplex-doc/master/docs/index.html). DOcplex is a python library for optimization problems.\n", + "Then the translator will automatically generate Ising Hamiltonians from the models. Optimization models are short and intuitive. It is easier to write optimization models compared to writing Ising Hamiltonians manually. \n", + "\n", + "The quantum variational approach works with the translator in Qiskit Aqua as follows:\n", + "1. Write an optimization model of the formulation with DOcplex.\n", + "2. Call the translator to transform the model into an Ising Hamiltonian.\n", + "3. Solve the problem with variational algorithms such as VQE and QAOA.\n", + "\n", + "\n", + "### Details of Optimization Models\n", + "For simplicity, we can generate Ising Hamiltonian from the following optimization models now.\n", + "- Binary decision variables. \n", + "- Linear and quadratic terms in objective functions.\n", + "- Only equality constraints.\n", + "\n", + "Even though there are restrictions, this type of optimization model can handle the following optimization problems, maxcut, tsp and etc.\n", + "They are typical optimization problems. The usage examples of the translator for Maxcut and TSP are written in the following link.\n", + "- [Qiskit Aqua: Experimenting with MaxCut problem and Traveling Salesman problem with variational quantum eigensolve](maxcut_and_tsp.ipynb)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### A Usage Example: Maximize the number of variables which takes the value 1\n", + "The following is a toy example of a maximization problem with constrains.\n", + "\\begin{aligned}\n", + " & \\text{maximize}\n", + " & \\sum_{i} x_{i}\\\\\n", + " & \\text{subject to}\n", + " & \\sum_{i} i * x_{i}=3\\\\\n", + " & & i \\in \\{1,2,3,4\\} \\\\\n", + " & & x_i \\in \\{0,1\\}\\\\\n", + "\\end{aligned}" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "from docplex.mp.model import Model\n", + "\n", + "from qiskit import BasicAer\n", + "from qiskit.aqua import Operator, run_algorithm\n", + "from qiskit.aqua.algorithms import VQE, ExactEigensolver\n", + "from qiskit.aqua.components.optimizers import SPSA\n", + "from qiskit.aqua.components.variational_forms import RY\n", + "from qiskit.aqua import QuantumInstance\n", + "from qiskit.aqua.translators.ising import docplex\n", + "\n", + "# setup aqua logging\n", + "import logging\n", + "from qiskit.aqua import set_qiskit_aqua_logging\n", + "# set_qiskit_aqua_logging(logging.DEBUG) # choose INFO, DEBUG to see the log" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Create an optimization model of the above problem using DOcplex\n", + "An optimization model of the problem with DOcplex is written as follows. \n", + "An instance of `Model` is created and variables for the model are created in the first paragraph. Then object function is written in the second paragraph. The objective function is a function that we would like to minimize (or maximize). Finally constrains are written in the third paragraph. " + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\\ This file has been generated by DOcplex\n", + "\\ ENCODING=ISO-8859-1\n", + "\\Problem name: max_vars\n", + "\n", + "Maximize\n", + " obj: x_1 + x_2 + x_3 + x_4\n", + "Subject To\n", + " c1: x_1 + 2 x_2 + 3 x_3 + 4 x_4 = 3\n", + "\n", + "Bounds\n", + "0 <= x_1 <= 1\n", + "0 <= x_2 <= 1\n", + "0 <= x_3 <= 1\n", + "0 <= x_4 <= 1\n", + "\n", + "Binaries\n", + " x_1 x_2 x_3 x_4\n", + "End\n", + "\n" + ] + } + ], + "source": [ + "# Create an instance of a model and variables\n", + "mdl = Model(name='max_vars')\n", + "x = {i: mdl.binary_var(name='x_{0}'.format(i)) for i in range(1,5)}\n", + "\n", + "# Object function\n", + "max_vars_func = mdl.sum(x[i] for i in range(1,5))\n", + "mdl.maximize(max_vars_func)\n", + "\n", + "# Constrains\n", + "mdl.add_constraint(mdl.sum(i*x[i] for i in range(1,5)) == 3)\n", + "\n", + "print(mdl.export_to_string())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Generate an Ising Hamiltonian from the model using ```docplex.get_qubitops(mdl)```\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "qubitOp, offset = docplex.get_qubitops(mdl)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Checking that the full Hamiltonian gives the right cost" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "energy: -57.5\n", + "objective: -2.0\n", + "solution: [1. 1. 0. 0.]\n" + ] + } + ], + "source": [ + "ee = ExactEigensolver(qubitOp, k=1)\n", + "result = ee.run()\n", + "\n", + "print('energy:', result['energy'])\n", + "print('objective:', result['energy'] + offset)\n", + "\n", + "x = docplex.sample_most_likely(result['eigvecs'][0])\n", + "print('solution:', x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Running it on quantum computer\n", + "We run the optimization routine using a feedback loop with a quantum computer that uses trial functions built with Y single-qubit rotations, $U_\\mathrm{single}(\\theta) = \\prod_{i=1}^n Y(\\theta_{i})$, and entangler steps $U_\\mathrm{entangler}$." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "energy: -56.20499759137974\n", + "time: 9.663682699203491\n", + "solution objective: -0.7049975913797368\n", + "solution: [0. 0. 1. 0.]\n" + ] + } + ], + "source": [ + "seed = 10598\n", + "\n", + "spsa = SPSA(max_trials=300)\n", + "ry = RY(qubitOp.num_qubits, depth=5, entanglement='linear')\n", + "vqe = VQE(qubitOp, ry, spsa, 'matrix')\n", + "\n", + "backend = BasicAer.get_backend('statevector_simulator')\n", + "quantum_instance = QuantumInstance(backend, seed=seed, seed_mapper=seed)\n", + "\n", + "result = vqe.run(quantum_instance)\n", + "\n", + "\"\"\"declarative approach\n", + "algorithm_cfg = {\n", + " 'name': 'VQE',\n", + " 'operator_mode': 'matrix'\n", + "}\n", + "\n", + "optimizer_cfg = {\n", + " 'name': 'SPSA',\n", + " 'max_trials': 300\n", + "}\n", + "\n", + "var_form_cfg = {\n", + " 'name': 'RY',\n", + " 'depth': 5,\n", + " 'entanglement': 'linear'\n", + "}\n", + "\n", + "params = {\n", + " 'problem': {'name': 'ising', 'random_seed': seed},\n", + " 'algorithm': algorithm_cfg,\n", + " 'optimizer': optimizer_cfg,\n", + " 'variational_form': var_form_cfg,\n", + " 'backend': {provider': 'qiskit.BasicAer', 'name': 'statevector_simulator'}\n", + "}\n", + "\n", + "result = run_algorithm(params, algo_input)\n", + "\"\"\"\n", + "\n", + "x = docplex.sample_most_likely(result['eigvecs'][0])\n", + "print('energy:', result['energy'])\n", + "print('time:', result['eval_time'])\n", + "print('solution objective:', result['energy'] + offset)\n", + "print('solution:', x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### [Optional] A Case when the validation of the input model fails.\n", + "If the following unsupported elemts exist in the input model, the error will be raised.\n", + "- Variables which are not binary decision variables \n", + "- Inequality constraints. \n", + "Note: Cubic or higher order terms can not be input of DOcplex." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\\ This file has been generated by DOcplex\n", + "\\ ENCODING=ISO-8859-1\n", + "\\Problem name: max_vars\n", + "\n", + "Maximize\n", + " obj: x_1 + x_2 + x_3 + x_4\n", + "Subject To\n", + " c1: x_1 + 2 x_2 + 3 x_3 + 4 x_4 <= 3\n", + "\n", + "Bounds\n", + "End\n", + "\n" + ] + } + ], + "source": [ + "# Create an instance of a model and variables\n", + "# Continuous variables are used\n", + "mdl = Model(name='max_vars')\n", + "x = {i: mdl.continuous_var(name='x_{0}'.format(i)) for i in range(1,5)}\n", + "\n", + "# Object function\n", + "max_vars_func = mdl.sum(x[i] for i in range(1,5))\n", + "mdl.maximize(max_vars_func)\n", + "\n", + "# Constrains\n", + "# Inequality constraint is used\n", + "mdl.add_constraint(mdl.sum(i*x[i] for i in range(1,5)) <= 3)\n", + "\n", + "print(mdl.export_to_string())" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "The type of Variable x_1 is continuous. It must be a binary variable. \n", + "The type of Variable x_2 is continuous. It must be a binary variable. \n", + "The type of Variable x_3 is continuous. It must be a binary variable. \n", + "The type of Variable x_4 is continuous. It must be a binary variable. \n", + "Constraint x_1+2x_2+3x_3+4x_4 <= 3 is not an equality constraint.\n" + ] + }, + { + "ename": "AquaError", + "evalue": "'The input model has unsupported elements.'", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mAquaError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mqubitOp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moffset\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdocplex\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_qubitops\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmdl\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;32m~/github/qiskit-aqua-docplex/qiskit/aqua/translators/ising/docplex.py\u001b[0m in \u001b[0;36mget_qubitops\u001b[0;34m(mdl, auto_penalty, default_penalty)\u001b[0m\n\u001b[1;32m 83\u001b[0m \"\"\"\n\u001b[1;32m 84\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 85\u001b[0;31m \u001b[0m_validate_input_model\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmdl\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 86\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 87\u001b[0m \u001b[0;31m# set the penalty coefficient by _auto_define_penalty() or manually.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/github/qiskit-aqua-docplex/qiskit/aqua/translators/ising/docplex.py\u001b[0m in \u001b[0;36m_validate_input_model\u001b[0;34m(mdl)\u001b[0m\n\u001b[1;32m 222\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 223\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mvalid\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 224\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mAquaError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'The input model has unsupported elements.'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 225\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 226\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mAquaError\u001b[0m: 'The input model has unsupported elements.'" + ] + } + ], + "source": [ + "qubitOp, offset = docplex.get_qubitops(mdl)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.5" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/qiskit/aqua/optimization/maxcut_and_tsp.ipynb b/qiskit/aqua/optimization/maxcut_and_tsp.ipynb index dbd9f213f..91296bd69 100644 --- a/qiskit/aqua/optimization/maxcut_and_tsp.ipynb +++ b/qiskit/aqua/optimization/maxcut_and_tsp.ipynb @@ -97,18 +97,9 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/Users/manoel/Documents/Quantum/qiskit-terra/qiskit/tools/qcvv/__init__.py:13: DeprecationWarning: The qiskit.tools.qcvv package is deprecated. Please use qiskit-ignis available on PIP for similar functionality and more.\n", - " 'functionality and more.', DeprecationWarning)\n" - ] - } - ], + "outputs": [], "source": [ "# useful additional packages \n", "import matplotlib.pyplot as plt\n", @@ -145,9 +136,21 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 3, "metadata": {}, - "outputs": [], + "outputs": [ + { + "ename": "ImportError", + "evalue": "cannot import name 'IBMQ'", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mImportError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mIBMQ\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2\u001b[0m \u001b[0;31m# IBMQ.load_accounts()\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mImportError\u001b[0m: cannot import name 'IBMQ'" + ] + } + ], "source": [ "from qiskit import IBMQ\n", "# IBMQ.load_accounts()" @@ -162,20 +165,12 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 58, "metadata": {}, "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/Users/manoel/anaconda3/envs/QISKitenv/lib/python3.6/site-packages/networkx/drawing/nx_pylab.py:611: MatplotlibDeprecationWarning: isinstance(..., numbers.Number)\n", - " if cb.is_numlike(alpha):\n" - ] - }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -204,7 +199,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 59, "metadata": {}, "outputs": [ { @@ -240,7 +235,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 60, "metadata": {}, "outputs": [ { @@ -269,7 +264,7 @@ }, { "data": { - "image/png": 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\n", + "image/png": 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ckjSRqxgJfyexceNGxo0bx/Tp02nXrp3Z5Qjh8KSJXNkk/J3At99+y/jx44mOjpbgF6KSijeRGzRoEA8++KDbfwhI+Du4r7/+mokTJzJ9+nTatm1rdjlCOK3CJnKJiYmcO3eOAQMGuHUTOQl/B7ZhwwaioqKYMWMGN954o9nlCOEStNb88ssvbt9ETsLfQUnwC2F77txEThq7OaCvvvqKqKgoZs6cKcEvhA1JE7nySfjbyZdffsl7771HTEwMN9xwg9nlCOEWpIlc6ST87WD9+vVMmjSJmJgY2rRpY3Y5QrgdaSJ3Pdnnb2Pr169nypQpxMTE0Lp1a7PLEUIAZ8+eZfHixaxcuZL77ruPAQMGEBYWZtVtZGTAnj2wdy+kpxuv1asHN95o/AQEWHVzV8kBXwfw+eefM23aNGJjY2nVqpXZ5QghisnMzGTJkiUsXbqUO+64g4EDB9KyZcsqr89ige+/hzlzYPNm8PKC3FzQ2vjx9ARvb8jPhwcegIgI6NgRrHmRsoS/yf773/8yffp0YmNjq/WPSQhhexcvXuTjjz/mww8/pH379kRERFT6wsujR2H4cPj1V+N5YCCUdr2ZxQKZmUbo//WvEBUFdetWcxAFJPxNtHbtWmbMmMGsWbNo0aKF2eUIISqoqk3k1qyBV16BvDwIDq74TF5r40PA39/4tvCXv1RzAEj4m+azzz5j5syZEvxCOLHKNJFbudII/ho1oKrXk126ZOwKmj8f7rijerVL+JtgzZo1xMbGMmvWLJo3b252OUKIaiqvidxvv8HjjxuhX90LiS9dMr4xrF8PjRtXfT0S/nb26aefMmvWLGbPnk14eLjZ5QghrKikJnJ//euDdOvmQUoKBAVZZzsZGdCpEyxeXPrxgvJI+NvR6tWriYuLY9asWRL8Qriwok3ktm+/ldTUCBo39kcp61wyVXgMIC7OOBuoKqS9g52sWrWKuLg4mfEL4QaUUnTt2pWEhLlcuRJBbu55Dhw4SHr6ObS2lPg7+fnnSUl5hb177+LAgX+Qmfl5Ges3ZvwJCbYawZ+8bL8J17Vy5UoSEhKIi4ujadOmZpcjhLCT5GRFTk4AzZsHkJOTTVpaGmlpadSuXZtatWrh4eF5ddlTp6JQyps2bdaTk7Of48dfws+vDb6+JZ8QEhgIycmQkgJNmthuDDLzr6Lly5dL8AvhprZvN07rVApq1KhBWFgYTZs2JScnhwMHDnDmzBny8/OxWLLJytpA3bpD8PDwx9+/A4GBfyUz87NS1104+9+507ZjkPCvguXLl5OYmEh8fLwEvxBu6KefjKt3i/L19aNx4yaEh4eTl3eFgwcPcPJkMlp74OPTtMhyrbl8+VCZ679yxfbh73a7fbKyjL+4nTuNr1ZZWcYl182aGUfZO3SAtm1Lv0hj2bJlzJs3j/j4eJrY8juZEMJhpaYabRqupdFa4+npSWhoKEFBQZw+fYicHMWxY0cJCwtDKQ88PAKwWC6WuX5vbzhyxFbVG9wm/I8dMw6ifPKJcWl1bi74+BjBr7XxYbB6tfF1q3lzGDwYevQw3i/08ccfs2DBAgl+IZyQ1prc3Fyys7PJyckhOzv76uPC58VfL/5+4fMdO/7JxYvBKHUZi0WjtQWLxYJSCg8Pj4KQV2jtjVI5pKen06hRY7y8PLBYLuLhUbPcei0lHz+2GpcPf4vFuGruvfeMfXSBgdd/XStKazh+HF591fi96Gho0QKWLl3KwoULiY+Pp3F1rsAQQpRIa82VK1euC9/SAriy4Z2Tk4OXlxd+fn74+flRo0aNq/8t/Cn+XlBQEPXr17/mNT8/Pw4dasrBg37UrGmEvYeHKrjw69pdBtnZddi3L58mTbzwKgiey5f3l3qwt1B+vtEmwpasEv5KqYeB6YAnMFdrHVXsfV9gIXA7cBborbU+Yo1tlyU7G4YMge++g5o1jeAvj1LGsv7+sHs3PPooPPnkBn75ZREJCQk0atTI1mUL4ZCKhnNFZsjlzZ6Lh3dOTg6enp7XhXDxkC76XlBQEPXq1Ss1vIu/7ln0q3w13Hcf/P67sfegNJcv55CScoagoPvJyfkQi+VNcnL2k5X1LeHh88rdRgVaClVLtcNfKeUJxAIPAinAz0qp1Vrr3UUWGwSka61bKaX6AO8Bvau77bLk5sLzz8MPP0CtWpVvmaoUhITAqVMZTJ16A4sWzaNRo1DbFCuEFRSGc3VmyOUFe0nhXFJIF74fEBBA3bp1Sw3v4r9jrXC2tVtvLWmf/58uX87h2LFj1K9fn5o13+LEiXfYv/9BPD2DadDgjXJn/l5eRs9/W7LGzL8zcEBrfQhAKbUE6AEUDf8ewNsFj5cBMUoppW14efHMmVUP/kLnzp3lwoVzNGoUzptvetO1K9Svb906hfsoHs4V3b9cXngXfc/Dw6PckC0ezqGhoaWGd/HXnSWcbe3OO41cycu7fjdyTk4Ox48fo379BgQV9H0IC5tS4XXn5Bg3emnf3poVX88a4d8YOF7keQpQvDHp1WW01nlKqUygDpBmhe1fZ9cu4/LooKDqBf+5c+do1qwZ3t7eZGTA669DUpJ1b7wgHEfRcK7uDLm08C4M5/JCtvCxv78/derUKXPXR9H/epV1QEtYTXAw9OwJy5YZE8xCOTnGjL9Bgz+Dv7Kys2Ho0LKPTVqDQ/1LUUo9DzwPVOv8+QkTjAO3Vf3DM4I/nWbNwvEu+G4XHGzcoeeXX+C226pcmqgGrTV5eXlWmSGXFt4eHh7lhmzRx/7+/tSuXfu6g4alBbuEs+sYMsRo51x45mBh8Dds2IDAwKoHf0AA9Olj5WJLYI1/ialA0ZtfNil4raRlUpRSXkAwxoHfa2itE4AEMBq7VaWYY8eM8/jL+9C1WHI5dSqKS5e2kJ9/Hm/vJtSr9wKXL99Aenr61Rl/IaWMD5R58yT8y1L0gKA1dm8Uf08pVeYsuKQzOGrVqlXuvunC1yWcRUWFhxtnBU6cCPn52Rw/frxawW+xwOXLMHUq1K5t3VpLYo1/6T8DrZVSzTFCvg/wTLFlVgP9gc1AL2CDrfb3f/aZ8YdYfjvUfLy9G9C0aQLe3g24cOEHjhx5GR+fybRo0Rkvr+uP5gQGwuefG5/ONWrYonrbK5w5W+v0ueKva60rNAsu+l6tWrUqdGaHn5/fNR/IQpht4EBYsyaDdesuERZWveDPyDBm/A89ZOUiS1Ht8C/Yh/8CsA7jVM8krfUupdRYYKvWejWQCCxSSh0AzmF8QNjE5s1lH4Uv5OFRg7p1n7/6PDe3LRZLHerWvVhi8INxwZenp3GKl60OxhTdrVGdGXJp4V00nCu6e6NoOJc3e5ZwFu5k377dZGWN5J575vL770ElHgAuT24uXLxo3BRm3Dj7HVO0yndcrfVaYG2x18YUeZwDPGmNbZXnt9/Az69yv5OWlkZ6+hG8vc/i79+mzGXz8ixs355Lw4ZZNtm9YbFYKryLovBxSEhIhS9c8fLyKvFWdEKIytm9ezfDhg3jrbf+zR13NGDWLIiJMXYPBwWVv/chPx/OnzeOF4wdC08/XfUbuFSFy93MpWVL4+BsRf8Q09LOcPJkCp6e0/DyaoS//z+xWCzXXLJtsWgsFgtaW7hyJZimTRfTosWXpQZ0ZcO76Hve3t4SzkI4uF27djFs2DDefPNN7rnnnquv79kDkyfDxo1/7n728zO+DWhtnBqak2Ms6+EBjzxi3P83LKyUDVVBRW/m4nJHtyqbmz4+3lgsswCoXftf1KwZeE1vjj8fG8/PnlW89tqrPPfcqzaoXgjh6H777TeGDx/OmDFjuPvuu695r21bSEyEEydg3bo/m0hmZhrZVKuWccJIly7w97/b58BuaVwu/ENC/jz1qjxaay5cmE5IiCI4+H3Ons0iJyeX0NBQatasQfE+HWB8goeEWL9uIYTj+/XXXxkxYgRvv/02d955Z6nLNWpkHAweONCOxVWSy/Xzv/nmP79WlefUqYnk5h4mLCyakJD6tGzZktq163D69BkOHz7M+fPngWt3i3l62v6yayGE49m5cycjRozgnXfeKTP4nYXLzfy7djX2t5XnypWTZGQsRykffv/971dfb9BgFC1aPMyFCxdIS0vjzJnTBb25g7FYFFpD69Y2HIAQwuHs2LGDV155hXfeeYeuXbuaXY5VuFz4d+sG779f/rn+3t4Nadu29APKAQGBBAQEcPHipYIPgTP4+jakT58a+PpKfxMh3MX27dt59dVXGTt2LHfccYfZ5ViNy+32adLEmP2fP2+NtSlq1qxJs2bNaNSoMZcvZ7N1679YvHgx2dnZ1tiAEMKB/fLLL7z66quMGzfOpYIfXDD8AUaPNmb9V65Yb525uf707l2XxMSX2LlzJ927dycxMZGsrCzrbUQI4TCSk5N59dVXGT9+PF26dDG7HKtzyfBv0wZeesm4P681LmO4dMm4wcuECXDjjTfw3nvvkZCQwNGjR+nZsyezZs0iPT29+hsSQjiE5ORkRo4cyYQJE+jcubPZ5diES4Y/QGQk3H8/pKdX7wPg0iXjSrw5c6BOnT9fb968OWPHjmXhwoVkZGTwxBNPMHXqVE6fPl394oUQptm2bRuvvfYaEydOdNngBxcOfy8viI01LqTIyDC65VWG1sbvKQULFkBp/wYaN27MqFGjWLJkCQB9+vRhwoQJnDhxopojEELY29atW68Gf6dOncwux6ZcNvzBuNArNtZouZqXZ3wLyM0t+3e0NnYXZWZCx47GVXoV2d1Xr149RowYwSeffEJISAh9+/ZlzJgxHD582DqDEULY1M8//8wbb7zBe++9R8eO5XZHcHou19unNCdPGjP4Dz4wDgRfufJnl06tjeeF/TduvhkGD4YHH6x6o6WsrCyWLl3KkiVLuO2224iIiOCGG26w2niEENazZcsWRo0axaRJk7jNyW/YUdHePm4T/oVyciA52bjVY3KycUqolxc0awa33260am7e3Hrbu3TpEitWrOCDDz6gTZs2DBo0iPa2vjmnEKLCfvrpJ0aPHu0SwQ8S/g4nNzeXTz/9lPnz59O4cWMiIiLo1KmTdPAUwkQ//vgjb775Ju+//z4dOnQwuxyrkPB3UHl5eXz++efMmzePwMBABg0axF133SUfAkLY2ebNmxkzZgyTJ0/m1ltvNbscq5Hwd3AWi4WvvvqKefPmATBw4EDuv/9+POx5Nwch3NSmTZt46623mDJlisvthpXwdxJaa77//nuSkpI4f/48AwYM4JFHHpEbiQthIz/88ANvv/22SwY/SPg7Ha01W7duJTExkdTUVPr370/37t3xqciNCYQQFfL999/zzjvvMHXqVG655Razy7EJCX8ntnPnTpKSkti3bx99+/bl8ccfp0aNGmaXJYRT++677xg7dizTpk3j5ptvNrscm6lo+MsOZgfUvn17oqOjiY6OliZyQljBxo0bGTt2LNHR0S4d/JUh4e/AbrjhzyZyx44do0ePHsTGxkoTOSEq4dtvv+Xdd99l+vTp3HTTTWaX4zAk/J1A8+bNeeedd/jggw84f/68NJETooK++eYbxo8fT3R0NO3atTO7HIci4e9EGjVqxBtvvCFN5ISogK+//poJEyYwffp0Cf4SSPg7IWkiJ0TZNmzYwMSJE5kxYwZt27Y1uxyHJOHvxGrVqsXQoUNZtWoV4eHhREZGMnLkSPbt22d2aUKY5quvviIqKoqZM2dy4403ml2Ow5JTPV1IdnY2K1asYNGiRdJETrilL7/8kkmTJhETE0ObNm3MLscUcp6/GytsIrdgwQIaNmzIoEGDpImccHlffPEFkydPZubMmW4b/CDhL7i+iVxERAR33323fAgIl7N+/XqmTJlCTEwMrVu3NrscU0n4i6ssFgsbNmwgKSkJrTUDBw7kgQcekCZywiWsW7eOqVOnEhsbS6tWrcwux3QS/uI6Wmt++OEHEhMTyczMZODAgdJETji1zz//nOjoaGJjY2nZsqXZ5TgECX9RqsImcklJSaSkpEgTOeGU1q5dy4wZM5g1axYtWrQwuxyHIeEvKqSwidzevXuvNpHz9/c3uywhyrR27VpmzpxJbGysBH8x0thNVEhhE7kZM2bw22+/0aNHD+bOnSsBoRciAAARI0lEQVRN5ITDWrNmDTNnzpQZfzVJ+AsA2rRpQ1RUFHPmzOH48ePSRE44pE8//ZTY2Fhmz55N8+bNzS7HqUn4i2uEh4dLEznhkFavXs3s2bOJi4sjPDzc7HKcnoS/KFFpTeRSU1NNrky4o9WrVxMXF8fs2bNp1qyZ2eW4BAl/UabiTeT69evHmDFjOHTokNmlCTexcuVK4uLiiIuLk+C3omqFv1KqtlLqC6XU7wX/rVXKcvlKqe0FP6urs01hjsImcitXriQ8PJzBgwdLEzlhc8uXL2fOnDnExcXRtGlTs8txKdU61VMpNQk4p7WOUkq9DtTSWr9WwnIXtNYBlVm3nOrp2Io2kWvdujXPPfecNJETVrV8+XISExOJi4sjLCzM7HKchl3O81dK7QPu1VqfVEo1BL7RWt9QwnIS/i4qNzeXNWvWMH/+fGkiJ6zmk08+Yd68ecTFxdGkSROzy3Eq9gr/DK11SMFjBaQXPi+2XB6wHcgDorTWK8tbt4S/c8nLy2PdunXMmzePmjVrMmjQIGkiJ6rk448/ZsGCBcTHx9O4cWOzy3E6Vgt/pdSXQIMS3hoNLCga9kqpdK31dfv9lVKNtdapSqkWwAbgfq31wRKWex54HqBp06a3Hz16tLz6hYORJnKiOpYuXcqiRYuIi4uT4K8ih9rtU+x35gNrtNbLylpOZv7OrbCJXFJSEhkZGdJETpTro48+YvHixcTFxdGoUSOzy3Fa9mrvsBroX/C4P7CqhEJqKaV8Cx6HAncCu6u5XeHglFLcddddJCYmMmrUKNauXctjjz3Gxx9/TG5urtnlCQezZMkSCX47q+7Mvw6wFGgKHAWe0lqfU0p1BAZrrZ9TSnUF4gELxodNtNY6sbx1y8zf9fz6668kJSWxZ88eaSInrvrwww9ZsmQJ8fHxNGzY0OxynJ509RQOa//+/SQlJbFt2zZ69+5N7969CQwMNLssYYIPP/yQjz76iPj4eBo0KOnQoqgs6eopHFbRJnIpKSnSRM5NffDBByxdupSEhAQJfhNI+AvThIeH8/bbb1/TRG7KlCnSRM4NLFq0iGXLlhEfH0/9+vXNLsctSfgL0xU2kfvoo4/w8PCQJnIubuHChSxfvpyEhAQJfhNJ+AuHUbduXYYPH87y5culiZyLmj9/PitXriQ+Pp569eqZXY5bk/AXDickJIShQ4eyatUqaSLnQubNm3e1NbMEv/kk/IXDCggIICIiglWrVtGhQweGDRvGiy++yI4dO8wuTVRSUlISa9askRm/A5FTPYXTkCZyzikxMZG1a9cSHx9PaGio2eW4PDnPX7gsaSLnPObMmcO6deuIj4+nTp06ZpfjFiT8hcuzWCx8/fXXJCYmYrFYiIiIkCZyDiQhIYEvvviCuLg4CX47kvAXbqN4E7kBAwbQrVs3aSJnEq01CQkJfPXVV8TFxVG7dm2zS3IrEv7C7Wit2bZtG4mJiaSkpNCvXz969OiBj4+P2aW5Da018fHxbNiwQYLfJBL+wq0VbSL37LPP8sQTT0gTORvTWhMXF8c333zD7NmzJfhNIr19hFu75ZZbmDZtGjNmzGD37t306NGDuXPnkpWVZXZpLklrzezZs/n2229lxu8kJPyFS2vTpg0TJ068polcTEwM586dM7s0l6G1JjY2lu+++464uDhq1bruZn7CAUn4C7dQtIlcVlYWvXr1kiZyVqC1JiYmhk2bNjF79mxCQq67hbdwUBL+wq2U1ERu/PjxpKSkmF2a09FaM3PmTDZv3izB74Qk/IVbKtpErnbt2vTv31+ayFWC1prp06fz008/MXv2bIKDg80uSVSShL9wayEhIQwZMuS6JnJ79+41uzSHpbUmOjqarVu3SvA7MQl/Ibi+idzw4cOliVwJtNZMmzaN5ORkZs2aRVBQkNkliSqS8/yFKEHRJnINGjRg0KBBdO7c2a37B2mtmTp1Kjt27CAmJkaC30HJRV5CWEF+fj7r1q0jKSnpahO5u+66y+36B2mtmTx5Mr/++iuxsbEEBgaaXZIohYS/EFbkzk3ktNa8//777Nq1i9jYWAICAswuSZRBwl8IG9Bas2nTJhITE92iiZzWmkmTJrFnzx5iYmIk+J2AhL8QNlTYRC4pKYljx45dbSLn6+trdmlWY7FYmDRpEvv27SMmJoaaNWuaXZKoAAl/Iezk119/Zd68eezevdtlmshZLBaioqI4cOAAM2fOlOB3ItLYTQg7ueWWW5g6deo1TeTmzJnD+fPnzS6tSgqD/+DBgzLjd2ES/kJYSdEmcqmpqfTs2dPpmshZLBYmTJjAoUOHmDlzptN/gxGlk/AXwsqKNpG7cOECvXr1YvLkyQ7fRM5isTB+/HiOHj3KjBkzJPhdnIS/EDbSqFEjXn/9dZYuXYqXl5f9msjl5MC5c5CeDnl5FfoVi8XCu+++y/Hjx5k+fboEvxuQA75C2ElGRgb/+c9/WLZsGV27dmXgwIG0aNGi+iu2WOD772H5cti6FU6cAE/PP99v1Qq6doXevaFNmxJ+3cK4ceNITU0lOjpagt/Jydk+QjioCxcusHTpUpYsWUKHDh2IiIjgxhtvrPyKtIaVKyEqypjl5+dDjRrg6wuFbSgsFuObwOXLxmu33AJjxxr/xQj+sWPHcvLkSaKjo6lRo4YVRyrMIOEvhIPLzs5mxYoVfPDBB7Rq1YqIiAg6dOhQsV8+cwZeecWY8fv5GaFfHq2h8AykyEgsL77I2+++y+nTp4mOjsbPz6/qgxEOQ8JfCCdR6SZyqanw1FNw6hSEhPw5y6+ovDz0+fNsCw5mfqdOTJ4xQ4Lfhch5/kI4CR8fHx5//HFWrFhBz549mTx5Mv3792fjxo1YLJZrF87MNPbdnz4NtWpVPvgB7eXFiUuXaHbwINGenvi50FXJouIk/IVwEJ6ennTr1o2PPvqIAQMGEBcXxzPPPMP69ev//BB46y04eRKqeAMVDZxITSXPYqFOy5Z4ffEFrFljvUEIpyG7fYRwUMWbyI3o1Ik7585FBQdDFbqJaiA1NRVLfj5NwsLwUMo4GKwUfPst1K5t/UEIu6vobh/XbEUohAtQSnHnnXfStWtXkpOT8XzySVJPn8Yf4/aTHqXs8nkzNZUtly6RbbEQ6uVFvzp16BEScn3wg3GwOCMDPvkE/t//s9/ghOkk/IVwcEopbg8KAk9Psps2Je3sWdLS0qhTuzYhtWrhWexbwMDQUN709sbHw4Mjly/z/NGjBGdm0tLD49rgL+TnB3PmQETEtdcHCJdWrX3+SqknlVK7lFIWpVSpXzOUUg8rpfYppQ4opV6vzjaFcEsbN0J+PjX8/QkLC6NpWBjZOTkcPHCAM2lp5OfnX120ha8vPoUfCFpz+fJlTuTl0aRJk5K/Lfj5GQeSDxyw02CEI6juAd/fgMeBjaUtoJTyBGKBR4B2wNNKqXbV3K4Q7mXLlmtm5X5+fjRp3Jhm4eFcyc3lwMGD/HH6NHkF7RyiTp3izr176b5vH7WUokd4eKm7iQDjGoA9e2w9CuFAqrXbR2u9ByjvptadgQNa60MFyy4BegC7q7NtIdzKnj3GDL0YXx8fGjVqRO6VK5w9e5aDhw4RHBzMiDp1ePrKFfb4+HA8MBC/8g4QX7libKNnTxsNQDgae5zq2Rg4XuR5SsFrQoiKys4u85x+H29vGjZoQIsWLVDAkSNH8FCKh5o350xeHsvS08tev4cHZGVZt2bh0Mqd+SulvgQalPDWaK31KmsWo5R6HngeoGnTptZctRDOzdvb6M9T3mJeXtSvX5969etT+FGRD6Tk5pb9i1qDj0+1yxTOo9yZv9b6Aa31zSX8VDT4U4GwIs+bFLxW0rYStNYdtdYd69atW8HVC+EGmjaF8gIcOJeXx/rz58m2WLBozeYLF1iXmUnn8u7GpZTR/VO4DXuc6vkz0Fop1Rwj9PsAz9hhu0K4jr/8BX76CQICylxMAcvS05lw8iQWoKG3Ny/Xr889gYFlr9/bG9q2tVq5wvFVK/yVUo8BM4G6wGdKqe1a678rpRoBc7XW3bTWeUqpF4B1gCeQpLXeVe3KhXAnf/kLeJX/v2stLy8SmjWr3Lrz8oyZv4S/W6nu2T4rgBUlvH4C6Fbk+VpgbXW2JYRb69LFaL9w4ULF2jdXRlaW0SxObuLiVqSxmxDOwMMDBg82evFYsx9Xfr6x7gEDrLdO4RQk/IVwFn37GgdlC2/IYg1ZWUbwl3B7R+HaJPyFcBbe3jB9unGlb05O9deXmQlNmsCIEdVfl3A6Ev5COJMbb4TZs43TPi9dqto6tDY6edauDR9+aP1jCMIpSPgL4Wzuuw/mzze+CWRkGDdpr6grV4wZf+vWxs3fGzWyWZnCsUn4C+GMunaFr7+Ghx4y9tunpxvBXhKtjfYQGRnG7qIRI+DTT6FhQ/vWLByK9PMXwlnVrg2zZsH+/bBoEaxYYewK8vQ0vg0oZfxcuQINGhgHdp94Qu7YJQC5jaMQrkNrOHEC9u0zrgfw8IA6dYyLt0JCzK5O2IncxlEId6MUNG5s/AhRDtnnL4QQbshhd/sopc4AR82uo4pCgTSzi7AjdxsvuN+Y3W284Lxjbqa1LrctssOGvzNTSm2tyD43V+Fu4wX3G7O7jRdcf8yy20cIIdyQhL8QQrghCX/bSDC7ADtzt/GC+43Z3cYLLj5m2ecvhBBuSGb+QgjhhiT8rUApVVsp9YVS6veC/9YqY9kgpVSKUirGnjVaU0XGq5TqoJTarJTapZTaqZTqbUat1aWUelgptU8pdUAp9XoJ7/sqpT4qeP8npVS4/au0ngqMd4RSanfB3+lXSqlK3jPS8ZQ35iLLPaGU0koplzgDSMLfOl4HvtJatwa+KnhemnHARrtUZTsVGe8loJ/W+ibgYSBaKeVUPQaUUp5ALPAI0A54WinVrthig4B0rXUrYBrwnn2rtJ4KjvcXoKPWuj2wDJhk3yqtq4JjRikVCLwE/GTfCm1Hwt86egALCh4vAHqWtJBS6nagPrDeTnXZSrnj1Vrv11r/XvD4BHAaKPfCEwfTGTigtT6ktc4FlmCMvaiifxbLgPuVUsqONVpTuePVWn+ttS68kcCPQBM712htFfk7BmPS9h5ghbvoOAYJf+uor7U+WfD4FEbAX0Mp5QFMAV6xZ2E2Uu54i1JKdQZ8gIO2LszKGgPHizxPKXitxGW01nlAJlDHLtVZX0XGW9Qg4L82rcj2yh2zUuo2IExr/Zk9C7M1aexWQUqpL4EGJbw1uugTrbVWSpV0CtVQYK3WOsUZJoZWGG/hehoCi4D+WutK3HVEODKlVF+gI/BXs2uxpYJJ21RggMmlWJ2EfwVprR8o7T2l1B9KqYZa65MFYXe6hMXuAO5WSg0FAgAfpdQFrXVZxwdMY4XxopQKAj4DRmutf7RRqbaUCoQVed6k4LWSlklRSnkBwcBZ+5RndRUZL0qpBzAmAX/VWl+2U222Ut6YA4GbgW8KJm0NgNVKqe5aa6fuOS+7faxjNdC/4HF/YFXxBbTWz2qtm2qtwzF2/Sx01OCvgHLHq5TyAVZgjHOZHWuzpp+B1kqp5gXj6YMx9qKK/ln0AjZo5714ptzxKqX+B4gHumutS/zQdzJljllrnam1DtVahxf8v/sjxtidOvhBwt9aooAHlVK/Aw8UPEcp1VEpNdfUymyjIuN9CrgHGKCU2l7w08GccqumYB/+C8A6YA+wVGu9Syk1VinVvWCxRKCOUuoAMIKyz/RyaBUc7/sY31w/Lvg7Lf5h6FQqOGaXJFf4CiGEG5KZvxBCuCEJfyGEcEMS/kII4YYk/IUQwg1J+AshhBuS8BdCCDck4S+EEG5Iwl8IIdzQ/wc1PZjJsDIxAQAAAABJRU5ErkJggg==\n", 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" ] @@ -307,7 +302,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 61, "metadata": {}, "outputs": [], "source": [ @@ -315,6 +310,43 @@ "algo_input = EnergyInput(qubitOp)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### [Optional] Using DOcplex for mapping to the Ising problem\n", + "Using ```docplex.get_qubitops``` is a different way to create an Ising Hamiltonian of Maxcut. ```docplex.get_qubitops``` can create a corresponding Ising Hamiltonian from an optimization model of Maxcut. An example of using ```docplex.get_qubitops``` is as below. " + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": {}, + "outputs": [], + "source": [ + "from docplex.mp.model import Model\n", + "from qiskit.aqua.translators.ising import docplex\n", + "\n", + "# Create an instance of a model and variables.\n", + "mdl = Model(name='max_cut')\n", + "x = {i: mdl.binary_var(name='x_{0}'.format(i)) for i in range(n)}\n", + "\n", + "# Object function\n", + "maxcut_func = mdl.sum(w[i,j]* x[i] * ( 1 - x[j] ) for i in range(n) for j in range(n))\n", + "mdl.maximize(maxcut_func)\n", + "\n", + "# No constraints for MaxCut problems." + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": {}, + "outputs": [], + "source": [ + "qubitOp_docplex, offset_docplex = docplex.get_qubitops(mdl)" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -324,7 +356,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 64, "metadata": {}, "outputs": [ { @@ -339,7 +371,7 @@ }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -386,7 +418,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 15, "metadata": { "scrolled": true }, @@ -395,16 +427,16 @@ "name": "stdout", "output_type": "stream", "text": [ - "energy: -1.4999670167944144\n", - "time: 26.714055061340332\n", - "maxcut objective: -3.9999670167944146\n", - "solution: [1. 0. 1. 0.]\n", + "energy: -1.4919238629420386\n", + "time: 11.324347019195557\n", + "maxcut objective: -3.9919238629420386\n", + "solution: [0. 1. 0. 1.]\n", "solution objective: 4.0\n" ] }, { "data": { - "image/png": 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3797MmjWLWbNmobXm0KFD2Gw2vvzyS5566ilCQ0PNGUayB4I4nStaAD4Y3TpJGDd+G3Cl1npHg2P6a63z6j9eANyttT63pfN2hBYAwGuvvcaRI0e4//77rS5FiEYcDgd79uwxu4u2bNnC4MGDzSUrJkyY0CH2QKipgb17Yf9+qK4GHx+IiIBRo0BW3PghK6aBzgaexpgG+qrW+i9KqYeADK31R0qpvwJzATtQCNyotd7d0jk7SgCcOHGCSy+9lI8//pigoCCryxGiWbW1tWzbts1csiIrK4vRo0ebLYQxY8bg7e1tdZkA1NXBF1/Ayy9DWppx09caHA7w8gKloLYWoqNh8WK46CLoAFnmFvIgmJvdddddTJ48mZSUFKtLEcJpFRUVjQaU8/LyiI2NNccQoqKiLBnb2rIFbr0VjtR3JAcHGzf902kN5eVGWAQHw+OPQ2KLI4tdgwSAm23YsIG///3vMhgsOrTCwsJGS1ZUVVWZ3UXx8fH079+/Xa+vNTz9NDz3nHHDP5PhiooKo3to3jxYsgS68qMSEgBu5nA4mD9/PkuWLJHBYNFp5ObmmmGQkZFBYGBgoz0QQkNDXXYtreGPf4S33jLezZ/NbpwOB5SUwHnnGV1HXTUEJAAs8Oqrr5KXl8d9991ndSlCuJzD4SA7O9uccrpp0yYGDhxoTjeNiYlp0x4Ir7wCjzwCISFNd/c4S2soLobLLjNaAl2RBIAFjh8/zmWXXcbq1atlMxDR6Z3aA+HUkhW7du1i1KhRZiCMGTPG6T0QsrNh9mxjENcV2yacagksXw7nn9/283U0EgAWufPOO5kyZQrJyclWlyKEW1VWVrJ582azhXDw4EFiYmLMQBg+fHizS1YsWgQbN4ILe5QoLzfGEL7++uy6kzoy2RTeIgsWLOCFF16QABBdTkBAAFOmTGHKlCkAlJSUmAPKK1asoLS0lLi4ODMQBg4ciFKKrCzj5h8S0vo16upKyct7iLKyDfj4hBIefjMhITObPDYoCAoL4fPPISnJlT9p5yIB4ELnnnsuf/3rX9m1axfR0dFWlyOEZUJCQkhKSiKp/u6bn59vtg5efPFF/Pz8iI+PJyvrcuz2KIznSVuWn78EpXwZOfJ/VFXt4dChW/H3H0m3blFNHq+UMRgsAdA8CQAX8vLyYv78+XzwwQcSAEI00K9fP+bMmcOcOXPQWrN//35sNhsvvwwnThyitNRBUFAQQUFBBAYG4uXV+IE0h6OSkydTiYr6P7y8AgkMjCE4eDolJavp0+c3TV4zKAgyM43nBDzk+TaPI+vIutjcuXP57LPPqKiosLoUITySUoqoqCjmz1+Er+9IRo0aQv/+A/D29qGwsJCsrCwOHNjPsWMFVFSUo7WDmpqDgDd+fpHmebp1G0F19b5mr3Pqpn/gQPv+PB2ZtABcLDw8nNjYWD755BMWLFhgdTlCeKyjR40BWi8vRUBAAAEBAUBvtHZQUVFJeXk5R48WUFNTjY9PNnV1flRVVeLvHwCAl1d3HI7yFq/h5QW5uTBsmBt+oA5IWgDtIDk5mQ8++MDqMoTwaHa70U9/OqW8CAoKok+fPgwdOoSIiAi8vAKpri5m//79VFVVAeBwlOPl1fL6W1obawaJpkkAtINzzz2XwsJCdu9ucb07Ibq0gACjf/6HNJWVFRw9epS9e/eSm5tHQMBQ/P19CQ2tori4CIDq6j3NDgCfopRxHdE0CYB20HAwWAjRtL59jX56IwQ0FRXl5Ofnk5WVRV5eHl5eikGDIhg+fBj9+g0hJORC7PZ3KSkpoKwsk5MnPyck5OJmz3/q3b90/zRPAqCdzJ07l08//VQGg4VoRl1dLf36Hefw4WPs2bOHo0eP4uPjw+DBg4mKGkZ4eJ/6/QqMfqJ+/e4B7FRX/5xDh+6hX797W2wB2O3QvTuEh7vn5+mIZBC4nfTp04eYmBg+/fRT5s2bZ3U5QniE6upqvv32W1JTU/nqq6+oq7sSL69FDB06FF/flldv8/buQUTEE4SFneTYseOEhAxt8fiyMli4sOlxBmGQAGhHycnJvPTSSxIAokurqKjgq6++Yu3atWzYsIHo6GgSExP5zW9+g69vOJMnn9lNunv37uTn5zeaEXQ6rY1zXnedi36ITkoCoB1NnTqVRx55hD179jBy5EiryxHCbUpLS/n8889JTU1l48aNxMTEkJSUxL333vuDZaSvuspYuC0szNmzK0JDQykqKqZ//6YDoKQEzj0XzjmnbT9HZyeLwbWzZcuWUVRUxN133211KUK0q8LCQtavX8/atWvZvn07CQkJzJgxg2nTphEcHNzs91VUGMs1FBUZffbOsNtryc7ex4gRw3/w1HB1tdH/v3YtDBjQlp+oY5LVQD1IQUEBl19+OatXr65/0EWIzuPo0aOkpqaSmppKVlYWU6dOJSkpialTp57R3/fMTLjiCuPBMGe/7fDhQ3Tv3p3Q0O+bDrW1Rt//U0/B3Lln+tN0DrIaqAdpOBg8t6v+jRSdyqFDh0hNTWXt2rUcPnyY6dOnc+211zJ58mT8znIbrthYeOkl+MUv4ORJY1ew1oSGhnHsWIEZAJWVUFUFDz7YdW/+Z0oCwA0WLFjAK6+8IgEgOiStNfv27TPf6Z84cYIZM2Zw0003MWnSJHxctOD+BRfAe+/BzTcbG8J3797yBjHduweRn19HeXkltbUBdO8OzzwjG8OfCekCcoO6ujrmzJnD008/LYPBokPQWrN7927znX51dTWJiYkkJiYyYcKEZjd3cYWqKuNG/vrrUFNjzOY5tVuYUsYMH7vdOK6oqASHw85Pf9qLe++Fnj3brawOQ8YAPNCyZcsoLi7mrrvusroUIZrkcDjYtm0ba9euZd26dfj4+JCYmEhSUhLR0dEoN0+or6iANWvgv/+FLVvgxAljcTeHw+giGjcOJk8+ybvvXsUnn7xNUFDL6wJ1FRIAHig/P58rr7ySNWvW1D/dKIT16urqyMzMJDU1lXXr1pkbucyYMYPhw4e7/abfkooKo0Xg6wuBgd8/O3DXXXeRkJDApZdeam2BHkIGgT1Qv379GD9+PJ9++ilz5syxuhzRhdXU1GCz2Vi7di1ffPEF/fv3JzExkWXLlhEZGdn6CSwSGGj8OV1KSgpLly4lJSXFowKrI5AAcKPk5GRef/11CQDhdlVVVXzzzTekpqby9ddfExUVRVJSEr/4xS/o37+/1eW1SXx8POXl5ezYsYOxY8daXU6HIgHgRueddx5Llixh7969DB8+3OpyRCdXXl5uLsGQlpbGmDFjSExM5Le//S29e/e2ujyX8fLyIjk5mRUrVkgAnCEZA3CzF198kZKSEhkMFu2ipKTEXIIhMzOTiRMnkpSUxAUXXPCDJRg6k8LCQpKTk1m1alWLTx13BTIG4MHmzZvHlVdeyS233CKDwcIlTpw4wbp160hNTWXHjh1MnjyZmTNn8vDDD9Pd2bUVOriePXty7rnn8p///IeFCxdaXU6HIQHgZv369WPcuHF89tlnXHLJJVaXIzqovLw886afnZ3Neeedx6WXXsoTTzzRZZccSU5O5oknnuCyyy6TwWAnSQBYIDk5meXLl0sAiDNy8OBB82ncI0eOMH36dK6//noSEhLOegmGziQuLo6amhq2bdvG+PHjrS6nQ5AAsMD555/PkiVLyM7OZpjsVyeaobUmOzvbfBq3uLiYGTNmcPPNNzNp0iS8vb1bP0kX4uXlxYIFC/j3v/8tAeAkCQALeHt7M3fuXD744APuuOMOq8sRHkRrza5du8x3+jU1NSQmJnLvvfcyfvz4dl2CoTOYM2cOCxYsoLS0lB49elhdjseTALDIvHnzuPrqq/nNb35Dt27drC5HWMjhcLB161bzpu/n50diYiIPP/ywJUswdGRhYWFMnTqV1atXc8UVV1hdjseTALDIgAEDGDt2LGvXrmX27NlWlyPczG63k5mZydq1a1m/fj1hYWEkJiaydOlSoqKi5KbfBikpKSxZsoTLL79cfo+tkACw0IIFC3jrrbckALqImpoa0tLSWLduHZ9//jkDBw4kKSmJl156yaOXYOhoYmNjcTgcbNmyhZiYGKvL8WgSABaaNm0ajz76KPv27SMqKsrqckQ7qKys5Ntvv2Xt2rV88803DB8+nBkzZrB48WL69etndXmdklLKfDJYAqBlLgkApdRMYCngDbystV5y2te7AW8Ak4ATwCKt9QFXXLsj8/HxMQeDf/e731ldjnCRsrIyvvzyS1JTU0lLS2Ps2LEkJSVx++2306tXL6vL6xIuueQSXnrpJUpKSggJCbG6HI/V5ikFSilv4DlgFjAauEIpNfq0w24AirTWw4GngEfbet3OYv78+axZs4bq6mqrSxFtUFxczEcffcStt97K7Nmz+d///se0adNYtWoVzz//PCkpKXLzd6OQkBCmTZvG6tWrrS7Fo7miBZAA7NVa7wNQSr0DzAN2NjhmHvBg/cfvA88qpZT21IWI3GjAgAGMHj1aBoM7oOPHj5tP4+7cuZPJkycze/ZsHnnkEdmcxAMkJyfz8MMPc8UVV8hgcDNcEQADgUMNXh8GJjd3jNbarpQqAXoBx11w/Q5vwYIFvP322xIAHUBubi7r1q1j7dq17N+/n/PPP5+FCxcyZcoUWdvJw8TExODl5cWmTZuIjY21uhyP5FGDwEqpxcBioEvNirjgggt49NFH2b9/P0OHDrW6HHGanJwcc45+Xl4e06dP54YbbiA+Pl6WYPBgpwaD//3vf0sANMMVAXAEiGjwelD955o65rBSygcIwRgMbkRrvQxYBsZy0C6orUNoOBh8++23W11Ol6e1Zu/eveYSDKWlpcyYMYNbbrmF2NhYWYKhA7n44ot58cUXKS4u7tTLYZ8tVwSADRihlBqKcaO/HLjytGM+Aq4DvgUuBVKl/7+x+fPnc91113HzzTfLu0oLaK3ZuXOnuSG63W4nMTGR+++/n7Fjx8oSDB1Ujx49mD59OqtWreKaa66xuhyP0+YAqO/Tvxn4BGMa6Kta6x1KqYeADK31R8ArwD+VUnuBQoyQEA0MHDiQUaNGkZqaysyZM60up0twOBxs3rzZHMj19/cnKSmJRx55hHPOOUcGDjuJlJQUHnzwQa6++mr5f3oal4wBaK3XAGtO+9wDDT6uAi5zxbU6s+TkZN59910JgHZkt9vZuHGjuQRDr169SExM5JlnnmHo0KFyg+iExo0bh6+vLxkZGcTHx1tdjkfxqEHgrm769Ok8+uijHDhwgCFDhlhdTqdRU1PDhg0bSE1N5YsvviAiIoKkpCReeeUVIiIiWj+B6NCUUqSkpLBixQoJgNNIAHiQhoPBt912m9XldGgVFRV88803pKam8s033zBy5EgSExO58cYb6du3r9XlCTebNWsWzz//PIWFhfTs2dPqcjyGBICHmT9/Ptdffz033XSTDAafoZMnT5pLMKSnpzNu3DiSkpK444475B99FxccHExiYiKrVq3iuuuus7ocjyEB4GEGDRrEyJEjWbduHT/5yU+sLsfjFRUV8fnnn5OamsrmzZuJi4sjMTGRBx54QDYEEY0kJydz3333cc0118isrnoSAB4oOTmZ9957TwKgGQUFBaxfv57U1FR27drFlClTuOSSS1iyZAmBgYFWlyc81JgxYwgMDMRmszF58umLFXRNEgAeaPr06Tz22GMcPHiwSz0R3ZLc3FzzadwDBw5w/vnnc/nllzNlyhTZUU04peGTwRIABgkAD+Tr68sll1zCBx98wK233mp1OZY5cOCA+TRuQUEB06dP5+c//znx8fH4+vpaXZ7ogGbNmsVzzz3HiRMnZHVWJAA81vz587nhhhu48cYbu8xgsNaarKws853+yZMnmTFjBrfddhsTJ06UJRhEm3Xv3p2kpCQ+/PBDfvazn1ldjuUkADxUZGQkw4cPZ/369Vx00UVWl9NuHA4HO3fuNN/pa61lCQbRrlJSUrjnnnu4/vrru/zfLwkAD7ZgwQI++OCDThcAp5ZgOLXuTmBgIImJiTz22GOMHDlSnsYV7So6Oprg4GDS0tKYMmWK1eVYSgLAg82YMYPHH3+8UwwG2+12bDYb69atY/369fTu3ZukpCSeffaO+a8cAAAcf0lEQVRZ2Q9ZuFXDJ4MlAITHOjUYvHLlSm655Raryzlj1dXVpKWlsXbtWr788ksiIyNJTEzk1VdfZdCgQVaXJ7qwmTNn8swzz3Ds2DHCw8OtLscyEgAebv78+fz85z/nV7/6VYcYDK6oqODrr78mNTWVb7/9lpEjR5KUlMRNN91Enz59rC5PCAACAwP58Y9/zEcffcQNN9xgdTmWkQDwcJGRkQwdOowXXthMSUkC6emwdy9UVYG3N/TvDzExcMEFMGsWBAe7v8bS0lJzCQabzcaECROYMWMGd955pyzBIDxWcnIyd9xxBz/96U+77GCw8tR9WeLi4nRGRobVZVjK4YCVK+GBB4o4fLiWnj374O8P3bqBlxdoDbW1UFkJSoGPD1x2Gdx+O7T35keFhYXmEgxbtmwhLi6OpKQkpk2bJkswiA7j2muv5Ze//CXnnXee1aW4jFJqo9Y6zpljpQXgofLy4I47YMMG8PMLoa5uL927hzbqBlLKCINTD8La7fDWW/Dxx/DEEzBjhmtrKigoMDdE/+6775g6dSpz587l0UcflSUYRId06sngzhQAZ0ICwANlZ8OiRVBcbLyTV8qL0NAQiouL6NOn+aWMfXwgLAwqKuAXv4D774frr29bLUeOHDGna+bk5DBt2jSuuuoqzj33XFmCQXR4F110EX//+98pKCjokmNUEgAeJjfXuPmXljbuxgkLC+XAgRzCw8NRquX+ysBA8PWFP/8ZgoKMbqEzsX//fvPBrGPHjvGjH/2IxYsXExcXJ0swiE4lMDCQiy66iJUrV7J48WKry3E7GQPwIA4HXHEFZGQY7+RPl5NzgJ49exIc7Fwfe02N8ec//4GhQ5s/TmvNnj17WLt2LampqVRUVDBjxgySkpKIiYnpsgNkomvYs2cPv/3tb1m1alWnWG5ExgA6qP/7P+Pm39wAblhYGEVFRU4HgJ+f0R10222wYoUxcHyKw+Fg+/bt5ro7SimSkpL44x//yJgxY+SmL7qMkSNH0qdPH77++msuuOACq8txKwkAD1FXZwzcBgQYg7tNCQ4OJj8/n5qaGqefCQgJgR07jGCZNKnOXIJh/fr1BAUFkZiYyOOPP86IESNkCQbRZSUnJ7NixQoJAGGNL7+EkhJoaQalUl706BFITs4fUGoHdXWl+PoOok+fm+nefWoz3+WgsrKam27aRWjo3fTp04ekpCSee+45hrbULyREF3LRRRfx9NNPk5+fT79+/awux20kADzEqlVGK6A1oaHBHD/enREj/oGf3wDKyr7myJF7GDr0Hfz8BgCgtYOysnJOniylrKwMX19/Dh4cznvvvc6QIQPb+ScRouPx9/dn5syZrFy5kl/96ldWl+M20tHrITZuNLp/WuPvH0pw8DXU1PRAKS+Cg6fh6zuAysodlJaWcOTIYfbs2UNhYSEBAQFERUUxdOhgQkN7UFUlN38hmpOSksKHH35InTPvxDoJCQAPYLfDwYPfP9DVmtDQMIqKiqmrq6OwcD8nT+4lN9eLkpISgoKCGD58OIMHDyYsrCc+Pt9P28zKaqcfQIhOYNiwYfTv358vv/zS6lLcRgLAA1RXGwO/zo7B9ugRTFVVJTt2bCE393569JjFqFE/IiIiktDQMLy9f9izV1dnzAgSQjTv1DLRXYUEgAfw9jaeAXCWUl5ERkYSELAcLy8/qqsXcfDgIY4dK6Ciohytf3iyU2sFCSGad+GFF7Jjxw5yc3OtLsUtJAA8QLduxhO7drtzx2utKSx8DD+/Ks455x+MGjWa8PBwtIajRwvYs2cPBw/mcOLEcaqqKgGNtzf0bX4VCSEE0K1bN2bNmsXKlSutLsUtJAA8gFIwdqyxqqcz8vP/Sk3NfiIinsLLqxtKeREUFESfPn0YOnQoI0aMICysJ7W1dnJzc/nuuz3k5x9nz54PycnJwVOf/hbCEyQnJ/Phhx9id/YdWQcmnQIe4oILwGZr/bja2jyKi1eglB9ZWT8xP9+v3+8JCZkFgJeXN8HBwQTXbw5QVlaLUmUcPLiJG298EYD4+HgSEhKIj4/vkotgCdGcqKgoIiIi+OKLL0hMTLS6nHYlawF5iPx8OP9840EwV6/CUFQEv/893HCD0X106NAh0tPTSU9PJyMjg549e5phMGnSJFnPX3R5a9asYc2aNTz77LNWl3LGzmQtIAkAD/LLX8Lata7dzKWmxtg05uuvoanNuRwOB9999x02m4309HS2bt3KkCFDzBZCTEyMLPssupyamhpmz57N8uXLGTiwYz0/IwHQQR0+DD/+sTFbxxX3XK2NPQXuvx9++lPnvqempobt27ebLYSsrCzGjBljthBGjx7dKVZMFKI1Tz75JH5+ftx8881Wl3JGJAA6sHfegfvuM7qC2nqfLS6GCRPgvffOvlupoqKCzMxMMxDy8/OJjY01WwhRUVGyiJzolA4cOMDixYtZvXp1h9oHQ5aD7sAWLTKe2H39dWOD97OZu6+1sbDcoEHw0kttG1MIDAzk/PPP5/zzzweMvYAzMjJIT0/n7bffpqqqioSEBLOF0L9//7O/mBAeZMiQIQwZMoTPP/+cCy+80Opy2oW0ADyQ1vD00/Dcc0YroH4yj1Nqa6GszJhW+uqr0KtX+9UJkJuba7YObDYbQUFBZhjEx8cT2t670wvRjj755BM+/PBDnn/+eatLcZp0AXUSmZlw663GDCEvL+jevfnlIqqrjaUefHzgd78zZvy4u6ve4XCQnZ1tDihv2rSJgQMHmi2EmJgY2TxedCg1NTVcfPHFvPrqq0RERFhdjlMkADqRmhpITYV//AO2bTN2+aqpMdb2Ucp4rbURDj/7GSxcCJ4yrd9ut7Nz506zhbBr1y5GjRplthDGjh3bofpWRde0dOlSlFLccsstVpfiFLcFgFKqJ/AuMAQ4ACzUWhc1cVwdsK3+5UGt9dzWzi0B8EMlJbB7N2Rnf/9uf8AAOOcco7/f03dxrKysZPPmzWYL4eDBg8TExJgthOHDh8tWlMLjHDx4kBtuuIHVq1c7vROfldwZAI8BhVrrJUqpe4AwrfXdTRxXprXufibnlgDo/EpKSti4caPZQigtLSUuLs5sIQwaNEhmGAmPcOONN7JgwQIuuugiq0tplTsD4DvgR1rrPKVUf2C91npUE8dJAIhWHT161BxMTk9Px8fHp9EMo17tPaItRDM+/fRT3n//fV588UWrS2mVOwOgWGsdWv+xAopOvT7tODuwGbADS7TWrS61JwHQtWmtOXDggBkGGzduJDw83AyE2NhYunc/o/cUQpy12tpaLr74Yl566SUGDx5sdTktcmkAKKU+A5raJfk+YHnDG75SqkhrHdbEOQZqrY8opaKAVCBJa53dxHGLgcUAkZGRk3Jycpz5GUQXUFdXx+7du80WwrZt2xg2bJgZCOPHj+8Q/bOi43rmmWew2+3cdtttVpfSIo/rAjrte14HPtZav9/ScdICEC2pqalhy5YtZgth3759jB071gyEc845RwaUhUsdPnyY66+/njVr1nj0mw13BsDfgBMNBoF7aq3vOu2YMKBCa12tlOoNfAvM01rvbOncEgDiTJw8edJcssJms3H8+HFiY2PN8YMhQ4bIgLJos5tuuolLLrmEWbNmWV1Ks9wZAL2A/wMigRyMaaCFSqk44Fda658rpaYCLwIOjA1ontZav9LauSUARFscP34cm82GzWYjLS0Nh8Nhrl+UkJAgeyCIs5Kamsrbb7/NSy+9ZHUpzZIHwYRo4NQeCKe6izIyMggJCTHDIC4uTvZAEE6x2+1cfPHFvPDCC0RFRVldTpMkAIRogcPhICsry+wu2rx5M4MHD260B4K/v7/VZQoP9fzzz1NZWcnvfvc7q0tpkgSAEGegtraWbdu2mS2EPXv2EB0dbbYQRo8ejc/ZLMsqOqXc3FyuueYa1qxZ45GbJUkACNEGFRUVbNq0yWwh5ObmMnHiRLOFMGzYMBlQ7uJuueUWZs6cyezZs60u5QckAIRwoaKiInMPhPT0dCorK80lKxISEhgwYIDVJQo3W7duHW+++SavvNLqfBa3kwAQoh3l5uaa3UU2mw1/f38mT55s7oEQFvaDZyFFJ2O327nkkkt4/vnnPW4wWAJACDfRWpOdnW2GQWZmJgMGDDC7i2JjY2UPhE7qhRdeoKysjDvvvNPqUhqRABDCInV1dezYscNsIezcuZORI0eaD6SNGzdO9kDoJPLy8rjqqqtYs2aNR80akwAQwkNUVVWxZcsW0tLSsNls5OTkMGHCBLOFMHLkSFmyogO79dZbufDCC5kzZ47VpZgkAITwUKWlpWRkZJgthOLi4kZ7IERERMgMow7kiy++4LXXXuO1116zuhSTBIAQHURBQYG5XIXNZsPLy8sMg4SEBHr37m11iaIFdXV1zJkzh6VLlzJixAirywEkAITokLTW5OTkmAPKGzdupFevXo32QAgODra6THGaZcuWUVRUxN13/2AzREtIAAjRCTgcDnbv3m22ELZv387QoUPNFkJMTIxHL0vcVRQUFHD55ZezevVqAgICrC5HAkCIzqimpoatW7eaLYTs7GzGjBljthCio6NlQNkit99+O9OnT2fevHlWlyIBIERXUFZWRmZmptlCOHbsWKM9EIYOHSoDym7y1VdfsWzZMt544w2rS5EAEKIrOnHiRKMnlGtraxvtgdC3b1+rS+y0HA4Hc+fO5YknnmDUqBY3RWx3EgBCdHFaa44cOWKGgc1mo0ePHmYgxMXFERISYnWZncrLL79MQUEBv//97y2tQwJACNGIw+Fg79695oJ2mzdvJiIiwmwdxMTEeMQAZkd27NgxFi5cyOrVqy1d/kMCQAjRotraWnbs2GG2EHbv3k10dLTZQhgzZozsgXAW7rjjDqZOnUpycrJlNUgACCHOSEVFBZs3bzZbCEeOHCEmJsYcUB4+fLjMMHLCN998w/PPP8+bb75pWQ0SAEKINikuLjb3QLDZbJSVlZnLXSckJDBw4ECrS/RIDoeD+fPns2TJEkaPHm1JDRIAQgiXysvLM2cYpaen4+/vb4ZBfHw8PXv2tLpEj/Hqq6+Sl5fHfffdZ8n1JQCEEO1Ga83+/fvNMMjMzKRfv35mGMTGxhIUFGR1mZY5ceIEl156KR9//LElvwcJACGE29TV1bFz506zhbBjxw5GjBhhthDGjRvX5ZasuOuuu5g8eTIpKSluv7YEgBDCMtXV1WzZssVsIRw4cIDx48ebLYRRo0Z1+gHltLQ0li5dyltvveX2p7HPJABknpcQwqW6detmPl8Axh4ImZmZpKen84c//IHCwkLi4uLMFkJkZGSnW7IiPj6e8vJydu7cyZgxY6wup1nSAhBCuFVBQYE5wyg9PR3ADIz4+HjCw8MtrtA1li9fTk5ODg888IBbrytdQEKIDkFrzaFDh8wNcTIyMujZs6cZBpMmTaJHjx5Wl3lWCgsLSUlJYdWqVXTv3t1t15UAEEJ0SA6Hg++++84cUN66dStDhgwxWwgTJkygW7duVpfptHvuuYfY2FgWLlzotmtKAAghOoWamhq2b99uthCysrLMPRDi4+MZPXo03t7eVpfZrPT0dJ588knefvvt78c5Tp6E6mrw84PgYHDx+IcEgBCiUyovLzf3QEhPTyc/P9/cAyEhIcHj9kBwOBxcNXcuS6ZNY/DOnbB1K5SWgpcXOBwQEABjxsCFF0JyMvTq1eZrSgAIIbqEwsLCRgPK1dXVjZ5Q7t+/v3XFVVTAU09R8txz2Kur6dWrl3HD9/H5/l2/3Q5VVcZ/vbxgzhy47z5ow5PVEgBCiC7p9D0QgoKCzNZBXFwcoaGh7ikkMxN+8xvIz8ceGEj2gQMMHz685e6qujqjdRAcDI8/brQKzoIEgBCiy3M4HGRnZ5vdRZs2bWLgwIGN9kBol3X7166FX//aeJdfP/vn8JEjBAYEOLdmUmWlMUbwwANw7bVnfHkJACGEOI3dbm+0B8KuXbsYNWqUGQhjxozB19e3bRdJT4errzYGeP39zU+XV1SQn59PVFQUTo1Q1NZCWRk89RTMnXtGJUgACCFEKyorK9m8eTM2m420tDQOHTpk7oGQkJBw5nsglJVBYqIxy+e0ReA0kJ2dzYD+/Z1vdVRXG91Cn30GAwY4XYYsBSGEEK0ICAhgypQpTJkyBYCSkhJzQHnFihWUlpYSFxdnBsLAgQNbnmH06KNQWAhNjDMoICwsjKLiYucDoFs3KC6Gu++Gf/7zLH7C1kkLQAghmnD06FGzuyg9PR1fX99GM4x6NZyyWVgI555rvPNvZqDXXldH9t69vBEUREZlJZUOB719fLi2Vy/mNzc4rbUxMPzxxzBqlFN1SxeQEEK40Kk9EE6FQWZmJuHh4WbrIGH7dvyffLLJd/8NHcnNJd/bm3Hh4fh5eXGguprFOTksjYggOiCg6W8qKoJFi+CRR5yq1W1dQEqpy4AHgWggQWvd5B1bKTUTWAp4Ay9rrZe05bpCCOFOSimioqKIiopi0aJF1NXVsXv3btLT03nnnXdQ775LlN2Ob20tQUFBBAQE4NVEd1FYaCiVeXn49u1rnLf+3Idra5sPgKAg+O9/nQ6AM/q52tICUEpFAw7gReCOpgJAKeUN7AF+DBwGbMAVWuudLZ1bWgBCiA7B4cBxzjlUAuVVVZRXVFBdXU1AQABBQUEEBQXh7++PwhgM3rdvH2/5+PBJRQXVWjPK35+XBg8msLkBZ62hpAQ2bIDevVstx20tAK31rvoLtnRYArBXa72v/th3gHlAiwEghBAdQl4eXkBQjx4E1a9cWudwUFFeTnl5Obm5udjtdgIDAwkKCqJ79+7cUFvL/aNGsbWyko0VFfi1dA9VCnx9Yd8+pwLgTLhjFtBA4FCD14eByW64rhBCtL/KSmMZhwa8vbwIDg4mODgYgFq73QyEsvJy0BqlFDGBgawpKeH9oiIub+khMa2N67hYqwGglPoM6NfEl+7TWn/oymKUUouBxQCRkZGuPLUQQrQPHx/jBt0CXx8fQkJCCAkJQWMMKp96z18HHK6pafkap1oBLtZqAGitz25Biu8dASIavB5U/7mmrrUMWAbGGEAbryuEEO2vXz9jMTeH4wctgdMV2u1kVFRwfvfu+ANp5eV8UlLCIwMHtnyNurozehjMWe7oArIBI5RSQzFu/JcDV7rhukII0f78/SEyEgoKjNU+W6CA94uKeCQvDwfQ39eX3/XtywX1XUVNqqszgqUdekXaOg10AfAMEA6sVkpt1lr/RCk1AGO652yttV0pdTPwCcY00Fe11jvaXLkQQniKGTNg+fJWAyDMx4dlgwef2bnLymDKlFZbF2ejrbOAPgA+aOLzucDsBq/XAGvaci0hhPBYl19uLNegtct3+EIp+NnPXHvOeq6PFCGE6GpGjoSJE435+q5UVgbh4TBtmmvPW08CQAghXGHJEmMdoNpa15yvrs441xNPNLu+UFtJAAghhCtERcFddxnv2h2Otp3r1CJwV15pLDLXTiQAhBDCVX72M2NDmJISY2ro2XA4jGWgZ8wwdgVrRxIAQgjhKkrBgw/CrbcaLYHS0jP7/vJyIzwuuwxeeKFdHv5qSAJACCFcSSm45RZYsQIGDTJCoKSk+W4hh8PYRezUhvCvv26MJ7TzzR9kRzAhhGgf48cb2zl+9RW8/DJ8+60xmKv199NFlTIGesePh8WLISnJ2E/YTSQAhBCivXh5wQUXGH9qa40VPffvN/b79fWFiAhjCmm3bpaUJwEghBDu4OtrbOvo5NaO7iBjAEII0UV57J7ASqljQM5pn+4NHLegHGd5en0gNbqK1Nh2nl4fdMwaB2utw535Ro8NgKYopTKc3erMCp5eH0iNriI1tp2n1wedv0bpAhJCiC5KAkAIIbqojhYAy6wuoBWeXh9Ija4iNbadp9cHnbzGDjUGIIQQwnU6WgtACCGEi3h0ACileiqlPlVKZdX/N6yZ4x5TSu1QSu1SSv1dKVdvydPm+iKVUv+rr2+nUmqIO+o7kxrrj+2hlDqslHrWXfU5W6NSKkYp9W39/+etSqlFbqhrplLqO6XUXqXUPU18vZtS6t36r6e58//rGdR4e/3fua1KqbVKqTPcj7D9a2xwXIpSSiul3D7rxpkalVIL63+XO5RS//K0GuvvM+uUUpvq/3/Pbuo8jWitPfYP8BhwT/3H9wCPNnHMVOBrjP2GvYFvgR95Sn31X1sP/Lj+4+5AoCf9DhscuxT4F/CsB/5/HgmMqP94AJAHhLZjTd5ANhAF+AFbgNGnHfNr4B/1H18OvOvm35szNc449fcNuNETa6w/Lhj4AtgAxHlajcAIYBMQVv+6jwfWuAy4sf7j0cCB1s7r0S0AYB6wvP7j5cD8Jo7RgD/GL6Ub4AscdUt1TtSnlBoN+GitPwXQWpdprSvcVB849ztEKTUJ6Av8z011NdRqjVrrPVrrrPqPc4ECwKmHXc5SArBXa71Pa10DvFNfZ0MN634fSHJX69PZGrXW6xr8fdsADHJjfU7VWO/PwKNAlTuLq+dMjb8AntNaFwForQs8sEYN9Kj/OATIbe2knh4AfbXWefUf52PcoBrRWn8LrMN4R5gHfKK13uUp9WG8cy1WSq2ob5r9TSnVPvu7Na3VGpVSXsATwB1urKshZ36PJqVUAkbgZ7djTQOBQw1eH67/XJPHaK3tQAnQqx1rOp0zNTZ0A/Cfdq3oh1qtUSkVC0RorVe7s7AGnPk9jgRGKqW+VkptUErNdFt1BmdqfBC4Wil1GFgD/Ka1k1q+GJxS6jOgXxNfuq/hC621Vkr9YMqSUmo4EM3372w+VUpN01p/6Qn1YfyOpwETgYPAu8D1wCuuqM9FNf4aWKO1Ptxeb2BdUOOp8/QH/glcp7Vu4757XYdS6mogDphudS0N1b/5eBLj34Qn88HoBvoRxr3mC6XUOK11saVVNXYF8LrW+gml1BTgn0qpsS39O7E8ALTWFzb3NaXUUaVUf611Xv0//KaaXQuADVrrsvrv+Q8wBXBJALigvsPAZq31vvrvWQmciwsDwAU1TgGmKaV+jTFG4aeUKtNaNztgZ0GNKKV6AKuB+7TWG1xVWzOOABENXg+q/1xTxxxWSvlgNLtPtHNdTV3/lKZqRCl1IUbQTtdaV7uptlNaqzEYGAusr3/z0Q/4SCk1V2ud4SE1gvHvOE1rXQvsV0rtwQgEm3tKdKrGG4CZYPSMKKX8MdYJara7ytO7gD4Crqv/+DrgwyaOOQhMV0r5KKV8Md7huKsLyJn6bECoUupUf3UisNMNtZ3Sao1a66u01pFa6yEY3UBvuPLm74RWa1RK+QEf1Nf2vhtqsgEjlFJD6699eX2dDTWs+1IgVdePwLlJqzUqpSYCLwJzLei3brVGrXWJ1rq31npI/d+/DfW1uuvm32qN9VZivPtHKdUbo0ton4fVeBBIqq8xGmNs9FiLZ3XnSPZZjHz3AtYCWcBnQM/6z8cBLzcYHX8R46a/E3jSk+qrf/1jYCuwDXgd8PO0Ghscfz3unwXkzP/nq4FaYHODPzHtXNdsYA/GWMN99Z97COMGRf0/sPeAvUA6EOXO35uTNX6GMSni1O/sI0+r8bRj1+PmWUBO/h4VRlfVzvp/x5d7YI2jMWZEbqn/f31Ra+eUJ4GFEKKL8vQuICGEEO1EAkAIIbooCQAhhOiiJACEEKKLkgAQQoguSgJACCG6KAkAIYTooiQAhBCii/p/K9d8/GvFkz8AAAAASUVORK5CYII=\n", + "image/png": 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\n", 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" ] @@ -528,6 +560,56 @@ "nx.draw_networkx(G, node_color=colors, node_size=600, alpha = .8, pos=pos)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### [Optional] Checking that the full Hamiltonian made by ```docplex.get_qubitops``` gives the right cost" + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "energy: -1.5\n", + "maxcut objective: -4.0\n", + "solution: [0. 1. 0. 1.]\n", + "solution objective: 4.0\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#Making the Hamiltonian in its full form and getting the lowest eigenvalue and eigenvector\n", + "ee = ExactEigensolver(qubitOp_docplex, k=1)\n", + "result = ee.run()\n", + "\n", + "x = docplex.sample_most_likely(result['eigvecs'][0])\n", + "print('energy:', result['energy'])\n", + "print('maxcut objective:', result['energy'] + offset_docplex)\n", + "print('solution:', maxcut.get_graph_solution(x))\n", + "print('solution objective:', maxcut.maxcut_value(x, w))\n", + "\n", + "colors = ['r' if maxcut.get_graph_solution(x)[i] == 0 else 'b' for i in range(n)]\n", + "nx.draw_networkx(G, node_color=colors, node_size=600, alpha = .8, pos=pos)" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -564,7 +646,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 66, "metadata": {}, "outputs": [ { @@ -572,14 +654,14 @@ "output_type": "stream", "text": [ "distance\n", - " [[ 0. 54. 74.]\n", - " [54. 0. 34.]\n", - " [74. 34. 0.]]\n" + " [[ 0. 61. 6.]\n", + " [61. 0. 57.]\n", + " [ 6. 57. 0.]]\n" ] }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -613,20 +695,20 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 67, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "order = (0, 1, 2) Distance = 162.0\n", - "Best order from brute force = (0, 1, 2) with total distance = 162.0\n" + "order = (0, 1, 2) Distance = 124.0\n", + "Best order from brute force = (0, 1, 2) with total distance = 124.0\n" ] }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -681,7 +763,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 68, "metadata": {}, "outputs": [], "source": [ @@ -689,6 +771,44 @@ "algo_input = EnergyInput(qubitOp)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### [Optional] Using DOcplex for mapping to the Ising problem\n", + "Using ```docplex.get_qubitops``` is a different way to create an Ising Hamiltonian of TSP. ```docplex.get_qubitops``` can create a corresponding Ising Hamiltonian from an optimization model of TSP. An example of using ```docplex.get_qubitops``` is as below. " + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "metadata": {}, + "outputs": [], + "source": [ + "# Create an instance of a model and variables\n", + "mdl = Model(name='tsp')\n", + "x = {(i,p): mdl.binary_var(name='x_{0}_{1}'.format(i,p)) for i in range(n) for p in range(n)}\n", + "\n", + "# Object function\n", + "tsp_func = mdl.sum(ins.w[i,j] * x[(i,p)] * x[(j,(p+1)%n)] for i in range(n) for j in range(n) for p in range(n))\n", + "mdl.minimize(tsp_func)\n", + "\n", + "# Constrains\n", + "for i in range(n):\n", + " mdl.add_constraint(mdl.sum(x[(i,p)] for p in range(n)) == 1)\n", + "for p in range(n):\n", + " mdl.add_constraint(mdl.sum(x[(i,p)] for i in range(n)) == 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "metadata": {}, + "outputs": [], + "source": [ + "qubitOp_docplex, offset_docplex = docplex.get_qubitops(mdl)" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -698,22 +818,23 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 76, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "energy: -600081.0\n", + "energy: -600062.0\n", + "tsp objective: 124.0\n", "feasible: True\n", - "solution: [1, 2, 0]\n", - "solution objective: 162.0\n" + "solution: [0, 1, 2]\n", + "solution objective: 124.0\n" ] }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -741,7 +862,7 @@ "result = run_algorithm(params,algo_input)\n", "\"\"\"\n", "print('energy:', result['energy'])\n", - "#print('tsp objective:', result['energy'] + offset)\n", + "print('tsp objective:', result['energy'] + offset)\n", "x = tsp.sample_most_likely(result['eigvecs'][0])\n", "print('feasible:', tsp.tsp_feasible(x))\n", "z = tsp.get_tsp_solution(x)\n", @@ -849,6 +970,57 @@ "draw_tsp_solution(G, z, colors, pos)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### [Optional] Checking that the full Hamiltonian made by ```docplex.get_qubitops``` gives the right cost" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "energy: -4532.0\n", + "tsp objective: 124.0\n", + "feasible: True\n", + "solution: [0, 1, 2]\n", + "solution objective: 124.0\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "ee = ExactEigensolver(qubitOp_docplex, k=1)\n", + "result = ee.run()\n", + "\n", + "print('energy:', result['energy'])\n", + "print('tsp objective:', result['energy'] + offset_docplex)\n", + "\n", + "x = docplex.sample_most_likely(result['eigvecs'][0])\n", + "print('feasible:', tsp.tsp_feasible(x))\n", + "z = tsp.get_tsp_solution(x)\n", + "print('solution:', z)\n", + "print('solution objective:', tsp.tsp_value(z, ins.w))\n", + "draw_tsp_solution(G, z, colors, pos)" + ] + }, { "cell_type": "code", "execution_count": null, @@ -874,7 +1046,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.7" + "version": "3.6.5" } }, "nbformat": 4, From dd46ec62c3cf05ca9cbd6c9cce3ac43bfad5db0d Mon Sep 17 00:00:00 2001 From: Atsushi Matsuo Date: Fri, 12 Apr 2019 17:43:37 +0900 Subject: [PATCH 040/116] Added header and removed error examples. Fixed the problem name --- qiskit/aqua/optimization/docplex.ipynb | 131 ++++++------------------- 1 file changed, 31 insertions(+), 100 deletions(-) diff --git a/qiskit/aqua/optimization/docplex.ipynb b/qiskit/aqua/optimization/docplex.ipynb index 9f079ef0f..77eeb9fb2 100644 --- a/qiskit/aqua/optimization/docplex.ipynb +++ b/qiskit/aqua/optimization/docplex.ipynb @@ -1,5 +1,27 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# _*Qiskit Aqua: Generatin Ising Hamiltonians from optimization models with DOcplex*_\n", + "\n", + "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorial.\n", + "\n", + "***\n", + "### Contributors\n", + "Atsushi Matsuo[1], Takashi Imamichi[1], Marco Pistoia[1], Stephen Wood[1]\n", + "### Affiliation\n", + "- [1]IBMQ" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -21,7 +43,9 @@ "For simplicity, we can generate Ising Hamiltonian from the following optimization models now.\n", "- Binary decision variables. \n", "- Linear and quadratic terms in objective functions.\n", - "- Only equality constraints.\n", + "- Only equality constraints. \n", + "\n", + "Input models are validated before transormation. If the model containts elements that are not from the supported set, an error will be raised.\n", "\n", "Even though there are restrictions, this type of optimization model can handle the following optimization problems, maxcut, tsp and etc.\n", "They are typical optimization problems. The usage examples of the translator for Maxcut and TSP are written in the following link.\n", @@ -32,7 +56,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### A Usage Example: Maximize the number of variables which takes the value 1\n", + "### A Usage Example: Maximize the number of variables by taking into account constraints\n", "The following is a toy example of a maximization problem with constrains.\n", "\\begin{aligned}\n", " & \\text{maximize}\n", @@ -182,17 +206,17 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "energy: -56.20499759137974\n", - "time: 9.663682699203491\n", - "solution objective: -0.7049975913797368\n", - "solution: [0. 0. 1. 0.]\n" + "energy: -57.16261789728296\n", + "time: 10.59960389137268\n", + "solution objective: -1.6626178972829635\n", + "solution: [1. 1. 0. 0.]\n" ] } ], @@ -242,99 +266,6 @@ "print('solution objective:', result['energy'] + offset)\n", "print('solution:', x)" ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### [Optional] A Case when the validation of the input model fails.\n", - "If the following unsupported elemts exist in the input model, the error will be raised.\n", - "- Variables which are not binary decision variables \n", - "- Inequality constraints. \n", - "Note: Cubic or higher order terms can not be input of DOcplex." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\\ This file has been generated by DOcplex\n", - "\\ ENCODING=ISO-8859-1\n", - "\\Problem name: max_vars\n", - "\n", - "Maximize\n", - " obj: x_1 + x_2 + x_3 + x_4\n", - "Subject To\n", - " c1: x_1 + 2 x_2 + 3 x_3 + 4 x_4 <= 3\n", - "\n", - "Bounds\n", - "End\n", - "\n" - ] - } - ], - "source": [ - "# Create an instance of a model and variables\n", - "# Continuous variables are used\n", - "mdl = Model(name='max_vars')\n", - "x = {i: mdl.continuous_var(name='x_{0}'.format(i)) for i in range(1,5)}\n", - "\n", - "# Object function\n", - "max_vars_func = mdl.sum(x[i] for i in range(1,5))\n", - "mdl.maximize(max_vars_func)\n", - "\n", - "# Constrains\n", - "# Inequality constraint is used\n", - "mdl.add_constraint(mdl.sum(i*x[i] for i in range(1,5)) <= 3)\n", - "\n", - "print(mdl.export_to_string())" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "The type of Variable x_1 is continuous. It must be a binary variable. \n", - "The type of Variable x_2 is continuous. It must be a binary variable. \n", - "The type of Variable x_3 is continuous. It must be a binary variable. \n", - "The type of Variable x_4 is continuous. It must be a binary variable. \n", - "Constraint x_1+2x_2+3x_3+4x_4 <= 3 is not an equality constraint.\n" - ] - }, - { - "ename": "AquaError", - "evalue": "'The input model has unsupported elements.'", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mAquaError\u001b[0m Traceback (most recent call last)", - "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mqubitOp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moffset\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdocplex\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_qubitops\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmdl\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", - "\u001b[0;32m~/github/qiskit-aqua-docplex/qiskit/aqua/translators/ising/docplex.py\u001b[0m in \u001b[0;36mget_qubitops\u001b[0;34m(mdl, auto_penalty, default_penalty)\u001b[0m\n\u001b[1;32m 83\u001b[0m \"\"\"\n\u001b[1;32m 84\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 85\u001b[0;31m \u001b[0m_validate_input_model\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmdl\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 86\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 87\u001b[0m \u001b[0;31m# set the penalty coefficient by _auto_define_penalty() or manually.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;32m~/github/qiskit-aqua-docplex/qiskit/aqua/translators/ising/docplex.py\u001b[0m in \u001b[0;36m_validate_input_model\u001b[0;34m(mdl)\u001b[0m\n\u001b[1;32m 222\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 223\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mvalid\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 224\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mAquaError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'The input model has unsupported elements.'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 225\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 226\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;31mAquaError\u001b[0m: 'The input model has unsupported elements.'" - ] - } - ], - "source": [ - "qubitOp, offset = docplex.get_qubitops(mdl)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { From ba26c4e6cb1581286e05598dd46c96b2c505ab54 Mon Sep 17 00:00:00 2001 From: Albert Akhriev Date: Fri, 12 Apr 2019 13:26:06 +0100 Subject: [PATCH 041/116] random number generator notebook --- .../finance/generating_random_variates.ipynb | 285 ++++++++++++++++++ 1 file changed, 285 insertions(+) create mode 100644 qiskit/aqua/finance/generating_random_variates.ipynb diff --git a/qiskit/aqua/finance/generating_random_variates.ipynb b/qiskit/aqua/finance/generating_random_variates.ipynb new file mode 100644 index 000000000..d4e5236f3 --- /dev/null +++ b/qiskit/aqua/finance/generating_random_variates.ipynb @@ -0,0 +1,285 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# _*Qiskit Aqua: Generating Random Variates*_ \n", + "\n", + "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", + "\n", + "***\n", + "### Contributors\n", + "Albert Akhriev[1], Jakub Marecek[1], Stephen Wood[1], Marco Pistoia[1]\n", + "### Affliation\n", + "- [1]IBMQ" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Uniformly-distributed scalars and vectors\n", + "\n", + "Functions in the base class \\textbf{UnivariateDistribution}\n", + "\n", + "```python\n", + "def uniform_rand_float64(self, size: int, vmin: float, vmax: float) -> np.ndarray:\n", + " \"\"\"\n", + " Generates a vector of random float64 values in the range [vmin, vmax].\n", + " :param size: length of the vector.\n", + " :param vmin: lower bound.\n", + " :param vmax: upper bound.\n", + " :return: vector of random values.\n", + " \"\"\"\n", + " assert sys.maxsize == np.iinfo(np.int64).max # sizeof(int) == 64 bits\n", + " assert isinstance(size, int) and size > 0\n", + " assert isinstance(vmin, float) and isinstance(vmax, float) and vmin <= vmax\n", + " nbits = 7 * 8 # nbits > mantissa of float64\n", + " bit_str_len = (nbits * size + self.num_target_qubits - 1) // self.num_target_qubits\n", + " job = execute(self.circuit, self.backend, shots=bit_str_len, memory=True)\n", + " bit_str = ''.join(job.result().get_memory())\n", + " scale = float(vmax - vmin) / float(2**nbits - 1)\n", + " return np.array([vmin + scale * float(int(bit_str[i:i+nbits], 2))\n", + " for i in range(0, nbits * size, nbits)], dtype=np.float64)\n", + "```\n", + "\n", + "```python\n", + "def uniform_rand_int64(self, size: int, vmin: int, vmax: int) -> np.ndarray:\n", + " \"\"\"\n", + " Generates a vector of random int64 values in the range [vmin, vmax].\n", + " :param size: length of the vector.\n", + " :param vmin: lower bound.\n", + " :param vmax: upper bound.\n", + " :return: vector of random values.\n", + " \"\"\"\n", + " assert sys.maxsize == np.iinfo(np.int64).max # sizeof(int) == 64 bits\n", + " assert isinstance(size, int) and size > 0\n", + " assert isinstance(vmin, int) and isinstance(vmax, int) and vmin <= vmax\n", + " assert abs(vmin) <= 2**52 and abs(vmax) <= 2**52 # 52 == mantissa of float64\n", + " return np.rint(self.uniform_rand_float64(size, float(vmin), float(vmax))).astype(np.int64)\n", + "```\n", + "\n", + "Function in the base class \\textbf{NormalDistribution}\n", + "\n", + "```python\n", + "def normal_rand_float64(self, size: int) -> np.ndarray:\n", + " \"\"\"\n", + " Draws a sample vector from standard normal distribution (mu=0, std=1)\n", + " using Box-Muller method.\n", + " \"\"\"\n", + " EPS = np.sqrt(np.finfo(np.float64).tiny)\n", + " assert isinstance(size, int) and size > 0\n", + " rand_vec = np.zeros((size,), dtype=np.float64)\n", + "\n", + " # Generate array of uniformly distributed samples.\n", + " n = 2 * size\n", + " x = np.reshape(self.uniform_rand_float64(n, float(0.0), float(1.0)), (-1, 2))\n", + "\n", + " x1 = 0.0 # first sample in a pair\n", + " c = 0 # counter\n", + " for d in range(size):\n", + " r2 = 2.0\n", + " while r2 >= 1.0 or r2 < EPS:\n", + " # Regenerate array of uniformly distributed samples upon shortage.\n", + " if c > n:\n", + " c = 0\n", + " n = max(((size // 10) // 2) * 2, 2)\n", + " x = np.reshape(self.uniform_rand_float64(n, float(0.0), float(1.0)), (-1, 2))\n", + "\n", + " x1 = 2.0 * x[c, 0] - 1.0 # first sample in a pair\n", + " x2 = 2.0 * x[c, 1] - 1.0 # second sample in a pair\n", + " r2 = x1 * x1 + x2 * x2\n", + " c += 1\n", + "\n", + " f = np.sqrt(np.abs(-2.0 * np.log(r2) / r2))\n", + " rand_vec[d] = f * x1\n", + " return rand_vec\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "import numpy as np\n", + "import time\n", + "from qiskit import BasicAer\n", + "from qiskit.aqua.algorithms import AmplitudeEstimation\n", + "from qiskit.aqua.components.random_distributions import MultivariateNormalDistribution\n", + "from qiskit.aqua.components.uncertainty_problems import FixedIncomeExpectedValue\n", + "from qiskit.aqua.components.random_distributions import *\n", + "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister, execute\n", + "from qiskit.tools.visualization import plot_histogram, circuit_drawer\n", + "import scipy.stats as stats\n", + "\n", + "# In this example we use 'qasm_simulator' backend.\n", + "glo_backend = BasicAer.get_backend(\"qasm_simulator\")\n", + "\n", + "# Parameters.\n", + "glo_num_qubits = 5" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Uniform distribution of floating point numbers." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "# Create uniform distribution sampler.\n", + "start_time = time.time()\n", + "uniform = UniformDistribution(glo_num_qubits, backend=glo_backend)\n", + "creation_time = time.time() - start_time\n", + "\n", + "# Draw a sample.\n", + "start_time = time.time()\n", + "sample = uniform.uniform_rand_float64(size=54321, vmin=-7.67, vmax=19.52)\n", + "sampling_time = time.time() - start_time\n", + "\n", + "# Print out some details.\n", + "print(\"Uniform distribution of floating point numbers:\")\n", + "print(\"sample type:\", type(sample), \", element type:\", sample.dtype, \", shape:\", sample.shape)\n", + "print(\"sample min: {:.4f}, max: {:.4f}\".format(np.amin(sample), np.amax(sample)))\n", + "print(\"time: creation: {:.5f}, sampling: {:.2f}\".format(creation_time, sampling_time))\n", + "\n", + "# Plotting the distribution.\n", + "plt.hist(sample.ravel(),\n", + " bins=min(int(np.ceil(np.sqrt(sample.size))), 100),\n", + " density=True, facecolor='b', alpha=0.75)\n", + "plt.xlabel(\"random variable\", size=12)\n", + "plt.ylabel(\"probability\", size=12)\n", + "plt.title(\"Uniform distribution of float64 numbers [{:.2f} ... {:.2f}]\".format(\n", + " np.amin(sample), np.amax(sample)), size=12)\n", + "plt.grid(True)\n", + "# plt.savefig(\"uniform_distrib_float.png\", bbox_inches=\"tight\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Uniform distribution of integer numbers." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Draw a sample, reuse the previous instance of the sampler.\n", + "start_time = time.time()\n", + "sample = uniform.uniform_rand_int64(size=54321, vmin=37, vmax=841)\n", + "sampling_time = time.time() - start_time\n", + "\n", + "# Print out some details.\n", + "print(\"Uniform distribution of integer numbers:\")\n", + "print(\"sample type:\", type(sample), \", element type:\", sample.dtype, \", shape:\", sample.shape)\n", + "print(\"sample min: {:d}, max: {:d}\".format(np.amin(sample), np.amax(sample)))\n", + "print(\"time: sampling: {:.2f}\".format(sampling_time))\n", + "\n", + "# Plotting the distribution.\n", + "plt.hist(sample.ravel(),\n", + " bins=min(int(np.ceil(np.sqrt(sample.size))), 100),\n", + " density=True, facecolor='g', alpha=0.75)\n", + "plt.xlabel(\"random variable\", size=12)\n", + "plt.ylabel(\"probability\", size=12)\n", + "plt.title(\"Uniform distribution of int64 numbers [{:d} ... {:d}]\".format(\n", + " np.amin(sample), np.amax(sample)), size=12)\n", + "plt.grid(True)\n", + "# plt.savefig(\"uniform_distrib_int.png\", bbox_inches=\"tight\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Standard normal distribution" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Create uniform distribution sampler.\n", + "start_time = time.time()\n", + "normal = NormalDistribution(glo_num_qubits, backend=glo_backend)\n", + "creation_time = time.time() - start_time\n", + "\n", + "# Draw a sample from the standard normal distribution.\n", + "start_time = time.time()\n", + "sample = normal.normal_rand_float64(size=4321)\n", + "sampling_time = time.time() - start_time\n", + "\n", + "# Print out some details.\n", + "print(\"Standard normal distribution:\")\n", + "print(\"sample type:\", type(sample), \", element type:\", sample.dtype, \", shape:\", sample.shape)\n", + "print(\"sample min: {:.4f}, max: {:.4f}\".format(np.amin(sample), np.amax(sample)))\n", + "print(\"time: creation: {:.5f}, sampling: {:.2f}\".format(creation_time, sampling_time))\n", + "\n", + "# Plotting the distribution.\n", + "plt.hist(sample.ravel(),\n", + " bins=min(int(np.ceil(np.sqrt(sample.size))), 100),\n", + " density=True, facecolor='r', alpha=0.75)\n", + "plt.xlabel(\"random variable\", size=12)\n", + "plt.ylabel(\"probability\", size=12)\n", + "plt.title(\"Standard normal distribution\", size=12)\n", + "plt.grid(True)\n", + "# plt.savefig(\"std_normal_distrib.png\", bbox_inches=\"tight\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.3" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} From 0f83aa0fdf764c25d173746a553d26bc7c436ef5 Mon Sep 17 00:00:00 2001 From: Albert Akhriev Date: Fri, 12 Apr 2019 16:11:41 +0100 Subject: [PATCH 042/116] new random generator --- qiskit/aqua/finance/generating_random_variates.ipynb | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/qiskit/aqua/finance/generating_random_variates.ipynb b/qiskit/aqua/finance/generating_random_variates.ipynb index d4e5236f3..cb7123ecd 100644 --- a/qiskit/aqua/finance/generating_random_variates.ipynb +++ b/qiskit/aqua/finance/generating_random_variates.ipynb @@ -114,7 +114,7 @@ "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "import numpy as np\n", - "import time\n", + "import sys, math, time\n", "from qiskit import BasicAer\n", "from qiskit.aqua.algorithms import AmplitudeEstimation\n", "from qiskit.aqua.components.random_distributions import MultivariateNormalDistribution\n", @@ -122,7 +122,6 @@ "from qiskit.aqua.components.random_distributions import *\n", "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister, execute\n", "from qiskit.tools.visualization import plot_histogram, circuit_drawer\n", - "import scipy.stats as stats\n", "\n", "# In this example we use 'qasm_simulator' backend.\n", "glo_backend = BasicAer.get_backend(\"qasm_simulator\")\n", @@ -242,9 +241,12 @@ "print(\"time: creation: {:.5f}, sampling: {:.2f}\".format(creation_time, sampling_time))\n", "\n", "# Plotting the distribution.\n", + "x = np.linspace(-4.0, 4.0, 1000)\n", + "analyt = np.exp(-0.5 * x**2) / math.sqrt(2.0 * math.pi)\n", "plt.hist(sample.ravel(),\n", " bins=min(int(np.ceil(np.sqrt(sample.size))), 100),\n", " density=True, facecolor='r', alpha=0.75)\n", + "plt.plot(x, analyt, '-b', lw=2)\n", "plt.xlabel(\"random variable\", size=12)\n", "plt.ylabel(\"probability\", size=12)\n", "plt.title(\"Standard normal distribution\", size=12)\n", From 4f97244846702db7c1202b3a69cee13211f5b1d8 Mon Sep 17 00:00:00 2001 From: Albert Akhriev Date: Fri, 12 Apr 2019 16:38:43 +0100 Subject: [PATCH 043/116] minor improvements --- .../finance/generating_random_variates.ipynb | 22 ++++++++++--------- 1 file changed, 12 insertions(+), 10 deletions(-) diff --git a/qiskit/aqua/finance/generating_random_variates.ipynb b/qiskit/aqua/finance/generating_random_variates.ipynb index cb7123ecd..f6ba44fbf 100644 --- a/qiskit/aqua/finance/generating_random_variates.ipynb +++ b/qiskit/aqua/finance/generating_random_variates.ipynb @@ -215,7 +215,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "#### Standard normal distribution" + "#### Normal distribution" ] }, { @@ -224,34 +224,36 @@ "metadata": {}, "outputs": [], "source": [ - "# Create uniform distribution sampler.\n", + "# Create normal distribution sampler.\n", + "mu = 2.4\n", + "sigma = 5.1\n", "start_time = time.time()\n", - "normal = NormalDistribution(glo_num_qubits, backend=glo_backend)\n", + "normal = NormalDistribution(glo_num_qubits, mu=mu, sigma=sigma, backend=glo_backend)\n", "creation_time = time.time() - start_time\n", "\n", - "# Draw a sample from the standard normal distribution.\n", + "# Draw a sample from the normal distribution.\n", "start_time = time.time()\n", "sample = normal.normal_rand_float64(size=4321)\n", "sampling_time = time.time() - start_time\n", "\n", "# Print out some details.\n", - "print(\"Standard normal distribution:\")\n", + "print(\"Normal distribution (mu={:.3f}, sigma={:.3f}):\".format(mu, sigma))\n", "print(\"sample type:\", type(sample), \", element type:\", sample.dtype, \", shape:\", sample.shape)\n", "print(\"sample min: {:.4f}, max: {:.4f}\".format(np.amin(sample), np.amax(sample)))\n", "print(\"time: creation: {:.5f}, sampling: {:.2f}\".format(creation_time, sampling_time))\n", "\n", "# Plotting the distribution.\n", - "x = np.linspace(-4.0, 4.0, 1000)\n", - "analyt = np.exp(-0.5 * x**2) / math.sqrt(2.0 * math.pi)\n", + "x = np.linspace(mu - 4.0 * sigma, mu + 4.0 * sigma, 1000)\n", + "analyt = np.exp(-0.5 * ((x - mu) / sigma)**2) / (sigma * math.sqrt(2.0 * math.pi))\n", "plt.hist(sample.ravel(),\n", " bins=min(int(np.ceil(np.sqrt(sample.size))), 100),\n", " density=True, facecolor='r', alpha=0.75)\n", - "plt.plot(x, analyt, '-b', lw=2)\n", + "plt.plot(x, analyt, '-b', lw=1)\n", "plt.xlabel(\"random variable\", size=12)\n", "plt.ylabel(\"probability\", size=12)\n", - "plt.title(\"Standard normal distribution\", size=12)\n", + "plt.title(\"Normal distribution: empirical vs analytic\", size=12)\n", "plt.grid(True)\n", - "# plt.savefig(\"std_normal_distrib.png\", bbox_inches=\"tight\")\n", + "# plt.savefig(\"normal_distrib.png\", bbox_inches=\"tight\")\n", "plt.show()" ] }, From 9907068ae81723dbe349524772be6ad7b09d7396 Mon Sep 17 00:00:00 2001 From: Jakub Marecek Date: Fri, 12 Apr 2019 16:43:50 +0100 Subject: [PATCH 044/116] Moving the drivers to tutorials --- qiskit/finance/data_providers/__init__.py | 20 + .../data_providers/drivers/__init__.py | 26 + .../data_providers/drivers/_basedriver.py | 154 ++++ .../data_providers/drivers/algorithminput.py | 67 ++ .../drivers/dataondemand/README.md | 14 + .../drivers/dataondemand/__init__.py | 21 + .../dataondemand/dataondemanddriver.py | 156 ++++ .../drivers/exchangedata/README.md | 22 + .../drivers/exchangedata/__init__.py | 21 + .../exchangedata/exchangedatadriver.py | 138 ++++ .../drivers/wikipedia/README.md | 11 + .../drivers/wikipedia/__init__.py | 21 + .../drivers/wikipedia/wikipediadriver.py | 136 ++++ .../finance/data_providers/time_series.ipynb | 112 +++ .../portfolio_diversification.ipynb | 731 ++++++++++++++++++ 15 files changed, 1650 insertions(+) create mode 100644 qiskit/finance/data_providers/__init__.py create mode 100644 qiskit/finance/data_providers/drivers/__init__.py create mode 100644 qiskit/finance/data_providers/drivers/_basedriver.py create mode 100644 qiskit/finance/data_providers/drivers/algorithminput.py create mode 100644 qiskit/finance/data_providers/drivers/dataondemand/README.md create mode 100644 qiskit/finance/data_providers/drivers/dataondemand/__init__.py create mode 100644 qiskit/finance/data_providers/drivers/dataondemand/dataondemanddriver.py create mode 100644 qiskit/finance/data_providers/drivers/exchangedata/README.md create mode 100644 qiskit/finance/data_providers/drivers/exchangedata/__init__.py create mode 100644 qiskit/finance/data_providers/drivers/exchangedata/exchangedatadriver.py create mode 100644 qiskit/finance/data_providers/drivers/wikipedia/README.md create mode 100644 qiskit/finance/data_providers/drivers/wikipedia/__init__.py create mode 100644 qiskit/finance/data_providers/drivers/wikipedia/wikipediadriver.py create mode 100644 qiskit/finance/data_providers/time_series.ipynb create mode 100644 qiskit/finance/optimization/portfolio_diversification.ipynb diff --git a/qiskit/finance/data_providers/__init__.py b/qiskit/finance/data_providers/__init__.py new file mode 100644 index 000000000..300002f49 --- /dev/null +++ b/qiskit/finance/data_providers/__init__.py @@ -0,0 +1,20 @@ +# -*- coding: utf-8 -*- + +# Copyright 2018 IBM. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +# ============================================================================= + +from .drivers import * + +__all__ = ['drivers'] diff --git a/qiskit/finance/data_providers/drivers/__init__.py b/qiskit/finance/data_providers/drivers/__init__.py new file mode 100644 index 000000000..3c737a444 --- /dev/null +++ b/qiskit/finance/data_providers/drivers/__init__.py @@ -0,0 +1,26 @@ +# -*- coding: utf-8 -*- + +# Copyright 2018 IBM. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +# ============================================================================= + +from ._basedriver import BaseDriver, UnitsType +from .dataondemand import DataOnDemandDriver +from .exhangedata import ExchangeDataDriver +from .wikipedia import WikipediaDriver + +__all__ = ['BaseDriver', + 'DataOnDemandDriver', + 'ExchangeDataDriver', + 'WikipediaDriver'] diff --git a/qiskit/finance/data_providers/drivers/_basedriver.py b/qiskit/finance/data_providers/drivers/_basedriver.py new file mode 100644 index 000000000..1993d517a --- /dev/null +++ b/qiskit/finance/data_providers/drivers/_basedriver.py @@ -0,0 +1,154 @@ +# -*- coding: utf-8 -*- + +# Copyright 2018 IBM. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +# ============================================================================= + +""" +This module implements the abstract base class for driver modules +within Qiskit Finance. + +To create add-on driver modules subclass the BaseDriver class in this module. +Doing so requires that the required driver interface is implemented. +""" + +from abc import ABC, abstractmethod +import copy +from qiskit.aqua.parser import JSONSchema +from enum import Enum +import logging + +logger = logging.getLogger(__name__) + + +class DataType(Enum): + DAILYADJUSTED = 'Daily (adj)' + DAILY = 'Daily' + + +class BaseDriver(ABC): + """ + Base class for Drivers. + + This method should initialize the module and its configuration, and + use an exception if a component of the module is available. + + """ + @abstractmethod + def __init__(self): + self.check_driver_valid() + self._configuration = copy.deepcopy(self.CONFIGURATION) + self._work_path = None + + @property + def configuration(self): + """Return driver configuration.""" + return self._configuration + + @classmethod + def init_from_input(cls, section): + """ + Initialize via section dictionary. + + Args: + params (dict): section dictionary + + Returns: + Driver: Driver object + """ + pass + + @staticmethod + def check_driver_valid(): + """Checks if driver is ready for use. Throws an exception if not""" + pass + + def validate(self, args_dict): + schema_dict = self.CONFIGURATION.get('input_schema', None) + if schema_dict is None: + return + + jsonSchema = JSONSchema(schema_dict) + schema_property_names = jsonSchema.get_default_section_names() + json_dict = {} + for property_name in schema_property_names: + if property_name in args_dict: + json_dict[property_name] = args_dict[property_name] + + jsonSchema.validate(json_dict) + + @property + def work_path(self): + return self._work_path + + @work_path.setter + def work_path(self, new_work_path): + self._work_path = new_work_path + + @abstractmethod + def run(self): + pass + + # gets coordinates suitable for plotting + # it does not have to be overridden in non-abstract derived classes. + def get_coordinates(self): + # Coordinates for visualisation purposes + xc = np.zeros([self.n, 1]) + yc = np.zeros([self.n, 1]) + xc = (np.random.rand(self.n) - 0.5) * 1 + yc = (np.random.rand(self.n) - 0.5) * 1 + #for (cnt, s) in enumerate(self.tickers): + #xc[cnt, 1] = self.data[cnt][0] + # yc[cnt, 0] = self.data[cnt][-1] + return xc, yc + + # it does not have to be overridden in non-abstract derived classes. + def get_covariance(self): + if not self._data: return None + self.cov = np.cov(self._data, rowvar = True) + return self.cov + + # it does not have to be overridden in non-abstract derived classes. + def get_similarity_matrix(self): + if not self.data: return None + try: + import fastdtw + for ii in range(0, self._n): + self.rho[ii,ii] = 1. + for jj in range(ii + 1, self.n): + thisRho, path = fastdtw.fastdtw(self._data[ii], self._data[jj]) + self.rho[ii, jj] = thisRho + self.rho[jj, ii] = self.rho[ii, jj] + self.rho = self.rho / np.nanmax(self.rho) + for ii in range(0, self.n): + self.rho[ii,ii] = 1. + except ImportError: + print("This requires fastdtw package.") + return self.rho + + # it does not have to be overridden in non-abstract derived classes. + def plot(self): + #for (cnt, s) in enumerate(self.tickers): + # plot(self.data[cnt], grid = True, label=s) + #plt.legend() + #plt.title("Evolution of the adjusted closing price") + #plt.show() + self.get_covariance() + self.get_similarity_matrix() + print("Top: a similarity measure. Bottom: covariance matrix.") + plt.subplot(211) + plt.imshow(self.rho) + plt.subplot(212) + plt.imshow(self.cov) + plt.show() \ No newline at end of file diff --git a/qiskit/finance/data_providers/drivers/algorithminput.py b/qiskit/finance/data_providers/drivers/algorithminput.py new file mode 100644 index 000000000..b68d5e96b --- /dev/null +++ b/qiskit/finance/data_providers/drivers/algorithminput.py @@ -0,0 +1,67 @@ +# -*- coding: utf-8 -*- + +# Copyright 2018 IBM. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +# ============================================================================= + +from qiskit.aqua import Pluggable +from abc import abstractmethod +import copy +from qiskit.aqua import AquaError + + +class AlgorithmInput(Pluggable): + + _PROBLEM_SET = ['portfoliodiversification', 'portfoliooptimisation'] + + @abstractmethod + def __init__(self): + super().__init__() + if 'problems' not in self.configuration or len(self.configuration['problems']) <= 0: + raise AquaError('Algorithm Input missing or empty configuration problems') + + for problem in self.configuration['problems']: + if problem not in AlgorithmInput._PROBLEM_SET: + raise AquaError('Problem {} not in known problem set {}'.format(problem, AlgorithmInput._PROBLEM_SET)) + + @property + def all_problems(self): + return copy.deepcopy(self._PROBLEM_SET) + + @property + def problems(self): + """ + Gets the set of problems that this input form supports + """ + return self.configuration.problems + + @abstractmethod + def to_params(self): + """ + Convert the derived algorithminput class fields to a dictionary where the values are in a + form that can be saved to json + Returns: + Dictionary of input fields + """ + raise NotImplementedError() + + @abstractmethod + def from_params(self, params): + """ + Load the dictionary into the algorithminput class fields. This dictionary being that as + created by to_params() + Args: + params: A dictionary as originally created by to_params() + """ + raise NotImplementedError() diff --git a/qiskit/finance/data_providers/drivers/dataondemand/README.md b/qiskit/finance/data_providers/drivers/dataondemand/README.md new file mode 100644 index 000000000..836eb7f04 --- /dev/null +++ b/qiskit/finance/data_providers/drivers/dataondemand/README.md @@ -0,0 +1,14 @@ +# Qiskit Finance + +## Stock market data driver for NASDAQ Data on Demand + +NASDAQ is a major vendor of stock market data. It provides data not only for NASDAQ +issues, but also for NYSE etc. + +This driver requires Data on Demand API Token. + +## Example query + +The data are obtained by running a query through the REST API. +``` +``` diff --git a/qiskit/finance/data_providers/drivers/dataondemand/__init__.py b/qiskit/finance/data_providers/drivers/dataondemand/__init__.py new file mode 100644 index 000000000..682ce312d --- /dev/null +++ b/qiskit/finance/data_providers/drivers/dataondemand/__init__.py @@ -0,0 +1,21 @@ +# -*- coding: utf-8 -*- + +# Copyright 2018 IBM. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +# ============================================================================= + +from .dataondemanddriver import DataOnDemandDriver + +__all__ = ['DataOnDemandDriver', + 'StockMarket'] diff --git a/qiskit/finance/data_providers/drivers/dataondemand/dataondemanddriver.py b/qiskit/finance/data_providers/drivers/dataondemand/dataondemanddriver.py new file mode 100644 index 000000000..6ef8e50d0 --- /dev/null +++ b/qiskit/finance/data_providers/drivers/dataondemand/dataondemanddriver.py @@ -0,0 +1,156 @@ +# -*- coding: utf-8 -*- + +# Copyright 2018 IBM. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +# ============================================================================= + +from qiskit.aqua.drivers import BaseDriver, UnitsType +import importlib +from enum import Enum +import logging + +logger = logging.getLogger(__name__) + + +class StockMarket(Enum): + NASDAQ = 'NASDAQ' + NYSE = 'NYSE' + +class DataOnDemandDriver(BaseDriver): + """Python implementation of an NASDAQ Data on Demand driver.""" + + CONFIGURATION = { + "name": "DOD", + "description": "NASDAQ Data on Demand Driver", + "input_schema": { + "$schema": "http://json-schema.org/schema#", + "id": "dod_schema", + "type": "object", + "properties": { + STOCKMARKET: { + "type": "string", + "default": StockMarket.NASDAQ.value, + "oneOf": [ + {"enum": [ + StockMarket.NASDAQ.value, + StockMarket.NYSE.value, + ]} + ] + }, + DATATYPE: { + "type": "string", + "default": DataType.DAILYADJUSTED.value, + "oneOf": [ + {"enum": [ + DataType.DAILYADJUSTED.value, + DataType.DAILY.value, + DataType.BID.value, + DataType.ASK.value, + ]} + ] + }, + }, + } + } + + def __init__(self, + token, + tickers, + stockmarket = StockMarket.NASDAQ, + start = datetime.datetime(2016,1,1), + end = datetime.datetime(2016,1,30)): + """ + Initializer + Args: + token (str): quandl access token + tickers (str or list): tickers + stockmarket (StockMarket): LONDON, EURONEXT, or SINGAPORE + """ + if not isinstance(atoms, list) and not isinstance(atoms, str): + raise QiskitFinanceError("Invalid atom input for DOD Driver '{}'".format(atoms)) + + if isinstance(tickers, list): + self._tickers = ';'.join(tickers) + else: + self._tickers = tickers.replace('\n', ';') + self._n = len(self._tickers.split(";")) + + self.validate(locals()) + super().__init__() + self._stockmarket = stockmarket # .value? + self._token = token + self._start = start + self._end = end + + @staticmethod + def check_driver_valid(): + err_msg = 'quandl is not installed.' + try: + spec = importlib.util.find_spec('quandl') + if spec is not None: + return + except Exception as e: + logger.debug('quandl check error {}'.format(str(e))) + raise QiskitFinanceError(err_msg) from e + + raise QiskitFinanceError(err_msg) + + @classmethod + def init_from_input(cls, section): + """ + Initialize via section dictionary. + + Args: + params (dict): section dictionary + + Returns: + Driver: Driver object + """ + if section is None or not isinstance(section, dict): + raise QiskitFinanceError('Invalid or missing section {}'.format(section)) + + params = section + kwargs = {} + #for k, v in params.items(): + # if k == ExchangeDataDriver. ...: v = UnitsType(v) + # kwargs[k] = v + logger.debug('init_from_input: {}'.format(kwargs)) + return cls(**kwargs) + + def run(self): + import re + import urllib + import urllib2 + import json + url = 'https://dataondemand.nasdaq.com/api/v1/quotes' + self._data = [] + for ticker in self._tickers: + values = {'_Token' : self._token, + 'symbols' : [ticker] + 'start' : start.strftime("%Y-%m-%d'T'%H:%M:%S.%f'Z'") , + 'end' : end.strftime("%Y-%m-%d'T'%H:%M:%S.%f'Z'") , + 'next_cursor': 0 + #'start' : start.strftime("%m/%d/%Y %H:%M:%S.%f") , + #'end' : end.strftime("%m/%d/%Y %H:%M:%S.%f") , + } + request_parameters = urllib.urlencode(values) + req = urllib2.Request(url, request_parameters) + try: + response = urllib2.urlopen(req) + quotes = json.loads(response)["quotes"] + priceEvolution = [] + for q in quotes: priceEvolution.append(q["ask_price"]) + self._data.append(priceEvolution) + except: + raise QiskitFinanceError('Accessing Qiskit failed') diff --git a/qiskit/finance/data_providers/drivers/exchangedata/README.md b/qiskit/finance/data_providers/drivers/exchangedata/README.md new file mode 100644 index 000000000..31ec5e883 --- /dev/null +++ b/qiskit/finance/data_providers/drivers/exchangedata/README.md @@ -0,0 +1,22 @@ +# Qiskit Finance + +## Stock market data driver for Exchange Data International + +Exchange Data International is a major vendor of stock-market data. See +https://www.exchange-data.com/about_us.php#edi + +For samples of the data, please see: +https://www.quandl.com/data/XSES-Singapore-Exchange-Prices +https://www.quandl.com/data/XBER-Berlin-Stock-Exchange-Prices +https://www.quandl.com/data/XPAR-Euronext-Paris-Stock-Prices/documentation + +This driver requires Quandl API Token. + +## Example query + +The data are obtained by running a query through quandl. See: +https://docs.quandl.com/docs/parameters-2#section-times-series-parameters +for details. + +``` +``` diff --git a/qiskit/finance/data_providers/drivers/exchangedata/__init__.py b/qiskit/finance/data_providers/drivers/exchangedata/__init__.py new file mode 100644 index 000000000..26e0bf76f --- /dev/null +++ b/qiskit/finance/data_providers/drivers/exchangedata/__init__.py @@ -0,0 +1,21 @@ +# -*- coding: utf-8 -*- + +# Copyright 2018 IBM. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +# ============================================================================= + +from .exchangedatadriver import ExchangeDataDriver, StockMarket + +__all__ = ['ExchangeDataDriver', + 'StockMarket'] diff --git a/qiskit/finance/data_providers/drivers/exchangedata/exchangedatadriver.py b/qiskit/finance/data_providers/drivers/exchangedata/exchangedatadriver.py new file mode 100644 index 000000000..b2458b165 --- /dev/null +++ b/qiskit/finance/data_providers/drivers/exchangedata/exchangedatadriver.py @@ -0,0 +1,138 @@ +# -*- coding: utf-8 -*- + +# Copyright 2018 IBM. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +# ============================================================================= + +from qiskit.aqua.drivers import BaseDriver, UnitsType +import importlib +from enum import Enum +import logging + +logger = logging.getLogger(__name__) + + +class StockMarket(Enum): + LONDON = 'XLON' + EURONEXT = 'XPAR' + SINGAPORE = 'XSES' + +class ExchangeDataDriver(BaseDriver): + """Python implementation of an Exchange Data driver.""" + + CONFIGURATION = { + "name": "EDI", + "description": "Exchange Data International Driver", + "input_schema": { + "$schema": "http://json-schema.org/schema#", + "id": "edi_schema", + "type": "object", + "properties": { + STOCKMARKET: { + "type": "string", + "default": StockMarket.LONDON.value, + "oneOf": [ + {"enum": [ + StockMarket.LONDON.value, + StockMarket.EURONEXT.value, + StockMarket.SINGAPORE.value, + ]} + ] + }, + DATATYPE: { + "type": "string", + "default": DataType.LONDON.value, + "oneOf": [ + {"enum": [ + DataType.DAILYADJUSTED.value, + DataType.DAILY.value, + ]} + ] + }, + }, + } + } + + def __init__(self, + token, + tickers, + stockmarket = StockMarket.LONDON, + start = datetime.datetime(2016,1,1), + end = datetime.datetime(2016,1,30)): + """ + Initializer + Args: + token (str): quandl access token + tickers (str or list): tickers + stockmarket (StockMarket): LONDON, EURONEXT, or SINGAPORE + """ + if not isinstance(atoms, list) and not isinstance(atoms, str): + raise QiskitFinanceError("Invalid atom input for PYQUANTE Driver '{}'".format(atoms)) + + if isinstance(tickers, list): + tickers = ';'.join(tickers) + else: + tickers = tickers.replace('\n', ';') + self._n = len(self._tickers.split(";")) + + self.validate(locals()) + super().__init__() + self._stockmarket = stockmarket # .value? + self._token = token + self._tickers = tickers + self._start = start + self._end = end + + @staticmethod + def check_driver_valid(): + err_msg = 'quandl is not installed.' + try: + spec = importlib.util.find_spec('quandl') + if spec is not None: + return + except Exception as e: + logger.debug('quandl check error {}'.format(str(e))) + raise QiskitFinanceError(err_msg) from e + + raise QiskitFinanceError(err_msg) + + @classmethod + def init_from_input(cls, section): + """ + Initialize via section dictionary. + + Args: + params (dict): section dictionary + + Returns: + Driver: Driver object + """ + if section is None or not isinstance(section, dict): + raise QiskitFinanceError('Invalid or missing section {}'.format(section)) + + params = section + kwargs = {} + #for k, v in params.items(): + # if k == ExchangeDataDriver. ...: v = UnitsType(v) + # kwargs[k] = v + logger.debug('init_from_input: {}'.format(kwargs)) + return cls(**kwargs) + + def run(self): + import quandl + quandl.ApiConfig.api_key = self._token + quandl.ApiConfig.api_version = '2015-04-09' + for (cnt, s) in enumerate(self._tickers): + d = quandl.get(self._stockmarket + "/" + s, start_date=self._start, end_date=self._end) + self._data.append(d["close"]) diff --git a/qiskit/finance/data_providers/drivers/wikipedia/README.md b/qiskit/finance/data_providers/drivers/wikipedia/README.md new file mode 100644 index 000000000..f5dc77c2f --- /dev/null +++ b/qiskit/finance/data_providers/drivers/wikipedia/README.md @@ -0,0 +1,11 @@ +# Qiskit Finance + +## Stock market data driver for Wikipedia + +Wikipedia contains stockmarket data, that are rather reliable up until 2018. + +## Example query + +The data are obtained by running a query through quandl. +``` +``` diff --git a/qiskit/finance/data_providers/drivers/wikipedia/__init__.py b/qiskit/finance/data_providers/drivers/wikipedia/__init__.py new file mode 100644 index 000000000..7324d1dd5 --- /dev/null +++ b/qiskit/finance/data_providers/drivers/wikipedia/__init__.py @@ -0,0 +1,21 @@ +# -*- coding: utf-8 -*- + +# Copyright 2018 IBM. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +# ============================================================================= + +from .wikipediadriver import WikipediaDriver, StockMarket + +__all__ = ['WikipediaDriver', + 'StockMarket'] diff --git a/qiskit/finance/data_providers/drivers/wikipedia/wikipediadriver.py b/qiskit/finance/data_providers/drivers/wikipedia/wikipediadriver.py new file mode 100644 index 000000000..e3900cd20 --- /dev/null +++ b/qiskit/finance/data_providers/drivers/wikipedia/wikipediadriver.py @@ -0,0 +1,136 @@ +# -*- coding: utf-8 -*- + +# Copyright 2018 IBM. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +# ============================================================================= + +from qiskit.aqua.drivers import BaseDriver, UnitsType +import importlib +from enum import Enum +import logging + +logger = logging.getLogger(__name__) + + +class StockMarket(Enum): + NASDAQ = 'NASDAQ' + NYSE = 'NYSE' + +class WikipediaDriver(BaseDriver): + """Python implementation of a Wikipedia driver.""" + + CONFIGURATION = { + "name": "WIKI", + "description": "Wikipedia Driver", + "input_schema": { + "$schema": "http://json-schema.org/schema#", + "id": "edi_schema", + "type": "object", + "properties": { + STOCKMARKET: { + "type": "string", + "default": StockMarket.NASDAQ.value, + "oneOf": [ + {"enum": [ + StockMarket.NASDAQ.value, + StockMarket.NYSE.value, + ]} + ] + }, + DATATYPE: { + "type": "string", + "default": DataType.DAILYADJUSTED.value, + "oneOf": [ + {"enum": [ + DataType.DAILYADJUSTED.value, + DataType.DAILY.value, + ]} + ] + }, + }, + } + } + + def __init__(self, + token = "", + tickers, + stockmarket = StockMarket.LONDON, + start = datetime.datetime(2016,1,1), + end = datetime.datetime(2016,1,30)): + """ + Initializer + Args: + token (str): quandl access token, which is not needed, strictly speaking + tickers (str or list): tickers + stockmarket (StockMarket): NASDAQ, NYSE + """ + if not isinstance(atoms, list) and not isinstance(atoms, str): + raise QiskitFinanceError("Invalid atom input for Wikipedia Driver '{}'".format(atoms)) + + if isinstance(tickers, list): + tickers = ';'.join(tickers) + else: + tickers = tickers.replace('\n', ';') + self._n = len(self._tickers.split(";")) + + self.validate(locals()) + super().__init__() + self._stockmarket = stockmarket # .value? + self._token = token + self._tickers = tickers + self._start = start + self._end = end + + @staticmethod + def check_driver_valid(): + err_msg = 'quandl is not installed.' + try: + spec = importlib.util.find_spec('quandl') + if spec is not None: + return + except Exception as e: + logger.debug('quandl check error {}'.format(str(e))) + raise QiskitFinanceError(err_msg) from e + + raise QiskitFinanceError(err_msg) + + @classmethod + def init_from_input(cls, section): + """ + Initialize via section dictionary. + + Args: + params (dict): section dictionary + + Returns: + Driver: Driver object + """ + if section is None or not isinstance(section, dict): + raise QiskitFinanceError('Invalid or missing section {}'.format(section)) + + params = section + kwargs = {} + #for k, v in params.items(): + # if k == ExchangeDataDriver. ...: v = UnitsType(v) + # kwargs[k] = v + logger.debug('init_from_input: {}'.format(kwargs)) + return cls(**kwargs) + + def run(self): + import quandl + quandl.ApiConfig.api_key = self._token + quandl.ApiConfig.api_version = '2015-04-09' + for (cnt, s) in enumerate(self._tickers): + d = quandl.get("WIKI/" + s, start_date=self._start, end_date=self._end) + self._data.append(d["close"]) diff --git a/qiskit/finance/data_providers/time_series.ipynb b/qiskit/finance/data_providers/time_series.ipynb new file mode 100644 index 000000000..5938dcdb5 --- /dev/null +++ b/qiskit/finance/data_providers/time_series.ipynb @@ -0,0 +1,112 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# _*Qiskit Finance: Loading Time Series Data*_\n", + "\n", + "The latest version of this notebook is available on https://github.com/qiskit/qiskit-tutorial.\n", + "\n", + "***\n", + "### Contributors\n", + "Jakub Marecek[1]\n", + "\n", + "### Affiliation\n", + "- [1]IBMQ" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Introduction\n", + "Across many problems in finance, one starts with time series. Here, we showcase how to download the time series from a number of common providers." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "['/Users/jmarecek/git/qiskit-tutorials/qiskit/aqua/artificial_intelligence', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python37.zip', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/lib-dynload', '', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/sympy-1.3-py3.7.egg', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/scipy-1.2.1-py3.7-macosx-10.7-x86_64.egg', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/psutil-5.6.1-py3.7-macosx-10.7-x86_64.egg', 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\u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msys\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpath\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mdrivers\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mAer\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'drivers'" + ] + } + ], + "source": [ + "import os, sys\n", + "sys.path.append(os.getcwd())\n", + "print(sys.path)\n", + "from drivers import *\n", + "\n", + "from qiskit import Aer\n", + "from qiskit_aqua import run_algorithm, QuantumInstance\n", + "\n", + "# setup aqua logging\n", + "import logging\n", + "from qiskit_aqua import set_aqua_logging" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### [Optional] Setup token to access recent, fine-grained time-series\n", + "\n", + "If you would like to download professional data, you will have to set-up a token with one of the major providers.\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [conda env:localqiskit]", + "language": "python", + "name": "conda-env-localqiskit-py" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.2" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/qiskit/finance/optimization/portfolio_diversification.ipynb b/qiskit/finance/optimization/portfolio_diversification.ipynb new file mode 100644 index 000000000..bcdcdca32 --- /dev/null +++ b/qiskit/finance/optimization/portfolio_diversification.ipynb @@ -0,0 +1,731 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Portfolio diversification: classical and quantum solutions\n", + "\n", + "## Contributors\n", + "Andrea Simonetto, Jakub Marecek, Martin Mevissen; IBM Research -- Ireland\n", + "\n", + "## Introduction \n", + "\n", + "In asset management, there are broadly two approaches: active and passive investment management. Within passive investment management, there are index-tracking funds and there are approaches based on portfolio diversification, which aim at representing a portfolio with large number of assets by a smaller number of representative stocks.\n", + "This notebook illustrates a portfolio diversification problem, which has recently become popular for two reasons:\n", + "1. it makes it possible to mimick the performance of an index (or a similarly large set of assets) with a limited budget, at limited transaction costs. That is: traditional index-tracking may purchase all assets in the index, ideally with the same weights as in the index. This may be impractical for a number of reasons: the total of even a single round lot per asset may amount to more than the assets under management, the large scale of the index-tracking problem with integrality constraints may render the optimisation problem difficult, and the transaction costs of the frequent rebalancing to adjust the positions to the weights in the index may render the approach expensive. Thus, a popular approach is to select a portfolio of $q$ assets that represent the market with $n$ assets, where $q$ is significantly smaller than $n$, but where the portfolio replicates the behaviour of the underlying market. To determine how to group assets into $q$ clusters and how to determine which $q$ assets should represent the $q$ clusters amounts to solving a large-scale optimization problem. In the following we describe the mathematical model for the portfolio diversification problem as introduced in [Cornuejols & Tutuncu, 2006] \n", + "2. it allows for similarity measures between time-series beyond the covariance matrix. Notice that traditionally, modern portfolio theory considers the covariance matrix as measure of similarity between the assets. As such, however, covariance matrix is imperfect. Consider, for instance, a company listed both in London and New York. Although both listings should be very similar, only parts of the time series of the prices of the two listings will overlap, because of the partial overlap of the times the markets open. Instead of covariance, one ca consider, for example, dynamic time warping of [Berndt and Clifford, 1994] as a measure of similarity between two time series, which allows for the fact that for some time periods, the data are captured by only one of the time series, while for others, both time series exhibit the similarity due to the parallel evolution of the stock price.\n", + "\n", + "The overall workflow we demonstrate comprises:\n", + "\n", + "1. pick the ground set of assets. In our case, this is a small number of US stocks.\n", + "\n", + "2. load the time series capturing the evolution of the prices of assets. In our case, this is an simplistic load of daily stock-price data from Wikipedia, whereas in a real asset management, this may come from a Reuters, Bloomberg, or similar at a much higher frequency.\n", + "\n", + "3. compute the pair-wise similarity among the time series. In our case, we run a linear-time approximation of the dynamic time warping, still on the classical computer.\n", + "\n", + "4. compute the actual portfolio of $q$ representative assets, based on the similarity measure. This step is run twice, actually. First, we obtain a reference value by a run of an IBM solver (CPLEX) on the classical computer. Second, we run an alternative, hybrid algorithm partly on the quantum computer.\n", + "\n", + "5. visualisation of the results. In our case, this is again a simplistic plot.\n", + "\n", + "In the following, we first explain the model used in (4) above, before we proceed with the installation of the pre-requisites and the data loading.\n", + "\n", + "\n", + "## The Model\n", + "\n", + "As discussed in [Cornuejols & Tutuncu, 2006], we describe a mathematical model that clusters assets into groups of similar ones and selects one representative asset from each group to be included in the index fund portfolio. The model is based on the following data, which we will discuss in more detail later:\n", + "\n", + "$$\n", + "\\rho_{ij} = \\textrm{similarity}\\, \\textrm{between}\\, \\textrm{stock}\\, i \\, \\textrm{and}\\, \\textrm{stock}\\, j.\n", + "$$\n", + "\n", + "For example, $\\rho_{ii} = 1$, $\\rho_{ij} \\leq 1$ for $i \\neq j$ and $\\rho_{ij}$ is larger for more similar stocks. An example of this is the correlation between the returns of stocks $i$ and $j$. But one could choose other similarity indices $\\rho_{ij}$.\n", + "\n", + "The problem that we are interested in solving is:\n", + "\n", + "$$\n", + "(M) \\quad f = \\max_{x_{ij}, y_{j}} \\,\\, \\sum_{i=1}^n \\sum_{j=1}^n \\rho_{ij} x_{ij}\n", + "$$\n", + "\n", + "subject to the clustering constraint:\n", + "\n", + "$$\n", + "\\sum_{j=1}^n y_j = q,\n", + "$$\n", + "\n", + "to consistency constraints:\n", + "\n", + "$$\n", + "\\sum_{j=1}^n x_{ij} = 1, \\,\\textrm{ for }\\, i = 1,\\ldots, n,\n", + "\\quad x_{ij} \\leq y_j,\\,\\textrm{ for }\\, i = 1,\\ldots, n; \\, j = 1,\\ldots, n,\n", + "\\quad x_{jj} = y_j,\\,\\textrm{ for }\\, j = 1,\\ldots, n,\n", + "$$\n", + "\n", + "and integral constraints:\n", + "\n", + "$$\n", + "\\quad x_{ij}, y_j \\in\\{0,1\\}, \\,\\textrm{ for }\\, i = 1,\\ldots, n; \\, j = 1,\\ldots, n.\n", + "$$\n", + "\n", + "The variables $y_j$ describe which stocks $j$ are in the index fund ($y_j = 1$ if $j$ is selected in the fund, $0$ otherwise). For each stock $i = 1,\\dots,n$, the variable $x_{ij}$ indicates which stock $j$ in the index fund is most similar to $i$ ($x_{ij} = 1$ if $j$ is the most similar stock in the index fund, $0$ otherwise).\n", + "\n", + "The first constraint selects $q$ stocks in the fund. The second constraint imposes that each stock $i$ has exactly one representative stock $j$ in the fund. The third and fourth constraints guarantee that stock $i$ can be represented by stock $j$ only if $j$ is in the fund. The objective of the model maximizes the similarity between the $n$ stocks and their representatives in the fund. Different cost functions can also be considered. \n", + "\n", + "Let us concatenate the decision variables in one vector \n", + "\n", + "$$\n", + "{\\bf z} = [x_{11},x_{12},\\ldots,x_{11}, x_{22},\\ldots,x_{nn}, y_{1},\\ldots,y_{n}],\n", + "$$\n", + "\n", + "whose dimension is ${\\bf z} \\in \\{0,1\\}^N$, with $N = n (n+1)$ and denote the optimal solution with ${\\bf z}^*$, and the optimal cost $f^*$. \n", + "\n", + "\n", + "## A Hybrid Approach\n", + "\n", + "Here, we demonstrate an approach that combines classical and quantum computing steps, following the quantum approximate optimization approach of Farhi, Goldstone, and Gutman (2014). \n", + "\n", + "### Construct a binary polynomial optimization\n", + "\n", + "From $(M)$ one can construct a binary polynomial optimization with equality constraints only, by substituting the $x_{ij} \\leq y_j$ inequality constraints with the equivalent equality constraints $x_{ij} (1- y_j) = 0$. Then the problem becomes:\n", + "\n", + "$$\n", + "(BPO) \\quad f = \\max_{x_{ij}, y_{j}} \\,\\, \\sum_{i=1}^n \\sum_{j=1}^n \\rho_{ij} x_{ij}\n", + "$$\n", + "\n", + "subject to the clustering constrain, the integral constraints, and the following modified consistency constraints:\n", + "\n", + "$$\\sum_{j=1}^n x_{ij} = 1, \\,\\textrm{ for }\\, i = 1,\\ldots, n,$$\n", + "$$\\quad x_{ij} (1- y_j) = 0,\\,\\textrm{ for }\\, i = 1,\\ldots, n; \\, j = 1,\\ldots, n,$$\n", + "$$\\quad x_{jj} = y_j,\\,\\textrm{ for }\\, j = 1,\\ldots, n.$$\n", + "\n", + "### Construct the Ising Hamiltonian\n", + "\n", + "We can now construct the Ising Hamiltonian by penalty methods (introducting a penalty coefficient $A$ for each equality constraint) as\n", + "\n", + "$$\n", + "(IH) \\quad H = \\sum_{i=1}^n \\sum_{j=1}^n \\rho_{ij} x_{ij} + A\\Big( \\sum_{j=1}^n y_j - q\\Big)^2 + \\sum_{i=1}^n A\\Big( \\sum_{j=1}^n x_{ij} - 1\\Big)^2 + \\sum_{j=1}^n A (x_{jj}-y_j)^2 +\\sum_{i=1}^n \\sum_{j=1}^n A \\left(x_{ij} (1- y_j)\\right).\n", + "$$\n", + "\n", + "### From Hamiltonian to QP formulation \n", + "\n", + "In the vector ${\\bf z}$, the Ising Hamiltonian elements can be rewritten as follows,\n", + "\n", + "First term:\n", + "\n", + "$$\n", + "\\sum_{i=1}^n \\sum_{j=1}^n \\rho_{ij} x_{ij} = [\\rho_{11},\\rho_{12},\\ldots,\\rho_{11}, \\rho_{22},\\ldots,\\rho_{nn}|{\\bf 0}_n ]{\\bf z} =: {\\bf c}_0^T {\\bf z}\n", + "$$\n", + "\n", + "Second term:\n", + "\n", + "$$\n", + "A\\Big( \\sum_{j=1}^n y_j - q\\Big)^2 = A \\Big(\\sum_{j=1}^n y_j\\Big)^2 - 2 A \\sum_{j=1}^n y_j + A q^2 = A {\\bf z}^T \\left[\\begin{array}{c}{\\bf 0}_{n^2} \\\\ \\hline {\\bf 1}_n \\end{array}\\right]\\left[\\begin{array}{cc}{\\bf 0}_{n^2} | {\\bf 1}_n \\end{array}\\right]{\\bf z} - 2 A q [{\\bf 0}_{n^2}|{\\bf 1}_n]{\\bf z} + A q^2 =: {\\bf z}^T {\\bf Q}_0 {\\bf z} + {\\bf c}_1^T {\\bf z} + r_0\n", + "$$\n", + "\n", + "Third term:\n", + "\n", + "$$\n", + "\\sum_{i=1}^n A\\Big( \\sum_{j=1}^n x_{ij} - 1\\Big)^2 = A\\sum_{i=1}^n \\Big(\\sum_{j=1}^n x_{ij}\\Big)^2 - 2 A \\sum_{i=1}^n\\sum_{j=1}^n x_{ij} + n A = \\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad $$\n", + "\n", + "which is equivalent to: \n", + "\n", + "$$\n", + "\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad = A {\\bf z}^T \\left(\\sum_{i=1}^n \\left[\\begin{array}{c}{\\bf 0}_{n(i-1)} \\\\ {\\bf 1}_n \\\\ {\\bf 0}_{n(n-i)} \\\\ \\hline {\\bf 0}_{n} \\end{array}\\right]\\left[\\begin{array}{cccc}{\\bf 0}_{n(i-1)} & {\\bf 1}_n & {\\bf 0}_{n(n-i)} & | {\\bf 0}_{n} \\end{array}\\right]\\right){\\bf z} - 2 A [{\\bf 1}_{n^2}|{\\bf 0}_n]{\\bf z} + n A =: {\\bf z}^T {\\bf Q}_1 {\\bf z} + {\\bf c}_2^T {\\bf z} + r_1\n", + "$$\n", + "\n", + "Fourth term:\n", + "\n", + "$$\n", + "A \\sum_{j=1}^n (x_{jj}-y_j)^2 = A {\\bf z}^T \\left(\\sum_{j=0}^{n-1} \\left[\\begin{array}{c}{\\bf 0}_{nj + j} \\\\ 1 \\\\ {\\bf 0}_{n^2-(nj+j+1)} \\\\ \\hline {\\bf 0}_{j} \\\\ -1 \\\\ {\\bf 0}_{n-j-1} \\end{array}\\right]\\left[\\begin{array}{cccccc}{\\bf 0}_{nj + j} & 1 & {\\bf 0}_{n^2-(nj+j+1)} & | {\\bf 0}_{j} & -1 & {\\bf 0}_{n-j-1} \\end{array}\\right]\\right){\\bf z} = A {\\bf z}^T {\\bf Q}_2 {\\bf z}\n", + "$$\n", + "\n", + "Fifth term:\n", + "\n", + "$$\n", + "\\sum_{i=1}^n \\sum_{j=1}^n A \\left(x_{ij} (1- y_j)\\right) = A [{\\bf 1}_{n^2}|{\\bf 0}_n]{\\bf z} + A {\\bf z}^T \\left( \\sum_{i=1}^n \\sum_{j=1}^n \\left[\\begin{array}{ccc|c} & & & \\\\ & {\\bf 0}_{n^2\\times n^2} & & -1/2_{(ij,j)} \\\\ & & & \\\\ \\hline & -1/2_{(j, ij)} & & {\\bf 0}_{n} \\end{array}\\right] \\right) {\\bf z} =: {\\bf z}^T {\\bf Q}_3 {\\bf z} + {\\bf c}_3^T {\\bf z}\n", + "$$\n", + "\n", + "Therefore, the formulation becomes,\n", + "\n", + "$$\n", + "(IH-QP)\\quad \\max_{{\\bf z}\\in\\{0,1\\}^{n(n+1)}} \\, {\\bf z}^T ({\\bf Q}_0+{\\bf Q}_1+ {\\bf Q}_2 + {\\bf Q}_3 ){\\bf z} + ({\\bf c}_0+{\\bf c}_1+{\\bf c}_2+{\\bf c}_3)^T {\\bf z} +r_0+r_1+r_2$$\n", + "\n", + "which can be passed to variational quantum eigensolver. \n", + "\n", + "\n", + "\n", + "## References\n", + "\n", + "[1] G. Cornuejols, M. L. Fisher, and G. L. Nemhauser, *Location of bank accounts to optimize float: an analytical study of exact and approximate algorithms*, Management Science, vol. 23(8), 1997\n", + "\n", + "[2] E. Farhi, J. Goldstone, S. Gutmann e-print arXiv 1411.4028, 2014\n", + "\n", + "[3] G. Cornuejols and R. Tutuncu, *Optimization methods in finance*, 2006\n", + "\n", + "[4] DJ. Berndt and J. Clifford, *Using dynamic time warping to find patterns in time series*. In KDD workshop 1994 (Vol. 10, No. 16, pp. 359-370).\n", + "\n", + "[5] https://github.com/Qiskit/qiskit-tutorial/blob/master/qiskit/aqua/optimization/maxcut_and_tsp.ipynb" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The Implementation\n", + "\n", + "If everything has been installed, the following should run without any errors. \n", + "If there are errors, please refer to Installation.ipynb for details." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "localqiskit\n", + "/Users/jmarecek/anaconda3/envs/localqiskit/bin/python\n" + ] + } + ], + "source": [ + "import os\n", + "print(os.environ['CONDA_DEFAULT_ENV'])\n", + "#!source activate localqiskit\n", + "#!conda list\n", + "#help(\"modules\")\n", + "# If you get errors, you can install from here using:\n", + "#!conda install -y --name localqiskit quandl\n", + "#!conda install -y -c bioconda --name localqiskit fastdtw\n", + "print(sys.executable)\n", + "\n", + "# Import requisite modules\n", + "import math\n", + "import operator\n", + "import logging\n", + "import datetime\n", + "import sys\n", + "import warnings\n", + "warnings.filterwarnings(\"error\") \n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Import Qiskit packages\n", + "warnings.filterwarnings('ignore')\n", + "import qiskit \n", + "from qiskit import BasicAer\n", + "from qiskit.aqua import QuantumInstance\n", + "from qiskit.aqua import Operator, run_algorithm\n", + "from qiskit.aqua.input import EnergyInput\n", + "from qiskit.aqua.translators.ising import portfolio\n", + "from qiskit.aqua.algorithms import VQE, QAOA, ExactEigensolver\n", + "from qiskit.aqua.components.optimizers import COBYLA\n", + "from qiskit.aqua.components.variational_forms import RY\n", + "# setup aqua logging\n", + "from qiskit.aqua._logging import set_logging_config, build_logging_config\n", + "# set_logging_config(build_logging_config(logging.DEBUG)) # choose INFO, DEBUG to see the log\n", + "\n", + "from qiskit.aqua.translators.ising import portfoliodiv" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We then initialize the variables" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [], + "source": [ + "# Initialize the problem by defining the parameters\n", + "\n", + "n = 2 # Number of inner variables\n", + "q = 1 # Number of clusters, q less or equal than n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We define get data either by randomly placing the assets in a 2-D plane and computing the distance between them (the closer they are in this plane, the more similar they are), or by actually downloading stock-market price data and computing the dynamic time warping distance and normalising it to (0,1]. Either way, we obtain the `rho` matrix. " + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "# The code for generating a random rho or obtain stock-market data\n", + "\n", + "from qiskit.aqua.input.portfoliodata import *" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[-1. -0.83591861]\n", + " [-0.83591861 -1. ]]\n" + ] + } + ], + "source": [ + "# Initialize the problem by randomly generating the similarity matrix rho\n", + "\n", + "data = RandomData(n)\n", + "xc,yc,rho = data.generate_instance()\n", + "try:\n", + " data = RealData(n, plots=True)\n", + " #data = RealData(n, plots=False)\n", + "except:\n", + " print(\"Cannot load real data, possibly due to issues with pandas.\")\n", + "print(rho)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Classical solution using IBM CPLEX\n", + "\n", + "For a classical solution, we use IBM CPLEX. CPLEX is able to find the exact solution of this problem. We first define a ClassicalOptimizer class that encodes the problem in a way that CPLEX can solve, and then instantiate the class and solve it. \n" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": {}, + "outputs": [], + "source": [ + "class ClassicalOptimizer:\n", + " def __init__(self, rho, n, q):\n", + "\n", + " self.rho = rho\n", + " self.n = n # number of inner variables\n", + " self.q = q # number of required selection\n", + "\n", + " def compute_allowed_combinations(self):\n", + " f = math.factorial\n", + " return int(f(self.n) / f(self.q) / f(self.n - self.q))\n", + "\n", + " def cplex_solution(self):\n", + "\n", + " # refactoring\n", + " rho = self.rho\n", + " n = self.n\n", + " q = self.q\n", + "\n", + " my_obj = list(rho.reshape(1, n ** 2)[0]) + [0. for x in range(0, n)]\n", + " my_ub = [1 for x in range(0, n ** 2 + n)]\n", + " my_lb = [0 for x in range(0, n ** 2 + n)]\n", + " my_ctype = \"\".join(['I' for x in range(0, n ** 2 + n)])\n", + "\n", + " my_rhs = [q] + [1 for x in range (0, n)] +[0 for x in range (0, n)] + [0.1 for x in range(0, n ** 2)]\n", + " my_sense = \"\".join(['E' for x in range(0, 1+n)]) + \"\".join(['E' for x in range(0, n)]) + \"\".join(\n", + " ['L' for x in range(0, n ** 2)])\n", + "\n", + " try:\n", + " my_prob = cplex.Cplex()\n", + " self.populatebyrow(my_prob, my_obj, my_ub, my_lb, my_ctype, my_sense, my_rhs)\n", + "\n", + " my_prob.solve()\n", + "\n", + " except CplexError as exc:\n", + " print(exc)\n", + " return\n", + "\n", + " x = my_prob.solution.get_values()\n", + " x = np.array(x)\n", + " cost = my_prob.solution.get_objective_value()\n", + "\n", + " return x, cost\n", + "\n", + " def populatebyrow(self, prob, my_obj, my_ub, my_lb, my_ctype, my_sense, my_rhs):\n", + "\n", + " n = self.n\n", + "\n", + " prob.objective.set_sense(prob.objective.sense.minimize)\n", + " prob.variables.add(obj=my_obj, lb=my_lb, ub=my_ub, types=my_ctype)\n", + "\n", + " prob.set_log_stream(None)\n", + " prob.set_error_stream(None)\n", + " prob.set_warning_stream(None)\n", + " prob.set_results_stream(None)\n", + "\n", + " rows = []\n", + " col = [x for x in range(n**2, n**2+n)]\n", + " coef = [1 for x in range(0, n)]\n", + " rows.append([col, coef])\n", + "\n", + " for ii in range(0, n):\n", + " col = [x for x in range(0+n*ii, n+n*ii)]\n", + " coef = [1 for x in range(0, n)]\n", + "\n", + " rows.append([col, coef])\n", + "\n", + " for ii in range(0, n):\n", + " col = [ii * n + ii, n ** 2 + ii]\n", + " coef = [1, -1]\n", + " rows.append([col, coef])\n", + "\n", + " for ii in range(0, n):\n", + " for jj in range(0, n):\n", + " col = [ii*n + jj, n ** 2 + jj]\n", + " coef = [1, -1]\n", + "\n", + " rows.append([col, coef])\n", + " \n", + " prob.linear_constraints.add(lin_expr=rows, senses=my_sense, rhs=my_rhs)" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Number of feasible combinations= 2\n", + "Total number of combinations= 64\n" + ] + } + ], + "source": [ + "# Instantiate the classical optimizer class\n", + "classical_optimizer = ClassicalOptimizer(rho,n,q)\n", + "\n", + "# Compute the number of feasible solutions:\n", + "print('Number of feasible combinations= ' + str(classical_optimizer.compute_allowed_combinations()))\n", + "\n", + "# Compute the total number of possible combinations (feasible + unfeasible)\n", + "print('Total number of combinations= ' + str(2 ** (n*(n+1))))" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": {}, + "outputs": [], + "source": [ + "# Visualize the solution\n", + "\n", + "def visualize_solution(xc, yc, x, C, n, K, title_str):\n", + " plt.figure()\n", + " plt.scatter(xc, yc, s=200)\n", + " for i in range(len(xc)):\n", + " plt.annotate(i, (xc[i] + 0.015, yc[i]), size=16, color='r')\n", + " \n", + " plt.grid()\n", + "\n", + " for ii in range(n ** 2, n **2 + n):\n", + "\n", + " if x[ii] > 0:\n", + " plt.plot(xc[ii-n**2], yc[ii-n**2], 'r*', ms=20)\n", + "\n", + " for ii in range(0, n ** 2):\n", + "\n", + " if x[ii] > 0:\n", + " iy = ii // n\n", + " ix = ii % n\n", + " plt.plot([xc[ix], xc[iy]], [yc[ix], yc[iy]], 'C2')\n", + "\n", + " plt.title(title_str+' cost = ' + str(int(C * 100) / 100.))\n", + " plt.show()\n", + " \n", + "\n", + "# Eventually, you can runvisualize_solution(xc, yc, x, classical_cost, n, q, 'Classical')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Solution shows the selected stocks via the stars and in green the links (via similarities) with other stocks that are represented in the fund by the linked stock. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Quantum solution using IBM-Q simulator\n", + "\n", + "For the quantum solution, we use Qskit. We first define a class QuantumOptimizer that encodes the quantum approach to solve the problem and then we instantiate it and solve it. We define the following methods inside the class:\n", + "- `binary_representation` : encodes the problem $(M)$ into a the Ising Hamiltonian QP (that's basically linear algebra);\n", + "- `construct_hamiltonian` : constructs the Ising Hamiltonian in terms of the $Z$ basis;\n", + "- `check_hamiltonian` : makes sure that the Ising Hamiltonian is correctly encoded in the $Z$ basis: to do this, it solves a eigenvalue-eigenvector problem for a symmetric matrix of dimension $2^N \\times 2^N$. For the problem at hand $n=3$, that is $N = 12$ seems the limit; \n", + "- `vqe_solution` : solves the problem $(M)$ via VQE by using the SPSA solver (with default parameters);\n", + "- `_q_solution` : internal routine to represent the solution in a usable format.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": {}, + "outputs": [], + "source": [ + "class QuantumOptimizer:\n", + "\n", + " def __init__(self, rho,n,q,max_trials=1000):\n", + "\n", + " self.rho = rho\n", + " self.n = n\n", + " self.q = q\n", + " self.max_trials = max_trials\n", + "\n", + " def construct_hamiltonian(self):\n", + "\n", + " return portfoliodiv.get_portfoliodiversification_qubitops(self.rho, self.n, self.q, self.max_trials)\n", + "\n", + " def check_hamiltonian(self):\n", + "\n", + " Op = self.construct_hamiltonian()\n", + " qubitOp, offset = Op, 0\n", + " algo_input = EnergyInput(qubitOp)\n", + "\n", + " # Making the Hamiltonian in its full form and getting the lowest eigenvalue and eigenvector\n", + "\n", + " algorithm_cfg = {\n", + " 'name': 'ExactEigensolver',\n", + " }\n", + "\n", + " params = {\n", + " 'problem': {'name': 'ising'},\n", + " 'algorithm': algorithm_cfg\n", + " }\n", + " result = run_algorithm(params, algo_input)\n", + "\n", + " quantum_solution = self._q_solution(result['eigvecs'][0],self.n*(self.n+1))\n", + " ground_level = result['energy'] + offset\n", + "\n", + " return quantum_solution, ground_level\n", + "\n", + " def vqe_solution(self):\n", + "\n", + " qubitOp = self.construct_hamiltonian()\n", + " algo_input = EnergyInput(qubitOp)\n", + "\n", + " backend = BasicAer.get_backend('statevector_simulator')\n", + " seed = 50\n", + " cobyla = COBYLA()\n", + " cobyla.set_options(maxiter=250)\n", + " ry = RY(qubitOp.num_qubits, depth=3, entanglement='full')\n", + " vqe = VQE(qubitOp, ry, cobyla, 'matrix')\n", + " vqe.random_seed = seed\n", + " quantum_instance = QuantumInstance(backend=backend, seed=seed, seed_mapper=seed)\n", + " result = vqe.run(algo_input)\n", + "\n", + " #quantum_solution = self._q_solution(result['eigvecs'][0], self.n * (self.n + 1))\n", + " quantum_solution_dict = result['eigvecs'][0]\n", + "\n", + " q_s = max(quantum_solution_dict.items(), key=operator.itemgetter(1))[0]\n", + " quantum_solution= [int(chars) for chars in q_s]\n", + " quantum_solution = np.flip(quantum_solution, axis=0)\n", + "\n", + " #_,_,_,level = self.binary_representation(x_sol=quantum_solution)\n", + " return quantum_solution_dict, quantum_solution\n", + "\n", + " def _q_solution(self, v, N):\n", + "\n", + " index_value = [x for x in range(len(v)) if v[x] == max(v)][0]\n", + " string_value = \"{0:b}\".format(index_value)\n", + "\n", + " while len(string_value)\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;31m# Check if the binary representation is correct\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mQ\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mg\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mc\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mquantum_cost\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mquantum_optimizer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvqe_solution\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 3\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0msol\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mclassical_cost\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mClassicalOptimizer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcplex_solution\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m\u001b[0m in \u001b[0;36mvqe_solution\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 48\u001b[0m \u001b[0mvqe\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrandom_seed\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mseed\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 49\u001b[0m \u001b[0mquantum_instance\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mQuantumInstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbackend\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mbackend\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mseed\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mseed\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mseed_mapper\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mseed\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 50\u001b[0;31m \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mvqe\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0malgo_input\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 51\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 52\u001b[0m \u001b[0;31m#quantum_solution = self._q_solution(result['eigvecs'][0], self.n * (self.n + 1))\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/qiskit_aqua/algorithms/quantum_algorithm.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self, quantum_instance, **kwargs)\u001b[0m\n\u001b[1;32m 101\u001b[0m \u001b[0mquantum_instance\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_config\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 102\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_quantum_instance\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mquantum_instance\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 103\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_run\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 104\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 105\u001b[0m \u001b[0;34m@\u001b[0m\u001b[0mabstractmethod\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/qiskit_aqua/algorithms/adaptive/vqe/vqe.py\u001b[0m in \u001b[0;36m_run\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 266\u001b[0m \u001b[0mDictionary\u001b[0m \u001b[0mof\u001b[0m \u001b[0mresults\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 267\u001b[0m \"\"\"\n\u001b[0;32m--> 268\u001b[0;31m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_quantum_instance\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mis_statevector\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_operator_mode\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'matrix'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 269\u001b[0m logger.warning('Qasm simulation does not work on {} mode, changing '\n\u001b[1;32m 270\u001b[0m 'the operator_mode to \"paulis\"'.format(self._operator_mode))\n", + "\u001b[0;31mAttributeError\u001b[0m: 'EnergyInput' object has no attribute 'is_statevector'" + ] + } + ], + "source": [ + "# Check if the binary representation is correct\n", + "Q,g,c,quantum_cost = quantum_optimizer.vqe_solution()\n", + "\n", + "sol, classical_cost = ClassicalOptimizer.cplex_solution()\n", + "\n", + "print(quantum_cost, classical_cost)\n", + "if np.abs(quantum_cost - classical_cost)<0.01:\n", + " print('Binary formulation is correct')\n", + "else: print('Error in the binary formulation')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Step 3\n", + "\n", + "Encode the problem as an Ising Hamiltonian in the Z basis. \n", + "\n", + "Sanity check: make sure that the formulation is correct (i.e., yields the same cost given the same solution)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "ground_state, ground_level = quantum_optimizer.check_hamiltonian()\n", + "\n", + "print(ground_level,classical_cost)\n", + "print(ground_state)\n", + "if np.abs(ground_level - classical_cost)<0.01:\n", + " print('Ising Hamiltonian in Z basis is correct')\n", + "else: print('Error in the Ising Hamiltonian formulation')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Step 4\n", + "\n", + "Solve the problem via VQE. Notice that depending on the number of qubits, this can take a while: for 6 qubits it takes 15 minutes on a 2015 Macbook Pro, for 12 qubits it takes more than 12 hours. For longer runs, logging may be useful to observe the workings; otherwise, you just have to wait until the solution is printed." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "quantum_dictionary, quantum_solution, quantum_cost = quantum_optimizer.vqe_solution()\n", + "\n", + "print(quantum_solution,quantum_cost)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Step 5\n", + "Visualize the solution" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "visualize_solution(xc, yc, quantum_solution, quantum_cost, n, q, 'Quantum')\n", + "visualize_solution(xc, yc, x, classical_cost, n, q, 'Classical')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Solution shows the selected stocks via the stars and in green the links (via similarities) with other stocks that are represented in the fund by the linked stock. Note that in this particular case, we can find the optimal solution of the QP formulation, which happens to coincide with the optimal solution of the ILP.\n", + "\n", + "Keep in mind that VQE is an heuristic working on the QP formulation of the Ising Hamiltonian, though. For suitable choices of A, local optima of the QP formulation will be feasible solutions to the ILP. While for some small instances, as above, we can find optimal solutions of the QP formulation which coincide with optima of the ILP, finding optimal solutions of the ILP is harder than finding local optima of the QP formulation, in general. Even within the VQE, one may provide stronger guarantees, for specific variational forms (trial wave functions). " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From dd41459b49b42cb79ddc3951f6b501f85f3cc52f Mon Sep 17 00:00:00 2001 From: Albert Frisch Date: Fri, 12 Apr 2019 17:55:54 +0200 Subject: [PATCH 045/116] update ExactLSsolver naming --- .../aqua/general/linear_systems_of_equations.ipynb | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/qiskit/aqua/general/linear_systems_of_equations.ipynb b/qiskit/aqua/general/linear_systems_of_equations.ipynb index 58e2a5e06..92383b7d1 100644 --- a/qiskit/aqua/general/linear_systems_of_equations.ipynb +++ b/qiskit/aqua/general/linear_systems_of_equations.ipynb @@ -51,7 +51,7 @@ "from qiskit.aqua import run_algorithm\n", "from qiskit.aqua.input import LinearSystemInput\n", "from qiskit.quantum_info import state_fidelity\n", - "from qiskit.aqua.algorithms.classical import ExactLPsolver\n", + "from qiskit.aqua.algorithms.classical import ExactLSsolver\n", "import numpy as np" ] }, @@ -147,7 +147,7 @@ "result = run_algorithm(params)\n", "print(\"solution \", np.round(result['solution'], 5))\n", "\n", - "result_ref = ExactLPsolver(matrix, vector).run()\n", + "result_ref = ExactLSsolver(matrix, vector).run()\n", "print(\"classical solution \", np.round(result_ref['solution'], 5))\n", "\n", "print(\"probability %f\" % result['probability_result'])\n", @@ -186,7 +186,7 @@ "result = run_algorithm(params2)\n", "print(\"solution \", np.round(result['solution'], 5))\n", "\n", - "result_ref = ExactLPsolver(matrix, vector).run()\n", + "result_ref = ExactLSsolver(matrix, vector).run()\n", "print(\"classical solution \", np.round(result_ref['solution'], 5))\n", "\n", "print(\"probability %f\" % result['probability_result'])\n", @@ -275,7 +275,7 @@ "result = run_algorithm(params3)\n", "print(\"solution \", np.round(result['solution'], 5))\n", "\n", - "result_ref = ExactLPsolver(matrix, vector).run()\n", + "result_ref = ExactLSsolver(matrix, vector).run()\n", "print(\"classical solution \", np.round(result_ref['solution'], 5))\n", "\n", "print(\"probability %f\" % result['probability_result'])\n", @@ -378,7 +378,7 @@ "result = run_algorithm(params4)\n", "print(\"solution \", np.round(result['solution'], 5))\n", "\n", - "result_ref = ExactLPsolver(matrix, vector).run()\n", + "result_ref = ExactLSsolver(matrix, vector).run()\n", "print(\"classical solution \", np.round(result_ref['solution'], 5))\n", "\n", "print(\"probability %f\" % result['probability_result'])\n", @@ -521,7 +521,7 @@ "result = hhl.run(quantum_instance)\n", "print(\"solution \", np.round(result['solution'], 5))\n", "\n", - "result_ref = ExactLPsolver(matrix, vector).run()\n", + "result_ref = ExactLSsolver(matrix, vector).run()\n", "print(\"classical solution \", np.round(result_ref['solution'], 5))\n", "\n", "print(\"probability %f\" % result['probability_result'])\n", From 1b69ff74ed670f74ebaa2d7f746a73fb7d38beb2 Mon Sep 17 00:00:00 2001 From: Jakub Marecek Date: Fri, 12 Apr 2019 16:59:44 +0100 Subject: [PATCH 046/116] Deprecation of warnings, addition of outputs --- .../finance/generating_random_variates.ipynb | 88 +++++++++++++++++-- 1 file changed, 80 insertions(+), 8 deletions(-) diff --git a/qiskit/aqua/finance/generating_random_variates.ipynb b/qiskit/aqua/finance/generating_random_variates.ipynb index f6ba44fbf..986d9edbb 100644 --- a/qiskit/aqua/finance/generating_random_variates.ipynb +++ b/qiskit/aqua/finance/generating_random_variates.ipynb @@ -107,7 +107,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "metadata": {}, "outputs": [], "source": [ @@ -115,6 +115,9 @@ "%matplotlib inline\n", "import numpy as np\n", "import sys, math, time\n", + "import warnings\n", + "warnings.filterwarnings(\"ignore\",category=DeprecationWarning)\n", + "\n", "from qiskit import BasicAer\n", "from qiskit.aqua.algorithms import AmplitudeEstimation\n", "from qiskit.aqua.components.random_distributions import MultivariateNormalDistribution\n", @@ -139,11 +142,34 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 8, "metadata": { "scrolled": true }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Uniform distribution of floating point numbers:\n", + "sample type: , element type: float64 , shape: (54321,)\n", + "sample min: -7.6697, max: 19.5199\n", + "time: creation: 0.00043, sampling: 6.49\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ "# Create uniform distribution sampler.\n", "start_time = time.time()\n", @@ -183,9 +209,32 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Uniform distribution of integer numbers:\n", + "sample type: , element type: int64 , shape: (54321,)\n", + "sample min: 37, max: 841\n", + "time: sampling: 6.36\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ "# Draw a sample, reuse the previous instance of the sampler.\n", "start_time = time.time()\n", @@ -220,9 +269,32 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 10, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Normal distribution (mu=2.400, sigma=5.100):\n", + "sample type: , element type: float64 , shape: (4321,)\n", + "sample min: -14.4205, max: 20.7960\n", + "time: creation: 0.01026, sampling: 1.60\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ "# Create normal distribution sampler.\n", "mu = 2.4\n", @@ -281,7 +353,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.3" + "version": "3.7.2" } }, "nbformat": 4, From d635094f4c1fe5c311bb1b994e627d5c331a9690 Mon Sep 17 00:00:00 2001 From: woodsp Date: Fri, 12 Apr 2019 14:47:13 -0400 Subject: [PATCH 047/116] Minor spelling and text fixups --- qiskit/aqua/optimization/docplex.ipynb | 39 ++++++++++++++------------ 1 file changed, 21 insertions(+), 18 deletions(-) diff --git a/qiskit/aqua/optimization/docplex.ipynb b/qiskit/aqua/optimization/docplex.ipynb index 77eeb9fb2..e2570c306 100644 --- a/qiskit/aqua/optimization/docplex.ipynb +++ b/qiskit/aqua/optimization/docplex.ipynb @@ -11,7 +11,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# _*Qiskit Aqua: Generatin Ising Hamiltonians from optimization models with DOcplex*_\n", + "# _*Qiskit Aqua: Generating Ising Hamiltonians from optimization models with DOcplex*_\n", "\n", "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorial.\n", "\n", @@ -27,11 +27,11 @@ "metadata": {}, "source": [ "## Introduction\n", - "There has been a growing interest in using quantum computers to find solutions of combinatorial problems. One of heuristic approach for finding solutions of combinatorial problems on quantum computers is a quantum variational approach, such as the Variational Quantum \n", - "Eigensolver (VQE) algorithm (see https://arxiv.org/abs/1802.00171 and the Quantum Approximate Optimization Algorithm (QAOA) (see https://arxiv.org/abs/1411.4028). In order to use a quantum variational approach on quantum computers, first, we need to map a combinatorial problem to an Ising Hamiltonians. However Ising Hamiltonians are complicated and unintuitive. Mapping a combinatorial problem to Ising Hamiltonians is difficult and time-consuming task, which requires specialized knowledge.\n", + "There has been a growing interest in using quantum computers to find solutions of combinatorial problems. A heuristic approach for finding solutions of combinatorial problems on quantum computers is the quantum variational approach, such as the Variational Quantum \n", + "Eigensolver (VQE) algorithm (see https://arxiv.org/abs/1802.00171 and the Quantum Approximate Optimization Algorithm (QAOA) (see https://arxiv.org/abs/1411.4028). In order to use a quantum variational approach on quantum computers, first, we need to map a combinatorial problem to an Ising Hamiltonian. However Ising Hamiltonians are complicated and unintuitive. Mapping a combinatorial problem to Ising Hamiltonians can be a difficult and time-consuming task, requiring specialized knowledge.\n", "\n", - "In this tutorial, we introduce a translator to automatically generate Ising Hamiltonians from classical optimization models. We will explain about classical optimization models later. The translator dramatically simplifies the task of designing and implementing quantum-computing-based solutions for optimization problems by automatically generating Ising Hamiltoniansfor different optimization problems. With the translator, All a user has to do is to write optimization models using DOcplex (see https://cdn.rawgit.com/IBMDecisionOptimization/docplex-doc/master/docs/index.html). DOcplex is a python library for optimization problems.\n", - "Then the translator will automatically generate Ising Hamiltonians from the models. Optimization models are short and intuitive. It is easier to write optimization models compared to writing Ising Hamiltonians manually. \n", + "In this tutorial, we introduce a translator to automatically generate Ising Hamiltonians from classical optimization models. We will explain about classical optimization models later. The translator dramatically simplifies the task of designing and implementing quantum-computing-based solutions, for optimization problems, by automatically generating Ising Hamiltonians for different optimization problems. With the translator, all a user has to do is to write optimization models using DOcplex (see https://cdn.rawgit.com/IBMDecisionOptimization/docplex-doc/master/docs/index.html). DOcplex is a python library for optimization problems.\n", + "Then the translator will automatically generate Ising Hamiltonians from the models. Optimization models are short and intuitive. It is much easier to write optimization models compared to writing Ising Hamiltonians manually. \n", "\n", "The quantum variational approach works with the translator in Qiskit Aqua as follows:\n", "1. Write an optimization model of the formulation with DOcplex.\n", @@ -40,16 +40,16 @@ "\n", "\n", "### Details of Optimization Models\n", - "For simplicity, we can generate Ising Hamiltonian from the following optimization models now.\n", + "The translator supports the generation of an Ising Hamiltonian from the following optimization model elements:\n", "- Binary decision variables. \n", "- Linear and quadratic terms in objective functions.\n", "- Only equality constraints. \n", "\n", - "Input models are validated before transormation. If the model containts elements that are not from the supported set, an error will be raised.\n", + "Input models are validated before transformation. If the model contains elements that are not from the supported set, an error will be raised.\n", "\n", - "Even though there are restrictions, this type of optimization model can handle the following optimization problems, maxcut, tsp and etc.\n", - "They are typical optimization problems. The usage examples of the translator for Maxcut and TSP are written in the following link.\n", - "- [Qiskit Aqua: Experimenting with MaxCut problem and Traveling Salesman problem with variational quantum eigensolve](maxcut_and_tsp.ipynb)" + "Even though there are restrictions, this type of optimization model can handle optimization problems such as maxcut, traveling salesman etc.\n", + "These are typical optimization problems. Examples of the translator being used for Maxcut and TSP problems can be found in the following tutorial:\n", + "- [Qiskit Aqua: Experimenting with MaxCut problem and Traveling Salesman problem with variational quantum eigensolver](maxcut_and_tsp.ipynb)" ] }, { @@ -57,7 +57,8 @@ "metadata": {}, "source": [ "### A Usage Example: Maximize the number of variables by taking into account constraints\n", - "The following is a toy example of a maximization problem with constrains.\n", + "The following is a toy example of a maximization problem with constraints.\n", + "\n", "\\begin{aligned}\n", " & \\text{maximize}\n", " & \\sum_{i} x_{i}\\\\\n", @@ -70,7 +71,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -94,14 +95,16 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Create an optimization model of the above problem using DOcplex\n", + "### Creating an optimization model of the above problem using DOcplex\n", "An optimization model of the problem with DOcplex is written as follows. \n", - "An instance of `Model` is created and variables for the model are created in the first paragraph. Then object function is written in the second paragraph. The objective function is a function that we would like to minimize (or maximize). Finally constrains are written in the third paragraph. " + "* First an instance of `Model` is created and variables for the model are defined. \n", + "* Next an objective function is written and passed to the model. The objective function is a function that we would like to minimize (or maximize).\n", + "* Finally constraints are added. " ] }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 3, "metadata": { "scrolled": true }, @@ -137,11 +140,11 @@ "mdl = Model(name='max_vars')\n", "x = {i: mdl.binary_var(name='x_{0}'.format(i)) for i in range(1,5)}\n", "\n", - "# Object function\n", + "# Objective function\n", "max_vars_func = mdl.sum(x[i] for i in range(1,5))\n", "mdl.maximize(max_vars_func)\n", "\n", - "# Constrains\n", + "# Constraints\n", "mdl.add_constraint(mdl.sum(i*x[i] for i in range(1,5)) == 3)\n", "\n", "print(mdl.export_to_string())" @@ -284,7 +287,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.5" + "version": "3.6.1" } }, "nbformat": 4, From ab744319f5094868444e190c1fe5a41200d4b497 Mon Sep 17 00:00:00 2001 From: Jakub Marecek Date: Fri, 12 Apr 2019 19:58:22 +0100 Subject: [PATCH 048/116] A simple tutorial for the Qiskit Finance data loading --- .../finance/generating_random_variates.ipynb | 159 +++++++++--------- .../finance/data_providers/time_series.ipynb | 54 ++---- 2 files changed, 99 insertions(+), 114 deletions(-) diff --git a/qiskit/aqua/finance/generating_random_variates.ipynb b/qiskit/aqua/finance/generating_random_variates.ipynb index 986d9edbb..71f0f2faa 100644 --- a/qiskit/aqua/finance/generating_random_variates.ipynb +++ b/qiskit/aqua/finance/generating_random_variates.ipynb @@ -17,7 +17,8 @@ "\n", "***\n", "### Contributors\n", - "Albert Akhriev[1], Jakub Marecek[1], Stephen Wood[1], Marco Pistoia[1]\n", + "Albert Akhriev[1], Jakub Marecek[1], Marco Pistoia[1]\n", + "\n", "### Affliation\n", "- [1]IBMQ" ] @@ -26,83 +27,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Uniformly-distributed scalars and vectors\n", - "\n", - "Functions in the base class \\textbf{UnivariateDistribution}\n", - "\n", - "```python\n", - "def uniform_rand_float64(self, size: int, vmin: float, vmax: float) -> np.ndarray:\n", - " \"\"\"\n", - " Generates a vector of random float64 values in the range [vmin, vmax].\n", - " :param size: length of the vector.\n", - " :param vmin: lower bound.\n", - " :param vmax: upper bound.\n", - " :return: vector of random values.\n", - " \"\"\"\n", - " assert sys.maxsize == np.iinfo(np.int64).max # sizeof(int) == 64 bits\n", - " assert isinstance(size, int) and size > 0\n", - " assert isinstance(vmin, float) and isinstance(vmax, float) and vmin <= vmax\n", - " nbits = 7 * 8 # nbits > mantissa of float64\n", - " bit_str_len = (nbits * size + self.num_target_qubits - 1) // self.num_target_qubits\n", - " job = execute(self.circuit, self.backend, shots=bit_str_len, memory=True)\n", - " bit_str = ''.join(job.result().get_memory())\n", - " scale = float(vmax - vmin) / float(2**nbits - 1)\n", - " return np.array([vmin + scale * float(int(bit_str[i:i+nbits], 2))\n", - " for i in range(0, nbits * size, nbits)], dtype=np.float64)\n", - "```\n", - "\n", - "```python\n", - "def uniform_rand_int64(self, size: int, vmin: int, vmax: int) -> np.ndarray:\n", - " \"\"\"\n", - " Generates a vector of random int64 values in the range [vmin, vmax].\n", - " :param size: length of the vector.\n", - " :param vmin: lower bound.\n", - " :param vmax: upper bound.\n", - " :return: vector of random values.\n", - " \"\"\"\n", - " assert sys.maxsize == np.iinfo(np.int64).max # sizeof(int) == 64 bits\n", - " assert isinstance(size, int) and size > 0\n", - " assert isinstance(vmin, int) and isinstance(vmax, int) and vmin <= vmax\n", - " assert abs(vmin) <= 2**52 and abs(vmax) <= 2**52 # 52 == mantissa of float64\n", - " return np.rint(self.uniform_rand_float64(size, float(vmin), float(vmax))).astype(np.int64)\n", - "```\n", - "\n", - "Function in the base class \\textbf{NormalDistribution}\n", - "\n", - "```python\n", - "def normal_rand_float64(self, size: int) -> np.ndarray:\n", - " \"\"\"\n", - " Draws a sample vector from standard normal distribution (mu=0, std=1)\n", - " using Box-Muller method.\n", - " \"\"\"\n", - " EPS = np.sqrt(np.finfo(np.float64).tiny)\n", - " assert isinstance(size, int) and size > 0\n", - " rand_vec = np.zeros((size,), dtype=np.float64)\n", - "\n", - " # Generate array of uniformly distributed samples.\n", - " n = 2 * size\n", - " x = np.reshape(self.uniform_rand_float64(n, float(0.0), float(1.0)), (-1, 2))\n", - "\n", - " x1 = 0.0 # first sample in a pair\n", - " c = 0 # counter\n", - " for d in range(size):\n", - " r2 = 2.0\n", - " while r2 >= 1.0 or r2 < EPS:\n", - " # Regenerate array of uniformly distributed samples upon shortage.\n", - " if c > n:\n", - " c = 0\n", - " n = max(((size // 10) // 2) * 2, 2)\n", - " x = np.reshape(self.uniform_rand_float64(n, float(0.0), float(1.0)), (-1, 2))\n", - "\n", - " x1 = 2.0 * x[c, 0] - 1.0 # first sample in a pair\n", - " x2 = 2.0 * x[c, 1] - 1.0 # second sample in a pair\n", - " r2 = x1 * x1 + x2 * x2\n", - " c += 1\n", - "\n", - " f = np.sqrt(np.abs(-2.0 * np.log(r2) / r2))\n", - " rand_vec[d] = f * x1\n", - " return rand_vec\n", - "```" + "### Uniformly-distributed scalars and vectors\n" ] }, { @@ -329,6 +254,84 @@ "plt.show()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Background\n", + "\n", + "In order to understand the implementation, it may be useful to see:\n", + "\n", + "Functions in the base class *UnivariateDistribution*\n", + "\n", + "```python\n", + "def uniform_rand_float64(self, size: int, vmin: float, vmax: float) -> np.ndarray:\n", + " \"\"\"\n", + " Generates a vector of random float64 values in the range [vmin, vmax].\n", + " :param size: length of the vector.\n", + " :param vmin: lower bound.\n", + " :param vmax: upper bound.\n", + " :return: vector of random values.\n", + " \"\"\"\n", + " nbits = 7 * 8 # nbits > mantissa of float64\n", + " bit_str_len = (nbits * size + self.num_target_qubits - 1) // self.num_target_qubits\n", + " job = execute(self.circuit, self.backend, shots=bit_str_len, memory=True)\n", + " bit_str = ''.join(job.result().get_memory())\n", + " scale = float(vmax - vmin) / float(2**nbits - 1)\n", + " return np.array([vmin + scale * float(int(bit_str[i:i+nbits], 2))\n", + " for i in range(0, nbits * size, nbits)], dtype=np.float64)\n", + "```\n", + "\n", + "```python\n", + "def uniform_rand_int64(self, size: int, vmin: int, vmax: int) -> np.ndarray:\n", + " \"\"\"\n", + " Generates a vector of random int64 values in the range [vmin, vmax].\n", + " :param size: length of the vector.\n", + " :param vmin: lower bound.\n", + " :param vmax: upper bound.\n", + " :return: vector of random values.\n", + " \"\"\"\n", + " return np.rint(self.uniform_rand_float64(size, float(vmin), float(vmax))).astype(np.int64)\n", + "```\n", + "\n", + "Function in the base class *NormalDistribution*:\n", + "\n", + "```python\n", + "def normal_rand_float64(self, size: int) -> np.ndarray:\n", + " \"\"\"\n", + " Draws a sample vector from standard normal distribution (mu=0, std=1)\n", + " using Box-Muller method.\n", + " \"\"\"\n", + " EPS = np.sqrt(np.finfo(np.float64).tiny)\n", + " assert isinstance(size, int) and size > 0\n", + " rand_vec = np.zeros((size,), dtype=np.float64)\n", + "\n", + " # Generate array of uniformly distributed samples.\n", + " n = 2 * size\n", + " x = np.reshape(self.uniform_rand_float64(n, float(0.0), float(1.0)), (-1, 2))\n", + "\n", + " x1 = 0.0 # first sample in a pair\n", + " c = 0 # counter\n", + " for d in range(size):\n", + " r2 = 2.0\n", + " while r2 >= 1.0 or r2 < EPS:\n", + " # Regenerate array of uniformly distributed samples upon shortage.\n", + " if c > n:\n", + " c = 0\n", + " n = max(((size // 10) // 2) * 2, 2)\n", + " x = np.reshape(self.uniform_rand_float64(n, float(0.0), float(1.0)), (-1, 2))\n", + "\n", + " x1 = 2.0 * x[c, 0] - 1.0 # first sample in a pair\n", + " x2 = 2.0 * x[c, 1] - 1.0 # second sample in a pair\n", + " r2 = x1 * x1 + x2 * x2\n", + " c += 1\n", + "\n", + " f = np.sqrt(np.abs(-2.0 * np.log(r2) / r2))\n", + " rand_vec[d] = f * x1\n", + " return rand_vec\n", + "```" + ] + }, { "cell_type": "code", "execution_count": null, diff --git a/qiskit/finance/data_providers/time_series.ipynb b/qiskit/finance/data_providers/time_series.ipynb index 5938dcdb5..aed94d68d 100644 --- a/qiskit/finance/data_providers/time_series.ipynb +++ b/qiskit/finance/data_providers/time_series.ipynb @@ -33,42 +33,17 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": null, "metadata": { - "scrolled": false + "scrolled": true }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "['/Users/jmarecek/git/qiskit-tutorials/qiskit/aqua/artificial_intelligence', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python37.zip', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/lib-dynload', '', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/sympy-1.3-py3.7.egg', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/scipy-1.2.1-py3.7-macosx-10.7-x86_64.egg', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/psutil-5.6.1-py3.7-macosx-10.7-x86_64.egg', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/ply-3.11-py3.7.egg', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/Pillow-5.4.1-py3.7-macosx-10.7-x86_64.egg', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/numpy-1.16.2-py3.7-macosx-10.7-x86_64.egg', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/networkx-2.2-py3.7.egg', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/marshmallow_polyfield-3.2-py3.7.egg', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/marshmallow-2.19.1-py3.7.egg', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/jsonschema-2.6.0-py3.7.egg', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/mpmath-1.1.0-py3.7.egg', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/decorator-4.4.0-py3.7.egg', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/pyeda-0.28.0-py3.7-macosx-10.7-x86_64.egg', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/dlx-1.0.4-py3.7.egg', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/cvxopt-1.2.3-py3.7-macosx-10.7-x86_64.egg', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/scikit_learn-0.20.3-py3.7-macosx-10.7-x86_64.egg', '/Users/jmarecek/git/qiskit-aer', '/Users/jmarecek/git/qiskit-ignis', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/requests-2.21.0-py3.7.egg', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/requests_ntlm-1.1.0-py3.7.egg', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/urllib3-1.24.1-py3.7.egg', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/idna-2.8-py3.7.egg', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/chardet-3.0.4-py3.7.egg', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/ntlm_auth-1.2.0-py3.7.egg', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/cryptography-2.6.1-py3.7-macosx-10.7-x86_64.egg', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/six-1.12.0-py3.7.egg', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/cffi-1.12.2-py3.7-macosx-10.7-x86_64.egg', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/asn1crypto-0.24.0-py3.7.egg', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/pycparser-2.19-py3.7.egg', '/Users/jmarecek/git/qiskit-aqua', '/Users/jmarecek/git/qiskit', '/Users/jmarecek/git/qiskit-terra', '/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/IPython/extensions', '/Users/jmarecek/.ipython', '/Users/jmarecek/git/qiskit-tutorials/qiskit/aqua/artificial_intelligence', '/Users/jmarecek/git/qiskit-tutorials/qiskit/aqua/artificial_intelligence', '/Users/jmarecek/git/qiskit-tutorials/qiskit/aqua/artificial_intelligence']\n" - ] - }, - { - "ename": "ModuleNotFoundError", - "evalue": "No module named 'drivers'", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mModuleNotFoundError\u001b[0m Traceback (most recent call last)", - "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0msys\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpath\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mos\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgetcwd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msys\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpath\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mdrivers\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mAer\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'drivers'" - ] - } - ], + "outputs": [], "source": [ - "import os, sys\n", - "sys.path.append(os.getcwd())\n", - "print(sys.path)\n", - "from drivers import *\n", - "\n", - "from qiskit import Aer\n", - "from qiskit_aqua import run_algorithm, QuantumInstance\n", - "\n", - "# setup aqua logging\n", - "import logging\n", - "from qiskit_aqua import set_aqua_logging" + "from qiskit.aqua.input.finance import *\n", + "from qiskit.aqua.input.finance.wikipedia import StockMarket\n", + "import warnings\n", + "warnings.filterwarnings(\"ignore\",category=DeprecationWarning)\n", + "import datetime" ] }, { @@ -76,7 +51,14 @@ "execution_count": null, "metadata": {}, "outputs": [], - "source": [] + "source": [ + "wiki = WikipediaDriver(token = \"\",\n", + " tickers = [\"GOOG\"],\n", + " stockmarket = StockMarket.NASDAQ.value,\n", + " start = datetime.datetime(2016,1,1),\n", + " end = datetime.datetime(2016,1,30))\n", + "wiki.run()" + ] }, { "cell_type": "markdown", @@ -90,9 +72,9 @@ ], "metadata": { "kernelspec": { - "display_name": "Python [conda env:localqiskit]", + "display_name": "Python 3", "language": "python", - "name": "conda-env-localqiskit-py" + "name": "python3" }, "language_info": { "codemirror_mode": { From 6bb134068f4fe1a1c756373deb613df5ffe1fdbf Mon Sep 17 00:00:00 2001 From: Jakub Marecek Date: Fri, 12 Apr 2019 20:29:33 +0100 Subject: [PATCH 049/116] Updates to the random variates notebook --- .../finance/generating_random_variates.ipynb | 66 +++++++++++++++++-- .../finance/data_providers/time_series.ipynb | 44 +++++++++++-- 2 files changed, 101 insertions(+), 9 deletions(-) diff --git a/qiskit/aqua/finance/generating_random_variates.ipynb b/qiskit/aqua/finance/generating_random_variates.ipynb index 71f0f2faa..f14f562b4 100644 --- a/qiskit/aqua/finance/generating_random_variates.ipynb +++ b/qiskit/aqua/finance/generating_random_variates.ipynb @@ -27,12 +27,46 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Uniformly-distributed scalars and vectors\n" + "## Introduction\n", + "\n", + "While classical computers use only pseudo-random routines, quantum computers\n", + "can generate true random variates.\n", + "For example, the measurement of a quantum superposition is intrinsically random,\n", + "as suggested by Born's rule.\n", + "Consequently, some of the\n", + "best random-number generators are based on such quantum-mechanical effects.\n", + "Further, with a logarithmic amount of random bits, quantum computers can produce\n", + "linearly many more bits, which is known as \n", + "randomness expansion protocols. \n", + "\n", + "In practical applications, one wishes to use random variates of well-known\n", + "distributions, rather than random bits.\n", + "In this notebook, we illustrate ways of generating random variates of several popular\n", + "distributions on IBM Q.\n", + "\n", + "## Random Bits and the Bernoulli distribution\n", + "\n", + "It is clear that there are many options for generating Bernoulli-distributed scalars (i.e. either 0 or 1). Starting from a simple circuit such as a Hadamard gate followed by measurement, one can progress to\n", + "Bernoulli-distributed vectors.\n", + "\n", + "By addition of such random variates, we could get binomial distributions. \n", + "By multiplication we could get geometric distributions.\n", + "Both may lead to unacceptable circuit depth, though.\n", + "\n", + "\n", + "## Uniformly-distributed scalars and vectors\n", + "\n", + "It is clear that there are many options for approximating uniformly-distributed scalars\n", + "by the choice of an integer from a finite range uniformly at random,\n", + "e.g., by a binary-code construction from the Bernoulli-distributed vectors.\n", + "In the following snippet, we generate random bits,\n", + "which we then convert using the binary-code construction, up to the \n", + "machine precision of a classical computer." ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 12, "metadata": {}, "outputs": [], "source": [ @@ -62,7 +96,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "#### Uniform distribution of floating point numbers." + "### Uniform distribution over floating point numbers." ] }, { @@ -129,7 +163,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "#### Uniform distribution of integer numbers." + "### Uniform distribution over integers." ] }, { @@ -189,7 +223,23 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "#### Normal distribution" + "## Normal distribution\n", + "\n", + "To generate random variates with a standard normal distribution using two independent \n", + "samples $u_1, u_2$ of the uniform distribution on the unit interval [0, 1], one can\n", + "consider the Box-Muller transform to obtain a 2-vector:\n", + "\n", + "\\begin{align}\n", + "\\begin{bmatrix}\n", + "%R\\cos(\\Theta )=\n", + "{\\sqrt {-2\\ln u_{1}}}\\cos(2\\pi u_{2}) \\\\\n", + "% R\\sin(\\Theta )=\n", + "{\\sqrt {-2\\ln u_{1}}}\\sin(2\\pi u_{2})\n", + "\\end{bmatrix},\n", + "\\end{align}\n", + "\n", + "wherein we have two independent samples of the standard normal distribution.\n", + "In IBM Q, this is implemented as follows: " ] }, { @@ -258,6 +308,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ + "Using basic linear algebra, we can correlate multivariate variables. Indeed, when $L$ is \n", + "the left Cholesky factor of the $n \\times n$ covariance matrix $\\Sigma= L L^T$,\n", + "and $\\mu$ is an $n$-vector,\n", + "and $x$ is an $n$-vector distributed according to the standard normal distribution,\n", + "then $\\mu + Lx$ is a random sample from $N(\\mu, \\Sigma)$.\n", + "\n", "## Background\n", "\n", "In order to understand the implementation, it may be useful to see:\n", diff --git a/qiskit/finance/data_providers/time_series.ipynb b/qiskit/finance/data_providers/time_series.ipynb index aed94d68d..95b7ea478 100644 --- a/qiskit/finance/data_providers/time_series.ipynb +++ b/qiskit/finance/data_providers/time_series.ipynb @@ -33,11 +33,20 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": { "scrolled": true }, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/jmarecek/git/qiskit-terra/qiskit/tools/qcvv/__init__.py:13: DeprecationWarning: The qiskit.tools.qcvv package is deprecated. Please use qiskit-ignis available on PIP for similar functionality and more.\n", + " 'functionality and more.', DeprecationWarning)\n" + ] + } + ], "source": [ "from qiskit.aqua.input.finance import *\n", "from qiskit.aqua.input.finance.wikipedia import StockMarket\n", @@ -48,9 +57,36 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": {}, - "outputs": [], + "outputs": [ + { + "ename": "KeyError", + "evalue": "'close'", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mKeyError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m~/anaconda3/envs/localqiskit/lib/python3.7/site-packages/pandas/core/indexes/base.py\u001b[0m in \u001b[0;36mget_loc\u001b[0;34m(self, key, method, tolerance)\u001b[0m\n\u001b[1;32m 2656\u001b[0m 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"\u001b[0;32mpandas/_libs/hashtable_class_helper.pxi\u001b[0m in \u001b[0;36mpandas._libs.hashtable.PyObjectHashTable.get_item\u001b[0;34m()\u001b[0m\n", + "\u001b[0;31mKeyError\u001b[0m: 'close'", + "\nDuring handling of the above exception, another exception occurred:\n", + "\u001b[0;31mKeyError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0mstart\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdatetime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdatetime\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2016\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m end = datetime.datetime(2016,1,30))\n\u001b[0;32m----> 6\u001b[0;31m 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"\u001b[0;32mpandas/_libs/hashtable_class_helper.pxi\u001b[0m in \u001b[0;36mpandas._libs.hashtable.PyObjectHashTable.get_item\u001b[0;34m()\u001b[0m\n", + "\u001b[0;31mKeyError\u001b[0m: 'close'" + ] + } + ], "source": [ "wiki = WikipediaDriver(token = \"\",\n", " tickers = [\"GOOG\"],\n", From a8c8fef4777f4b8c0eb9d0f1aa23ac273cd0708e Mon Sep 17 00:00:00 2001 From: Jakub Marecek Date: Fri, 12 Apr 2019 20:35:15 +0100 Subject: [PATCH 050/116] A bugfix --- .../finance/data_providers/time_series.ipynb | 44 ++----------------- 1 file changed, 4 insertions(+), 40 deletions(-) diff --git a/qiskit/finance/data_providers/time_series.ipynb b/qiskit/finance/data_providers/time_series.ipynb index 95b7ea478..aed94d68d 100644 --- a/qiskit/finance/data_providers/time_series.ipynb +++ b/qiskit/finance/data_providers/time_series.ipynb @@ -33,20 +33,11 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": { "scrolled": true }, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/Users/jmarecek/git/qiskit-terra/qiskit/tools/qcvv/__init__.py:13: DeprecationWarning: The qiskit.tools.qcvv package is deprecated. Please use qiskit-ignis available on PIP for similar functionality and more.\n", - " 'functionality and more.', DeprecationWarning)\n" - ] - } - ], + "outputs": [], "source": [ "from qiskit.aqua.input.finance import *\n", "from qiskit.aqua.input.finance.wikipedia import StockMarket\n", @@ -57,36 +48,9 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "ename": "KeyError", - "evalue": "'close'", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mKeyError\u001b[0m Traceback (most recent call last)", - "\u001b[0;32m~/anaconda3/envs/localqiskit/lib/python3.7/site-packages/pandas/core/indexes/base.py\u001b[0m in \u001b[0;36mget_loc\u001b[0;34m(self, key, method, tolerance)\u001b[0m\n\u001b[1;32m 2656\u001b[0m \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2657\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_engine\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_loc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2658\u001b[0m \u001b[0;32mexcept\u001b[0m \u001b[0mKeyError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;32mpandas/_libs/index.pyx\u001b[0m in \u001b[0;36mpandas._libs.index.IndexEngine.get_loc\u001b[0;34m()\u001b[0m\n", - "\u001b[0;32mpandas/_libs/index.pyx\u001b[0m in \u001b[0;36mpandas._libs.index.IndexEngine.get_loc\u001b[0;34m()\u001b[0m\n", - "\u001b[0;32mpandas/_libs/hashtable_class_helper.pxi\u001b[0m in \u001b[0;36mpandas._libs.hashtable.PyObjectHashTable.get_item\u001b[0;34m()\u001b[0m\n", - "\u001b[0;32mpandas/_libs/hashtable_class_helper.pxi\u001b[0m in \u001b[0;36mpandas._libs.hashtable.PyObjectHashTable.get_item\u001b[0;34m()\u001b[0m\n", - "\u001b[0;31mKeyError\u001b[0m: 'close'", - "\nDuring handling of the above exception, another exception occurred:\n", - "\u001b[0;31mKeyError\u001b[0m Traceback (most recent call last)", - "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0mstart\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdatetime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdatetime\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2016\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m end = datetime.datetime(2016,1,30))\n\u001b[0;32m----> 6\u001b[0;31m \u001b[0mwiki\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", - "\u001b[0;32m~/git/qiskit-aqua/qiskit/aqua/input/finance/wikipedia/wikipediadriver.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 137\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mcnt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_tickers\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 138\u001b[0m \u001b[0md\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mquandl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"WIKI/\"\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0ms\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstart_date\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_start\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mend_date\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_end\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 139\u001b[0;31m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_data\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"close\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", - "\u001b[0;32m~/anaconda3/envs/localqiskit/lib/python3.7/site-packages/pandas/core/frame.py\u001b[0m in \u001b[0;36m__getitem__\u001b[0;34m(self, key)\u001b[0m\n\u001b[1;32m 2925\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcolumns\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnlevels\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2926\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_getitem_multilevel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2927\u001b[0;31m \u001b[0mindexer\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcolumns\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_loc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2928\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mis_integer\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mindexer\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2929\u001b[0m \u001b[0mindexer\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mindexer\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;32m~/anaconda3/envs/localqiskit/lib/python3.7/site-packages/pandas/core/indexes/base.py\u001b[0m in \u001b[0;36mget_loc\u001b[0;34m(self, key, method, tolerance)\u001b[0m\n\u001b[1;32m 2657\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_engine\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_loc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2658\u001b[0m \u001b[0;32mexcept\u001b[0m \u001b[0mKeyError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2659\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_engine\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_loc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_maybe_cast_indexer\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2660\u001b[0m \u001b[0mindexer\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_indexer\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmethod\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mmethod\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtolerance\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mtolerance\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2661\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mindexer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m1\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mindexer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msize\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;32mpandas/_libs/index.pyx\u001b[0m in \u001b[0;36mpandas._libs.index.IndexEngine.get_loc\u001b[0;34m()\u001b[0m\n", - "\u001b[0;32mpandas/_libs/index.pyx\u001b[0m in \u001b[0;36mpandas._libs.index.IndexEngine.get_loc\u001b[0;34m()\u001b[0m\n", - "\u001b[0;32mpandas/_libs/hashtable_class_helper.pxi\u001b[0m in \u001b[0;36mpandas._libs.hashtable.PyObjectHashTable.get_item\u001b[0;34m()\u001b[0m\n", - "\u001b[0;32mpandas/_libs/hashtable_class_helper.pxi\u001b[0m in \u001b[0;36mpandas._libs.hashtable.PyObjectHashTable.get_item\u001b[0;34m()\u001b[0m\n", - "\u001b[0;31mKeyError\u001b[0m: 'close'" - ] - } - ], + "outputs": [], "source": [ "wiki = WikipediaDriver(token = \"\",\n", " tickers = [\"GOOG\"],\n", From 401e3dbcda972de955b785049c41c0aeb7aeb626 Mon Sep 17 00:00:00 2001 From: stefan-woerner Date: Tue, 16 Apr 2019 00:17:17 +0200 Subject: [PATCH 051/116] move finance tutorials to qiskit / finance and add new tutorials as well --- .../european_call_option_pricing.ipynb | 490 ------ .../aqua/finance/fixed_income_pricing.ipynb | 346 ---- qiskit/aqua/finance/index.ipynb | 50 - .../portfolio_optimization.ipynb | 85 +- qiskit/finance/qiskit_finance.ipynb | 78 + .../asian_barrier_spread_pricing.ipynb | 631 ++++++++ .../simulation/basket_option_pricing.ipynb | 480 ++++++ .../simulation/bull_spread_pricing.ipynb | 516 ++++++ .../simulation/credit_risk_analysis.ipynb | 1386 +++++++++++++++++ .../european_call_option_pricing.ipynb | 515 ++++++ .../european_put_option_pricing.ipynb | 515 ++++++ .../simulation/fixed_income_pricing.ipynb | 351 +++++ .../simulation/iron_condor_pricing.ipynb | 408 +++++ .../finance/simulation/option_pricing.ipynb | 90 ++ 14 files changed, 5026 insertions(+), 915 deletions(-) delete mode 100644 qiskit/aqua/finance/european_call_option_pricing.ipynb delete mode 100644 qiskit/aqua/finance/fixed_income_pricing.ipynb delete mode 100644 qiskit/aqua/finance/index.ipynb rename qiskit/{aqua/finance => finance/optimization}/portfolio_optimization.ipynb (84%) create mode 100644 qiskit/finance/qiskit_finance.ipynb create mode 100644 qiskit/finance/simulation/asian_barrier_spread_pricing.ipynb create mode 100644 qiskit/finance/simulation/basket_option_pricing.ipynb create mode 100644 qiskit/finance/simulation/bull_spread_pricing.ipynb create mode 100644 qiskit/finance/simulation/credit_risk_analysis.ipynb create mode 100644 qiskit/finance/simulation/european_call_option_pricing.ipynb create mode 100644 qiskit/finance/simulation/european_put_option_pricing.ipynb create mode 100644 qiskit/finance/simulation/fixed_income_pricing.ipynb create mode 100644 qiskit/finance/simulation/iron_condor_pricing.ipynb create mode 100644 qiskit/finance/simulation/option_pricing.ipynb diff --git a/qiskit/aqua/finance/european_call_option_pricing.ipynb b/qiskit/aqua/finance/european_call_option_pricing.ipynb deleted file mode 100644 index 8b909fa9c..000000000 --- a/qiskit/aqua/finance/european_call_option_pricing.ipynb +++ /dev/null @@ -1,490 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# _*Qiskit Aqua: Pricing European Call Options*_ \n", - "\n", - "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", - "\n", - "***\n", - "### Contributors\n", - "Stefan Woerner[1], Daniel Egger[1], Shaohan Hu[1], Stephen Wood[1], Marco Pistoia[1]\n", - "### Affliation\n", - "- [1]IBMQ" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Introduction\n", - "
\n", - "Suppose a European call option with strike price $K$ and an underlying asset whose spot price at maturity $S_T$ follows a given random distribution.\n", - "The corresponding payoff function is defined as:\n", - "
\n", - "
\n", - "$$\\max\\{S - K, 0\\}$$\n", - "
\n", - "In the following, a quantum algorithm based on amplitude estimation is used to estimate the expected payoff, i.e., the fair price before discounting, for the option:\n", - "
\n", - "
\n", - "$$\\mathbb{E}\\left[ \\max\\{S - K, 0\\} \\right]$$\n", - "
\n", - "as well as the corresponding $\\Delta$, i.e., the derivative of the option price with respect to the spot price, defined as:\n", - "
\n", - "
\n", - "$$\n", - "\\Delta = \\mathbb{P}\\left[S \\geq K\\right]\n", - "$$\n", - "
\n", - "The approximation of the objective function is explained in detail in the following paper:
\n", - "Quantum Risk Analysis. Woerner, Egger. 2018." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import matplotlib.pyplot as plt\n", - "%matplotlib inline\n", - "import numpy as np\n", - "from qiskit import BasicAer\n", - "from qiskit.aqua.algorithms import AmplitudeEstimation\n", - "from qiskit.aqua.components.uncertainty_problems import EuropeanCallExpectedValue, EuropeanCallDelta\n", - "from qiskit.aqua.components.uncertainty_models import LogNormalDistribution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Uncertainty Model\n", - "\n", - "We construct a circuit factory to load a log-normal random distribution into a quantum state.\n", - "The distribution is truncated to a given interval $[low, high]$ and discretized using $2^n$ grid points, where $n$ denotes the number of qubits used.\n", - "The unitary operator corresponding to the circuit factory implements the following: \n", - "$$\\big|0\\rangle_{n} \\mapsto \\big|\\psi\\rangle_{n} = \\sum_{i=0}^{2^n-1} \\sqrt{p_i}\\big|i\\rangle_{n},$$\n", - "where $p_i$ denote the probabilities corresponding to the truncated and discretized distribution and where $i$ is mapped to the right interval using the affine map:\n", - "$$ \\{0, \\ldots, 2^n-1\\} \\ni i \\mapsto \\frac{high - low}{2^n - 1} * i + low \\in [low, high].$$" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "# number of qubits to represent the uncertainty\n", - "num_uncertainty_qubits = 3\n", - "\n", - "# parameters for considered random distribution\n", - "S = 2.0 # initial spot price\n", - "vol = 0.4 # volatility of 40%\n", - "r = 0.05 # annual interest rate of 4%\n", - "T = 40 / 365 # 40 days to maturity\n", - "\n", - "# resulting parameters for log-normal distribution\n", - "mu = ((r - 0.5 * vol**2) * T + np.log(S))\n", - "sigma = vol * np.sqrt(T)\n", - "mean = np.exp(mu + sigma**2/2)\n", - "variance = (np.exp(sigma**2) - 1) * np.exp(2*mu + sigma**2)\n", - "stddev = np.sqrt(variance)\n", - "\n", - "# lowest and highest value considered for the spot price; in between, an equidistant discretization is considered.\n", - "low = np.maximum(0, mean - 3*stddev)\n", - "high = mean + 3*stddev\n", - "\n", - "# construct circuit factory for uncertainty model\n", - "uncertainty_model = LogNormalDistribution(num_uncertainty_qubits, mu=mu, sigma=sigma, low=low, high=high)" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# plot probability distribution\n", - "x = uncertainty_model.values\n", - "y = uncertainty_model.probabilities\n", - "plt.bar(x, y, width=0.2)\n", - "plt.xticks(x, size=15, rotation=90)\n", - "plt.yticks(size=15)\n", - "plt.grid()\n", - "plt.xlabel('Spot Price at Maturity $S_T$ (\\$)', size=15)\n", - "plt.ylabel('Probability ($\\%$)', size=15)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Payoff Function\n", - "\n", - "The payoff function equals zero as long as the spot price at maturity $S_T$ is less than the strike price $K$ and then increases linearly.\n", - "The implementation uses a comparator, that flips an ancilla qubit from $\\big|0\\rangle$ to $\\big|1\\rangle$ if $S_T \\geq K$, and this ancilla is used to control the linear part of the payoff function.\n", - "\n", - "The linear part itself is then approximated as follows.\n", - "We exploit the fact that $\\sin^2(y + \\pi/4) \\approx y + 1/2$ for small $|y|$.\n", - "Thus, for a given approximation scaling factor $c_{approx} \\in [0, 1]$ and $x \\in [0, 1]$ we consider\n", - "$$ \\sin^2( \\pi/2 * c_{approx} * ( x - 1/2 ) + \\pi/4) \\approx \\pi/2 * c_{approx} * ( x - 1/2 ) + 1/2 $$ for small $c_{approx}$.\n", - "\n", - "We can easily construct an operator that acts as \n", - "$$\\big|x\\rangle \\big|0\\rangle \\mapsto \\big|x\\rangle \\left( \\cos(a*x+b) \\big|0\\rangle + \\sin(a*x+b) \\big|1\\rangle \\right),$$\n", - "using controlled Y-rotations.\n", - "\n", - "Eventually, we are interested in the probability of measuring $\\big|1\\rangle$ in the last qubit, which corresponds to\n", - "$\\sin^2(a*x+b)$.\n", - "Together with the approximation above, this allows to approximate the values of interest.\n", - "The smaller we choose $c_{approx}$, the better the approximation.\n", - "However, since we are then estimating a property scaled by $c_{approx}$, the number of evaluation qubits $m$ needs to be adjusted accordingly.\n", - "\n", - "For more details on the approximation, we refer to:\n", - "Quantum Risk Analysis. Woerner, Egger. 2018." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "# set the strike price (should be within the low and the high value of the uncertainty)\n", - "strike_price = 2\n", - "\n", - "# set the approximation scaling for the payoff function\n", - "c_approx = 0.25\n", - "\n", - "# construct circuit factory for payoff function\n", - "european_call = EuropeanCallExpectedValue(\n", - " uncertainty_model,\n", - " strike_price=strike_price,\n", - " c_approx=c_approx\n", - ")" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# plot exact payoff function (evaluated on the grid of the uncertainty model)\n", - "x = uncertainty_model.values\n", - "y = np.maximum(0, x - strike_price)\n", - "plt.plot(x, y, 'ro-')\n", - "plt.grid()\n", - "plt.title('Payoff Function', size=15)\n", - "plt.xlabel('Spot Price', size=15)\n", - "plt.ylabel('Payoff', size=15)\n", - "plt.xticks(x, size=15, rotation=90)\n", - "plt.yticks(size=15)\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "exact (normalized) expected value:\t0.1133\n", - "exact (normalized) delta value: \t0.4700\n" - ] - } - ], - "source": [ - "# evaluate exact expected value (normalized to the [0, 1] interval)\n", - "exact_value = np.dot(uncertainty_model.probabilities, y)\n", - "exact_delta = sum(uncertainty_model.probabilities[x >= strike_price])\n", - "print('exact (normalized) expected value:\\t%.4f' % exact_value)\n", - "print('exact (normalized) delta value: \\t%.4f' % exact_delta)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Evaluate Expected Payoff" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "# set number of evaluation qubits (samples)\n", - "m = 5\n", - "\n", - "# construct amplitude estimation \n", - "ae = AmplitudeEstimation(m, european_call)" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [], - "source": [ - "# result = ae.run(quantum_instance=LegacySimulators.get_backend('qasm_simulator'), shots=100)\n", - "result = ae.run(quantum_instance=LegacySimulators.get_backend('statevector_simulator'))" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Exact value: \t0.1133\n", - "Estimated value:\t0.2307\n", - "Probability: \t0.7701\n" - ] - } - ], - "source": [ - "print('Exact value: \\t%.4f' % exact_value)\n", - "print('Estimated value:\\t%.4f' % result['estimation'])\n", - "print('Probability: \\t%.4f' % result['max_probability'])" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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\n", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# plot estimated values for \"a\"\n", - "plt.bar(result['values'], result['probabilities'], width=0.5/len(result['probabilities']))\n", - "plt.xticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", - "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", - "plt.title('\"a\" Value', size=15)\n", - "plt.ylabel('Probability', size=15)\n", - "plt.ylim((0,1))\n", - "plt.grid()\n", - "plt.show()\n", - "\n", - "# plot estimated values for option price (after re-scaling and reversing the c_approx-transformation)\n", - "plt.bar(result['mapped_values'], result['probabilities'], width=1/len(result['probabilities']))\n", - "plt.plot([exact_value, exact_value], [0,1], 'r--', linewidth=2)\n", - "plt.xticks(size=15)\n", - "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", - "plt.title('Estimated Option Price', size=15)\n", - "plt.ylabel('Probability', size=15)\n", - "plt.ylim((0,1))\n", - "plt.grid()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Evaluate Delta\n", - "\n", - "The Delta is a bit simplier to evaluate than the expected payoff.\n", - "Similarly to the expected payoff, we use a comparator circuit and an ancilla qubit to identify the cases where $S_T \\geq K$.\n", - "However, since we are only interested in the probability of this condition being true, we can directly use this ancilla qubit as the objective qubit in amplitude estimation without any futher approximation." - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "european_call_delta = EuropeanCallDelta(\n", - " uncertainty_model,\n", - " strike_price\n", - ")" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "# set number of evaluation qubits (=log(samples)\n", - "m = 5\n", - "\n", - "# construct amplitude estimation \n", - "ae_delta = AmplitudeEstimation(m, european_call_delta)" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "# result_delta = ae_delta.run(quantum_instance=LegacySimulators.get_backend('qasm_simulator'), shots=100)\n", - "result_delta = ae_delta.run(quantum_instance=LegacySimulators.get_backend('statevector_simulator'))" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Exact delta: \t0.4700\n", - "Esimated value:\t0.5000\n", - "Probability: \t0.7291\n" - ] - } - ], - "source": [ - "print('Exact delta: \\t%.4f' % exact_delta)\n", - "print('Esimated value:\\t%.4f' % result_delta['estimation'])\n", - "print('Probability: \\t%.4f' % result_delta['max_probability'])" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# plot estimated values for delta\n", - "plt.bar(result_delta['values'], result_delta['probabilities'], width=0.5/len(result_delta['probabilities']))\n", - "plt.plot([exact_delta, exact_delta], [0,1], 'r--', linewidth=2)\n", - "plt.xticks(size=15)\n", - "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", - "plt.title('Estimated Option Delta', size=15)\n", - "plt.ylabel('Probability', size=15)\n", - "plt.ylim((0,1))\n", - "plt.grid()\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/qiskit/aqua/finance/fixed_income_pricing.ipynb b/qiskit/aqua/finance/fixed_income_pricing.ipynb deleted file mode 100644 index fd7a9d810..000000000 --- a/qiskit/aqua/finance/fixed_income_pricing.ipynb +++ /dev/null @@ -1,346 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# _*Qiskit Aqua: Pricing Fixed-Income Assets*_ \n", - "\n", - "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", - "\n", - "***\n", - "### Contributors\n", - "Stefan Woerner[1], Daniel Egger[1], Shaohan Hu[1], Stephen Wood[1], Marco Pistoia[1]\n", - "### Affliation\n", - "- [1]IBMQ" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Introduction\n", - "\n", - "We seek to price a fixed-income asset knowing the distributions describing the relevant interest rates. The cash flows $c_t$ of the asset and the dates at which they occur are known. The total value $V$ of the asset is thus the expectation value of:\n", - "\n", - "$$V = \\sum_{t=1}^T \\frac{c_t}{(1+r_t)^t}$$\n", - "\n", - "Each cash flow is treated as a zero coupon bond with a corresponding interest rate $r_t$ that depends on its maturity. The user must specify the distribution modelling the uncertainty in each $r_t$ (possibly correlated) as well as the number of qubits he wishes to use to sample each distribution. In this example we expand the value of the asset to first order in the interest rates $r_t$. This corresponds to studying the asset in terms of its duration.\n", - "
\n", - "
\n", - "The approximation of the objective function follows the following paper:
\n", - "Quantum Risk Analysis. Woerner, Egger. 2018." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "import matplotlib.pyplot as plt\n", - "%matplotlib inline\n", - "import numpy as np\n", - "from qiskit import BasicAer\n", - "from qiskit.aqua.algorithms import AmplitudeEstimation\n", - "from qiskit.aqua.components.uncertainty_problems import FixedIncomeExpectedValue\n", - "from qiskit.aqua.components.uncertainty_models import MultivariateNormalDistribution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Uncertainty Model\n", - "\n", - "We construct a circuit factory to load a multivariate normal random distribution in $d$ dimensions into a quantum state.\n", - "The distribution is truncated to a given box $\\otimes_{i=1}^d [low_i, high_i]$ and discretized using $2^{n_i}$ grid points, where $n_i$ denotes the number of qubits used for dimension $i = 1,\\ldots, d$.\n", - "The unitary operator corresponding to the circuit factory implements the following: \n", - "$$\\big|0\\rangle_{n_1}\\ldots\\big|0\\rangle_{n_d} \\mapsto \\big|\\psi\\rangle = \\sum_{i_1=0}^{2^n_-1}\\ldots\\sum_{i_d=0}^{2^n_-1} \\sqrt{p_{i_1,...,i_d}}\\big|i_1\\rangle_{n_1}\\ldots\\big|i_d\\rangle_{n_d},$$\n", - "where $p_{i_1, ..., i_d}$ denote the probabilities corresponding to the truncated and discretized distribution and where $i_j$ is mapped to the right interval $[low_j, high_j]$ using the affine map:\n", - "$$ \\{0, \\ldots, 2^{n_{j}}-1\\} \\ni i_j \\mapsto \\frac{high_j - low_j}{2^{n_j} - 1} * i_j + low_j \\in [low_j, high_j].$$\n", - "\n", - "In addition the the uncertainty model, we can also apply an affine map, e.g. resulting from a principal componant analyis. The interest rates used are then given by:\n", - "$$ \\vec{r} = A * \\vec{x} + b,$$\n", - "where $\\vec{x} \\in \\otimes_{i=1}^d [low_i, high_i]$ follows the given random distribution." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "# can be used in case a principal component analysis has been done to derive the uncertainty model, ignored in this example.\n", - "A = np.eye(2)\n", - "b = np.zeros(2) \n", - "\n", - "# specify the number of qubits that are used to represent the different dimenions of the uncertainty model\n", - "num_qubits = [2, 2]\n", - "\n", - "# specify the lower and upper bounds for the different dimension\n", - "low = [0, 0]\n", - "high = [0.12, 0.24]\n", - "mu = [0.12, 0.24]\n", - "sigma = 0.01*np.eye(2)\n", - "\n", - "# construct corresponding distribution\n", - "u = MultivariateNormalDistribution(num_qubits, low, high, mu, sigma)" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# plot contour of probability density function\n", - "x = np.linspace(low[0], high[0], 2**num_qubits[0])\n", - "y = np.linspace(low[1], high[1], 2**num_qubits[1])\n", - "z = u.probabilities.reshape(2**num_qubits[0], 2**num_qubits[1])\n", - "plt.contourf(x, y, z)\n", - "plt.xticks(x, size=15)\n", - "plt.yticks(y, size=15)\n", - "plt.grid()\n", - "plt.xlabel('$r_1$ (%)', size=15)\n", - "plt.ylabel('$r_2$ (%)', size=15)\n", - "plt.colorbar()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Cash flow, payoff function, and exact expected value\n", - "\n", - "In the following we define the cash flow per period, the resulting payoff function and evaluate the exact expected value.\n", - "\n", - "For the payoff function we first use a first order approximation and then apply the same approximation technique as for the linear part of the payoff function of the [European Call Option](european_call_option_pricing.ipynb)." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# specify cash flow\n", - "cf = [1.0, 2.0]\n", - "periods = range(1, len(cf)+1)\n", - "\n", - "# plot cash flow\n", - "plt.bar(periods, cf)\n", - "plt.xticks(periods, size=15)\n", - "plt.yticks(size=15)\n", - "plt.grid()\n", - "plt.xlabel('periods', size=15)\n", - "plt.ylabel('cashflow ($)', size=15)\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Exact value: \t2.1942\n" - ] - } - ], - "source": [ - "# estimate real value\n", - "cnt = 0\n", - "exact_value = 0.0\n", - "for x1 in np.linspace(low[0], high[0], pow(2, num_qubits[0])):\n", - " for x2 in np.linspace(low[1], high[1], pow(2, num_qubits[1])):\n", - " prob = u.probabilities[cnt]\n", - " for t in range(len(cf)):\n", - " # evaluate linear approximation of real value w.r.t. interest rates\n", - " exact_value += prob * (cf[t]/pow(1 + b[t], t+1) - (t+1)*cf[t]*np.dot(A[:, t], np.asarray([x1, x2]))/pow(1 + b[t], t+2))\n", - " cnt += 1\n", - "print('Exact value: \\t%.4f' % exact_value)" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "# specify approximation factor\n", - "c_approx = 0.125\n", - "\n", - "# get fixed income circuit appfactory\n", - "fixed_income = FixedIncomeExpectedValue(u, A, b, cf, c_approx)" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "# set number of evaluation qubits (samples)\n", - "m = 5\n", - "\n", - "# construct amplitude estimation \n", - "ae = AmplitudeEstimation(m, fixed_income)" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "# result = ae.run(quantum_instance=LegacySimulators.get_backend('qasm_simulator'), shots=100)\n", - "result = ae.run(quantum_instance=LegacySimulators.get_backend('statevector_simulator'))" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Exact value: \t2.1942\n", - "Estimated value:\t2.4600\n", - "Probability: \t0.8487\n" - ] - } - ], - "source": [ - "print('Exact value: \\t%.4f' % exact_value)\n", - "print('Estimated value:\\t%.4f' % result['estimation'])\n", - "print('Probability: \\t%.4f' % result['max_probability'])" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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Fh0WblWXhwqojMKuUE45ZWfoeMW3WpdylZmZmpXDCMSvL9OlpMetSTjhmZbnk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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# plot estimated values for \"a\" (direct result of amplitude estimation, not rescaled yet)\n", - "plt.bar(result['values'], result['probabilities'], width=0.5/len(result['probabilities']))\n", - "plt.xticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", - "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", - "plt.title('\"a\" Value', size=15)\n", - "plt.ylabel('Probability', size=15)\n", - "plt.xlim((0,1))\n", - "plt.ylim((0,1))\n", - "plt.grid()\n", - "plt.show()\n", - "\n", - "# plot estimated values for fixed-income asset (after re-scaling and reversing the c_approx-transformation)\n", - "plt.bar(result['mapped_values'], result['probabilities'], width=3/len(result['probabilities']))\n", - "plt.plot([exact_value, exact_value], [0,1], 'r--', linewidth=2)\n", - "plt.xticks(size=15)\n", - "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", - "plt.title('Estimated Option Price', size=15)\n", - "plt.ylabel('Probability', size=15)\n", - "plt.ylim((0,1))\n", - "plt.grid()\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/qiskit/aqua/finance/index.ipynb b/qiskit/aqua/finance/index.ipynb deleted file mode 100644 index 6003d95bb..000000000 --- a/qiskit/aqua/finance/index.ipynb +++ /dev/null @@ -1,50 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Qiskit Aqua Finance\n", - "\n", - "Qiskit Aqua Finance is a set of tools, algorithms and software for use with quantum computers to carry out research and investigate how to take advantage of quantum computing power to solve problems in the Financial domain. \n", - "\n", - "## Contents\n", - "\n", - "* [Portfolio Optimization](portfolio_optimization.ipynb)\n", - "* [European Call Option Pricing](european_call_option_pricing.ipynb)\n", - "* [Fixed-Income Asset Pricing](fixed_income_pricing.ipynb)\n", - "* More examples can be found in [commuity/aqua/finance](../../../community/aqua/finance)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "qiskit_wor", - "language": "python", - "name": "qiskit_wor" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.6" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/qiskit/aqua/finance/portfolio_optimization.ipynb b/qiskit/finance/optimization/portfolio_optimization.ipynb similarity index 84% rename from qiskit/aqua/finance/portfolio_optimization.ipynb rename to qiskit/finance/optimization/portfolio_optimization.ipynb index 3b2da35d7..17c1fb0e1 100644 --- a/qiskit/aqua/finance/portfolio_optimization.ipynb +++ b/qiskit/finance/optimization/portfolio_optimization.ipynb @@ -13,8 +13,9 @@ "collapsed": true }, "source": [ - "# _*Qiskit Aqua: Financial Portfolio Optimization*_ \n", + "# _*Qiskit Finance: Financial Portfolio Optimization*_ \n", "\n", + "Qiskit Finance is part of Qiskit Aqua.
\n", "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", "\n", "***\n", @@ -57,20 +58,17 @@ { "cell_type": "code", "execution_count": 1, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "from qiskit import BasicAer\n", - "from qiskit.aqua import QuantumInstance\n", - "from qiskit.aqua import Operator, run_algorithm\n", - "from qiskit.aqua.input import EnergyInput\n", - "from qiskit.aqua.translators.ising import portfolio\n", - "from qiskit.aqua.algorithms import VQE, QAOA, ExactEigensolver\n", - "from qiskit.aqua.components.optimizers import COBYLA\n", - "from qiskit.aqua.components.initial_states import Zero\n", - "from qiskit.aqua.components.variational_forms import RY\n", + "from qiskit_aqua import QuantumInstance\n", + "from qiskit_aqua import Operator, run_algorithm\n", + "from qiskit_aqua.input import EnergyInput\n", + "from qiskit_aqua.translators.ising import portfolio\n", + "from qiskit_aqua.algorithms import VQE, QAOA, ExactEigensolver\n", + "from qiskit_aqua.components.optimizers import COBYLA\n", + "from qiskit_aqua.components.variational_forms import RY\n", "import numpy as np" ] }, @@ -86,7 +84,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -105,7 +103,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -131,7 +129,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ @@ -169,7 +167,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -231,7 +229,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -263,16 +261,16 @@ } ], "source": [ - "backend = LegacySimulators.get_backend('statevector_simulator')\n", + "backend = BasicAer.get_backend('statevector_simulator')\n", "seed = 50\n", "\n", "cobyla = COBYLA()\n", "cobyla.set_options(maxiter=250)\n", - "init_state = Zero(qubitOp.num_qubits)\n", - "ry = RY(qubitOp.num_qubits, depth=3, entanglement='full', initial_state=init_state)\n", + "ry = RY(qubitOp.num_qubits, depth=3, entanglement='full')\n", "vqe = VQE(qubitOp, ry, cobyla, 'matrix')\n", "vqe.random_seed = seed\n", - "quantum_instance = QuantumInstance(backend, seed=seed, seed_mapper=seed)\n", + "\n", + "quantum_instance = QuantumInstance(backend=backend, seed=seed, seed_mapper=seed)\n", "\n", "result = vqe.run(quantum_instance)\n", "\n", @@ -315,18 +313,47 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Optimal: selection [1 1 0 0], value -0.5110\n", + "\n", + "----------------- Full result ---------------------\n", + "selection\tvalue\t\tprobability\n", + "---------------------------------------------------\n", + " [1 1 0 0]\t-0.5110\t\t0.1907\n", + " [0 0 1 1]\t-0.7012\t\t0.1853\n", + " [1 0 0 1]\t-0.4158\t\t0.1839\n", + " [0 1 1 0]\t-0.5149\t\t0.1789\n", + " [0 1 0 1]\t2.1421\t\t0.1584\n", + " [1 0 1 0]\t-0.2876\t\t0.0948\n", + " [1 1 1 0]\t2.6688\t\t0.0033\n", + " [0 0 0 1]\t4.0314\t\t0.0020\n", + " [1 0 1 1]\t3.0617\t\t0.0009\n", + " [0 1 1 1]\t4.9012\t\t0.0007\n", + " [1 0 0 0]\t4.0242\t\t0.0006\n", + " [0 1 0 0]\t4.5153\t\t0.0003\n", + " [0 0 1 0]\t3.4782\t\t0.0002\n", + " [1 1 1 1]\t15.6136\t\t0.0001\n", + " [0 0 0 0]\t16.0000\t\t0.0001\n", + " [1 1 0 1]\t4.6445\t\t0.0000\n" + ] + } + ], "source": [ - "backend = LegacySimulators.get_backend('statevector_simulator')\n", + "backend = BasicAer.get_backend('statevector_simulator')\n", "seed = 50\n", "\n", "cobyla = COBYLA()\n", "cobyla.set_options(maxiter=250)\n", - "qaoa = QAOA(qubitOp, cobyla, 3, operator_mode='matrix')\n", + "qaoa = QAOA(qubitOp, cobyla, 3, 'matrix')\n", "qaoa.random_seed = seed\n", - "quantum_instance = QuantumInstance(backend, seed=seed, seed_mapper=seed)\n", + "\n", + "quantum_instance = QuantumInstance(backend=backend, seed=seed, seed_mapper=seed)\n", "\n", "result = qaoa.run(quantum_instance)\n", "\n", @@ -362,9 +389,9 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3", + "display_name": "qiskit_stable", "language": "python", - "name": "python3" + "name": "qiskit_stable" }, "language_info": { "codemirror_mode": { @@ -376,7 +403,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.7" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/qiskit/finance/qiskit_finance.ipynb b/qiskit/finance/qiskit_finance.ipynb new file mode 100644 index 000000000..8cb272e63 --- /dev/null +++ b/qiskit/finance/qiskit_finance.ipynb @@ -0,0 +1,78 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# _*Qiskit Finance: Overview*_ \n", + "\n", + "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", + "\n", + "***\n", + "### Contributors\n", + "Stefan Woerner[1], Daniel Egger[1], Christa Zoufal[1], Andrea Simonetto[1], Jakub Marecek[1], Martin Mevissen[1], Shaohan Hu[1], Stephen Wood[1], Marco Pistoia[1]\n", + "\n", + "### Affliation\n", + "- [1]IBMQ" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this notebook we provide an overview of Qiskit Finance tutorials and tutorials from other domains which might be relevant in finance.\n", + "\n", + "#### Machine Learning:\n", + "- Quantum Support Vector Machine for Credit Risk Rating\n", + "- Quantum Generative Adversarial Networks (qGANs) for data loading in option pricing\n", + "\n", + "#### Optimization:\n", + "- Portfolio Optimization\n", + "- Portfolio Diversification\n", + " \n", + "#### Simulation:\n", + "- Option Pricing\n", + "- Credit Risk Analysis\n", + "- Fixed Income Pricing\n", + "\n", + "#### Data Providers:\n", + "- Stock Market Time Series" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "qiskit_master", + "language": "python", + "name": "qiskit_master" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/qiskit/finance/simulation/asian_barrier_spread_pricing.ipynb b/qiskit/finance/simulation/asian_barrier_spread_pricing.ipynb new file mode 100644 index 000000000..2844697bf --- /dev/null +++ b/qiskit/finance/simulation/asian_barrier_spread_pricing.ipynb @@ -0,0 +1,631 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# _*Qiskit Finance: Pricing Asian Barrier Spreads*_ \n", + "\n", + "Qiskit Finance is part of Qiskit Aqua.
\n", + "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", + "\n", + "***\n", + "### Contributors\n", + "Stefan Woerner[1], Daniel Egger[1]\n", + "### Affliation\n", + "- [1]IBMQ" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Introduction\n", + "
\n", + "An Asian barrier spread is a combination of 3 different option types, and as such, combines multiple possible features that the Qiskit Finance option pricing framework supports::\n", + "\n", + "- Asian option: The payoff depends on the average price over the considered time horizon.\n", + "- Barrier Option: The payoff is zero if a certain threshold is exceeded at any time within the considered time horizon.\n", + "- (Bull) Spread: The payoff follows a piecewise linear function (depending on the average price) starting at zero, increasing linear, staying constant.\n", + "\n", + "Suppose strike prices $K_1 < K_2$ and time periods $t=1,2$, with corresponding spot prices $(S_1, S_2)$ following a given multivariate distribution (e.g. generated by some stochastic process), and a barrier threshold $B>0$.\n", + "The corresponding payoff function is defined as:\n", + "
\n", + "
\n", + "$$\n", + "P(S_1, S_2) =\n", + "\\begin{cases}\n", + "\\min\\left\\{\\max\\left\\{\\frac{1}{2}(S_1 + S_2) - K_1, 0\\right\\}, K_2 - K_1\\right\\}, & \\text{ if } S_1, S_2 \\leq B \\\\\n", + "0, & \\text{otherwise.}\n", + "\\end{cases}\n", + "$$\n", + "\n", + "
\n", + "In the following, a quantum algorithm based on amplitude estimation is used to estimate the expected payoff, i.e., the fair price before discounting, for the option:\n", + "
\n", + "
\n", + "$$\\mathbb{E}\\left[ P(S_1, S_2) \\right].$$\n", + "
\n", + "The approximation of the objective function is explained in detail in the following paper:
\n", + "Quantum Risk Analysis. Woerner, Egger. 2018." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "c:\\workspaces\\sandbox-git-quantum-apps\\qiskit-terra-wor\\qiskit\\tools\\qcvv\\__init__.py:13: DeprecationWarning: The qiskit.tools.qcvv package is deprecated. Please use qiskit-ignis available on PIP for similar functionality and more.\n", + " 'functionality and more.', DeprecationWarning)\n" + ] + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "from scipy.interpolate import griddata\n", + "%matplotlib inline\n", + "import numpy as np\n", + "\n", + "from qiskit import QuantumRegister, QuantumCircuit, BasicAer, execute\n", + "from qiskit.aqua.algorithms import AmplitudeEstimation\n", + "\n", + "from arithmetic.weighted_sum_operator import WeightedSumOperator\n", + "from arithmetic.univariate_piecewise_linear_objective import UnivariatePiecewiseLinearObjective as PwlObjective\n", + "from uncertainty_problems.multivariate_objective import MultivariateObjective\n", + "from arithmetic.fixed_value_comparator import FixedValueComparator as Comparator\n", + "from random_distributions.multivariate_log_normal_distribution import MultivariateLogNormalDistribution" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "backend = BasicAer.get_backend('statevector_simulator')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Uncertainty Model\n", + "\n", + "We construct a circuit factory to load a multivariate log-normal random distribution into a quantum state on $n$ qubits.\n", + "For every dimension $j = 1,\\ldots,d$, the distribution is truncated to a given interval $[low_j, high_j]$ and discretized using $2^{n_j}$ grid points, where $n_j$ denotes the number of qubits used to represent dimension $j$, i.e., $n_1+\\ldots+n_d = n$.\n", + "The unitary operator corresponding to the circuit factory implements the following: \n", + "$$\\big|0\\rangle_{n} \\mapsto \\big|\\psi\\rangle_{n} = \\sum_{i_1,\\ldots,i_d} \\sqrt{p_{i_1\\ldots i_d}}\\big|i_1\\rangle_{n_1}\\ldots\\big|i_d\\rangle_{n_d},$$\n", + "where $p_{i_1\\ldots i_d}$ denote the probabilities corresponding to the truncated and discretized distribution and where $i_j$ is mapped to the right interval using the affine map:\n", + "$$ \\{0, \\ldots, 2^{n_j}-1\\} \\ni i_j \\mapsto \\frac{high_j - low_j}{2^{n_j} - 1} * i_j + low_j \\in [low_j, high_j].$$\n", + "\n", + "For simplicity, we assume both stock prices are independent and indentically distributed.\n", + "This assumption just simplifies the parametrization below and can be easily relaxed to more complex and also correlated multivariate distributions.\n", + "The only important assumption for the current implementation is that the discretization grid of the different dimensions has the same step size." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "# number of qubits per dimension to represent the uncertainty \n", + "num_uncertainty_qubits = 3\n", + "\n", + "# parameters for considered random distribution\n", + "S = 2.0 # initial spot price\n", + "vol = 0.4 # volatility of 40%\n", + "r = 0.05 # annual interest rate of 4%\n", + "T = 40 / 365 # 40 days to maturity\n", + "\n", + "# resulting parameters for log-normal distribution\n", + "mu = ((r - 0.5 * vol**2) * T + np.log(S))\n", + "sigma = vol * np.sqrt(T)\n", + "mean = np.exp(mu + sigma**2/2)\n", + "variance = (np.exp(sigma**2) - 1) * np.exp(2*mu + sigma**2)\n", + "stddev = np.sqrt(variance)\n", + "\n", + "# lowest and highest value considered for the spot price; in between, an equidistant discretization is considered.\n", + "low = np.maximum(0, mean - 3*stddev)\n", + "high = mean + 3*stddev\n", + "\n", + "# map to higher dimensional distribution\n", + "# for simplicity assuming dimensions are independent and identically distributed)\n", + "dimension = 2\n", + "num_qubits=[num_uncertainty_qubits]*dimension\n", + "low=low*np.ones(dimension)\n", + "high=high*np.ones(dimension)\n", + "mu=mu*np.ones(dimension)\n", + "cov=sigma**2*np.eye(dimension)\n", + "\n", + "# construct circuit factory\n", + "u = MultivariateLogNormalDistribution(num_qubits=num_qubits, low=low, high=high, mu=mu, cov=cov)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot PDF of uncertainty model\n", + "x = [ v[0] for v in u.values ]\n", + "y = [ v[1] for v in u.values ]\n", + "z = u.probabilities\n", + "#z = map(float, z)\n", + "#z = list(map(float, z))\n", + "resolution = np.array([2**n for n in num_qubits])*1j\n", + "grid_x, grid_y = np.mgrid[min(x):max(x):resolution[0], min(y):max(y):resolution[1]]\n", + "grid_z = griddata((x, y), z, (grid_x, grid_y))\n", + "fig = plt.figure(figsize=(10, 8))\n", + "ax = fig.gca(projection='3d')\n", + "ax.plot_surface(grid_x, grid_y, grid_z, cmap=plt.cm.Spectral)\n", + "ax.set_xlabel('Spot Price $S_1$ (\\$)', size=15)\n", + "ax.set_ylabel('Spot Price $S_2$ (\\$)', size=15)\n", + "ax.set_zlabel('Probability (\\%)', size=15)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Payoff Function\n", + "\n", + "For simplicity, we consider the sum of the spot prices instead of their average.\n", + "The result can be transformed to the average by just dividing it by 2.\n", + "\n", + "The payoff function equals zero as long as the sum of the spot prices $(S_1 + S_2)$ is less than the strike price $K_1$ and then increases linearly until the sum of the spot prices reaches $K_2$.\n", + "Then payoff stays constant to $K_2 - K_1$ unless any of the two spot prices exceeds the barrier threshold $B$, then the payoff goes immediately down to zero.\n", + "The implementation first uses a weighted sum operator to compute the sum of the spot prices into an ancilla register, and then uses a comparator, that flips an ancilla qubit from $\\big|0\\rangle$ to $\\big|1\\rangle$ if $(S_1 + S_2) \\geq K_1$ and another comparator/ancilla to capture the case that $(S_1 + S_2) \\geq K_2$.\n", + "These ancillas are used to control the linear part of the payoff function.\n", + "\n", + "In addition, we add another ancilla variable for each time step and use additional comparators to check whether $S_1$, respectively $S_2$, exceed the barrier threshold $B$. The payoff function is only applied if $S_1, S_2 \\leq B$.\n", + "\n", + "The linear part itself is approximated as follows.\n", + "We exploit the fact that $\\sin^2(y + \\pi/4) \\approx y + 1/2$ for small $|y|$.\n", + "Thus, for a given approximation scaling factor $c_{approx} \\in [0, 1]$ and $x \\in [0, 1]$ we consider\n", + "$$ \\sin^2( \\pi/2 * c_{approx} * ( x - 1/2 ) + \\pi/4) \\approx \\pi/2 * c_{approx} * ( x - 1/2 ) + 1/2 $$ for small $c_{approx}$.\n", + "\n", + "We can easily construct an operator that acts as \n", + "$$\\big|x\\rangle \\big|0\\rangle \\mapsto \\big|x\\rangle \\left( \\cos(a*x+b) \\big|0\\rangle + \\sin(a*x+b) \\big|1\\rangle \\right),$$\n", + "using controlled Y-rotations.\n", + "\n", + "Eventually, we are interested in the probability of measuring $\\big|1\\rangle$ in the last qubit, which corresponds to\n", + "$\\sin^2(a*x+b)$.\n", + "Together with the approximation above, this allows to approximate the values of interest.\n", + "The smaller we choose $c_{approx}$, the better the approximation.\n", + "However, since we are then estimating a property scaled by $c_{approx}$, the number of evaluation qubits $m$ needs to be adjusted accordingly.\n", + "\n", + "For more details on the approximation, we refer to:\n", + "Quantum Risk Analysis. Woerner, Egger. 2018.\n", + "\n", + "Since the weighted sum operator (in its current implementation) can only sum up integers, we need to map from the original ranges to the representable range to estimate the result, and reverse this mapping before interpreting the result. The mapping essentially corresponds to the affine mapping described in the context of the uncertainty model above." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "# determine number of qubits required to represent total loss\n", + "weights = []\n", + "for n in num_qubits:\n", + " for i in range(n):\n", + " weights += [2**i]\n", + "n_s = WeightedSumOperator.get_required_sum_qubits(weights)\n", + "\n", + "# create circuit factory\n", + "agg = WeightedSumOperator(sum(num_qubits), weights)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "# set the strike price (should be within the low and the high value of the uncertainty)\n", + "strike_price_1 = 3\n", + "strike_price_2 = 4\n", + "\n", + "# set the barrier threshold\n", + "barrier = 2.5\n", + "\n", + "# map strike prices and barrier threshold from [low, high] to {0, ..., 2^n-1}\n", + "max_value = 2**n_s - 1\n", + "low_ = low[0]\n", + "high_ = high[0]\n", + "\n", + "mapped_strike_price_1 = (strike_price_1 - dimension*low_) / (high_ - low_) * (2**num_uncertainty_qubits - 1)\n", + "mapped_strike_price_2 = (strike_price_2 - dimension*low_) / (high_ - low_) * (2**num_uncertainty_qubits - 1)\n", + "mapped_barrier = (barrier - low) / (high - low) * (2**num_uncertainty_qubits - 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "# condition and condition result\n", + "conditions = []\n", + "barrier_thresholds = [2]*dimension\n", + "for i in range(dimension):\n", + " # target dimension of random distribution and corresponding condition (which is required to be True)\n", + " conditions += [(i, Comparator(num_qubits[i], mapped_barrier[i] + 1, geq=False))]\n", + " break # TODO" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "# set the approximation scaling for the payoff function\n", + "c_approx = 0.25\n", + "\n", + "# setup piecewise linear objective fcuntion\n", + "breakpoints = [0, mapped_strike_price_1, mapped_strike_price_2]\n", + "slopes = [0, 1, 0]\n", + "offsets = [0, 0, mapped_strike_price_2 - mapped_strike_price_1]\n", + "f_min = 0\n", + "f_max = mapped_strike_price_2 - mapped_strike_price_1\n", + "bull_spread_objective = PwlObjective(\n", + " n_s,\n", + " 0,\n", + " max_value,\n", + " breakpoints,\n", + " slopes,\n", + " offsets,\n", + " f_min,\n", + " f_max,\n", + " c_approx\n", + ")\n", + "\n", + "# define overall multivariate problem\n", + "asian_barrier_spread = MultivariateObjective(u, agg, bull_spread_objective, conditions=conditions)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot exact payoff function\n", + "plt.figure(figsize=(15,5))\n", + "plt.subplot(1,2,1)\n", + "x = np.linspace(sum(low), sum(high))\n", + "y = (x <= 5)*np.minimum(np.maximum(0, x - strike_price_1), strike_price_2 - strike_price_1)\n", + "plt.plot(x, y, 'r-')\n", + "plt.grid()\n", + "plt.title('Payoff Function (for $S_1 = S_2$)', size=15)\n", + "plt.xlabel('Sum of Spot Prices ($S_1 + S_2)$', size=15)\n", + "plt.ylabel('Payoff', size=15)\n", + "plt.xticks(size=15, rotation=90)\n", + "plt.yticks(size=15)\n", + "\n", + "# plot contour of payoff function with respect to both time steps, including barrier\n", + "plt.subplot(1,2,2)\n", + "z = np.zeros((17, 17))\n", + "x = np.linspace(low[0], high[0], 17)\n", + "y = np.linspace(low[1], high[1], 17)\n", + "for i, x_ in enumerate(x):\n", + " for j, y_ in enumerate(y):\n", + " z[i, j] = np.minimum(np.maximum(0, x_ + y_ - strike_price_1), strike_price_2 - strike_price_1)\n", + " if x_ > barrier or y_ > barrier:\n", + " z[i, j] = 0\n", + " \n", + "plt.title('Payoff Function', size =15)\n", + "plt.contourf(x, y, z)\n", + "plt.colorbar()\n", + "# plt.plot(x, x, 'r')\n", + "plt.xlabel('Spot Price $S_1$', size=15)\n", + "plt.ylabel('Spot Price $S_2$', size=15)\n", + "plt.xticks(size=15)\n", + "plt.yticks(size=15)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "exact expected value:\t0.8023\n" + ] + } + ], + "source": [ + "# evaluate exact expected value\n", + "sum_values = np.sum(u.values, axis=1)\n", + "payoff = np.minimum(np.maximum(sum_values - strike_price_1, 0), strike_price_2 - strike_price_1)\n", + "leq_barrier = [ np.max(v) <= barrier for v in u.values ]\n", + "exact_value = np.dot(u.probabilities[leq_barrier], payoff[leq_barrier])\n", + "print('exact expected value:\\t%.4f' % exact_value)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Evaluate Expected Payoff\n", + "\n", + "We first verify the quantum circuit by simulating it and analyzing the resulting probability to measure the $|1\\rangle$ state in the objective qubit" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "state qubits: 5\n", + "circuit width: 19\n", + "circuit depth: 7760\n" + ] + } + ], + "source": [ + "num_req_qubits = asian_barrier_spread.num_target_qubits\n", + "num_req_ancillas = asian_barrier_spread.required_ancillas()\n", + "\n", + "q = QuantumRegister(num_req_qubits, name='q')\n", + "q_a = QuantumRegister(num_req_ancillas, name='q_a')\n", + "qc = QuantumCircuit(q, q_a)\n", + "\n", + "asian_barrier_spread.build(qc, q, q_a)\n", + "print('state qubits: ', num_req_qubits)\n", + "print('circuit width:', qc.width())\n", + "print('circuit depth:', qc.depth())" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "int" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "type(qc.width())" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "ename": "ModelValidationError", + "evalue": "{'n_qubits': [\"Value '19' is not the expected type \"]}", + "output_type": "error", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[1;31mModelValidationError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mjob\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mexecute\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mqc\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mbackend\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mbackend\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[1;32mc:\\workspaces\\sandbox-git-quantum-apps\\qiskit-terra-wor\\qiskit\\execute.py\u001b[0m in \u001b[0;36mexecute\u001b[1;34m(circuits, backend, qobj_header, config, basis_gates, coupling_map, initial_layout, shots, max_credits, seed, qobj_id, seed_mapper, pass_manager, memory, **kwargs)\u001b[0m\n\u001b[0;32m 85\u001b[0m job = execute_circuits(circuits, backend, qobj_header=qobj_header,\n\u001b[0;32m 86\u001b[0m \u001b[0mrun_config\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mrun_config\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 87\u001b[1;33m transpile_config=transpile_config, **kwargs)\n\u001b[0m\u001b[0;32m 88\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 89\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mjob\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;32mc:\\workspaces\\sandbox-git-quantum-apps\\qiskit-terra-wor\\qiskit\\execute.py\u001b[0m in \u001b[0;36mexecute_circuits\u001b[1;34m(circuits, backend, qobj_header, transpile_config, run_config, **kwargs)\u001b[0m\n\u001b[0;32m 128\u001b[0m \u001b[1;31m# assembling the circuits into a qobj to be run on the backend\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 129\u001b[0m qobj = assemble_circuits(new_circuits, qobj_header=qobj_header,\n\u001b[1;32m--> 130\u001b[1;33m run_config=run_config)\n\u001b[0m\u001b[0;32m 131\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 132\u001b[0m \u001b[1;31m# executing the circuits on the backend and returning the job\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;32mc:\\workspaces\\sandbox-git-quantum-apps\\qiskit-terra-wor\\qiskit\\compiler\\assembler.py\u001b[0m in \u001b[0;36massemble_circuits\u001b[1;34m(circuits, run_config, qobj_header, qobj_id)\u001b[0m\n\u001b[0;32m 70\u001b[0m name=circuit.name)\n\u001b[0;32m 71\u001b[0m \u001b[1;31m# TODO: why do we need n_qubits and memory_slots in both the header and the config\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 72\u001b[1;33m \u001b[0mexperimentconfig\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mQasmQobjExperimentConfig\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn_qubits\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mn_qubits\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmemory_slots\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mmemory_slots\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 73\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 74\u001b[0m \u001b[0minstructions\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;32mc:\\workspaces\\sandbox-git-quantum-apps\\qiskit-terra-wor\\qiskit\\validation\\base.py\u001b[0m in \u001b[0;36m_decorated\u001b[1;34m(self, **kwargs)\u001b[0m\n\u001b[0;32m 243\u001b[0m \u001b[1;32mexcept\u001b[0m \u001b[0mValidationError\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mex\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 244\u001b[0m raise ModelValidationError(\n\u001b[1;32m--> 245\u001b[1;33m ex.messages, ex.field_names, ex.fields, ex.data, **ex.kwargs) from None\n\u001b[0m\u001b[0;32m 246\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 247\u001b[0m \u001b[0minit_method\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;31mModelValidationError\u001b[0m: {'n_qubits': [\"Value '19' is not the expected type \"]}" + ] + } + ], + "source": [ + "job = execute(qc, backend=backend)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# evaluate resulting statevector\n", + "value = 0\n", + "for i, a in enumerate(job.result().get_statevector()):\n", + " b = ('{0:0%sb}' % asian_barrier_spread.num_target_qubits).format(i)[-asian_barrier_spread.num_target_qubits:]\n", + " prob = np.abs(a)**2\n", + " if prob > 1e-4 and b[0] == '1':\n", + " value += prob\n", + "\n", + "# map value to original range\n", + "mapped_value = asian_barrier_spread.value_to_estimation(value) / (2**num_uncertainty_qubits - 1) * (high_ - low_)\n", + "print('Exact Operator Value: %.4f' % value)\n", + "print('Mapped Operator value: %.4f' % mapped_value)\n", + "print('Exact Expected Payoff: %.4f' % exact_value) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we use amplitude estimation to estimate the expected payoff." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# set number of evaluation qubits (=log(samples))\n", + "m = 6\n", + "\n", + "# construct amplitude estimation \n", + "ae = AmplitudeEstimation(m, asian_barrier_spread)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# result = ae.run(quantum_instance=BasicAer.get_backend('qasm_simulator'), shots=100)\n", + "result = ae.run(quantum_instance=BasicAer.get_backend('statevector_simulator'))" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exact value: \t0.8407\n", + "Estimated value:\t0.8696\n", + "Probability: \t0.7163\n" + ] + } + ], + "source": [ + "print('Exact value: \\t%.4f' % exact_value)\n", + "print('Estimated value:\\t%.4f' % (result['estimation'] / (2**num_uncertainty_qubits - 1) * (high_ - low_)))\n", + "print('Probability: \\t%.4f' % result['max_probability'])" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot estimated values for \"a\"\n", + "plt.bar(result['values'], result['probabilities'], width=0.5/len(result['probabilities']))\n", + "plt.xticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.title('\"a\" Value', size=15)\n", + "plt.ylabel('Probability', size=15)\n", + "plt.ylim((0,1))\n", + "plt.grid()\n", + "plt.show()\n", + "\n", + "# plot estimated values for option price (after re-scaling and reversing the c_approx-transformation)\n", + "mapped_values = np.array(result['mapped_values']) / (2**num_uncertainty_qubits - 1) * (high_ - low_)\n", + "plt.bar(mapped_values, result['probabilities'], width=1/len(result['probabilities']))\n", + "plt.plot([exact_value, exact_value], [0,1], 'r--', linewidth=2)\n", + "plt.xticks(size=15)\n", + "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.title('Estimated Option Price', size=15)\n", + "plt.ylabel('Probability', size=15)\n", + "plt.ylim((0,1))\n", + "plt.grid()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "qiskit_master", + "language": "python", + "name": "qiskit_master" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/qiskit/finance/simulation/basket_option_pricing.ipynb b/qiskit/finance/simulation/basket_option_pricing.ipynb new file mode 100644 index 000000000..5f6026a98 --- /dev/null +++ b/qiskit/finance/simulation/basket_option_pricing.ipynb @@ -0,0 +1,480 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# _*Qiskit Finance: Pricing Basket Options*_ \n", + "\n", + "Qiskit Finance is part of Qiskit Aqua.
\n", + "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", + "\n", + "***\n", + "### Contributors\n", + "Stefan Woerner[1], Daniel Egger[1]\n", + "### Affliation\n", + "- [1]IBMQ" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Introduction\n", + "
\n", + "Suppose a basket option with strike price $K$ and two underlying assets whose spot pricse at maturity $S_T^1$, $S_T^2$ follow given random distributions.\n", + "The corresponding payoff function is defined as:\n", + "
\n", + "
\n", + "$$\\max\\{S_T^1 + S_T^2 - K, 0\\}$$\n", + "
\n", + "In the following, a quantum algorithm based on amplitude estimation is used to estimate the expected payoff, i.e., the fair price before discounting, for the option:\n", + "
\n", + "
\n", + "$$\\mathbb{E}\\left[ \\max\\{S_T^1 + S_T^2 - K, 0\\} \\right].$$\n", + "
\n", + "The approximation of the objective function is explained in detail in the following paper:
\n", + "Quantum Risk Analysis. Woerner, Egger. 2018." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "from scipy.interpolate import griddata\n", + "%matplotlib inline\n", + "import numpy as np\n", + "\n", + "from qiskit import BasicAer, QuantumRegister, QuantumCircuit, execute\n", + "from qiskit.aqua.algorithms import AmplitudeEstimation\n", + "from qiskit.aqua.components.uncertainty_problems import MultivariateProblem\n", + "from qiskit.aqua.components.uncertainty_problems import UnivariatePiecewiseLinearObjective as PwlObjective\n", + "from qiskit.aqua.components.uncertainty_models import MultivariateLogNormalDistribution\n", + "from qiskit.aqua.circuits import WeightedSumOperator" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Uncertainty Model\n", + "\n", + "We construct a circuit factory to load a multivariate log-normal random distribution into a quantum state on $n$ qubits.\n", + "For every dimension $j = 1,\\ldots,d$, the distribution is truncated to a given interval $[low_j, high_j]$ and discretized using $2^{n_j}$ grid points, where $n_j$ denotes the number of qubits used to represent dimension $j$, i.e., $n_1+\\ldots+n_d = n$.\n", + "The unitary operator corresponding to the circuit factory implements the following: \n", + "$$\\big|0\\rangle_{n} \\mapsto \\big|\\psi\\rangle_{n} = \\sum_{i_1,\\ldots,i_d} \\sqrt{p_{i_1\\ldots i_d}}\\big|i_1\\rangle_{n_1}\\ldots\\big|i_d\\rangle_{n_d},$$\n", + "where $p_{i_1\\ldots i_d}$ denote the probabilities corresponding to the truncated and discretized distribution and where $i_j$ is mapped to the right interval using the affine map:\n", + "$$ \\{0, \\ldots, 2^{n_j}-1\\} \\ni i_j \\mapsto \\frac{high_j - low_j}{2^{n_j} - 1} * i_j + low_j \\in [low_j, high_j].$$\n", + "\n", + "For simplicity, we assume both stock prices are independent and indentically distributed.\n", + "This assumption just simplifies the parametrization below and can be easily relaxed to more complex and also correlated multivariate distributions.\n", + "The only important assumption for the current implementation is that the discretization grid of the different dimensions has the same step size." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# number of qubits per dimension to represent the uncertainty \n", + "num_uncertainty_qubits = 2\n", + "\n", + "# parameters for considered random distribution\n", + "S = 2.0 # initial spot price\n", + "vol = 0.4 # volatility of 40%\n", + "r = 0.05 # annual interest rate of 4%\n", + "T = 40 / 365 # 40 days to maturity\n", + "\n", + "# resulting parameters for log-normal distribution\n", + "mu = ((r - 0.5 * vol**2) * T + np.log(S))\n", + "sigma = vol * np.sqrt(T)\n", + "mean = np.exp(mu + sigma**2/2)\n", + "variance = (np.exp(sigma**2) - 1) * np.exp(2*mu + sigma**2)\n", + "stddev = np.sqrt(variance)\n", + "\n", + "# lowest and highest value considered for the spot price; in between, an equidistant discretization is considered.\n", + "low = np.maximum(0, mean - 3*stddev)\n", + "high = mean + 3*stddev\n", + "\n", + "# map to higher dimensional distribution\n", + "# for simplicity assuming dimensions are independent and identically distributed)\n", + "dimension = 2\n", + "num_qubits=[num_uncertainty_qubits]*dimension\n", + "low=low*np.ones(dimension)\n", + "high=high*np.ones(dimension)\n", + "mu=mu*np.ones(dimension)\n", + "cov=sigma**2*np.eye(dimension)\n", + "\n", + "# construct circuit factory\n", + "u = MultivariateLogNormalDistribution(num_qubits=num_qubits, low=low, high=high, mu=mu, cov=cov)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot PDF of uncertainty model\n", + "x = [ v[0] for v in u.values ]\n", + "y = [ v[1] for v in u.values ]\n", + "z = u.probabilities\n", + "#z = map(float, z)\n", + "#z = list(map(float, z))\n", + "resolution = np.array([2**n for n in num_qubits])*1j\n", + "grid_x, grid_y = np.mgrid[min(x):max(x):resolution[0], min(y):max(y):resolution[1]]\n", + "grid_z = griddata((x, y), z, (grid_x, grid_y))\n", + "fig = plt.figure(figsize=(10, 8))\n", + "ax = fig.gca(projection='3d')\n", + "ax.plot_surface(grid_x, grid_y, grid_z, cmap=plt.cm.Spectral)\n", + "ax.set_xlabel('Spot Price $S_T^1$ (\\$)', size=15)\n", + "ax.set_ylabel('Spot Price $S_T^2$ (\\$)', size=15)\n", + "ax.set_zlabel('Probability (\\%)', size=15)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Payoff Function\n", + "\n", + "The payoff function equals zero as long as the sum of the spot prices at maturity $(S_T^1 + S_T^2)$ is less than the strike price $K$ and then increases linearly.\n", + "The implementation first uses a weighted sum operator to compute the sum of the spot prices into an ancilla register, and then uses a comparator, that flips an ancilla qubit from $\\big|0\\rangle$ to $\\big|1\\rangle$ if $(S_T^1 + S_T^2) \\geq K$.\n", + "This ancilla is used to control the linear part of the payoff function.\n", + "\n", + "The linear part itself is approximated as follows.\n", + "We exploit the fact that $\\sin^2(y + \\pi/4) \\approx y + 1/2$ for small $|y|$.\n", + "Thus, for a given approximation scaling factor $c_{approx} \\in [0, 1]$ and $x \\in [0, 1]$ we consider\n", + "$$ \\sin^2( \\pi/2 * c_{approx} * ( x - 1/2 ) + \\pi/4) \\approx \\pi/2 * c_{approx} * ( x - 1/2 ) + 1/2 $$ for small $c_{approx}$.\n", + "\n", + "We can easily construct an operator that acts as \n", + "$$\\big|x\\rangle \\big|0\\rangle \\mapsto \\big|x\\rangle \\left( \\cos(a*x+b) \\big|0\\rangle + \\sin(a*x+b) \\big|1\\rangle \\right),$$\n", + "using controlled Y-rotations.\n", + "\n", + "Eventually, we are interested in the probability of measuring $\\big|1\\rangle$ in the last qubit, which corresponds to\n", + "$\\sin^2(a*x+b)$.\n", + "Together with the approximation above, this allows to approximate the values of interest.\n", + "The smaller we choose $c_{approx}$, the better the approximation.\n", + "However, since we are then estimating a property scaled by $c_{approx}$, the number of evaluation qubits $m$ needs to be adjusted accordingly.\n", + "\n", + "For more details on the approximation, we refer to:\n", + "Quantum Risk Analysis. Woerner, Egger. 2018.\n", + "\n", + "Since the weighted sum operator (in its current implementation) can only sum up integers, we need to map from the original ranges to the representable range to estimate the result, and reverse this mapping before interpreting the result. The mapping essentially corresponds to the affine mapping described in the context of the uncertainty model above." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# determine number of qubits required to represent total loss\n", + "weights = []\n", + "for n in num_qubits:\n", + " for i in range(n):\n", + " weights += [2**i]\n", + "n_s = WeightedSumOperator.get_required_sum_qubits(weights)\n", + "\n", + "# create circuit factory\n", + "agg = WeightedSumOperator(sum(num_qubits), weights)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# set the strike price (should be within the low and the high value of the uncertainty)\n", + "strike_price = 3.5\n", + "\n", + "# map strike price from [low, high] to {0, ..., 2^n-1}\n", + "max_value = 2**n_s - 1\n", + "low_ = low[0]\n", + "high_ = high[0]\n", + "mapped_strike_price = (strike_price - dimension*low_) / (high_ - low_) * (2**num_uncertainty_qubits - 1)\n", + "\n", + "# set the approximation scaling for the payoff function\n", + "c_approx = 0.25\n", + "\n", + "# setup piecewise linear objective fcuntion\n", + "breakpoints = [0, mapped_strike_price]\n", + "slopes = [0, 1]\n", + "offsets = [0, 0]\n", + "f_min = 0\n", + "f_max = 2*(2**num_uncertainty_qubits - 1) - mapped_strike_price\n", + "basket_objective = PwlObjective(\n", + " n_s,\n", + " 0,\n", + " max_value,\n", + " breakpoints,\n", + " slopes,\n", + " offsets,\n", + " f_min,\n", + " f_max,\n", + " c_approx\n", + ")\n", + "\n", + "# define overall multivariate problem\n", + "basket_option = MultivariateProblem(u, agg, basket_objective)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot exact payoff function (evaluated on the grid of the uncertainty model)\n", + "x = np.linspace(sum(low), sum(high))\n", + "y = np.maximum(0, x - strike_price)\n", + "plt.plot(x, y, 'r-')\n", + "plt.grid()\n", + "plt.title('Payoff Function', size=15)\n", + "plt.xlabel('Sum of Spot Prices ($S_T^1 + S_T^2)$', size=15)\n", + "plt.ylabel('Payoff', size=15)\n", + "plt.xticks(size=15, rotation=90)\n", + "plt.yticks(size=15)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "exact expected value:\t0.4870\n" + ] + } + ], + "source": [ + "# evaluate exact expected value\n", + "sum_values = np.sum(u.values, axis=1)\n", + "exact_value = np.dot(u.probabilities[sum_values>= strike_price], sum_values[sum_values>= strike_price]-strike_price)\n", + "print('exact expected value:\\t%.4f' % exact_value)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Evaluate Expected Payoff\n", + "\n", + "We first verify the quantum circuit by simulating it and analyzing the resulting probability to measure the $|1\\rangle$ state in the objective qubit" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "state qubits: 5\n", + "circuit width: 14\n", + "circuit depth: 188\n" + ] + } + ], + "source": [ + "num_qubits = basket_option.num_target_qubits\n", + "num_ancillas = basket_option.required_ancillas()\n", + "\n", + "q = QuantumRegister(num_qubits, name='q')\n", + "q_a = QuantumRegister(num_ancillas, name='q_a')\n", + "qc = QuantumCircuit(q, q_a)\n", + "\n", + "basket_option.build(qc, q, q_a)\n", + "print('state qubits: ', num_qubits)\n", + "print('circuit width:', qc.width())\n", + "print('circuit depth:', qc.depth())" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "job = execute(qc, backend=BasicAer.get_backend('statevector_simulator'))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exact Operator Value: 0.3954\n", + "Mapped Operator value: 0.4969\n", + "Exact Expected Payoff: 0.4870\n" + ] + } + ], + "source": [ + "# evaluate resulting statevector\n", + "value = 0\n", + "for i, a in enumerate(job.result().get_statevector()):\n", + " b = ('{0:0%sb}' % basket_option.num_target_qubits).format(i)[-basket_option.num_target_qubits:]\n", + " prob = np.abs(a)**2\n", + " if prob > 1e-4 and b[0] == '1':\n", + " value += prob\n", + "\n", + "# map value to original range\n", + "mapped_value = basket_option.value_to_estimation(value) / (2**num_uncertainty_qubits - 1) * (high_ - low_)\n", + "print('Exact Operator Value: %.4f' % value)\n", + "print('Mapped Operator value: %.4f' % mapped_value)\n", + "print('Exact Expected Payoff: %.4f' % exact_value) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we use amplitude estimation to estimate the expected payoff." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# set number of evaluation qubits (=log(samples))\n", + "m = 5\n", + "\n", + "# construct amplitude estimation \n", + "ae = AmplitudeEstimation(m, basket_option)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "# result = ae.run(quantum_instance=BasicAer.get_backend('qasm_simulator'), shots=100)\n", + "result = ae.run(quantum_instance=BasicAer.get_backend('statevector_simulator'))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print('Exact value: \\t%.4f' % exact_value)\n", + "print('Estimated value:\\t%.4f' % (result['estimation'] / (2**num_uncertainty_qubits - 1) * (high_ - low_)))\n", + "print('Probability: \\t%.4f' % result['max_probability'])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# plot estimated values for \"a\"\n", + "plt.bar(result['values'], result['probabilities'], width=0.5/len(result['probabilities']))\n", + "plt.xticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.title('\"a\" Value', size=15)\n", + "plt.ylabel('Probability', size=15)\n", + "plt.ylim((0,1))\n", + "plt.grid()\n", + "plt.show()\n", + "\n", + "# plot estimated values for option price (after re-scaling and reversing the c_approx-transformation)\n", + "mapped_values = np.array(result['mapped_values']) / (2**num_uncertainty_qubits - 1) * (high_ - low_)\n", + "plt.bar(mapped_values, result['probabilities'], width=1/len(result['probabilities']))\n", + "plt.plot([exact_value, exact_value], [0,1], 'r--', linewidth=2)\n", + "plt.xticks(size=15)\n", + "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.title('Estimated Option Price', size=15)\n", + "plt.ylabel('Probability', size=15)\n", + "plt.ylim((0,1))\n", + "plt.grid()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "qiskit_master", + "language": "python", + "name": "qiskit_master" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/qiskit/finance/simulation/bull_spread_pricing.ipynb b/qiskit/finance/simulation/bull_spread_pricing.ipynb new file mode 100644 index 000000000..ea7a786b1 --- /dev/null +++ b/qiskit/finance/simulation/bull_spread_pricing.ipynb @@ -0,0 +1,516 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# _*Qiskit Finance: Pricing Bull Spreads*_ \n", + "\n", + "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", + "\n", + "***\n", + "### Contributors\n", + "Stefan Woerner[1], Daniel Egger[1]\n", + "### Affliation\n", + "- [1]IBMQ" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Introduction\n", + "
\n", + "Suppose a bull spread with strike prices $K_1 < K_2$ and an underlying asset whose spot price at maturity $S_T$ follows a given random distribution.\n", + "The corresponding payoff function is defined as:\n", + "
\n", + "
\n", + "$$\\min\\{\\max\\{S_T - K_1, 0\\}, K_2 - K_1\\}$$\n", + "
\n", + "In the following, a quantum algorithm based on amplitude estimation is used to estimate the expected payoff, i.e., the fair price before discounting, for the option:\n", + "
\n", + "
\n", + "$$\\mathbb{E}\\left[ \\min\\{\\max\\{S_T - K_1, 0\\}, K_2 - K_1\\} \\right]$$\n", + "
\n", + "as well as the corresponding $\\Delta$, i.e., the derivative of the option price with respect to the spot price, defined as:\n", + "
\n", + "
\n", + "$$\n", + "\\Delta = \\mathbb{P}\\left[K_1 \\leq S \\leq K_2\\right]\n", + "$$\n", + "
\n", + "The approximation of the objective function is explained in detail in the following paper:
\n", + "Quantum Risk Analysis. Woerner, Egger. 2018." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "import numpy as np\n", + "\n", + "from qiskit import BasicAer\n", + "from qiskit.aqua.algorithms import AmplitudeEstimation\n", + "from qiskit.aqua.components.uncertainty_models import LogNormalDistribution\n", + "from qiskit.aqua.components.uncertainty_problems import UnivariateProblem\n", + "from qiskit.aqua.components.uncertainty_problems import UnivariatePiecewiseLinearObjective as PwlObjective" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Uncertainty Model\n", + "\n", + "We construct a circuit factory to load a log-normal random distribution into a quantum state.\n", + "The distribution is truncated to a given interval $[low, high]$ and discretized using $2^n$ grid points, where $n$ denotes the number of qubits used.\n", + "The unitary operator corresponding to the circuit factory implements the following: \n", + "$$\\big|0\\rangle_{n} \\mapsto \\big|\\psi\\rangle_{n} = \\sum_{i=0}^{2^n-1} \\sqrt{p_i}\\big|i\\rangle_{n},$$\n", + "where $p_i$ denote the probabilities corresponding to the truncated and discretized distribution and where $i$ is mapped to the right interval using the affine map:\n", + "$$ \\{0, \\ldots, 2^n-1\\} \\ni i \\mapsto \\frac{high - low}{2^n - 1} * i + low \\in [low, high].$$" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# number of qubits to represent the uncertainty\n", + "num_uncertainty_qubits = 3\n", + "\n", + "# parameters for considered random distribution\n", + "S = 2.0 # initial spot price\n", + "vol = 0.4 # volatility of 40%\n", + "r = 0.05 # annual interest rate of 4%\n", + "T = 40 / 365 # 40 days to maturity\n", + "\n", + "# resulting parameters for log-normal distribution\n", + "mu = ((r - 0.5 * vol**2) * T + np.log(S))\n", + "sigma = vol * np.sqrt(T)\n", + "mean = np.exp(mu + sigma**2/2)\n", + "variance = (np.exp(sigma**2) - 1) * np.exp(2*mu + sigma**2)\n", + "stddev = np.sqrt(variance)\n", + "\n", + "# lowest and highest value considered for the spot price; in between, an equidistant discretization is considered.\n", + "low = np.maximum(0, mean - 3*stddev)\n", + "high = mean + 3*stddev\n", + "\n", + "# construct circuit factory for uncertainty model\n", + "uncertainty_model = LogNormalDistribution(num_uncertainty_qubits, mu=mu, sigma=sigma, low=low, high=high)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot probability distribution\n", + "x = uncertainty_model.values\n", + "y = uncertainty_model.probabilities\n", + "plt.bar(x, y, width=0.2)\n", + "plt.xticks(x, size=15, rotation=90)\n", + "plt.yticks(size=15)\n", + "plt.grid()\n", + "plt.xlabel('Spot Price at Maturity $S_T$ (\\$)', size=15)\n", + "plt.ylabel('Probability ($\\%$)', size=15)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Payoff Function\n", + "\n", + "The payoff function equals zero as long as the spot price at maturity $S_T$ is less than the strike price $K_1$, then increases linearly, and is bounded by $K_2$.\n", + "The implementation uses two comparators, that flip an ancilla qubit each from $\\big|0\\rangle$ to $\\big|1\\rangle$ if $S_T \\geq K_1$ and $S_T \\leq K_2, and these ancillas are used to control the linear part of the payoff function.\n", + "\n", + "The linear part itself is then approximated as follows.\n", + "We exploit the fact that $\\sin^2(y + \\pi/4) \\approx y + 1/2$ for small $|y|$.\n", + "Thus, for a given approximation scaling factor $c_{approx} \\in [0, 1]$ and $x \\in [0, 1]$ we consider\n", + "$$ \\sin^2( \\pi/2 * c_{approx} * ( x - 1/2 ) + \\pi/4) \\approx \\pi/2 * c_{approx} * ( x - 1/2 ) + 1/2 $$ for small $c_{approx}$.\n", + "\n", + "We can easily construct an operator that acts as \n", + "$$\\big|x\\rangle \\big|0\\rangle \\mapsto \\big|x\\rangle \\left( \\cos(a*x+b) \\big|0\\rangle + \\sin(a*x+b) \\big|1\\rangle \\right),$$\n", + "using controlled Y-rotations.\n", + "\n", + "Eventually, we are interested in the probability of measuring $\\big|1\\rangle$ in the last qubit, which corresponds to\n", + "$\\sin^2(a*x+b)$.\n", + "Together with the approximation above, this allows to approximate the values of interest.\n", + "The smaller we choose $c_{approx}$, the better the approximation.\n", + "However, since we are then estimating a property scaled by $c_{approx}$, the number of evaluation qubits $m$ needs to be adjusted accordingly.\n", + "\n", + "For more details on the approximation, we refer to:\n", + "Quantum Risk Analysis. Woerner, Egger. 2018." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# set the strike price (should be within the low and the high value of the uncertainty)\n", + "strike_price_1 = 1.5\n", + "strike_price_2 = 2.5\n", + "\n", + "# set the approximation scaling for the payoff function\n", + "c_approx = 0.25\n", + "\n", + "# setup piecewise linear objective fcuntion\n", + "breakpoints = [uncertainty_model.low, strike_price_1, strike_price_2]\n", + "slopes = [0, 1, 0]\n", + "offsets = [0, 0, strike_price_2 - strike_price_1]\n", + "f_min = 0\n", + "f_max = strike_price_2 - strike_price_1\n", + "bull_spread_objective = PwlObjective(\n", + " uncertainty_model.num_target_qubits, \n", + " uncertainty_model.low, \n", + " uncertainty_model.high,\n", + " breakpoints,\n", + " slopes,\n", + " offsets,\n", + " f_min,\n", + " f_max,\n", + " c_approx\n", + ")\n", + "\n", + "# construct circuit factory for payoff function\n", + "bull_spread = UnivariateProblem(\n", + " uncertainty_model,\n", + " bull_spread_objective\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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UCkWu20hmkNYWEl3a24C0tpM0uwIflhQRADP7BfgQ2LEGcjrnKuLxx8PUuO3bwxNPhAmqXMHIdSF5EegoqVHKus7AT8DkMvabDewh6dd3p6QNgT2AWTWQ0zmXrVGjwvhYBx4Y5hKpVy/uRC7Hcl1IBgHLgacktY8axHsBt1nKJcGSPpM0JGW/+4FtgKclHS7pCOAZQtvJ4Jyld86tbezYMGbWPvvA889DgwZxJ3IxyGkhMbNFQDugDqGx/AbCZbw90zatG21Tst80QgN7I+AhYBhQHzjESrlqyzlXw155BY4+Gn77W3jxRdh447gTuZjkvDXMzKYDbcvZpijDuvHA+BqK5ZyriDfeCHOKFBXByy/DZpvFncjFyOcjcc5VzP/+B4ceCk2bwrhx0KRJ3IlczLyQOOeyN306HHIINGoE48fDNtvEncjlAS8kzrnsfPZZuLy3bl2YMCHMaOgcPrGVcy4bs2dDu3awYgVMngw77RR3IpdHvJA458o2b14oIkuWhCOR3XaLO5HLM15InHOl++67cDpr/vzQsL733nEncnnIC4lzLrNFi0LD+qxZoZ/Ifj6ztcvMC4lzbl1LloRLfD/6KAyB0qqseedcofNC4pxbW3FxGMH37bdh5Ejo0CHuRC7PeSFxzq3x889wzDHw6qvwyCNw1FFxJ3IJ4IXEOResWAEnnRQGYhw6FDp3jjuRSwjvkOicg5Urw1Dwo0bBwIFwxhlxJ3IJ4oXEuUK3ejWcfXaYkOqWW+C88+JO5BLGC4lzhcwMLrgAhg2D3r3h8svjTuQSyAuJc4XKLBSOQYPgmmvgb3+LO5FLKC8kzhWq66+HAQPg4ouhXz+Q4k7kEsoLiXOF6B//gBtvhHPOCcXEi4irAi8kzhWaO+6A664LV2kNGgTr+ceAqxp/BzlXSO67Dy69FI47LvQVqVMn7kSuFvBC4lyhePhh+Mtf4LDD4NFHwwRVzlUDLyTOFYInnwydDNu0Cb9vsEHciVwt4oXEudruhRfglFNg//3h2Wdho43iTuRqGS8kztVm48fD8cfDXnvB6NHQsGHciVwt5IXEudpk+HAoKqJV27aw1VbQqRPsvDOMGQONG8edztVS3trmXG0xfDh06wbFxQjC9LhSGDtr883jTudqMT8ica626NEjTEqVygz6948njysYOS8kknaTNF5SsaR5knpLyupidknHSZoq6SdJ30t6SVKDms7sXCLMmVOx9c5Vk5wWEkmbAuMAA44GegOXAzdkse85wCPAi0An4BzgU/z0nHPB1ltnXt+sWW5zuIKT6w/h7sBGwHFmtgQYK2ljoJek/tG6dUjaAhgAXGRm96Xc9XSNJ3YuCb78EpYvX3d9/frQt2/u87iCkutTW52AMWkFYwShuLQqY7+Top8P1lQw5xLrm2+gXbswVW6fPtC8OSZB8+YweHAYU8u5GlRuIZF0uqTquuRjV2BG6gozmwMUR/eVZj/gY+BsSV9JWiHpDUl/rKZcziXTggXQvj3MmwcvvhjmFJk1i8kTJsCsWV5EXE7IzMreQFoFHGBmb6b+Xqknk1YAV5rZ7WnrvwKGmdl1pew3BvgjsAS4Cvg++tkS2NnM5mfYpxvQDaBp06YtRowYUZnILFu2jIYJ6sSVpLxJygr5l7fusmXsddll1J89m/dvuonFe+/96335lrU8ScqbpKxQtbxt2rSZZmYty93QzMq8AQuAY6LfVwP7lrdPGY+1Argkw/q5QN8y9htLaKA/NGXdxsAioE95z9uiRQurrIkTJ1Z63zgkKW+SsprlWd4lS8z2399s/fXNRo9e5+68ypqFJOVNUlazquUF3rIsPtuzaWwfBzwk6ePow3yopB/LKEx/KOOxFgGbZFjfGFhcxn4Lo5+TUp5niaRpwG5l7Odc7VNcDEcdBVOnwhNPhN7rzsUom0JyFnA+8H/APsBM4LtKPt8M0tpCJG0HNCCt7STNR4Qilj6NmwhHSc4VhuXLw1wikyeHnuzHHht3IufKLyRmVgzcAiCpPdDDzN6t5PO9CFwpqZGZLY3WdQZ+AiaXsd/zQE+gDTA6ytIYaFGSzblab8UKOPnkMG7WkCFhRF/n8kA2V22tkrRvtDiJ0OBdWYOA5cBTktpHDeK9gNss5ZJgSZ9JGlKybGZvAc8CQySdIelw4DlCm8vdVcjjXDKsWgWnnw7PPAP/+hecdVbciZz7VTb9SH4BNox+Px3YsrJPZmaLgHZAHWAUoUf7AMLRRqq60TapTgOeAW4DniQUkbbRYzpXe61eDeeeCyNGwM03w4UXxp3IubVk00YyndDz/BlCm8QJkkq7HMzM7J6yHszMpgNty9mmKMO6ZcB50c25wmAGF18MDzwAPXvCVVfFnci5dWRTSC4C7iUcORhwRRnbGlBmIXHOZcksFI6774YrrgiFxLk8VO6pLTN7zcz2NLP1CUck+5vZeqXcshrF1zmXhRtugFtugfPPD0PBK/2iRefyQ0XH2mpDONXlnKtJ/fuHQnLmmaFx3YuIy2MVGv3XzCYDSNoPOAjYjNBZcIqZvVH98ZwrQHfdBVdfHS71ve8+WM/nn3P5rUKFJJpE6gmgI7CKMObV5kAdSS8BJ0b9TpxzlfHvf8NFF8HRR8OwYVDHzxa7/FfRrzr9gQOAk4F6ZrY1UC9aPgC4uXrjOVdAHn0UzjkHOnaExx6D9dePO5FzWaloITkeuNrMnjCz1QBmttrMngCuAU6s7oDOFYSnn4Y//xn+9Cd46inYcMPy93EuT1S0kDQGvizlvi8JI/I65yripZegc2fYd18YNSrMauhcglS0kLwLnCetfQlJtHxedL9zLlsTJ4aBF/fYI0xM1ahR3Imcq7CKztl+HWHgxRmSngbmA02AY4EiwlS6zrlsvPYaHHkk7LADvPwybJJphgXn8l9FL/+dIGlv4HpCe8jWwNfAG8Bx0fAnzrnyTJsW5hHZZhsYNw622CLuRM5VWkWPSErGyjq5BrI4Vxg++AA6dIBNN4Xx42HrreNO5FyVVKiNRNItknxGQucq65NPoH17qFcvFJHttos7kXNVVpnLf9+X9Kak7tHkUs65bMycCe3ahWHhx4+HHXeMO5Fz1aJChcTMtgfaE6bF/SfwtaRHopkTnXOl+eqrUER+/BHGjoVddy1/H+cSosKD+JjZRDM7ndDQfhGwLTBG0mxJN0jaobpDOpdo8+eH01kLFoRpcvfaK+5EzlWrSo8GZ2bLzGwIYXbDV4HtgGuBTyQ9K6l5NWV0Lrm+/x4OOQS+/BJGjw6dDp2rZSpVSCQVSeop6QvgZWAZ4XLgRsBRhD4lI6orpHOJ9MMPYdysTz6BZ5+Fgw6KO5FzNaKio//+GTgT+BMwB3gAeMDMvkrZbLSkH4Fx1ZbSuaRZtgwOOwzeey+Mo9XemxFd7VXRfiSDgaeBjmY2voztPgFurHQq55Lsp5/CMPCvvx5G8T388LgTOVejKlpItjGzReVtZGZfAzdULpJzCfbLL3DCCWEMrWHDwu/O1XIVHSKl3CLiXMFauRJOOSU0qt97L5x2WtyJnMuJCg+RIqkzcC6wC2FSq7WYWZNqyOVcsqxaBV27hrlEBgyAbt3iTuRczlR0iJRTgQeBzwj9R54Dno8eZwlwV3UHdC7vmUH37jB8OPTrB5deGnci53Kqopf/Xgn0AS6Ilgea2VnA9sACwOdrd4XFLBSO+++HHj3g2mvjTuRczlW0kOwMvGpmq4BVRDMimtlSwnztF1ZvPOfymBlcdx3ceSf89a/Qp0/ciZyLRUULyQ9AyWTSc4HfptwnYPPqCOVcIvTtCzfdFE5r3XorrD1xqHMFo6KF5C3gd9HvzwHXSzpX0hmEQRzfKO8BJO0mabykYknzJPWWVCfbAJLWkzRNkkk6ooL5naset90Gf/87nH463H23FxFX0Cp61dY/gJIxtK6Pfh8I1AGmAmVeqiJpU0KP9+nA0cCOwK2Egva3LDOcA/ymgrmdqz733AOXXw4nnghDhsB6lR6yzrlaIatCImkj4DDCGFrfSGpqZvOBoyVtCGxoZkuyeKjuwEaEaXmXAGMlbQz0ktS/vMeIClFf4Brg/myyO1etHnwQzj8/zLX+8MNQt8JX0DtX65T7vyAaFn4coYiUWCLpJDN72cyWA8uzfL5OwJi0gjGC0FDfChhVzv59CCMNlzU8i3PVa/hw6NGDVrNnh+U99oDHH4cNNog3l3N5Iptj8v7AauBgoD6wO/AOcG8lnm9XwqRYvzKzOYTLhsuc6UfS7wgDRl5Ried1rnKGDw+dC2fP5tdWkM8/h5Ej40zlXF6RmZW9gTQXuNzMRqSs2wX4CNg2GlcruyeTVgBXmtntaeu/AoaZ2XVl7DsZeMPMrpJUBMwEjjSz50vZvhtRm03Tpk1bjBhRuVHtly1bRsOGDSu1bxySlDcJWfc/+WTqzZ+/zvqfmzbl9Uq+p3IhCa9tqiTlTVJWqFreNm3aTDOzluVuaGZl3ghHI39IW1cnWr93efun7bcCuCTD+rlA3zL2Oxn4Btg4Wi4CDDgim+dt0aKFVdbEiRMrvW8ckpQ3EVkls9BjZO2bFHeyMiXitU2RpLxJympWtbzAW5bFZ2y2l5uUfdiSvUXAJhnWNwYWZ9pB0vqES4tvBtaTtAlRR0iggaRG1ZTNubW9UcbV7M2a5S6Hc3ku20tOxkhamWH9+PT1VvagjTNIawuRtB3QgLS2kxQNCON63RbdUo0APgd2KuM5nau4d96BQw+FLbeEpUvDHCMl6tcPnRGdc0B2haQ65xV5EbhSUiMLw6oAdAZ+AiaXss8yoE3auq2AR4HrgAnVmM85mD4dOnSARo3gP/+BKVOgRw9szhzUrFkoIl26xJ3SubxRbiExs+osJIOAi4GnJN0M7AD0Am6zlEuCJX0GTDazs81sJTAp9UGixnaA982s3N70zmXt00+hXTtYf32YMAGaNw+3Ll2YPGkSrVu3jjuhc3knp72pzGyRpHaE4eZHEdpFBhCKSXqurIdNca5azJ4disjKlTB5MuzkZ0ydy0bOu+Wa2XSgbTnbFJVz/yzABzdy1WfevFBEli4NRyK77RZ3IucSw8d3cO7bb0MRmT8fxo2DvfeOO5FzieKFxBW2hQtDw/rs2fDii7DffnEnci5xvJC4wrVkCXTqBB99BKNGQatWcSdyLpG8kLjC9OOPcMQR8PbbYdysDh3iTuRcYnkhcYXn55/hmGPg1VfhkUfgqKPiTuRconkhcYXll1/ChFTjxsHQodC5c9yJnEs8n9rNFY6VK+G00+D552HgQDjjjLgTOVcreCFxhWH1ajjrLHjiCbj1VjjvvLgTOVdreCFxtZ9ZmB73oYegd2+47LK4EzlXq3ghcbWbWSgc994L11wDf/tb3Imcq3W8kLja7e9/h9tvh4svhn79QD6yjnPVzQuJq7369QtDvp9zTigmXkScqxFeSFztdPvt0KNHmDdk0CAvIs7VIC8krvYZPBj++lc4/vjQV6SOz0jgXE3yQuJql4cegu7d4bDDQq/1ut7n1rma5oXE1R5PPgldu0KbNuH3DTaIO5FzBcELiasdXngBTjkF9t8fnn0WNtoo7kTOFQwvJC75xo0L7SF77QWjR0PDhnEncq6geCFxyTZlChx9NOyyC4wZA40bx53IuYLjhcQl19SpoVF9u+1g7FjYfPO4EzlXkLyQuGR6913o2BG22CKc2mraNO5EzhUsLyQueT76CA45BBo0gPHjYdtt407kXEHzQuKS5fPPoX17WG+9UES23z7uRM4VPO+t5ZJjzhxo1w6WL4dJk0IDu3Mudl5IXDJ8/XUoIosXw4QJsMcecSdyzkW8kLj899134XTW11+Hq7P22SfuRM65FDlvI5G0m6TxkoolzZPUW1KZo+pJ2lfSA5I+i/b7WFJPSfVyldvFZPHicHXWF1/AqFFwwAFxJ3LOpcnpEYmkTYFxwHTgaGBH4FZCQStr6rrO0bY3A58CvwP6RD+Pr8HILk5Ll0KnTvDBB/Dcc2EMLedc3sn1qa3uwEbAcWa2BBgraWOgl6T+0bpMbjaz71KWJ0n6GbhXUnMzm13DuV2uFRfDkUeGTodPPAGHHhp3IudcKXJ9aqsTMCatYIwgFJdWpe2UVkQ+iNQJAAAc4klEQVRKvBP9bFJ98VxeWL4cjj0WXnklDAt/7LFxJ3LOlSHXhWRXYEbqCjObAxRH91XEH4HVwMfVE83lhRUroHNnePlluP/+MKKvcy6vycxy92TSCuBKM7s9bf1XwDAzuy7Lx9kKeA8YbWZdS9mmG9ANoGnTpi1GjBhRqczLli2jYYJGk01S3nWyrlrFbn370mTiRD69+GLm5tmRSKJf2zyXpLxJygpVy9umTZtpZtay3A3NLGc3YAVwSYb1c4G+WT7GBsArwBfAptns06JFC6usiRMnVnrfOCQp71pZV60y69rVDMz6948tU1kS+9omQJLyJimrWdXyAm9ZFp+xuW5sXwRskmF9Y2BxeTtLEjAM2B040MwWVW88FwszuOiiML96z55w5ZVxJ3LOVUCuC8kM0tpCJG0HNCCt7aQUAwiXDR9iZtls7/KdWSgcAweGnz17xp3IOVdBuS4kLwJXSmpkZkujdZ2Bn4DJZe0o6VrgIuAkM5tSszFdjRo+HHr0oNWcObDxxvDDD3DBBXDzzSDFnc45V0G5vmprELAceEpS+6hBvBdwm6VcEhz1YB+Ssnwq0I9wWmuupP1Tblvm9k9wVTJ8OHTrBrNnI7NQROrUCXOtexFxLpFyWkiiNo12QB1gFHAD4XRV+vmMutE2JTpEP7sC/027HV5ziV2169EjdDZMtWoV/K2sgQ2cc/ks54M2mtl0oG052xSlLXclFBGXdHPmVGy9cy7v+cRWLndefTVMSJVJs2a5zeKcqzZeSFzNM4Nbb4VWrWDzzaFe2qDN9etD377xZHPOVZkXElezFi0KY2VdcQUccwx88kkY+qR5c0yC5s1h8GDo0iXupM65SvJC4mrOtGnQogW88ALcfnsYxbdx41A0Zs1i8oQJMGuWFxHnEs4Liat+ZqGD4R//CCtXwn/+A5dc4pf3OldLeSFx1WvpUjj11NDBsF07eOed0EfEOVdreSFx1ef992HffeHxx6FfP3j++dC47pyr1XLej8TVUkOHwvnnhzaQ8eOhdeu4EznncsSPSFzVFBfD2WfDmWeGU1jvvONFxLkC44XEVd4nn4Ti8e9/hyFOxo6FrbaKO5VzLsf81JarnMcfD0ciG24IL74Ihx4adyLnXEz8iMRVzPLlYRKqzp1hzz3DqSwvIs4VNC8kLnuzZsHBB8Ndd8Fll8HkybDddnGncs7FzE9tueyMGgWnnx46Gz71VBj2xDnn8CMSV54VK+Dqq+Goo2D77cOwJ15EnHMp/IjElW7uXDj5ZJgyBbp3hwED1h251zlX8LyQuMzGjg2DKRYXh+lxTz017kTOuTzlp7bc2latgl69oGNHaNIEpk71IuKcK5Mfkbg1vv02HIWMGxca1gcOhAYN4k7lnMtzXkhcMGVK6BuycGGYeOqss3zYd+dcVvzUVqEzg3/+M4yPVb8+vP566LHuRcQ5lyU/IilkixbBGWeEPiInnABDhsDGG8edyjmXMH5EUqimToV99oGXXoI77wxjZ3kRcc5VgheSQmMGd98NBx0Eq1eHaXAvushPZTnnKs0LSSFZuhROOQUuvBAOOSQMuLjffnGncs4lnBeSQvHee9CyJTz5JNx0Ezz3HGy2WdypnHO1gDe2F4IHHgjT4G66KUyYAH/6U9yJnHO1SM6PSCTtJmm8pGJJ8yT1llQni/0aS3pA0iJJP0gaLmnzXGROrOLiMAXuWWfBgQeGU1leRJxz1SynRySSNgXGAdOBo4EdgVsJBe1v5ez+GPB/wDnAauBm4Bng4JrKm2gffxwu6f3wQ7j++nCrU269ds65Csv1EUl3YCPgODMba2aDgBuAyySVeu2ppAOAjsAZZjbSzJ4GTgMOktS+RpIOHw5FRbRq2xaKisJyPkvNu+WWsNde8M034fLeG27wIuKcqzG5LiSdgDFmtiRl3QhCcWlVzn7zzeyVkhVm9iYwM7qveg0fDt26wezZyAxmzw7L+VpM0vMuWBDmEbn+eujQIe50zrlaLteN7bsCE1JXmNkcScXRfaPK2G9GhvUfRfdVrx49QvtCquJi6NoV+vWr9qersk8+gZUr1163ejXcemvoI+KcczUo14VkU2BxhvWLovsqs98OmXaQ1A3oBtC0aVMmTZqUdchWc+aQqXuerVzJd1tumfXj5MqW06dnzjtnDpMr8Hfn2rJlyyr07xK3JOVNUlZIVt4kZYXc5I3j8l/LsE6lrK/0fmY2GBgM0LJlS2vdunX2CZs1C6ez0p+seXOa5OMbqKgoc95mzajQ351jkyZNyut86ZKUN0lZIVl5k5QVcpM3120ki4BNMqxvTOYjjvL226Sc/Sqnb98wEm6q+vXD+nyUtLzOuVol14VkBmltGpK2AxqQuQ2k1P0ipbWdVE2XLjB4MDRvjknQvHlY7tKl2p+qWiQtr3OuVsl1IXkR6CipUcq6zsBPwORy9ttK0kElKyS1JLSPvFgTQenSBWbNYvKECTBrVv5/KCctr3Ou1sh1IRkELAeektQ+ahDvBdyWekmwpM8kDSlZNrP/AmOAYZKOk3QMMByYYmbjcvoXOOecW0tOC4mZLQLaAXUIl/reAAwAeqZtWjfaJtXJhKOWfwPDgGnAsTWZ1znnXPlyftWWmU0H2pazTVGGdYuBM6Obc865POHDyDvnnKsSLyTOOeeqRGbl9QNMPknfAev22MvOFsCCaoxT05KUN0lZIVl5k5QVkpU3SVmhanmbm1m5w3kURCGpCklvmVnLuHNkK0l5k5QVkpU3SVkhWXmTlBVyk9dPbTnnnKsSLyTOOeeqxAtJ+QbHHaCCkpQ3SVkhWXmTlBWSlTdJWSEHeb2NxDnnXJX4EYlzzrkq8ULinHOuSryQOOecqxIvJM4556rEC4lzzrkqiWPOdlcNopklDyPMW/+EmX0vaVvgCmBHYBYw2Mzejy8lSLoaGB13jmxJ2gioa2ZLU9ZtCVwI7AasBv4HDDSzH+JJ6Vx+8ct/I5JEmN/kcOC3wGbAKmA+8Dow1Mw+iS/hGpL+ALwMNARWAguBjsBoQuYPgT2ArYD2ZvafmKIiaTVghCmRHwEeM7PP4spTHkmjgU/N7JJo+QDCLJyrCXPgCGgB/AK0NbMPY8y6N7CRmb2Wsu5Q4FrWFL13gV6p2+SL6P/ckcA+hPfIW4QvHXn9oSRpY8LYVW3NbErceeDXTG2BDYAXzOzH6AvQBYSZZL8gfLGcVyPPn+f/ZjkRveCjCR8Q8wmzOP6G8OZ+kfAP8X9AHzPrE1fOEpLGEo4mjwV+JEwOdgzhg+4EM1shaUPgGaCembWJMetq4GZgT+AQQu63CUXlcTObG1e2TCQtAM42s2ej5dcJr/ExJUcpkhoDzwE/m1nHGLO+Dowys77R8lnA/cBEYAKh6LUDDgaOL/mbYsr6GuF1/Sha3pTwZagFsCzarCHhS1vH1CPCOEg6v4y7NwL+CdwBfApgZgNzkSsTSTsB44HtolUzgQ7AWGAT4HPC59dPQAsz+6raQ5hZwd+ARwlviD1T1m0DvASMjJZbEd7wZ+VB3u+BTinLTQjfPjukbXc4sCDmrKuBP0S/bwp0i970K6PbpGjd5nG/rlHGYuBPKcu/pL+uKa/tjzFnXZKaDfgM+FeG7QYB7+bL+yBaHkI4kj40Zd2hwCJgQB68D1YTju5Xl3JLvW9VzFkfJxx57kQ4k/JQ9Hn2GtAo2maLaJt7ayKDN7YHnYBrLOU8voVDwO7AMZK2NrPJQD/gkpgyprLolrpM2rpMy7Eys0VmNtjM2gHbApcTDsUHAfMkvRBrwOADIPUIbj7hP2e6zQlFJ06r05abA09m2O5JwjfSfHIU0NvMXipZEf3eFzgutlRrPAd8C5wN1DGz9UpuhPeDgNbRuvRpwXPtIKCvmX1mZguBvxHaSW+x6MjOzBYAt7P2e7vaeCEJRPiGkW5VdF/jaPkNYJdchSrDNOAKSY0krQdcB8wFzpNUB0BSXeB8wgdj3jGzb8zsDjP7I7A90JNwFBi3m4BrJJ0VvYZ9gX9KOkTSBpI2jNoh/kH4Jhin/wBdUpY/BDINF74v4f2RTzYhtImkm0Zo24uVmR0DnAFcCUyVdGDq3fGkKtWmwDcpyyX/1ulzMH1B+AJX7fyqrWAccKOk98zsC/j1HO6dhH+gkkb2hkA+XKnTg3D+cyHh9FAxoaHtSeBTSSWN7dsQThfkNTObTfgAvykPsjwl6SLCt7cBwMeELxIl35yN8OXiOcKHTJyuA16Nvkz8i9DI/qCkzQinDCG0kVwKXBNLwrUdL6mk0C0CMk2YtAXhlF3szOxlSb8jvH4vSHqJcFVkrO03GXxLOBotsQq4l3A0naoJNZTdG9uB6LLZlwiH/7MJ58W3JzS6n2JmL0bb9SfMGNY5rqwlosxHEL4MjDSzryVtBVzFmr/jfjN7O8aYSOoJ3Gc1dLVITZG0OdAZ+APhG/J6hML9EfC8mU2LMd6vJP0euAfYjzVFjpTfFxFOId0RT8Iguugi3VAzOyttu3uB3czs4Nwky070f6s/4bTbvYTi0sbMXok1GCDpGWBh+muZYbt/Ab81s/bVnsELSRCdEjoJ2AuoR2i4fCQ65+hcXpP0W0IxSS96r5nZijizVYSkc4HPzWxC3FkyiS4HH0D4sna45cFl1ZKaAvXNbGY5211GuOhifLVn8EJS+0iqY2aZ2nzyhqR6hAbB1cBn+fhhF7WR7EBKnyIzmxNvKufyjze2p5G0u6TjJZ0j6ezo993jzpVO0nGSnpE0WtKR0brOkmYBv0iaHX27i5Wk06L+DSXLdSXdRPjG/B7hYoCFkvLhHD4AklpIeo5wPvkj4FVC/4aZkuZK6i2pfqwhaxFF4s6RiaSN0v+tJf0++lxoEVeuvBPn9c/5dAPOIrQrZLp2fBVhyJEz484ZZT0pyjUFeJbQ2H4uoW1nCKE366NR7o4xZ50OnJeyfGuU9+/AgYRLF3sROktdlwevbQdC29hbhCuzehE6pf4SZb6ccHXU/4BN8yDvEYR+Oe8Dj5HSByZlm/2Iv69DB6I+DSnrjiF0Tl0JrIhe88Pjfk2jbI2Bp6NcK4H7gDrAg2mfC68CW8SdN8u/6fiaeh/E/sflww24KHrD3E3oBbxF9KapE/1+EHBX9AFzQR7knQoMSlnuEmW7NW27B4BxMWctBlqlLH8LXJJhuyuA2Xnw2k4DHizlPTKLcBRfL/oAHBhz1kNSPszuirKvioq1UrbLh0KyirU7JB4bfRi/Fv3bXxH9vpIMHUBjyHsnYRiUi4DToy8PI4Evo6K4JaH/2VzgnrjzZvk31Vgh8TYSQNIXhA/m/uVsdxXQ3cx2yE2yUnMsAY4zs3HRcmPC1TntLaWRMjrlda+ZxdY/Q9LXwIVmNjJaXk44SpqUtt0hwHNmtlHuU66V4yfgKDMbm7Z+U8KIArub2UeSTgduNrOt48gZZZpCGBfszJR1ZxE+BMcSrjj8WdJ+hEb32DrORVdt7W9mb0bLbwNzzezItO1GAw3MrFUMMVNzzAT6mdl90fLehEJ9ppk9mLLduYQj6e3jSQqS/p3lps0JnSir/X3gbSTBVsCbWWz3JnnQWYpwaWfqm6FkrKLFadstI3T8itNzhM6TG0TL44BTMmx3CuFbX9y+JVy5l24vwute0o9oNms6qsZlD+Dh1BVm9m/CcD77AxOiPiX5aA/CZbTpBhMGcYxbE9b0H4NoTC3CuFWpPiNzf5hcOoNwlLRnObfmpT1AVXmHxOA94FxJr5hZpuvdS0YqPTfaNm6zCaO7jgEws1XRZYkfpW23A2v3eI3DtYQe2B9Iuh8YBdwsaQ/WdJprC+xNGAk2boOBPpIaENoefiH0DO8BTLQ1/WF2AOK+gutnoEH6SjObFvXEHkM4XdQrx7lKk3r64wfWfAFK9SP58QV3JqEgT46WDyacivsjoW2yxIHE/z74FHjTzE4vayNJJxDa0aqdF5LgckKHxOmSniIMeb6Y8MbfBNiVcE53W/Kjp/hTpA11YGZvZNjuVNZ+0+ecmS2UtD/hg/gywjc9gAOi2y+E0zAHm9nUeFKuYWZ9o9Mw1xCGbYHwPniU0AmtxArC2Gtxeo9wnv659DvM7IuomIwGhuY4V2nGSFoZ/d4Y+D1rvkyU2BX4OpehSjEIuEPSnoSidxLhS9H1khoSBkDcB/grEPeI4K8TClx5UjusVitvI4lI2pHQK/xQ1gzHXOJLwpU7/zSz9EPbvCWpGbDYzPJiyAkASUWs3Wnuc8vPPiTrE/q51AO+yKfXsISkvxCGSdnbSuk4Gx1ZPU1oP4vtm340wkG6T83skbTtJkXr8+HS9YsJp1zXJ4wSMUjSKYQ2qJJBOwcDV8f5Ho4uQz7QzO4sZ7stCG18k8varlIZvJCsK7puvKRtYbGZxT3Kq3MuT0Snubcws+/izpIvvJDUMtFh99tAl3w4VaQETl2rhExj7Fy+8EKSIvoAaQJ8bGbrNARGh4aHmdmwnIdbO8dhZdzdgNCgdg3REPJmNjoXuTJRgqauhWRNY5ytaByuE82sd8w5Yp0OtqqiI5HUqYGnEf6O2D9EFUZVPp7w/2momc2QtBdwA2u+/NxtKfO/VKu4O8nkww3YEHiC8EGxitCQOgRonLZd7B27ohxJmr1tAXB0yvLrhKuhGqWsa0y4OmZMHry2YwlT1W5CODd+F/AVYQSB9VPeLy8SruKK/f2bxd9UYx3RKpBhJ8LVhiXvy88JH3BfEIr1VMLw8fOBbfPgNXuNMFJuyfKmUcbVUc4lrOlQ2SiunFG2joQvYt9Er+sSwgRWiwidVe+O/t+tIkwZXf0Z4v4Hy4cbcD3hKq1zCRMDXRK9oT8Fdk7ZLl8KyTTClS1nEq4NT739LnqDn1SyLuasiZm6NsqRpGmMm2V56x73+5Y8mA62gnkTMzVwVCyeIMzkCOECjEXAkLTtHgJer5EMcf+D5cONcLnvhWnrtgJeAb4DDojW5UshEWGe828JwzZsn3Jf4+g/wTpjLsWU9U2gZ8ryl8DJGbY7HfguD/IuSPuw2DJ6PQ9J2+6wPCgkJUef5d3y4ch0HnBSynLzKNdxadudCXySB++D9ELyHXBphu1iH9qHcHly+5TlTaP8bdO260C4eKjaM3g/kmA70joamtk3ktoRqvg4SV3Ij+vbsfCuGCzpceBG4D1Jd0W/55ubgOGSvgSGsWbq2u8Jp7NEOAzPh6lrYc00xq8SOselTmM8wULnz3yZxngpMAG4v5ztDiJc2h6n2KeDraJ8nhr4J9bumFrye/pwQ/UJnVirnReSYB6wM+EI5FcWrg0/WdLthEPHWBvZ05nZYuBCSYMJ17Z/CtxMHs0pbcmauhaSNY3xm4R2vBfK2iia+yVusU8HWwlJmRr4VUJHyU+jLLcQRt2+OhqtY2k0Ht9VhMJX7fyqLX4d9GwHM2tdxjbXEr5Nm8U4+F1ZJJ1MmA50W8LgbLFPA1pCCZm6FhI1jfHfgW5mlt6BNn27PwE3mFmb3CTLmCH26WArQgmaGljSToQx7EreB7MIR/lPEkYKmA0UEb4YtTGz/1V7Bi8kv1461xm4ycy+L2O7Uwnnys8sbZu4RaddGgDLLM9nSXSFQ3kwHWxNUJ5MDRz1HzuQcKXheDP7KepYfQ5rvvw8YmZf1cjzeyFxzjlXFfkwyqarIZLukzQk7hzZSFJWSF5e52qSN7ZXgKT7gPXM7Oy4s2SpDcn5spCkrJCgvJLGEc4+tIs7S3mSlBWSlbcms3ohqZjEfHgAmNlOcWfIVpKyQuLyiuS8b5OUFZKVt8ayehtJLRZd9tnEzOKeeKdcScoKycvrXE1KSiXNC5LqRXN8JMXhhJnekiBJWSFBeSWtn5T3bZKyQrLy1mRWLyQVk5gPD1cYJF0g6XNJSyW9IenPGTbbhzx43yYpKyQrb9xZvY0kgSRle816pp64OZWkrJCsvFEH1H8RpgF+h9CPYKiko4E/m9lPceZLlaSskKy8+ZDV20io8IfHbnH3bFeY9/pjwjAIZfkNsF+ceZOUFZKVV9JbwAQzuyplXTtgOKF38+EWJuXaD3jNs2YvSXnzIasXEpL14QEg6X+Eybc6l7PdCcBjMb/JE5M1ypGYvJKWAkea2aS09UWE+VLqAJ0I40HF/WGXmKyQrLz5kNXbSIIPgA/M7MSybsBtcQeNvAHsn8V2JQMixilJWSFZeX8gfDisxcxmAX8kDIn/GrBvbmNllKSskKy8sWf1IxJ+HXjtUDNrXs52xxPm8I61AEvaEdjdzJ4rZ7uNCJeopg/VnTNJyhrlSExeSc8CS83stFLu34gwcF8nYh5sNElZozyJyZsPWb2QkKwPD+dKSDoR+CtwhJktLGWbOsA9hMFGt89lvrQcickaZUlM3nzI6oXEOedclXgbiXPOuSrxQuKcc65KvJC4giKpq6RpUQ/gRZLekVQjV+NJ2kVSL0mbZLFtL0mWcpsnaWTUflfevl2jfRpWT3LnKsYLiSsYCtMl3w+MAY4DTgeeBY6qoafcBegJlFtIIj8AB0S3K4DfA+MlNShnvxeifYormdO5KvEhUlwhuRC418yuS1k3StINcQVKs9LMXo9+f13SHOA/wGHAE+kbR1fi1DGz74DvchfTubX5EYkrJJsA36SvtJRLFyUVRaeJTpX0UHQK7FtJPdP3k9Q2GiDvZ0nzJQ0sOb0kqTUwKtp0ZvSYsyqYd1r0syh6zKGS3pJ0jKQPgZ+B/TKd2pK0kaT+kmZLWi5ppqR/pOU/R9KH0f2zJV2Fc5XgRySukLwNXBR903/ezL4vY9t/As8DJwB/AnpKWmBmdwNI2g14CRgLHA9sB9wE7AAcGj3XFcAthNNoXwPLK5i3KPr5Tdq6/kBvYD5hNNe12lEkiXDK7gCgD6Eg/QY4OGWbK4F+0WNNAloAfSQVm9ldFczpCp2Z+c1vBXEDfgd8QRjeZDXwIeEDeeOUbYqi+19O2/c+YC5hqmWAEcCnhFNLJducFO17QLR8RLRclEW2XoShLOpGt12AicASYOtom6HR4/0+bd+u0fqG0XLHaPmoUp5rY2AZ0DNtfW9C0apTXl6/+S315qe2XMEws/eA3xIa1wcSxsr6O/BWhiuenk5bfgrYBtg2Wv4D8LSZrUrZZiSwEjiokhE3B1ZEt48JRzedzezrlG3mmtn/ynmctsBCK32khgOABsATkuqW3IAJQFPW/I3OZcVPbbmCYmbLCW0XowAknU24kuts4I6UTb9N27VkeWtgTvRzftpjr5L0PbBZJeP9ALQnHE18A8wzs/ShJ+avs9e6NiecSitNyQB/H5Zy/3aADwPksuaFxBU0MxsiqT+wa9pdTUpZ/jrl51rbRFdRbQ5kHO8oCyvN7K1ytslmTKPvCYWuNCX5jiBzYfo4i+dw7ld+assVDEnpxQFJWwKNWfcD9di05ZIG86+i5TeAY6PikbpNXWBKtPxL9LNeFWJXxnhgM0lHlHL/f4GfgG3M7K0Mt6W5i+pqAz8icYXk/WjI7ZcJp6qaE66sKgYeTNt292h6gZGEq7bOBi4xs9XR/TcSpjV9RtI9hHaFm4ExZvbfaJuSb/Z/kTQCKDaz92vmT1vLWEKny0ck9SZcQbY18Ccz+4uZLZbUC7hDUnPgFcKXyl2ANmaWXkSdK5MXEldIegNHA3cS2jG+IUz409nMZqZtexXh1M9IQn+NPsCvl8Wa2YeSOhEuoX2KcHXVo9F+JdvMlnQFcDFwEeFopqgm/rBUZmaSjo0yX0qYInoe8EjKNv0lzSMMP3454W/8BHispvO52seHkXcuRTQ96UzC1KXPx5vGuWTwNhLnnHNV4oXEOedclfipLeecc1XiRyTOOeeqxAuJc865KvFC4pxzrkq8kDjnnKsSLyTOOeeq5P8BYAgkm/oTYvEAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot exact payoff function (evaluated on the grid of the uncertainty model)\n", + "x = uncertainty_model.values\n", + "y = np.minimum(np.maximum(0, x - strike_price_1), strike_price_2 - strike_price_1)\n", + "plt.plot(x, y, 'ro-')\n", + "plt.grid()\n", + "plt.title('Payoff Function', size=15)\n", + "plt.xlabel('Spot Price', size=15)\n", + "plt.ylabel('Payoff', size=15)\n", + "plt.xticks(x, size=15, rotation=90)\n", + "plt.yticks(size=15)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "exact expected value:\t0.5049\n", + "exact delta value: \t0.9291\n" + ] + } + ], + "source": [ + "# evaluate exact expected value (normalized to the [0, 1] interval)\n", + "exact_value = np.dot(uncertainty_model.probabilities, y)\n", + "exact_delta = sum(uncertainty_model.probabilities[np.logical_and(x >= strike_price_1, x <= strike_price_2)])\n", + "print('exact expected value:\\t%.4f' % exact_value)\n", + "print('exact delta value: \\t%.4f' % exact_delta)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Evaluate Expected Payoff" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "# set number of evaluation qubits (=log(samples))\n", + "m = 6\n", + "\n", + "# construct amplitude estimation \n", + "ae = AmplitudeEstimation(m, bull_spread)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "# result = ae.run(quantum_instance=BasicAer.get_backend('qasm_simulator'), shots=100)\n", + "result = ae.run(quantum_instance=BasicAer.get_backend('statevector_simulator'))" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exact value: \t0.5049\n", + "Estimated value:\t0.5000\n", + "Probability: \t0.9955\n" + ] + } + ], + "source": [ + "print('Exact value: \\t%.4f' % exact_value)\n", + "print('Estimated value:\\t%.4f' % result['estimation'])\n", + "print('Probability: \\t%.4f' % result['max_probability'])" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot estimated values for \"a\"\n", + "plt.bar(result['values'], result['probabilities'], width=0.5/len(result['probabilities']))\n", + "plt.xticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.title('\"a\" Value', size=15)\n", + "plt.ylabel('Probability', size=15)\n", + "plt.ylim((0,1))\n", + "plt.grid()\n", + "plt.show()\n", + "\n", + "# plot estimated values for option price (after re-scaling and reversing the c_approx-transformation)\n", + "plt.bar(result['mapped_values'], result['probabilities'], width=1/len(result['probabilities']))\n", + "plt.plot([exact_value, exact_value], [0,1], 'r--', linewidth=2)\n", + "plt.xticks(size=15)\n", + "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.title('Estimated Option Price', size=15)\n", + "plt.ylabel('Probability', size=15)\n", + "plt.ylim((0,1))\n", + "plt.grid()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Evaluate Delta\n", + "\n", + "The Delta is a bit simplier to evaluate than the expected payoff.\n", + "Similarly to the expected payoff, we use comparator circuits and ancilla qubits to identify the cases where $K_1 \\leq S_T \\leq K_2$.\n", + "However, since we are only interested in the probability of this condition being true, we can directly use an ancilla qubit as the objective qubit in amplitude estimation without any futher approximation." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "# setup piecewise linear objective fcuntion\n", + "breakpoints = [uncertainty_model.low, strike_price_1, strike_price_2]\n", + "slopes = [0, 0, 0]\n", + "offsets = [0, 1, 0]\n", + "f_min = 0\n", + "f_max = 1\n", + "c_approx = 1 # no approximation necessary\n", + "bull_spread_delta_objective = PwlObjective(\n", + " uncertainty_model.num_target_qubits, \n", + " uncertainty_model.low, \n", + " uncertainty_model.high,\n", + " breakpoints,\n", + " slopes,\n", + " offsets,\n", + " f_min,\n", + " f_max,\n", + " c_approx\n", + ")\n", + "\n", + "# construct circuit factory for payoff function\n", + "bull_spread_delta = UnivariateProblem(\n", + " uncertainty_model,\n", + " bull_spread_delta_objective\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "# set number of evaluation qubits (=log(samples))\n", + "m = 6\n", + "\n", + "# construct amplitude estimation \n", + "ae_delta = AmplitudeEstimation(m, bull_spread_delta)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "# result_delta = ae_delta.run(quantum_instance=BasicAer.get_backend('qasm_simulator'), shots=100)\n", + "result_delta = ae_delta.run(quantum_instance=BasicAer.get_backend('statevector_simulator'))" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exact delta: \t0.9291\n", + "Esimated value:\t0.9410\n", + "Probability: \t0.4189\n" + ] + } + ], + "source": [ + "print('Exact delta: \\t%.4f' % exact_delta)\n", + "print('Esimated value:\\t%.4f' % result_delta['estimation'])\n", + "print('Probability: \\t%.4f' % result_delta['max_probability'])" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot estimated values for delta\n", + "plt.bar(result_delta['values'], result_delta['probabilities'], width=0.5/len(result_delta['probabilities']))\n", + "plt.plot([exact_delta, exact_delta], [0,1], 'r--', linewidth=2)\n", + "plt.xticks(size=15)\n", + "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.title('Estimated Option Delta', size=15)\n", + "plt.ylabel('Probability', size=15)\n", + "plt.ylim((0,1))\n", + "plt.grid()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "qiskit_master", + "language": "python", + "name": "qiskit_master" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/qiskit/finance/simulation/credit_risk_analysis.ipynb b/qiskit/finance/simulation/credit_risk_analysis.ipynb new file mode 100644 index 000000000..90b4e34b4 --- /dev/null +++ b/qiskit/finance/simulation/credit_risk_analysis.ipynb @@ -0,0 +1,1386 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# _*Qiskit Finance: Credit Risk Analysis*_ \n", + "\n", + "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", + "\n", + "***\n", + "### Contributors\n", + "Stefan Woerner[1], Daniel Egger[1]\n", + "\n", + "### Affliation\n", + "- [1]IBMQ" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Introduction\n", + "This tutorial shows how quantum algorithms can be used for credit risk analysis.\n", + "More precisecly, how Quantum Amplitude Estimation (QAE) can be used to estimate risk measures with a quadratic speed-up over classical Monte Carlo simulation.\n", + "The tutorial is based on the following two papers:\n", + "- Quantum Risk Analysis. Stefan Woerner, Daniel J. Egger. [Woerner2019]\n", + "- Quantum Credit Risk Analysis. Daniel J. Egger et al. [Egger2019]\n", + "\n", + "A general introduction to QAE can be found in the following paper and tutorial:\n", + "- Quantum Amplitude Amplification and Estimation. Gilles Brassard et al.\n", + "- Qiskit Tutorial on Quantum Amplitude Estimation\n", + "\n", + "The structure of the tutorial is as follows:\n", + "1. [Problem Definition](#Problem-Definition)\n", + "2. [Uncertainty Model](#Uncertainty-Model)\n", + "3. [Expected Loss](#Expected-Loss)\n", + "4. [Cumulative Distribution Function](#Cumulative-Distribution-Function)\n", + "5. [Value at Risk](#Value-at-Risk)\n", + "6. [Conditional Value at Risk](#Conditional-Value-at-Risk)" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit import QuantumRegister, QuantumCircuit, BasicAer, execute\n", + "\n", + "from qiskit.aqua.components.uncertainty_models import GaussianConditionalIndependenceModel as GCI\n", + "from qiskit.aqua.components.uncertainty_problems import UnivariatePiecewiseLinearObjective as PwlObjective\n", + "from qiskit.aqua.components.uncertainty_problems import MultivariateProblem\n", + "from qiskit.aqua.circuits import WeightedSumOperator\n", + "from qiskit.aqua.circuits import FixedValueComparator as Comparator\n", + "from qiskit.aqua.algorithms import AmplitudeEstimation\n", + "\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# define backend to be used\n", + "backend = BasicAer.get_backend('statevector_simulator')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Problem Definition\n", + "\n", + "In this tutorial we want to analyze the credit risk of a portfolio of $K$ assets.\n", + "The default probability of every asset $k$ follows a *Gaussian Conditional Independence* model, i.e., given a value $z$ sampled from a latent random variable $Z$ following a standard normal distribution, the default probability of asset $k$ is given by\n", + "\n", + "$$p_k(z) = F\\left( \\frac{F^{-1}(p_k^0) - \\sqrt{\\rho_k}z}{\\sqrt{1 - \\rho_k}} \\right) $$\n", + "\n", + "where $F$ denotes the cummulative distribution function of $Z$, $p_k^0$ is the default probability of asset $k$ for $z=0$ and $\\rho_k$ is the sensitivity of the default probability of asset $k$ with respect to $Z$. Thus, given a concrete realization of $Z$ the individual default events are assumed to be independent from each other.\n", + "\n", + "We are interested in analyzing risk measures of the total loss\n", + "\n", + "$$ L = \\sum_{k=1}^K \\lambda_k X_k(Z) $$\n", + "\n", + "where $\\lambda_k$ denotes the \\emph{loss given default} of asset $k$, and given $Z$, $X_k(Z)$ denotes a Bernoulli variable representing the default event of asset $k$. More precisely, we are interested in the expected value $\\mathbb{E}[L]$, the Value at Risk (VaR) of $L$ and the Conditional Value at Risk of $L$ (also called Expected Shortfall). Where VaR and CVaR are defined as\n", + "\n", + "$$ \\text{VaR}_{\\alpha}(L) = \\inf \\{ x \\mid \\mathbb{P}[L <= x] \\geq 1 - \\alpha \\}$$\n", + "\n", + "with confidence level $\\alpha \\in [0, 1]$, and\n", + "\n", + "$$ \\text{CVaR}_{\\alpha}(L) = \\mathbb{E}[ L \\mid L \\geq \\text{VaR}_{\\alpha}(L) ].$$\n", + "\n", + "For more details on the considered problem see [Egger2019].\n", + "\n", + "The problem is defined by the following parameters:\n", + "- number of qubits used to represent $Z$, denoted by $n_z$\n", + "- trunaction value for $Z$, denoted by $z_{\\text{max}}$, i.e., Z is assumed to take $2^{n_z}$ equidistant values in $\\{-z_{max}, ..., +z_{max}\\}$ \n", + "- the base default probabilities for each asset $p_0^k \\in (0, 1)$, $k=1, ..., K$\n", + "- sensitivities of the default probabilities with respect to $Z$, denoted by $\\rho_k \\in [0, 1)$\n", + "- loss given default for asset $k$, denoted by $\\lambda_k$\n", + "- confidence level for VaR / CVaR $\\alpha \\in [0, 1]$." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# set problem parameters\n", + "n_z = 2\n", + "z_max = 2\n", + "z_values = np.linspace(-z_max, z_max, 2**n_z)\n", + "p_zeros = [0.15, 0.25]\n", + "rhos = [0.1, 0.05]\n", + "lgd = [1, 2]\n", + "K = len(p_zeros)\n", + "alpha = 0.05" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Uncertainty Model\n", + "\n", + "We now construct a circuit that loads the uncertainty model. This can be achieved by creating a quantum state in a register of $n_z$ qubits that represents $Z$ following a standard normal distribution. This state is then used to control single qubit Y-rotations on a second qubit register of $K$ qubits, where a $|1\\rangle$ state of qubit $k$ represent the default event of asset $k$. The resulting quantum state can be written as\n", + "\n", + "$$ |\\Psi\\rangle = \\sum_{i=0}^{2^{n_z}-1} \\sqrt{p_z^i} |z_i \\rangle \\bigotimes_{k=1}^K \n", + "\\left( \\sqrt{1 - p_k(z_i)}|0\\rangle + \\sqrt{p_k(z_i)}|1\\rangle\\right),$$\n", + "\n", + "where we denote by $z_i$ the $i$-th value of the discretized and trucated $Z$." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# construct circuit factory for uncertainty model (Gaussian Conditional Independence model)\n", + "u = GCI(n_z, z_max, p_zeros, rhos)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "# determine the number of qubits required to represent the uncertainty model\n", + "num_qubits = u.num_target_qubits\n", + "\n", + "# initialize quantum register and circuit\n", + "q = QuantumRegister(num_qubits, name='q')\n", + "qc = QuantumCircuit(q)\n", + "\n", + "# construct circuit\n", + "u.build(qc, q)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We now use the simulator to validate the circuit that constructs $|\\Psi\\rangle$ and compute the corresponding exact values for\n", + "- expected loss $\\mathbb{E}[L]$\n", + "- PDF and CDF of $L$ \n", + "- value at risk $VaR(L)$ and corresponding probability\n", + "- conditional value at risk $CVaR(L)$" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "# run the circuit and analyze the results\n", + "job = execute(qc, backend=BasicAer.get_backend('statevector_simulator'))" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "# analyze uncertainty circuit and determine exact solutions\n", + "p_z = np.zeros(2**n_z)\n", + "p_default = np.zeros(K)\n", + "values = []\n", + "probabilities = []\n", + "for i, a in enumerate(job.result().get_statevector()):\n", + " \n", + " # get binary representation\n", + " b = ('{0:0%sb}' % num_qubits).format(i)\n", + " prob = np.abs(a)**2\n", + "\n", + " # extract value of Z and corresponding probability \n", + " i_normal = int(b[-n_z:], 2)\n", + " p_z[i_normal] += prob\n", + "\n", + " # determine overall default probability for k \n", + " loss = 0\n", + " for k in range(K):\n", + " if b[K - k - 1] == '1':\n", + " p_default[k] += prob\n", + " loss += lgd[k]\n", + " values += [loss]\n", + " probabilities += [prob] \n", + "\n", + "values = np.array(values)\n", + "probabilities = np.array(probabilities)\n", + " \n", + "expected_loss = np.dot(values, probabilities)\n", + "\n", + "losses = np.sort(np.unique(values))\n", + "pdf = np.zeros(len(losses))\n", + "for i, v in enumerate(losses):\n", + " pdf[i] += sum(probabilities[values == v])\n", + "cdf = np.cumsum(pdf)\n", + "\n", + "i_var = np.argmax(cdf >= 1-alpha)\n", + "exact_var = losses[i_var]\n", + "exact_cvar = np.dot(pdf[(i_var+1):], losses[(i_var+1):])/sum(pdf[(i_var+1):])" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Expected Loss E[L]: 0.6409\n", + "Value at Risk VaR[L]: 2.0000\n", + "P[L <= VaR[L]]: 0.9591\n", + "Conditional Value at Risk CVaR[L]: 3.0000\n" + ] + }, + { + "data": { + "image/png": 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\n", 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "print('Expected Loss E[L]: %.4f' % expected_loss)\n", + "print('Value at Risk VaR[L]: %.4f' % exact_var)\n", + "print('P[L <= VaR[L]]: %.4f' % cdf[exact_var])\n", + "print('Conditional Value at Risk CVaR[L]: %.4f' % exact_cvar)\n", + "\n", + "# plot loss PDF, expected loss, var, and cvar\n", + "plt.bar(losses, pdf)\n", + "plt.axvline(expected_loss, color='green', linestyle='--', label='E[L]')\n", + "plt.axvline(exact_var, color='orange', linestyle='--', label='VaR(L)')\n", + "plt.axvline(exact_cvar, color='red', linestyle='--', label='CVaR(L)')\n", + "plt.legend(fontsize=15)\n", + "plt.xlabel('Loss L ($)', size=15)\n", + "plt.ylabel('probability (%)', size=15)\n", + "plt.title('Loss Distribution', size=20)\n", + "plt.xticks(size=15)\n", + "plt.yticks(size=15)\n", + "plt.show()\n", + "\n", + "# plot results for Z\n", + "plt.plot(z_values, p_z, 'o-', linewidth=3, markersize=8)\n", + "plt.grid()\n", + "plt.xlabel('Z value', size=15)\n", + "plt.ylabel('probability (%)', size=15)\n", + "plt.title('Z Distribution', size=20)\n", + "plt.xticks(size=15)\n", + "plt.yticks(size=15)\n", + "plt.show()\n", + "\n", + "# plot results for default probabilities\n", + "plt.bar(range(K), p_default)\n", + "plt.xlabel('Asset', size=15)\n", + "plt.ylabel('probability (%)', size=15)\n", + "plt.title('Individual Default Probabilities', size=20)\n", + "plt.xticks(range(K), size=15)\n", + "plt.yticks(size=15)\n", + "plt.grid()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Expected Loss\n", + "\n", + "To estimate the expected loss, we first apply a weighted sum operator to sum up individual losses to total loss:\n", + "\n", + "$$ \\mathcal{S}: |x_1, ..., x_K \\rangle_K |0\\rangle_{n_S} \\mapsto |x_1, ..., x_K \\rangle_K |\\lambda_1x_1 + ... + \\lambda_K x_K\\rangle_{n_S}. $$\n", + "\n", + "The required number of qubits to represent the result is given by\n", + "\n", + "$$ n_s = \\lfloor \\log_2( \\lambda_1 + ... + \\lambda_K ) \\rfloor + 1. $$\n", + "\n", + "Once we have the total loss distribution in a quantum register, we can use the techniques described in [Woerner2019] to map a total loss $L \\in \\{0, ..., 2^{n_s}-1\\}$ to the amplitude of an objective qubit by an operator\n", + "\n", + "$$ | L \\rangle_{n_s}|0\\rangle \\mapsto \n", + "| L \\rangle_{n_s} \\left( \\sqrt{1 - L/(2^{n_s}-1)}|0\\rangle + \\sqrt{L/(2^{n_s}-1)}|1\\rangle \\right), $$\n", + "\n", + "which allows to run amplitude estimation to evaluate the expected loss." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "# determine number of qubits required to represent total loss\n", + "n_s = WeightedSumOperator.get_required_sum_qubits(lgd)\n", + "\n", + "# create circuit factory (add Z qubits with weight/loss 0)\n", + "agg = WeightedSumOperator(n_z + K, [0]*n_z + lgd)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "# define linear objective function\n", + "breakpoints = [0]\n", + "slopes = [1]\n", + "offsets = [0]\n", + "f_min = 0\n", + "f_max = sum(lgd)\n", + "c_approx = 0.25\n", + "\n", + "objective = PwlObjective(\n", + " agg.num_sum_qubits,\n", + " 0,\n", + " 2**agg.num_sum_qubits-1, # max value that can be reached by the qubit register (will not always be reached)\n", + " breakpoints, \n", + " slopes, \n", + " offsets, \n", + " f_min, \n", + " f_max, \n", + " c_approx\n", + ")\n", + "\n", + "# define overall multivariate problem\n", + "multivariate = MultivariateProblem(u, agg, objective)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Before we use QAE to estimate the expected loss, we validate the quantum circuit representing the objective function by just simulating it directly and analyzing the probability of the objective qubit being in the $|1\\rangle$ state, i.e., the value QAE will eventually approximate." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "num_qubits = multivariate.num_target_qubits\n", + "num_ancillas = multivariate.required_ancillas()\n", + "\n", + "q = QuantumRegister(num_qubits, name='q')\n", + "q_a = QuantumRegister(num_ancillas, name='q_a')\n", + "qc = QuantumCircuit(q, q_a)\n", + "\n", + "multivariate.build(qc, q, q_a)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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+       "«       ┌─┴─┐     └─┬─┘     ┌─┴─┐└───┘└─┬─┘      ░               »\n",
+       "«q_a_2: ┤ X ├───────■───────┤ X ├───────■────────░───────────────»\n",
+       "«       └───┘               └───┘                ░               »\n",
+       "«q_a_3: ─────────────────────────────────────────░───────────────»\n",
+       "«                                                ░               »\n",
+       "«                                                                             »\n",
+       "«  q_0: ──────────────────────────────────────────────────────────────────────»\n",
+       "«                                                                             »\n",
+       "«  q_1: ──────────────────────────────────────────────────────────────────────»\n",
+       "«                                                                             »\n",
+       "«  q_2: ──────────────────────────────────────────────────────────────────────»\n",
+       "«                                                                             »\n",
+       "«  q_3: ──────────────────────────────────────────────────────────────────────»\n",
+       "«       ┌────────────────┐┌───┐┌─────────────────┐┌───┐┌────────────────┐┌───┐»\n",
+       "«  q_4: ┤ U3(0.1309,0,0) ├┤ X ├┤ U3(-0.1309,0,0) ├┤ X ├┤ U3(0.2618,0,0) ├┤ X ├»\n",
+       "«       └────────────────┘└─┬─┘└─────────────────┘└─┬─┘└────────────────┘└─┬─┘»\n",
+       "«q_a_0: ────────────────────■───────────────────────■──────────────────────┼──»\n",
+       "«                                                                          │  »\n",
+       "«q_a_1: ───────────────────────────────────────────────────────────────────■──»\n",
+       "«                                                                             »\n",
+       "«q_a_2: ──────────────────────────────────────────────────────────────────────»\n",
+       "«                                                                             »\n",
+       "«q_a_3: ──────────────────────────────────────────────────────────────────────»\n",
+       "«                                                                             »\n",
+       "«                                ░                                          ░ \n",
+       "«  q_0: ─────────────────────────░──────────────────────────────────────────░─\n",
+       "«                                ░                                          ░ \n",
+       "«  q_1: ─────────────────────────░──────────────────────────────────────────░─\n",
+       "«                                ░                                          ░ \n",
+       "«  q_2: ─────────────────────────░──────────────────■────■─────────■────■───░─\n",
+       "«                                ░                  │    │         │    │   ░ \n",
+       "«  q_3: ─────────────────────────░───■─────────■────┼────┼─────────┼────┼───░─\n",
+       "«       ┌─────────────────┐┌───┐ ░   │         │    │    │         │    │   ░ \n",
+       "«  q_4: ┤ U3(-0.2618,0,0) ├┤ X ├─░───┼─────────┼────┼────┼─────────┼────┼───░─\n",
+       "«       └─────────────────┘└─┬─┘ ░   │  ┌───┐  │    │    │  ┌───┐┌─┴─┐  │   ░ \n",
+       "«q_a_0: ─────────────────────┼───░───┼──┤ X ├──┼────■────┼──┤ X ├┤ X ├──■───░─\n",
+       "«                            │   ░ ┌─┴─┐└───┘┌─┴─┐  │  ┌─┴─┐└───┘└───┘  │   ░ \n",
+       "«q_a_1: ─────────────────────■───░─┤ X ├─────┤ X ├──┼──┤ X ├────────────┼───░─\n",
+       "«                                ░ └─┬─┘     └───┘┌─┴─┐└─┬─┘          ┌─┴─┐ ░ \n",
+       "«q_a_2: ─────────────────────────░───■────────────┤ X ├──■────────────┤ X ├─░─\n",
+       "«                                ░                └───┘               └───┘ ░ \n",
+       "«q_a_3: ─────────────────────────░──────────────────────────────────────────░─\n",
+       "«                                ░                                          ░
" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc.draw()" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "job = execute(qc, backend=BasicAer.get_backend('statevector_simulator'))" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exact Expected Loss: 0.6409\n", + "Exact Operator Value: 0.3906\n", + "Mapped Operator value: 0.6640\n" + ] + } + ], + "source": [ + "# evaluate resulting statevector\n", + "value = 0\n", + "for i, a in enumerate(job.result().get_statevector()):\n", + " b = ('{0:0%sb}' % multivariate.num_target_qubits).format(i)[-multivariate.num_target_qubits:]\n", + " am = np.round(np.real(a), decimals=4)\n", + " if np.abs(am) > 1e-6 and b[0] == '1':\n", + " value += am**2\n", + "\n", + "print('Exact Expected Loss: %.4f' % expected_loss) \n", + "print('Exact Operator Value: %.4f' % value)\n", + "print('Mapped Operator value: %.4f' % multivariate.value_to_estimation(value))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we run QAE to estimate the expected loss with a quandratic speed-up over classical Monte Carlo simulation." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exact value: \t0.6409\n", + "Estimated value:\t0.7548\n", + "Probability: \t0.9507\n" + ] + } + ], + "source": [ + "# run amplitude estimation\n", + "num_eval_qubits = 5\n", + "ae = AmplitudeEstimation(num_eval_qubits, multivariate)\n", + "# result = ae.run(quantum_instance=BasicAer.get_backend('qasm_simulator'), shots=100)\n", + "result = ae.run(quantum_instance=BasicAer.get_backend('statevector_simulator'))\n", + "\n", + "# print results\n", + "print('Exact value: \\t%.4f' % expected_loss)\n", + "print('Estimated value:\\t%.4f' % result['estimation'])\n", + "print('Probability: \\t%.4f' % result['max_probability'])" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot estimated values for \"a\"\n", + "plt.bar(result['values'], result['probabilities'], width=0.5/len(result['probabilities']))\n", + "plt.xticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.title('\"a\" Value', size=15)\n", + "plt.ylabel('Probability', size=15)\n", + "plt.ylim((0,1))\n", + "plt.grid()\n", + "plt.show()\n", + "\n", + "# plot estimated values for expected loss (after re-scaling and reversing the c_approx-transformation)\n", + "plt.bar(result['mapped_values'], result['probabilities'], width=1/len(result['probabilities']))\n", + "plt.axvline(expected_loss, color='red', linestyle='--', linewidth=2)\n", + "plt.xticks(size=15)\n", + "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.title('Expected Loss', size=15)\n", + "plt.ylabel('Probability', size=15)\n", + "plt.ylim((0,1))\n", + "plt.grid()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Cumulative Distribution Function\n", + "\n", + "Instead of the expected loss (which could also be estimated efficiently using classical techniques) we now estimate the cummulitave distribution function (CDF) of the loss.\n", + "Classically, this either involves evaluating all the possible combinations of defaulting assets, or many classical samples in a Monte Carlo simulation. Algoritms based on QAE have the potential to significantly speed up this analysis in the future.\n", + "\n", + "To estimate the CDF, i.e., in the probability $ \\mathbb{P}[L \\leq x] $, we again apply $\\mathcal{S}$ to compute the total loss, and then apply a comparator that for a given value $x$ acts as\n", + "\n", + "$$ \\mathcal{C}: |L\\rangle_n|0> \\mapsto \n", + "\\begin{cases} \n", + "|L\\rangle_n|1> & \\text{if}\\quad L \\leq x \\\\\n", + "|L\\rangle_n|0> & \\text{if}\\quad L > x.\n", + "\\end{cases} $$\n", + "\n", + "The resulting quantum state can be written as\n", + "\n", + "$$ \\sum_{L = 0}^{x} \\sqrt{p_{L}}|L\\rangle_{n_s}|1\\rangle + \n", + "\\sum_{L = x+1}^{2^{n_s}-1} \\sqrt{p_{L}}|L\\rangle_{n_s}|1\\rangle, $$\n", + "\n", + "where we directly assume the summed up loss values and corresponding probabilities instead of presenting the details of the uncertainty model.\n", + "\n", + "The CDF($x$) equals the probability of measuring $|1\\rangle$ in the objective qubit and QAE can be directly used to estimate it." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "# define value x to evaluate the CDF(x)\n", + "def get_cdf_operator_factory(x_eval):\n", + "\n", + " # comparator as objective\n", + " cdf_objective = Comparator(agg.num_sum_qubits, x_eval+1, geq=False)\n", + " \n", + " # define overall uncertainty problem\n", + " multivariate_cdf = MultivariateProblem(u, agg, cdf_objective)\n", + " \n", + " return multivariate_cdf" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again, we first use quantum simulation to validate the quantum circuit." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "# set x value to estimate the CDF\n", + "x_eval = 2" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# get operator\n", + "multivariate_cdf = get_cdf_operator_factory(x_eval)\n", + "\n", + "# get required number of qubits\n", + "num_qubits = multivariate_cdf.num_target_qubits\n", + "num_ancillas = multivariate_cdf.required_ancillas() # TODO: why do we need two more ancillas?\n", + "\n", + "# construct circuit\n", + "q = QuantumRegister(num_qubits, name='q')\n", + "q_a = QuantumRegister(num_ancillas, name='q_a')\n", + "qc = QuantumCircuit(q, q_a)\n", + "\n", + "multivariate_cdf.build(qc, q, q_a)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "job = execute(qc, backend=BasicAer.get_backend('statevector_simulator'))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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+       "«q_a_0: ──────────────────────────────────────────────────────»\n",
+       "«                                                             »\n",
+       "«q_a_1: ──────────────────────────────────────────────────────»\n",
+       "«                                                             »\n",
+       "«q_a_2: ──────────────────────────────────────────────────────»\n",
+       "«                                                             »\n",
+       "«q_a_3: ──────────────────────────────────────────────────────»\n",
+       "«                                                             »\n",
+       "«                                                                            ░ »\n",
+       "«  q_0: ─────────────────────────────────────────────────────────────────────░─»\n",
+       "«                                                                            ░ »\n",
+       "«  q_1: ────────────────────────────■────────────■───────────────────────■───░─»\n",
+       "«       ┌─────────────────┐┌────────┴─────────┐  │                       │   ░ »\n",
+       "«  q_2: ┤ U3(0.28365,0,0) ├┤        X         ├──┼───────────────────────┼───░─»\n",
+       "«       └─────────────────┘├──────────────────┤┌─┴─┐┌─────────────────┐┌─┴─┐ ░ »\n",
+       "«  q_3: ───────────────────┤ U3(-0.22349,0,0) ├┤ X ├┤ U3(0.22349,0,0) ├┤ X ├─░─»\n",
+       "«                          └──────────────────┘└───┘└─────────────────┘└───┘ ░ »\n",
+       "«  q_4: ─────────────────────────────────────────────────────────────────────░─»\n",
+       "«                                                                            ░ »\n",
+       "«q_a_0: ─────────────────────────────────────────────────────────────────────░─»\n",
+       "«                                                                            ░ »\n",
+       "«q_a_1: ─────────────────────────────────────────────────────────────────────░─»\n",
+       "«                                                                            ░ »\n",
+       "«q_a_2: ─────────────────────────────────────────────────────────────────────░─»\n",
+       "«                                                                            ░ »\n",
+       "«q_a_3: ─────────────────────────────────────────────────────────────────────░─»\n",
+       "«                                                                            ░ »\n",
+       "«                                                ░                 ░           »\n",
+       "«  q_0: ─────────────────────────────────────────░─────────────────░───────────»\n",
+       "«                                                ░                 ░           »\n",
+       "«  q_1: ─────────────────────────────────────────░─────────────────░───────────»\n",
+       "«                                                ░                 ░           »\n",
+       "«  q_2: ──■────■────■─────────■──────────────────░─────────────────░───────────»\n",
+       "«         │    │    │         │                  ░                 ░           »\n",
+       "«  q_3: ──┼────┼────┼─────────┼────■────■────────░─────────────────░───■───────»\n",
+       "«         │    │    │         │    │    │        ░      ┌───┐┌───┐ ░   │       »\n",
+       "«  q_4: ──┼────┼────┼─────────┼────┼────┼────────░──────┤ X ├┤ X ├─░───┼───────»\n",
+       "«         │  ┌─┴─┐  │  ┌───┐  │    │    │  ┌───┐ ░      └─┬─┘└───┘ ░   │  ┌───┐»\n",
+       "«q_a_0: ──■──┤ X ├──┼──┤ X ├──■────┼────┼──┤ X ├─░───■────┼────■───░───┼──┤ X ├»\n",
+       "«         │  └───┘┌─┴─┐└───┘  │  ┌─┴─┐┌─┴─┐└───┘ ░   │    │    │   ░ ┌─┴─┐└───┘»\n",
+       "«q_a_1: ──┼───────┤ X ├───────┼──┤ X ├┤ X ├──────░───┼────■────┼───░─┤ X ├─────»\n",
+       "«       ┌─┴─┐     └─┬─┘     ┌─┴─┐└───┘└─┬─┘      ░   │    │    │   ░ └─┬─┘     »\n",
+       "«q_a_2: ┤ X ├───────■───────┤ X ├───────■────────░───┼────┼────┼───░───■───────»\n",
+       "«       └───┘               └───┘                ░ ┌─┴─┐  │  ┌─┴─┐ ░           »\n",
+       "«q_a_3: ─────────────────────────────────────────░─┤ X ├──■──┤ X ├─░───────────»\n",
+       "«                                                ░ └───┘     └───┘ ░           »\n",
+       "«                                      ░ \n",
+       "«  q_0: ───────────────────────────────░─\n",
+       "«                                      ░ \n",
+       "«  q_1: ───────────────────────────────░─\n",
+       "«                                      ░ \n",
+       "«  q_2: ───────■────■─────────■────■───░─\n",
+       "«              │    │         │    │   ░ \n",
+       "«  q_3: ──■────┼────┼─────────┼────┼───░─\n",
+       "«         │    │    │         │    │   ░ \n",
+       "«  q_4: ──┼────┼────┼─────────┼────┼───░─\n",
+       "«         │    │    │  ┌───┐┌─┴─┐  │   ░ \n",
+       "«q_a_0: ──┼────■────┼──┤ X ├┤ X ├──■───░─\n",
+       "«       ┌─┴─┐  │  ┌─┴─┐└───┘└───┘  │   ░ \n",
+       "«q_a_1: ┤ X ├──┼──┤ X ├────────────┼───░─\n",
+       "«       └───┘┌─┴─┐└─┬─┘          ┌─┴─┐ ░ \n",
+       "«q_a_2: ─────┤ X ├──■────────────┤ X ├─░─\n",
+       "«            └───┘               └───┘ ░ \n",
+       "«q_a_3: ───────────────────────────────░─\n",
+       "«                                      ░
" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc.draw()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Operator CDF(2) = 0.9591\n", + "Exact CDF(2) = 0.9591\n" + ] + } + ], + "source": [ + "# evaluate resulting statevector\n", + "var_prob = 0\n", + "for i, a in enumerate(job.result().get_statevector()):\n", + " b = ('{0:0%sb}' % multivariate_cdf.num_target_qubits).format(i)[-multivariate_cdf.num_target_qubits:]\n", + " prob = np.abs(a)**2\n", + " if prob > 1e-6 and b[0] == '1':\n", + " var_prob += prob\n", + "print('Operator CDF(%s)' % x_eval + ' = %.4f' % var_prob)\n", + "print('Exact CDF(%s)' % x_eval + ' = %.4f' % cdf[x_eval])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we run QAE to estimate the CDF for a given $x$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# run amplitude estimation\n", + "num_eval_qubits = 4\n", + "ae_cdf = AmplitudeEstimation(num_eval_qubits, multivariate_cdf)\n", + "# result_cdf = ae_cdf.run(quantum_instance=BasicAer.get_backend('qasm_simulator'), shots=100)\n", + "result_cdf = ae_cdf.run(quantum_instance=BasicAer.get_backend('statevector_simulator'))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exact value: \t0.9591\n", + "Estimated value:\t0.9619\n", + "Probability: \t0.9958\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# print results\n", + "print('Exact value: \\t%.4f' % cdf[x_eval])\n", + "print('Estimated value:\\t%.4f' % result_cdf['estimation'])\n", + "print('Probability: \\t%.4f' % result_cdf['max_probability'])\n", + "\n", + "# plot estimated values for \"a\"\n", + "plt.bar(result_cdf['values'], result_cdf['probabilities'], width=0.5/len(result['probabilities']))\n", + "plt.axvline(cdf[x_eval], color='red', linestyle='--', linewidth=2)\n", + "plt.xticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.title('CDF(%s)' % x_eval, size=15)\n", + "plt.ylabel('Probability', size=15)\n", + "plt.ylim((0,1))\n", + "plt.grid()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Value at Risk\n", + "\n", + "In the following we use a bisection search and QAE to efficiently evaluate the CDF to estimate the value at risk." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def run_ae_for_cdf(x_eval, num_eval_qubits=3, simulator='statevector_simulator'):\n", + " \n", + " # run amplitude estimation\n", + " multivariate_var = get_cdf_operator_factory(x_eval)\n", + " ae_var = AmplitudeEstimation(num_eval_qubits, multivariate_var)\n", + " result_var = ae_var.run(BasicAer.get_backend(simulator))\n", + " \n", + " return result_var['estimation']" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def bisection_search(objective, target_value, low_level, high_level, low_value=None, high_value=None):\n", + " \"\"\"\n", + " Determines the smallest level such that the objective value is still larger than the target\n", + " :param objective: objective function\n", + " :param target: target value\n", + " :param low_level: lowest level to be considered\n", + " :param high_level: highest level to be considered\n", + " :param low_value: value of lowest level (will be evaluated if set to None)\n", + " :param high_value: value of highest level (will be evaluated if set to None)\n", + " :return: dictionary with level, value, num_eval\n", + " \"\"\"\n", + "\n", + " # check whether low and high values are given and evaluated them otherwise\n", + " print('--------------------------------------------------------------------')\n", + " print('start bisection search for target value %.3f' % target_value)\n", + " print('--------------------------------------------------------------------')\n", + " num_eval = 0\n", + " if low_value is None:\n", + " low_value = objective(low_level)\n", + " num_eval += 1\n", + " if high_value is None:\n", + " high_value = objective(high_level)\n", + " num_eval += 1 \n", + " \n", + " # check if low_value already satisfies the condition\n", + " if low_value > target_value:\n", + " return {'level': low_level, 'value': low_value, 'num_eval': num_eval, 'comment': 'returned low value'}\n", + " elif low_value == target_value:\n", + " return {'level': low_level, 'value': low_value, 'num_eval': num_eval, 'comment': 'success'}\n", + "\n", + " # check if high_value is above target\n", + " if high_value < target_value:\n", + " return {'level': high_level, 'value': high_value, 'num_eval': num_eval, 'comment': 'returned low value'}\n", + " elif high_value == target_value:\n", + " return {'level': high_level, 'value': high_value, 'num_eval': num_eval, 'comment': 'success'}\n", + "\n", + " # perform bisection search until\n", + " print('low_level low_value level value high_level high_value')\n", + " print('--------------------------------------------------------------------')\n", + " while high_level - low_level > 1:\n", + "\n", + " level = int(np.round((high_level + low_level) / 2.0))\n", + " num_eval += 1\n", + " value = objective(level)\n", + "\n", + " print('%2d %.3f %2d %.3f %2d %.3f' \\\n", + " % (low_level, low_value, level, value, high_level, high_value))\n", + "\n", + " if value >= target_value:\n", + " high_level = level\n", + " high_value = value\n", + " else:\n", + " low_level = level\n", + " low_value = value\n", + "\n", + " # return high value after bisection search\n", + " print('--------------------------------------------------------------------')\n", + " print('finished bisection search')\n", + " print('--------------------------------------------------------------------')\n", + " return {'level': high_level, 'value': high_value, 'num_eval': num_eval, 'comment': 'success'}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--------------------------------------------------------------------\n", + "start bisection search for target value 0.950\n", + "--------------------------------------------------------------------\n", + "low_level low_value level value high_level high_value\n", + "--------------------------------------------------------------------\n", + "-1 0.000 1 0.691 3 1.000\n", + " 1 0.691 2 0.962 3 1.000\n", + "--------------------------------------------------------------------\n", + "finished bisection search\n", + "--------------------------------------------------------------------\n" + ] + } + ], + "source": [ + "# run bisection search to determine VaR\n", + "num_eval_qubits = 4\n", + "objective = lambda x: run_ae_for_cdf(x, num_eval_qubits=num_eval_qubits)\n", + "bisection_result = bisection_search(objective, 1-alpha, min(losses)-1, max(losses), low_value=0, high_value=1)\n", + "var = bisection_result['level']" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Estimated Value at Risk: 2\n", + "Exact Value at Risk: 2\n", + "Estimated Probability: 0.962\n", + "Exact Probability: 0.959\n" + ] + } + ], + "source": [ + "print('Estimated Value at Risk: %2d' % var)\n", + "print('Exact Value at Risk: %2d' % exact_var)\n", + "print('Estimated Probability: %.3f' % bisection_result['value'])\n", + "print('Exact Probability: %.3f' % cdf[exact_var])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Conditional Value at Risk\n", + "\n", + "Last, we compute the CVaR, i.e. the expected value of the loss conditional to it being larger than or equal to the VaR.\n", + "To do so, we evaluate a piecewise linear objective function $f(L)$, dependent on the total loss $L$, that is given by\n", + "\n", + "$$ f(L) = \\begin{cases} \n", + "0 & \\text{if}\\quad L \\leq VaR \\\\\n", + "L & \\text{if}\\quad L > VaR.\n", + "\\end{cases} $$\n", + "\n", + "To normalize, we have to devide the resulting expected value by the VaR-probability, i.e. $\\mathbb{P}[L \\leq VaR]$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# define linear objective\n", + "breakpoints = [0, var]\n", + "slopes = [0, 1]\n", + "offsets = [0, 0] # subtract VaR and add it later to the estimate\n", + "f_min = 0\n", + "f_max = 3 - var\n", + "c_approx = 0.25\n", + "\n", + "cvar_objective = PwlObjective(\n", + " agg.num_sum_qubits,\n", + " 0,\n", + " 2**agg.num_sum_qubits-1, # max value that can be reached by the qubit register (will not always be reached)\n", + " breakpoints, \n", + " slopes, \n", + " offsets, \n", + " f_min, \n", + " f_max, \n", + " c_approx\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "var = 2" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "multivariate_cvar = MultivariateProblem(u, agg, cvar_objective)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "num_qubits = multivariate_cvar.num_target_qubits\n", + "num_ancillas = multivariate_cvar.required_ancillas()\n", + "\n", + "q = QuantumRegister(num_qubits, name='q')\n", + "q_a = QuantumRegister(num_ancillas, name='q_a')\n", + "qc = QuantumCircuit(q, q_a)\n", + "\n", + "multivariate_cvar.build(qc, q, q_a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again, we first use quantum simulation to validate the quantum circuit." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "job = execute(qc, backend=BasicAer.get_backend('statevector_simulator'))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Estimated CVaR: 3.3796\n", + "Exact CVaR: 3.0000\n" + ] + } + ], + "source": [ + "# evaluate resulting statevector\n", + "value = 0\n", + "for i, a in enumerate(job.result().get_statevector()):\n", + " b = ('{0:0%sb}' % multivariate_cvar.num_target_qubits).format(i)[-multivariate_cvar.num_target_qubits:]\n", + " am = np.round(np.real(a), decimals=4)\n", + " if np.abs(am) > 1e-6 and b[0] == '1':\n", + " value += am**2\n", + "\n", + "# normalize and add VaR to estimate\n", + "value = multivariate_cvar.value_to_estimation(value)\n", + "normalized_value = value / (1.0 - bisection_result['value']) + var\n", + "print('Estimated CVaR: %.4f' % normalized_value)\n", + "print('Exact CVaR: %.4f' % exact_cvar)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we run QAE to estimate the CVaR." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# run amplitude estimation\n", + "num_eval_qubits = 7\n", + "ae_cvar = AmplitudeEstimation(num_eval_qubits, multivariate_cvar)\n", + "# result_cvar = ae_cvar.run(quantum_instance=BasicAer.get_backend('qasm_simulator'), shots=100)\n", + "result_cvar = ae_cvar.run(quantum_instance=BasicAer.get_backend('statevector_simulator'))\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# print results\n", + "print('Exact CVaR: \\t%.4f' % exact_cvar)\n", + "print('Estimated CVaR:\\t%.4f' % (result_cvar['estimation'] / (1.0 - bisection_result['value']) + var))\n", + "print('Probability: \\t%.4f' % result_cvar['max_probability'])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# plot estimated values for \"a\"\n", + "plt.bar(result_cvar['values'], result_cvar['probabilities'], width=0.5/len(result_cvar['probabilities']))\n", + "plt.xticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.title('\"a\" Value', size=15)\n", + "plt.ylabel('Probability', size=15)\n", + "plt.ylim((0,1))\n", + "plt.grid()\n", + "plt.show()\n", + "\n", + "# plot estimated values for expected loss (after re-scaling and reversing the c_approx-transformation)\n", + "normalized_values = np.array(result_cvar['mapped_values']) / (1.0 - bisection_result['value']) + var\n", + "plt.bar(normalized_values, result_cvar['probabilities'])\n", + "plt.axvline(exact_cvar, color='red', linestyle='--', linewidth=2)\n", + "plt.xticks(size=15)\n", + "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.title('CvaR', size=15)\n", + "plt.ylabel('Probability', size=15)\n", + "plt.ylim((0,1))\n", + "plt.grid()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "qiskit_master", + "language": "python", + "name": "qiskit_master" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/qiskit/finance/simulation/european_call_option_pricing.ipynb b/qiskit/finance/simulation/european_call_option_pricing.ipynb new file mode 100644 index 000000000..b1dd21893 --- /dev/null +++ b/qiskit/finance/simulation/european_call_option_pricing.ipynb @@ -0,0 +1,515 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# _*Qiskit Finance: Pricing European Call Options*_ \n", + "\n", + "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", + "\n", + "***\n", + "### Contributors\n", + "Stefan Woerner[1], Daniel Egger[1], Shaohan Hu[1], Stephen Wood[1], Marco Pistoia[1]\n", + "### Affliation\n", + "- [1]IBMQ" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Introduction\n", + "
\n", + "Suppose a European call option with strike price $K$ and an underlying asset whose spot price at maturity $S_T$ follows a given random distribution.\n", + "The corresponding payoff function is defined as:\n", + "
\n", + "
\n", + "$$\\max\\{S_T - K, 0\\}$$\n", + "
\n", + "In the following, a quantum algorithm based on amplitude estimation is used to estimate the expected payoff, i.e., the fair price before discounting, for the option:\n", + "
\n", + "
\n", + "$$\\mathbb{E}\\left[ \\max\\{S_T - K, 0\\} \\right]$$\n", + "
\n", + "as well as the corresponding $\\Delta$, i.e., the derivative of the option price with respect to the spot price, defined as:\n", + "
\n", + "
\n", + "$$\n", + "\\Delta = \\mathbb{P}\\left[S_T \\geq K\\right]\n", + "$$\n", + "
\n", + "The approximation of the objective function is explained in detail in the following paper:
\n", + "Quantum Risk Analysis. Woerner, Egger. 2018." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "import numpy as np\n", + "\n", + "from qiskit import BasicAer\n", + "from qiskit.aqua.algorithms import AmplitudeEstimation\n", + "from qiskit.aqua.components.uncertainty_models import LogNormalDistribution\n", + "from qiskit.aqua.components.uncertainty_problems import UnivariateProblem\n", + "from qiskit.aqua.components.uncertainty_problems import UnivariatePiecewiseLinearObjective as PwlObjective" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Uncertainty Model\n", + "\n", + "We construct a circuit factory to load a log-normal random distribution into a quantum state.\n", + "The distribution is truncated to a given interval $[low, high]$ and discretized using $2^n$ grid points, where $n$ denotes the number of qubits used.\n", + "The unitary operator corresponding to the circuit factory implements the following: \n", + "$$\\big|0\\rangle_{n} \\mapsto \\big|\\psi\\rangle_{n} = \\sum_{i=0}^{2^n-1} \\sqrt{p_i}\\big|i\\rangle_{n},$$\n", + "where $p_i$ denote the probabilities corresponding to the truncated and discretized distribution and where $i$ is mapped to the right interval using the affine map:\n", + "$$ \\{0, \\ldots, 2^n-1\\} \\ni i \\mapsto \\frac{high - low}{2^n - 1} * i + low \\in [low, high].$$" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# number of qubits to represent the uncertainty\n", + "num_uncertainty_qubits = 2\n", + "\n", + "# parameters for considered random distribution\n", + "S = 2.0 # initial spot price\n", + "vol = 0.4 # volatility of 40%\n", + "r = 0.05 # annual interest rate of 4%\n", + "T = 40 / 365 # 40 days to maturity\n", + "\n", + "# resulting parameters for log-normal distribution\n", + "mu = ((r - 0.5 * vol**2) * T + np.log(S))\n", + "sigma = vol * np.sqrt(T)\n", + "mean = np.exp(mu + sigma**2/2)\n", + "variance = (np.exp(sigma**2) - 1) * np.exp(2*mu + sigma**2)\n", + "stddev = np.sqrt(variance)\n", + "\n", + "# lowest and highest value considered for the spot price; in between, an equidistant discretization is considered.\n", + "low = np.maximum(0, mean - 3*stddev)\n", + "high = mean + 3*stddev\n", + "\n", + "# construct circuit factory for uncertainty model\n", + "uncertainty_model = LogNormalDistribution(num_uncertainty_qubits, mu=mu, sigma=sigma, low=low, high=high)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot probability distribution\n", + "x = uncertainty_model.values\n", + "y = uncertainty_model.probabilities\n", + "plt.bar(x, y, width=0.2)\n", + "plt.xticks(x, size=15, rotation=90)\n", + "plt.yticks(size=15)\n", + "plt.grid()\n", + "plt.xlabel('Spot Price at Maturity $S_T$ (\\$)', size=15)\n", + "plt.ylabel('Probability ($\\%$)', size=15)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Payoff Function\n", + "\n", + "The payoff function equals zero as long as the spot price at maturity $S_T$ is less than the strike price $K$ and then increases linearly.\n", + "The implementation uses a comparator, that flips an ancilla qubit from $\\big|0\\rangle$ to $\\big|1\\rangle$ if $S_T \\geq K$, and this ancilla is used to control the linear part of the payoff function.\n", + "\n", + "The linear part itself is then approximated as follows.\n", + "We exploit the fact that $\\sin^2(y + \\pi/4) \\approx y + 1/2$ for small $|y|$.\n", + "Thus, for a given approximation scaling factor $c_{approx} \\in [0, 1]$ and $x \\in [0, 1]$ we consider\n", + "$$ \\sin^2( \\pi/2 * c_{approx} * ( x - 1/2 ) + \\pi/4) \\approx \\pi/2 * c_{approx} * ( x - 1/2 ) + 1/2 $$ for small $c_{approx}$.\n", + "\n", + "We can easily construct an operator that acts as \n", + "$$\\big|x\\rangle \\big|0\\rangle \\mapsto \\big|x\\rangle \\left( \\cos(a*x+b) \\big|0\\rangle + \\sin(a*x+b) \\big|1\\rangle \\right),$$\n", + "using controlled Y-rotations.\n", + "\n", + "Eventually, we are interested in the probability of measuring $\\big|1\\rangle$ in the last qubit, which corresponds to\n", + "$\\sin^2(a*x+b)$.\n", + "Together with the approximation above, this allows to approximate the values of interest.\n", + "The smaller we choose $c_{approx}$, the better the approximation.\n", + "However, since we are then estimating a property scaled by $c_{approx}$, the number of evaluation qubits $m$ needs to be adjusted accordingly.\n", + "\n", + "For more details on the approximation, we refer to:\n", + "Quantum Risk Analysis. Woerner, Egger. 2018." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# set the strike price (should be within the low and the high value of the uncertainty)\n", + "strike_price = 2\n", + "\n", + "# set the approximation scaling for the payoff function\n", + "c_approx = 0.25\n", + "\n", + "# setup piecewise linear objective fcuntion\n", + "breakpoints = [uncertainty_model.low, strike_price]\n", + "slopes = [0, 1]\n", + "offsets = [0, 0]\n", + "f_min = 0\n", + "f_max = uncertainty_model.high - strike_price\n", + "european_call_objective = PwlObjective(\n", + " uncertainty_model.num_target_qubits, \n", + " uncertainty_model.low, \n", + " uncertainty_model.high,\n", + " breakpoints,\n", + " slopes,\n", + " offsets,\n", + " f_min,\n", + " f_max,\n", + " c_approx\n", + ")\n", + "\n", + "# construct circuit factory for payoff function\n", + "european_call = UnivariateProblem(\n", + " uncertainty_model,\n", + " european_call_objective\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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IJG0saYqkhZLmSxotqdICjZXqDpf0oKRFkl6TdJuk3tWO2cysRQ8+CIcfDsOGwciRRUeTu1wTiaR+wF2kbXV3BkYDvwRObEPdg4ErSXuabA8cDDyNu+fMrEivvprGRQYMgCuugOXb9Hdxj5L3l/AhwKrA8Gz/kTsl9QFGSRpTuidJKUlrk5abPyIiLip56rqqR2xm1pwPPkjLwr/8Mtx3X7qCvQ7l3bW1PXB7WcKYREouW7dQb/fs/o/VCszMrN1OOCFtVHXuuTBkSNHRFCbvRDKYsr3ZI2IusJCyvdzLbA48CRwkaZ6k9yU9IOnr1QvVzKwFN94Ip54KBx8MBx1UdDSFyrtrqx9pV8Ryjdlzzfkk8HngeOBo4LXs/jZJn4uIl8orZNv4jgDo378/DQ0NHQp4wYIFHa5r1ePzUnvq6ZysOm8emx5yCIs22oiHd9uNpTX8ufM4L0UMVEeFMjVT3mQ5YDVgt4i4DUDS/cAc4HDgN8u8ScR4YDzAkCFDYujQoR0KtqGhgY7Wterxeak9dXNO3nkn7bW+8sqsfscdfGvgwKIjalEe5yXvRNIIrFGhvC+VWypNXs/uG5oKIuItSdOBjbssOjOzlkTAiBHw+ONpPa0aTyJ5yTuRzKRsLETSekBvysZOyvyL1GIpX7RGwNKuDNDMrFnnngtXXgknnZSuGTEg/8H2W4FhklYvKdsDWARMbaHezaSksU1TgaS+wKbAo1WI08zs4+6/H37xi3TV+q9/XXQ0NSXvRHIBsBiYLOnb2YD4KGBs6ZRgSc9IuqTpcURMA24ALpG0v6QdgRuB94Fz8/wAZlaHXnoJdtstdWVddhks59WlSuXatRURjZK2A84BbiKNi4wjJZPyuMovD90HOAMYC/QC/gZsGxGN1YzZzOrckiWwxx7Q2Jg2qlqj0jBvfct91lZEzAC2beWYQRXKFgCHZjczs3wceyxMnQp//CN86UtFR1OT3D4zM2vOn/8Mv/sd/Pd/p90OrSInEjOzSmbOhAMPTPutjxtXdDQ1zYnEzKzc22/D8OGw6qpwzTWw0kpFR1TTvAS7mVmpiLR21pNPwp13wrrrFh1RzXMiMTMrNW5caoWcfjps2+K8IMu4a8vMrMm998LRR8Muu8BRRxUdTbfhRGJmBjB/Puy+O2y4IUycCCpfkcma464tM7P33ktXrr/9NkyZAn36FB1Rt+JEYmZ21FFpLa2rroJNNik6mm7HXVtmVt+uugrOPht+/nPYc8+io+mWnEjMrH49/njaKnerrWDMmKKj6bZyTySSNpY0RdJCSfMljZZUvkBjeZ1BkqLCbVJecZtZD/Pmm+miwz594OqrYcUVi46o28p1jERSP+AuYAawM7AhcCYpoR3fhpf4FWnV3yavdnWMZlYHli6F/feHZ5+Fe+6BAQOKjqhby3uw/RBgVWB4tv/InZL6AKMkjSndk6QZT0bE36sepZn1bGPGwA03pIsPv/nNoqPp9vLu2toeuL0sYUwiJZetc47FzOrRlClw3HFpj5Ejjyw6mh4h70QymLK92SNiLrCQsr3cmzFB0geSXpA0VtKq1QjSzHqo555LM7MGD4aLL/ZFh10k766tfqRdEcs1Zs81ZzFpS907gLeAocAxpDGWnStVyLbxHQHQv39/GhoaOhTwggULOlzXqsfnpfbU+jnRe+/xlSOPpNfChUw/5hgWTZtWdEi5yOO8FHFBYlQoUzPlqULEC8DhJUUNkl4CzpP05Yh4pEKd8cB4gCFDhsTQoUM7FGxDQwMdrWvV4/NSe2r+nBx6aNpj5Npr2Xz48KKjyU0e56XVri1J+0laq4verxGotOFxXyq3VFry5+z+q52KyMx6vokT4YIL0oKMdZRE8tKWMZIJpC4ksvGJr3Xi/WZSNhYiaT2gN2VjJ20QZfdmZst65JHUGtlmGzjllKKj6ZHakkgagU9lP7fYBdUGtwLDJK1eUrYHsAiY2s7X2jW7n96JeMysJ2tsTC2QtdaCSZNgBS8vWA1t+Ve9C7hM0pOkJDJR0jvNHRwRLbVYLgB+BkyWdDqwATAKGFs6JVjSM8DUiDgoezwKWJ10MeJbwLeAo4DJEfHPNnwGM6s3S5fCPvvAvHlpn5F11ik6oh6rLYnkJ8B/A58njUfMAl7pyJtFRKOk7YBzgJtI4yLjSMmkPK7SZVNmkq5qP5h0zclc4AzA7VQzq+zkk+GWW+Dcc2GLLYqOpkdrNZFExELgdwCSvg0cFxGPdvQNI2IG0OL+lRExqOzxJNKFi2Zmrbv1Vhg1CvbdN42PWFW1ZdbWB5I2yx42kLqWzMxq06xZsPfe8IUvpJlavuiw6toy2P4esHL2837AJ6oXjplZJyxaBLvumsZHJk+GXr2KjqgutGWMZAZpUcXrSbO2dpU0pJljIyLO77LozMzaKgIOOwweeghuuintvW65aEsiOQK4kDQoHqRB7+YE4ERiZvm7+GKYMAGOPx522qnoaOpKq11bEXF/RHwhIlYktUi2iIjlmrm1uEGVmVlVPPggHH44fPe7aZDdctXe1X+3IXV1mZnVhldfTeMiAwbAlVfC8v57Nm/tuswzIqYCSNoc2ApYE3gduC8iHuj68MzMWvDBB7DXXvDSS3DffekKdstduxKJpN7ANcAw4APgNWAtYHlJtwG7ZdedmJlV38iRcOedcNFFMKS5OUBWbe3t2hoDbAnsCawSEQOAVbLHWwKnd214ZmbNuPHGtAjjQQfBwQcXHU1da28i+RFwTERcExFLASJiaURcA/w/YLeuDtDMbBnPPJOuWt90UzjnnKKjqXvtTSR9geeaee45oE/nwjEza8XChWlF3xVWgD//GVZZpeiI6l57E8mjwKHSx9ccyB4fmj1vZlYdEfDTn8Ljj6cZWoMGFR2R0f5E8mvSQPtMSadJ+oWk3wL/Ar6bPd8iSRtLmiJpoaT5kkZLavN8PUnLSZouKST5qiOzenLeeXD55XDiiTBsWNHRWKa903/vlvQV4ATSeMgA4AXgAWB4trJvsyT1I+1vMgPYmbTz4pmkhHZ8G8M4GPh0e+I2sx7g/vvh5z+HHXeE444rOhor0e7twrJksWcH3+8Q0n4iw7ONrO6U1Ie0lteY0s2tKskS0Smkgf2LOxiDmXU3L70Eu+0G668Pl10Gy7W3M8WqqV1nQ9LvJG3ciffbHri9LGFMIiWXrdtQ/yTSLolTOhGDmXUnS5bAnnvC66+nFX379Ss6IivTkem/j0n6h6RDJPVtZ/3BpN0OPxQRc4GF2XPNkvRF4EBaXjTSzHqaX/8aGhrgwgvhS18qOhqroL1jJJ+RtA3pC/0MYGy2vPwfIuKuNrxEP9L2uuUas+da8r/AuRHxjKRBrb2RpBHACID+/fvT0NDQhvCWtWDBgg7Xterxeak91Tgna0+dyn+ecQbP/+AHPL3++imhWLvk8rsSER26AasBBwH3kpZLmQOcCGzQQp33gSMrlD8PnNJCvT2BF4E+2eNBpCXrd2pLrJtuuml01D333NPhulY9Pi+1p8vPyb/+FbHaahGbbx7x7rtd+9p1pDPnBZgWbfiO7fCIVUQsiIhLgJGkcYv1gGOBpyTdIGlghWqNwBoVyvtSuaWCpBVJrZ/TgeUkrcFHFz72lrR6Rz+DmdWoBQvSRYerrpouOlx55dbrWGE6lEgkDZI0UtKzwB3AAtJ04NWBH5BaDJMqVJ1J2ViIpPWA3pSNnZToDawLjCUlokY+uvBxEvBwRz6DmdWoiLR+1pNPwqRJsO66RUdkrWjv6r/7ksZHvgXMBSYAEyJiXslht0h6h3S9SLlbgaMkrR4Rb2dlewCLgKnNvO0C0j4opT4JXEW6APLu9nwGM6txv/89XH01nHYabLtt0dFYG7T3OpLxwHXAsIhoaQruU8DJFcovAH4GTJZ0OrABMAoYGyVTgiU9A0yNiIMiYgnQUPoiJYPtj4X3QTHrOe69F446CnbZBY4+uuhorI3am0g+FRGNrR0UES+QBt7LyxslbQecA9xEGhcZR0om5XF5mzOzejJ/Puy+O2y4Ydp7/eNL+lkNa+/031aTSBteYwbQYns1Iga18vxs0v7xZtYTvP9+SiJvvw1TpkDf9l6iZkVq9xIpkvYA/gvYiLSp1cdExDpdEJeZ1ZOjjoK//Q2uugo22aToaKyd2rtEyl7AH4FnSDOpbgRuzl7nLVKXlZlZ2111FZx1Fhx5ZFoKxbqd9k7/PYq03tVh2ePzIuInwGeAV0lLnZiZtc3jj6dtcr/xDTjjjKKjsQ5qbyL5HPC3iPiAdDV7H4BsKu/pwOFdG56Z9VhvvpkuOuzTB665BlZcseiIrIPam0jeBJouMX0e+I+S5wSs1RVBmVkPFwEHHADPPpuuGRkwoOiIrBPaO9g+DfgicDtpfOQESUuA90ibXfmaDjNr3ZgxcP31MHYsfPObRUdjndTeRPJboGkNrROyn88jXfPxINlqu2ZmzZoyJS0Nv/vuacdD6/balEgkrQrsQFpD60VJ/SPiJWBnSSsDK0cruxuamfHcc2lm1uc/D5dc4osOe4hWE4mkDUjrZg0qKX5L0u4RcUdELAYWVyk+M+spFi+GXXdN95Mnw2qrFR2RdZG2DLaPAZYC3wR6AZuQVty9sIpxmVlP84tfwD/+ARMnwuAWN0S1bqYtiWRL4PiI+FtEvBsR/wJ+CqwvyVMtzKx1f/wjnH9+uoJ9+PCio7Eu1pZEMgB4tqzs36Tpvp9s7xtK2ljSFEkLJc2XNFpSiws0StpE0m3Z8YslzZV0sROZWTfwyCNwyCEwdCicemrR0VgVtHXWVnTFm0nqRxpvmQHsDGwInElKaMe3ULUvMAu4FJhPupJ+JLCppM2ypebNrNY0NqYWyFprpU2qVmj38n7WDbT1rN6eXS9Sbkp5eSuLNh4CrAoMz2Z53SmpDzBK0pjmZn5FxP3A/SVFDZLmkXZn/CLwUBs/h5nlZelS2GcfmDcPpk6F/v2LjsiqpC2JZJl9RTphe+D2soQxibS8ytakPUra6rXsfqUuis3MutIpp8Att8C558KWWxYdjVVRq4kkIroykQymbGvciJgraWH2XIuJRNJypJg/A5xGugjyH10Yn5l1hdtug5EjU4vk0EOLjsaqLO8Oy36kXRHLNWbPteYWYFj283Rgh4hYWulASSPIrrTv378/DQ0N7Q4WYMGCBR2ua9Xj81J7ms7JKi+8wKY//SmLP/MZHtp7b5ZOnVp0aHUtj9+VIka+Kg3cq5nyckcAa5JWIT4euFXSNyLi3WXeJGI8aY95hgwZEkOHDu1QsA0NDXS0rlWPz0vtaWhoYOjmm8NWW8Fyy7Hi7bfzrc9+tuiw6l4evyt5J5JGYI0K5X2p3FL5mIh4OvvxAUl/Jc3k2gv4Q5dFaGbtc8UVcNxxbD13LvTqBe+8AzfeCE4idSPvRDKTNBbyIUnrAb2z59osIuZIeh3YoOvCM7N2ueIKGDECFi5EkJLICivAW156r560dz+SzroVGCZp9ZKyPYBFQLs6UiV9nrT/yayuC8/M2uW442Bh2caoS5akcqsbebdILgB+BkyWdDqpNTEKGFs6JVjSM8DUiDgoe/w7YAlpv5M3SBtqHU26wn5Snh/AzErMndu+cuuRck0kEdEoaTvgHNJU3zeAcaRkUh5X6bIp00gD7SOAVYC5wLXAbyPinSqHbWaVPPggLL98aoGUW3/9/OOxwuQ+aysiZgDbtnLMoLLHk3DLw6w2LF4Mo0alXQ779k1dW4tLdpLo1StdjGh1I+8xEjPrzh58EL76VTjttLTn+qxZaYOqgQMJCQYOhPHjYe+9i47UcuREYmatW7wYjj0Wttgizci69daUQPr2TUlj9mym3n03zJ7tJFKHvBSnmbXswQdT62PGDPjJT2Ds2JRAzDJukZhZZYsXw69/nRZcfPPNtABjUyvErIRbJGa2rPJWyJlnwhqVFqUwc4vEzEo11wpxErEWuEViZsm0aakV8sQTboVYu7hFYlbvFi9OS5pssQW88YZbIdZubpGY1bPSVsiBB6YZWU4g1k5ukZjVo/JWyF/+An/4g5OIdYhbJGb1xq0Q62K5t0gkbSxpiqSFkuZLGi1p+VbqbCZpgqRnsnpPShopaZW84jbr9tzUv3RxAAAXpElEQVQKsSrJtUUiqR9wFzAD2BnYEDiTlNCOb6HqHtmxpwNPA18ETsruf1TFkM16hmnTUuvj8cfdCrEul3fX1iHAqsDwbP+ROyX1AUZJGlO6J0mZ0yPilZLHDZLeBS6UNDAi5lQ5brPuafFiGD0aTj8d+vdPrZAddig6Kuth8u7a2h64vSxhTCIll62bq1SWRJo8nN2v03XhmfUg06bBkCFw6qmw775pTMRJxKog70QymLK92SNiLrCQsr3c2+DrwFLgya4JzayHKB0Lef311AqZMMFdWVY1eXdt9SPtiliuMXuuTSR9EjgOuKy57jBJI0g7KtK/f38aGhraHSzAggULOlzXqsfnpbLVnnySwaefzmqzZvHC977Hvw87jCW9ekEO/1Y+J7Upj/NSxPTfqFCmZsqXPVBaCbgaWAD8otk3iRgPjAcYMmRIDB06tN2BAjQ0NNDRulY9Pi9lFi+Gk05KG05lYyEDdtiBATmG4HNSm/I4L3knkkagUvu6L5VbKh8jScClwCbANyKisWvDM+uGpk9P14U8/ni6HzsW+rW5gW/WaXmPkcykbCxE0npAb8rGTpoxjjRteOeIaMvxZj3X4sVw/PGw+eZpLOTmm9NYiJOI5SzvRHIrMEzS6iVlewCLgKktVZR0LHAEsE9E3Fe9EM26genT04ysU05JM7Iefxx23LHoqKxO5Z1ILgAWA5MlfTsbEB8FjC0dNM+uYL+k5PFewKmkbq3nJW1RcvtEvh/BrECLF8NvfuNWiNWUXMdIIqJR0nbAOcBNpHGRcaRkUh5X6bIp383uD8hupQ4EJnZtpGY1qHQsZP/9Ydw4JxCrCbnP2oqIGcC2rRwzqOzxASybQMzqw+LFcPLJ8NvfphlZN9/sbiyrKV7916yWPfRQan24FWI1zPuRmNWi995LYyFf+9pHYyETJzqJWE1yi8Ss1jz0UBoLeewxt0KsW3CLxKxWlLZCXn0VbrrJrRDrFtwiMasFpa2Q/faD3//eCcS6DbdIzIpUqRXyxz86iVi34haJWVHcCrEewi0Ss7y99x6ccIJbIdZjuEVilie3QqwHcovELA/lrZAbb3QrxHoMt0jMqu3hh1Mr5J//dCvEeqTcWySSNpY0RdJCSfMljZa0fCt1VpJ0hqS/SlokqU27KZoV6r33YOTI1Ap55RW3QqzHyjWRSOoH3EXaVndnYDTwS+DEVqr2Ag4GFgL3VzNGsy7x8MOw2WYwejT8+MfwxBPw/e8XHZVZVeTdIjkEWBUYHhF3RsQFpCTyP5L6NFcpIt4A1oyIYcB1+YRq1gGlrZCXX06tkEsvdSvEerS8E8n2wO2lm1gBk0jJZeuWKkaEu7OstrkVYnUq70QymLK92SNiLqnLanDFGma1rrlWyJprFh2ZWS7ynrXVj7QrYrnG7Dmz7uWRR9KMrEcfTXun//73TiBWd4qY/lupi0rNlHdYth/8CID+/fvT0NDQoddZsGBBh+ta9RR9XvT++wy8/HLWv+IK3u/bl6dOOYXXvv71NMW3ThV9TqyyPM5L3omkEVijQnlfKrdUOiwixgPjAYYMGRJDhw7t0Os0NDTQ0bpWPYWel9JWyD77sPJZZ/EFt0L8u1Kj8jgveY+RzKRsLETSekBvysZOzGpO01jIZpvBSy/BDTfAZZe5K8vqXt6J5FZgmKTVS8r2ABYBU3OOxaztHnkkDaaPHg177plmZP3gB0VHZVYT8k4kFwCLgcmSvp2NY4wCxpZOCZb0jKRLSitK2l7SrsCXs8e7ZreB+YVvdee992DUKLdCzFqQ6xhJRDRK2g44B7iJNC4yjpRMyuMqXzblfKA0aVyT3R8ITOzqWM3Kx0I46ywnELMKcp+1FREzgG1bOWZQW8rMquK99+DUU+GUU2DttVMrxN1YZs3y6r9mpdwKMWs370diBqkVcuKJHgsx6wC3SMzcCjHrFLdIrH65FWLWJdwisfr06KOw//7pfu+94eyznUDMOsgtEqsv77+fWiFDhsCLL8L118PllzuJmHWCWyRWPx59NI2FPPKIWyFmXcgtEuv5SlshL7zgVohZF3OLxHq20lbIXnulVshaaxUdlVmP4haJ9UzlrZDrroMrrnASMasCt0is53ErxCxXbpFYz/H++2mZd7dCzHKVeyKRtLGkKZIWSpovabSk8pV+K9XrK2mCpEZJb0q6QpK/ISx59NG0X8jIkbD77mm/kB/+sOiozOpCrolEUj/gLtL+7DsDo4FfAie2ofqfgKHAwcABwGbA9dWI07oRt0LMCpd3i+QQYFVgeETcGREXkJLI/0jq01wlSVsCw4D9I+LaiLgO2AfYStK3qxLpFVfAoEFsve22MGhQemzFKz0vn/oUfO5zboWYFSzvRLI9cHvpbojAJFJy2bqVei9FxL1NBRHxD2BW9lzXuuIKGDEC5sxBETBnTnrsZFKs8vPywgvp3Pz8526FmBUo71lbg4G7SwsiYq6khdlzN7VQb2aF8n9lz3Wt446DhQs/XrZwYZoJdOqpXf521kZPPQVLlixbft11MG5c/vGYGZB/IulH2l63XGP2XEfqbVCpQrYf/AiA/v3709DQ0OYgt547F1UojyVLeOUTn2jz61jX+sSMGZXPy9y5TG3H+bXqWLBgQbt+zywfeZyXIq4jiQplaqa8w/UiYjwwHmDIkCExdOjQtke4/vqpy6T8zQYOZB3/ohRn0KDK52X99WnX+bWqaGho8HmoQXmcl7zHSBqBNSqU96Vyi6O1emu0Uq9jTjkFevX6eFmvXqnciuPzYlaT8k4kMykb05C0HtCbymMgzdbLNDd20jl77w3jx8PAgYQEAwemx3vv3eVvZe3g82JWk/JOJLcCwyStXlK2B7AImNpKvU9K2qqpQNIQ0vjIrdUIlL33htmzmXr33TB7tr+saoXPi1nNyTuRXAAsBiZL+nY2ID4KGFs6JVjSM5IuaXocEf8H3A5cKmm4pB8CVwD3RcRduX4CMzP7mFwTSUQ0AtsBy5Om+p4IjANGlh26QnZMqT1JrZY/AJcC04FdqhmvmZm1LvdZWxExA9i2lWMGVSh7Azgwu5mZWY3w6r9mZtYpTiRmZtYpimjtOsDuT9IrwLJXsrXN2sCrXRiOdQ2fl9rjc1KbOnNeBkZEq8t51EUi6QxJ0yJiSNFx2Mf5vNQen5PalMd5cdeWmZl1ihOJmZl1ihNJ68YXHYBV5PNSe3xOalPVz4vHSMzMrFPcIjEzs05xIjEzs05xIjEzs05xIjEzs05xIjEzs05xIrFuSdJqkp6StFnRsZjVu9yXka9VkkTa32RH4D+ANYEPgJeAvwMTI+Kp4iKsP5J2aOHp3sBngW0kfQIgIm7JJbA6J2ln0v5AAs6PiKmSvguMATYEZgPnRMSFxUVZXyT1IW3PsRLwl4h4J/u9OIy0k+yzwPiImF+V9/d1JJD9g98CbEpKHIuBTwNB2sp3A+DzwEkRcVJRcdYbSUtJ50DNHFL6XERE+WZo1sUk7QVcDjwMvAF8HfgJacO567LyIcCuwE8j4uKCQq0bkj4LTAHWy4pmAd8F7gTWAP5N+v5aBGwaEfO6OgZ3bSVnk/7BvxQRA7KNtQYCdwNLIuILwHeAYyT9pLgw687DwMvAQcBnym5fJiWRPbPHGxQUY735FakVsmlEbAccCkwAzoqIvSLijIjYg/Q7dViRgdaRU0lJfSPSSr/3A7cBL5JW792M9PvxIvCbqkQQEXV/y07CjyqUDyJ1bw3IHv8aeLToeOvlRkoUI0jJ5FrgMyXP9QWWAt8qOs56ugFvA9uUPF690nkgban9VtHx1sMNmA/sXvJ4YHZOhpcddyDwVDVicIskESlhlPsge65v9vgBUta3HEQynvRv/gLwT0m/ldS74NDq2ZtA/5LHTT+X71nxCeCtXCKyfqTWRpPns/vyPZieBdatRgBOJMldwMmSPuwekdSP1Dx/EWgaZF+N9ItkOYqINyLicOAbwJbA08ABpDESy9edpN+VHSRtRVoQ8K/AqKbfH0mfI3Wh/K24MOvKy6RWSJMPgAtJ472l1iG1KLucE0lyZHb/pKRnJM0gNRe3AQ6KiKXZ898AphYRoEFE/DMihgL/A/yS5gfhrXqOBRqBm4F7gVWAnUl//T4t6W1gJmlW3bFFBVlnHiZ9VwEftuQPjWUH1b8FPFaNADxrKyNpeWB34EukX45ngCsj4vVCA7OKJK1A+rJaEBGVuiWtSrKp8hsBK0bE4yVl3yfNDpoD3BIRC4qLsn5I6g/0iohZrRz3P6Qx3ildHoMTiXVHWSLZHbgzIl4pOh6zeuZEUkbSJsBg0gBWkGZ0zYyIJwoNzD5GUl/gdWBoRPy16HjqhaTNgQdLunvNnEiaZNeHjCTNaijvew/gOeDEiJiQd2z1StI/Wnh6eeArwJNkA4gR8bU84qpn2UWirwDXAFdFhAfUuwlJPwKujipcuOslUgBJRwBjSTNQJgH/Ig0oQmqZDCZd+HaBpF4RcW4hgdafIaRZc7exbHJfiZRIZvPxqY9WfY8APwYOlfQ86XdmUkQ8VGxYVhS3SABJzwIXRMSYVo47GjgkInwVdQ4k/RA4E5gHHBkRj5Q8twYfdW3dW1CIdSdrkWxBmim0PekPrJ1IEx+eAa4kJZUnCwuyzkj6QxsPHUj6fenyFokTCSBpIbBDRDS0ctxQ0myUXnnEZSBpZeBo4CjSX77HRcQr2RhJI04kuWpKJBHxj5KyVYEfkJLK90itxUdJXV9nFBJoHZH0AemC3RdaObQfaXUIJ5JqkPR30sJm+zY3iJhNb7wc2DAitsgzPgNJ65NaJ98BTgIuJV1w5USSo0qJpOz5PsBwUlLZJiJWzjO+eiRpJvCPiNivleN2Bf7kMZLq+SWpH36GpMmkC6reIA2yr0EaI9mFNBD/vaKCrGcRMRfYTdI2wFnAz/CV7TUnIt4CJgITJa1VcDj14u+kVZhb09JK2p3iRAJExN8kfZnUhbI3Hy3H3OQ50nLyZ0TEv/OOzz4SEfdI+gppMceNSOMnlp+ptHENrYh4rcqxWPK/QFsmOkyl5Ar4ruSurQok9SK1RADeiIiFRcZjZlbLnEisZkk6hjS5oSrrA5lZ1/CijSUkrSdpU0mrNfP82pJaHNCyLvVb4BFJT0g6LtsJzmqApG9K+pGk/2jm+U9LOiHvuOqVpCHZFgunSRqclX1J0vWSHpN0k6Sqje+6RcKHU0wvJ802gbQpzKXA/0TEmyXHbQ7cX41ZD7asbIbQ6UDTDpUrkPqCryRdoft8C9WtCrJp17cDm5EGbgNoAH4SEXNKjvPvSk4kDQNuIl1X9Q5pL5idgcnADNIFpJuSztmPIuL6ro7BLZLkGNIX1SHA5qTtRHcCpmV7K1hxrouInYBPkrZ1fQs4A5gjqUHSCM8OytWJpMko3yPtbzEc+BTpd6UtM4es650A3AB8OiI2BE4jJZHJEfGNiDgsu2ThSuD/VSMAJ5JkL+D4iLgoIqZFxFmk5eRfAO6XtGWx4VlENEbE+Ej7hK9LmrK9EnABMF/SXwoNsH58n3RR6J0R8WpE3AB8lbQ53F3Zek6Wr/8ELizZTuF80q6uV5QddxnpUoYu50SSrAf8s7QgIl4k7Ts9hfQL8sMiArNlRcSLEXFWRHwd+Axpsc1PFRxWvfgkacvWD0XEooj4MXAO8CdJPysksvq1iLRETZOmn1ctO64X8G41AnAiSeYDy3RhRcT7EbEncBFptdMReQdmLYuIORFxWkR8pehY6sQc0pjVMiKiaSmbcaTkbvn4G3CCpI0lrQv8jjQ2coyk1eHDsa2jgenVCMCD7Xy46NkG2TauzR1zLHAKaSdLDyDmQNJI4KKImF90LJZIOhfYMiK+2sIxewETgBX8u1J92WzGu/joQurZpAsP/0zqypoDDAKWkJateWTZV+lkDE4kaeocsAdwWktX42a/IN+JiANzC86shkjaiDQx5cqIaGzhuK1J66CdmFtwdSy7ZOEbwIrAlIhYlF1YfTAfbX98ZYV93Lvm/Z1IzMysMzxGYt2epIskXVJ0HGb1yos2toOki4DlIuKgomOxj9kG/1FUUyTdRerx2K7oWCyp5jlxImkff2HVoIjw0im1R/h3pdZU7Zx4jMS6PUmrAOtke5aYWc78F0M7SFol26nPasuOwKyig7CPSFrRvyu1pZrnxImkffyFZXVP0mGS/i3pbUkPSNq3wmFfxb8ruSn6nHiMxGqWpLvbeOgnqhqIfUjSnqQd+a4CHiZduzBR0s7AvhGxqMj46lEtnBOPkdDuL6yNfbVuPiQtAZ4kLffQkk8Dm/u8VJ+kacDd2XIoTWXbkRYInA3sGBGveRn5/NTCOXEiwV9YtUrSI8CTEbFHK8ftCvzJ56X6JL0NfD8iGsrKBwG3AssD2wNr40SSi1o4J+7aSh6nHV9Y+YRkwAOkfS9aE6SpjVZ9b5K+kD4mImZn+5H8BbgfOCnvwOpY4efEg+3JA8AWbTjOX1j5GgMc0YbjbiEtJ2/VNx2ouKVCtvbWdsA04Ow8g6pzhZ8TJ5LEX1g1KCL+HRE3tuG4RaXbvFpVXQ5sIGnNSk9mA7s/AC4GfF1PPgo/Jx4jMTOzTnGLxMzMOsWJxMzMOsWJxOqKpAMkTc+uAG6U9LCksVV6r40kjZK0RhuOHSUpSm7zJV0racM21D0gq7Na10Ru1j5OJFY3su2SLwZuB4YD+wE3kAYiq2Ej0t7lrSaSzJvAltntV8CXgSmSerdS7y9ZnYUdjNOsU3wdidWTw4ELI+LXJWU3SaqV7WCXRMTfs5//Lmku8FdgB+Ca8oMlLQ8sHxGvAK/kF6bZx7lFYvVkDeDF8sIombooaVDWTbSXpMuyLrCXJY0srydp22yBvHclvSTpvKbuJUlDgZuyQ2dlrzm7nfFOz+4HZa85UdI0ST+U9ATwLrB5pa4tSatKGiNpjqTFkmZJ+m1Z/AdLeiJ7fo6kozHrALdIrJ48BByR/aV/c0S81sKxZwA3A7sC3wJGSno1Is4FkLQxcBtwJ/AjYD3gNGAD0tX4D5G6p35H6kZ7AVjczngHZfcvlpWNAUYDL5FWc/3YOIokkbrstiRdzTydtLzPN0uOOQo4NXutBmBT4CRJCyPinHbGafUuInzzrS5uwBeBZ0krFCwFniB9IfcpOWZQ9vwdZXUvAp4nbbUMMAl4mtS11HTM7lndLbPHO2WPB7UhtlHAq6Q/7lYgja/cA7wFDMiOmZi93pfL6h6Qla+WPR6WPf5BM+/VB1gAjCwrH01KWsu3Fq9vvpXe3LVldSMi/gn8B2lw/TzScje/AaZVmPF0XdnjycCngHWzx18DrouID0qOuRZYAmzVwRDXAt7Pbk+SWjd7RMQLJcc8HxGPtPI62wKvR/OrAmwJ9AaukbRC0w24G+jPR5/RrE3ctWV1JSIWk8YubgKQdBBpJtdBwFklh75cVrXp8QDSMhMDSF1Lpa/9gaTXgIpLVbTBm8C3Sa2JF4H5EVG+9MRLy9Ra1lqkrrTmNC3w90Qzz68HeMkZazMnEqtrEXGJpDHA4LKn1mnm8Qsl9x87JptFtRbwegfDWRIR01o5pi1rGr1GSnTNaYpvJyonpifb8B5mH3LXltUNSeXJAUmfAPqy7BfqLmWPmwbM52WPHwB2yZJH6TErAPdlj9/L7lfpRNgdMQVYU9JOzTz/f8Ai4FMRMa3C7e38QrWewC0SqyePSboBuIPUVTWQNLNqIfDHsmM3kXQhadzjW6SuryMjYmn2/MmkbU2vl3Q+aVzhdOD2iPi/7Jimv+x/KmkSsDAiHqvOR/uYO0kXXV4paTRpBtkA4FsR8dOIeEPSKOAsSQOBe0l/VG4EbBMR5UnUrEVOJFZPRgM7k/ZlWJM0DnE/aUB7VtmxR5O6fq4lXa9xEvDhtNiIeELS9qQptJNJs6uuyuo1HTNH0q+An5G2KZjHR1N6qyYiQtIuWcw/J20RPR+4suSYMZLmA78Afkn6jE/hjdusA7yMvFmJbHvSWaStS28uNhqz7sFjJGZm1ilOJGZm1inu2jIzs05xi8TMzDrFicTMzDrFicTMzDrFicTMzDrFicTMzDrl/wMGQWFBW3mZCgAAAABJRU5ErkJggg==\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot exact payoff function (evaluated on the grid of the uncertainty model)\n", + "x = uncertainty_model.values\n", + "y = np.maximum(0, x - strike_price)\n", + "plt.plot(x, y, 'ro-')\n", + "plt.grid()\n", + "plt.title('Payoff Function', size=15)\n", + "plt.xlabel('Spot Price', size=15)\n", + "plt.ylabel('Payoff', size=15)\n", + "plt.xticks(x, size=15, rotation=90)\n", + "plt.yticks(size=15)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "exact expected value:\t0.1342\n", + "exact delta value: \t0.4446\n" + ] + } + ], + "source": [ + "# evaluate exact expected value (normalized to the [0, 1] interval)\n", + "exact_value = np.dot(uncertainty_model.probabilities, y)\n", + "exact_delta = sum(uncertainty_model.probabilities[x >= strike_price])\n", + "print('exact expected value:\\t%.4f' % exact_value)\n", + "print('exact delta value: \\t%.4f' % exact_delta)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Evaluate Expected Payoff" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "# set number of evaluation qubits (=log(samples))\n", + "m = 6\n", + "\n", + "# construct amplitude estimation \n", + "ae = AmplitudeEstimation(m, european_call)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "# result = ae.run(quantum_instance=BasicAer.get_backend('qasm_simulator'), shots=100)\n", + "result = ae.run(quantum_instance=BasicAer.get_backend('statevector_simulator'))" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exact value: \t0.1342\n", + "Estimated value:\t0.1061\n", + "Probability: \t0.6636\n" + ] + } + ], + "source": [ + "print('Exact value: \\t%.4f' % exact_value)\n", + "print('Estimated value:\\t%.4f' % result['estimation'])\n", + "print('Probability: \\t%.4f' % result['max_probability'])" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot estimated values for \"a\"\n", + "plt.bar(result['values'], result['probabilities'], width=0.5/len(result['probabilities']))\n", + "plt.xticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.title('\"a\" Value', size=15)\n", + "plt.ylabel('Probability', size=15)\n", + "plt.ylim((0,1))\n", + "plt.grid()\n", + "plt.show()\n", + "\n", + "# plot estimated values for option price (after re-scaling and reversing the c_approx-transformation)\n", + "plt.bar(result['mapped_values'], result['probabilities'], width=1/len(result['probabilities']))\n", + "plt.plot([exact_value, exact_value], [0,1], 'r--', linewidth=2)\n", + "plt.xticks(size=15)\n", + "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.title('Estimated Option Price', size=15)\n", + "plt.ylabel('Probability', size=15)\n", + "plt.ylim((0,1))\n", + "plt.grid()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Evaluate Delta\n", + "\n", + "The Delta is a bit simplier to evaluate than the expected payoff.\n", + "Similarly to the expected payoff, we use a comparator circuit and an ancilla qubit to identify the cases where $S_T > K$.\n", + "However, since we are only interested in the probability of this condition being true, we can directly use this ancilla qubit as the objective qubit in amplitude estimation without any futher approximation." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [], + "source": [ + "# setup piecewise linear objective fcuntion\n", + "breakpoints = [uncertainty_model.low, strike_price]\n", + "slopes = [0, 0]\n", + "offsets = [0, 1]\n", + "f_min = 0\n", + "f_max = 1\n", + "c_approx = 1 # no approximation necessary\n", + "european_delta_objective = PwlObjective(\n", + " uncertainty_model.num_target_qubits, \n", + " uncertainty_model.low, \n", + " uncertainty_model.high,\n", + " breakpoints,\n", + " slopes,\n", + " offsets,\n", + " f_min,\n", + " f_max,\n", + " c_approx\n", + ")\n", + "\n", + "# construct circuit factory for payoff function\n", + "european_call_delta = UnivariateProblem(\n", + " uncertainty_model,\n", + " european_delta_objective\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "# set number of evaluation qubits (=log(samples))\n", + "m = 6\n", + "\n", + "# construct amplitude estimation \n", + "ae_delta = AmplitudeEstimation(m, european_call_delta)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "# result_delta = ae_delta.run(quantum_instance=BasicAer.get_backend('qasm_simulator'), shots=100)\n", + "result_delta = ae_delta.run(quantum_instance=BasicAer.get_backend('statevector_simulator'))" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exact delta: \t0.4446\n", + "Esimated value:\t0.4510\n", + "Probability: \t0.9452\n" + ] + } + ], + "source": [ + "print('Exact delta: \\t%.4f' % exact_delta)\n", + "print('Esimated value:\\t%.4f' % result_delta['estimation'])\n", + "print('Probability: \\t%.4f' % result_delta['max_probability'])" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot estimated values for delta\n", + "plt.bar(result_delta['values'], result_delta['probabilities'], width=0.5/len(result_delta['probabilities']))\n", + "plt.plot([exact_delta, exact_delta], [0,1], 'r--', linewidth=2)\n", + "plt.xticks(size=15)\n", + "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.title('Estimated Option Delta', size=15)\n", + "plt.ylabel('Probability', size=15)\n", + "plt.ylim((0,1))\n", + "plt.grid()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "qiskit_master", + "language": "python", + "name": "qiskit_master" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/qiskit/finance/simulation/european_put_option_pricing.ipynb b/qiskit/finance/simulation/european_put_option_pricing.ipynb new file mode 100644 index 000000000..24df0749c --- /dev/null +++ b/qiskit/finance/simulation/european_put_option_pricing.ipynb @@ -0,0 +1,515 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# _*Qiskit Finance: Pricing European Put Options*_ \n", + "\n", + "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", + "\n", + "***\n", + "### Contributors\n", + "Stefan Woerner[1], Daniel Egger[1], Shaohan Hu[1], Stephen Wood[1], Marco Pistoia[1]\n", + "### Affliation\n", + "- [1]IBMQ" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Introduction\n", + "
\n", + "Suppose a European put option with strike price $K$ and an underlying asset whose spot price at maturity $S_T$ follows a given random distribution.\n", + "The corresponding payoff function is defined as:\n", + "
\n", + "
\n", + "$$\\max\\{K - S_T, 0\\}$$\n", + "
\n", + "In the following, a quantum algorithm based on amplitude estimation is used to estimate the expected payoff, i.e., the fair price before discounting, for the option:\n", + "
\n", + "
\n", + "$$\\mathbb{E}\\left[ \\max\\{K - S_T, 0\\} \\right]$$\n", + "
\n", + "as well as the corresponding $\\Delta$, i.e., the derivative of the option price with respect to the spot price, defined as:\n", + "
\n", + "
\n", + "$$\n", + "\\Delta = -\\mathbb{P}\\left[S_T \\leq K\\right]\n", + "$$\n", + "
\n", + "The approximation of the objective function is explained in detail in the following paper:
\n", + "Quantum Risk Analysis. Woerner, Egger. 2018." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "import numpy as np\n", + "\n", + "from qiskit import BasicAer\n", + "from qiskit.aqua.algorithms import AmplitudeEstimation\n", + "from qiskit.aqua.components.uncertainty_models import LogNormalDistribution\n", + "from qiskit.aqua.components.uncertainty_problems import UnivariateProblem\n", + "from qiskit.aqua.components.uncertainty_problems import UnivariatePiecewiseLinearObjective as PwlObjective" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Uncertainty Model\n", + "\n", + "We construct a circuit factory to load a log-normal random distribution into a quantum state.\n", + "The distribution is truncated to a given interval $[low, high]$ and discretized using $2^n$ grid points, where $n$ denotes the number of qubits used.\n", + "The unitary operator corresponding to the circuit factory implements the following: \n", + "$$\\big|0\\rangle_{n} \\mapsto \\big|\\psi\\rangle_{n} = \\sum_{i=0}^{2^n-1} \\sqrt{p_i}\\big|i\\rangle_{n},$$\n", + "where $p_i$ denote the probabilities corresponding to the truncated and discretized distribution and where $i$ is mapped to the right interval using the affine map:\n", + "$$ \\{0, \\ldots, 2^n-1\\} \\ni i \\mapsto \\frac{high - low}{2^n - 1} * i + low \\in [low, high].$$" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# number of qubits to represent the uncertainty\n", + "num_uncertainty_qubits = 3\n", + "\n", + "# parameters for considered random distribution\n", + "S = 2.0 # initial spot price\n", + "vol = 0.4 # volatility of 40%\n", + "r = 0.05 # annual interest rate of 4%\n", + "T = 40 / 365 # 40 days to maturity\n", + "\n", + "# resulting parameters for log-normal distribution\n", + "mu = ((r - 0.5 * vol**2) * T + np.log(S))\n", + "sigma = vol * np.sqrt(T)\n", + "mean = np.exp(mu + sigma**2/2)\n", + "variance = (np.exp(sigma**2) - 1) * np.exp(2*mu + sigma**2)\n", + "stddev = np.sqrt(variance)\n", + "\n", + "# lowest and highest value considered for the spot price; in between, an equidistant discretization is considered.\n", + "low = np.maximum(0, mean - 3*stddev)\n", + "high = mean + 3*stddev\n", + "\n", + "# construct circuit factory for uncertainty model\n", + "uncertainty_model = LogNormalDistribution(num_uncertainty_qubits, mu=mu, sigma=sigma, low=low, high=high)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot probability distribution\n", + "x = uncertainty_model.values\n", + "y = uncertainty_model.probabilities\n", + "plt.bar(x, y, width=0.2)\n", + "plt.xticks(x, size=15, rotation=90)\n", + "plt.yticks(size=15)\n", + "plt.grid()\n", + "plt.xlabel('Spot Price at Maturity $S_T$ (\\$)', size=15)\n", + "plt.ylabel('Probability ($\\%$)', size=15)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Payoff Function\n", + "\n", + "The payoff function decreases linearly with an increasing spot price at maturity $S_T$ until it reaches zero for a spot price equal to the strike price $K$, it stays constant to zero for larger spot prices.\n", + "The implementation uses a comparator, that flips an ancilla qubit from $\\big|0\\rangle$ to $\\big|1\\rangle$ if $S_T \\leq K$, and this ancilla is used to control the linear part of the payoff function.\n", + "\n", + "The linear part itself is then approximated as follows.\n", + "We exploit the fact that $\\sin^2(y + \\pi/4) \\approx y + 1/2$ for small $|y|$.\n", + "Thus, for a given approximation scaling factor $c_{approx} \\in [0, 1]$ and $x \\in [0, 1]$ we consider\n", + "$$ \\sin^2( \\pi/2 * c_{approx} * ( x - 1/2 ) + \\pi/4) \\approx \\pi/2 * c_{approx} * ( x - 1/2 ) + 1/2 $$ for small $c_{approx}$.\n", + "\n", + "We can easily construct an operator that acts as \n", + "$$\\big|x\\rangle \\big|0\\rangle \\mapsto \\big|x\\rangle \\left( \\cos(a*x+b) \\big|0\\rangle + \\sin(a*x+b) \\big|1\\rangle \\right),$$\n", + "using controlled Y-rotations.\n", + "\n", + "Eventually, we are interested in the probability of measuring $\\big|1\\rangle$ in the last qubit, which corresponds to\n", + "$\\sin^2(a*x+b)$.\n", + "Together with the approximation above, this allows to approximate the values of interest.\n", + "The smaller we choose $c_{approx}$, the better the approximation.\n", + "However, since we are then estimating a property scaled by $c_{approx}$, the number of evaluation qubits $m$ needs to be adjusted accordingly.\n", + "\n", + "For more details on the approximation, we refer to:\n", + "Quantum Risk Analysis. Woerner, Egger. 2018." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# set the strike price (should be within the low and the high value of the uncertainty)\n", + "strike_price = 2\n", + "\n", + "# set the approximation scaling for the payoff function\n", + "c_approx = 0.25\n", + "\n", + "# setup piecewise linear objective fcuntion\n", + "breakpoints = [uncertainty_model.low, strike_price]\n", + "slopes = [-1, 0]\n", + "offsets = [strike_price - uncertainty_model.low, 0]\n", + "f_min = 0\n", + "f_max = strike_price - uncertainty_model.low\n", + "european_put_objective = PwlObjective(\n", + " uncertainty_model.num_target_qubits, \n", + " uncertainty_model.low, \n", + " uncertainty_model.high,\n", + " breakpoints,\n", + " slopes,\n", + " offsets,\n", + " f_min,\n", + " f_max,\n", + " c_approx\n", + ")\n", + "\n", + "# construct circuit factory for payoff function\n", + "european_put = UnivariateProblem(\n", + " uncertainty_model,\n", + " european_put_objective\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot exact payoff function (evaluated on the grid of the uncertainty model)\n", + "x = uncertainty_model.values\n", + "y = np.maximum(0, strike_price - x)\n", + "plt.plot(x, y, 'ro-')\n", + "plt.grid()\n", + "plt.title('Payoff Function', size=15)\n", + "plt.xlabel('Spot Price', size=15)\n", + "plt.ylabel('Payoff', size=15)\n", + "plt.xticks(x, size=15, rotation=90)\n", + "plt.yticks(size=15)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "exact expected value:\t0.1040\n", + "exact delta value: \t-0.5300\n" + ] + } + ], + "source": [ + "# evaluate exact expected value (normalized to the [0, 1] interval)\n", + "exact_value = np.dot(uncertainty_model.probabilities, y)\n", + "exact_delta = -sum(uncertainty_model.probabilities[x <= strike_price])\n", + "print('exact expected value:\\t%.4f' % exact_value)\n", + "print('exact delta value: \\t%.4f' % exact_delta)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Evaluate Expected Payoff" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "# set number of evaluation qubits (=log(samples))\n", + "m = 6\n", + "\n", + "# construct amplitude estimation \n", + "ae = AmplitudeEstimation(m, european_put)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "# result = ae.run(quantum_instance=BasicAer.get_backend('qasm_simulator'), shots=100)\n", + "result = ae.run(quantum_instance=BasicAer.get_backend('statevector_simulator'))" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exact value: \t0.1040\n", + "Estimated value:\t0.1032\n", + "Probability: \t0.9826\n" + ] + } + ], + "source": [ + "print('Exact value: \\t%.4f' % exact_value)\n", + "print('Estimated value:\\t%.4f' % result['estimation'])\n", + "print('Probability: \\t%.4f' % result['max_probability'])" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot estimated values for \"a\"\n", + "plt.bar(result['values'], result['probabilities'], width=0.5/len(result['probabilities']))\n", + "plt.xticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.title('\"a\" Value', size=15)\n", + "plt.ylabel('Probability', size=15)\n", + "plt.ylim((0,1))\n", + "plt.grid()\n", + "plt.show()\n", + "\n", + "# plot estimated values for option price (after re-scaling and reversing the c_approx-transformation)\n", + "plt.bar(result['mapped_values'], result['probabilities'], width=1/len(result['probabilities']))\n", + "plt.plot([exact_value, exact_value], [0,1], 'r--', linewidth=2)\n", + "plt.xticks(size=15)\n", + "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.title('Estimated Option Price', size=15)\n", + "plt.ylabel('Probability', size=15)\n", + "plt.ylim((0,1))\n", + "plt.grid()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Evaluate Delta\n", + "\n", + "The Delta is a bit simplier to evaluate than the expected payoff.\n", + "Similarly to the expected payoff, we use a comparator circuit and an ancilla qubit to identify the cases where $S_T \\leq K$.\n", + "However, since we are only interested in the (negative) probability of this condition being true, we can directly use this ancilla qubit as the objective qubit in amplitude estimation without any futher approximation." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "# setup piecewise linear objective fcuntion\n", + "breakpoints = [uncertainty_model.low, strike_price]\n", + "slopes = [0, 0]\n", + "offsets = [1, 0]\n", + "f_min = 0\n", + "f_max = 1\n", + "c_approx = 1\n", + "european_delta_objective = PwlObjective(\n", + " uncertainty_model.num_target_qubits, \n", + " uncertainty_model.low, \n", + " uncertainty_model.high,\n", + " breakpoints,\n", + " slopes,\n", + " offsets,\n", + " f_min,\n", + " f_max,\n", + " c_approx\n", + ")\n", + "\n", + "# construct circuit factory for payoff function\n", + "european_call_delta = UnivariateProblem(\n", + " uncertainty_model,\n", + " european_delta_objective\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "# set number of evaluation qubits (=log(samples))\n", + "m = 6\n", + "\n", + "# construct amplitude estimation \n", + "ae_delta = AmplitudeEstimation(m, european_call_delta)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "# result_delta = ae_delta.run(quantum_instance=BasicAer.get_backend('qasm_simulator'), shots=100)\n", + "result_delta = ae_delta.run(quantum_instance=BasicAer.get_backend('statevector_simulator'))" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exact delta: \t-0.5300\n", + "Esimated value:\t-0.5490\n", + "Probability: \t0.5918\n" + ] + } + ], + "source": [ + "print('Exact delta: \\t%.4f' % exact_delta)\n", + "print('Esimated value:\\t%.4f' % -result_delta['estimation'])\n", + "print('Probability: \\t%.4f' % result_delta['max_probability'])" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot estimated values for delta\n", + "plt.bar(-np.array(result_delta['values']), result_delta['probabilities'], width=0.5/len(result_delta['probabilities']))\n", + "plt.plot([exact_delta, exact_delta], [0,1], 'r--', linewidth=2)\n", + "plt.xticks(size=15)\n", + "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.title('Estimated Option Delta', size=15)\n", + "plt.ylabel('Probability', size=15)\n", + "plt.ylim((0,1))\n", + "plt.grid()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "qiskit_master", + "language": "python", + "name": "qiskit_master" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/qiskit/finance/simulation/fixed_income_pricing.ipynb b/qiskit/finance/simulation/fixed_income_pricing.ipynb new file mode 100644 index 000000000..82c826368 --- /dev/null +++ b/qiskit/finance/simulation/fixed_income_pricing.ipynb @@ -0,0 +1,351 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# _*Qiskit Finance: Pricing Fixed-Income Assets*_ \n", + "\n", + "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", + "\n", + "***\n", + "### Contributors\n", + "Stefan Woerner[1], Daniel Egger[1], Shaohan Hu[1], Stephen Wood[1], Marco Pistoia[1]\n", + "### Affliation\n", + "- [1]IBMQ" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Introduction\n", + "\n", + "We seek to price a fixed-income asset knowing the distributions describing the relevant interest rates. The cash flows $c_t$ of the asset and the dates at which they occur are known. The total value $V$ of the asset is thus the expectation value of:\n", + "\n", + "$$V = \\sum_{t=1}^T \\frac{c_t}{(1+r_t)^t}$$\n", + "\n", + "Each cash flow is treated as a zero coupon bond with a corresponding interest rate $r_t$ that depends on its maturity. The user must specify the distribution modelling the uncertainty in each $r_t$ (possibly correlated) as well as the number of qubits he wishes to use to sample each distribution. In this example we expand the value of the asset to first order in the interest rates $r_t$. This corresponds to studying the asset in terms of its duration.\n", + "
\n", + "
\n", + "The approximation of the objective function follows the following paper:
\n", + "Quantum Risk Analysis. Woerner, Egger. 2018." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "import numpy as np\n", + "from qiskit import BasicAer\n", + "from qiskit.aqua.algorithms.single_sample.amplitude_estimation.ae import AmplitudeEstimation\n", + "from qiskit.aqua.components.uncertainty_models import MultivariateNormalDistribution\n", + "from qiskit.aqua.components.uncertainty_problems import FixedIncomeExpectedValue" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "backend = BasicAer.get_backend('statevector_simulator')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Uncertainty Model\n", + "\n", + "We construct a circuit factory to load a multivariate normal random distribution in $d$ dimensions into a quantum state.\n", + "The distribution is truncated to a given box $\\otimes_{i=1}^d [low_i, high_i]$ and discretized using $2^{n_i}$ grid points, where $n_i$ denotes the number of qubits used for dimension $i = 1,\\ldots, d$.\n", + "The unitary operator corresponding to the circuit factory implements the following: \n", + "$$\\big|0\\rangle_{n_1}\\ldots\\big|0\\rangle_{n_d} \\mapsto \\big|\\psi\\rangle = \\sum_{i_1=0}^{2^n_-1}\\ldots\\sum_{i_d=0}^{2^n_-1} \\sqrt{p_{i_1,...,i_d}}\\big|i_1\\rangle_{n_1}\\ldots\\big|i_d\\rangle_{n_d},$$\n", + "where $p_{i_1, ..., i_d}$ denote the probabilities corresponding to the truncated and discretized distribution and where $i_j$ is mapped to the right interval $[low_j, high_j]$ using the affine map:\n", + "$$ \\{0, \\ldots, 2^{n_{j}}-1\\} \\ni i_j \\mapsto \\frac{high_j - low_j}{2^{n_j} - 1} * i_j + low_j \\in [low_j, high_j].$$\n", + "\n", + "In addition the the uncertainty model, we can also apply an affine map, e.g. resulting from a principal componant analyis. The interest rates used are then given by:\n", + "$$ \\vec{r} = A * \\vec{x} + b,$$\n", + "where $\\vec{x} \\in \\otimes_{i=1}^d [low_i, high_i]$ follows the given random distribution." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# can be used in case a principal component analysis has been done to derive the uncertainty model, ignored in this example.\n", + "A = np.eye(2)\n", + "b = np.zeros(2) \n", + "\n", + "# specify the number of qubits that are used to represent the different dimenions of the uncertainty model\n", + "num_qubits = [2, 2]\n", + "\n", + "# specify the lower and upper bounds for the different dimension\n", + "low = [0, 0]\n", + "high = [0.12, 0.24]\n", + "mu = [0.12, 0.24]\n", + "sigma = 0.01*np.eye(2)\n", + "\n", + "# construct corresponding distribution\n", + "u = MultivariateNormalDistribution(num_qubits, low, high, mu, sigma)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot contour of probability density function\n", + "x = np.linspace(low[0], high[0], 2**num_qubits[0])\n", + "y = np.linspace(low[1], high[1], 2**num_qubits[1])\n", + "z = u.probabilities.reshape(2**num_qubits[0], 2**num_qubits[1])\n", + "plt.contourf(x, y, z)\n", + "plt.xticks(x, size=15)\n", + "plt.yticks(y, size=15)\n", + "plt.grid()\n", + "plt.xlabel('$r_1$ (%)', size=15)\n", + "plt.ylabel('$r_2$ (%)', size=15)\n", + "plt.colorbar()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Cash flow, payoff function, and exact expected value\n", + "\n", + "In the following we define the cash flow per period, the resulting payoff function and evaluate the exact expected value.\n", + "\n", + "For the payoff function we first use a first order approximation and then apply the same approximation technique as for the linear part of the payoff function of the [European Call Option](european_call_option_pricing.ipynb)." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# specify cash flow\n", + "cf = [1.0, 2.0]\n", + "periods = range(1, len(cf)+1)\n", + "\n", + "# plot cash flow\n", + "plt.bar(periods, cf)\n", + "plt.xticks(periods, size=15)\n", + "plt.yticks(size=15)\n", + "plt.grid()\n", + "plt.xlabel('periods', size=15)\n", + "plt.ylabel('cashflow ($)', size=15)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exact value: \t2.1942\n" + ] + } + ], + "source": [ + "# estimate real value\n", + "cnt = 0\n", + "exact_value = 0.0\n", + "for x1 in np.linspace(low[0], high[0], pow(2, num_qubits[0])):\n", + " for x2 in np.linspace(low[1], high[1], pow(2, num_qubits[1])):\n", + " prob = u.probabilities[cnt]\n", + " for t in range(len(cf)):\n", + " # evaluate linear approximation of real value w.r.t. interest rates\n", + " exact_value += prob * (cf[t]/pow(1 + b[t], t+1) - (t+1)*cf[t]*np.dot(A[:, t], np.asarray([x1, x2]))/pow(1 + b[t], t+2))\n", + " cnt += 1\n", + "print('Exact value: \\t%.4f' % exact_value)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "# specify approximation factor\n", + "c_approx = 0.125\n", + "\n", + "# get fixed income circuit appfactory\n", + "fixed_income = FixedIncomeExpectedValue(u, A, b, cf, c_approx)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "# set number of evaluation qubits (samples)\n", + "m = 5\n", + "\n", + "# construct amplitude estimation \n", + "ae = AmplitudeEstimation(m, fixed_income)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "# result = ae.run(quantum_instance=LegacySimulators.get_backend('qasm_simulator'), shots=100)\n", + "result = ae.run(quantum_instance=backend)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exact value: \t2.1942\n", + "Estimated value:\t2.4600\n", + "Probability: \t0.8487\n" + ] + } + ], + "source": [ + "print('Exact value: \\t%.4f' % exact_value)\n", + "print('Estimated value:\\t%.4f' % result['estimation'])\n", + "print('Probability: \\t%.4f' % result['max_probability'])" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot estimated values for \"a\" (direct result of amplitude estimation, not rescaled yet)\n", + "plt.bar(result['values'], result['probabilities'], width=0.5/len(result['probabilities']))\n", + "plt.xticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.title('\"a\" Value', size=15)\n", + "plt.ylabel('Probability', size=15)\n", + "plt.xlim((0,1))\n", + "plt.ylim((0,1))\n", + "plt.grid()\n", + "plt.show()\n", + "\n", + "# plot estimated values for fixed-income asset (after re-scaling and reversing the c_approx-transformation)\n", + "plt.bar(result['mapped_values'], result['probabilities'], width=3/len(result['probabilities']))\n", + "plt.plot([exact_value, exact_value], [0,1], 'r--', linewidth=2)\n", + "plt.xticks(size=15)\n", + "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.title('Estimated Option Price', size=15)\n", + "plt.ylabel('Probability', size=15)\n", + "plt.ylim((0,1))\n", + "plt.grid()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "qiskit_master", + "language": "python", + "name": "qiskit_master" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/qiskit/finance/simulation/iron_condor_pricing.ipynb b/qiskit/finance/simulation/iron_condor_pricing.ipynb new file mode 100644 index 000000000..511e62073 --- /dev/null +++ b/qiskit/finance/simulation/iron_condor_pricing.ipynb @@ -0,0 +1,408 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# _*Qiskit Finance: Pricing Iron Condor Option*_ \n", + "\n", + "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", + "\n", + "***\n", + "### Contributors\n", + "Stefan Woerner[1], Daniel Egger[1]\n", + "### Affliation\n", + "- [1]IBMQ" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Introduction\n", + "
\n", + "Suppose a iron condor option with strike prices $K_1 < K_2 < K_3 < K_4$ and an underlying asset whose spot price at maturity $S_T$ follows a given random distribution.\n", + "The corresponding payoff function is defined as:\n", + "
\n", + "
\n", + "$$ F(S_T) = \n", + "\\begin{cases}\n", + "0 ,& S_T < K_1 \\\\\n", + "S_T - K_1 ,& K_1 \\leq S_T < K_2 \\\\\n", + "K_2 - K_1 ,& K_2 \\leq S_T < K_3 \\\\\n", + "K_3 - S_T ,& K_3 \\leq S_T < K_4 \\\\\n", + "0 ,& S_T \\geq K_4. \n", + "\\end{cases}$$\n", + "
\n", + "In the following, a quantum algorithm based on amplitude estimation is used to estimate the expected payoff, i.e., the fair price before discounting, for the option:\n", + "
\n", + "
\n", + "$$\\mathbb{E}\\left[ F(S_T) \\right].$$\n", + "
\n", + "The approximation of the objective function is explained in detail in the following paper:
\n", + "Quantum Risk Analysis. Woerner, Egger. 2018." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "import numpy as np\n", + "\n", + "from qiskit import BasicAer\n", + "from qiskit.aqua.algorithms import AmplitudeEstimation\n", + "from qiskit.aqua.components.uncertainty_models import LogNormalDistribution\n", + "from qiskit.aqua.components.uncertainty_problems import UnivariateProblem\n", + "from qiskit.aqua.components.uncertainty_problems import UnivariatePiecewiseLinearObjective as PwlObjective" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Uncertainty Model\n", + "\n", + "We construct a circuit factory to load a log-normal random distribution into a quantum state.\n", + "The distribution is truncated to a given interval $[low, high]$ and discretized using $2^n$ grid points, where $n$ denotes the number of qubits used.\n", + "The unitary operator corresponding to the circuit factory implements the following: \n", + "$$\\big|0\\rangle_{n} \\mapsto \\big|\\psi\\rangle_{n} = \\sum_{i=0}^{2^n-1} \\sqrt{p_i}\\big|i\\rangle_{n},$$\n", + "where $p_i$ denote the probabilities corresponding to the truncated and discretized distribution and where $i$ is mapped to the right interval using the affine map:\n", + "$$ \\{0, \\ldots, 2^n-1\\} \\ni i \\mapsto \\frac{high - low}{2^n - 1} * i + low \\in [low, high].$$" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# number of qubits to represent the uncertainty\n", + "num_uncertainty_qubits = 3\n", + "\n", + "# parameters for considered random distribution\n", + "S = 2.0 # initial spot price\n", + "vol = 0.4 # volatility of 40%\n", + "r = 0.05 # annual interest rate of 4%\n", + "T = 40 / 365 # 40 days to maturity\n", + "\n", + "# resulting parameters for log-normal distribution\n", + "mu = ((r - 0.5 * vol**2) * T + np.log(S))\n", + "sigma = vol * np.sqrt(T)\n", + "mean = np.exp(mu + sigma**2/2)\n", + "variance = (np.exp(sigma**2) - 1) * np.exp(2*mu + sigma**2)\n", + "stddev = np.sqrt(variance)\n", + "\n", + "# lowest and highest value considered for the spot price; in between, an equidistant discretization is considered.\n", + "low = np.maximum(0, mean - 3*stddev)\n", + "high = mean + 3*stddev\n", + "\n", + "# construct circuit factory for uncertainty model\n", + "uncertainty_model = LogNormalDistribution(num_uncertainty_qubits, mu=mu, sigma=sigma, low=low, high=high)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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lbRoRj2Tlx2TxfjQilgA3SHodcKKkH0ZENBGjmZn1g1Yvwb0f2DQivtZL8iEi/h4RzXRI2BO4ppBoJpKS0s697P/fNYr/lP3coLD/S7Pkk9//a0mXDc3MrCStJqCRpGkYViBpI0kntLi/rYHp+YKIeBSYn61rxbuAZaQ2KSStCWxS3D9pLqOeY5uZWUlaTUAnks4eanlNtr4VQ4E5NcpnZ+uaImlD4CvAT3JnU+tkP4v7n507tpmZlaTVNiAB9dpNXstLH+6tqLW/3o6zfEVpNeBXwFzgC03uv265pMNIHSsYNmwYkydPbiaMfjF37txSj19PVeOC/ovtqO2WNK7UwLBB7e+n+NyqGlenDMT3WruqGlctDROQpJ5eb5A+tL8nqdg5YA1gO+DaFo8/m5fOVPKGUPvMqBibSN293wTsGBH5BNizfXH/QwvrlxMR40mjPTBy5MgYPXp0ozD6zeTJkynz+PVUNS7ov9gOPu7Ktvdx1HZLOHNqe7fHzTxo9HLLVY2rUwbie61dVY2rlmbedfOBp7PfBTwLPFOo8wJwNXB+i8efTqEtRtImpKm+i203tZxN6r793ogotiXNk/SP4v5zy83s38zM+knDBBQRvybdXIqki4CTeusB16KrgWMkrRURz2dlY4EFwE29bSjpy8DngAMj4pZe9v8BSV+NiKW5/f8D+Fvb0ZuZWZ+1OhbcIR1MPgAXAIuASyXtlrW/jAPOynfNzkY8+GFu+SPAN0mX32ZJ2iH3WD+3/zNIbVM/kTRG0rHAp0lJ1PcAmZmVqNTx2iJitqRdgfOAy0ntMmeTklDeqkB+eJ7ds58HZ4+8Q0g3yhIRMyS9DziLdDb0L+Aoj4JgZla+Zjoh3AUcHBHTJN1Ng95pEfGOVgKIiGnALg3qDC8sH8yKiafetreQhuAxM7MKaeYM6F5Sm0zP7750ZWZmbWumE8Ihud8P7tdozMxswOjzdAxmZmbtaKYNqGG7T16rbUBmZjYwNdsG5HYfMzPrqGbagA7uQhxmZjbAuA3IzMxKUfp9QGZmNjD5PiAzMyuF7wMyM7NStDwWXDYB3MGk4W02Av4J3An8OCJe6Gh0Zma20mqpE4KkNwIPAN8FtgWWZj+/C8yQtE3HIzQzs5VSq2dA40kT0r07Ih7tKZT0OuBK0vQK7+lceGZmtrJqNQGNBD6cTz4AEfGopBOAn3csMhtwhndoeul2p6meeerebcdhZo21eh/QTGCNOuvWAB6ts87MzGw5rSag44BvSHpnvlDSDsBJwJc6FZiZma3c+jIY6drAbZKeBJ4ENsgeTwPHA5f1Q5xmZraS6ctgpPf2UyxmZjaAlD4YadZ1+1xgFDAHuBD4ekQs7WWb1YBTgB1IHSPWiAjVqDcB+HiNXbwxIqa3H72ZmfVVyzeidpKkocB1wDRgH2AL4ExS29RXe9n0VcAngbuA24Bdeqk7HTikUDazbxGbmVmnlJqAgMOBQcB+EfEcMEnS2sA4SadnZSuIiDmSXh0RIekIek9A8yLijs6HbmZm7Wh5OgZJYyVdJ+lRSU8WHy3ubk/gmkKimUhKSjv3tmFEeFBUM7OXsVaH4vkI8GNgBvBa4HfAFdl+ngPOa/H4W5Mukb0ou8l1frauE7aR9JykRZJukdRrYjMzs+5QKycSkv4E/AY4FVgMjIyIP0paC5gE/CYivt3C/hYDx0TEdwrljwEXR8TxTezjCODcOp0QPg+8QGpjWh84ChgB7BQRd9XZ32HAYQDDhg0bMXHixGafTsfNnTuXwYMHl3b8evorrqmznm17H8MGwRMLGtfrzXYbD1mhrKqxVTWuTqnq/wBUN7ay4xozZsyUiBjZTN1W24C2BG6NiKWSlpLuCSIinpd0GnA20HQCytTKgKpT3tqOI85ZbqfSlaRkdDywb51txpPGvGPkyJExevTodsPos8mTJ1Pm8evpr7jaHUIH0lA8Z05tr2lz5kGjVyiramxVjatTqvo/ANWNrapx1dJqG9CzwOrZ77OAN+bWCVi3xf3NBtapUT6E1CW7oyJiAXAV8LZO79vMzFrT6teee4A3A9eQ2n9OkLSEdJnrBNK8QK2YTqGtR9ImwJoU2oY6zB0YzMxK1moC+hawafb7Cdnv5wOrAHeTtZ204GrgGElrRcTzWdlY0hTgN7W4r4YkDSL1vJvS6X2bmVlrWkpA2f00d2S/zwH2kbQ6sHq9e3YauAA4Erg0a0PaHBgHnJXfn6QZwE0RcWiubE/SmdL22fIHs1V3R8QjkoaQeuj9lNRrbz3gC8DGwIF9iNXMzDqoY1NyS2p5Su6ImC1pV1L37ctJ7T5nk5JQMc5VCmXf46WzMYBfZz8PASYAi4B/k0ZU2ABYCNwO7BwR97QSp5mZdV5LCSibkvv3wGtIl7GeJE3J/V/A1yS9LyKmtbLPrH5vIxkQEcObKSusXwjs10osZmbWPZ6S28zMStFqN+yRwAm1puQmdUp4e6cCMzOzlZun5DYzs1K0egnuOOBMSQ9HxIv3/OSm5D6mk8GZ2cvX8A6N0tDuaA8zT9277Tisf3hKbjMzK4Wn5DYzs1KUPiW3mZkNTH0aAlfSa4BRwKtJl97uiIjHOxmYmZmt3Fq9EXUV4FzgUyw/MsFSSeOBz0XEsg7GZ2ZmK6lWu2F/HfgEqbPBcNLU2cOz5U+w4hA6ZmZmNbV6Ce6/gK8WZj19FDhDUpAGFj2hU8GZmdnKq9UzoA2Av9ZZ99dsvZmZWUOtJqC/Ax+qs+5DwP3thWNmZgNFq5fgvgFMzAYf/Q3wBOms5wBgDPWTk5mZ2XJanZDuV5LmkDojnAO8ElhMmprhfRExqfMhmpnZyqjpBCTplaRJ6P4WEaMkvYI0y+hT7nptZmataqUNaClwA/BGgIhYFhFPOvmYmVlfNJ2AskTzADCskwFI2kbS9ZLmS3pc0knZDa+9bbOapDMk/UHSgqwLeL26+0iaKmmhpGmSxnYyfjMz65tWe8F9BThB0nadOLikocB1pMFO9yFN6XAUqY2pN68CPgnMB27rZf87AZcANwJ7kmZt/YWk3dsO3szM2tJqL7ivAusCf5Y0i9QLbrmzj4h4Rwv7O5w0msJ+EfEcMEnS2sA4SadnZSuIiDmSXh0RIekIYJc6+/8acHNEHJkt3yjpTaSbZa9tIU4zM+uwVhPQvcDfOnj8PYFrColmInAasDNweb0NI6LuZTcASauTuoYfWVg1EbhI0pCIeLZPUZuZWdta7YZ9cIePvzWpY0P+GI9Kmp+tq5uAmrAFqZv49EL5faRLj28A7m5j/2Zm1oamEpCkQcBepIFH/wlcHxFPdOD4Q4E5NcpnZ+va3Tc19j+7sN7MzEqgBleykLQ5qaPA8Fzxc8CBEdFWO4qkxcDREXFOoXwWMCEivtLEPo4Azo0IFcp3BG4Bto+Iv+TKtyQNKbR7rRtnJR0GHAYwbNiwERMnTmz9iXXI3LlzGTx4cGnHr6e/4po6q/0rosMGwRML2tvHdhsPWaGsqrFVNS6odmydMND+P5s1ZsyYKRExspm6zZwBnQ4sA95NGvFgM+B84PvZ7+2YDaxTo3wItc+MWt03Nfbfs1xz/xExHhgPMHLkyBg9enSbYfTd5MmTKfP49fRXXAcfd2Xb+zhquyWcObVP8yy+aOZBo1coq2psVY0Lqh1bJwy0/8/+0Ew37FGkKRhujYiFEXEf8GngdZI2avP400ltPS+StAmwJiu23bTqQdIwQVsXyrcmJdS/t7l/MzNrQzMJaCPgoULZg4CADds8/tXAHpLWypWNBRYAN7Wz44hYRLr/54DCqrHA7e4BZ2ZWrmbPbXtvKOq7C0jdpC+VdBqwOWlW1bPyXbMlzQBuiohDc2V7ks6Uts+WP5itujsiHsl+PxmYLOk7wGWkjhR7Ae/rp+djZmZNajYBXSNpSY3y64vlEdH0pHQRMVvSrsB5pC7Xc4CzWXFq71WB4vA83wM2zS3/Ovt5CDAh2/8tWWL6BvAZ4GHgI+12njAzs/Y1k4AaDYvTloiYRv2RDHrqDG+mrM62l5HOfszMrEIaJqCI6NcEZGZmA1Org5GamZl1hBOQmZmVwgnIzMxK4QRkZmalcAIyM7NSOAGZmVkpnIDMzKwUTkBmZlYKJyAzMyuFE5CZmZXCCcjMzErhBGRmZqVwAjIzs1I4AZmZWSmcgMzMrBROQGZmVgonIDMzK0XpCUjSNpKulzRf0uOSTpK0ShPbDZF0kaTZkp6V9DNJ6xbqTJAUNR5b998zMjOzZjSckrs/SRoKXAdMA/YBtgDOJCXGrzbY/JfAVsAngWXAacBlwLsL9aYDhxTKZrYTt5mZta/UBAQcDgwC9ouI54BJktYGxkk6PStbgaRRwB7AzhFxc1Y2C7hT0m4RcV2u+ryIuKN/n4aZmbWq7EtwewLXFBLNRFJS2rnBdk/0JB+AiLgLeDhbZ2ZmFVd2AtqadInsRRHxKDA/W9f0dpn7amy3jaTnJC2SdIuk3hKbmZl1iSKivINLi4FjIuI7hfLHgIsj4vg6200iXVrbt1D+U2DziHhXtvx54AVSG9P6wFHACGCn7Iyp1r4PAw4DGDZs2IiJEye28QzbM3fuXAYPHlza8evpr7imznq27X0MGwRPLGhvH9ttPGSFsqrGVtW4oNqxdcJA+/9s1pgxY6ZExMhm6pbdBgRQKwOqTnlL20XEOcutlK4kJaPjgX2pISLGA+MBRo4cGaNHj24QRv+ZPHkyZR6/nv6K6+Djrmx7H0dtt4Qzp7b3tp550OgVyqoaW1XjgmrH1gkD7f+zP5R9CW42sE6N8iHAnD5st05v20XEAuAq4G0txGhmZv2g7AQ0nUKbjaRNgDWp3cZTd7tMvbahovKuO5qZGVB+Aroa2EPSWrmyscAC4KYG220oaaeeAkkjgc2zdTVJGkTqJTelnaDNzKx9ZSegC4BFwKWSdss6AIwDzsp3zZY0Q9IPe5Yj4nbgGuBiSftJ2hf4GXBLzz1A2UgJf5D0aUm7ShoL3AhsDHyzW0/QzMxqK7UTQkTMlrQrcB5wOan95mxSEspbFSgOz/OhrO6PSIn0CuDI3PpFwL9JIypsACwEbifdvHpPR5+ImZm1rPRecBExDdilQZ3hNcrmkIbYKQ6z07N+IbBfB0I0s5XM8A710Gunp9/MU/duO4aXu7IvwZmZ2QDlBGRmZqVwAjIzs1I4AZmZWSmcgMzMrBROQGZmVgonIDMzK4UTkJmZlcIJyMzMSlH6SAjWXVW4Axx8F7iZ+QzIzMxK4gRkZmalcAIyM7NSOAGZmVkpnIDMzKwUTkBmZlYKJyAzMytF6QlI0jaSrpc0X9Ljkk6SVJx+u9Z2QyRdJGm2pGcl/UzSujXq7SNpqqSFkqZJGts/z8TMzFpR6o2okoYC1wHTgH2ALYAzSYnxqw02/yWwFfBJYBlwGnAZ8O7c/ncCLgHOB44E9gJ+IWl2RFzb0SdjZtamgXajeNkjIRwODAL2i4jngEmS1gbGSTo9K1uBpFHAHsDOEXFzVjYLuFPSbhFxXVb1a8DNEXFktnyjpDcBJwBOQGZmJSr7EtyewDWFRDORlJR2brDdEz3JByAi7gIeztYhaXVgDPCrwrYTgVGShrQfvpmZ9VXZCWhrYHq+ICIeBeZn65reLnNfbrstgFfWqHcf6Xm/oQ/xmplZh5SdgIYCc2qUz87WtbNdz89ivdmF9WZmVgJFRHkHlxYDR0fEOYXyWcCEiPhKne0mAXMj4gOF8p8BwyNiR0k7ArcA20fEX3J1tgT+DuweEZNq7Psw4LBscSvg/j4/wfatBzxV4vHrqWpc4Nj6oqpxgWPri7Lj2jQi1m+mYtmdEGYD69QoH0LtM5z8drWe4Dq57Wbnyop1qLf/iBgPjO/l2F0j6Z6IGFl2HEVVjQscW19UNS5wbH1R1bhqKfsS3HQKbT2SNgHWpHYbT93tMvm2oQeBxTXqbU3qtv33PsRrZmYdUnYCuhrYQ9JaubKxwALgpgbbbZjd5wOApJHA5tk6ImIRcCNwQGHbscDtEfFs++GbmVlflZ2ALgAWAZdK2i1rfxkHnJXvmi1phqQf9ixHxO3ANcDFkvaTtC/wM+CW3D1AACcDoyV9R9JoSaeTbkY9qd+fWWdU4lI65KO6AAAYxUlEQVRgDVWNCxxbX1Q1LnBsfVHVuFZQaicESEPxAOcBo0jtMhcC4yJiaa7OTGByRBycK1sHOBv4ACmRXgEcGRHLNb5lyekbwJak+4TGRcTEfnxKZmbWhNITkJmZDUxlX4IzM7MBygnIzMxK4QRkZmalcAIyM7NSlD0SggGSROrNtzfwRuDVwFLgCeAO0rBEpdw4m90YvBcg4NcR8bSk1wJHkwZ8nQmMj4ipXYzpS8BV3TxmsyQNAlaNiOdzZesDRwDbkG6C/jNwfjfvRZP0VmBQRNyWK3sf8OVcXH8h9RK9rfZeuif7n3g/8DYggHtIf/NK9JrKpo15CtglIm4pMYZdgNWAKyNiXvZe+yzpnsiHSP+bj5cRXzPcC65k2RvmKmAEKeEsAjYm/dNdTXojbQWcHBEndzm2d5DmTRoMLAGeIc3DdBUpQd4LbAtsCOwWEX/oUlzLSK/PdODnwC8jYkY3jt2IpKuAByLi89nyKNLfcRkwhZTIRwAvkD687u1SXHcAl0fEKdnyJ0i3PNwI3JDFtStpQsf9I+K33Ygri+U24NCIuC9bHkp6340A5mbVBpO+jO2RT+79HNd/97J6EHAGcA7wAEBEnN+NuAAkvR64HtgkK3oY2B2YRBpu7EHS58YCYEREPNat2FoSEX6U+AB+QXoDb5crew3we+CSbHln0j/iJ7oc2yTSB9Q6pKktzgMeA34LvDKrszrpA/bGLsa1DPgW6d6vRaRkeDfwBWDjkv+eTwH75JbvIH1QrJUrG0Ia6eOaLsb1HGkA3p7lGcC5NepdAPyly6/ZMuAdueUfkr7svC9X9j7S+I5ndzmupdnPWo/8uqVdfs1+RTpjfT3pislPss+R23rea6RBSf8CfL+bsbX0PMoOYKA/SDff7l+jfHj2Bt8oWz6+hA+Gp4E9c8sbZP9suxfq7Q081cW4XvzAIk2rcVj2Ib8ke0zOytYt4e85H3hPbvmF4uuVe83mdfl9lk9Ai0kzChfr7QYs7PJrVkxA/wb+p0a9o4FHuhjXZcA/gUPIrhbl1q2Txf2ebsVTOP7jwIG55U2zePYr1DsE+HsZMTbzcCeE8omUaIqWZut6Zm69k+5PohfZI79MoazWctdExOyIGB8RuwKvBY4iXRO/AHhc0pVdDulvpJl4ezxB+oZatC4pWXXLH4CDcsv3ArVGTH47MKsrEdW3DqnNp2gK6XJvV0TEvsDHgWOAu7MpXl5c3a046hgK/Cu33PM3e6RQ7yHS/0UluRNC+a4DviHprxHxELx4Dfx/SW+wns4Hg4FuD6A6BTha0q3APNJZ2CzgM5JuiIilklYF/pv0wVuqiPgX6Zr8OZI2BT5MGny2m04FfibpH8DFwCnAGZKeJl12EylBfYsVp4vvT8cDt0p6BXAuqfPBjyW9mnTGCKkN6H+A47oYV4/9swGFof50K+uRLiV2TURcK+nNpNflSkm/J52JdaUdqhdPks56eiwFvk/6wpO3AeXHWl/Zp2AD/UH6dvI30iWRGcA0UsPhHJa//HU6qbG9m7GNJH0YLM5iehp4C+la80PA5aTGz0XAmC7Gtdwlm6o9gE+SPiifBe7Kfl+aPZZkP/8PeFWX49oeuJ0a7RfZz6eBz5fwetVqX/lRjXrfB/5Q4t91Q9KXirnAmdnrVtYluMtqvUY16p0LXFfWa9bo4V5wFSBpFeBA0of7GqRE9POIeKbUwICsy/V/kM6WL4mIf0raEDiW1MvmEeDCiPhjF2M6EfhBVLl7qbQu6ezrHaQPrleQGtbvA66IiCklxvZG4J014rotIhaXFVcjkj4FPBgRN5QcxyjSQMhbAXtHCd3WJQ0jfYF5uEG9L5Lajq/vTmStcQIyM7NSuA2oQiS9iTRj61BSI+ccYHp06V6RVklaJXLTZpRN0hqkm2OXATPK/jaftY9tTu7G4oh4tMyYXm6yG1KJEr8pZzcXKyLm58q2J7sRu8yz2Ze9sq8B+hEAnyBdyqp1z8FS0mgDh5QU236k681XAe/PysZmMS3N4v5Ul2P6KLl7okhfpE4l9SrraWt5HjiupNdsBPA7UrvZ0sJjFmlCxK62/2Rx/Qepu/pU4JfUaL8gXZrr9j0tu5O7Tyor2xf4I6nNbDGpV9zeXY5rCKmtbnEWxw+AVYAfF/4/bwXWK+O91sRz2L/bf89WHu6GXTJJnyM1rl4BjCb1Wnll9tiAdBPqFcAFkj7b5dgOBH5D6n20GPhldh3+J6QPsiNJN75dIGmPLoZ2POkG2B6nZbF8C3gP6TU7EzhR0vFdjAtJu5Nek9cA3yHNynst6YNqHHAW6UPhtqy3Y7fiei/pBuI1SL3xXg/cKOnMnrOMEl1NGoIKAEkfAC4FFpJ65H2ZdD/Vb7PXt1tOJo0M8UXSl8R3kXou7kK6MXYYKakPz+pai9wGVDJJDwEXRMTpDeodCxweEZt3JzKQdDcwJSIOz5YPAn4EnBcRR+XqXQRsEhG7dSmu+aQegjdly08Cp0TEOYV6RwOfi4hNa+ymv2KbAvwtIj5eKP8c6R6lzUn3Kd0G3BERvQ330sm4biENEXRIruwTpO7+k4APR8RCSe8kdUZYpRtxZXEsA3aIiLuy5T8CsyLi/YV6VwFrRsTOXYrrYeCbEfGDbPmtpFsTDomIH+fqfQo4PiI260Zc2TF/1GTVTYHR3fx7tsJnQOXbkNRVt5G76OJNeJmtSGdAPa4gnZkVb+68lDSgZbc8Szor6zGENORI0V9IZ5HdtA3w0xrlPwVeB2wVEQtJZ0cf6GJc2xbjiogfkc4WdwBuyO4JqoJtSVcFisaTBiftlg146T48yMZ8I42zljeD2vct9aePky5dbtfg0bUvX33hBFS+vwKfym4QrCm7RPKprG43Bemad4+egSHnFOrNJd293i2/I90gu1q2fB3pptOiD5Pu+O+mJ0nd6YveQno9e24mfoSXRrnohoXAmsXCSA3oO5I+QG8DuvYtvhhK7vdneem9ljeP7n5mPUxK0D3eTWr3eVeh3o5AtzuXPADcEBFv7+1BOTcVN8294Mp3FGng0WmSLiWN8DyH9A+5DqlX3AdIN6y+r8uxPUL6Rn8NQKSRD0aR7hnJ25zlhwXpb18mDS3zN0kXkm6IPU3Strx0V/8uwFtJQ/p303jgZElrktrJXiANb/MV0oCtPfcubU53P7T+CuxJSt7LiYiHsmFmrgImdDGmvGskLcl+H0K6aXZyoc7WpLHZuuUC0qga25GS4oGk994JkgaTzrDfRhoEt9ttQHewYiKsJUijb1SSE1DJIuLWrEvnsaSxujYpVPkHqZH2jIgonvr3t0spjCMVEXfWqPcRoGtzokTEM5J2IH2of5GXLrONyh4vkNo13h0Rd3crriy2U7I2jeOAE3uKSaOe/0+u6mLgm10M7RLgeEmvjho3OEfEk5J2JvX66kpbXs7Xa5Q9WaNsf9Lo7F0REedlVyY+TDozPDYiLpD0GKntrGc8vwuAb3crrsy5pF6CjdzE8mMTVoo7IVSMpFfx0uWsOZG796CqJL2OFGtXx+nKHX84y9/V/2CUfw/QK0n3iawBPFTWa2P9I7ssvl5E/LvsWF7OnIDMzKwUvgRXEdnU1xsA90fECg2wktYD9oqIi7seXA3ZNfA/Agd1+zJXVae9zsVSuWnMm5WNE3dARJzU5eO+LKaXrjFV+BRSvF3/Jp+NHr4/6X02ISKmS3oL6ZJmz/vsuxHx+27H1iyfAZVM0uqk7rH7ZUXLSCPufjH/4VnS/Rl79bJ6TdLd9MeRTcUQEVd1Ka5KTnudxVLJacybJWl/4Fddfp9Vcnrpqk4VnsWyB6nzzTOk3oHrA/uQ2m2nkb6AjSB1gNk/Ii7rVmwtKXsohoH+AE4g9Xr7FGn6g8+T5vR4ANgyV6+MIVIqOSUxFZ32OjtuVacxf12Tj8NLeJ9VcnppKjpVeHbcW4FfA6tky8dncfywUO8npBueuxZbS8+j7AAG+oPU7fqIQtmGwM2kqYlHZWVlJKApvDQl8aaFx5uzf9ADe8q6GFclp73OjlnlacyL49LVenT1y0QWWyWnl66RgCoxVXh2zGdJZ9A9y0OzeHcp1Nud1EGoa7G18nAbUPk2oXCDaUT8S9KupG8v12VD4HTz/oceI0lnZqeR7rs5OrL5RyT13ET5r4goTgPc33qmvb45W67KtNdQ3WnMnwduAC5sUG8n0i0B3fRymV66ElOFZxaw/I3FPb8PKtR7Fekm5EpyAirf48CWvPRhCkCkbsQfkvQd0ql21zsfRPoKNV7Sr4BvAH+VdF72e5mqOu01VHca87uAIRFRHEZpOdmUFt1W5emlKzlVOOkS3AmSHsiO/W1S28+XJN0cEc9nXxKPJb0nq6nsU7CB/iAN7jm5QZ0vU8KlkRpxvJl0d/rjpLaqMqckruq011WdxvxrwD+aqPceutg2lR2zktNLU+GpwkntZTNz7/kHSW14Pf8LU0nJejawfTdja+XhXnAly75djQVOjYine6n3EeC9kRvNuCySPgScTrocMjoibm6wSX/FUclpr6s4jXmVvdynly5rqvDsVogdSZ1dro+IBdmN7J/kpffZz6NLvQb7wgnI+iS7jLQmMDcqNCuqmb18OAGZmVkpPB3Dy4SkH0j6Ydlx1FLV2KoaF1Q3NknXSarUJa4eVY2tqnFBtWMD94J7ORlDdb8wVDW2qsYF1Y1NVDMuqG5sVY0Lqh2bL8GZmVk5KpsZbXmS1simPaicqsZW1bigurFJemUV44LqxlbVuKDasYET0MvJ3qT7R6qoqrFVNS4oITZJn5X0oKTnJd0p6WM1qr2t23FVObaqxlX12JrlBGQ2AGT3bp1LGrj166SbiSdI+k02vYVje5nEVfXYWuE2oJJJavbmtfWBbaK7w+RXMraqxgXVjU3SPcANEXFsrmxX4GekO+r3jjRvURnTflQytqrGVfXYWuEzoPK9BxhGGrKlt0e3x8CqcmxVjavKsW1FmpPoRdmIAjuQpq64XdIWXY6pR1Vjq2pcUO3YmuZu2OX7G2kW1LG9VZL0QdIEcN1U1diqGhdUN7ZnSYNmLiciZkp6F3Alaf6dk7sYU4+qxlbVuKDasTXNZ0Dlu5P0raWRIPXp76aqxlbVuKC6sU0B9q0ZSMRsYFfSVAP/28WYelQ1tqrGBdWOrWlOQOU7HfhcE/WuAjbr51iKqhpbVeOC6sb2U2BzSbXmTSIiFgD/SZov6NEuxgXVja2qcUG1Y2uaOyGYmVkpfAZkZmalcAIyM7NSOAGZmVkpnIDMzKwUTkDWK0kHS5qSjTc1W9KfJJ3VT8c6UNLBTdQbJylyj8clXdLsjXeSJmR3kpeu2eec1e153g/UWT8jWz+uv2Jocb/Lvc6dPo6kV0g6IntPLpD0nKR7Jf2vpD51cVfyF0kfr7N+gqThddZ9VxWc46nKnICsLklfJnXjvAbYD/gv4Lek7p394UDg4CbrPguMyh5HA9sD10tas4ltT27hOP2tlecMsBDYTNLIfKGktwObZuv7O4ZmFV/nTh9nIvAN4FLSe/LjpO7t74q+d+89EBgK/LwP254BHCTp9X089oDjkRCsN0cA34+I43Nll0v6elkB5SyJiDuy3++Q9CjwB2Av4NfFypJWAVaJiBci4sEuxtlp84A/Ah8i3WjY40PADcCIMoLq0a3XWdKewAHAXhFxdW7V//X17CdzJPCTiFicO9aqpGT6MeA1wIclPQh8PSJeHM0iG4XgFuAzwFFtxDBg+AzIerMO8K9iYf7bZc9lFkn7SpouaaGkWyRtU9wuuwQzVdIiSf+QdEr2z42kCcD+wM65S2vjWoh1SvZzeI247iWdGbwzv64Q23sk3ShprqRnJU2W9Nbc+p0k3SRpvqSnlabUXqu3gCSNkvS77BLhPEl/lnRQ/rXr43OeCBzY80Gb/TwwK+9YDNlr8JvC/kZndbbNv5aNXud6x5G0t6RlkjYrHGezrLze2fbO2c8VBn/t69lPdubyLuA3hVWfB44ljSpwFfAJ4EfAujV2cwnpLMifrU3wGZD15o/A57Kziysi4uk69TYFzgK+BiwgDQ9/jaQtI2IhgKTdSWOfXQwcA7yZ9K1yXeDw7PfXkZLef2f7fayFWIdnP/9VKDsdOAl4gjrzokgaDUwCbiRdxpkH7AhsDPxJ0o7A9cBlwAezmE8lXar5YC8xbQrcClxA+mDeEbhI0rKI+AV9f86XAt8DdiKd9b2bNLr2/5EuA3UjhrzhNH6d6x3nn6SpBD4OjMvVPxj4N4UBN3PmZT/PkHRmRDzSYsy17Jrt9y+F8p1JI0+fnn2xujUiZtbZx22kwWi3q7EfK4oIP/yo+SAliYdI45YtA+4lfcisnaszIVv/rlzZpsAS4PBc2R3AjYX9HwssBV6bLf8GmNxEXOOAp0hfoFYF3kBKHs8BGxXi2r7G9hOAe3LLt5MuZ6nO8f5QI/Zdsv1v2+RrqSzW75M+zHrKm3rO+eed/f5b4LvZ7+cDl2W/PwWM60QMwGTgN4Wy0fnn3eLrXO843yAlLeXinAl8u5fXYkPgr9mxgzQI7PHA4Dbe7+OBu2uUfx/4R3bMCcDwXvaxavbe/1Rf4xhID58mWl0R8VfgjaQG3vNJHwxfA+6RNDhX9cmIuC233SOkS2LvgBfbBd7Gim0zvyRdBh7Vh/DWBRZnj/uBzYGxEfHPXJ1ZEfHn3naSdVp4J/DjyD5BCutflcX3K0mr9jyAW7Jj121zkTRUqUfWI7lYDyMlzHZNBD4oaXXSWdgKl9+6EEOPhq9zAz8ifWkZnS2PyZYvqrdBRPwLeCuwB+lscB3gFOA2SavBiz04/5w9FmWXiP+s1KvzlTV2uyEpgRedQjozepj0v3B0dlZcK64lwJxsX9aAE5D1KiIWRcTlEXFERGwDfBLYEjg0V+3JGps+CWyU/b4e8ErS5Zm8nuWaAyo28CzwdmAk8FrSt9KrC3WKx6tlKCmx/rOX9auQEvDi3GMR6Tlt0su+JwBjSZfFds/i/RGwRhNxNfI7YDDpw3FN4PISYujRzOtcV0Q8RDrbOiQrOgS4KyLubbDd0oi4NiL+m3R57yLSpa9R2foJEbE96cvPEmDHiNg+IkZErpNBzhqkv2vxOI9m+/0A6YrATsAtqn87wiI6+/qutNwGZC2JiB9KOh3YOle8QY2qG5Au2UH6Vrm4Rr1h2c9n+hDKkohodC9PM43Rs0mXFzeqs35Otp9x1G6PeLzWRpLWAPYGjoiIC3LlHfnSFxHzJF0BfAH4dUTMK9bpQAwLgdUKZbW+LHRiROMLgR8odf3fjxZ7kUXEMknXkpJX8cN/S2B21G/D7PEMdc5csoT1e6WpsMeRpkI4W9J3sgSVtw59e08POD4DsrokrZBYJK1PmnEx/613A6VJsHrqvI70rfMuSN9USZfkDijs7kDSh//t2fILdPmbY/bBfSfwXz29ymqsvwPYKiLuqfGomYCA1UlnTi9+o856zRV7dbXznL9HOvO5oM76dmN4jOW/aAC8t0+R9n4cSB0rXiBdSnwFdS4pAkgaVmfVfwLzSX/PvLfQXIeA+6kxRUat9wVwd/bz1YW66wOvAv7exPEGPJ8BWW+mSvotcC3pktqmpJs+5wM/ztV7CviJpJ5ecCdl9Sfk6pxI6hl3EenDZTtSz6gfRERPr6vpwD6S9iV9+D3eywd8Jx0HXAdcLWk86Xr/KFID+hWkzhLXS1pGakh/nnTJZ2/gKxGxwodNRDwr6W7gBEnPkRLtcaRLh2vnqvb5OUfEZNKlq3rr243h/4BDJZ1NmmFzDKnNpa/qPteIWCjpZ8BngV9ExJxe9vMrSc8DvyJ1VtgAOAjYh9T4X9z2LaQOC43cSnqt1o+If+fKfy7pT8DNpMudI0hnnrOA+wr7GEk6I7wNa6zsXhB+VPdB+jC4lnSZaSHpn/3nwNa5OhNIPcj2I33rW0T6R16hdxipLWIq6ZvuY6T2i1Vz69cjfeg9Q3bZq05c48h6g/US+wRyPbAarSN1tb2ZlFznkHrVbZ9b/07g96SedvOAaaSu50N6ieH1pPtU5pEmBTu2GHuzz7mF571cL7h2YwC+TOoB9jxpErT/ZMVecE29zo2eK7BbVr5bg+f4iexv8Vj2XnqGlCBH16l/OfChJt7vqwFPAx8rlH8gO96/SEn8OVLif2uNfZxDocekH/UfnpDO2pLdYLhtRIxsVNesN1nb4lhgs4hY1sH9PgrsERHFs5Vadc8BXh8Re9dZP4GUOGfWWLcK8AhwXET8tK2gBwhfgjOzUknaCtiGNITN1zucfIaSbtJttk3mDOB+SW+IGpdWGziAdAm6bvuVLc+dEMysbN8nXdq9ijTcTcdExOyIGBSpI0wz9R8j3WJQr1fkZaRLtLUIODTSvUDWBF+CMzOzUvgMyMzMSuEEZGZmpXACMjOzUjgBmZlZKZyAzMysFE5AZmZWCicgMzMrhROQmZmV4v8Bzzme+z7FdgYAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot probability distribution\n", + "x = uncertainty_model.values\n", + "y = uncertainty_model.probabilities\n", + "plt.bar(x, y, width=0.2)\n", + "plt.xticks(x, size=15, rotation=90)\n", + "plt.yticks(size=15)\n", + "plt.grid()\n", + "plt.xlabel('Spot Price at Maturity $S_T$ (\\$)', size=15)\n", + "plt.ylabel('Probability ($\\%$)', size=15)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Payoff Function\n", + "\n", + "The payoff function equals zero as long as the spot price at maturity $S_T$ is less than the strike price $K_1$, then increases linearly, and is bounded by $K_2$.\n", + "The implementation uses two comparators, that flip an ancilla qubit each from $\\big|0\\rangle$ to $\\big|1\\rangle$ if $S_T \\geq K_1$ and $S_T \\leq K_2, and these ancillas are used to control the linear part of the payoff function.\n", + "\n", + "The linear part itself is then approximated as follows.\n", + "We exploit the fact that $\\sin^2(y + \\pi/4) \\approx y + 1/2$ for small $|y|$.\n", + "Thus, for a given approximation scaling factor $c_{approx} \\in [0, 1]$ and $x \\in [0, 1]$ we consider\n", + "$$ \\sin^2( \\pi/2 * c_{approx} * ( x - 1/2 ) + \\pi/4) \\approx \\pi/2 * c_{approx} * ( x - 1/2 ) + 1/2 $$ for small $c_{approx}$.\n", + "\n", + "We can easily construct an operator that acts as \n", + "$$\\big|x\\rangle \\big|0\\rangle \\mapsto \\big|x\\rangle \\left( \\cos(a*x+b) \\big|0\\rangle + \\sin(a*x+b) \\big|1\\rangle \\right),$$\n", + "using controlled Y-rotations.\n", + "\n", + "Eventually, we are interested in the probability of measuring $\\big|1\\rangle$ in the last qubit, which corresponds to\n", + "$\\sin^2(a*x+b)$.\n", + "Together with the approximation above, this allows to approximate the values of interest.\n", + "The smaller we choose $c_{approx}$, the better the approximation.\n", + "However, since we are then estimating a property scaled by $c_{approx}$, the number of evaluation qubits $m$ needs to be adjusted accordingly.\n", + "\n", + "For more details on the approximation, we refer to:\n", + "Quantum Risk Analysis. Woerner, Egger. 2018." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# set the strike price (should be within the low and the high value of the uncertainty)\n", + "strike_price_1 = 1.438\n", + "strike_price_2 = 1.896\n", + "strike_price_3 = 2.126\n", + "strike_price_4 = strike_price_3 + strike_price_2 - strike_price_1\n", + "\n", + "# set the approximation scaling for the payoff function\n", + "c_approx = 0.25\n", + "\n", + "# setup piecewise linear objective fcuntion\n", + "breakpoints = [uncertainty_model.low, strike_price_1, strike_price_2, strike_price_3, strike_price_4]\n", + "slopes = [0, 1, 0, -1, 0]\n", + "offsets = [0, 0, strike_price_2 - strike_price_1, strike_price_2 - strike_price_1, 0]\n", + "f_min = 0\n", + "f_max = strike_price_2 - strike_price_1\n", + "iron_condor_objective = PwlObjective(\n", + " uncertainty_model.num_target_qubits, \n", + " uncertainty_model.low, \n", + " uncertainty_model.high,\n", + " breakpoints,\n", + " slopes,\n", + " offsets,\n", + " f_min,\n", + " f_max,\n", + " c_approx\n", + ")\n", + "\n", + "# construct circuit factory for payoff function\n", + "iron_condor = UnivariateProblem(\n", + " uncertainty_model,\n", + " iron_condor_objective\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot exact payoff function (evaluated on the grid of the uncertainty model)\n", + "x = uncertainty_model.values\n", + "def payoff(x):\n", + " if x <= strike_price_1:\n", + " return 0\n", + " elif x < strike_price_2:\n", + " return x - strike_price_1\n", + " elif x < strike_price_3:\n", + " return strike_price_2 - strike_price_1\n", + " elif x < strike_price_4:\n", + " return strike_price_2 - strike_price_1 + strike_price_3 - x\n", + " else:\n", + " return 0\n", + "y = [payoff(x_) for x_ in x]\n", + "plt.plot(x, y, 'ro-')\n", + "plt.grid()\n", + "plt.title('Payoff Function', size=15)\n", + "plt.xlabel('Spot Price', size=15)\n", + "plt.ylabel('Payoff', size=15)\n", + "plt.xticks(x, size=15, rotation=90)\n", + "plt.yticks(size=15)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "exact expected value:\t0.3569\n" + ] + } + ], + "source": [ + "# evaluate exact expected value (normalized to the [0, 1] interval)\n", + "exact_value = np.dot(uncertainty_model.probabilities, y)\n", + "print('exact expected value:\\t%.4f' % exact_value)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Evaluate Expected Payoff" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "# set number of evaluation qubits (=log(samples))\n", + "m = 5\n", + "\n", + "# construct amplitude estimation \n", + "ae = AmplitudeEstimation(m, iron_condor)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "# result = ae.run(quantum_instance=BasicAer.get_backend('qasm_simulator'), shots=100)\n", + "result = ae.run(quantum_instance=BasicAer.get_backend('statevector_simulator'))" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exact value: \t0.3569\n", + "Estimated value:\t0.3428\n", + "Probability: \t0.9697\n" + ] + } + ], + "source": [ + "print('Exact value: \\t%.4f' % exact_value)\n", + "print('Estimated value:\\t%.4f' % result['estimation'])\n", + "print('Probability: \\t%.4f' % result['max_probability'])" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot estimated values for \"a\"\n", + "plt.bar(result['values'], result['probabilities'], width=0.5/len(result['probabilities']))\n", + "plt.xticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.title('\"a\" Value', size=15)\n", + "plt.ylabel('Probability', size=15)\n", + "plt.ylim((0,1))\n", + "plt.grid()\n", + "plt.show()\n", + "\n", + "# plot estimated values for option price (after re-scaling and reversing the c_approx-transformation)\n", + "plt.bar(result['mapped_values'], result['probabilities'], width=1/len(result['probabilities']))\n", + "plt.plot([exact_value, exact_value], [0,1], 'r--', linewidth=2)\n", + "plt.xticks(size=15)\n", + "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.title('Estimated Option Price', size=15)\n", + "plt.ylabel('Probability', size=15)\n", + "plt.ylim((0,1))\n", + "plt.grid()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "qiskit_master", + "language": "python", + "name": "qiskit_master" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/qiskit/finance/simulation/option_pricing.ipynb b/qiskit/finance/simulation/option_pricing.ipynb new file mode 100644 index 000000000..b69deeaf9 --- /dev/null +++ b/qiskit/finance/simulation/option_pricing.ipynb @@ -0,0 +1,90 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# _*Qiskit Finance: Option Pricing*_ \n", + "\n", + "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", + "\n", + "***\n", + "### Contributors\n", + "Stefan Woerner[1], Daniel Egger[1], Christa Zoufal[1], Shaohan Hu[1], Stephen Wood[1], Marco Pistoia[1]\n", + "\n", + "### Affliation\n", + "- [1]IBMQ" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this notebook we provide an overview of the available Qiskit Finance tutorials on how to use Quantum Amplitude Estimation (QAE) for option pricing. We analyze different types of options with increasing complexity, featuring:\n", + "- single asset / multi asset (basket) options\n", + "- piecewise linear payoff functions (arbitrary number of break points, possibly non-continuous)\n", + "- path-dependency (sum/average, barrier, etc.)\n", + "\n", + "The basic ideas on using QAE for option pricing and risk analysis are provided here:
\n", + "Quantum Risk Analysis. Stefan Woerner, Daniel J. Egger (2019).\n", + "\n", + "A Qiskit Aqua tutorial on QAE can be found here:
\n", + "Qiskit Tutorial on QAE\n", + "\n", + "We provide tutorials for the following types simple options:\n", + "\n", + "- European Call Option (univariate, payoff with 2 segments)\n", + "- European Put Option (univariate, payoff with 2 segments)\n", + "- Bull Spread (univariate, payoff with 3 segments)\n", + "- Iron Condor (univariate, payoff with 5 segments)\n", + "\n", + "Note that the provided framework can cover all options of this type, i.e., options that are fully determined by a piecewise linear payoff with respect to the spot price at maturity of the underlying asset.\n", + "However, the framework also allows to price more complex options, for instance, options that depend on multiple assets or are path-dependent:\n", + "\n", + "- Basket Option (multivariate, payoff with 2 segments)\n", + "- Asian Barrier Spread (multivariate, path-dependent, payoff with 3 segments)\n", + "\n", + "All examples illustrate how to use the genereric Qiskit Finance framework to construct operators that can be analyzed with QAE. The same framework can be easily adjusted to estimate risk as well, for instance, the Value at Risk (VaR) or the Conditional Value at Risk (CVaR, also known as Expected Shortfall). How to use Qiskit Finance for risk analysis is illustrated in the following tutorial:\n", + "Credit Risk Analysis\n", + "\n", + "An example of how quantum Generative Adversarial Networks (qGANs) can be used to learn and efficiently load generic random distributions for option pricing can be found here:\n", + "QGANs to learn and load random distributions for option pricing" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "qiskit_master", + "language": "python", + "name": "qiskit_master" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From 16fda551b484811a76df7d84cf758bd652ebae41 Mon Sep 17 00:00:00 2001 From: CZ Date: Tue, 16 Apr 2019 19:36:45 +0200 Subject: [PATCH 052/116] Create execute_qgan.ipynb --- .../machine_learning/execute_qgan.ipynb | 12528 ++++++++++++++++ 1 file changed, 12528 insertions(+) create mode 100644 qiskit/finance/machine_learning/execute_qgan.ipynb diff --git a/qiskit/finance/machine_learning/execute_qgan.ipynb b/qiskit/finance/machine_learning/execute_qgan.ipynb new file mode 100644 index 000000000..32a914048 --- /dev/null +++ b/qiskit/finance/machine_learning/execute_qgan.ipynb @@ -0,0 +1,12528 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# _*Qiskit Finance: qGANs for Loading Random Distributions*_ \n", + "\n", + "Qiskit Finance is part of Qiskit Aqua.
\n", + "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", + "\n", + "***\n", + "### Contributors\n", + "Christa Zoufal[1,2], Stefan Woerner[1]\n", + "### Affliation\n", + "- [1]IBMQ\n", + "- [2]ETH Zurich\n", + "\n", + "### Introduction\n", + "Given $k$-dimensional data samples, we employ a quantum Generative Adversarial Network (qGAN) to learn the data's underlying random distribution and to load it directly into a quantum state: \n", + "$$\\lvert g_{\\theta}\\rangle = \\sum\\limits_{j=0}^{2^n-1}\\sqrt{p_{\\theta}^{j}}\\lvert{j}\\rangle$$\n", + "where $p_{\\theta}^{j}$ describe the occurrence probabilities of the basis states $\\vert j\\rangle$. \n", + "\n", + "The aim of the qGAN training is to generate a state $\\lvert g_{\\theta}\\rangle$ where $p_{\\theta}^{j}$, for $j\\in \\left\\{0, \\ldots, {2^n-1} \\right\\}$, describe a probability distribution that is close to the distribution underlying the training data $X=\\left\\{x^0, \\ldots, x^{k-1} \\right\\}$.\n", + "\n", + "For further details please refer to https://arxiv.org/abs/1904.00043." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "#!/usr/bin/env python\n", + "# coding: utf-8\n", + "from __future__ import absolute_import, division, print_function\n", + "\n", + "import numpy as np\n", + "\n", + "import matplotlib\n", + "matplotlib.use('TkAgg')\n", + "import matplotlib.pyplot as plt\n", + "\n", + "%matplotlib inline\n", + "\n", + "\n", + "import time\n", + "\n", + "start = time.time()\n", + "\n", + "from torch import optim\n", + "from qiskit.aqua.algorithms.adaptive.qgan.discriminator import DiscriminatorNet\n", + "\n", + "from qiskit.aqua.components.optimizers import ADAM\n", + "from qiskit.aqua.components.uncertainty_models import UniformDistribution, UnivariateVariationalDistribution \n", + "from qiskit.aqua.components.variational_forms import RY\n", + "\n", + "from qiskit.aqua.algorithms.adaptive.qgan.qgan import QGAN\n", + "\n", + "from qiskit.aqua import aqua_globals, QuantumInstance\n", + "\n", + "from qiskit.providers.ibmq import IBMQ\n", + "from qiskit import Aer" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Load the Training Data\n", + "First, we need to load the $k$-dimensional training data samples (here k=1).
\n", + "Next, the data resolution is set, i.e. the min/max data values and the number of qubits used to represent each data dimension." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# Number training data samples\n", + "N = 10000 \n", + "\n", + "# Load data samples from log-normal distribution with mean=1 and standard deviation=1\n", + "mu = 1\n", + "sigma = 1\n", + "real_data = np.random.lognormal(mean = mu, sigma=sigma, size=N)\n", + "\n", + "# Set the data resolution\n", + "# Set upper and lower data values as list of k min/max data values [[min_0,max_0],...,[min_k-1,max_k-1]]\n", + "bounds = np.array([0.,3.]) \n", + "# Set number of qubits per data dimension as list of k qubit values[#q_0,...,#q_k-1]\n", + "num_qubits = [2]\n", + "k = len(num_qubits)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Initialize the qGAN\n", + "The qGAN consists of a quantum generator $G_{\\theta}$, a variational quantum circuit, and a classical discriminator $D_{\\phi}$, a neural network.
\n", + "To implement the quantum generator, we choose a depth-$1$ variational form that implements $R_Y$ rotations and $CZ$ gates which takes a uniform distribution as an input state. Notably, for $k>1$ the generator's parameters must be chosen carefully. For example, the circuit depth should $>1$ becaue the higher the circuit depth the because higher circuit depths enable the representation of more complex structures.
\n", + "The classical discriminator is given by a $3$-layer neural network that applies linear transformations, leaky ReLU functions in the hidden layers and a sigmoid function in the output layer. Notably, the neural network is implemented with PyTorch. Please refer to https://pytorch.org/get-started/locally/ for PyTorch installation instructions.
\n", + "Here, both networks are updated with the ADAM optimization algorithm." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# Set number of training epochs\n", + "# Note: The algorithm's runtime can be shortened by reducing the number of training epochs.\n", + "num_epochs = 3000\n", + "# Batch size\n", + "batch_size = 1000\n", + "\n", + "# Initialize qGAN\n", + "qgan = QGAN(real_data, bounds, num_qubits, batch_size, num_epochs, snapshot_dir=None)\n", + "\n", + "# Set quantum instance to run the quantum generator\n", + "backend = Aer.get_backend('statevector_simulator')\n", + "qgan.set_quantum_instance(QuantumInstance(backend=backend, shots=batch_size, coupling_map=None, circuit_caching=False))\n", + "\n", + "\n", + "# Set entangler map\n", + "entangler_map = [[0, 1]]\n", + " \n", + "# Set variational form\n", + "var_form = RY(int(np.sum(num_qubits)), depth=1, entangler_map=entangler_map, entanglement_gate='cz')\n", + "# Set generator's initial parameters\n", + "init_params = aqua_globals.random.rand(var_form._num_parameters) * 2 * 1e-2\n", + "# Set an initial state for the generator circuit\n", + "init_dist = UniformDistribution(np.sum(num_qubits), low=bounds[0], high=bounds[1])\n", + "# Set generator circuit\n", + "g_circuit = UnivariateVariationalDistribution(np.sum(num_qubits), var_form, init_params,\n", + " initial_distribution=init_dist, low=bounds[0], high=bounds[1])\n", + "# Set generator optimizer\n", + "g_optimizer = ADAM(maxiter=1, tol=1e-6, lr=1e-5, beta_1=0.9, beta_2=0.99, noise_factor=1e-6,\n", + " eps=1e-10, amsgrad=True)\n", + "# Set quantum generator\n", + "qgan.set_generator(generator_circuit=g_circuit, generator_optimizer=g_optimizer)\n", + "\n", + "# Set discriminator network\n", + "d_net = DiscriminatorNet(n_features=k)\n", + "# Set discriminator optimizer\n", + "d_optimizer = optim.Adam(d_net.parameters(), lr=1e-5, amsgrad=True)\n", + "# Set classical discriminator neural network\n", + "qgan.set_discriminator(discriminator_net=d_net, discriminator_optimizer=d_optimizer)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Run the qGAN Training\n", + "During the training the discriminator's and the generator's parameters are updated alternately w.r.t the following loss functions:\n", + "$$ L_G\\left(\\phi, \\theta\\right) = -\\frac{1}{m}\\sum\\limits_{l=1}^{m}\\left[\\log\\left(D_{\\phi}\\left(g^{l}\\right)\\right)\\right] $$\n", + "and\n", + "$$ L_D\\left(\\phi, \\theta\\right) =\n", + "\t\\frac{1}{m}\\sum\\limits_{l=1}^{m}\\left[\\log D_{\\phi}\\left(x^{l}\\right) + \\log\\left(1-D_{\\phi}\\left(g^{l}\\right)\\right)\\right], $$\n", + "with $m$ denoting the batch size and $g^l$ describing the data samples generated by the quantum generator." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 1/3000...\n", + "Loss Discriminator: 0.6973\n", + "Loss Generator: 0.6708\n", + "Relative Entropy: 0.1718\n", + "Epoch 2/3000...\n", + "Loss Discriminator: 0.6962\n", + "Loss Generator: 0.679\n", + "Relative Entropy: 0.1719\n", + "Epoch 3/3000...\n", + "Loss Discriminator: 0.6948\n", + "Loss Generator: 0.6824\n", + "Relative Entropy: 0.172\n", + "Epoch 4/3000...\n", + "Loss Discriminator: 0.6934\n", + "Loss Generator: 0.6843\n", + "Relative Entropy: 0.172\n", + "Epoch 5/3000...\n", + "Loss Discriminator: 0.692\n", + "Loss Generator: 0.6861\n", + "Relative Entropy: 0.1719\n", + "Epoch 6/3000...\n", + "Loss Discriminator: 0.6909\n", + "Loss Generator: 0.6863\n", + "Relative Entropy: 0.1719\n", + "Epoch 7/3000...\n", + "Loss Discriminator: 0.6896\n", + "Loss Generator: 0.6854\n", + "Relative Entropy: 0.1718\n", + "Epoch 8/3000...\n", + "Loss Discriminator: 0.689\n", + "Loss Generator: 0.6867\n", + "Relative Entropy: 0.1718\n", + "Epoch 9/3000...\n", + "Loss Discriminator: 0.6882\n", + "Loss Generator: 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"output_type": "stream", + "text": [ + "Loss Discriminator: 0.6803\n", + "Loss Generator: 0.7099\n", + "Relative Entropy: 0.075\n", + "Epoch 1800/3000...\n", + "Loss Discriminator: 0.6828\n", + "Loss Generator: 0.7106\n", + "Relative Entropy: 0.0749\n", + "Epoch 1801/3000...\n", + "Loss Discriminator: 0.682\n", + "Loss Generator: 0.711\n", + "Relative Entropy: 0.0749\n", + "Epoch 1802/3000...\n", + "Loss Discriminator: 0.6833\n", + "Loss Generator: 0.7099\n", + "Relative Entropy: 0.0749\n", + "Epoch 1803/3000...\n", + "Loss Discriminator: 0.6827\n", + "Loss Generator: 0.7101\n", + "Relative Entropy: 0.0748\n", + "Epoch 1804/3000...\n", + "Loss Discriminator: 0.6817\n", + "Loss Generator: 0.7106\n", + "Relative Entropy: 0.0748\n", + "Epoch 1805/3000...\n", + "Loss Discriminator: 0.6822\n", + "Loss Generator: 0.7102\n", + "Relative Entropy: 0.0747\n", + "Epoch 1806/3000...\n", + "Loss Discriminator: 0.6842\n", + "Loss Generator: 0.71\n", + "Relative Entropy: 0.0747\n", + "Epoch 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+ "Relative Entropy: 0.0677\n", + "Epoch 1970/3000...\n", + "Loss Discriminator: 0.6825\n", + "Loss Generator: 0.711\n", + "Relative Entropy: 0.0677\n", + "Epoch 1971/3000...\n", + "Loss Discriminator: 0.6832\n", + "Loss Generator: 0.7086\n", + "Relative Entropy: 0.0677\n", + "Epoch 1972/3000...\n", + "Loss Discriminator: 0.6837\n", + "Loss Generator: 0.7103\n", + "Relative Entropy: 0.0676\n", + "Epoch 1973/3000...\n", + "Loss Discriminator: 0.6838\n", + "Loss Generator: 0.7076\n", + "Relative Entropy: 0.0676\n", + "Epoch 1974/3000...\n", + "Loss Discriminator: 0.6838\n", + "Loss Generator: 0.708\n", + "Relative Entropy: 0.0675\n", + "Epoch 1975/3000...\n", + "Loss Discriminator: 0.6837\n", + "Loss Generator: 0.7058\n", + "Relative Entropy: 0.0675\n", + "Epoch 1976/3000...\n", + "Loss Discriminator: 0.6839\n", + "Loss Generator: 0.7074\n", + "Relative Entropy: 0.0675\n", + "Epoch 1977/3000...\n", + "Loss Discriminator: 0.6862\n", + "Loss Generator: 0.711\n", + "Relative Entropy: 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0.6976\n", + "Relative Entropy: 0.0333\n", + "Epoch 2979/3000...\n", + "Loss Discriminator: 0.6903\n", + "Loss Generator: 0.6978\n", + "Relative Entropy: 0.0333\n", + "Epoch 2980/3000...\n", + "Loss Discriminator: 0.6898\n", + "Loss Generator: 0.7008\n", + "Relative Entropy: 0.0333\n", + "Epoch 2981/3000...\n", + "Loss Discriminator: 0.6887\n", + "Loss Generator: 0.7016\n", + "Relative Entropy: 0.0333\n", + "Epoch 2982/3000...\n", + "Loss Discriminator: 0.6872\n", + "Loss Generator: 0.7015\n", + "Relative Entropy: 0.0332\n", + "Epoch 2983/3000...\n", + "Loss Discriminator: 0.6883\n", + "Loss Generator: 0.6983\n", + "Relative Entropy: 0.0332\n", + "Epoch 2984/3000...\n", + "Loss Discriminator: 0.6883\n", + "Loss Generator: 0.6995\n", + "Relative Entropy: 0.0332\n", + "Epoch 2985/3000...\n", + "Loss Discriminator: 0.6894\n", + "Loss Generator: 0.7019\n", + "Relative Entropy: 0.0331\n", + "Epoch 2986/3000...\n", + "Loss Discriminator: 0.6884\n", + "Loss Generator: 0.6991\n", + "Relative Entropy: 0.0331\n", + "Epoch 2987/3000...\n", + "Loss Discriminator: 0.6883\n", + "Loss Generator: 0.7004\n", + "Relative Entropy: 0.0331\n", + "Epoch 2988/3000...\n", + "Loss Discriminator: 0.6891\n", + "Loss Generator: 0.7001\n", + "Relative Entropy: 0.0331\n", + "Epoch 2989/3000...\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Loss Discriminator: 0.689\n", + "Loss Generator: 0.703\n", + "Relative Entropy: 0.033\n", + "Epoch 2990/3000...\n", + "Loss Discriminator: 0.6899\n", + "Loss Generator: 0.7007\n", + "Relative Entropy: 0.033\n", + "Epoch 2991/3000...\n", + "Loss Discriminator: 0.6885\n", + "Loss Generator: 0.6984\n", + "Relative Entropy: 0.033\n", + "Epoch 2992/3000...\n", + "Loss Discriminator: 0.6884\n", + "Loss Generator: 0.6993\n", + "Relative Entropy: 0.033\n", + "Epoch 2993/3000...\n", + "Loss Discriminator: 0.6891\n", + "Loss Generator: 0.703\n", + "Relative Entropy: 0.0329\n", + "Epoch 2994/3000...\n", + "Loss Discriminator: 0.6886\n", + "Loss Generator: 0.6997\n", + "Relative Entropy: 0.0329\n", + "Epoch 2995/3000...\n", + "Loss Discriminator: 0.6896\n", + "Loss Generator: 0.6955\n", + "Relative Entropy: 0.0329\n", + "Epoch 2996/3000...\n", + "Loss Discriminator: 0.6885\n", + "Loss Generator: 0.7014\n", + "Relative Entropy: 0.0329\n", + "Epoch 2997/3000...\n", + "Loss Discriminator: 0.6896\n", + "Loss Generator: 0.7038\n", + "Relative Entropy: 0.0328\n", + "Epoch 2998/3000...\n", + "Loss Discriminator: 0.6895\n", + "Loss Generator: 0.6972\n", + "Relative Entropy: 0.0328\n", + "Epoch 2999/3000...\n", + "Loss Discriminator: 0.6898\n", + "Loss Generator: 0.6993\n", + "Relative Entropy: 0.0328\n", + "Epoch 3000/3000...\n", + "Loss Discriminator: 0.6896\n", + "Loss Generator: 0.7021\n", + "Relative Entropy: 0.0328\n", + "qGAN training runtime: 162.18758081595104 min\n" + ] + } + ], + "source": [ + "# Run qGAN\n", + "qgan.run()\n", + "\n", + "# Runtime\n", + "end = time.time()\n", + "print('qGAN training runtime: ', (end - start)/60., ' min')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Training Progress & Outcome\n", + "Now, we plot the evolution of the generator's and the discriminator's loss functions during the training as well as the progress in the relative entropy between the trained and the target distribution.\n", + "
Finally, we also compare the cumulative distribution function (CDF) of the trained distribution to the CDF of the target distribution." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Plot progress w.r.t the generator's and the discriminator's loss function\n", + "t_steps = np.arange(num_epochs)\n", + "plt.figure(figsize=(6,5))\n", + "plt.title(\"Progress in the loss function\")\n", + "plt.plot(t_steps, qgan.g_loss, label = \"Generator loss function\", color = 'mediumvioletred', linewidth = 2)\n", + "plt.plot(t_steps, qgan.d_loss, label = \"Discriminator loss function\", color = 'rebeccapurple', linewidth = 2)\n", + "plt.grid()\n", + "plt.legend(loc = 'best')\n", + "plt.xlabel('time steps')\n", + "plt.ylabel('loss')\n", + "plt.show()\n", + "\n", + "\n", + "# Plot progress w.r.t relative entropy\n", + "plt.figure(figsize=(6,5))\n", + "plt.title(\"Relative Entropy \")\n", + "plt.plot(np.linspace(0, num_epochs, len(qgan.rel_entr)), qgan.rel_entr, color ='mediumblue', lw=4, ls=':')\n", + "plt.grid()\n", + "plt.xlabel('time steps')\n", + "plt.ylabel('relative entropy')\n", + "plt.show()\n", + "\n", + "#Plot the PDF of the resulting distribution against the target distribution, i.e. log-normal\n", + "log_normal = np.random.lognormal(mean=1, sigma=1, size=100000)\n", + "log_normal = np.round(log_normal)\n", + "log_normal = log_normal[log_normal <= bounds[1]]\n", + "temp = []\n", + "for i in range(int(bounds[1]+1)):\n", + " temp += [np.sum(log_normal==i)]\n", + "log_normal = np.array(temp / sum(temp))\n", + "\n", + "plt.figure(figsize=(6,5))\n", + "plt.title(\"CDF\")\n", + "samples_g, prob_g = qgan.generator.get_samples(qgan.quantum_instance, shots=10000)\n", + "samples_g = np.array(samples_g)\n", + "samples_g = samples_g.flatten()\n", + "num_bins = len(prob_g)\n", + "plt.bar(samples_g, np.cumsum(prob_g), color='royalblue', width= 0.8, label='simulation')\n", + "plt.plot( np.cumsum(log_normal),'-o', label='log-normal', color='deepskyblue', linewidth=4, markersize=12)\n", + "plt.xticks(np.arange(min(samples_g), max(samples_g)+1, 1.0))\n", + "plt.grid()\n", + "plt.xlabel('x')\n", + "plt.ylabel('p(x)')\n", + "plt.legend(loc='best')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "QiskitDevenv", + "language": "python", + "name": "qiskitdevenv" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.3" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} From acb2a7886dbd1530f600caa12196129c57304e1b Mon Sep 17 00:00:00 2001 From: Jakub Marecek Date: Tue, 16 Apr 2019 18:44:56 +0100 Subject: [PATCH 053/116] Time series tutorial --- .../finance/data_providers/time_series.ipynb | 198 +++++++++++++++++- 1 file changed, 188 insertions(+), 10 deletions(-) diff --git a/qiskit/finance/data_providers/time_series.ipynb b/qiskit/finance/data_providers/time_series.ipynb index aed94d68d..a3c423018 100644 --- a/qiskit/finance/data_providers/time_series.ipynb +++ b/qiskit/finance/data_providers/time_series.ipynb @@ -33,31 +33,121 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": { "scrolled": true }, "outputs": [], "source": [ - "from qiskit.aqua.input.finance import *\n", - "from qiskit.aqua.input.finance.wikipedia import StockMarket\n", + "%matplotlib inline\n", + "from qiskit.aqua.translators.data_providers import *\n", + "from qiskit.aqua.translators.data_providers.wikipediadataprovider import StockMarket\n", "import warnings\n", - "warnings.filterwarnings(\"ignore\",category=DeprecationWarning)\n", + "warnings.filterwarnings(\"ignore\", category=DeprecationWarning)\n", "import datetime" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Evolution of the stock price:\n", + "GOOG\n", + "Date\n", + "2016-01-04 741.84\n", + "2016-01-05 742.58\n", + "2016-01-06 743.62\n", + "2016-01-07 726.39\n", + "2016-01-08 714.47\n", + "2016-01-11 716.03\n", + "2016-01-12 726.07\n", + "2016-01-13 700.56\n", + "2016-01-14 714.72\n", + "2016-01-15 694.45\n", + "2016-01-19 701.79\n", + "2016-01-20 698.45\n", + "2016-01-21 706.59\n", + "2016-01-22 725.25\n", + "2016-01-25 711.67\n", + "2016-01-26 713.04\n", + "2016-01-27 699.99\n", + "2016-01-28 730.96\n", + "2016-01-29 742.95\n", + "Name: Adj. Close, dtype: float64\n", + "AAPL\n", + "Date\n", + "2016-01-04 101.783763\n", + "2016-01-05 99.233131\n", + "2016-01-06 97.291172\n", + "2016-01-07 93.185040\n", + "2016-01-08 93.677776\n", + "2016-01-11 95.194629\n", + "2016-01-12 96.576222\n", + "2016-01-13 94.093220\n", + "2016-01-14 96.151117\n", + "2016-01-15 93.842021\n", + "2016-01-19 93.387931\n", + "2016-01-20 93.513531\n", + "2016-01-21 93.040118\n", + "2016-01-22 97.986799\n", + "2016-01-25 96.073825\n", + "2016-01-26 96.605206\n", + "2016-01-27 90.257610\n", + "2016-01-28 90.904929\n", + "2016-01-29 94.044912\n", + "Name: Adj. Close, dtype: float64\n" + ] + }, + { + "data": { + "image/png": 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+BqwF6sNtRUQkImkFvbsvAyo7WHVJB9s6MO8E6xIRkR6iT8aKiMScgl5EJOYU9CIiMaegFxGJOQW9iEjMKehFRGJOQS8iEnMKehGRmFPQi4jEnIJeRCTmFPQiIjGnoBcRiTkFvYhIzCnoRURiTkEvIhJzCnoRkZhT0IuIxJyCXkQk5hT0IiIxp6AXEYk5Bb2ISMylFfRmtsHMlpvZMjOrCtvKzOx5M1sT3g4O283Mfmhma83sbTOb0ZsdEBGR4+vKGf2H3X2au1eGy7cDC919IrAwXAa4HJgYTnOB+3qqWBER6boTGbq5Cpgfzs8Hrk5pf8gDrwGlZjbiBB5HREROQLpB78B/m9kSM5sbtg13920A4e2wsH0UsDll3+qwTUREIpCX5nbnu/tWMxsGPG9mq46zrXXQ5kdtFBww5gKMGTMmzTJERKSr0jqjd/et4W0N8ARwDrCjdUgmvK0JN68GRqfsXgFs7eA+73f3SnevLC8v734PRETkuDoNejMbYGbFrfPAR4F3gKeBOeFmc4CnwvmngRvCq2/OA/a2DvGIiEjfS2foZjjwhJm1bv9Ld3/OzP4EPGpmNwGbgOvC7Z8FPgasBeqBG3u8ahERSVunQe/u64GzOmivBS7poN2BeT1SnYiInDB9MlZEJOYU9CIiMaegFxGJOQW9iEjMpfuBKRGRPtfc3Ex1dTUNDQ1RlxKpwsJCKioqyM/P79b+CnoRyVjV1dUUFxczduxYwku8TzruTm1tLdXV1YwbN65b96GhGxHJWA0NDQwZMuSkDXkAM2PIkCEn9KpGQS8iGe1kDvlWJ/pvoKAXETmOHTt2cP311zN+/HhmzpzJBz7wAZ544gkAFi9ezDnnnMPkyZOZPHky999//xH73n///W3rzjnnHBYvXty2rqWlha9//etMnDiRadOmMW3aNL75zW/2Sh80Ri8icgzuztVXX82cOXP45S9/CcDGjRt5+umn2b59O9dffz1PPvkkM2bMYNeuXVx66aWMGjWKj3/84zzzzDP85Cc/YfHixQwdOpSlS5dy9dVX88Ybb3DKKadwxx13sH37dpYvX05hYSH79+/ne9/7Xu91JOpp5syZLiLS3rvvvhvp47/wwgt+0UUXdbjujjvu8DvvvPOo7S+44AJ3d7/gggt84cKFR+1zxx13+MGDB72srMz37duXdi0d/VsAVZ5GxuqMXkSywl3/tYJ3t+7r0fucOnIQ//SJ04+5fsWKFcyY0fHPXq9YsYI5c+Yc0VZZWcmKFSva1s+cOfOo9fPnz2ft2rWMGTOG4uLiE+xBejRGLyKSpnnz5nHWWWdx9tln4+4dvkl6vDdOj7XPz3/+c6ZNm8bo0aPZvHlzB3ueGJ3Ri0hWON6Zd285/fTTefzxx9uWf/SjH7Fr1y4qKyu59NJLqaqq4sorr2xbv2TJEqZOnQrA1KlTWbJkCbNmzWpbv3TpUqZOncqECRPYtGkT+/fvp7i4mBtvvJEbb7yRM844g0Qi0eP90Bm9iMgxzJo1i4aGBu677762tvr6eiA4u3/wwQdZtmwZALW1tdx2223ceuutANx6663cdttt1NbWArBs2TIefPBBvvSlL9G/f39uuukmbr755rbr4xOJBE1NTb3SD53Ri4gcg5nx5JNP8vd///d897vfpby8nAEDBvCd73yHESNG8PDDD/P5z3+e/fv34+7ccsstfOITnwDgyiuvZMuWLXzwgx/EzCguLubhhx9mxIgRAHzzm9/kzjvv5IwzzqC4uJiioiLmzJnDyJEje74fwRu30aqsrPSqqqqoyxCRDLNy5UqmTJkSdRkZoaN/CzNb4u6Vne2roRsRkZhT0IuIxJyCXkQk5hT0IiIxp6AXEYm5tIPezHLN7E0zeyZcHmdmr5vZGjP7lZkVhO39wuW14fqxvVO6iIikoytn9F8BVqYsfwe4190nAnuAm8L2m4A97j4BuDfcTkQkaz3xxBOYGatWrTqi/d5776WwsJC9e/e2tS1atIiSkhKmT5/OlClTuOuuu9rar7jiij6tu1VaQW9mFcDHgZ+GywbMAh4LN5kPXB3OXxUuE66/xPTLASKSxRYsWMAFF1zAI488clT72Wef3fb99K0uvPBC3nzzTaqqqnj44YdZsmRJX5Z7lHTP6L8P3Aokw+UhQJ27t4TL1cCocH4UsBkgXL833P4IZjbXzKrMrGrnzp3dLF9EpHcdOHCAV155hQceeOCIoF+3bh0HDhzg7rvvZsGCBR3uO2DAAGbOnMm6dev6qtwOdfoVCGZ2BVDj7kvM7OLW5g429TTWHW5wvx+4H4JPxqZVrYicvH53O2xf3rP3ecqZcPk9x93kySef5LLLLuO0006jrKyMpUuXMmPGDBYsWMBnPvMZLrzwQlavXk1NTQ3Dhg07Yt/a2lpee+017rzzTqI8oU3njP584Eoz2wA8QjBk832g1MxaDxQVwNZwvhoYDRCuLwF292DNIiJ9ZsGCBcyePRuA2bNnt529P/LII8yePZucnBw++clP8utf/7ptn5dffpnp06fz0Y9+lNtvv53TT+/7b95M1ekZvbt/DfgaQHhG/z/d/a/M7NfAXxKE/xzgqXCXp8PlV8P1L3omfKGOiGS3Ts68e0NtbS0vvvgi77zzDmZGIpHAzPjsZz/LmjVr+MhHPgJAU1MT48ePZ968eUAwRv/MM8/0eb3HciLX0d8GfNXM1hKMwT8Qtj8ADAnbvwrcfmIliohE47HHHuOGG25g48aNbNiwgc2bNzNu3DhuueUWvvGNb7BhwwY2bNjA1q1b2bJlCxs3boy65A51KejdfZG7XxHOr3f3c9x9grtf5+6NYXtDuDwhXL++NwoXEeltCxYs4Jprrjmi7dprr2XDhg1HtV9zzTVHXZXT3sKFC6moqGibXn311R6vuSP6mmIRyVj6muLD9DXFIiJyTAp6EZGYU9CLiMScgl5EMlomvI8YtRP9N1DQi0jGKiwspLa29qQOe3entraWwsLCbt9Hpx+YEhGJSkVFBdXV1ZF+fUAmKCwspKKiotv7K+hFJGPl5+czbty4qMvIehq6ERGJOQW9iEjMKehFRGJOQS8iEnMKehGRmFPQi4jEnIJeRCTmFPQiIjGnoBcRiTkFvYhIzCnoRURiTkEvIhJzCnoRkZjrNOjNrNDM3jCzt8xshZndFbaPM7PXzWyNmf3KzArC9n7h8tpw/dje7YKIiBxPOmf0jcAsdz8LmAZcZmbnAd8B7nX3icAe4KZw+5uAPe4+Abg33E5ERCLSadB74EC4mB9ODswCHgvb5wNXh/NXhcuE6y8xM+uxikVEpEvSGqM3s1wzWwbUAM8D64A6d28JN6kGRoXzo4DNAOH6vcCQDu5zrplVmVnVyf7rMSIivSmtoHf3hLtPAyqAc4ApHW0W3nZ09n7UDz66+/3uXunuleXl5enWKyIiXdSlq27cvQ5YBJwHlJpZ608RVgBbw/lqYDRAuL4E2N0TxYqISNelc9VNuZmVhvNFwF8AK4GXgL8MN5sDPBXOPx0uE65/0U/mn3AXEYlYOj8OPgKYb2a5BAeGR939GTN7F3jEzO4G3gQeCLd/APhPM1tLcCY/uxfqFhGRNHUa9O7+NjC9g/b1BOP17dsbgOt6pDoRETlh+mSsiEjMKehFRGJOQS8iEnMKehGRmFPQi4jEnIJeRCTmFPQiIjGnoBcRiTkFvYhIzCnoRURiTkEvIhJzCnoRkZhT0IuIxJyCXkQk5hT0IiIxp6AXEYk5Bb2ISMwp6EVEYk5BLyIScwp6EZGYU9CLiMRcp0FvZqPN7CUzW2lmK8zsK2F7mZk9b2ZrwtvBYbuZ2Q/NbK2ZvW1mM3q7EyIicmzpnNG3AP/g7lOA84B5ZjYVuB1Y6O4TgYXhMsDlwMRwmgvc1+NVi4hI2joNenff5u5Lw/n9wEpgFHAVMD/cbD5wdTh/FfCQB14DSs1sRI9XLiIiaenSGL2ZjQWmA68Dw919GwQHA2BYuNkoYHPKbtVhm4iIRCDtoDezgcDjwC3uvu94m3bQ5h3c31wzqzKzqp07d6ZbhoiIdFFaQW9m+QQh/wt3/03YvKN1SCa8rQnbq4HRKbtXAFvb36e73+/ule5eWV5e3t36RUSkE+lcdWPAA8BKd/+XlFVPA3PC+TnAUyntN4RX35wH7G0d4hERkb6Xl8Y25wN/DSw3s2Vh29eBe4BHzewmYBNwXbjuWeBjwFqgHrixRysWEZEu6TTo3X0xHY+7A1zSwfYOzDvBukREpIfok7EiIjGnoBcRiTkFvYhIzCnoRURiTkEvIhJzCnoRkZhT0IuIxJyCXkQk5hT0IiIxp6AXEYk5Bb2ISMwp6EVEYk5BLyIScwp6EZGYU9CLiMScgl5EJOYU9CIiMaegFxGJOQW9iEjMKehFRGJOQS8iEnOdBr2Z/czMaszsnZS2MjN73szWhLeDw3Yzsx+a2Voze9vMZvRm8SIi0rl0zugfBC5r13Y7sNDdJwILw2WAy4GJ4TQXuK9nyhQRke7K62wDd/+DmY1t13wVcHE4Px9YBNwWtj/k7g68ZmalZjbC3bf1VMFH2LUGdq6GwhIoKg1uC0ugoBhyNColIgJpBP0xDG8Nb3ffZmbDwvZRwOaU7arDtt4J+lXPwAvfOLrdcqDfoMPBf8SBoBQKBkLBgHAaCP0GHp5PXdevGHLze6V0kazhDg11sH9H8LeVkws5ee2m9m25YBZ15RLqbtAfS0f/s97hhmZzCYZ3GDNmTPcebcYcOHUWNOwNpkN1h+cb9gZPztb52nWH1zcfTP8xcgtgwDAYNAKKT4Hi9rcjg9vCkt5/YrtDMgGegGRLynwyWPZESlu7+bZ9kinrWw7vn9qWbIGWRmg5FNw2H4KWhvA2bG9uOHybaIT8/kceWNsfaAsHBQfZ1nWehKYD0Lg/mJoOQOMBaNof3rZbxsP7HBTcHjFfHM6Hj6ODc9e4Q30t1G2Eus1Qtwn2hrety037u36/1i78czs5MKRz8Gibzw+W8ZTnb8vRz//Uv4tkAgr6w9DTYOhEGDopmB8wpMf/SdPmHvwt5OT26sN0N+h3tA7JmNkIoCZsrwZGp2xXAWzt6A7c/X7gfoDKysoODwad6l8WTF2VTEJzfRAmTQdTQiWcP6J9Pxyogf3bgqGiP/8hOFi0l1d0+ACQVxA+4ZIdBHOygwDuKJTbz7dwjGNm38krhLx+QV/zCw/f5vYLDqI7Vx0+sHqyhx6zKHjFBcH/RUtDenXm9w8PvOHBt3W+7WBsHa8/YlvabZvufu237Wi/Y61vN+8O+OHbI9pIWRfKyQkDNjclaHMPn4mnrks0BkG+d3Pw95Cq3yAoHRNMYy+A0tHBcxuOPCFofV4fd7m1rbkL+ySgueno9YnmI+8PCw8A7fub23H7vq3B33Dq86ioDMonHRn+QycGfU83gFtPwhKNcGhPcOCsr4X63SnztR23f/x7MOOG9B6nm7ob9E8Dc4B7wtunUtpvNrNHgHOBvb02Pn8icnKC8GgNkK5qqocD22H/9uCJs397cCDYH7Y11R9+guX1O/oPrMM/xpS2nLyU9TlHP3k7ajvqMTr6A2/XdsTjtLuf/MIw2AshvygI83Tf93APDpJtr6z2tXultTe4r4LicNisdfisODg7b20rGBicBaZqaQwCv2Fv+GpgX3D/jfvC9n3QuDd49dFROKbOtwWkpxxDjxGqx9yv/fyxtqXzbdvv19FB4rgHFjo+YfAkJJqObsvJCwJtwl8EQV46BkrC26LSY/73Zr1kMji47XovmHauDk7iVj0L9Q8d3i6vEAaNInjVcIyDUeuBxxOdPKhB0WDoPyQ4OS0dAyOnBcvDpvZmb4NH99QnYkcbmC0geON1KLAD+CfgSeBRYAywCbjO3XebmQH/RnCVTj1wo7tXdVZEZWWlV1V1upmISO+q333kAWDfluDEJzf/GMNL7abcvOAVQv8hR05Fpb0yPGNmS9y9stPtOgv6vqCgFxHpunSDXtcgiojEnIJeRCTmFPQiIjGnoBcRiTkFvYhIzCnoRURiTkEvIhJzCnoRkZjLiA9MmdlOYGMfPdxQYFcfPVZvUR8yQ7b3IdvrB/Xhfe5e3tlGGRH0fcnMqtL5JFkmUx9Qj17jAAAJRElEQVQyQ7b3IdvrB/UhXRq6ERGJOQW9iEjMnYxBf3/UBfQA9SEzZHsfsr1+UB/SctKN0YuInGxOxjN6EZGTioJeRCTmFPQiIjGnoM8iZjbYzIqjrqMnmFk3ftU9GmYW4x9QBTPr5o8nRy+bnketzKzczKab2Zl99W8f66A3s79Jma8ws4VmVmdmfzSz06KsLV1mNtLMHjKzvQSfnlthZpvM7Btmlh91fekws/PNbKWZrTCzc83seaDKzDab2Qeiri8Nu8zsBTO7Kaah/27UBaTDzO5ImZ9qZu8BS8xsg5mdG2FpaQlrfgF4FXgd+Cmw3MweNLOS3nzsWAc9cHPK/L8Q/KB5GfDPwH2RVNR1DwM/c/cS4DrgcWAKkAf8KMrCuuBe4FPA3wK/Be5y9/HAVcD/i7KwNK0Evg/MAtaZ2VNmNtvMiiKuK21m9tVjTP8AZMsZ/SdT5v8Z+Iq7jyN4bt0bTUld8jNgnrtPAC4AVoX1vwI80JsPHPegT3Wau//E3ZPu/gRB4GeDIe6+CMDdfwNc5O4H3f0O4KJIK0tfvrsvd/dXgZ3uvhjA3ZcC2RCWze7+jLv/FVAB/IIgXKrN7JfRlpa2bwGDgeJ200CyMwdGuvvvANz9DbLjeVTk7quhreYzw/n/AKb25gPn9eadZ4AKM/shYEC5meW7e3O4LiuGPYCdZvZZ4EXgWmADgJkZ2fMHmlrn19qtK+jLQrrJWmfc/RDBK8NHw5fbV0dWVdcsBZ509yXtV5jZ30ZQT3eMN7OnCf4/Ksysv7vXh+uy4e95nZndCSwkeHWyDCAcgu3VLI570P9jynwVwdnLHjM7BXg6mpK67G8IhjduJ3hitA5HlXF0aGaqO1v/KN39ydZGMzsVeCjCutL1i44a3X0vML+Pa+muG4Hdx1iXLV8KdlW75RwAMxtOdgzF/g3w9XB6C/hK2N4fuKE3H1ifjBURiblseenfLWaWZ2ZfMLPfmdnbZvZWOP/FLLpiJev7cDxmltXfVZIt9ZtZbvg8+r9mdn67dXcca79Mku19aFf/B9ut69X6Y31Gb2YLgDqCl9fVYXMFMAcoc/dPR1VbumLSh2O98W3AW+5e0Zf1dFW21w9gZj8lGCJ4A/hr4Pfu/tVw3VJ3nxFlfenI9j5EWX/cg361u086xrr33D3jr6WPSR8SBL8gZinNHi6PcveMfkM22+sHMLO33f394Xwe8O8Ev2z0GeA1d58eZX3pyPY+RFl/rIduCN54vc7M2vppZjlm9mlgT4R1dUUc+rAeuNjdx6VM48NriHdEXVwasr1+SLm6yd1b3H0uwZv7L5I919Fnex8iqz/uQT8b+Etgh5m9F36SbgfBpU2zI60sfXHow/cJruHuyHf7spBuyvb6Ifgk8mWpDe7+f4CfA2Mjqajrsr0PkdUf66GbVGY2hKC/WftDwnHog4j0vbif0bdx91p335UtV0l0JA59aJXtfcj2+kF9yAR9Vf9JE/QpsuXDIcejPkQv2+sH9SET9En9J2PQ10RdQA9QH6KX7fWD+pAJ+qT+k2aMXkTkZHUyntED2T+2B+pDJsj2+kF9yAS9XX+sv9Ssk080fqwva+ku9SF62V4/qA+ZIMr6Yz10E5NPNKoPEcv2+kF9yARR1h/rM3qCTzRe4u6b2q8ws80R1NMd6kP0sr1+UB8yQWT1x32MPg6faFQfopft9YP6kAkiqz/WQzciIhL/oRvMbDLBL9OMIhgP2wo87e4rIy2sC9SH6GV7/aA+ZIKo6o/10I2Z3QY8QvBmxxvAn8L5BWZ2e5S1pUt9iF621w/qQyaIsv5YD92E3/R4esoPgre2FwAr3H1iNJWlT32IXrbXD+pDJoiy/lif0QNJYGQH7SPCddlAfYhettcP6kMmiKz+uI/R3wIsNLM1QOvlS2OACcDNkVXVNepD9LK9flAfMkFk9cd66AaCX2MCziF488MIfnf1T+6eiLSwLlAfopft9YP6kAmiqj/2Qd+emc1192z/Xgz1IWLZXj+oD5mgr+qP+xh9R74YdQE9QH2IXrbXD+pDJuiT+k/GoLfON8l46kP0sr1+UB8yQZ/UfzIO3VS4e3XUdZwI9SF62V4/qA+ZoK/qj/UZvZmda2aDwvkiM7sLuM/MvmNmJRGXlxb1IXrZXj+oD5kgyvpjHfTAz4D6cP4HQAnwnbDt51EV1UXqQ/SyvX5QHzJBZPXH/Tr6HHdvCecr3X1GOL/YzJZFVVQXqQ/Ry/b6QX3IBJHVH/cz+nfM7MZw/i0zqwQws9OA5mPvllHUh+hle/2gPmSCyOqP9Zux4bjXD4ALgV3ADIJPpG0G/s7d34qwvLSoD9HL9vpBfcgEUdYf66BvZWbFwHiCoapqd98RcUldpj5EL9vrB/UhE0RR/0kR9B0xs4HufiDqOk6E+hC9bK8f1IdM0Nv1x32M/njejbqAHqA+RC/b6wf1IRP0av2xvurGzL56rFXAwL6spbvUh+hle/2gPmSCKOuP+xn9twh+jLe43TSQ7Om7+hC9bK8f1IdMEFn9sT6jB5YCT7r7kvYrzOxvI6inO9SH6GV7/aA+ZILI6o/1m7FmNgnY7e47O1g3PBverVcfopft9YP6kAmirD/WQS8iItkxrtVtZlZiZveY2Sozqw2nlWFbadT1pUN9iF621w/qQyaIsv5YBz3wKLAHuNjdh7j7EODDYduvI60sfepD9LK9flAfMkFk9cd66MbMVrv7pK6uyyTqQ/SyvX5QHzJBlPXH/Yx+o5ndambDWxvMbLiZ3cbhX2HPdOpD9LK9flAfMkFk9cc96D8NDAF+b2Z7zGw3sAgoAz4VZWFdoD5EL9vrB/UhE0RWf6yHbgDMbDJQAbyW+l0SZnaZuz8XXWXpUx+il+31g/qQCSKr391jOwF/B6wGngQ2AFelrFsadX3qQ3b0IdvrVx8yY4qy/rh/MvbzwEx3P2BmY4HHzGysu/8AsubX49WH6GV7/aA+ZILI6o970Od6+PLI3TeY2cUE/7jvIzueGKA+ZIJsrx/Uh0wQWf1xfzN2u5lNa10I/5GvAIYCZ0ZWVdeoD9HL9vpBfcgEkdUf6zdjzawCaHH37R2sO9/dX4mgrC5RH6KX7fWD+pAJoqw/1kEvIiLxH7oRETnpKehFRGJOQS8iEnMKehGRmFPQi4jE3P8H50NuO7MIc7MAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A time-series similarity measure:\n", + "[[1.00000000e+00 8.44268222e-05]\n", + " [8.44268222e-05 1.00000000e+00]]\n", + "A covariance matrix:\n", + "[[269.60118129 25.42252332]\n", + " [ 25.42252332 7.86304499]]\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ - "wiki = WikipediaDriver(token = \"\",\n", - " tickers = [\"GOOG\"],\n", + "wiki = WikipediaDataProvider(token = \"\",\n", + " tickers = [\"GOOG\", \"AAPL\"],\n", " stockmarket = StockMarket.NASDAQ.value,\n", " start = datetime.datetime(2016,1,1),\n", " end = datetime.datetime(2016,1,30))\n", - "wiki.run()" + "wiki.run()\n", + "wiki.plot()" ] }, { @@ -68,6 +158,94 @@ "\n", "If you would like to download professional data, you will have to set-up a token with one of the major providers.\n" ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "You need to replace REPLACE-ME with a valid token.\n" + ] + } + ], + "source": [ + "from qiskit.aqua.translators.data_providers.dataondemandprovider import StockMarket\n", + "try:\n", + " nasdaq = DataOnDemandProvider(token = \"REPLACE-ME\",\n", + " tickers = [\"GOOG\", \"AAPL\"],\n", + " stockmarket = StockMarket.NASDAQ.value,\n", + " start = datetime.datetime(2016,1,1),\n", + " end = datetime.datetime(2016,1,30))\n", + " nasdaq.run()\n", + " nasdaq.plot()\n", + "except QiskitFinanceError: \n", + " print(\"You need to replace REPLACE-ME with a valid token.\")" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "You need to replace REPLACE-ME with a valid token.\n" + ] + } + ], + "source": [ + "from qiskit.aqua.translators.data_providers.dataondemandprovider import StockMarket\n", + "try:\n", + " nasdaq = DataOnDemandProvider(token = \"REPLACE-ME\",\n", + " tickers = [\"GOOG\", \"AAPL\"],\n", + " stockmarket = StockMarket.NASDAQ.value,\n", + " start = datetime.datetime(2016,1,1),\n", + " end = datetime.datetime(2016,1,30))\n", + " nasdaq.run()\n", + " nasdaq.plot()\n", + "except QiskitFinanceError: \n", + " print(\"You need to replace REPLACE-ME with a valid token.\")" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "You need to replace REPLACE-ME with a valid token.\n" + ] + } + ], + "source": [ + "from qiskit.aqua.translators.data_providers.exchangedataprovider import StockMarket\n", + "try:\n", + " lse = ExchangeDataProvider(token = \"REPLACE-ME\",\n", + " tickers = [\"AIBGl\", \"AVSTl\"],\n", + " stockmarket = StockMarket.LONDON.value,\n", + " start = datetime.datetime(2019,1,1),\n", + " end = datetime.datetime(2019,1,30))\n", + " lse.run()\n", + " lse.plot()\n", + "except QiskitFinanceError: \n", + " print(\"You need to replace REPLACE-ME with a valid token.\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { @@ -90,5 +268,5 @@ } }, "nbformat": 4, - "nbformat_minor": 1 + "nbformat_minor": 2 } From f8408aa5384869e8e9a37cb879069a6b8cc39a84 Mon Sep 17 00:00:00 2001 From: Jakub Marecek Date: Tue, 16 Apr 2019 19:15:07 +0100 Subject: [PATCH 054/116] Minor improvements --- .../finance/data_providers/time_series.ipynb | 49 ++++++------------- 1 file changed, 16 insertions(+), 33 deletions(-) diff --git a/qiskit/finance/data_providers/time_series.ipynb b/qiskit/finance/data_providers/time_series.ipynb index a3c423018..bb6641b93 100644 --- a/qiskit/finance/data_providers/time_series.ipynb +++ b/qiskit/finance/data_providers/time_series.ipynb @@ -161,40 +161,22 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 3, "metadata": {}, "outputs": [ { - "name": "stdout", + "name": "stderr", "output_type": "stream", "text": [ - "You need to replace REPLACE-ME with a valid token.\n" + "/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/urllib3/connectionpool.py:847: InsecureRequestWarning: Unverified HTTPS request is being made. Adding certificate verification is strongly advised. See: https://urllib3.readthedocs.io/en/latest/advanced-usage.html#ssl-warnings\n", + " InsecureRequestWarning)\n" ] - } - ], - "source": [ - "from qiskit.aqua.translators.data_providers.dataondemandprovider import StockMarket\n", - "try:\n", - " nasdaq = DataOnDemandProvider(token = \"REPLACE-ME\",\n", - " tickers = [\"GOOG\", \"AAPL\"],\n", - " stockmarket = StockMarket.NASDAQ.value,\n", - " start = datetime.datetime(2016,1,1),\n", - " end = datetime.datetime(2016,1,30))\n", - " nasdaq.run()\n", - " nasdaq.plot()\n", - "except QiskitFinanceError: \n", - " print(\"You need to replace REPLACE-ME with a valid token.\")" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ + }, { "name": "stdout", "output_type": "stream", "text": [ + "'Accessing NASDAQ Data on Demand failed.'\n", "You need to replace REPLACE-ME with a valid token.\n" ] } @@ -202,20 +184,21 @@ "source": [ "from qiskit.aqua.translators.data_providers.dataondemandprovider import StockMarket\n", "try:\n", - " nasdaq = DataOnDemandProvider(token = \"REPLACE-ME\",\n", + " nasdaq = DataOnDemandProvider(token = \"REPLACE-ME\",\n", " tickers = [\"GOOG\", \"AAPL\"],\n", " stockmarket = StockMarket.NASDAQ.value,\n", " start = datetime.datetime(2016,1,1),\n", - " end = datetime.datetime(2016,1,30))\n", - " nasdaq.run()\n", - " nasdaq.plot()\n", - "except QiskitFinanceError: \n", + " end = datetime.datetime(2016,1,2))\n", + " nasdaq.run()\n", + " nasdaq.plot()\n", + "except QiskitFinanceError as e:\n", + " print(e)\n", " print(\"You need to replace REPLACE-ME with a valid token.\")" ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -229,13 +212,13 @@ "source": [ "from qiskit.aqua.translators.data_providers.exchangedataprovider import StockMarket\n", "try:\n", - " lse = ExchangeDataProvider(token = \"REPLACE-ME\",\n", + " lse = ExchangeDataProvider(token = \"REPLACE-ME\",\n", " tickers = [\"AIBGl\", \"AVSTl\"],\n", " stockmarket = StockMarket.LONDON.value,\n", " start = datetime.datetime(2019,1,1),\n", " end = datetime.datetime(2019,1,30))\n", - " lse.run()\n", - " lse.plot()\n", + " lse.run()\n", + " lse.plot()\n", "except QiskitFinanceError: \n", " print(\"You need to replace REPLACE-ME with a valid token.\")" ] From 56aa0ea33ea9888c12e1f7532378ed627328d5c0 Mon Sep 17 00:00:00 2001 From: stefan-woerner Date: Thu, 18 Apr 2019 10:51:58 +0200 Subject: [PATCH 055/116] streamline all tutorials --- .../optimization/portfolio_optimization.ipynb | 1 - .../asian_barrier_spread_pricing.ipynb | 136 ++++++------------ .../simulation/basket_option_pricing.ipynb | 64 +++++++-- .../simulation/credit_risk_analysis.ipynb | 117 ++++++++------- .../european_call_option_pricing.ipynb | 42 +++--- 5 files changed, 179 insertions(+), 181 deletions(-) diff --git a/qiskit/finance/optimization/portfolio_optimization.ipynb b/qiskit/finance/optimization/portfolio_optimization.ipynb index 17c1fb0e1..042776d81 100644 --- a/qiskit/finance/optimization/portfolio_optimization.ipynb +++ b/qiskit/finance/optimization/portfolio_optimization.ipynb @@ -15,7 +15,6 @@ "source": [ "# _*Qiskit Finance: Financial Portfolio Optimization*_ \n", "\n", - "Qiskit Finance is part of Qiskit Aqua.
\n", "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", "\n", "***\n", diff --git a/qiskit/finance/simulation/asian_barrier_spread_pricing.ipynb b/qiskit/finance/simulation/asian_barrier_spread_pricing.ipynb index 2844697bf..fb7233aed 100644 --- a/qiskit/finance/simulation/asian_barrier_spread_pricing.ipynb +++ b/qiskit/finance/simulation/asian_barrier_spread_pricing.ipynb @@ -4,7 +4,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" + "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" ] }, { @@ -13,7 +13,6 @@ "source": [ "# _*Qiskit Finance: Pricing Asian Barrier Spreads*_ \n", "\n", - "Qiskit Finance is part of Qiskit Aqua.
\n", "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", "\n", "***\n", @@ -61,16 +60,7 @@ "cell_type": "code", "execution_count": 1, "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "c:\\workspaces\\sandbox-git-quantum-apps\\qiskit-terra-wor\\qiskit\\tools\\qcvv\\__init__.py:13: DeprecationWarning: The qiskit.tools.qcvv package is deprecated. Please use qiskit-ignis available on PIP for similar functionality and more.\n", - " 'functionality and more.', DeprecationWarning)\n" - ] - } - ], + "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D\n", @@ -80,21 +70,10 @@ "\n", "from qiskit import QuantumRegister, QuantumCircuit, BasicAer, execute\n", "from qiskit.aqua.algorithms import AmplitudeEstimation\n", - "\n", - "from arithmetic.weighted_sum_operator import WeightedSumOperator\n", - "from arithmetic.univariate_piecewise_linear_objective import UnivariatePiecewiseLinearObjective as PwlObjective\n", - "from uncertainty_problems.multivariate_objective import MultivariateObjective\n", - "from arithmetic.fixed_value_comparator import FixedValueComparator as Comparator\n", - "from random_distributions.multivariate_log_normal_distribution import MultivariateLogNormalDistribution" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "backend = BasicAer.get_backend('statevector_simulator')" + "from qiskit.aqua.circuits import WeightedSumOperator, FixedValueComparator as Comparator\n", + "from qiskit.aqua.components.uncertainty_problems import UnivariatePiecewiseLinearObjective as PwlObjective\n", + "from qiskit.aqua.components.uncertainty_problems import MultivariateProblem\n", + "from qiskit.aqua.components.uncertainty_models import MultivariateLogNormalDistribution" ] }, { @@ -117,12 +96,12 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# number of qubits per dimension to represent the uncertainty \n", - "num_uncertainty_qubits = 3\n", + "num_uncertainty_qubits = 2\n", "\n", "# parameters for considered random distribution\n", "S = 2.0 # initial spot price\n", @@ -156,12 +135,12 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 3, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -230,7 +209,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -247,7 +226,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ @@ -270,7 +249,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 6, "metadata": {}, "outputs": [], "source": [ @@ -279,13 +258,12 @@ "barrier_thresholds = [2]*dimension\n", "for i in range(dimension):\n", " # target dimension of random distribution and corresponding condition (which is required to be True)\n", - " conditions += [(i, Comparator(num_qubits[i], mapped_barrier[i] + 1, geq=False))]\n", - " break # TODO" + " conditions += [(i, Comparator(num_qubits[i], mapped_barrier[i] + 1, geq=False))]" ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 7, "metadata": {}, "outputs": [], "source": [ @@ -311,12 +289,12 @@ ")\n", "\n", "# define overall multivariate problem\n", - "asian_barrier_spread = MultivariateObjective(u, agg, bull_spread_objective, conditions=conditions)" + "asian_barrier_spread = MultivariateProblem(u, agg, bull_spread_objective, conditions=conditions)" ] }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 8, "metadata": {}, "outputs": [ { @@ -370,7 +348,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 9, "metadata": {}, "outputs": [ { @@ -401,7 +379,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 10, "metadata": {}, "outputs": [ { @@ -409,8 +387,8 @@ "output_type": "stream", "text": [ "state qubits: 5\n", - "circuit width: 19\n", - "circuit depth: 7760\n" + "circuit width: 15\n", + "circuit depth: 1441\n" ] } ], @@ -430,22 +408,11 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 11, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "int" - ] - }, - "execution_count": 13, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "type(qc.width())" + "job = execute(qc, backend=BasicAer.get_backend('statevector_simulator'))" ] }, { @@ -454,30 +421,15 @@ "metadata": {}, "outputs": [ { - "ename": "ModelValidationError", - "evalue": "{'n_qubits': [\"Value '19' is not the expected type \"]}", - "output_type": "error", - "traceback": [ - "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[1;31mModelValidationError\u001b[0m Traceback (most recent call last)", - "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mjob\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mexecute\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mqc\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mbackend\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mbackend\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", - "\u001b[1;32mc:\\workspaces\\sandbox-git-quantum-apps\\qiskit-terra-wor\\qiskit\\execute.py\u001b[0m in \u001b[0;36mexecute\u001b[1;34m(circuits, backend, qobj_header, config, basis_gates, coupling_map, initial_layout, shots, max_credits, seed, qobj_id, seed_mapper, pass_manager, memory, **kwargs)\u001b[0m\n\u001b[0;32m 85\u001b[0m job = execute_circuits(circuits, backend, qobj_header=qobj_header,\n\u001b[0;32m 86\u001b[0m \u001b[0mrun_config\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mrun_config\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 87\u001b[1;33m transpile_config=transpile_config, **kwargs)\n\u001b[0m\u001b[0;32m 88\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 89\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mjob\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;32mc:\\workspaces\\sandbox-git-quantum-apps\\qiskit-terra-wor\\qiskit\\execute.py\u001b[0m in \u001b[0;36mexecute_circuits\u001b[1;34m(circuits, backend, qobj_header, transpile_config, run_config, **kwargs)\u001b[0m\n\u001b[0;32m 128\u001b[0m \u001b[1;31m# assembling the circuits into a qobj to be run on the backend\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 129\u001b[0m qobj = assemble_circuits(new_circuits, qobj_header=qobj_header,\n\u001b[1;32m--> 130\u001b[1;33m run_config=run_config)\n\u001b[0m\u001b[0;32m 131\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 132\u001b[0m \u001b[1;31m# executing the circuits on the backend and returning the job\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;32mc:\\workspaces\\sandbox-git-quantum-apps\\qiskit-terra-wor\\qiskit\\compiler\\assembler.py\u001b[0m in \u001b[0;36massemble_circuits\u001b[1;34m(circuits, run_config, qobj_header, qobj_id)\u001b[0m\n\u001b[0;32m 70\u001b[0m name=circuit.name)\n\u001b[0;32m 71\u001b[0m \u001b[1;31m# TODO: why do we need n_qubits and memory_slots in both the header and the config\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 72\u001b[1;33m \u001b[0mexperimentconfig\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mQasmQobjExperimentConfig\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn_qubits\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mn_qubits\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmemory_slots\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mmemory_slots\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 73\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 74\u001b[0m \u001b[0minstructions\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;32mc:\\workspaces\\sandbox-git-quantum-apps\\qiskit-terra-wor\\qiskit\\validation\\base.py\u001b[0m in \u001b[0;36m_decorated\u001b[1;34m(self, **kwargs)\u001b[0m\n\u001b[0;32m 243\u001b[0m \u001b[1;32mexcept\u001b[0m \u001b[0mValidationError\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mex\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 244\u001b[0m raise ModelValidationError(\n\u001b[1;32m--> 245\u001b[1;33m ex.messages, ex.field_names, ex.fields, ex.data, **ex.kwargs) from None\n\u001b[0m\u001b[0;32m 246\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 247\u001b[0m \u001b[0minit_method\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;31mModelValidationError\u001b[0m: {'n_qubits': [\"Value '19' is not the expected type \"]}" + "name": "stdout", + "output_type": "stream", + "text": [ + "Exact Operator Value: 0.6303\n", + "Mapped Operator value: 0.8319\n", + "Exact Expected Payoff: 0.8023\n" ] } ], - "source": [ - "job = execute(qc, backend=backend)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], "source": [ "# evaluate resulting statevector\n", "value = 0\n", @@ -486,6 +438,9 @@ " prob = np.abs(a)**2\n", " if prob > 1e-4 and b[0] == '1':\n", " value += prob\n", + " # all other states should have zero probability due to ancilla qubits\n", + " if i > 2**num_req_qubits:\n", + " break\n", "\n", "# map value to original range\n", "mapped_value = asian_barrier_spread.value_to_estimation(value) / (2**num_uncertainty_qubits - 1) * (high_ - low_)\n", @@ -498,17 +453,18 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Next we use amplitude estimation to estimate the expected payoff." + "Next we use amplitude estimation to estimate the expected payoff.\n", + "Note that this can take a while since we are simulating a large number of qubits. The way we designed the operator (asian_barrier_spread) impliesthat the number of actual state qubits is significantly smaller, thus, helping to reduce the overall simulation time a bit." ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "# set number of evaluation qubits (=log(samples))\n", - "m = 6\n", + "m = 3\n", "\n", "# construct amplitude estimation \n", "ae = AmplitudeEstimation(m, asian_barrier_spread)" @@ -516,7 +472,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 14, "metadata": {}, "outputs": [], "source": [ @@ -526,33 +482,33 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Exact value: \t0.8407\n", - "Estimated value:\t0.8696\n", - "Probability: \t0.7163\n" + "Exact value: \t0.8023\n", + "Estimated value:\t0.5000\n", + "Probability: \t0.6958\n" ] } ], "source": [ "print('Exact value: \\t%.4f' % exact_value)\n", - "print('Estimated value:\\t%.4f' % (result['estimation'] / (2**num_uncertainty_qubits - 1) * (high_ - low_)))\n", + "print('Estimated value:\\t%.4f' % (result['estimation'] / (2**num_uncertainty_qubits - 1) * (high_ - low_)))\n", "print('Probability: \\t%.4f' % result['max_probability'])" ] }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 16, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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\n", 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\n", 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" ] diff --git a/qiskit/finance/simulation/basket_option_pricing.ipynb b/qiskit/finance/simulation/basket_option_pricing.ipynb index 5f6026a98..230c1dd28 100644 --- a/qiskit/finance/simulation/basket_option_pricing.ipynb +++ b/qiskit/finance/simulation/basket_option_pricing.ipynb @@ -13,7 +13,6 @@ "source": [ "# _*Qiskit Finance: Pricing Basket Options*_ \n", "\n", - "Qiskit Finance is part of Qiskit Aqua.
\n", "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", "\n", "***\n", @@ -208,7 +207,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ @@ -248,7 +247,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": {}, "outputs": [ { @@ -280,7 +279,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "metadata": {}, "outputs": [ { @@ -309,7 +308,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 8, "metadata": {}, "outputs": [ { @@ -317,8 +316,8 @@ "output_type": "stream", "text": [ "state qubits: 5\n", - "circuit width: 14\n", - "circuit depth: 188\n" + "circuit width: 11\n", + "circuit depth: 184\n" ] } ], @@ -338,7 +337,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, "metadata": {}, "outputs": [], "source": [ @@ -347,7 +346,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 10, "metadata": {}, "outputs": [ { @@ -385,7 +384,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 11, "metadata": {}, "outputs": [], "source": [ @@ -398,7 +397,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 12, "metadata": { "scrolled": true }, @@ -410,9 +409,19 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 13, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exact value: \t0.4870\n", + "Estimated value:\t0.5351\n", + "Probability: \t0.9826\n" + ] + } + ], "source": [ "print('Exact value: \\t%.4f' % exact_value)\n", "print('Estimated value:\\t%.4f' % (result['estimation'] / (2**num_uncertainty_qubits - 1) * (high_ - low_)))\n", @@ -421,9 +430,34 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 14, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ "# plot estimated values for \"a\"\n", "plt.bar(result['values'], result['probabilities'], width=0.5/len(result['probabilities']))\n", diff --git a/qiskit/finance/simulation/credit_risk_analysis.ipynb b/qiskit/finance/simulation/credit_risk_analysis.ipynb index 90b4e34b4..c7c70ffec 100644 --- a/qiskit/finance/simulation/credit_risk_analysis.ipynb +++ b/qiskit/finance/simulation/credit_risk_analysis.ipynb @@ -444,8 +444,6 @@ " »\n", "q_a_2: |0>──────────────────────────────────────────────────────────────────»\n", " »\n", - "q_a_3: |0>──────────────────────────────────────────────────────────────────»\n", - " »\n", "« ┌────────────────┐┌───┐┌───────┐┌───┐┌───────┐ »\n", "« q_0: ┤ U3(1.5708,0,0) ├┤ X ├┤ U1(0) ├┤ X ├┤ U1(0) ├──■─────────────────────»\n", "« └────────────────┘└─┬─┘└───────┘└─┬─┘└───────┘ │ »\n", @@ -463,8 +461,6 @@ "« »\n", "«q_a_2: ──────────────────────────────────────────────────────────────────────»\n", "« »\n", - "«q_a_3: ──────────────────────────────────────────────────────────────────────»\n", - "« »\n", "« »\n", "« q_0: ──■────■───────────────────────────────────────────■──»\n", "« │ │ │ »\n", @@ -482,8 +478,6 @@ "« »\n", "«q_a_2: ──────────────────────────────────────────────────────»\n", "« »\n", - "«q_a_3: ──────────────────────────────────────────────────────»\n", - "« »\n", "« ░ »\n", "« q_0: ─────────────────────────────────────────────────────────────────────░─»\n", "« ░ »\n", @@ -501,8 +495,6 @@ "« ░ »\n", "«q_a_2: ─────────────────────────────────────────────────────────────────────░─»\n", "« ░ »\n", - "«q_a_3: ─────────────────────────────────────────────────────────────────────░─»\n", - "« ░ »\n", "« ░ »\n", "« q_0: ─────────────────────────────────────────░───────────────»\n", "« ░ »\n", @@ -520,8 +512,6 @@ "« ┌─┴─┐ └─┬─┘ ┌─┴─┐└───┘└─┬─┘ ░ »\n", "«q_a_2: ┤ X ├───────■───────┤ X ├───────■────────░───────────────»\n", "« └───┘ └───┘ ░ »\n", - "«q_a_3: ─────────────────────────────────────────░───────────────»\n", - "« ░ »\n", "« »\n", "« q_0: ──────────────────────────────────────────────────────────────────────»\n", "« »\n", @@ -539,8 +529,6 @@ "« »\n", "«q_a_2: ──────────────────────────────────────────────────────────────────────»\n", "« »\n", - "«q_a_3: ──────────────────────────────────────────────────────────────────────»\n", - "« »\n", "« ░ ░ \n", "« q_0: ─────────────────────────░──────────────────────────────────────────░─\n", "« ░ ░ \n", @@ -557,12 +545,10 @@ "«q_a_1: ─────────────────────■───░─┤ X ├─────┤ X ├──┼──┤ X ├────────────┼───░─\n", "« ░ └─┬─┘ └───┘┌─┴─┐└─┬─┘ ┌─┴─┐ ░ \n", "«q_a_2: ─────────────────────────░───■────────────┤ X ├──■────────────┤ X ├─░─\n", - "« ░ └───┘ └───┘ ░ \n", - "«q_a_3: ─────────────────────────░──────────────────────────────────────────░─\n", - "« ░ ░ " + "« ░ └───┘ └───┘ ░ " ], "text/plain": [ - "" + "" ] }, "execution_count": 12, @@ -766,7 +752,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 19, "metadata": {}, "outputs": [], "source": [ @@ -787,7 +773,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 20, "metadata": {}, "outputs": [], "source": [ @@ -796,7 +782,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 21, "metadata": { "scrolled": true }, @@ -821,8 +807,6 @@ " »\n", "q_a_2: |0>──────────────────────────────────────────────────────────────────»\n", " »\n", - "q_a_3: |0>──────────────────────────────────────────────────────────────────»\n", - " »\n", "« ┌────────────────┐┌───┐┌───────┐┌───┐┌───────┐ »\n", "« q_0: ┤ U3(1.5708,0,0) ├┤ X ├┤ U1(0) ├┤ X ├┤ U1(0) ├──■─────────────────────»\n", "« └────────────────┘└─┬─┘└───────┘└─┬─┘└───────┘ │ »\n", @@ -840,8 +824,6 @@ "« »\n", "«q_a_2: ──────────────────────────────────────────────────────────────────────»\n", "« »\n", - "«q_a_3: ──────────────────────────────────────────────────────────────────────»\n", - "« »\n", "« »\n", "« q_0: ──■────■───────────────────────────────────────────■──»\n", "« │ │ │ »\n", @@ -859,8 +841,6 @@ "« »\n", "«q_a_2: ──────────────────────────────────────────────────────»\n", "« »\n", - "«q_a_3: ──────────────────────────────────────────────────────»\n", - "« »\n", "« ░ »\n", "« q_0: ─────────────────────────────────────────────────────────────────────░─»\n", "« ░ »\n", @@ -878,8 +858,6 @@ "« ░ »\n", "«q_a_2: ─────────────────────────────────────────────────────────────────────░─»\n", "« ░ »\n", - "«q_a_3: ─────────────────────────────────────────────────────────────────────░─»\n", - "« ░ »\n", "« ░ ░ »\n", "« q_0: ─────────────────────────────────────────░─────────────────░───────────»\n", "« ░ ░ »\n", @@ -894,11 +872,9 @@ "«q_a_0: ──■──┤ X ├──┼──┤ X ├──■────┼────┼──┤ X ├─░───■────┼────■───░───┼──┤ X ├»\n", "« │ └───┘┌─┴─┐└───┘ │ ┌─┴─┐┌─┴─┐└───┘ ░ │ │ │ ░ ┌─┴─┐└───┘»\n", "«q_a_1: ──┼───────┤ X ├───────┼──┤ X ├┤ X ├──────░───┼────■────┼───░─┤ X ├─────»\n", - "« ┌─┴─┐ └─┬─┘ ┌─┴─┐└───┘└─┬─┘ ░ │ │ │ ░ └─┬─┘ »\n", - "«q_a_2: ┤ X ├───────■───────┤ X ├───────■────────░───┼────┼────┼───░───■───────»\n", - "« └───┘ └───┘ ░ ┌─┴─┐ │ ┌─┴─┐ ░ »\n", - "«q_a_3: ─────────────────────────────────────────░─┤ X ├──■──┤ X ├─░───────────»\n", - "« ░ └───┘ └───┘ ░ »\n", + "« ┌─┴─┐ └─┬─┘ ┌─┴─┐└───┘└─┬─┘ ░ ┌─┴─┐ │ ┌─┴─┐ ░ └─┬─┘ »\n", + "«q_a_2: ┤ X ├───────■───────┤ X ├───────■────────░─┤ X ├──■──┤ X ├─░───■───────»\n", + "« └───┘ └───┘ ░ └───┘ └───┘ ░ »\n", "« ░ \n", "« q_0: ───────────────────────────────░─\n", "« ░ \n", @@ -915,12 +891,10 @@ "«q_a_1: ┤ X ├──┼──┤ X ├────────────┼───░─\n", "« └───┘┌─┴─┐└─┬─┘ ┌─┴─┐ ░ \n", "«q_a_2: ─────┤ X ├──■────────────┤ X ├─░─\n", - "« └───┘ └───┘ ░ \n", - "«q_a_3: ───────────────────────────────░─\n", - "« ░ " + "« └───┘ └───┘ ░ " ], "text/plain": [ - "" + "" ] }, "execution_count": 21, @@ -934,7 +908,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 22, "metadata": {}, "outputs": [ { @@ -967,7 +941,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 23, "metadata": {}, "outputs": [], "source": [ @@ -980,7 +954,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 24, "metadata": {}, "outputs": [ { @@ -1034,7 +1008,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 25, "metadata": {}, "outputs": [], "source": [ @@ -1050,7 +1024,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 26, "metadata": {}, "outputs": [], "source": [ @@ -1118,7 +1092,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 27, "metadata": {}, "outputs": [ { @@ -1148,7 +1122,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 28, "metadata": {}, "outputs": [ { @@ -1188,7 +1162,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 29, "metadata": {}, "outputs": [], "source": [ @@ -1215,7 +1189,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 30, "metadata": {}, "outputs": [], "source": [ @@ -1224,7 +1198,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 31, "metadata": {}, "outputs": [], "source": [ @@ -1233,7 +1207,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 32, "metadata": {}, "outputs": [], "source": [ @@ -1256,7 +1230,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 33, "metadata": {}, "outputs": [], "source": [ @@ -1265,7 +1239,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 34, "metadata": {}, "outputs": [ { @@ -1302,7 +1276,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 35, "metadata": {}, "outputs": [], "source": [ @@ -1315,9 +1289,19 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 36, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exact CVaR: \t3.0000\n", + "Estimated CVaR:\t3.8670\n", + "Probability: \t0.7146\n" + ] + } + ], "source": [ "# print results\n", "print('Exact CVaR: \\t%.4f' % exact_cvar)\n", @@ -1327,9 +1311,34 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 37, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ "# plot estimated values for \"a\"\n", "plt.bar(result_cvar['values'], result_cvar['probabilities'], width=0.5/len(result_cvar['probabilities']))\n", diff --git a/qiskit/finance/simulation/european_call_option_pricing.ipynb b/qiskit/finance/simulation/european_call_option_pricing.ipynb index b1dd21893..464abe28f 100644 --- a/qiskit/finance/simulation/european_call_option_pricing.ipynb +++ b/qiskit/finance/simulation/european_call_option_pricing.ipynb @@ -88,7 +88,7 @@ "outputs": [], "source": [ "# number of qubits to represent the uncertainty\n", - "num_uncertainty_qubits = 2\n", + "num_uncertainty_qubits = 3\n", "\n", "# parameters for considered random distribution\n", "S = 2.0 # initial spot price\n", @@ -118,7 +118,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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\n", + "image/png": 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\n", 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" ] @@ -248,8 +248,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "exact expected value:\t0.1342\n", - "exact delta value: \t0.4446\n" + "exact expected value:\t0.1133\n", + "exact delta value: \t0.4700\n" ] } ], @@ -270,7 +270,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 7, "metadata": {}, "outputs": [], "source": [ @@ -283,7 +283,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 8, "metadata": {}, "outputs": [], "source": [ @@ -293,16 +293,16 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Exact value: \t0.1342\n", + "Exact value: \t0.1133\n", "Estimated value:\t0.1061\n", - "Probability: \t0.6636\n" + "Probability: \t0.9378\n" ] } ], @@ -314,12 +314,12 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 10, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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\n", 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\n", 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" ] @@ -378,7 +378,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 11, "metadata": {}, "outputs": [], "source": [ @@ -410,7 +410,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 12, "metadata": {}, "outputs": [], "source": [ @@ -423,7 +423,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 13, "metadata": {}, "outputs": [], "source": [ @@ -433,16 +433,16 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Exact delta: \t0.4446\n", + "Exact delta: \t0.4700\n", "Esimated value:\t0.4510\n", - "Probability: \t0.9452\n" + "Probability: \t0.5918\n" ] } ], @@ -454,12 +454,12 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 15, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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1K0RpUM2sCxQdcC4EXgKukHRgdsJ+NnBe5KZKS1ou6XsVjj8KWA9cXr5D0ihJv5A0S9IBkqYBC4Adga+2oC1mZlaDQi/8jIheSQcA3wZ+Tjpvcz4p6JTXq9JyN0cBN0XEygr7XgJWklYsGAu8CNwG7B8Ri5rSADMzq1vhi3dGxL3AewbJM76f9LcNcMyLwOENVc6saBOzmf2LPeprnc+rRZu105Il7a6BWWF8AzYzMyuEA46ZmRXCAcfMzArhgGNmZoVwwDEzs0J4lppZO82Y0e4amBXGAcesnUq3mDbrAh5SMzOzQtQUcCRVWm7GzOq1eLFXGbCuUeuQ2mOSLgUujoj7WlEhs64yKbtRoleMti5Q65DaHOBI4HeSfiVppqStW1AvMzPrMDUFnIg4PSJ2BQ4ClgHnAU9I+qGkA1tRQTMz6wx1TRqIiJsj4uPA9sBngTcB10taIWm2pL9qZiXNzGz4a3SW2iTg3aTbRvcCvwCOBZZL+liDZZuZWQepOeBI2kXS6ZIeAG4CdgD+AfiriPh7YBfSuZ5zm1pTMzMb1mqapSbpZlKP5lHgEtJstYfyeSLiZUk/Aj7XrEqamdnwV+u06KeAqcCNEQPO47wTeH3dtTLrFot893PrHrUGnG8DSyoFG0kjgb0i4paIWAc81OdoM9tY6RbTZl2g1nM4C4A9+tn3pmy/mZlZH7UGHA2wbySwpoG6mHWfmTPTZtYFBh1Sk/RuYHIu6VhJ7yvLtgVwKHB386pm1gUuuig9etVo6wLVnMPZh3RxJ0AAHwLWl+X5M7AUOLF5VTMzs04yaMCJiHPJrqmR9CDwwYi4s9UVMzOzzlLTLLWI8FRnMzOrSzXncKYCt0bEquznAUXENU2pmZmZdZRqejhXAfsCv85+DvqfrRaAb9JmljP+5Kv7pK342qFtqIlZe1UTcF4PPJH72cyaZa+92l0Ds8JUM2ngoUo/m1kT+PbS1kWqOYfzmloKjAhf/GlmZn1UM6S2mnRuplo+h2NmZn1UE3D+gdoCjplVS9n8mwEXXzfrDNWcw7mkgHqYmVmHa/QW02ZmZlWpZtLAr4HpEXGvpDsYZHgtIvZuVuXMzKxzVHMO5x5gbe5nDzabmVnNqjmH88ncz9NbWhszM+tYdZ/DUbKdpIFuymZmZgbUuFo0/GUxz9OAidnx6yUtBr4SEX0XjTKz/s2Z0+4amBWmpoAjaRbwHeAm4HPAn4CxwOHAf0v6x4jwX5BZtXx7aesitfZwTgXmRsSny9IvlHQh8AXAAcfMzPqo9RzOa4Er+tn3U2CbwQqQtIekmyStkfS4pDMlDbgcjqTxkqLCNq9C3sMk3S3pRUn3SppWVcvM2mHu3LSZdYFaezgLgP2BGyvs2x+4ZaCDJY0B5gP3AocBuwHfIAW+06p4/ROAX+aeP1VW/rtIge87wHHAVOAySb0RcUMV5ZsVa9as9OihNesC1Vz4uUfu6TeB70p6LXAlr5zD+SBwCHDsIMV9ChgBHB4Rq4AbJW0NzJZ0TpY2kGURcfsA+78I3BIRx2XPF0jaE/gS4IBjZtZG1fRwfsfGF3sKmJVt5Xf/vI6BV4s+BLi+LLDMA84m9ZB+XkV9KpL0amAKqWeTNw+4WNKoiHiu3vLNzKwx1QScKU18vQnAzfmEiHhY0pps32AB52JJ25B6VpcBX4iI0ioIuwGbA0vLjrmPNGS3O3BHY9U3M7N6VbPSwMImvt4Y4NkK6b3Zvv68BPwbaVhsFTAZOIkUZA7LlU2F8nvL9m9E0kxgJsC4cePo6ekZqP6DWr16dcNlDCdu7+COf8v6PmmlMiaXPR9q/Pl2tqLbW/OFnyWSNgG2KE+v4o6fldZiUz/ppTKfAP4pl9Qj6UngO5LeFhF3DlC++kkvlT0XmAswadKkmDx58sC1H0RPTw+NljGcuL2Dm35y3+uhV3x04zKG6nvoz7ezFd3emqZFZ8vZnCRpObAOeL7CNpBeYHSF9FFU7vkM5PLsca9c2VQov/S81vLNzKyJar0O5zjgZOB7pJ7DV4AzgfuBFWRDUwNYSjpX8xeSdgK2pO+5l8FE2eMDpCA4oSzfBGBDVkezoSXCd/u0rlFrwJkBnA6ckz2/MiLOAPYkBYw3DnL8tcDBkrbKpU0j3f6g1nNFR2aPiwEi4iXSdUIfKss3DbjNM9TMzNqr1nM4rwfujIiXJa0jG66KiA2SvgN8l9QD6s+FpF7SFZLOBnYFZgPn5adKZ0N2CyPimOz5bGAr0kWfq4B3AycCV0TEb3Pln0U6v3MB6Tqhqdn2vhrbaWZmTVZrD+dpYGT288PA23P7xpAu6uxXRPQCB5Cu1fk5cAZwPqnXlLcZG1/Ps5R0nc7FwDXA0cC52WO+/FtJPZ8DgeuBvwOO9ioDNmRNnJg2sy5Qaw/nl8A7SF/6PyKtELAN8GfgM6RVpAcUEfcC7xkkz/iy5/NIF3AOKiKuJPVuzIa+JUvaXQOzwtQacGYDO2Y/f5U0pDad1LO5EfhssypmZmadpaaAExHLgGXZzy+R7onzuRbUy8zMOkwjF36+DtgBeDwiHmtelczMrBPVOmkASZ+W9AjwEPAr4GFJj0r6x6bXzszMOkatKw18Cfg26XqaQ4FJ2eO1wDez/WZmZn3UOqT2GeCrEfHFsvTrsrXNPkNaecDMqjFjRrtrYFaYWgPOCPq/q+dCPEvNrDa+vbR1kVrP4VwJHN7PviOAqxqrjpmZdapqbjE9Nff0WuAcSePpe4vpPYHPN7+KZh1s8eL06NUGrAtUM6R2FX1vJb0jcHCFvD8g3YnTzKoxaVJ69IrR1gWqCTivb3ktzMys41Vzi+mHiqiImZl1tppXGpC0GWmCwLuAbYBngF+QbhXQ9+btZmZm1BhwJI0FbgDeSrrD55PAfqTrb+6S9N6IWNnsSpqZ2fBX67To84DXAvtExK4RsV9E7Arsk6Wf1+wKmplZZ6g14EwFToqIO/KJ2fNTSMvcmJmZ9VHrOZxXA8/3s+954FWNVcesyyxa1O4amBWm1oBzO3CSpJsj4oVSoqQtgZOy/WZWLV/waV2k1oBzPLAAeETSDaRJA2NJF4EKmNzU2pmZWceo6RxORNwJvBGYC2wHHEQKOBcCb4yIu5peQ7NONnNm2sy6QNU9HEmbA3sDD0bEya2rklkXueii9OhVo60L1NLDeRm4GXhzi+piZmYdrOqAExEbgN8D41pXHTMz61S1XofzBeBLkt7SisqYmVnnqnWW2mmkFQXulPQYaZbaRuuqR8TeTaqbmZl1kFoDzu+yzczMrCZVBRxJI0jL2vwO+CMwPyKebGXFzLrCXnu1uwZmhanmFtO7AvOB8bnkVZI+HBE3tKpiZl2hdItpsy5QzaSBc4ANwN8CrwH2BH4DzGlhvczMrMNUE3D2A06LiF9GxIsRcR8wC9hZ0g6trZ6ZmXWKagLODsAfytIeIK2dtn3Ta2TWTaS0mXWBaq/DicGzmJmZ9a/aadHXS1pfIf2m8vSIGNt4tczMrNNUE3DOaHktzMys4w0acCLCAcfMzBpW61pqZmZmdXHAMTOzQtS6lpqZNdMcXz9t3cMBx6ydfHtp6yIeUjMzs0I44Ji109y5aTPrAoUHHEl7SLpJ0hpJj0s6U9KmgxzzDkkXS1qeHbdM0umStijLN1tSVNje19pWmdVp1qy0mXWBQs/hSBpDutXBvcBhwG7AN0iB77QBDp2W5T0b+D3wVuCs7PGIsrzPAeUB5r5G625mZo0petLAp4ARwOERsQq4UdLWwGxJ52RplZwdEStzz3skvQjMkbRLRDyU27c+Im5vTfXNzKxeRQ+pHQJcXxZY5pGC0P79HVQWbEp+kz167TYzs2Gg6IAzAViaT4iIh4E12b5avJN0Y7hlZemjJT0laZ2k30g6vO7amplZ0yiiuDsPSFoHnBgRF5SlPwpcGhGnVlnO9sBvgWsiYnou/WOkHs+dwEjSjeKmAkdExBX9lDUTmAkwbty4ifPmzau1WRtZvXo1I0eObKiM4cTtHdzdjz3XJ+0tO44CYPKUKQD0LFjQeOVawJ9vZ2tGe6dMmbI4IiZVk7cdAeeEiPjXsvTHgEsi4gtVlPEq0sSD1wETI6J3gLwC/gcYERFvG6zsSZMmxaJFiwbLNqCenh4mT57cUBnDids7uPEnX90nbcXXDk0/lG6+VuDfYS38+Xa2ZrRXUtUBp+ghtV5gdIX0UcCzgx2cBZBLgT2BqQMFG4BI0fQK4K2DTb02a4uIIRtszJqt6FlqSyk7VyNpJ2BLys7t9ON80nTqgyKimvwl/ou2Yam8d/SXnpHZMFR0D+da4GBJW+XSpgFrgYUDHSjpFOCzwMci4tZqXizrEX0QuCsiXq6vymZm1gxF93AuBI4DrpB0NrArMBs4Lz9VWtJyYGFEHJM9Pxr4KnAJ8JikfXNlPlCaNi1pIfBTUm9pS2AGsC/wgdY2y6xOEyemx8WL21sPswIUGnAiolfSAcC3gZ+TztucTwo65fXKn3N5b/Y4PdvyPkkKRADLgX8GdiBNmV4CHBoR1zaj/mZNt2RJu2tgVpjCb08QEfcC7xkkz/iy59PpG2gqHXdMA1UzM7MW8mrRZmZWCAccMzMrhAOOmZkVwgHHzMwKUfikATPLmTGj3TUwK4wDjlk7+fbS1kU8pGZmZoVwwDFrp8WLvcqAdQ0PqZm106RsVXevGG1dwD0cMzMrhAOOmZkVwgHHzMwK4YBjZmaFcMAxM7NCOOCYmVkhPC3arJ0WLWp3DcwK44Bj1k6lW0ybdQEPqZmZWSEccMzaaebMtJl1AQccs3a66KK0mXUBBxwzMyuEA46ZmRXCAcfMzArhgGNmZoVwwDEzs0L4wk+zdtprr3bXwKwwDjhm7eTbS1sX8ZCamZkVwgHHzMwK4YBj1k5S2sy6gAOOmZkVwgHHzMwK4YBjZmaFcMAxM7NCOOCYmVkhHHDMzKwQXmnArJ3mzGl3DcwK44BjVoXxJ18NwPFvWc/07OcVXzu08YJ9e2nrIh5SMzOzQriHY9ZOc+emxyb3dEo9srym9MjMGuCAY9ZOs2alRw+tWRfwkJqZmRWi8IAjaQ9JN0laI+lxSWdK2rSK40ZJulhSr6TnJP1Q0msr5DtM0t2SXpR0r6RprWmJmZnVotAhNUljgPnAvcBhwG7AN0iB77RBDv8x8CbgWGADcDZwJfC3ufLfBfwU+A5wHDAVuExSb0Tc0NTG2LDkcxtm7VP0OZxPASOAwyNiFXCjpK2B2ZLOydL6kLQfcDCwf0TckqU9BvxK0oERMT/L+kXglog4Lnu+QNKewJcABxyzKuSD8vFvWc/k9lXFOkzRAecQ4PqywDKP1FvZH/j5AMc9WQo2ABHxa0kPZvvmS3o1MIXUs8mbB1wsaVREPNekdlibuacy9PgzscEUHXAmADfnEyLiYUlrsn39BZwJwNIK6fdl+yANz21eId99pCG73YE76qv28FH+R9/fH3y1+RrNO1j+eo+xzlHU70ytx7Tqb6SbKSKKezFpHXBiRFxQlv4ocGlEnNrPcTcCL0TEB8rSfwDsGhHvlPQ3wK3A2yPizlyeNwC/Bw6udB5H0kygNCf1TcCyuhuYbAs81WAZw4nb29nc3s7WjPbuEhHbVZOxHdfhVIpw6ie9nuPKn6uf9JQYMReYO8hrV03SooiY1Kzyhjq3t7O5vZ2t6PYWPS26FxhdIX0U8Gwdx43OHdebSyvPwyDlm5lZixUdcJbyyjkXACTtBGxJ5XM0/R6XyZ/beQBYVyHfBNI06vvrqK+ZmTVJ0QHnWuBgSVvl0qYBa4GFgxy3fXadDQCSJgG7ZvuIiJeABcCHyo6dBtxW4Ay1pg3PDRNub2dzeztboe0tetLAGNJFn78jTYXeFTgPuCAiTsvlWw4sjIhjcmnXkWaancArF37+KSLKL/zsAb5Nuih0apb/fb7w08ysvQrt4UREL3AAsClpCvQZwPnA6WVZN8vy5B1F6gV9H7gUWAx8sKz8W4EjgQOB64G/A452sDEza79CezhmZta9vFp0lVq96OhQU097Jb0ja+vy7Lhlkk6XtEVR9a5XvZ9v7vhNJC2WFJLe38q6NkMj7ZV0uKQ7JK2V9LSk6yRt2eo6N6KBv99Jkm7I2vkcdGfsAAAEjklEQVSMpPmS9imizo2Q9AZJcyTdJellST1VHtfS7yvfD6cKrV50dKhpoL3Tsrxnky62fStwVvZ4RAur3JAGP9+SY4EdW1LBJmukvZKOJZ0jPQc4ERgDvIch/F1Sb3uzGbTzgSXAx7PkE4EbJL01Ih5qZb0btCfpHPbtwKtqOK6131cR4W2QDTiFdJ3P1rm0zwNr8mkVjtuPdMHpu3Npe2dpB7a7XS1o73YV0mZm7d2l3e1qdntzeccAK4Fjsra+v91tatHnuy3wPDCj3W0oqL2fAl4GRpd91i8Dn253uwZp8ya5ny8Heqo4puXfVx5Sq05/i46OIC06OtBxfRYdBUqLjg5VdbU3IlZWSP5N9ji2edVruno/35KzgF8CN7Wgbq1Qb3s/nD3+R6sq1iL1tndzYD2wOpe2OktTxSOGiIjYUMdhLf++csCpTp/FQyPiYdJ/SJUuSO33uEx+0dGhqN72VvJOUte80TXqWqnu9kp6K/BJ0vT74aLe9u5D+hyPkfSopHWSfiXpna2ralPU296fZnm+IWmspLGkWbW9wE9aVNd2avn3lQNOdcZQeWmc3mxfs49rt6bUW9L2wBeA/x/93OtoiGikvd8C/i0ilje9Vq1Tb3u3J43vnwacBPxf4AXgOknjml3JJqqrvRHxOOmWJ0cAT2bb4aSFgCv15oe7ln9fOeBUr9WLjg41DdVb0quA/yQNQfxLE+vVKjW3V9JRpC/gL7eqUi1Uz+e7CTASOCYifhgR1wEfIJ3T+KfmV7Gp6vl8dyCd/1hMGlI6JPv5akk7t6KSQ0BLv68ccKrTykVHh6J62wuAJJEuzt0TmBrpgt+hrOb2StocOJc0i2cTSaOBrbPdW5Yt3zTU1Pv5PpM99pQSsp7rYmCPZlWuBept74mk2XdHRsR1WYA9ghRgh9MQarVa/n3lgFOdVi46OhTV296S80nTTw+LiKHczpJ62rsl8DrS0ky92XZXtm8er0yWGIrq/XzvI/2nW37CXKTzdENVve2dANwTEetKCRHxZ+Ae0tTqTtPy7ysHnOq0bNHRIare9iLpFOCzwMciLTU0HNTT3tWk8f389pFs36nAR1tT1aao9/O9ihRcppQSJI0CJvJKsB2K6m3vQ8BfZ8PDACjdyv6vgRUtqGe7tf77qt3zxYfDRjph9gRwI2mdtpmkL5wvl+VbDnyvLO064A+kk40fIM3y+UW729SK9gJHk/4DvhjYt2zrc43OUNka+XzL9o9neFyH08jv85XZsZ8ADiV9Ya8ExrS7Xc1uLymQrgOuztr6ftIX7zrg/7S7XYO0+TWkdSWPBG4j9cpKz18zwOfb0u+rtr8xw2UjjVHfTPqv6AnStRebluVZAVxSljY6+wJ+FlgF/AjYtt3taUV7gUuyL9xK2/R2t6kVn2/Z/mERcBppL2nSwL8DT2fHzgfe0u72tLC9BwC3kM5fPUMKsJPb3Z4q2lv6Xay0jR+gvS39vvLinWZmVgifwzEzs0I44JiZWSEccMzMrBAOOGZmVggHHDMzK4QDjpmZFcIBx8zMCuGAY2Zmhfhf0iRe8/WZSJgAAAAASUVORK5CYII=\n", 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" ] From 4727ba2e4b44d8648b21ca68c470de484ac158e3 Mon Sep 17 00:00:00 2001 From: CZ Date: Thu, 18 Apr 2019 13:44:53 +0200 Subject: [PATCH 056/116] notebooks qgans --- .../aqua/artificial_intelligence/index.ipynb | 1 + ...ns_for_loading_random_distributions.ipynb} | 6 +- .../european_call_option_pricing.ipynb | 2 +- .../qgans_option_pricing.ipynb | 193 ++++++++++++++++++ 4 files changed, 197 insertions(+), 5 deletions(-) rename qiskit/{finance/machine_learning/execute_qgan.ipynb => aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb} (99%) create mode 100644 qiskit/finance/machine_learning/qgans_option_pricing.ipynb diff --git a/qiskit/aqua/artificial_intelligence/index.ipynb b/qiskit/aqua/artificial_intelligence/index.ipynb index b0c063914..d36d3ccac 100644 --- a/qiskit/aqua/artificial_intelligence/index.ipynb +++ b/qiskit/aqua/artificial_intelligence/index.ipynb @@ -13,6 +13,7 @@ "## Contents\n", "\n", "* [Quantum SVM for Classification](qsvm_kernel_classification.ipynb)\n", + "* [qGANs for Loading Random Distributions](qgans_for_loading_random_distributions.ipynb)\n", "* More examples can be found in [commuity/aqua/artificial_intelligence](../../../community/aqua/artificial_intelligence)" ] }, diff --git a/qiskit/finance/machine_learning/execute_qgan.ipynb b/qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb similarity index 99% rename from qiskit/finance/machine_learning/execute_qgan.ipynb rename to qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb index 32a914048..f9c3abb7b 100644 --- a/qiskit/finance/machine_learning/execute_qgan.ipynb +++ b/qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb @@ -4,9 +4,8 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# _*Qiskit Finance: qGANs for Loading Random Distributions*_ \n", + "# _*Qiskit Aqua: qGANs for Loading Random Distributions*_ \n", "\n", - "Qiskit Finance is part of Qiskit Aqua.
\n", "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", "\n", "***\n", @@ -23,7 +22,7 @@ "\n", "The aim of the qGAN training is to generate a state $\\lvert g_{\\theta}\\rangle$ where $p_{\\theta}^{j}$, for $j\\in \\left\\{0, \\ldots, {2^n-1} \\right\\}$, describe a probability distribution that is close to the distribution underlying the training data $X=\\left\\{x^0, \\ldots, x^{k-1} \\right\\}$.\n", "\n", - "For further details please refer to https://arxiv.org/abs/1904.00043." + "For further details please refer to Quantum Generative Adversarial Networks for Learning and Loading Random Distributions. Zoufal, Lucchi, Woerner. 2019." ] }, { @@ -60,7 +59,6 @@ "\n", "from qiskit.aqua import aqua_globals, QuantumInstance\n", "\n", - "from qiskit.providers.ibmq import IBMQ\n", "from qiskit import Aer" ] }, diff --git a/qiskit/aqua/finance/european_call_option_pricing.ipynb b/qiskit/aqua/finance/european_call_option_pricing.ipynb index 4ef0c1a31..14d879bee 100644 --- a/qiskit/aqua/finance/european_call_option_pricing.ipynb +++ b/qiskit/aqua/finance/european_call_option_pricing.ipynb @@ -280,7 +280,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": null, "metadata": {}, "outputs": [ { diff --git a/qiskit/finance/machine_learning/qgans_option_pricing.ipynb b/qiskit/finance/machine_learning/qgans_option_pricing.ipynb new file mode 100644 index 000000000..c3b9ea5c1 --- /dev/null +++ b/qiskit/finance/machine_learning/qgans_option_pricing.ipynb @@ -0,0 +1,193 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# _*Qiskit Finance: qGAN Option Pricing*_ \n", + "\n", + "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", + "\n", + "***\n", + "### Contributors\n", + "Christa Zoufal[1,2], Stefan Woerner[1]\n", + "### Affliation\n", + "- [1]IBMQ\n", + "- [2]ETH Zurich\n", + "\n", + "### Introduction\n", + "We can train a quantum Generative Adversarial Network (qGAN) - see [qGANs for Loading Random Distributions](../../aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb) - to learn and load a model for the spot price of an asset underlying a European call option. The resulting model can then be integrated into a Quantum Amplitude Estimation based algorithm to evaluate the expected payoff - see [European Call Option Pricing](../../aqua/finance/european_call_option_pricing.ipynb)." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/ouf/anaconda3/envs/QiskitDevenv/lib/python3.7/site-packages/qiskit_terra-0.8.0-py3.7-macosx-10.7-x86_64.egg/qiskit/circuit/variabletable.py:10: DeprecationWarning: Using or importing the ABCs from 'collections' instead of from 'collections.abc' is deprecated, and in 3.8 it will stop working\n", + " from collections import MutableMapping\n" + ] + } + ], + "source": [ + "#!/usr/bin/env python\n", + "# coding: utf-8\n", + "from __future__ import absolute_import, division, print_function\n", + "\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "import numpy as np\n", + "from qiskit.aqua.algorithms import AmplitudeEstimation\n", + "from qiskit.aqua.components.uncertainty_problems import EuropeanCallExpectedValue\n", + "from qiskit.aqua.components.uncertainty_models import UnivariateVariationalDistribution, NormalDistribution\n", + "from qiskit.aqua.components.variational_forms import RY\n", + "\n", + "from qiskit.aqua import aqua_globals, QuantumInstance\n", + "\n", + "from qiskit import BasicAer" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Uncertainty Model\n", + "\n", + "The Black-Scholes model assumes that the spot price at maturity $S_T$ for a European call option is log-normally distributed. Thus, we can train a qGAN on samples from a log-normal distribution, as it is shown in [qGANs for Loading Random Distributions](../../aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb), and use the resulting model as uncertainty model underlying the option.\n", + "In the following, we construct the quantum circuit for loading the uncertainty model. The circuit output reads $$\\lvert g_{\\theta}\\rangle = \\sum\\limits_{j=0}^{2^n-1}\\sqrt{p_{\\theta}^{j}}\\lvert{j}\\rangle,$$ whereby the probabilites $p_{\\theta}^{j}$, for $j\\in \\left\\{0, \\ldots, {2^n-1} \\right\\}$, represent a model of the target distribution." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# Set upper and lower data values\n", + "bounds = np.array([0.,7.])\n", + "# Set number of qubits used in the uncertainty model\n", + "num_qubits = [3]\n", + "\n", + "# Set entangler map\n", + "entangler_map = []\n", + "for i in range(sum(num_qubits)):\n", + " entangler_map.append([i, int(np.mod(i+1, sum(num_qubits)))])\n", + "\n", + "# Set variational form\n", + "var_form = RY(int(np.sum(num_qubits)), depth=1, entangler_map=entangler_map, entanglement_gate='cz')\n", + "# Load the trained circuit parameters\n", + "g_params = [0.29399714, 0.38853322, 0.9557694, 0.07245791, 6.02626428, 0.13537225]\n", + "# Set an initial state for the generator circuit\n", + "init_dist = NormalDistribution(int(sum(num_qubits)), mu=1., sigma=1., low=bounds[0], high=bounds[1])\n", + "# Set generator circuit\n", + "g_circuit = UnivariateVariationalDistribution(int(sum(num_qubits)), var_form, g_params,\n", + " initial_distribution=init_dist, low=bounds[0], high=bounds[1])\n", + "\n", + "# construct circuit factory for uncertainty model\n", + "uncertainty_model = g_circuit" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot probability distribution\n", + "x = uncertainty_model.values\n", + "y = uncertainty_model.probabilities\n", + "plt.bar(x, y, width=0.2)\n", + "plt.xticks(x, size=15, rotation=90)\n", + "plt.yticks(size=15)\n", + "plt.grid()\n", + "plt.xlabel('Spot Price at Maturity $S_T$ (\\$)', size=15)\n", + "plt.ylabel('Probability ($\\%$)', size=15)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Evaluate Expected Payoff\n", + "Now, the trained uncertainty model can be used as part of a quantum circuit to evaluate the expectation value of the option's payoff function." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Estimated value:\t1.2580\n", + "Probability: \t0.8785\n" + ] + } + ], + "source": [ + "# set the strike price (should be within the low and the high value of the uncertainty)\n", + "strike_price = 2\n", + "\n", + "# set the approximation scaling for the payoff function\n", + "c_approx = 0.25\n", + "\n", + "# construct circuit factory for payoff function\n", + "european_call = EuropeanCallExpectedValue(\n", + " uncertainty_model,\n", + " strike_price=strike_price,\n", + " c_approx=c_approx\n", + ")\n", + "# set number of evaluation qubits (samples)\n", + "m = 5\n", + "\n", + "# construct amplitude estimation \n", + "ae = AmplitudeEstimation(m, european_call)\n", + "# result = ae.run(quantum_instance=BasicAer.get_backend('qasm_simulator'), shots=100)\n", + "result = ae.run(quantum_instance=BasicAer.get_backend('statevector_simulator'))\n", + "print('Estimated value:\\t%.4f' % result['estimation'])\n", + "print('Probability: \\t%.4f' % result['max_probability'])" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "QiskitDevenv", + "language": "python", + "name": "qiskitdevenv" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From 877c9f9e48d4c6f15747a00c6c6f6b52de6fcc2f Mon Sep 17 00:00:00 2001 From: CZ Date: Thu, 18 Apr 2019 18:58:13 +0200 Subject: [PATCH 057/116] update --- .../qgans_for_loading_random.ipynb | 12526 +++++++++++ ...ans_for_loading_random_distributions.ipynb | 17778 ++++++++-------- ...ricing.ipynb => qgan_option_pricing.ipynb} | 11 +- qiskit/finance/machine_learning/qgans.ipynb | 194 + 4 files changed, 21615 insertions(+), 8894 deletions(-) create mode 100644 qiskit/aqua/artificial_intelligence/qgans_for_loading_random.ipynb rename qiskit/finance/machine_learning/{qgans_option_pricing.ipynb => qgan_option_pricing.ipynb} (92%) create mode 100644 qiskit/finance/machine_learning/qgans.ipynb diff --git a/qiskit/aqua/artificial_intelligence/qgans_for_loading_random.ipynb b/qiskit/aqua/artificial_intelligence/qgans_for_loading_random.ipynb new file mode 100644 index 000000000..8288dcfb8 --- /dev/null +++ b/qiskit/aqua/artificial_intelligence/qgans_for_loading_random.ipynb @@ -0,0 +1,12526 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# _*Qiskit Aqua: qGANs for Loading Random Distributions*_ \n", + "\n", + "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", + "\n", + "***\n", + "### Contributors\n", + "Christa Zoufal[1,2], Stefan Woerner[1]\n", + "### Affliation\n", + "- [1]IBMQ\n", + "- [2]ETH Zurich\n", + "\n", + "### Introduction\n", + "Given $k$-dimensional data samples, we employ a quantum Generative Adversarial Network (qGAN) to learn the data's underlying random distribution and to load it directly into a quantum state: \n", + "$$\\lvert g_{\\theta}\\rangle = \\sum\\limits_{j=0}^{2^n-1}\\sqrt{p_{\\theta}^{j}}\\lvert{j}\\rangle$$\n", + "where $p_{\\theta}^{j}$ describe the occurrence probabilities of the basis states $\\vert j\\rangle$. \n", + "\n", + "The aim of the qGAN training is to generate a state $\\lvert g_{\\theta}\\rangle$ where $p_{\\theta}^{j}$, for $j\\in \\left\\{0, \\ldots, {2^n-1} \\right\\}$, describe a probability distribution that is close to the distribution underlying the training data $X=\\left\\{x^0, \\ldots, x^{k-1} \\right\\}$.\n", + "\n", + "For further details please refer to Quantum Generative Adversarial Networks for Learning and Loading Random Distributions. Zoufal, Lucchi, Woerner. 2019." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "#!/usr/bin/env python\n", + "# coding: utf-8\n", + "from __future__ import absolute_import, division, print_function\n", + "\n", + "import numpy as np\n", + "\n", + "import matplotlib\n", + "matplotlib.use('TkAgg')\n", + "import matplotlib.pyplot as plt\n", + "\n", + "%matplotlib inline\n", + "\n", + "\n", + "import time\n", + "\n", + "start = time.time()\n", + "\n", + "from torch import optim\n", + "from qiskit.aqua.algorithms.adaptive.qgan.discriminator import DiscriminatorNet\n", + "\n", + "from qiskit.aqua.components.optimizers import ADAM\n", + "from qiskit.aqua.components.uncertainty_models import UniformDistribution, UnivariateVariationalDistribution \n", + "from qiskit.aqua.components.variational_forms import RY\n", + "\n", + "from qiskit.aqua.algorithms.adaptive.qgan.qgan import QGAN\n", + "\n", + "from qiskit.aqua import aqua_globals, QuantumInstance\n", + "\n", + "from qiskit import BasicAer" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Load the Training Data\n", + "First, we need to load the $k$-dimensional training data samples (here k=1).
\n", + "Next, the data resolution is set, i.e. the min/max data values and the number of qubits used to represent each data dimension." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# Number training data samples\n", + "N = 10000 \n", + "\n", + "# Load data samples from log-normal distribution with mean=1 and standard deviation=1\n", + "mu = 1\n", + "sigma = 1\n", + "real_data = np.random.lognormal(mean = mu, sigma=sigma, size=N)\n", + "\n", + "# Set the data resolution\n", + "# Set upper and lower data values as list of k min/max data values [[min_0,max_0],...,[min_k-1,max_k-1]]\n", + "bounds = np.array([0.,3.]) \n", + "# Set number of qubits per data dimension as list of k qubit values[#q_0,...,#q_k-1]\n", + "num_qubits = [2]\n", + "k = len(num_qubits)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Initialize the qGAN\n", + "The qGAN consists of a quantum generator $G_{\\theta}$, a variational quantum circuit, and a classical discriminator $D_{\\phi}$, a neural network.
\n", + "To implement the quantum generator, we choose a depth-$1$ variational form that implements $R_Y$ rotations and $CZ$ gates which takes a uniform distribution as an input state. Notably, for $k>1$ the generator's parameters must be chosen carefully. For example, the circuit depth should $>1$ becaue the higher the circuit depth the because higher circuit depths enable the representation of more complex structures.
\n", + "The classical discriminator is given by a $3$-layer neural network that applies linear transformations, leaky ReLU functions in the hidden layers and a sigmoid function in the output layer. Notably, the neural network is implemented with PyTorch. Please refer to https://pytorch.org/get-started/locally/ for PyTorch installation instructions.
\n", + "Here, both networks are updated with the ADAM optimization algorithm." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "# Set number of training epochs\n", + "# Note: The algorithm's runtime can be shortened by reducing the number of training epochs.\n", + "num_epochs = 3000\n", + "# Batch size\n", + "batch_size = 1000\n", + "\n", + "# Initialize qGAN\n", + "qgan = QGAN(real_data, bounds, num_qubits, batch_size, num_epochs, snapshot_dir=None)\n", + "\n", + "# Set quantum instance to run the quantum generator\n", + "backend = BasicAer.get_backend('statevector_simulator')\n", + "qgan.set_quantum_instance(QuantumInstance(backend=backend, shots=batch_size, coupling_map=None, circuit_caching=False))\n", + "\n", + "\n", + "# Set entangler map\n", + "entangler_map = [[0, 1]]\n", + " \n", + "# Set variational form\n", + "var_form = RY(int(np.sum(num_qubits)), depth=1, entangler_map=entangler_map, entanglement_gate='cz')\n", + "# Set generator's initial parameters\n", + "init_params = aqua_globals.random.rand(var_form._num_parameters) * 2 * 1e-2\n", + "# Set an initial state for the generator circuit\n", + "init_dist = UniformDistribution(np.sum(num_qubits), low=bounds[0], high=bounds[1])\n", + "# Set generator circuit\n", + "g_circuit = UnivariateVariationalDistribution(sum(num_qubits), var_form, init_params,\n", + " initial_distribution=init_dist, low=bounds[0], high=bounds[1])\n", + "# Set generator optimizer\n", + "g_optimizer = ADAM(maxiter=1, tol=1e-6, lr=1e-5, beta_1=0.9, beta_2=0.99, noise_factor=1e-6,\n", + " eps=1e-10, amsgrad=True)\n", + "# Set quantum generator\n", + "qgan.set_generator(generator_circuit=g_circuit, generator_optimizer=g_optimizer)\n", + "\n", + "# Set discriminator network\n", + "d_net = DiscriminatorNet(n_features=k)\n", + "# Set discriminator optimizer\n", + "d_optimizer = optim.Adam(d_net.parameters(), lr=1e-5, amsgrad=True)\n", + "# Set classical discriminator neural network\n", + "qgan.set_discriminator(discriminator_net=d_net, discriminator_optimizer=d_optimizer)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Run the qGAN Training\n", + "During the training the discriminator's and the generator's parameters are updated alternately w.r.t the following loss functions:\n", + "$$ L_G\\left(\\phi, \\theta\\right) = -\\frac{1}{m}\\sum\\limits_{l=1}^{m}\\left[\\log\\left(D_{\\phi}\\left(g^{l}\\right)\\right)\\right] $$\n", + "and\n", + "$$ L_D\\left(\\phi, \\theta\\right) =\n", + "\t\\frac{1}{m}\\sum\\limits_{l=1}^{m}\\left[\\log D_{\\phi}\\left(x^{l}\\right) + \\log\\left(1-D_{\\phi}\\left(g^{l}\\right)\\right)\\right], $$\n", + "with $m$ denoting the batch size and $g^l$ describing the data samples generated by the quantum generator." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 1/3000...\n", + "Loss Discriminator: 0.6977\n", + "Loss Generator: 0.6754\n", + "Relative Entropy: 0.1783\n", + "Epoch 2/3000...\n", + "Loss Discriminator: 0.6964\n", + "Loss Generator: 0.6806\n", + "Relative Entropy: 0.1783\n", + "Epoch 3/3000...\n", + "Loss Discriminator: 0.6948\n", + "Loss Generator: 0.6832\n", + "Relative Entropy: 0.1784\n", + "Epoch 4/3000...\n", + "Loss Discriminator: 0.6935\n", + "Loss Generator: 0.6851\n", + "Relative Entropy: 0.1784\n", + "Epoch 5/3000...\n", + "Loss Discriminator: 0.6923\n", + "Loss Generator: 0.687\n", + "Relative Entropy: 0.1784\n", + "Epoch 6/3000...\n", + "Loss Discriminator: 0.6912\n", + "Loss Generator: 0.6864\n", + "Relative Entropy: 0.1783\n", + "Epoch 7/3000...\n", + "Loss Discriminator: 0.6901\n", + "Loss Generator: 0.6865\n", + "Relative Entropy: 0.1783\n", + "Epoch 8/3000...\n", + "Loss Discriminator: 0.689\n", + "Loss Generator: 0.6879\n", + "Relative Entropy: 0.1782\n", + "Epoch 9/3000...\n", + "Loss Discriminator: 0.6875\n", + "Loss Generator: 0.6894\n", + "Relative Entropy: 0.1781\n", + "Epoch 10/3000...\n", + "Loss Discriminator: 0.6868\n", + "Loss Generator: 0.6924\n", + "Relative Entropy: 0.1781\n", + "Epoch 11/3000...\n", + "Loss Discriminator: 0.6857\n", + "Loss Generator: 0.6923\n", + "Relative Entropy: 0.178\n", + "Epoch 12/3000...\n", + "Loss Discriminator: 0.6862\n", + "Loss Generator: 0.6922\n", + "Relative Entropy: 0.1779\n", + "Epoch 13/3000...\n", + "Loss Discriminator: 0.6845\n", + "Loss Generator: 0.6939\n", + "Relative Entropy: 0.1779\n", + "Epoch 14/3000...\n", + "Loss Discriminator: 0.6846\n", + "Loss Generator: 0.6968\n", + "Relative Entropy: 0.1778\n", + "Epoch 15/3000...\n", + "Loss Discriminator: 0.6825\n", + "Loss Generator: 0.7001\n", + "Relative Entropy: 0.1777\n", + "Epoch 16/3000...\n", + "Loss Discriminator: 0.6821\n", + "Loss Generator: 0.7018\n", + "Relative Entropy: 0.1777\n", + "Epoch 17/3000...\n", + "Loss Discriminator: 0.6815\n", + "Loss Generator: 0.7014\n", + "Relative Entropy: 0.1776\n", + "Epoch 18/3000...\n", + "Loss Discriminator: 0.6814\n", + "Loss Generator: 0.7014\n", + "Relative Entropy: 0.1775\n", + "Epoch 19/3000...\n", + "Loss Discriminator: 0.6809\n", + "Loss Generator: 0.7023\n", + "Relative Entropy: 0.1775\n", + "Epoch 20/3000...\n", + "Loss Discriminator: 0.6796\n", + "Loss Generator: 0.7043\n", + "Relative Entropy: 0.1774\n", + "Epoch 21/3000...\n", + "Loss Discriminator: 0.6816\n", + "Loss Generator: 0.7066\n", + "Relative Entropy: 0.1773\n", + "Epoch 22/3000...\n", + "Loss Discriminator: 0.6793\n", + "Loss Generator: 0.7076\n", + "Relative Entropy: 0.1772\n", + "Epoch 23/3000...\n", + "Loss Discriminator: 0.68\n", + "Loss Generator: 0.7073\n", + "Relative Entropy: 0.1772\n", + "Epoch 24/3000...\n", + "Loss Discriminator: 0.6775\n", + "Loss Generator: 0.7097\n", + "Relative Entropy: 0.1771\n", + "Epoch 25/3000...\n", + "Loss Discriminator: 0.6782\n", + "Loss Generator: 0.7111\n", + "Relative Entropy: 0.177\n", + "Epoch 26/3000...\n", + "Loss 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+ "Loss Generator: 0.7092\n", + "Relative Entropy: 0.0735\n", + "Epoch 1955/3000...\n", + "Loss Discriminator: 0.6818\n", + "Loss Generator: 0.71\n", + "Relative Entropy: 0.0734\n", + "Epoch 1956/3000...\n", + "Loss Discriminator: 0.6827\n", + "Loss Generator: 0.7077\n", + "Relative Entropy: 0.0734\n", + "Epoch 1957/3000...\n", + "Loss Discriminator: 0.6841\n", + "Loss Generator: 0.7111\n", + "Relative Entropy: 0.0733\n", + "Epoch 1958/3000...\n", + "Loss Discriminator: 0.6822\n", + "Loss Generator: 0.7084\n", + "Relative Entropy: 0.0733\n", + "Epoch 1959/3000...\n", + "Loss Discriminator: 0.6832\n", + "Loss Generator: 0.7069\n", + "Relative Entropy: 0.0733\n", + "Epoch 1960/3000...\n", + "Loss Discriminator: 0.6834\n", + "Loss Generator: 0.7079\n", + "Relative Entropy: 0.0732\n", + "Epoch 1961/3000...\n", + "Loss Discriminator: 0.6838\n", + "Loss Generator: 0.7095\n", + "Relative Entropy: 0.0732\n", + "Epoch 1962/3000...\n", + "Loss Discriminator: 0.6834\n", + "Loss Generator: 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+ "Relative Entropy: 0.0375\n", + "Epoch 2980/3000...\n", + "Loss Discriminator: 0.6879\n", + "Loss Generator: 0.6981\n", + "Relative Entropy: 0.0374\n", + "Epoch 2981/3000...\n", + "Loss Discriminator: 0.6872\n", + "Loss Generator: 0.7012\n", + "Relative Entropy: 0.0374\n", + "Epoch 2982/3000...\n", + "Loss Discriminator: 0.6895\n", + "Loss Generator: 0.704\n", + "Relative Entropy: 0.0374\n", + "Epoch 2983/3000...\n", + "Loss Discriminator: 0.6879\n", + "Loss Generator: 0.6966\n", + "Relative Entropy: 0.0374\n", + "Epoch 2984/3000...\n", + "Loss Discriminator: 0.6875\n", + "Loss Generator: 0.6983\n", + "Relative Entropy: 0.0373\n", + "Epoch 2985/3000...\n", + "Loss Discriminator: 0.6882\n", + "Loss Generator: 0.7053\n", + "Relative Entropy: 0.0373\n", + "Epoch 2986/3000...\n", + "Loss Discriminator: 0.6875\n", + "Loss Generator: 0.7009\n", + "Relative Entropy: 0.0373\n", + "Epoch 2987/3000...\n", + "Loss Discriminator: 0.6884\n", + "Loss Generator: 0.6982\n", + "Relative Entropy: 0.0373\n", + "Epoch 2988/3000...\n", + "Loss Discriminator: 0.6879\n", + "Loss Generator: 0.701\n", + "Relative Entropy: 0.0372\n", + "Epoch 2989/3000...\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Loss Discriminator: 0.687\n", + "Loss Generator: 0.7023\n", + "Relative Entropy: 0.0372\n", + "Epoch 2990/3000...\n", + "Loss Discriminator: 0.6879\n", + "Loss Generator: 0.7025\n", + "Relative Entropy: 0.0372\n", + "Epoch 2991/3000...\n", + "Loss Discriminator: 0.6886\n", + "Loss Generator: 0.6976\n", + "Relative Entropy: 0.0372\n", + "Epoch 2992/3000...\n", + "Loss Discriminator: 0.6884\n", + "Loss Generator: 0.7018\n", + "Relative Entropy: 0.0371\n", + "Epoch 2993/3000...\n", + "Loss Discriminator: 0.6886\n", + "Loss Generator: 0.7024\n", + "Relative Entropy: 0.0371\n", + "Epoch 2994/3000...\n", + "Loss Discriminator: 0.6887\n", + "Loss Generator: 0.699\n", + "Relative Entropy: 0.0371\n", + "Epoch 2995/3000...\n", + "Loss Discriminator: 0.6886\n", + "Loss Generator: 0.696\n", + "Relative Entropy: 0.037\n", + "Epoch 2996/3000...\n", + "Loss Discriminator: 0.6887\n", + "Loss Generator: 0.703\n", + "Relative Entropy: 0.037\n", + "Epoch 2997/3000...\n", + "Loss Discriminator: 0.6879\n", + "Loss Generator: 0.7013\n", + "Relative Entropy: 0.037\n", + "Epoch 2998/3000...\n", + "Loss Discriminator: 0.6886\n", + "Loss Generator: 0.6993\n", + "Relative Entropy: 0.037\n", + "Epoch 2999/3000...\n", + "Loss Discriminator: 0.6884\n", + "Loss Generator: 0.7012\n", + "Relative Entropy: 0.0369\n", + "Epoch 3000/3000...\n", + "Loss Discriminator: 0.6887\n", + "Loss Generator: 0.7016\n", + "Relative Entropy: 0.0369\n", + "qGAN training runtime: 35.25595039923986 min\n" + ] + } + ], + "source": [ + "# Run qGAN\n", + "qgan.run()\n", + "\n", + "# Runtime\n", + "end = time.time()\n", + "print('qGAN training runtime: ', (end - start)/60., ' min')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Training Progress & Outcome\n", + "Now, we plot the evolution of the generator's and the discriminator's loss functions during the training as well as the progress in the relative entropy between the trained and the target distribution.\n", + "
Finally, we also compare the cumulative distribution function (CDF) of the trained distribution to the CDF of the target distribution." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Plot progress w.r.t the generator's and the discriminator's loss function\n", + "t_steps = np.arange(num_epochs)\n", + "plt.figure(figsize=(6,5))\n", + "plt.title(\"Progress in the loss function\")\n", + "plt.plot(t_steps, qgan.g_loss, label = \"Generator loss function\", color = 'mediumvioletred', linewidth = 2)\n", + "plt.plot(t_steps, qgan.d_loss, label = \"Discriminator loss function\", color = 'rebeccapurple', linewidth = 2)\n", + "plt.grid()\n", + "plt.legend(loc = 'best')\n", + "plt.xlabel('time steps')\n", + "plt.ylabel('loss')\n", + "plt.show()\n", + "\n", + "\n", + "# Plot progress w.r.t relative entropy\n", + "plt.figure(figsize=(6,5))\n", + "plt.title(\"Relative Entropy \")\n", + "plt.plot(np.linspace(0, num_epochs, len(qgan.rel_entr)), qgan.rel_entr, color ='mediumblue', lw=4, ls=':')\n", + "plt.grid()\n", + "plt.xlabel('time steps')\n", + "plt.ylabel('relative entropy')\n", + "plt.show()\n", + "\n", + "#Plot the PDF of the resulting distribution against the target distribution, i.e. log-normal\n", + "log_normal = np.random.lognormal(mean=1, sigma=1, size=100000)\n", + "log_normal = np.round(log_normal)\n", + "log_normal = log_normal[log_normal <= bounds[1]]\n", + "temp = []\n", + "for i in range(int(bounds[1]+1)):\n", + " temp += [np.sum(log_normal==i)]\n", + "log_normal = np.array(temp / sum(temp))\n", + "\n", + "plt.figure(figsize=(6,5))\n", + "plt.title(\"CDF\")\n", + "samples_g, prob_g = qgan.generator.get_samples(qgan.quantum_instance, shots=10000)\n", + "samples_g = np.array(samples_g)\n", + "samples_g = samples_g.flatten()\n", + "num_bins = len(prob_g)\n", + "plt.bar(samples_g, np.cumsum(prob_g), color='royalblue', width= 0.8, label='simulation')\n", + "plt.plot( np.cumsum(log_normal),'-o', label='log-normal', color='deepskyblue', linewidth=4, markersize=12)\n", + "plt.xticks(np.arange(min(samples_g), max(samples_g)+1, 1.0))\n", + "plt.grid()\n", + "plt.xlabel('x')\n", + "plt.ylabel('p(x)')\n", + "plt.legend(loc='best')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "QiskitDevenv", + "language": "python", + "name": "qiskitdevenv" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.3" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb b/qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb index f9c3abb7b..8288dcfb8 100644 --- a/qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb +++ b/qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb @@ -27,7 +27,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ @@ -59,7 +59,7 @@ "\n", "from qiskit.aqua import aqua_globals, QuantumInstance\n", "\n", - "from qiskit import Aer" + "from qiskit import BasicAer" ] }, { @@ -73,7 +73,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -106,7 +106,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 7, "metadata": {}, "outputs": [], "source": [ @@ -120,7 +120,7 @@ "qgan = QGAN(real_data, bounds, num_qubits, batch_size, num_epochs, snapshot_dir=None)\n", "\n", "# Set quantum instance to run the quantum generator\n", - "backend = Aer.get_backend('statevector_simulator')\n", + "backend = BasicAer.get_backend('statevector_simulator')\n", "qgan.set_quantum_instance(QuantumInstance(backend=backend, shots=batch_size, coupling_map=None, circuit_caching=False))\n", "\n", "\n", @@ -134,7 +134,7 @@ "# Set an initial state for the generator circuit\n", "init_dist = UniformDistribution(np.sum(num_qubits), low=bounds[0], high=bounds[1])\n", "# Set generator circuit\n", - "g_circuit = UnivariateVariationalDistribution(np.sum(num_qubits), var_form, init_params,\n", + "g_circuit = UnivariateVariationalDistribution(sum(num_qubits), var_form, init_params,\n", " initial_distribution=init_dist, low=bounds[0], high=bounds[1])\n", "# Set generator optimizer\n", "g_optimizer = ADAM(maxiter=1, tol=1e-6, lr=1e-5, beta_1=0.9, beta_2=0.99, noise_factor=1e-6,\n", @@ -165,7 +165,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 8, "metadata": {}, "outputs": [ { @@ -173,353 +173,353 @@ "output_type": "stream", "text": [ "Epoch 1/3000...\n", - "Loss Discriminator: 0.6973\n", - "Loss Generator: 0.6708\n", - "Relative Entropy: 0.1718\n", + "Loss Discriminator: 0.6977\n", + "Loss Generator: 0.6754\n", + "Relative Entropy: 0.1783\n", "Epoch 2/3000...\n", - "Loss Discriminator: 0.6962\n", - "Loss Generator: 0.679\n", - "Relative Entropy: 0.1719\n", + "Loss Discriminator: 0.6964\n", + "Loss Generator: 0.6806\n", + "Relative Entropy: 0.1783\n", "Epoch 3/3000...\n", "Loss Discriminator: 0.6948\n", - "Loss Generator: 0.6824\n", - "Relative Entropy: 0.172\n", + "Loss Generator: 0.6832\n", + "Relative Entropy: 0.1784\n", "Epoch 4/3000...\n", - "Loss Discriminator: 0.6934\n", - "Loss Generator: 0.6843\n", - "Relative Entropy: 0.172\n", + "Loss Discriminator: 0.6935\n", + "Loss Generator: 0.6851\n", + "Relative Entropy: 0.1784\n", "Epoch 5/3000...\n", - "Loss Discriminator: 0.692\n", - "Loss Generator: 0.6861\n", - "Relative Entropy: 0.1719\n", + "Loss Discriminator: 0.6923\n", + "Loss Generator: 0.687\n", + "Relative Entropy: 0.1784\n", "Epoch 6/3000...\n", - "Loss Discriminator: 0.6909\n", - "Loss Generator: 0.6863\n", - "Relative Entropy: 0.1719\n", + "Loss Discriminator: 0.6912\n", + "Loss Generator: 0.6864\n", + "Relative Entropy: 0.1783\n", "Epoch 7/3000...\n", - "Loss Discriminator: 0.6896\n", - "Loss Generator: 0.6854\n", - "Relative Entropy: 0.1718\n", + "Loss Discriminator: 0.6901\n", + "Loss Generator: 0.6865\n", + "Relative Entropy: 0.1783\n", "Epoch 8/3000...\n", "Loss Discriminator: 0.689\n", - "Loss Generator: 0.6867\n", - "Relative Entropy: 0.1718\n", + "Loss Generator: 0.6879\n", + "Relative Entropy: 0.1782\n", "Epoch 9/3000...\n", - "Loss Discriminator: 0.6882\n", - "Loss Generator: 0.6898\n", - "Relative Entropy: 0.1717\n", + "Loss Discriminator: 0.6875\n", + "Loss Generator: 0.6894\n", + "Relative Entropy: 0.1781\n", "Epoch 10/3000...\n", - "Loss Discriminator: 0.6871\n", - "Loss Generator: 0.6905\n", - "Relative Entropy: 0.1717\n", + "Loss Discriminator: 0.6868\n", + "Loss Generator: 0.6924\n", + "Relative Entropy: 0.1781\n", "Epoch 11/3000...\n", - "Loss Discriminator: 0.6865\n", - "Loss Generator: 0.6892\n", - "Relative Entropy: 0.1716\n", + "Loss Discriminator: 0.6857\n", + "Loss Generator: 0.6923\n", + "Relative Entropy: 0.178\n", "Epoch 12/3000...\n", - "Loss Discriminator: 0.6856\n", - "Loss Generator: 0.6938\n", - "Relative Entropy: 0.1715\n", + "Loss Discriminator: 0.6862\n", + "Loss Generator: 0.6922\n", + "Relative Entropy: 0.1779\n", "Epoch 13/3000...\n", - "Loss Discriminator: 0.6849\n", - "Loss Generator: 0.6957\n", - "Relative Entropy: 0.1715\n", + "Loss Discriminator: 0.6845\n", + "Loss Generator: 0.6939\n", + "Relative Entropy: 0.1779\n", "Epoch 14/3000...\n", - "Loss Discriminator: 0.6849\n", - "Loss Generator: 0.6967\n", - "Relative Entropy: 0.1714\n", + "Loss Discriminator: 0.6846\n", + "Loss Generator: 0.6968\n", + "Relative Entropy: 0.1778\n", "Epoch 15/3000...\n", - "Loss Discriminator: 0.6829\n", - "Loss Generator: 0.6958\n", - "Relative Entropy: 0.1713\n", - "Epoch 16/3000...\n", - "Loss Discriminator: 0.6824\n", + "Loss Discriminator: 0.6825\n", "Loss Generator: 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-1227,349 +1227,349 @@ "name": "stdout", "output_type": "stream", "text": [ - "Loss Discriminator: 0.6706\n", - "Loss Generator: 0.7331\n", - "Relative Entropy: 0.1549\n", + "Loss Discriminator: 0.6705\n", + "Loss Generator: 0.7328\n", + "Relative Entropy: 0.1612\n", "Epoch 261/3000...\n", - "Loss Discriminator: 0.6708\n", - "Loss Generator: 0.7322\n", - "Relative Entropy: 0.1548\n", + "Loss Discriminator: 0.67\n", + "Loss Generator: 0.7339\n", + "Relative Entropy: 0.1611\n", "Epoch 262/3000...\n", - "Loss Discriminator: 0.6704\n", - "Loss Generator: 0.7358\n", - "Relative Entropy: 0.1547\n", + "Loss Discriminator: 0.6682\n", + "Loss Generator: 0.7332\n", + "Relative Entropy: 0.1611\n", "Epoch 263/3000...\n", - "Loss Discriminator: 0.6721\n", - "Loss Generator: 0.7342\n", - "Relative Entropy: 0.1547\n", + "Loss Discriminator: 0.6695\n", + "Loss Generator: 0.7336\n", + "Relative Entropy: 0.161\n", "Epoch 264/3000...\n", - "Loss Discriminator: 0.6686\n", - "Loss Generator: 0.7317\n", - 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+ "Relative Entropy: 0.0922\n", "Epoch 1544/3000...\n" ] }, @@ -6453,345 +6453,345 @@ "name": "stdout", "output_type": "stream", "text": [ - "Loss Discriminator: 0.6824\n", - "Loss Generator: 0.7138\n", - "Relative Entropy: 0.0865\n", + "Loss Discriminator: 0.6789\n", + "Loss Generator: 0.714\n", + "Relative Entropy: 0.0921\n", "Epoch 1545/3000...\n", - "Loss Discriminator: 0.6798\n", - "Loss Generator: 0.7107\n", - "Relative Entropy: 0.0865\n", + "Loss Discriminator: 0.6807\n", + "Loss Generator: 0.7132\n", + "Relative Entropy: 0.0921\n", "Epoch 1546/3000...\n", - "Loss Discriminator: 0.6837\n", - "Loss Generator: 0.7134\n", - "Relative Entropy: 0.0864\n", + "Loss Discriminator: 0.6811\n", + "Loss Generator: 0.7125\n", + "Relative Entropy: 0.092\n", "Epoch 1547/3000...\n", - "Loss Discriminator: 0.6815\n", - "Loss Generator: 0.7159\n", - "Relative Entropy: 0.0864\n", + "Loss Discriminator: 0.6808\n", + "Loss Generator: 0.7108\n", + "Relative Entropy: 0.092\n", "Epoch 1548/3000...\n", 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0.0803\n", "Epoch 1799/3000...\n" ] }, @@ -7491,345 +7491,345 @@ "name": "stdout", "output_type": "stream", "text": [ - "Loss Discriminator: 0.6803\n", - "Loss Generator: 0.7099\n", - "Relative Entropy: 0.075\n", + "Loss Discriminator: 0.6827\n", + "Loss Generator: 0.7073\n", + "Relative Entropy: 0.0803\n", "Epoch 1800/3000...\n", - "Loss Discriminator: 0.6828\n", - "Loss Generator: 0.7106\n", - "Relative Entropy: 0.0749\n", - "Epoch 1801/3000...\n", "Loss Discriminator: 0.682\n", - "Loss Generator: 0.711\n", - "Relative Entropy: 0.0749\n", + "Loss Generator: 0.7098\n", + "Relative Entropy: 0.0802\n", + "Epoch 1801/3000...\n", + "Loss Discriminator: 0.683\n", + "Loss Generator: 0.713\n", + "Relative Entropy: 0.0802\n", "Epoch 1802/3000...\n", - "Loss Discriminator: 0.6833\n", - "Loss Generator: 0.7099\n", - "Relative Entropy: 0.0749\n", - "Epoch 1803/3000...\n", - "Loss Discriminator: 0.6827\n", - "Loss Generator: 0.7101\n", - "Relative Entropy: 0.0748\n", + "Loss Discriminator: 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"Relative Entropy: 0.073\n", "Epoch 1967/3000...\n", - "Loss Discriminator: 0.6831\n", - "Loss Generator: 0.7084\n", - "Relative Entropy: 0.0678\n", + "Loss Discriminator: 0.6834\n", + "Loss Generator: 0.7086\n", + "Relative Entropy: 0.0729\n", "Epoch 1968/3000...\n", - "Loss Discriminator: 0.6842\n", - "Loss Generator: 0.7076\n", - "Relative Entropy: 0.0678\n", + "Loss Discriminator: 0.6836\n", + "Loss Generator: 0.7099\n", + "Relative Entropy: 0.0729\n", "Epoch 1969/3000...\n" ] }, @@ -8183,345 +8183,345 @@ "name": "stdout", "output_type": "stream", "text": [ - "Loss Discriminator: 0.683\n", - "Loss Generator: 0.708\n", - "Relative Entropy: 0.0677\n", + "Loss Discriminator: 0.6832\n", + "Loss Generator: 0.7086\n", + "Relative Entropy: 0.0728\n", "Epoch 1970/3000...\n", "Loss Discriminator: 0.6825\n", - "Loss Generator: 0.711\n", - "Relative Entropy: 0.0677\n", + "Loss Generator: 0.7112\n", + "Relative Entropy: 0.0728\n", "Epoch 1971/3000...\n", - "Loss Discriminator: 0.6832\n", - 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0.072\n", "Epoch 1990/3000...\n", - "Loss Discriminator: 0.6831\n", - "Loss Generator: 0.7086\n", - "Relative Entropy: 0.0669\n", + "Loss Discriminator: 0.6825\n", + "Loss Generator: 0.7115\n", + "Relative Entropy: 0.0719\n", "Epoch 1991/3000...\n", - "Loss Discriminator: 0.6842\n", - "Loss Generator: 0.7096\n", - "Relative Entropy: 0.0668\n", + "Loss Discriminator: 0.6846\n", + "Loss Generator: 0.7084\n", + "Relative Entropy: 0.0719\n", "Epoch 1992/3000...\n", - "Loss Discriminator: 0.6834\n", - "Loss Generator: 0.7087\n", - "Relative Entropy: 0.0668\n", + "Loss Discriminator: 0.6841\n", + "Loss Generator: 0.7057\n", + "Relative Entropy: 0.0719\n", "Epoch 1993/3000...\n", - "Loss Discriminator: 0.6845\n", - "Loss Generator: 0.7051\n", - "Relative Entropy: 0.0667\n", + "Loss Discriminator: 0.6852\n", + "Loss Generator: 0.7109\n", + "Relative Entropy: 0.0718\n", "Epoch 1994/3000...\n", - "Loss Discriminator: 0.6825\n", - "Loss Generator: 0.7078\n", - "Relative Entropy: 0.0667\n", + "Loss Discriminator: 0.6858\n", + "Loss Generator: 0.7085\n", + "Relative Entropy: 0.0718\n", "Epoch 1995/3000...\n", - "Loss Discriminator: 0.6834\n", - "Loss Generator: 0.7095\n", - "Relative Entropy: 0.0667\n", + "Loss Discriminator: 0.6818\n", + "Loss Generator: 0.7073\n", + "Relative Entropy: 0.0717\n", "Epoch 1996/3000...\n", - "Loss Discriminator: 0.6837\n", - "Loss Generator: 0.7087\n", - "Relative Entropy: 0.0666\n", + "Loss Discriminator: 0.6849\n", + "Loss Generator: 0.7081\n", + "Relative Entropy: 0.0717\n", "Epoch 1997/3000...\n", - "Loss Discriminator: 0.6835\n", - "Loss Generator: 0.707\n", - "Relative Entropy: 0.0666\n", + "Loss Discriminator: 0.6827\n", + "Loss Generator: 0.71\n", + "Relative Entropy: 0.0716\n", "Epoch 1998/3000...\n", - "Loss Discriminator: 0.6824\n", - "Loss Generator: 0.7092\n", - "Relative Entropy: 0.0665\n", + "Loss Discriminator: 0.6836\n", + "Loss Generator: 0.7081\n", + "Relative Entropy: 0.0716\n", "Epoch 1999/3000...\n", - "Loss 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0.0661\n", + "Loss Discriminator: 0.6833\n", + "Loss Generator: 0.7098\n", + "Relative Entropy: 0.0712\n", "Epoch 2009/3000...\n", - "Loss Discriminator: 0.6837\n", - "Loss Generator: 0.7087\n", - "Relative Entropy: 0.0661\n", + "Loss Discriminator: 0.6852\n", + "Loss Generator: 0.7093\n", + "Relative Entropy: 0.0711\n", "Epoch 2010/3000...\n", - "Loss Discriminator: 0.6834\n", - "Loss Generator: 0.7085\n", - "Relative Entropy: 0.0661\n", + "Loss Discriminator: 0.6824\n", + "Loss Generator: 0.7096\n", + "Relative Entropy: 0.0711\n", "Epoch 2011/3000...\n", - "Loss Discriminator: 0.6828\n", - "Loss Generator: 0.7073\n", - "Relative Entropy: 0.066\n", + "Loss Discriminator: 0.6833\n", + "Loss Generator: 0.7044\n", + "Relative Entropy: 0.0711\n", "Epoch 2012/3000...\n", - "Loss Discriminator: 0.6834\n", + "Loss Discriminator: 0.6845\n", "Loss Generator: 0.7085\n", - "Relative Entropy: 0.066\n", + "Relative Entropy: 0.071\n", "Epoch 2013/3000...\n", - "Loss Discriminator: 0.6827\n", - "Loss Generator: 0.7088\n", - "Relative Entropy: 0.0659\n", + "Loss Discriminator: 0.6837\n", + "Loss Generator: 0.7104\n", + "Relative Entropy: 0.071\n", "Epoch 2014/3000...\n", - "Loss Discriminator: 0.6853\n", - "Loss Generator: 0.7071\n", - "Relative Entropy: 0.0659\n", + "Loss Discriminator: 0.6827\n", + "Loss Generator: 0.7083\n", + "Relative Entropy: 0.0709\n", "Epoch 2015/3000...\n", - "Loss Discriminator: 0.6843\n", - "Loss Generator: 0.7067\n", - "Relative Entropy: 0.0658\n", + "Loss Discriminator: 0.6851\n", + "Loss Generator: 0.7093\n", + "Relative Entropy: 0.0709\n", "Epoch 2016/3000...\n", - "Loss Discriminator: 0.6826\n", - "Loss Generator: 0.7078\n", - "Relative Entropy: 0.0658\n", - "Epoch 2017/3000...\n", - "Loss Discriminator: 0.6844\n", + "Loss Discriminator: 0.6829\n", "Loss Generator: 0.7091\n", - "Relative Entropy: 0.0658\n", + "Relative Entropy: 0.0709\n", + "Epoch 2017/3000...\n", + "Loss Discriminator: 0.6839\n", + "Loss Generator: 0.7068\n", + "Relative 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"Relative Entropy: 0.0656\n", + "Loss Discriminator: 0.6848\n", + "Loss Generator: 0.7078\n", + "Relative Entropy: 0.0706\n", "Epoch 2023/3000...\n", - "Loss Discriminator: 0.6847\n", - "Loss Generator: 0.7058\n", - "Relative Entropy: 0.0655\n", - "Epoch 2024/3000...\n", - "Loss Discriminator: 0.684\n", + "Loss Discriminator: 0.6834\n", "Loss Generator: 0.708\n", - "Relative Entropy: 0.0655\n", + "Relative Entropy: 0.0706\n", + "Epoch 2024/3000...\n", + "Loss Discriminator: 0.6855\n", + "Loss Generator: 0.7088\n", + "Relative Entropy: 0.0705\n", "Epoch 2025/3000...\n", - "Loss Discriminator: 0.6833\n", - "Loss Generator: 0.7103\n", - "Relative Entropy: 0.0654\n", + "Loss Discriminator: 0.6846\n", + "Loss Generator: 0.7086\n", + "Relative Entropy: 0.0705\n", "Epoch 2026/3000...\n", - "Loss Discriminator: 0.6857\n", - "Loss Generator: 0.7087\n", - "Relative Entropy: 0.0654\n", + "Loss Discriminator: 0.683\n", + "Loss Generator: 0.7111\n", + "Relative Entropy: 0.0704\n", "Epoch 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0.7109\n", + "Relative Entropy: 0.0702\n", "Epoch 2032/3000...\n", "Loss Discriminator: 0.6848\n", - "Loss Generator: 0.7062\n", - "Relative Entropy: 0.0652\n", + "Loss Generator: 0.7047\n", + "Relative Entropy: 0.0702\n", "Epoch 2033/3000...\n", - "Loss Discriminator: 0.6829\n", - "Loss Generator: 0.7082\n", - "Relative Entropy: 0.0651\n", + "Loss Discriminator: 0.6842\n", + "Loss Generator: 0.7062\n", + "Relative Entropy: 0.0701\n", "Epoch 2034/3000...\n", - "Loss Discriminator: 0.684\n", - "Loss Generator: 0.7081\n", - "Relative Entropy: 0.0651\n", - "Epoch 2035/3000...\n", - "Loss Discriminator: 0.6839\n", + "Loss Discriminator: 0.6843\n", "Loss Generator: 0.7092\n", - "Relative Entropy: 0.065\n", + "Relative Entropy: 0.0701\n", + "Epoch 2035/3000...\n", + "Loss Discriminator: 0.6845\n", + "Loss Generator: 0.711\n", + "Relative Entropy: 0.0701\n", "Epoch 2036/3000...\n", - "Loss Discriminator: 0.6824\n", - "Loss Generator: 0.7086\n", - "Relative Entropy: 0.065\n", + "Loss 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0.6842\n", - "Loss Generator: 0.7064\n", - "Relative Entropy: 0.0648\n", + "Loss Discriminator: 0.6822\n", + "Loss Generator: 0.7096\n", + "Relative Entropy: 0.0698\n", "Epoch 2042/3000...\n", - "Loss Discriminator: 0.6841\n", - "Loss Generator: 0.7087\n", - "Relative Entropy: 0.0647\n", + "Loss Discriminator: 0.6834\n", + "Loss Generator: 0.7062\n", + "Relative Entropy: 0.0698\n", "Epoch 2043/3000...\n", - "Loss Discriminator: 0.6838\n", - "Loss Generator: 0.7082\n", - "Relative Entropy: 0.0647\n", + "Loss Discriminator: 0.683\n", + "Loss Generator: 0.7089\n", + "Relative Entropy: 0.0697\n", "Epoch 2044/3000...\n", - "Loss Discriminator: 0.6839\n", - "Loss Generator: 0.7068\n", - "Relative Entropy: 0.0647\n", + "Loss Discriminator: 0.684\n", + "Loss Generator: 0.7094\n", + "Relative Entropy: 0.0697\n", "Epoch 2045/3000...\n", - "Loss Discriminator: 0.6833\n", - "Loss Generator: 0.7067\n", - "Relative Entropy: 0.0646\n", + "Loss Discriminator: 0.6841\n", + "Loss Generator: 0.709\n", + "Relative Entropy: 0.0696\n", "Epoch 2046/3000...\n", - "Loss Discriminator: 0.6853\n", - "Loss Generator: 0.7097\n", - "Relative Entropy: 0.0646\n", + "Loss Discriminator: 0.6841\n", + "Loss Generator: 0.7085\n", + "Relative Entropy: 0.0696\n", "Epoch 2047/3000...\n", - "Loss Discriminator: 0.6854\n", - "Loss Generator: 0.7075\n", - "Relative Entropy: 0.0645\n", + "Loss Discriminator: 0.6827\n", + "Loss Generator: 0.7057\n", + "Relative Entropy: 0.0696\n", "Epoch 2048/3000...\n", - "Loss Discriminator: 0.6845\n", - "Loss Generator: 0.7072\n", - "Relative Entropy: 0.0645\n", + "Loss Discriminator: 0.6842\n", + "Loss Generator: 0.7093\n", + "Relative Entropy: 0.0695\n", "Epoch 2049/3000...\n", - "Loss Discriminator: 0.6848\n", - "Loss Generator: 0.707\n", - "Relative Entropy: 0.0645\n", - "Epoch 2050/3000...\n", "Loss Discriminator: 0.6837\n", - "Loss Generator: 0.7085\n", - "Relative Entropy: 0.0644\n", + "Loss Generator: 0.7075\n", + "Relative Entropy: 0.0695\n", + "Epoch 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"Loss Generator: 0.7114\n", + "Relative Entropy: 0.0693\n", "Epoch 2055/3000...\n", - "Loss Discriminator: 0.6857\n", - "Loss Generator: 0.7107\n", - "Relative Entropy: 0.0642\n", + "Loss Discriminator: 0.6849\n", + "Loss Generator: 0.7065\n", + "Relative Entropy: 0.0692\n", "Epoch 2056/3000...\n", - "Loss Discriminator: 0.6839\n", - "Loss Generator: 0.7069\n", - "Relative Entropy: 0.0642\n", + "Loss Discriminator: 0.6837\n", + "Loss Generator: 0.7066\n", + "Relative Entropy: 0.0692\n", "Epoch 2057/3000...\n", - "Loss Discriminator: 0.6834\n", - "Loss Generator: 0.7049\n", - "Relative Entropy: 0.0641\n", + "Loss Discriminator: 0.6839\n", + "Loss Generator: 0.7092\n", + "Relative Entropy: 0.0691\n", "Epoch 2058/3000...\n", - "Loss Discriminator: 0.6837\n", - "Loss Generator: 0.7107\n", - "Relative Entropy: 0.0641\n", - "Epoch 2059/3000...\n", "Loss Discriminator: 0.6831\n", - "Loss Generator: 0.7049\n", - "Relative Entropy: 0.0641\n", + "Loss Generator: 0.709\n", + "Relative Entropy: 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"Epoch 2812/3000...\n", - "Loss Discriminator: 0.6885\n", - "Loss Generator: 0.6999\n", - "Relative Entropy: 0.0379\n", + "Loss Discriminator: 0.6877\n", + "Loss Generator: 0.702\n", + "Relative Entropy: 0.0422\n", "Epoch 2813/3000...\n", - "Loss Discriminator: 0.6872\n", - "Loss Generator: 0.7009\n", - "Relative Entropy: 0.0379\n", + "Loss Discriminator: 0.688\n", + "Loss Generator: 0.7034\n", + "Relative Entropy: 0.0422\n", "Epoch 2814/3000...\n", - "Loss Discriminator: 0.6874\n", - "Loss Generator: 0.7036\n", - "Relative Entropy: 0.0379\n", + "Loss Discriminator: 0.6873\n", + "Loss Generator: 0.7008\n", + "Relative Entropy: 0.0421\n", "Epoch 2815/3000...\n", - "Loss Discriminator: 0.6892\n", - "Loss Generator: 0.7015\n", - "Relative Entropy: 0.0378\n", + "Loss Discriminator: 0.6876\n", + "Loss Generator: 0.7016\n", + "Relative Entropy: 0.0421\n", "Epoch 2816/3000...\n", - "Loss Discriminator: 0.6884\n", - "Loss Generator: 0.6991\n", - "Relative Entropy: 0.0378\n", + "Loss 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0.6891\n", - "Loss Generator: 0.7001\n", - "Relative Entropy: 0.0331\n", + "Loss Discriminator: 0.6879\n", + "Loss Generator: 0.701\n", + "Relative Entropy: 0.0372\n", "Epoch 2989/3000...\n" ] }, @@ -12335,54 +12335,54 @@ "name": "stdout", "output_type": "stream", "text": [ - "Loss Discriminator: 0.689\n", - "Loss Generator: 0.703\n", - "Relative Entropy: 0.033\n", + "Loss Discriminator: 0.687\n", + "Loss Generator: 0.7023\n", + "Relative Entropy: 0.0372\n", "Epoch 2990/3000...\n", - "Loss Discriminator: 0.6899\n", - "Loss Generator: 0.7007\n", - "Relative Entropy: 0.033\n", + "Loss Discriminator: 0.6879\n", + "Loss Generator: 0.7025\n", + "Relative Entropy: 0.0372\n", "Epoch 2991/3000...\n", - "Loss Discriminator: 0.6885\n", - "Loss Generator: 0.6984\n", - "Relative Entropy: 0.033\n", + "Loss Discriminator: 0.6886\n", + "Loss Generator: 0.6976\n", + "Relative Entropy: 0.0372\n", "Epoch 2992/3000...\n", "Loss Discriminator: 0.6884\n", - "Loss Generator: 0.6993\n", - "Relative Entropy: 0.033\n", + "Loss Generator: 0.7018\n", + "Relative Entropy: 0.0371\n", "Epoch 2993/3000...\n", - "Loss Discriminator: 0.6891\n", - "Loss Generator: 0.703\n", - "Relative Entropy: 0.0329\n", - "Epoch 2994/3000...\n", "Loss Discriminator: 0.6886\n", - "Loss Generator: 0.6997\n", - "Relative Entropy: 0.0329\n", + "Loss Generator: 0.7024\n", + "Relative Entropy: 0.0371\n", + "Epoch 2994/3000...\n", + "Loss Discriminator: 0.6887\n", + "Loss Generator: 0.699\n", + "Relative Entropy: 0.0371\n", "Epoch 2995/3000...\n", - "Loss Discriminator: 0.6896\n", - "Loss Generator: 0.6955\n", - "Relative Entropy: 0.0329\n", + "Loss Discriminator: 0.6886\n", + "Loss Generator: 0.696\n", + "Relative Entropy: 0.037\n", "Epoch 2996/3000...\n", - "Loss Discriminator: 0.6885\n", - "Loss Generator: 0.7014\n", - "Relative Entropy: 0.0329\n", + "Loss Discriminator: 0.6887\n", + "Loss Generator: 0.703\n", + "Relative Entropy: 0.037\n", "Epoch 2997/3000...\n", - "Loss Discriminator: 0.6896\n", - "Loss Generator: 0.7038\n", - "Relative Entropy: 0.0328\n", + "Loss Discriminator: 0.6879\n", + "Loss Generator: 0.7013\n", + "Relative Entropy: 0.037\n", "Epoch 2998/3000...\n", - "Loss Discriminator: 0.6895\n", - "Loss Generator: 0.6972\n", - "Relative Entropy: 0.0328\n", - "Epoch 2999/3000...\n", - "Loss Discriminator: 0.6898\n", + "Loss Discriminator: 0.6886\n", "Loss Generator: 0.6993\n", - "Relative Entropy: 0.0328\n", + "Relative Entropy: 0.037\n", + "Epoch 2999/3000...\n", + "Loss Discriminator: 0.6884\n", + "Loss Generator: 0.7012\n", + "Relative Entropy: 0.0369\n", "Epoch 3000/3000...\n", - "Loss Discriminator: 0.6896\n", - "Loss Generator: 0.7021\n", - "Relative Entropy: 0.0328\n", - "qGAN training runtime: 162.18758081595104 min\n" + "Loss Discriminator: 0.6887\n", + "Loss Generator: 0.7016\n", + "Relative Entropy: 0.0369\n", + "qGAN training runtime: 35.25595039923986 min\n" ] } ], @@ -12406,12 +12406,12 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 9, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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\n", 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\n", 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\n", 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rueVT+l68jT1JfDvdAH+/F37fwXJfKTWNFGwOMuyUBpO9MCBCITU1lWAwSE5OjoLBA845gsEgqampfpcig8BLZ+DOEjjawdYGw4/UMHX7aZLqo9hwXXpkQITC2LFjKSsr49SpU36XckF1dXVx+4M1NTWVsWPH+l2GDGD1IfiXg/Ctw+F5CK2lB+B7U+BXT5drMNljAyIUkpKSmDRpkt9ldKmwsJB58+b5XYZIzHmzBj5aAtsq2z+3IBN+Mx3y0+HX7Z+WPqYZzSLiG+fgieMwb1v7QDDgC+PgtfnhQJD+MSDOFEQk/pxpgFX74JkOrvqOSYZfFsCVw/q/rsFOoSAi/e7ls3BHCZR1cAPRjbnw46mQk9T/dYlCQUT6UUMIHjoI3+hkMPk/L4FPjGo3R036kUJBRPrF/hq4vQS2dDCYPL95MHmqxg58p4FmEfGUc/Cz4zBve8eB8MA42DhfgRArdKYgIp452wCf3AdPdzCYPCoZfjENVmT3f13SOYWCiHjilebB5MMdDCbfkAP/NRVy22+YJj5TKIhIn2oIwcOH4JFD0HYxirQA/MclsEqDyTFLoSAifeZAbXiZ680djB3MzYTfFEBBRv/XJdFTKIhIrzkHvzoB974JVU3tn//cWHjkYkjRrS0xT6EgIr1S0Qj/sA+ePNn+uZHJ8PNp8L80mBw3FAoi0mMbKsKXiw51MJj8gRz4yVQYrsHkuKJQEJFuawzB1w7Bv3YwmJwagH+fDJ8arcHkeKRQEJFu+VtteGbyxnPtn5udEZ6ZPEODyXFLoSAiUfv1ifD4QWUHg8mfHQvfmASpCf1fl/QdhYKIdKmiET69D37dwWByXhL8bBqszOn/uqTvKRRE5IJeqwhfLjpY1/6567LhiWkwQoPJA4ZCQUQ61BiCrx+Grx2EtleLUgy+Mxk+PUaDyQONQkFE2jlYG163aEMHg8kzM+DJApiZ2f91ifcUCiIS4ckT8Kl9cK6DweR/HAPfuliDyQOZp5POzWylme01s/1m9sUOnh9vZi+Z2RtmttPMrvWyHhHp3LlGuKsEPlrSPhBGJMHaWfDoFAXCQOfZmYKZJQA/AK4ByoCtZrbGOVfcqtuDwNPOucfMbDqwFpjoVU0i0rFNzYPJb3UwmPy+bPjpNMjTYPKg4OWZwmJgv3PuLedcPbAauKFNHwcMaf56KHDMw3pEpI0mB/96EN77RvtASDF49BJ4bpYCYTDxckxhDHCk1eMy4NI2fR4C/mJm/wfIAFZ4WI/IoONceAvM7xyBtUGoZRlp6+G6HLgjD759GF7tYDB5Rjo8OR1maTB50DHnnDdvbHYTsNI594nmx3cClzrn7mvV53PNNXzXzN4D/ASY6ZwLtXmvVcAqgLy8vAWrV6/2pGavVVVVkZmp/2U9pePXPY0Y32Aar5HLeQzX6sKA4XDNX7V1I2V8krdIabeqkf/2Ha739fOzM+o4XZ3q2+fnj+/5KduVV1653Tm3sKt+Xp4pHAXGtXo8trmttXuAlQDOuY1mlgrkAhHzJp1zjwOPAyxcuNAtX77co5K9VVhYSLzWHgvi/fhdde/hfvssBxRfmkP5mDRCie2vErsOwiCprolpW4OcPR7iWx4N7a374fhevf7hfjyGHbl1SSmrN03z7fPX3dW74xcNL8cUtgJTzGySmSUDtwJr2vQ5DFwNYGYFQCrQwRbfItId57KTOw2Ejgwpr2PRX46Te7yDkWYZVDwLBedcI3Af8GeghPBdRnvM7GEzu7652z8Bf29mO4AngY87r65niQwiR/KzCAWinGrsHCk1TaTUxd7lIul/nk5ec86tJXybaeu2r7b6uhhY6mUNIoNRcHQaRBsKZuH+Ing8eU1E/BFK6N6CRN3tLwOXQkFkAAo0de8qbHf7y8ClUBAZgNLPNUTfOeTIOVbrXTESVxQKIgPM8YkZVGWnRN0/EHKM31fpYUUSTxQKIgPIiXHplC7Kjrp/oDFE7tFask77OylMYoeWzhYZIE6NSaPk0pzIXW9CDnMOZxZ5N1LIEQg5co/WUrAl2MFUNhmsFAoiA0BwZCp7luTiWv3gt5Bj+mvlpNY1cTg/i+DoNFyCYU3hMYTxeysZckZnCBJJoSAS586MSGH3Zbm41reVOkfB5iAjmgeQZ24KAv4v0yCxT2MKInHsbE4yu5YOb7ecxbStp8k7UuNTVRLPFAoicercsGR2Xj6CpqTI/8b5208z6mC1T1VJvFMoiMShqqFJ7LhiOE3Jkf+FJxedYcyBKp+qkoFAoSASZ6qzEilaNoLGlMjNkiftOqv5BtJrCgWROFKbEQ6EhtTIQBhfUsGEkg62UBPpJoWCSJyoS0+gaPkI6tMjbxocu+8cF++q0FwD6RMKBZE4cD41QNGyEdRlRAbC6AOVXFJ0VoEgfUahIBLj6lPCgVCblRTRnnewmvztZxQI0qcUCiIxrCHJ2HHFCGqGRm7YPvxINdO2ankK6XsKBZEY1ZgYDoSqYZGBkHO0humbgwS0BYJ4QKEgEoOaEoydlw+nMidyCexhb9cyY2M5AW2nLB5RKIjEmKYA7FqaS8Xw1Ij2oSfrmLWhnAQFgnhIoSASQ0IB2HPZcM6MTItoHxI8z+xXT5GgbTPFYwoFkRgRMii+NJfg6MhAyDxTz+z1J0lsVCCI9xQKIjHAAaWLcjg1Lj2iPb2injnrT5LUoECQ/qFQEPGZA/YuyObExIyI9rTKBua+fJLk8xpEkP6jUBDxkQP2zx3G8cmZEe2p1Y3MLTxJSp0CQfqXQkHEJw54a9ZQyvKzItqTaxqZW3iC1NomfwqTQU2hIOKTQwVDOFwwNKItqa6JuS+fJK1agSD+UCiI+OBwfhZ/m3VRRFvi+XAgZFQ2+lSViEJBpN8dnZzJgbnDItoS6kPMXX+SzIoGn6oSCVMoiPSj4xMz2LcgO6ItoSHEnFdOknVGgSD+UyiI9JMT49IpXRQZCIHGELNePcXQYL1PVYlEUiiI9IM/nIKSS3PA3l3s2pocM18rZ9ip8z5WJhJJoSDiseeD8JFicIFWgRByzNhYTs7bdT5WJtKeQkHEQ+vOwI17IGKVCuco2Bxk+LFa3+oS6YxCQcQjGyrg+l3QdlLytK2nyTtS409RIl1QKIh4YNs5uHYnVLcJhPztpxl1sNqfokSioFAQ6WM7q+B/7YRzbSYlTy46w5gDVf4UJRIlhYJIHyqthmt2wJk2k5K/NhHG76v0pSaR7lAoiPSRA7Vw9Q442WYO2pfGwz9P8Kcmke5SKIj0gSN1cHURHGszB+0zY+DrkyKmJ4jENIWCSC8dPw9X7YBDbeagrRoF/3GJAkHii0JBpBdO1cOKHbC/zZSDO/PgsXwFgsQfhYJID51pCN9lVNxmysHNw+GJqRBQIEgc8jQUzGylme01s/1m9sVO+txiZsVmtsfMfuNlPSJ95VwjrNwJRW3uMP1ADvyqABL165bEqUSv3tjMEoAfANcAZcBWM1vjnCtu1WcK8CVgqXPujJmN8Koekb5S0wTv3wVb2txhes0weHo6JCsQJI55+c93MbDfOfeWc64eWA3c0KbP3wM/cM6dAXDOnfSwHpFeq2uCD+6GVyoi268YCn+cCakJ/tQl0lfMOdd1r568sdlNwErn3CeaH98JXOqcu69Vnz8C+4ClQALwkHPu+Q7eaxWwCiAvL2/B6tWrPanZa1VVVWRmZvpdRtzy+/g1YPwLM9hIbkR7Aef4DjtI58L7Ku877P+eCdkZdZyuTvXt8/PHJ/fq9X4fw3g+fldeeeV259zCrvp5dvkoSonAFGA5MBZYb2aznHNnW3dyzj0OPA6wcOFCt3z58n4us28UFhYSr7XHAj+PX2MIbiuBjaci2+dmwro5QxiWdHmX7/HwvYc9qi56ty4pZfWmab59/rq7xvfq9X4fw3g/ftHw8vLRUWBcq8djm9taKwPWOOcanHN/I3zWMMXDmkS6LeTg7/bCM20CYXo6vDAbhiX5U5eIF7wMha3AFDObZGbJwK3AmjZ9/kj4LAEzywXygbc8rEmkW5yDT+2DX52IbJ+SBn+dA7m9uxoiEnM8CwXnXCNwH/BnoAR42jm3x8weNrPrm7v9GQiaWTHwEvCAcy7oVU0i3eEcfHY//Ph4ZPuEFHhxDoxK8acuES95OqbgnFsLrG3T9tVWXzvgc81/RGKGc/Dlv8H32lzwHJ0M6+bCOP/GGkU8pTuqRTrw9UPwzTZjmiOSwmcIF6f5U5NIf1AoiLTx3SPwlYORbdmJ8MIcmJbhS0ki/UahINLKD4/C5w9Etg1JgL/MgdmaYiKDgEJBpNlPj8On34xsywjA/8yGBVn+1CTS3xQKIsCTJ+CevZFtqQH40yy4bKg/NYn4QaEgg94fTsGdJdB6wZckgz/MgCuH+VaWiC+6FQpmltG8+qnIgPB8ED5STMSqRQmEVztdmeNXVSL+uWAomFnAzD5qZs+Z2UmgFDjevP/Bt83skv4pU6TvvXQGbtwDDa1OEYzwfggfHO5bWSK+6upM4SVgMuE9D0Y658Y550YA7wU2Ad8yszs8rlGkz22ogA/sgrpQZPsTU+HWPH9qEokFXc1oXuGca2jb6Jw7DfwO+J2ZaTkwiSvbzsG1O6G6TSD8cAp8fJQ/NYnEigueKbwTCGa2ou1zZvax1n1E4sHOqvC+yufabH3w3cnwD2P8qUkklkQ70PxVM3useaA5z8z+BHzAy8JE+lppNVyzA840RrZ/bSJ8blyHLxEZdKINhWXAAaAIeBX4jXPuJs+qEuljB2rh6h1wss157ZfGwz9P8KcmkVgUbSgMI7zn8gHgPDDBzMyzqkT60JE6uLoIjrXZyfEzY+Drk0D/kkXeFW0obAKed86tBBYBo4ENnlUl0keOn4erdsCh85Htq0bBf1yiQBBpK9r9FFY45w4DOOdqgX80syu8K0uk907Vw4odsL82sv3OPHgsX4Eg0pGuJq9NBHgnEFpzzq23sLHelCbSc2cawncZFddEtt88PDwXIaBAEOlQV2cK3zazAPAssB04BaQClwBXAlcD/wKUeVmkSHeca4SVO6GoKrL9Aznh2cqJWvFLpFMXDAXn3M1mNh24HbgbGAnUEt5zeS3wdedcnedVikSppgnevwu2VEa2XzMsvJ5RsgJB5IK6HFNwzhWb2b8C9xJe3sIBW4FnFAiDy1X3truK2K9uXVLPwxeooSkAu947nDMjI/fLHHqyjvO/O8W1Ta6TV0Zn3Q/H9+r1IvEg2oHmnwPngO81P/4o8AvgFi+KEumuUAD2XNY+EIYEzzP71VMk9DIQRAaLaENhpnNueqvHL5lZsRcFiXRXyKD40lyCoyMDIfNMPbPXnySxUYEgEq1or7C+bmZL3nlgZpcC27wpSSR6DihdlMOpcekR7ekV9cx5+SRJDQoEke6I9kxhAfCamb1zQXc8sNfMdgHOOTfbk+pELsABexdkc2JiRkR7WmUDc18+SXJ9qOMXikinog2FlZ5WIdJNDtg/dxjHJ2dGtKdWNzK38CQpbTdKEJGoRBUKzrlDXhciEi0HvDVrKGX5WRHtyTWNzC08QWptU8cvFJEuRXumINLvHHAuO5kjU4cQHJXKSwnjCIx2pFY1UnNRckTfpLom5r58krRqBYJIbygUJCaFDEoW51A+Jo1QwFrWpQglWrtASDwfDoSMysaO3kpEukGhIDHH0SoQulqToskxZ/1JMiu0AaBIX9Ckf4k557KTowsEIIDTcqcifUihIDHnSH5W+JJRFEJmHG4z4CwiPadQkJgTHJ0W/drWAWs3k1lEek6hIDEnlNC9y0Hd7S8inVMoSMwJdHPxuu72F5HOKRQk5uQcqwUX5Q/6kAv3F5E+oVCQmJNR0RD1HUWBkGP8vsquO4pIVBQKElMqL0riUMGQqPoGGkPkHq0l63S9x1WJDB6avCYxoz4lwK6lw3Gt5yc4F57N1vpupJAjEHLkHq2lYEsQDTOL9B2FgsSEUAB2X5bL+YzIf5ITis9Rk5VIcHQaLsGwpvAYwvi9lQw5ozMEkb6mUJCY8ObcYVQMT41oG7vvHBfvqWh5fOuSUlZvmtbfpYkMKhpTEN8duziDY5dEzkq+6EQdk3ec9akikcFLoSC+OpuTzL552RFtqVWNzNhkUqYdAAAQJklEQVRYTkDTD0T6naehYGYrzWyvme03sy9eoN+HzcyZ2UIv65HYUpeWwJ7LhuNazUgONIaYteGUttIU8YlnoWBmCcAPgPcB04HbzGx6B/2ygM8Am72qRWJPU4Kxe2ku9WkJEe0FW4JaBlvER16eKSwG9jvn3nLO1QOrgRs66Pc14FtAnYe1SAxxwN4F2VRmp0S0TyiuYESZZieL+MnLUBgDHGn1uKy5rYWZzQfGOeee87AOiTFH8rM4MTEjoi3naA2Tdld08goR6S++3ZJqZgHg34GPR9F3FbAKIC8vj8LCQk9r80pVVVXc1g5w65LezwsoTs2mcPi4iLZRDVV8IbSZtCUX3l85O6OOW5eU9rqGniosfKtXr++L49dbOoa9E+/HLxrmol14rLtvbPYe4CHn3P9ufvwlAOfcN5ofDwUOAFXNLxkJnAaud85t6+x9Fy5c6LZt6/TpmFZYWMjy5cv9LqPHrrr3cK9eX5uRyLYVeTSmvDuOkFgfYsFf3ya9quv9lf2ep7Duh+N79freHr++oGPYO/F8/Mxsu3Ouy5t5vLx8tBWYYmaTzCwZuBVY886TzrkK51yuc26ic24isIkuAkHiV2Oiseu9uRGBgHNM31QeVSCISP/wLBScc43AfcCfgRLgaefcHjN72Myu9+pzJfY4oGRxDtVDkyPaL955lpy3dX+BSCzxdEzBObcWWNum7aud9F3uZS3in4PTh1A+Nj2ibcShasbv1ZLXIrFGM5rFU6dGp3Fw5kURbZln6pm27bRWNxWJQQoF8Uz1kCRKLs2JaEuqa2LWhlMkaAtNkZikUBBPNCQH2LU0l6akd/+JWcgx87VyUmsufOupiPhHoSB9LmSwZ0kOtVlJEe1T3jjDReXnfapKRKKhUJA+99bsizgzMi2ibdSBKkYfqOrkFSISKxQK0qfeHp/OkamReywPPVVH/hsaWBaJBwoF6TPnhiWzd1HkwHJKTfPeCFoJWyQuKBSkT5xPDbB7aS6h1nsjNDlmbignpU6JIBIvFArSa6EA7HlPLufTI+dCTt0WZMgZ/xeBE5HoKRSk196cN4yK4akRbeP2nmPkoRqfKhKRnlIoSK8cnZzJsclZEW3D3q7l4p1nfapIRHpDoSA9djY3hTfnDYtoS61qYMamIAFNWBaJSwoF6ZG69AR2X5aLC7w7sJzQEGLWq+Uk1WtgWSReKRSk25oSjF1Lh9OQmhDRXrAlSOa5Bp+qEpG+oFCQbnFA6cJsqoZF7o0wcU8Fw4/W+lOUiPQZhYJ0y5GpWZyckBHRlltWw8Q9FT5VJCJ9SaEgUQuOTOXA7Mi9ETIq6inYEtQSFiIDhEJBorKvBoqX5IK9++M/8XwTs14tJ7FRtxqJDBQKBenSuUb44G5oTG71zyXkmLEpSFp1o3+FiUifUyjIBYUc3FECJW0mJ0/eeZbsE3X+FCUinlEoyAU9dBD+FIxsyztYzbh9lb7UIyLeUihIp353Cr52KLIt6/R5pm7X3ggiA5VCQTq0swo+VhLZllzbxMwN5SQ0aWBZZKBSKEg7wYbwwHJ1q9UqkgxmvHaK1Nom/woTEc8pFCRCYwhu2QN/azOG/P0pcFFQeyOIDHQKBYnwwFuwrs2q1/8wGlaN9qceEelfCgVp8fO34T/LItsuHwr/eYk/9YhI/1MoCACbz8En90a2jUuBZ2ZAsv6ViAwa+u8uHD8PH9oN51vdVJQWgD/OhBHJnb9ORAYehcIgdz4EH9oDx9qMIf9kKszP6vg1IjJwKRQGMefg0/tg07nI9v87Dm7L86cmEfGXQmEQ+8FR+MnbkW0rs+GRi/2pR0T8p1AYpArPwGf3R7ZNSYPfFECC1rAQGbQUCoPQwVq4aQ+0npuclQDPzoRhSb6VJSIxQKEwyFQ3hZewCLbZBuFXBVCQ0fFrRGTwUCgMIs7B3aWwozqy/WsT4fpcX0oSkRijUBhEvnkYnj4V2fbhXPjnCf7UIyKxR6EwSDwXhH/+W2TbrAz42bSIbZdFZJBTKAwCpdXw0WJovQtCdmJ4YDkz0beyRCQGKRQGuLMNcMNuONfqVqME4OkZMCnNt7JEJEYpFAawJge3l8C+2sj2714CVw/zpyYRiW0KhQHsK3+Dtacj2z6WB/84xp96RCT2KRQGqKdOwjcOR7YtzoIf5WtgWUQ652komNlKM9trZvvN7IsdPP85Mys2s51m9qKZ6ebIPlBUCX9XGtk2Mhn+MBNSE/ypSUTig2ehYGYJwA+A9wHTgdvMbHqbbm8AC51zs4FngH/zqp7B4lR9eMZybejdtmSD38+A0Sn+1SUi8cHLM4XFwH7n3FvOuXpgNXBD6w7OuZecczXNDzcBYz2sZ8BrCMHNe+DQ+cj2x/LhPUP9qUlE4ouXoTAGONLqcVlzW2fuAf7Hw3oGvM8dgJcrItvuGwN3j/KnHhGJP+ac67pXT97Y7CZgpXPuE82P7wQudc7d10HfO4D7gGXOufMdPL8KWAWQl5e3YPXq1Z7U7LWqqioyMzM9ee/nGMl3mBbRNpczfJudJNI33+N9h+u77uSh7Iw6Tlen+vb5+eN7tzep38cPdAx7K56P35VXXrndObewq35ehsJ7gIecc/+7+fGXAJxz32jTbwXw/xIOhJNdve/ChQvdtm3bPKjYe4WFhSxfvrzP33djBSwrgoZW38oJKbBtAeT24R7LV917uOtOHrp1SSmrN03ruqNH1v1wfK9e7/fxAx3D3orn42dmUYWCl5ePtgJTzGySmSUDtwJrWncws3nA/wdcH00gSHtHz4f3WG4dCOkB+OPMvg0EERkcPAsF51wj4UtCfwZKgKedc3vM7GEzu76527eBTOC3ZlZkZms6eTvpQF0T3Lgb3m5zRv3TaTA3y5+aRCS+ebocmnNuLbC2TdtXW329wsvPH8icg0/tg62Vke1fGg+3jPCnJhGJf5rRHKe+dxR+fiKy7bps+Nokf+oRkYFBoRCHXjwD/7Q/sm1qGvx6OiRoCQsR6QWFQpx5qxZu2QOtVsJmSAI8OwuGam8EEeklhUIcqWoM741wuvHdNgOenA5T030rS0QGEIVCnHAOPl4Ku6sj278+Ca7N8acmERl4FApx4uuH4HflkW0fGQ5f7N1cIBGRCAqFOLCmHL5yMLJtTgb8ZJr2RhCRvqVQiHHF1XBHSWRbblJ4xnKG9kYQkT6mUIhhZxrCA8uVrW41SgB+Ox0mpvlWlogMYAqFGNXk4KMlsL82sv3RKbB8mD81icjAp1CIUV9+C54/Hdl2z0i4d7Q/9YjI4DCopjv5v+xuPQ9HUcOJ8ekUL8mNaBtSfp79z5zg6lAnL4pCb5ctFpGBT2cKMaZyWBKlC7Mj2pJrGpn52ikCvQgEEZFoKBRiSH1KgF2XDSeU+O63JdDkmPVaOSl1SgQR8Z5CIUaEArD7slzOZ0Re0Zu67TRDTvu/jaOIDA4KhRjx5txhVAyP3Pt17L5zjDxU3ckrRET6nkIhBhy7OINjl0RulTbsRB2Td5z1qSIRGawUCj47m5vCvnmRA8upVY3M2FhOwHXyIhERjygUfFSXlsDuy3JxrXbGSWgIMWvDKZLqNbAsIv1PoeCTpgRj99JcGlIjFzCatiVIZkWDT1WJyGCnUPCBA/YuyKYyOyWifcKeCkYcre34RSIi/WBQzWjubw44l53MkalDCI5K5aWEcQRGO9IqG6kelhzRN/doDZP2VPhTqIhIM4WCR0IGJYtzKB+TRihgEAiPG4QSjeqLkiL6plc0ULA5iLZGEBG/KRQ84GgVCIkdXKFrtTOONTlmbjhFYqNuNRIR/2lMwQPnspM7D4R2HE3J+jaISGzQTyMPHMnPCl8yioIz43B+VtcdRUT6gULBA8HRaS1jCF0KWLi/iEgMUCh4IJTQvSHj7vYXEfGKQsEDgabuDRp3t7+IiFcUCh7IOVYLoSh/0IdcuL+ISAxQKHhg3L5KAlGGQiDkGL+v0uOKRESio1DwwJDT9eQerSXQeOFF7QKNIXKP1pKlTXREJEYoFDxgQMGW4LvB0PasIeRaAqFgi2Yyi0js0IxmjwQcTN8cpDI7mcP5WQRHp+ESDGsKjyGM31vJkDM6QxCR2KJQ8JARvpQ0c1MQgFuXlLJ60zR/ixIRuQBdPhIRkRYKBRERaaFQEBGRFgoFERFpoVAQEZEWCgUREWmhUBARkRYKBRERaeFpKJjZSjPba2b7zeyLHTyfYmZPNT+/2cwmelmPiIhcmGehYGYJwA+A9wHTgdvMbHqbbvcAZ5xzlwD/AXzLq3pERKRrXp4pLAb2O+fecs7VA6uBG9r0uQH4efPXzwBXm5nWhxMR8YmXoTAGONLqcVlzW4d9nHONQAWQ42FNIiJyAeacN1tBmtlNwErn3CeaH98JXOqcu69Vn93NfcqaHx9o7lPe5r1WAauaH04F9npStPdygfIue0lndPx6T8ewd+L5+E1wzg3vqpOXq6QeBca1ejy2ua2jPmVmlggMBYJt38g59zjwuEd19hsz2+acW+h3HfFKx6/3dAx7ZzAcPy8vH20FppjZJDNLBm4F1rTpswb4WPPXNwHrnFenLiIi0iXPzhScc41mdh/wZyABeMI5t8fMHga2OefWAD8Bfmlm+4HThINDRER84ukmO865tcDaNm1fbfV1HXCzlzXEmLi/BOYzHb/e0zHsnQF//DwbaBYRkfijZS5ERKSFQqGfdLXkh3TOzJ4ws5PNtzBLN5nZODN7ycyKzWyPmX3G75riiZmlmtkWM9vRfPz+H79r8pIuH/WD5iU/9gHXEJ7EtxW4zTlX7GthccLMrgCqgF8452b6XU+8MbNRwCjn3OtmlgVsBz6of3/RaV5lIcM5V2VmScCrwGecc5t8Ls0TOlPoH9Es+SGdcM6tJ3x3mvSAc+64c+715q8rgRLary4gnXBhVc0Pk5r/DNjfphUK/SOaJT9EPNe8EvE8YLO/lcQXM0swsyLgJPCCc27AHj+FgsggYWaZwO+AzzrnzvldTzxxzjU55+YSXplhsZkN2MuYCoX+Ec2SHyKeab4W/jvg18653/tdT7xyzp0FXgJW+l2LVxQK/SOaJT9EPNE8UPoToMQ59+9+1xNvzGy4mV3U/HUa4RtGSv2tyjsKhX7QvCz4O0t+lABPO+f2+FtV/DCzJ4GNwFQzKzOze/yuKc4sBe4ErjKzouY/1/pdVBwZBbxkZjsJ/4L3gnPuv32uyTO6JVVERFroTEFERFooFEREpIVCQUREWigURESkhUJBRERaKBRERKSFQkFERFooFER6ycwWmdnO5nX3M5rX3B+wa+PIwKbJayJ9wMz+FUgF0oAy59w3fC5JpEcUCiJ9oHlNq61AHXCZc67J55JEekSXj0T6Rg6QCWQRPmMQiUs6UxDpA2a2hvCOepMIb315n88lifRIot8FiMQ7M7sLaHDO/aZ5P+7XzOwq59w6v2sT6S6dKYiISAuNKYiISAuFgoiItFAoiIhIC4WCiIi0UCiIiEgLhYKIiLRQKIiISAuFgoiItPj/ARKCaDJ0fB3qAAAAAElFTkSuQmCC\n", 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" ] diff --git a/qiskit/finance/machine_learning/qgans_option_pricing.ipynb b/qiskit/finance/machine_learning/qgan_option_pricing.ipynb similarity index 92% rename from qiskit/finance/machine_learning/qgans_option_pricing.ipynb rename to qiskit/finance/machine_learning/qgan_option_pricing.ipynb index c3b9ea5c1..d21327bbe 100644 --- a/qiskit/finance/machine_learning/qgans_option_pricing.ipynb +++ b/qiskit/finance/machine_learning/qgan_option_pricing.ipynb @@ -16,7 +16,8 @@ "- [2]ETH Zurich\n", "\n", "### Introduction\n", - "We can train a quantum Generative Adversarial Network (qGAN) - see [qGANs for Loading Random Distributions](../../aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb) - to learn and load a model for the spot price of an asset underlying a European call option. The resulting model can then be integrated into a Quantum Amplitude Estimation based algorithm to evaluate the expected payoff - see [European Call Option Pricing](../../aqua/finance/european_call_option_pricing.ipynb)." + "In this notebook, we discuss how a Quantum Machine Learning Algorithm, namely a quantum Generative Adversarial Network (qGAN), can facilitate the pricing of a European call option. More specifically, a qGAN can be trained such that a quantum circuit models the spot price of an asset underlying a European call option. The resulting model can then be integrated into a Quantum Amplitude Estimation based algorithm to evaluate the expected payoff - see [European Call Option Pricing](../../aqua/finance/european_call_option_pricing.ipynb).
\n", + "For further details on learning and loading random distributions by training a qGAN please refer to Quantum Generative Adversarial Networks for Learning and Loading Random Distributions. Zoufal, Lucchi, Woerner. 2019." ] }, { @@ -57,8 +58,8 @@ "source": [ "### Uncertainty Model\n", "\n", - "The Black-Scholes model assumes that the spot price at maturity $S_T$ for a European call option is log-normally distributed. Thus, we can train a qGAN on samples from a log-normal distribution, as it is shown in [qGANs for Loading Random Distributions](../../aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb), and use the resulting model as uncertainty model underlying the option.\n", - "In the following, we construct the quantum circuit for loading the uncertainty model. The circuit output reads $$\\lvert g_{\\theta}\\rangle = \\sum\\limits_{j=0}^{2^n-1}\\sqrt{p_{\\theta}^{j}}\\lvert{j}\\rangle,$$ whereby the probabilites $p_{\\theta}^{j}$, for $j\\in \\left\\{0, \\ldots, {2^n-1} \\right\\}$, represent a model of the target distribution." + "The Black-Scholes model assumes that the spot price at maturity $S_T$ for a European call option is log-normally distributed. Thus, we can train a qGAN on samples from a log-normal distribution and use the result as uncertainty model underlying the option. A notebook that explains the implementation of a qGAN to learn and load a random distribution is presented in [qGANs for Loading Random Distributions](../../aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb).
\n", + "In the following, we construct a quantum circuit that loads the uncertainty model. The circuit output reads $$\\lvert g_{\\theta}\\rangle = \\sum\\limits_{j=0}^{2^n-1}\\sqrt{p_{\\theta}^{j}}\\lvert{j}\\rangle,$$ where the probabilites $p_{\\theta}^{j}$, for $j\\in \\left\\{0, \\ldots, {2^n-1} \\right\\}$, represent a model of the target distribution." ] }, { @@ -127,12 +128,12 @@ "metadata": {}, "source": [ "### Evaluate Expected Payoff\n", - "Now, the trained uncertainty model can be used as part of a quantum circuit to evaluate the expectation value of the option's payoff function." + "Now, the trained uncertainty model can be used to evaluate the expectation value of the option's payoff function with Quantum Amplitude Estimation." ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 4, "metadata": {}, "outputs": [ { diff --git a/qiskit/finance/machine_learning/qgans.ipynb b/qiskit/finance/machine_learning/qgans.ipynb new file mode 100644 index 000000000..d21327bbe --- /dev/null +++ b/qiskit/finance/machine_learning/qgans.ipynb @@ -0,0 +1,194 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# _*Qiskit Finance: qGAN Option Pricing*_ \n", + "\n", + "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", + "\n", + "***\n", + "### Contributors\n", + "Christa Zoufal[1,2], Stefan Woerner[1]\n", + "### Affliation\n", + "- [1]IBMQ\n", + "- [2]ETH Zurich\n", + "\n", + "### Introduction\n", + "In this notebook, we discuss how a Quantum Machine Learning Algorithm, namely a quantum Generative Adversarial Network (qGAN), can facilitate the pricing of a European call option. More specifically, a qGAN can be trained such that a quantum circuit models the spot price of an asset underlying a European call option. The resulting model can then be integrated into a Quantum Amplitude Estimation based algorithm to evaluate the expected payoff - see [European Call Option Pricing](../../aqua/finance/european_call_option_pricing.ipynb).
\n", + "For further details on learning and loading random distributions by training a qGAN please refer to Quantum Generative Adversarial Networks for Learning and Loading Random Distributions. Zoufal, Lucchi, Woerner. 2019." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/ouf/anaconda3/envs/QiskitDevenv/lib/python3.7/site-packages/qiskit_terra-0.8.0-py3.7-macosx-10.7-x86_64.egg/qiskit/circuit/variabletable.py:10: DeprecationWarning: Using or importing the ABCs from 'collections' instead of from 'collections.abc' is deprecated, and in 3.8 it will stop working\n", + " from collections import MutableMapping\n" + ] + } + ], + "source": [ + "#!/usr/bin/env python\n", + "# coding: utf-8\n", + "from __future__ import absolute_import, division, print_function\n", + "\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "import numpy as np\n", + "from qiskit.aqua.algorithms import AmplitudeEstimation\n", + "from qiskit.aqua.components.uncertainty_problems import EuropeanCallExpectedValue\n", + "from qiskit.aqua.components.uncertainty_models import UnivariateVariationalDistribution, NormalDistribution\n", + "from qiskit.aqua.components.variational_forms import RY\n", + "\n", + "from qiskit.aqua import aqua_globals, QuantumInstance\n", + "\n", + "from qiskit import BasicAer" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Uncertainty Model\n", + "\n", + "The Black-Scholes model assumes that the spot price at maturity $S_T$ for a European call option is log-normally distributed. Thus, we can train a qGAN on samples from a log-normal distribution and use the result as uncertainty model underlying the option. A notebook that explains the implementation of a qGAN to learn and load a random distribution is presented in [qGANs for Loading Random Distributions](../../aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb).
\n", + "In the following, we construct a quantum circuit that loads the uncertainty model. The circuit output reads $$\\lvert g_{\\theta}\\rangle = \\sum\\limits_{j=0}^{2^n-1}\\sqrt{p_{\\theta}^{j}}\\lvert{j}\\rangle,$$ where the probabilites $p_{\\theta}^{j}$, for $j\\in \\left\\{0, \\ldots, {2^n-1} \\right\\}$, represent a model of the target distribution." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# Set upper and lower data values\n", + "bounds = np.array([0.,7.])\n", + "# Set number of qubits used in the uncertainty model\n", + "num_qubits = [3]\n", + "\n", + "# Set entangler map\n", + "entangler_map = []\n", + "for i in range(sum(num_qubits)):\n", + " entangler_map.append([i, int(np.mod(i+1, sum(num_qubits)))])\n", + "\n", + "# Set variational form\n", + "var_form = RY(int(np.sum(num_qubits)), depth=1, entangler_map=entangler_map, entanglement_gate='cz')\n", + "# Load the trained circuit parameters\n", + "g_params = [0.29399714, 0.38853322, 0.9557694, 0.07245791, 6.02626428, 0.13537225]\n", + "# Set an initial state for the generator circuit\n", + "init_dist = NormalDistribution(int(sum(num_qubits)), mu=1., sigma=1., low=bounds[0], high=bounds[1])\n", + "# Set generator circuit\n", + "g_circuit = UnivariateVariationalDistribution(int(sum(num_qubits)), var_form, g_params,\n", + " initial_distribution=init_dist, low=bounds[0], high=bounds[1])\n", + "\n", + "# construct circuit factory for uncertainty model\n", + "uncertainty_model = g_circuit" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot probability distribution\n", + "x = uncertainty_model.values\n", + "y = uncertainty_model.probabilities\n", + "plt.bar(x, y, width=0.2)\n", + "plt.xticks(x, size=15, rotation=90)\n", + "plt.yticks(size=15)\n", + "plt.grid()\n", + "plt.xlabel('Spot Price at Maturity $S_T$ (\\$)', size=15)\n", + "plt.ylabel('Probability ($\\%$)', size=15)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Evaluate Expected Payoff\n", + "Now, the trained uncertainty model can be used to evaluate the expectation value of the option's payoff function with Quantum Amplitude Estimation." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Estimated value:\t1.2580\n", + "Probability: \t0.8785\n" + ] + } + ], + "source": [ + "# set the strike price (should be within the low and the high value of the uncertainty)\n", + "strike_price = 2\n", + "\n", + "# set the approximation scaling for the payoff function\n", + "c_approx = 0.25\n", + "\n", + "# construct circuit factory for payoff function\n", + "european_call = EuropeanCallExpectedValue(\n", + " uncertainty_model,\n", + " strike_price=strike_price,\n", + " c_approx=c_approx\n", + ")\n", + "# set number of evaluation qubits (samples)\n", + "m = 5\n", + "\n", + "# construct amplitude estimation \n", + "ae = AmplitudeEstimation(m, european_call)\n", + "# result = ae.run(quantum_instance=BasicAer.get_backend('qasm_simulator'), shots=100)\n", + "result = ae.run(quantum_instance=BasicAer.get_backend('statevector_simulator'))\n", + "print('Estimated value:\\t%.4f' % result['estimation'])\n", + "print('Probability: \\t%.4f' % result['max_probability'])" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "QiskitDevenv", + "language": "python", + "name": "qiskitdevenv" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From 0c3915aea0f93dbb4ce4088564aa678b5a5a3e0f Mon Sep 17 00:00:00 2001 From: Albert Frisch Date: Thu, 18 Apr 2019 23:00:44 +0200 Subject: [PATCH 058/116] add HHL truncate parameters --- qiskit/aqua/general/linear_systems_of_equations.ipynb | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/qiskit/aqua/general/linear_systems_of_equations.ipynb b/qiskit/aqua/general/linear_systems_of_equations.ipynb index 92383b7d1..c899ff742 100644 --- a/qiskit/aqua/general/linear_systems_of_equations.ipynb +++ b/qiskit/aqua/general/linear_systems_of_equations.ipynb @@ -1,4 +1,4 @@ -{ +{ "cells": [ { "cell_type": "markdown", @@ -451,6 +451,10 @@ "outputs": [], "source": [ "params5 = params\n", + "params5[\"algorithm\"] = {\n", + " \"truncate_powerdim\": False,\n", + " \"truncate_hermitian\": False\n", + "}\n", "params5[\"reciprocal\"] = {\n", " \"name\": \"Lookup\",\n", " \"negative_evals\": True\n", From 560f6a854499c81cca0c04ce4b9b237c2c198c83 Mon Sep 17 00:00:00 2001 From: Albert Frisch Date: Fri, 19 Apr 2019 00:39:06 +0200 Subject: [PATCH 059/116] improve HHL example and clean up --- .../general/linear_systems_of_equations.ipynb | 52 +++++++++++-------- 1 file changed, 31 insertions(+), 21 deletions(-) diff --git a/qiskit/aqua/general/linear_systems_of_equations.ipynb b/qiskit/aqua/general/linear_systems_of_equations.ipynb index 92383b7d1..50bde1686 100644 --- a/qiskit/aqua/general/linear_systems_of_equations.ipynb +++ b/qiskit/aqua/general/linear_systems_of_equations.ipynb @@ -252,8 +252,14 @@ " 'name': 'LinearSystemInput',\n", " 'matrix': matrix,\n", " 'vector': vector\n", - "}" - ] + "}\n", + "params3['reciprocal'] = {\n", + " 'negative_evals': True\n", + "}\n", + "params3['eigs'] = {\n", + " 'negative_evals': True\n", + "}\n" + ] }, { "cell_type": "code", @@ -264,10 +270,10 @@ "name": "stdout", "output_type": "stream", "text": [ - "solution [0.22147+0.j 0.22034-0.j]\n", + "solution [0.13449+0.j 0.29238-0.j]\n", "classical solution [0.14286 0.28571]\n", - "probability 0.424639\n", - "fidelity 0.898454\n" + "probability 0.022362\n", + "fidelity 0.998942\n" ] } ], @@ -451,26 +457,30 @@ "outputs": [], "source": [ "params5 = params\n", - "params5[\"reciprocal\"] = {\n", - " \"name\": \"Lookup\",\n", - " \"negative_evals\": True\n", + "params5['algorithm'] = {\n", + " 'truncate_powerdim': False,\n", + " 'truncate_hermitian': False\n", + "}\n", + "params5['reciprocal'] = {\n", + " 'name': 'Lookup',\n", + " 'negative_evals': True\n", "}\n", - "params5[\"eigs\"] = {\n", - " \"expansion_mode\": \"suzuki\",\n", - " \"expansion_order\": 2,\n", - " \"name\": \"EigsQPE\",\n", - " \"negative_evals\": True,\n", - " \"num_ancillae\": 6,\n", - " \"num_time_slices\": 70\n", + "params5['eigs'] = {\n", + " 'expansion_mode': 'suzuki',\n", + " 'expansion_order': 2,\n", + " 'name': 'EigsQPE',\n", + " 'negative_evals': True,\n", + " 'num_ancillae': 6,\n", + " 'num_time_slices': 70\n", "}\n", - "params5[\"initial_state\"] = {\n", - " \"name\": \"CUSTOM\"\n", + "params5['initial_state'] = {\n", + " 'name': 'CUSTOM'\n", "}\n", - "params5[\"iqft\"] = {\n", - " \"name\": \"STANDARD\"\n", + "params5['iqft'] = {\n", + " 'name': 'STANDARD'\n", "}\n", - "params5[\"qft\"] = {\n", - " \"name\": \"STANDARD\"\n", + "params5['qft'] = {\n", + " 'name': 'STANDARD'\n", "}" ] }, From 0dcce6b8c2fbccf4e0c2b00524a38904c058b417 Mon Sep 17 00:00:00 2001 From: Albert Frisch Date: Fri, 19 Apr 2019 01:00:09 +0200 Subject: [PATCH 060/116] update results --- .../aqua/general/linear_systems_of_equations.ipynb | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/qiskit/aqua/general/linear_systems_of_equations.ipynb b/qiskit/aqua/general/linear_systems_of_equations.ipynb index 50bde1686..094ffd501 100644 --- a/qiskit/aqua/general/linear_systems_of_equations.ipynb +++ b/qiskit/aqua/general/linear_systems_of_equations.ipynb @@ -259,7 +259,7 @@ "params3['eigs'] = {\n", " 'negative_evals': True\n", "}\n" - ] + ] }, { "cell_type": "code", @@ -270,10 +270,10 @@ "name": "stdout", "output_type": "stream", "text": [ - "solution [0.13449+0.j 0.29238-0.j]\n", + "solution [0.14223-5.e-05j 0.28622+7.e-05j]\n", "classical solution [0.14286 0.28571]\n", - "probability 0.022362\n", - "fidelity 0.998942\n" + "probability 0.000316\n", + "fidelity 0.999994\n" ] } ], @@ -304,8 +304,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "circuit_width 7\n", - "circuit_depth 30254\n" + "circuit_width 11\n", + "circuit_depth 73313\n" ] } ], From 5df3b325c6995bf281cd37a03fe22ec9e82ce246 Mon Sep 17 00:00:00 2001 From: Albert Frisch Date: Fri, 19 Apr 2019 01:08:16 +0200 Subject: [PATCH 061/116] fix --- qiskit/aqua/general/linear_systems_of_equations.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/qiskit/aqua/general/linear_systems_of_equations.ipynb b/qiskit/aqua/general/linear_systems_of_equations.ipynb index b103cb602..094ffd501 100644 --- a/qiskit/aqua/general/linear_systems_of_equations.ipynb +++ b/qiskit/aqua/general/linear_systems_of_equations.ipynb @@ -1,4 +1,4 @@ -{ +{ "cells": [ { "cell_type": "markdown", From 33f09709567e6f7168c45d32504e112159021a5a Mon Sep 17 00:00:00 2001 From: Albert Frisch Date: Fri, 19 Apr 2019 01:12:56 +0200 Subject: [PATCH 062/116] text update --- qiskit/aqua/general/linear_systems_of_equations.ipynb | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/qiskit/aqua/general/linear_systems_of_equations.ipynb b/qiskit/aqua/general/linear_systems_of_equations.ipynb index 094ffd501..3d857aa4d 100644 --- a/qiskit/aqua/general/linear_systems_of_equations.ipynb +++ b/qiskit/aqua/general/linear_systems_of_equations.ipynb @@ -292,7 +292,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Compared to the the first example, the circuit depth is increased approximately by a factor 2,5" + "Compared to the the first example, the circuit depth is increased approximately by a factor of 6" ] }, { @@ -395,7 +395,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Considering the circuit depth, it is increased approximately by a factor 10 compared to the two dimensional matrices. The circuit width is increased by two additional qubits" + "Considering the circuit depth and circuit width" ] }, { From 6792791b6b93e7b717f14bd64e9b41addbb952e9 Mon Sep 17 00:00:00 2001 From: woodsp Date: Fri, 19 Apr 2019 16:42:32 -0400 Subject: [PATCH 063/116] Noisy simulation with AER on Aqua --- .../aqua/general/simulations_with_noise.ipynb | 308 ++++++++++++++++++ 1 file changed, 308 insertions(+) create mode 100644 community/aqua/general/simulations_with_noise.ipynb diff --git a/community/aqua/general/simulations_with_noise.ipynb b/community/aqua/general/simulations_with_noise.ipynb new file mode 100644 index 000000000..75d56803e --- /dev/null +++ b/community/aqua/general/simulations_with_noise.ipynb @@ -0,0 +1,308 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## _*Running simulations with noise in Aqua*_\n", + "\n", + "This notebook demonstrates using the [Qiskit Aer](https://qiskit.org/aer) `qasm_simulator` to run a simulation with noise, based on a noise model, in Aqua. This can be useful to investigate behavior under different noise conditions. Aer not only allows you to define your own custom noise model, but also allows a noise model to be easily created based on the properties of a real quantum device. The latter is what this notebook will demonstrate since the goal is to show how to do this in Aqua not how to build custom noise models.\n", + "\n", + "Further information on Qiskit Aer noise model can be found in the online Qiskit Aer documentation [here](https://qiskit.org/documentation/aer/device_noise_simulation.html) as well as in the [Qiskit Aer tutorials](https://github.com/Qiskit/qiskit-tutorials/tree/master/qiskit/aer).\n", + "\n", + "Note: this tutorial requires Qiskit Aer if you intend to run it. This can be installed using pip if you do not have it installed using `pip install qiskit-aer`" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pylab\n", + "\n", + "from qiskit import Aer, IBMQ\n", + "from qiskit.aqua import Operator, QuantumInstance, aqua_globals\n", + "from qiskit.aqua.algorithms.adaptive import VQE\n", + "from qiskit.aqua.algorithms.classical import ExactEigensolver\n", + "from qiskit.aqua.components.optimizers import SPSA\n", + "from qiskit.aqua.components.variational_forms import RY" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Noisy simulation will be demonstrated here with VQE, finding the minimum (ground state) energy of an Hamiltonian, but the technique applies to any quantum algorithm from Aqua.\n", + "\n", + "So for VQE we need a qubit operator as input. Here we will take a set of paulis that were originally computed by qiskit-chemistry, for an H2 molecule, so we can quickly create an Operator." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Number of qubits: 2\n" + ] + } + ], + "source": [ + "pauli_dict = {\n", + " 'paulis': [{\"coeff\": {\"imag\": 0.0, \"real\": -1.052373245772859}, \"label\": \"II\"},\n", + " {\"coeff\": {\"imag\": 0.0, \"real\": 0.39793742484318045}, \"label\": \"ZI\"},\n", + " {\"coeff\": {\"imag\": 0.0, \"real\": -0.39793742484318045}, \"label\": \"IZ\"},\n", + " {\"coeff\": {\"imag\": 0.0, \"real\": -0.01128010425623538}, \"label\": \"ZZ\"},\n", + " {\"coeff\": {\"imag\": 0.0, \"real\": 0.18093119978423156}, \"label\": \"XX\"}\n", + " ]\n", + "}\n", + "\n", + "qubit_op = Operator.load_from_dict(pauli_dict)\n", + "num_qubits = qubit_op.num_qubits\n", + "print('Number of qubits: {}'.format(num_qubits))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As the above problem is still easily tractable classically we can use ExactEigensolver to compute a reference value so we can compare later the results. \n", + "\n", + "_(A copy of the operator is used below as what is passed to ExactEigensolver will be converted to matrix form and we want the operator we use later, on the Aer qasm simuator, to be in paulis form.)_" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Reference value: -1.85727503020238\n" + ] + } + ], + "source": [ + "ee = ExactEigensolver(qubit_op.copy())\n", + "result = ee.run()\n", + "ref = result['energy']\n", + "print('Reference value: {}'.format(ref))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Performance *without* noise\n", + "\n", + "First we will run on the simulator without adding noise to see the result. I have created the backend and QuantumInstance, which holds the backend as well as various other run time configuration, which are defaulted here, so it easy to compare when we get to the next section where noise is added. There is no attempt to mitigate noise or anything in this notebook so the latter setup and running of VQE is identical." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "VQE on Aer qasm simulator (no noise): -1.8662346923695476\n", + "Delta from reference: -0.008959662167167703\n" + ] + } + ], + "source": [ + "backend = Aer.get_backend('qasm_simulator')\n", + "quantum_instance = QuantumInstance(backend=backend, seed=167, seed_mapper=167) \n", + "\n", + "counts = []\n", + "values = []\n", + "def store_intermediate_result(eval_count, parameters, mean, std):\n", + " counts.append(eval_count)\n", + " values.append(mean)\n", + "\n", + "aqua_globals.random_seed = 167\n", + "optimizer = SPSA(max_trials=200)\n", + "var_form = RY(num_qubits)\n", + "vqe = VQE(qubit_op, var_form, optimizer, 'paulis', callback=store_intermediate_result)\n", + "vqe_result = vqe.run(quantum_instance)\n", + "print('VQE on Aer qasm simulator (no noise): {}'.format(vqe_result['energy']))\n", + "print('Delta from reference: {}'.format(vqe_result['energy']-ref))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We captured the energy values above during the convergence so we can see what went on in the graph below." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pylab.rcParams['figure.figsize'] = (12, 4)\n", + "pylab.plot(counts, values)\n", + "pylab.xlabel('Eval count')\n", + "pylab.ylabel('Energy')\n", + "pylab.title('Convergence with no noise');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Performance *with* noise\n", + "\n", + "Now we will add noise. Here we will create a noise model for Aer from an actual device. You can create custom noise models with Aer but that goes beyond the scope of this notebook. Links to further information on Aer noise model, for those that may be interested in doing this, were given in instruction above.\n", + "\n", + "First we need to get an actual device backend and from its `configuration` and `properties` we can setup a coupling map and a noise model to match the device. While we could leave the simulator with the default all to all map, this shows how to set the coupling map too. Note: We can also use this coupling map as the entanglement map for the variational form if we choose.\n", + "\n", + "Note: simulation with noise takes significantly longer than without noise." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "VQE on Aer qasm simulator (with noise): -1.6539436913665533\n", + "Delta from reference: 0.20333133883582666\n" + ] + } + ], + "source": [ + "from qiskit.providers.aer import noise\n", + "\n", + "IBMQ.load_accounts(hub=None)\n", + "device = IBMQ.get_backend('ibmqx4')\n", + "coupling_map = device.configuration().coupling_map\n", + "noise_model = noise.device.basic_device_noise_model(device.properties())\n", + "basis_gates = noise_model.basis_gates\n", + "\n", + "backend = Aer.get_backend('qasm_simulator')\n", + "quantum_instance = QuantumInstance(backend=backend, seed=167, seed_mapper=167,\n", + " coupling_map=coupling_map,\n", + " noise_model=noise_model,\n", + " basis_gates=basis_gates)\n", + "\n", + "counts1 = []\n", + "values1 = []\n", + "def store_intermediate_result1(eval_count, parameters, mean, std):\n", + " counts1.append(eval_count)\n", + " values1.append(mean)\n", + "\n", + "aqua_globals.random_seed = 167\n", + "optimizer = SPSA(max_trials=200)\n", + "var_form = RY(num_qubits)\n", + "vqe = VQE(qubit_op, var_form, optimizer, 'paulis', callback=store_intermediate_result1)\n", + "vqe_result1 = vqe.run(quantum_instance)\n", + "print('VQE on Aer qasm simulator (with noise): {}'.format(vqe_result1['energy']))\n", + "print('Delta from reference: {}'.format(vqe_result1['energy']-ref))" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pylab.rcParams['figure.figsize'] = (12, 4)\n", + "pylab.plot(counts1, values1)\n", + "pylab.xlabel('Eval count')\n", + "pylab.ylabel('Energy')\n", + "pylab.title('Convergence with noise');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Declarative approach and noise model\n", + "\n", + "Note: if you are running an experiment using the declarative approach, with a dictionary/json, there are keywords in the `backend` section that let you define the noise model based on a device, as well as setup the coupling map too. The basis gate setup, that is shown above, will automatically be done. Here is an example of such a `backend` configuration:\n", + "```\n", + " 'backend': { \n", + "\t 'provider': 'qiskit.Aer',\n", + " 'name': 'qasm_simulator',\n", + "\t 'coupling_map_from_device': 'qiskit.IBMQ:ibmqx4',\n", + " 'noise_model': 'qiskit.IBMQ:ibmqx4',\n", + " 'shots': 1024\n", + "\t },\n", + "```\n", + "\n", + "If you call `run_algorithm` and override the `backend` section by explicity supplying a backend instance as a parameter to run_algorithm, please note that you can provide a QuantumInstance type there instead of BaseBackend. A QuantumInstance allows you to setup and define your own custom noise model and other run time configuration. \n", + "\n", + "(Note when a BaseBackend type is supplied to run_algorithm it is internally wrapped into a QuantumInstance, with default values supplied for noise, run time parameters etc., so you do not get the opportunity that way to set a noise model etc. But by explicitly providing a QuantumInstance you can setup these aspects to your choosing.)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From 2fd83d3927bef0ae37cb7eab9c7c1763b8cbef2f Mon Sep 17 00:00:00 2001 From: Manoel Marques Date: Fri, 19 Apr 2019 16:48:49 -0400 Subject: [PATCH 064/116] Fix Grover input file --- community/aqua/optimization/input_files/grover.json | 7 ++++--- 1 file changed, 4 insertions(+), 3 deletions(-) diff --git a/community/aqua/optimization/input_files/grover.json b/community/aqua/optimization/input_files/grover.json index bbf409359..84d511af7 100644 --- a/community/aqua/optimization/input_files/grover.json +++ b/community/aqua/optimization/input_files/grover.json @@ -4,11 +4,12 @@ }, "backend": { "provider": "qiskit.BasicAer", - "name": "qasm_simulator" + "name": "qasm_simulator", + "shots": 1000 }, "oracle": { - "expression": "p cnf 3 5 \n -1 -2 -3 0 \n 1 -2 3 0 \n 1 2 -3 0 \n 1 -2 -3 0 \n -1 2 3 0", - "name": "LogicExpressionOracle" + "expression": "c example DIMACS-CNF 3-SAT\np cnf 3 5\n-1 -2 -3 0\n1 -2 3 0\n1 2 -3 0\n1 -2 -3 0\n-1 2 3 0", + "name": "LogicalExpressionOracle" }, "problem": { "name": "search" From b5a1dc814b7edb6204acd31502795e5c1f589772 Mon Sep 17 00:00:00 2001 From: CZ Date: Sat, 20 Apr 2019 16:24:30 +0200 Subject: [PATCH 065/116] delete files --- .../qgans_for_loading_random.ipynb | 12526 ---------------- qiskit/finance/machine_learning/qgans.ipynb | 194 - 2 files changed, 12720 deletions(-) delete mode 100644 qiskit/aqua/artificial_intelligence/qgans_for_loading_random.ipynb delete mode 100644 qiskit/finance/machine_learning/qgans.ipynb diff --git a/qiskit/aqua/artificial_intelligence/qgans_for_loading_random.ipynb b/qiskit/aqua/artificial_intelligence/qgans_for_loading_random.ipynb deleted file mode 100644 index 8288dcfb8..000000000 --- a/qiskit/aqua/artificial_intelligence/qgans_for_loading_random.ipynb +++ /dev/null @@ -1,12526 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# _*Qiskit Aqua: qGANs for Loading Random Distributions*_ \n", - "\n", - "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", - "\n", - "***\n", - "### Contributors\n", - "Christa Zoufal[1,2], Stefan Woerner[1]\n", - "### Affliation\n", - "- [1]IBMQ\n", - "- [2]ETH Zurich\n", - "\n", - "### Introduction\n", - "Given $k$-dimensional data samples, we employ a quantum Generative Adversarial Network (qGAN) to learn the data's underlying random distribution and to load it directly into a quantum state: \n", - "$$\\lvert g_{\\theta}\\rangle = \\sum\\limits_{j=0}^{2^n-1}\\sqrt{p_{\\theta}^{j}}\\lvert{j}\\rangle$$\n", - "where $p_{\\theta}^{j}$ describe the occurrence probabilities of the basis states $\\vert j\\rangle$. \n", - "\n", - "The aim of the qGAN training is to generate a state $\\lvert g_{\\theta}\\rangle$ where $p_{\\theta}^{j}$, for $j\\in \\left\\{0, \\ldots, {2^n-1} \\right\\}$, describe a probability distribution that is close to the distribution underlying the training data $X=\\left\\{x^0, \\ldots, x^{k-1} \\right\\}$.\n", - "\n", - "For further details please refer to Quantum Generative Adversarial Networks for Learning and Loading Random Distributions. Zoufal, Lucchi, Woerner. 2019." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "#!/usr/bin/env python\n", - "# coding: utf-8\n", - "from __future__ import absolute_import, division, print_function\n", - "\n", - "import numpy as np\n", - "\n", - "import matplotlib\n", - "matplotlib.use('TkAgg')\n", - "import matplotlib.pyplot as plt\n", - "\n", - "%matplotlib inline\n", - "\n", - "\n", - "import time\n", - "\n", - "start = time.time()\n", - "\n", - "from torch import optim\n", - "from qiskit.aqua.algorithms.adaptive.qgan.discriminator import DiscriminatorNet\n", - "\n", - "from qiskit.aqua.components.optimizers import ADAM\n", - "from qiskit.aqua.components.uncertainty_models import UniformDistribution, UnivariateVariationalDistribution \n", - "from qiskit.aqua.components.variational_forms import RY\n", - "\n", - "from qiskit.aqua.algorithms.adaptive.qgan.qgan import QGAN\n", - "\n", - "from qiskit.aqua import aqua_globals, QuantumInstance\n", - "\n", - "from qiskit import BasicAer" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Load the Training Data\n", - "First, we need to load the $k$-dimensional training data samples (here k=1).
\n", - "Next, the data resolution is set, i.e. the min/max data values and the number of qubits used to represent each data dimension." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [], - "source": [ - "# Number training data samples\n", - "N = 10000 \n", - "\n", - "# Load data samples from log-normal distribution with mean=1 and standard deviation=1\n", - "mu = 1\n", - "sigma = 1\n", - "real_data = np.random.lognormal(mean = mu, sigma=sigma, size=N)\n", - "\n", - "# Set the data resolution\n", - "# Set upper and lower data values as list of k min/max data values [[min_0,max_0],...,[min_k-1,max_k-1]]\n", - "bounds = np.array([0.,3.]) \n", - "# Set number of qubits per data dimension as list of k qubit values[#q_0,...,#q_k-1]\n", - "num_qubits = [2]\n", - "k = len(num_qubits)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Initialize the qGAN\n", - "The qGAN consists of a quantum generator $G_{\\theta}$, a variational quantum circuit, and a classical discriminator $D_{\\phi}$, a neural network.
\n", - "To implement the quantum generator, we choose a depth-$1$ variational form that implements $R_Y$ rotations and $CZ$ gates which takes a uniform distribution as an input state. Notably, for $k>1$ the generator's parameters must be chosen carefully. For example, the circuit depth should $>1$ becaue the higher the circuit depth the because higher circuit depths enable the representation of more complex structures.
\n", - "The classical discriminator is given by a $3$-layer neural network that applies linear transformations, leaky ReLU functions in the hidden layers and a sigmoid function in the output layer. Notably, the neural network is implemented with PyTorch. Please refer to https://pytorch.org/get-started/locally/ for PyTorch installation instructions.
\n", - "Here, both networks are updated with the ADAM optimization algorithm." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [], - "source": [ - "# Set number of training epochs\n", - "# Note: The algorithm's runtime can be shortened by reducing the number of training epochs.\n", - "num_epochs = 3000\n", - "# Batch size\n", - "batch_size = 1000\n", - "\n", - "# Initialize qGAN\n", - "qgan = QGAN(real_data, bounds, num_qubits, batch_size, num_epochs, snapshot_dir=None)\n", - "\n", - "# Set quantum instance to run the quantum generator\n", - "backend = BasicAer.get_backend('statevector_simulator')\n", - "qgan.set_quantum_instance(QuantumInstance(backend=backend, shots=batch_size, coupling_map=None, circuit_caching=False))\n", - "\n", - "\n", - "# Set entangler map\n", - "entangler_map = [[0, 1]]\n", - " \n", - "# Set variational form\n", - "var_form = RY(int(np.sum(num_qubits)), depth=1, entangler_map=entangler_map, entanglement_gate='cz')\n", - "# Set generator's initial parameters\n", - "init_params = aqua_globals.random.rand(var_form._num_parameters) * 2 * 1e-2\n", - "# Set an initial state for the generator circuit\n", - "init_dist = UniformDistribution(np.sum(num_qubits), low=bounds[0], high=bounds[1])\n", - "# Set generator circuit\n", - "g_circuit = UnivariateVariationalDistribution(sum(num_qubits), var_form, init_params,\n", - " initial_distribution=init_dist, low=bounds[0], high=bounds[1])\n", - "# Set generator optimizer\n", - "g_optimizer = ADAM(maxiter=1, tol=1e-6, lr=1e-5, beta_1=0.9, beta_2=0.99, noise_factor=1e-6,\n", - " eps=1e-10, amsgrad=True)\n", - "# Set quantum generator\n", - "qgan.set_generator(generator_circuit=g_circuit, generator_optimizer=g_optimizer)\n", - "\n", - "# Set discriminator network\n", - "d_net = DiscriminatorNet(n_features=k)\n", - "# Set discriminator optimizer\n", - "d_optimizer = optim.Adam(d_net.parameters(), lr=1e-5, amsgrad=True)\n", - "# Set classical discriminator neural network\n", - "qgan.set_discriminator(discriminator_net=d_net, discriminator_optimizer=d_optimizer)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Run the qGAN Training\n", - "During the training the discriminator's and the generator's parameters are updated alternately w.r.t the following loss functions:\n", - "$$ L_G\\left(\\phi, \\theta\\right) = -\\frac{1}{m}\\sum\\limits_{l=1}^{m}\\left[\\log\\left(D_{\\phi}\\left(g^{l}\\right)\\right)\\right] $$\n", - "and\n", - "$$ L_D\\left(\\phi, \\theta\\right) =\n", - "\t\\frac{1}{m}\\sum\\limits_{l=1}^{m}\\left[\\log D_{\\phi}\\left(x^{l}\\right) + \\log\\left(1-D_{\\phi}\\left(g^{l}\\right)\\right)\\right], $$\n", - "with $m$ denoting the batch size and $g^l$ describing the data samples generated by the quantum generator." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Epoch 1/3000...\n", - "Loss Discriminator: 0.6977\n", - "Loss Generator: 0.6754\n", - "Relative Entropy: 0.1783\n", - "Epoch 2/3000...\n", - "Loss Discriminator: 0.6964\n", - "Loss Generator: 0.6806\n", - "Relative Entropy: 0.1783\n", - "Epoch 3/3000...\n", - "Loss Discriminator: 0.6948\n", - "Loss Generator: 0.6832\n", - "Relative Entropy: 0.1784\n", - "Epoch 4/3000...\n", - "Loss Discriminator: 0.6935\n", - "Loss Generator: 0.6851\n", - "Relative Entropy: 0.1784\n", - "Epoch 5/3000...\n", - "Loss Discriminator: 0.6923\n", - "Loss Generator: 0.687\n", - "Relative Entropy: 0.1784\n", - "Epoch 6/3000...\n", - "Loss Discriminator: 0.6912\n", - "Loss Generator: 0.6864\n", - "Relative Entropy: 0.1783\n", - "Epoch 7/3000...\n", - "Loss Discriminator: 0.6901\n", - "Loss Generator: 0.6865\n", - "Relative Entropy: 0.1783\n", - "Epoch 8/3000...\n", - "Loss Discriminator: 0.689\n", - "Loss Generator: 0.6879\n", - "Relative Entropy: 0.1782\n", - "Epoch 9/3000...\n", - "Loss Discriminator: 0.6875\n", - "Loss Generator: 0.6894\n", - "Relative Entropy: 0.1781\n", - 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"Relative Entropy: 0.0733\n", - "Epoch 1958/3000...\n", - "Loss Discriminator: 0.6822\n", - "Loss Generator: 0.7084\n", - "Relative Entropy: 0.0733\n", - "Epoch 1959/3000...\n", - "Loss Discriminator: 0.6832\n", - "Loss Generator: 0.7069\n", - "Relative Entropy: 0.0733\n", - "Epoch 1960/3000...\n", - "Loss Discriminator: 0.6834\n", - "Loss Generator: 0.7079\n", - "Relative Entropy: 0.0732\n", - "Epoch 1961/3000...\n", - "Loss Discriminator: 0.6838\n", - "Loss Generator: 0.7095\n", - "Relative Entropy: 0.0732\n", - "Epoch 1962/3000...\n", - "Loss Discriminator: 0.6834\n", - "Loss Generator: 0.7116\n", - "Relative Entropy: 0.0731\n", - "Epoch 1963/3000...\n", - "Loss Discriminator: 0.6825\n", - "Loss Generator: 0.7088\n", - "Relative Entropy: 0.0731\n", - "Epoch 1964/3000...\n", - "Loss Discriminator: 0.6837\n", - "Loss Generator: 0.7071\n", - "Relative Entropy: 0.073\n", - "Epoch 1965/3000...\n", - "Loss Discriminator: 0.6836\n", - "Loss Generator: 0.7106\n", - "Relative Entropy: 0.073\n", - "Epoch 1966/3000...\n", - "Loss Discriminator: 0.6826\n", - "Loss Generator: 0.7093\n", - "Relative Entropy: 0.073\n", - "Epoch 1967/3000...\n", - "Loss Discriminator: 0.6834\n", - "Loss Generator: 0.7086\n", - "Relative Entropy: 0.0729\n", - "Epoch 1968/3000...\n", - "Loss Discriminator: 0.6836\n", - "Loss Generator: 0.7099\n", - "Relative Entropy: 0.0729\n", - "Epoch 1969/3000...\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Loss Discriminator: 0.6832\n", - "Loss Generator: 0.7086\n", - "Relative Entropy: 0.0728\n", - "Epoch 1970/3000...\n", - "Loss Discriminator: 0.6825\n", - "Loss Generator: 0.7112\n", - "Relative Entropy: 0.0728\n", - "Epoch 1971/3000...\n", - "Loss Discriminator: 0.683\n", - "Loss Generator: 0.7077\n", - "Relative Entropy: 0.0727\n", - "Epoch 1972/3000...\n", - "Loss Discriminator: 0.6822\n", - "Loss Generator: 0.7089\n", - "Relative Entropy: 0.0727\n", - "Epoch 1973/3000...\n", - "Loss Discriminator: 0.6832\n", - "Loss Generator: 0.7102\n", - 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"Loss Generator: 0.7049\n", - "Relative Entropy: 0.0402\n", - "Epoch 2881/3000...\n", - "Loss Discriminator: 0.688\n", - "Loss Generator: 0.7018\n", - "Relative Entropy: 0.0402\n", - "Epoch 2882/3000...\n", - "Loss Discriminator: 0.6888\n", - "Loss Generator: 0.6981\n", - "Relative Entropy: 0.0402\n", - "Epoch 2883/3000...\n", - "Loss Discriminator: 0.6875\n", - "Loss Generator: 0.6994\n", - "Relative Entropy: 0.0401\n", - "Epoch 2884/3000...\n", - "Loss Discriminator: 0.6892\n", - "Loss Generator: 0.7022\n", - "Relative Entropy: 0.0401\n", - "Epoch 2885/3000...\n", - "Loss Discriminator: 0.6879\n", - "Loss Generator: 0.7008\n", - "Relative Entropy: 0.0401\n", - "Epoch 2886/3000...\n", - "Loss Discriminator: 0.6895\n", - "Loss Generator: 0.7\n", - "Relative Entropy: 0.04\n", - "Epoch 2887/3000...\n", - "Loss Discriminator: 0.6871\n", - "Loss Generator: 0.7018\n", - "Relative Entropy: 0.04\n", - "Epoch 2888/3000...\n", - "Loss Discriminator: 0.687\n", - "Loss Generator: 0.7036\n", - "Relative Entropy: 0.04\n", - "Epoch 2889/3000...\n", - "Loss Discriminator: 0.6879\n", - "Loss Generator: 0.7021\n", - "Relative Entropy: 0.04\n", - "Epoch 2890/3000...\n", - "Loss Discriminator: 0.6882\n", - "Loss Generator: 0.6992\n", - "Relative Entropy: 0.0399\n", - "Epoch 2891/3000...\n", - "Loss Discriminator: 0.6884\n", - "Loss Generator: 0.7013\n", - "Relative Entropy: 0.0399\n", - "Epoch 2892/3000...\n", - "Loss Discriminator: 0.6876\n", - "Loss Generator: 0.7028\n", - "Relative Entropy: 0.0399\n", - "Epoch 2893/3000...\n", - "Loss Discriminator: 0.6871\n", - "Loss Generator: 0.7018\n", - "Relative Entropy: 0.0398\n", - "Epoch 2894/3000...\n", - "Loss Discriminator: 0.6881\n", - "Loss Generator: 0.6993\n", - "Relative Entropy: 0.0398\n", - "Epoch 2895/3000...\n", - "Loss Discriminator: 0.6883\n", - "Loss Generator: 0.7009\n", - "Relative Entropy: 0.0398\n", - "Epoch 2896/3000...\n", - "Loss Discriminator: 0.6881\n", - "Loss Generator: 0.7006\n", - "Relative Entropy: 0.0398\n", - "Epoch 2897/3000...\n", - "Loss Discriminator: 0.6873\n", - "Loss Generator: 0.7019\n", - "Relative Entropy: 0.0397\n", - "Epoch 2898/3000...\n", - "Loss Discriminator: 0.6879\n", - "Loss Generator: 0.6996\n", - "Relative Entropy: 0.0397\n", - "Epoch 2899/3000...\n", - "Loss Discriminator: 0.6879\n", - "Loss Generator: 0.7001\n", - "Relative Entropy: 0.0397\n", - "Epoch 2900/3000...\n", - "Loss Discriminator: 0.687\n", - "Loss Generator: 0.7002\n", - "Relative Entropy: 0.0396\n", - "Epoch 2901/3000...\n", - "Loss Discriminator: 0.6883\n", - "Loss Generator: 0.7048\n", - "Relative Entropy: 0.0396\n", - "Epoch 2902/3000...\n", - "Loss Discriminator: 0.6881\n", - "Loss Generator: 0.7024\n", - "Relative Entropy: 0.0396\n", - "Epoch 2903/3000...\n", - "Loss Discriminator: 0.6887\n", - "Loss Generator: 0.7012\n", - "Relative Entropy: 0.0396\n", - "Epoch 2904/3000...\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Loss Discriminator: 0.6878\n", - "Loss Generator: 0.7009\n", - "Relative Entropy: 0.0395\n", - "Epoch 2905/3000...\n", - "Loss Discriminator: 0.6884\n", - "Loss Generator: 0.6999\n", - "Relative Entropy: 0.0395\n", - "Epoch 2906/3000...\n", - "Loss Discriminator: 0.6879\n", - "Loss Generator: 0.7008\n", - "Relative Entropy: 0.0395\n", - "Epoch 2907/3000...\n", - "Loss Discriminator: 0.6869\n", - "Loss Generator: 0.7023\n", - "Relative Entropy: 0.0394\n", - "Epoch 2908/3000...\n", - "Loss Discriminator: 0.6876\n", - "Loss Generator: 0.7005\n", - "Relative Entropy: 0.0394\n", - "Epoch 2909/3000...\n", - "Loss Discriminator: 0.6899\n", - "Loss Generator: 0.6992\n", - "Relative Entropy: 0.0394\n", - "Epoch 2910/3000...\n", - "Loss Discriminator: 0.6881\n", - "Loss Generator: 0.7027\n", - "Relative Entropy: 0.0394\n", - "Epoch 2911/3000...\n", - "Loss Discriminator: 0.6881\n", - "Loss Generator: 0.7018\n", - "Relative Entropy: 0.0393\n", - "Epoch 2912/3000...\n", - "Loss Discriminator: 0.6878\n", - "Loss Generator: 0.7006\n", - "Relative Entropy: 0.0393\n", - "Epoch 2913/3000...\n", - "Loss Discriminator: 0.6877\n", - "Loss Generator: 0.7017\n", - "Relative Entropy: 0.0393\n", - "Epoch 2914/3000...\n", - "Loss Discriminator: 0.6878\n", - "Loss Generator: 0.7004\n", - "Relative Entropy: 0.0393\n", - "Epoch 2915/3000...\n", - "Loss Discriminator: 0.6876\n", - "Loss Generator: 0.6998\n", - "Relative Entropy: 0.0392\n", - "Epoch 2916/3000...\n", - "Loss Discriminator: 0.6877\n", - "Loss Generator: 0.7049\n", - "Relative Entropy: 0.0392\n", - "Epoch 2917/3000...\n", - "Loss Discriminator: 0.6881\n", - "Loss Generator: 0.7019\n", - "Relative Entropy: 0.0392\n", - "Epoch 2918/3000...\n", - "Loss Discriminator: 0.6884\n", - "Loss Generator: 0.7003\n", - "Relative Entropy: 0.0391\n", - "Epoch 2919/3000...\n", - "Loss Discriminator: 0.6872\n", - "Loss Generator: 0.699\n", - "Relative Entropy: 0.0391\n", - "Epoch 2920/3000...\n", - "Loss Discriminator: 0.6887\n", - "Loss Generator: 0.7018\n", - "Relative Entropy: 0.0391\n", - "Epoch 2921/3000...\n", - "Loss Discriminator: 0.689\n", - "Loss Generator: 0.7025\n", - "Relative Entropy: 0.0391\n", - "Epoch 2922/3000...\n", - "Loss Discriminator: 0.6866\n", - "Loss Generator: 0.6973\n", - "Relative Entropy: 0.039\n", - "Epoch 2923/3000...\n", - "Loss Discriminator: 0.6871\n", - "Loss Generator: 0.6987\n", - "Relative Entropy: 0.039\n", - "Epoch 2924/3000...\n", - "Loss Discriminator: 0.6876\n", - "Loss Generator: 0.705\n", - "Relative Entropy: 0.039\n", - "Epoch 2925/3000...\n", - "Loss Discriminator: 0.6877\n", - "Loss Generator: 0.7027\n", - "Relative Entropy: 0.0389\n", - "Epoch 2926/3000...\n", - "Loss Discriminator: 0.6878\n", - "Loss Generator: 0.6986\n", - "Relative Entropy: 0.0389\n", - "Epoch 2927/3000...\n", - "Loss Discriminator: 0.6879\n", - "Loss Generator: 0.7016\n", - "Relative Entropy: 0.0389\n", - "Epoch 2928/3000...\n", - "Loss Discriminator: 0.6885\n", - "Loss Generator: 0.7013\n", - "Relative Entropy: 0.0389\n", - "Epoch 2929/3000...\n", - "Loss Discriminator: 0.6874\n", - "Loss Generator: 0.6999\n", - "Relative Entropy: 0.0388\n", - "Epoch 2930/3000...\n", - "Loss Discriminator: 0.6879\n", - "Loss Generator: 0.6988\n", - "Relative Entropy: 0.0388\n", - "Epoch 2931/3000...\n", - "Loss Discriminator: 0.6883\n", - "Loss Generator: 0.7012\n", - "Relative Entropy: 0.0388\n", - "Epoch 2932/3000...\n", - "Loss Discriminator: 0.6885\n", - "Loss Generator: 0.7019\n", - "Relative Entropy: 0.0388\n", - "Epoch 2933/3000...\n", - "Loss Discriminator: 0.6882\n", - "Loss Generator: 0.7003\n", - "Relative Entropy: 0.0387\n", - "Epoch 2934/3000...\n", - "Loss Discriminator: 0.6886\n", - "Loss Generator: 0.7012\n", - "Relative Entropy: 0.0387\n", - "Epoch 2935/3000...\n", - "Loss Discriminator: 0.6889\n", - "Loss Generator: 0.7027\n", - "Relative Entropy: 0.0387\n", - "Epoch 2936/3000...\n", - "Loss Discriminator: 0.6886\n", - "Loss Generator: 0.6993\n", - "Relative Entropy: 0.0386\n", - "Epoch 2937/3000...\n", - "Loss Discriminator: 0.6875\n", - "Loss Generator: 0.7011\n", - "Relative Entropy: 0.0386\n", - "Epoch 2938/3000...\n", - "Loss Discriminator: 0.6873\n", - "Loss Generator: 0.7006\n", - "Relative Entropy: 0.0386\n", - "Epoch 2939/3000...\n", - "Loss Discriminator: 0.6884\n", - "Loss Generator: 0.7012\n", - "Relative Entropy: 0.0386\n", - "Epoch 2940/3000...\n", - "Loss Discriminator: 0.6875\n", - "Loss Generator: 0.701\n", - "Relative Entropy: 0.0385\n", - "Epoch 2941/3000...\n", - "Loss Discriminator: 0.6892\n", - "Loss Generator: 0.6995\n", - "Relative Entropy: 0.0385\n", - "Epoch 2942/3000...\n", - "Loss Discriminator: 0.6888\n", - "Loss Generator: 0.7026\n", - "Relative Entropy: 0.0385\n", - "Epoch 2943/3000...\n", - "Loss Discriminator: 0.6889\n", - "Loss Generator: 0.7017\n", - "Relative Entropy: 0.0385\n", - "Epoch 2944/3000...\n", - "Loss Discriminator: 0.6889\n", - "Loss Generator: 0.7013\n", - "Relative Entropy: 0.0384\n", - "Epoch 2945/3000...\n", - "Loss Discriminator: 0.6875\n", - "Loss Generator: 0.6996\n", - "Relative Entropy: 0.0384\n", - "Epoch 2946/3000...\n", - "Loss Discriminator: 0.6874\n", - "Loss Generator: 0.7039\n", - "Relative Entropy: 0.0384\n", - "Epoch 2947/3000...\n", - "Loss Discriminator: 0.6889\n", - "Loss Generator: 0.7011\n", - "Relative Entropy: 0.0383\n", - "Epoch 2948/3000...\n", - "Loss Discriminator: 0.6873\n", - "Loss Generator: 0.6973\n", - "Relative Entropy: 0.0383\n", - "Epoch 2949/3000...\n", - "Loss Discriminator: 0.6892\n", - "Loss Generator: 0.6995\n", - "Relative Entropy: 0.0383\n", - "Epoch 2950/3000...\n", - "Loss Discriminator: 0.6871\n", - "Loss Generator: 0.7035\n", - "Relative Entropy: 0.0383\n", - "Epoch 2951/3000...\n", - "Loss Discriminator: 0.6883\n", - "Loss Generator: 0.7007\n", - "Relative Entropy: 0.0382\n", - "Epoch 2952/3000...\n", - "Loss Discriminator: 0.6879\n", - "Loss Generator: 0.6997\n", - "Relative Entropy: 0.0382\n", - "Epoch 2953/3000...\n", - "Loss Discriminator: 0.6892\n", - "Loss Generator: 0.7005\n", - "Relative Entropy: 0.0382\n", - "Epoch 2954/3000...\n", - "Loss Discriminator: 0.6887\n", - "Loss Generator: 0.7003\n", - "Relative Entropy: 0.0382\n", - "Epoch 2955/3000...\n", - "Loss Discriminator: 0.6884\n", - "Loss Generator: 0.7036\n", - "Relative Entropy: 0.0381\n", - "Epoch 2956/3000...\n", - "Loss Discriminator: 0.6888\n", - "Loss Generator: 0.7011\n", - "Relative Entropy: 0.0381\n", - "Epoch 2957/3000...\n", - "Loss Discriminator: 0.6883\n", - "Loss Generator: 0.6995\n", - "Relative Entropy: 0.0381\n", - "Epoch 2958/3000...\n", - "Loss Discriminator: 0.6876\n", - "Loss Generator: 0.6979\n", - "Relative Entropy: 0.038\n", - "Epoch 2959/3000...\n", - "Loss Discriminator: 0.6878\n", - "Loss Generator: 0.7045\n", - "Relative Entropy: 0.038\n", - "Epoch 2960/3000...\n", - "Loss Discriminator: 0.688\n", - "Loss Generator: 0.7021\n", - "Relative Entropy: 0.038\n", - "Epoch 2961/3000...\n", - "Loss Discriminator: 0.688\n", - "Loss Generator: 0.6981\n", - "Relative Entropy: 0.038\n", - "Epoch 2962/3000...\n", - "Loss Discriminator: 0.6893\n", - "Loss Generator: 0.7006\n", - "Relative Entropy: 0.0379\n", - "Epoch 2963/3000...\n", - "Loss Discriminator: 0.6886\n", - "Loss Generator: 0.7019\n", - "Relative Entropy: 0.0379\n", - "Epoch 2964/3000...\n", - "Loss Discriminator: 0.6884\n", - "Loss Generator: 0.7006\n", - "Relative Entropy: 0.0379\n", - "Epoch 2965/3000...\n", - "Loss Discriminator: 0.6891\n", - "Loss Generator: 0.7011\n", - "Relative Entropy: 0.0379\n", - "Epoch 2966/3000...\n", - "Loss Discriminator: 0.6878\n", - "Loss Generator: 0.7001\n", - "Relative Entropy: 0.0378\n", - "Epoch 2967/3000...\n", - "Loss Discriminator: 0.6889\n", - "Loss Generator: 0.6998\n", - "Relative Entropy: 0.0378\n", - "Epoch 2968/3000...\n", - "Loss Discriminator: 0.6884\n", - "Loss Generator: 0.7014\n", - "Relative Entropy: 0.0378\n", - "Epoch 2969/3000...\n", - "Loss Discriminator: 0.6881\n", - "Loss Generator: 0.702\n", - "Relative Entropy: 0.0377\n", - "Epoch 2970/3000...\n", - "Loss Discriminator: 0.6883\n", - "Loss Generator: 0.6995\n", - "Relative Entropy: 0.0377\n", - "Epoch 2971/3000...\n", - "Loss Discriminator: 0.6882\n", - "Loss Generator: 0.702\n", - "Relative Entropy: 0.0377\n", - "Epoch 2972/3000...\n", - "Loss Discriminator: 0.6883\n", - "Loss Generator: 0.7014\n", - "Relative Entropy: 0.0377\n", - "Epoch 2973/3000...\n", - "Loss Discriminator: 0.6891\n", - "Loss Generator: 0.6977\n", - "Relative Entropy: 0.0376\n", - "Epoch 2974/3000...\n", - "Loss Discriminator: 0.6884\n", - "Loss Generator: 0.7018\n", - "Relative Entropy: 0.0376\n", - "Epoch 2975/3000...\n", - "Loss Discriminator: 0.6888\n", - "Loss Generator: 0.705\n", - "Relative Entropy: 0.0376\n", - "Epoch 2976/3000...\n", - "Loss Discriminator: 0.688\n", - "Loss Generator: 0.6991\n", - "Relative Entropy: 0.0376\n", - "Epoch 2977/3000...\n", - "Loss Discriminator: 0.688\n", - "Loss Generator: 0.6981\n", - "Relative Entropy: 0.0375\n", - "Epoch 2978/3000...\n", - "Loss Discriminator: 0.6881\n", - "Loss Generator: 0.7028\n", - "Relative Entropy: 0.0375\n", - "Epoch 2979/3000...\n", - "Loss Discriminator: 0.687\n", - "Loss Generator: 0.6996\n", - "Relative Entropy: 0.0375\n", - "Epoch 2980/3000...\n", - "Loss Discriminator: 0.6879\n", - "Loss Generator: 0.6981\n", - "Relative Entropy: 0.0374\n", - "Epoch 2981/3000...\n", - "Loss Discriminator: 0.6872\n", - "Loss Generator: 0.7012\n", - "Relative Entropy: 0.0374\n", - "Epoch 2982/3000...\n", - "Loss Discriminator: 0.6895\n", - "Loss Generator: 0.704\n", - "Relative Entropy: 0.0374\n", - "Epoch 2983/3000...\n", - "Loss Discriminator: 0.6879\n", - "Loss Generator: 0.6966\n", - "Relative Entropy: 0.0374\n", - "Epoch 2984/3000...\n", - "Loss Discriminator: 0.6875\n", - "Loss Generator: 0.6983\n", - "Relative Entropy: 0.0373\n", - "Epoch 2985/3000...\n", - "Loss Discriminator: 0.6882\n", - "Loss Generator: 0.7053\n", - "Relative Entropy: 0.0373\n", - "Epoch 2986/3000...\n", - "Loss Discriminator: 0.6875\n", - "Loss Generator: 0.7009\n", - "Relative Entropy: 0.0373\n", - "Epoch 2987/3000...\n", - "Loss Discriminator: 0.6884\n", - "Loss Generator: 0.6982\n", - "Relative Entropy: 0.0373\n", - "Epoch 2988/3000...\n", - "Loss Discriminator: 0.6879\n", - "Loss Generator: 0.701\n", - "Relative Entropy: 0.0372\n", - "Epoch 2989/3000...\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Loss Discriminator: 0.687\n", - "Loss Generator: 0.7023\n", - "Relative Entropy: 0.0372\n", - "Epoch 2990/3000...\n", - "Loss Discriminator: 0.6879\n", - "Loss Generator: 0.7025\n", - "Relative Entropy: 0.0372\n", - "Epoch 2991/3000...\n", - "Loss Discriminator: 0.6886\n", - "Loss Generator: 0.6976\n", - "Relative Entropy: 0.0372\n", - "Epoch 2992/3000...\n", - "Loss Discriminator: 0.6884\n", - "Loss Generator: 0.7018\n", - "Relative Entropy: 0.0371\n", - "Epoch 2993/3000...\n", - "Loss Discriminator: 0.6886\n", - "Loss Generator: 0.7024\n", - "Relative Entropy: 0.0371\n", - "Epoch 2994/3000...\n", - "Loss Discriminator: 0.6887\n", - "Loss Generator: 0.699\n", - "Relative Entropy: 0.0371\n", - "Epoch 2995/3000...\n", - "Loss Discriminator: 0.6886\n", - "Loss Generator: 0.696\n", - "Relative Entropy: 0.037\n", - "Epoch 2996/3000...\n", - "Loss Discriminator: 0.6887\n", - "Loss Generator: 0.703\n", - "Relative Entropy: 0.037\n", - "Epoch 2997/3000...\n", - "Loss Discriminator: 0.6879\n", - "Loss Generator: 0.7013\n", - "Relative Entropy: 0.037\n", - "Epoch 2998/3000...\n", - "Loss Discriminator: 0.6886\n", - "Loss Generator: 0.6993\n", - "Relative Entropy: 0.037\n", - "Epoch 2999/3000...\n", - "Loss Discriminator: 0.6884\n", - "Loss Generator: 0.7012\n", - "Relative Entropy: 0.0369\n", - "Epoch 3000/3000...\n", - "Loss Discriminator: 0.6887\n", - "Loss Generator: 0.7016\n", - "Relative Entropy: 0.0369\n", - "qGAN training runtime: 35.25595039923986 min\n" - ] - } - ], - "source": [ - "# Run qGAN\n", - "qgan.run()\n", - "\n", - "# Runtime\n", - "end = time.time()\n", - "print('qGAN training runtime: ', (end - start)/60., ' min')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Training Progress & Outcome\n", - "Now, we plot the evolution of the generator's and the discriminator's loss functions during the training as well as the progress in the relative entropy between the trained and the target distribution.\n", - "
Finally, we also compare the cumulative distribution function (CDF) of the trained distribution to the CDF of the target distribution." - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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vhYOTinVeyo+7SFt1hIzVR8k/c5EtfWeiigwTo4KMXI69lsjhZ/SKX437iI6OZtOmTeb7GTNmsHTpUs6ePQsYTCDvv/8+SUlJJCUlcejQIfPMIjAw0FzP19eXgoIClFJER0eby2/bto0//ij+TltGOH344YeZOHEi27Zt45NPPqnU8syqRH+dPHkys2bNIjs7m759+7J792769+/P8uXLadq0KePGjePLL78ssw0/Pz+KiorM9yX7YHpHpvfjbGx9Bt5GjYk66ypUQZHN9F23zDVf5x4+z9FXl9FwZBy+YUHuEk3jpdiaAbh6A9igQYN49tln+eijj3jwwQcBrEwvV199NR999BGDBg3C39+fvXv30rRpU7vtdejQgbNnz7JmzRouu+wy8vPz2bt3L9HR0aXKpqWlmdv64osvzOmhoaGkp6eb7/v06cO8efO48847mTt3Lv369atQH/v168fcuXN54YUXSExMpH79+tSpU4cDBw4QGxtLbGws69evZ/fu3QQHBxMVFcV9991Hbm4umzZt4q677rLbdosWLdi5cye5ublkZ2ezdOnScn/ZDxkyhBkzZvDuu+8CBjNUREQE/v7+5Ofnl9op3a9fPz755BPGjh1Lamoqy5cv51//+pfZB+Lt6JmFkzg5Yy1bLp/Jptj3zGnZ+1M8KJHmUkJE+PHHH/nrr79o1aoVPXv2ZOzYsbz55puAwUbfuXNnunXrRkxMDA888ECZv14DAgJYsGABTz/9NF26dCE+Pt7uqp4pU6YwfPhwunfvTv369c3pN954Iz/88IPZwf3+++/z+eefExcXx5w5c5g+fXqF+jhlyhQ2btxIXFwckydPNiumd999l5iYGOLi4vD39+faa68lMTGRLl260LVrV7799lv++c9/ltl2s2bNuP3224mJieH222+na9eSwSRK8/zzz3P+/HliYmLo0qULy5YtA+D+++8nLi7O7OA2ccsttxAXF0eXLl0YNGgQb731Fo0aNarQO/AkNeYM7oSEBOXs8yyKcgr4u/lbVZKr55En8QmuXCyWyqBj9HuGXbt20alTJ7v5l1JoiepCTekHON4XW99TEdmolCrXwapnFmWQ/PaK8guVw98t/kVhVj5KKfJTssqvoNFoNF6IVhZlcOK9NeUXcoBz87exrtHrbOz0LmnLD5XKL8ovJDPppNlJrtFoNN6GVhZu4NBTv4NRD5yatbF0/hO/sf2qzzkxvWbs9NRoNDUPrSzcjMovRBUUkXemOOjc2W8MO1FPfV5akWg0Go03oJWFm7mw9ADrmrzBppj3OPnJ31ZKQ+UWcuHPAxTlet8aa41Gc2mjlYUHOfrynxz4R3G4rILz2ewe8S1HXlziQak0Go2mNFpZeBBVUETa8sOl0s/MKR1XRqMpD19fX+Lj44mOjqZLly6888475l3JGzZs4JFHHqnyMz7++GO+/vrrCtXp06dPpZ83e/ZsTpw4Uen6YNif8fbbb1epDXu89957dOrUqdSeiqpw+PBhq3fsrM+uqugd3Hbw5Moke7vGNZqyCA4ONgewO3PmDKNGjSI9PZ2XX36ZhIQEEhKqFqusoKCACRMmVPjAoKqE6J49ezYxMTE0adLE4TqFhYXlxplyFh9++CFLliwxx3VyBiZlMWrUKACnfHbOQM8s7JC++ohnn7/mKEV5hR6VQVN9adiwITNnzuSDDz5AKWUVgttWSG+AN998k9jYWLp06cLkyYYTAQYOHGgVjnzKlCm899575rxJkyaRkJBAp06dWL9+Pbfeeivt2rXj+eefN8tiCtFdVijuV155hR49ehATE8P999+PUooFCxawYcMGRo8eTXx8vDkMR9euXYmNjWX8+PHk5uYChjDiTz/9NN26deO7776z+16SkpLo3bs3cXFxjBo1ivPnzwOGGULnzp2Ji4tjxIgRZb4nExMmTODgwYNce+21TJs2rdQMJiYmhsOHD3P48GE6derEfffdR3R0NFdddRXZ2dkA7N+/n8GDB9OlSxe6devGgQMHmDx5MitWrCA+Pp5p06ZZfXb2wrRPnTqV8ePHM3DgQFq3bm3+jJyJVhZ22HVrxabazmbnzV9x5IX/eVQGTfWmdevWFBYWcubMGat0U0jvpKQkVqxYQXBwML/99hs//fQT69atY8uWLVYRYU3hyB9//PFSzwgICGDDhg1MmDCBm2++mRkzZrB9+3Zmz55NSkrpcDebN2/m3XffZefOnRw8eJBVq1YBhvMj1q9fz/bt28nOzuaXX35h2LBhJCQkMHfuXJKSkhARxo0bx7fffsu2bdsoKCjgo48+Mrddr149Nm3aZB7sbXHXXXfx5ptvsnXrVjp37szLL78MwBtvvMHmzZvZunUrH3/8sd33ZMnHH39MkyZNWLZsGZMmTSrzs9i3bx8PPfQQO3bsIDw83Bw9d/To0Tz00ENs2bKF1atX07hxY9544w369etHUlJSqXZNYdq3bt3K1KlTreJd7d69m8WLF/P333/z8ssvk5/v3HN3tBnKizn9+SZavnYV4ueDKizS52ZUEx5ImOmSdj/ZcL9T2rEV0nvJkiXcfffd1KpVC4C6deuay1uGIy/JTTfdBEBsbCzR0dHmMOatW7fm2LFj1KtXz6q8vVDcy5Yt46233iIrK4vU1FSio6O58cYbreru2bOHVq1a0b59ewDGjh3LjBkzePTRR8uVEwwBDy9cuMCAAQMAGDVqFHfffTeAOZbT0KFDGTp0qN33VFlatWplDpPevXt3Dh8+TEZGBsePH+eWW24BICio/CCk9sK0A1x//fUEBgYSGBhIw4YNOX36tFPNY3r0qQTujCy7rskbrG04lQ0dplGQkWtOLzifTc6h826TQ1P9OHjwIL6+vjRs2NAq3VZI77IoK3y4KbS2j4+PVZhtHx8fm4EKbYXizsnJ4R//+AcLFixg27Zt3HfffW4Pc/7rr7/y0EMPsWnTJnr06EFBQUGF31NZYc7dEYLc1c/QM4sK4t8ohE7fjWRrv/+49bmF6bmkJR6i3o0dSf73SpLfWA5At60PE9CoZgRDqynYmgG4O2jd2bNnmTBhAhMnTkRErPJshfQeMmQIr7zyCqNHj6ZWrVqkpqZazS5ciWlQrV+/PpmZmSxYsIBhw4YBhjDnJl9Bhw4dOHz4MPv376dt27bMmTPHPEtwhLCwMCIiIlixYgX9+vVj3rx5DBgwgKKiIo4dO8YVV1zB5Zdfzrx588jMzCQlJaXUe+rYsaPd9lu2bMkvv/wCwKZNmzh0qHRoH0tCQ0OJiorixx9/ZOjQoeTm5lJYWGjV55LYC9PuDrSyqABd1jxAUOu6FGV7ZtPcvnsW4v/zGLOiAMjeew6/8GAK0nIIiAzxiFwa78B09nN+fj5+fn7ceeedPPbYY6XKvfvuuyxbtgwfHx+io6O59tprCQwMJCkpiYSEBAICArjuuuuYOtU1J/6VJDw8nPvuu4+YmBgaNWpEjx49zHmm87mDg4NZs2YNn3/+OcOHD6egoIAePXpYnTnuCF988QUTJkwgKyuL5s2bM2fOHAoLCxkzZgxpaWkopXjkkUcIDw/nhRdeKPWeyuK2227jyy+/JDo6ml69epnNZWUxZ84cHnjgAV588UX8/f357rvviIuLw9fXly5dujBu3DircOlTpkxh/PjxxMXFUatWLavzQ1yNDlFupGQ4bFtHY1oeanP6y80ceuI3AEK6NyFzY9XWgleWTgtHcfDRReQevUDXjQ+x5sDmahPWuzx0iHLvpKb0pab0A9wTolzPLCpJ5F1dCRvQCr+wQHzDglgX+bpH5Mg/lUnu0QsAZKw7BsazZ1RhEed/20tor2b4NzDYctNXHyHnyAUajuziEVk1Gk31RTu4HaTN+zeWSgtqEY5feDAiQpNHLvOAVLDfIlyIJadnb2Lv+IVsjC4+jWzn0Lkc/OevZO895y7xNBpNDUHPLBygx6En8K0dUHYhL7Dm7f/HzwS0CaHwf5eR9lexc63gfDZ+EcVrxPPPXSS4fX1bTWg0Go1N9MzCBiVDfZSrKAAJLA4v0PvMswR3auB0uRzB50Amp7/YbNWH7H0pVve5x9I9IVqNp6b4/zQ1k6p+P7WysMG5BdsrXKfxAz0J7RlF6+nXAxD1RD9ni+UwR1/+kwt/7Dff73vwJ7Zf/bn5/sDD/9Vh0J1MUFAQKSkpWmFovBKlFCkpKQ5t/LOHS81QInINMB3wBWYppd4okT8NuMJ4WwtoqJQKF5EWwA8YlJk/8L5S6mNXympJzoHiMAUNRjvmDPYLCyL6l+Kt9/Vu7EjYnkn4RQRz/o997BljP16Nq8k7lkbesTSrtKLsfHwCtRXSWURFRZGcnMzZs2dt5ufk5FTpD9WbqCl9qSn9AMf6EhQUVKUd3S4bLUTEF5gBDAGSgfUi8rNSaqepjFJqkkX5hwHTguKTwGVKqVwRCQG2G+u6Z32qxSamyDu7llGwbEx+gvAr21D35k7U6dOcyLHdKEjJYs+478lcn1xlUSuNj5RfRuMw/v7+tGrVym5+YmKi1Xr56kxN6UtN6Qe4py+uNEP1BPYrpQ4qpfKAecDNZZQfCXwDoJTKU0qZYlsEuljO0lgoi+COVfc9iK8P7f9zC43u7o74CP4NahPz6120nTm0ym1rNBqNO3DlINwUOGZxn2xMK4XR7NQK+NMirZmIbDW28abbZhUAFj+6xYW/wOsP7eyytsvj7NwtHnu2RqOpfniL0XoEsEApZT7AQSl1DIgTkSbAjyKyQCl12rKSiNwP3A8QGRlJYmJipQXIzMw01/c9cgx/Y/rylcvBz3U61VMW04Pz17OnQ5ZXm6MsP5Pqju6L91FT+gHu6YsrlcVxoJnFfZQxzRYjgIdsZSilTojIdqAfsKBE3kxgJhjCfVQlNIRlaInkDStINk6KBlwx0KWhwXf2O076iiM0f+EK8lOzOTljrcueZYnvjnT8x2+g/vAYWr11jTnYXN7pTM7N30bDMfFWezM8QXUK91Eeui/eR03pB7inL65UFuuBdiLSCoOSGAGMKllIRDoCEcAai7QoIEUplS0iEcDlwDQXympF3unM4hsX//Lu+M0Icg6lUqtDAwov5qEKiqjVsT4HJy1y6XMBirLyOfPFZs58sZnYpeOpHduIPWPmc3HLKTI2HKfDF8NcLoNGo6keuOwns1KqAJgILAZ2AfOVUjtE5BURucmi6AhgnrJeoN4JWCciW4C/gLeVUttcJWtJznyx2XxdMryzs/EJ8KVWB4MT3bd2AC1fHUzteOvzhtt8UDrUiLPZduVnFGbmcXHLKQDSV3n2WFmNRuNduNRnoZRaBCwqkfZiifspNur9D4hzpWzeTGDzMKv7ute154Abnrtr+Dfm68L03DJKajSaSw1vcXBrLPALDaTbtkc4/dkGEME3JLD8Sk4gc6O1Syl97VHq9G7O8emr8Y8MoeGIS1Z/azSXPFpZeCkBkSE0e2agR2XYedNXdE2ayLHXEgEIjKpDYXouda/r4FG5NBqN+9HKQlMmR15cYr7edevXACQYw5hUhKL8Qnz8fcsvqNFovBIdSLCaEbtkPGGDWuNfv5Zbnpf6c+lD6gvSDGcmlxU0ryjPvGWGi9tP83fTNzn2eqLT5dNoNO5BK4tqQsL+x+i27RFqxzWi07wRdN/5qDmv809j3CqLKiwiNzmNDR2mkfzOylJKI33NUf6OepPj01cDFP8/bbVb5dRoNM5DK4tqgl+dIAIiQ2zmBbet51ZZirILSH5nJYUXckh+czl7x31vzlNFil23GcxVJl+Hi1cfazQaN6B9FjUAd5+hsG3Qp1b353/by/Zrv6Dp433J3HQCVVBkXUFrC42m2qOVRQmq4+E13nAuRebG4+wZNd92ptYVGk21R5uhSlJYfZRF2w9vouXrV+EXFkSHOcOpFd2Q3He7UrtrY0+LZqYot8Dlu+A1Go3r0cqiBLnHq8/51PWHxdDongQAIq5uR9yye1FNgoldfDe9Tk62Kutbxz0b+0py8sN1Vmao7dd9wdqGUzn50TqPyKPRaCqHVhYl2H37N+UXqgaIrw/1bo22SPDMr/usPWetgjFmbjDsEj/y0lIACjNzS/s4NBqN16GVRQlyDp03X0c91c+Dkjh4YgCwAAAgAElEQVSDYpNai5ev9IwIRcquzyL/7EXWt36HrYNmuVcmjUZTYbSyKIOoJ6q7siimwUjPxHVSyn7k3qQ+nwCQvfucO0XSaDSVQCuLmoyFr15EaPyPXub74E5VP1vcEVJ/2mV3ZlFo3AkOcOip390ij0ajqRxaWdRgIsd1AwyO8FIUus9PcPabreWWOT17kxsk0Wg0lcXzC/S9DAnyQ+UUeFoMp1DnsuZ03/2ozaB/qsj7lginrThM+qojRD3VH/His8E1mksRPbMoQd1r2gHFv8qrO/51a9n0GdicbXiYXbd9zfF/ryL119LBCytD7on0arUUWqPxZrSyKIlxYA3t3czDgriWpo/0odlzA8ssE/V0f/cIU4L8Mxed0s7m+A/Y3PWDarkrX6PxNrSyKIEy2fJrohnEYoYhfj7U6dPcKrveLZ3N140f6k3U45e7TbSyyN57jqIKmgYzNlic+ueFJjeNprqhfRYlMYb7EN8aqCxK4G8RxTZ+7QQCW4STfyaT9FVHqW+hOAACW4STe+SCW+RKX3mE8Cta4//eXo6ughPTi0Ob172hA1FP96dWh7JXc+247gvztSpSiD53SaOpElpZlECZlMUlEM8oqHk47T+7Ff/GoQS1rgtAp+9GkX/uIgGNQgFD/KnU3/cS3LYex/+9yi1ypf66h9Rf9+ALnFhpvQcj9Zc9pP6yh/ZfDCOoVQS1OhYrDaUUKQt3kr2vxL4NPbPQaKqMVhYlUPmGE97ECyK5uoO6N3S0uhc/H7OiAIMjvP6wGLL2nOX4v1dRp18Lmk7qaz5i1VPsHbsAgN5nni1OG/c953/bW6qsqkbBITUab+XSGBErgOk4UKmB50X7RQRVum6tDg0My3DDg71qWatSyjwLtKUoALszi3Pf7yD1tz20nXFTqTDvuclp+NTyx7+ue46v1Wi8Ha0sSmCaWfgE1jxl0eieBC5uOUV9ywCDFcAbB851ka8T0DiUqCfth2axtxpq/4M/AXBuYGsajok3pxdk5LK52wzAeuai0VzK6NVQJTCboWrgzMK3dgDtP72Vutd3cFqbMb+Pc1pblSXvZAYHH1tkv0CJ3eqqSHHk5T+LszNyrfLzT2Y4VT6NpibgUmUhIteIyB4R2S8ik23kTxORJOO/vSJywZgeLyJrRGSHiGwVkTtcKacl2XsMzlGfgJqnLFyBX3jlTVvuwnK3ulKK87/v5eSMtfYreI+VTaPxGlxmhhIRX2AGMARIBtaLyM9KqZ2mMkqpSRblHwa6Gm+zgLuUUvtEpAmwUUQWK6VcunazIC2Hwsw8gzxaWZRJx3kjyD2eZl5F5dUYlUX2/hS2DfmcwKahVtl6z55GUz6unFn0BPYrpQ4qpfKAecDNZZQfCXwDoJTaq5TaZ7w+AZwBXB4mNc8iNIRWFmUTPqg1kXcadLt/o5BySnuWQ08vJjPpJMfe+Iuii3lk700pu8IlsGxao6ko4qpQCCIyDLhGKXWv8f5OoJdSaqKNsi2AtUCUUqqwRF5P4AsgWilVVCLvfuB+gMjIyO7z5s2rtLyZmZmEpgqBT2wBIGdGN2jg/SaWkmRmZhIS4t7BW3alE/jSdrv5ylcQL16+mj+mBYU3NTXfy4lsAh/dDEDOnF7ghMUOnvhcXEVN6UtN6QdUrS9XXHHFRqVUQnnlvGU11AhggQ1F0RiYA4wtqSgAlFIzgZkACQkJauDAgZUWIDExkR5to9mKQVn06X85AZHV74uUmJhIVd5DpRgIaTFx7LrN9t6LoKZh5B51z+7vytCmTRuaDOwNQFFOAfvu+wHTeYkt/syn1ZtVP2XQI5+Li6gpfakp/QD39MWVyuI4YBmNL8qYZosRwEOWCSJSB/gVeE4pVYY30olYWB+0g7uC2LHcxK97kNOzN3Hyo3XulacCZO08w8HHFyEBvpz+dKNVXlriIQ9JpdF4F670WawH2olIKxEJwKAQfi5ZSEQ6AhHAGou0AOAH4Eul1AIXylhSluLrGrh01l3UG9oJgBavDSGoVQTNnh1Au1m3lCrX7Pkr3C2aTc59t50zc5JKKQownMmuo9ZqNC5UFkqpAmAisBjYBcxXSu0QkVdE5CaLoiOAecr6L/J2oD8wzmJpbTwuxnKJpfjpLSgVISS+MQC1uzamzYybiF06nkb3GsygPoF+1LupE23eu8FcPmpyf5o+cpnNtjr/ONr1AleAcwt2cHz6ag4+vkgrDs0li0t9FkqpRcCiEmkvlrifYqPeV8BXrpTNFpYxhHyCvMWdUz3wDQmk59GnkABfxEeoHduoVJkGI+II7lCfvFOZ1L22vd226vRp4UpRK0zqz7s4v3gfAI0n9CS4XX0PS6TRuB89IlpSZPCh14qJ9LAg1RNHFGxI1yZW9x3n3UH+mYsceOQXAKJ/G2toq5Y/RVn5zheyEiiLHeBn522j+QtXkJ+axZHn/kfusTTCBrUmsFk4AA2Ge98JhBqNM9DKwgJVYBgUtAnKfYQPaoMqLDIri9DuhiWs0f+9ky33f0tIQC2ydp31pIik/VXs5D7x/hrDvcDFLacAyPg72Zxff1h0qfD2qkgR8NJ2DiZk0fqd69wjtEbjZLSysEBdQgcfeRPi60OjB3paRbOtHduIvNe70KZeJ7Zd+akHpQOVb71q++LWU/YLFykwfn9M/o3sPWfx2ZXOmV1JWlloqi1aWVhQkJoFlA4sp3E9LV8dbDujmjmUVV4hEuyDUoqdN3+Fb+0Amr/gHau+NJqqoO0tFux/6L8A5YeD0LgNy9VH1SEEy6475pGfkkVhZh4Za49xYekBHZhQUyPQysKCwrQcT4ugKYHloUS1OjUg4tr2RI7v7kGJyiZj7TG29v8PKq84GMG+CT+Zr/XSW011RSsLjVcT3MF6mWqHL4bR6o2r6TD3dlq/dwNxifd6SDL75J+9yJ4x35nvsy0c9Ltu+9qmwlBKkb3vnNVeH4CC9Bx23DyHs/O2uk5gjcYBtM9C49VYrSyyGEcjhrQFoCi/kMCWEeQePo83kbnRdmSb9JVHKEzLQfx88KkdYO7fyQ/WcvTVZTS6NwG/erVI/tcKoh6/3GDOWnOMjDXHCL+yDf4NaruzGxqNGa0sNNUGv7rBpdJ8/H2JXzsBBDLWHGXn0LkekKxibGg/DYDwwW3o+LXhXK8THxrCn52atcFcLvlfK6zqHXxsER3mDCdrz1nOfJVE00l9vfKoW03NRJuhNF5P55/vJHxwG1r/2/ayU/ERRITgjsVHnrR8/Sp3iVdpLiw5YDYvldybYYvMTScA2HblZ5z6ZD1HnvufS+XTaCzRykLj9dTp3YyOX99BYFRYmeUsB1xnnjPuSg488othBdW5rHLLFl40nOJocp5n79er9jTuQysLC+rd2hmAppP6eFgSTVUJaBRKt22PeFoMh0hbdtCxgkqRdyqj+N7ObOTsvK0c/b9lTpBMoylG+yws8AkwvI7AlhEelkRTGUquMnLo8CrBynHuzRRlF7Ap7v3iBDuWK1PolHpDOxPUMhzfkEA3SKep6eiZhQXm2FC++rVUS2wM+pa7p8P6tyyV3+vkMy4UyMWIkLb8EBs6TeP4u6tKKcuzX29hfet3ODGj+Oyw7L3nKMopcLekmhqAHhUtMEUX1YEEaw6N7k2gwYg4Os67gw5zhhOzeBzNXxwEQPMXByE+QoNRXazqhA9u4wlRK8zFTSfYNewbClKyOTb1Ly78sd8q37Sy6ujLfwKQtvwQWy6fyY4bv6zQc3JPpJO184xzhNZUW/SoaIHKNzgOtbKoOfgE+9PmvRsIH9QGn2B/Qro2ocnE3nTb+jBNJhrO3a53U0erOnX6etd5Go5y4qN1JF32sd381EV7AUO03KNTEx1ud3P8B2wdOIu8M5lVlFBTndGjogWqwBR1Vr+W6ohl1NryCGgUar623OgWflVb8wl/1Y2M1UfJOZBqN98yBMmJd1dXuP3cY2mVkktTM9AObgvyUwzLF33DgzwsiaYy+EUE0/DOePwiSm/eK4vasY1o9uwAxM/XPNuo068F6SuOGApUIye4PfJOZ3LmqySrtMwtJzk29S9a/t9gh07/c2QviKbmon9CW1CUbTiZza+OXj1SXWn9znU0f77iIcGbPtrXrCgAQoyHMAHELL6btp/cbL5v9ECPMtuqf1t0hZ/valJ/3VMqbceNc0hbdpAtfWfqAIeactEzCwvMDm5thrrkiXrscgIa1ibi6vYENgsjJL4xPgF+FFzIpuHoeCIGt2XX8G9s1m09/QbOfb/DzRKXzalP/i6VpixWRaX+spt6N3Zyp0iaaoYeFS0wL53116/lUscnyI9G9/YgsFnxrvG613eg4eh4AMIGtKLjvDtK1UvY9xg+XnjuRs6hsgMt7rvnB9JWHC67EW2FuqTRo6Ilep+FpgKED2pD7NLxxfdXtcUvzODvCoiqY05vYe8UQC8j9dc9XNxxhsJMY1iRIkXqL7vN+QVpuWTtPovsz7DXhKYGo81QFpjMUOilsxoHqR3biIQ9kzj3w07qG8PFAFahOBo/0JMjLyzxgHQVI2PNUU5/tpGgdvWIX/UAZ+dt5eCjv5rzd99uMLsFAoUjrsY3JACAI1OWUpSdT72bO5G16yyN7qmeq8k0ZaNHRQvMZiitLDQVwC8imEbju+MXXrwKK2pSXwAaP9irzLrRv97lUtkqQpbxkKacfSmcnr3JSlGU5MzcJNZFvcnZ+ds4+eE6Tn++iZ1D53L4mT/M0XEBinLL3i2eezydnIP2l/tqvAeXjooico2I7BGR/SIy2Ub+NBFJMv7bKyIXLPJ+F5ELIvKLK2W0RIf70DiLhmPi6bp5Is2nGHaL54+2vdEvtEeUO8VymENP/V5m/pEXlqDyCjkw8b+l8kyb905+tI6/m73FhT/tB0rc3PUDknp/bDMESckVWic/+ZuTH5d21Gvcg8tGRRHxBWYA1wKdgZEi0tmyjFJqklIqXikVD7wPLLTI/hdwp6vks4WeWWicSWDTOua9CYU3N6XH4Sdp/8Uwc351CaNeUUx9PvLSUsP/U8o3wRVm5Frd553OZEOHaRx7c7k57cgLSzjy4pJic7HGrbhyVOwJ7FdKHVRK5QHzgJvLKD8SMK9FVEotBdzqSdPKQuNKfGv5W3232n54kwelcR15p63DgogIRTkFFOUX2qlBqbPHT83aQOGFHI6/s5LU3/ZahVw3/Z2W5PzSA+weM5/81PLPBtFUHFeOik2BYxb3yca0UohIC6AV8KcL5SkXbYbSuBOfYH+g+BwV8M4NfRXl0BO/ceyt4hmBKlL83fJfbO42w26d/HNZ7LlrAeeXHjAkWCiPvWMXcOK9NcXt2VE6e0Z+y4U/9pP8xnKb+Zqq4S2roUYAC5RS9n962EBE7gfuB4iMjCQxMbHSAmRmZhKYX4AAK1avhIDqqTAyMzOr9B68iZrYF59t5wkwppn7NiIcn6h2+P12kuQhQQR9b78dVdsXFeqPz6kcV4tcJY6/vdJ8nXUqDSlS5J82fp55hcjBi6j2oZgC62y7YhYA53/fS878PvgdOWJ3cFqRuBxC/Eulm9o6sfcoRxz43tTE75crcaWyOA40s7iPMqbZYgTwUEUfoJSaCcwESEhIUAMHDqxoE2YSExMR4+x2wKCB1dYUlZiYSFXegzdRE/tyvmA/e9gFYN23gcDzhsu1EzbabeeyQ0+jlGJd5Osuk9XZBAQFkp9mCKXTv/fl7Bkzn7Tlh2k+5UqO2ih/WduunGpayElO2MiFPj0us3mw1VoMwRF916bQ14HvTU38frkSVyqL9UA7EWmFQUmMAEaVLCQiHYEIYE3JPLeiFBQap76+equqxjUEty8/YF/tuEZc3HrKbn51C+iXb+HD+Lv5W+brc99vt1l+c7cZBDQJtZkHlO/gLtJxrlyBy34+K6UKgInAYmAXMF8ptUNEXhERS8/eCGCeKrFOTkRWAN8BV4pIsohc7SpZATB9/3yl2v0xaqoPQc3DiV0ynm5bH7ZbptOCkbSffRt+de1Hz231r2us7mvHNXKajN5A3oky1ra4SRfo4IrWuNRnoZRaBCwqkfZiifspdur2c51kNjDOKqqr+UlTfShvYPcLD6budR0Iv7INfzd7y2aZyLHdCOvXkovbTxN2RWt8QwKqlWkKIGvb6UrVO/nx35yatR7x8yGkaxOif3b+CvvzSw+w756FtPtkKBFXt3N6+9URPTKaKNIHH2m8C59AP+r0bW6+j1k8zio/qHVd6t3UCb/QQESEqKf7u1lCz3Dqk7+hUKFyC8lYe4zzS/aTse6YVZmCjFy2DPgP+x/8ifxzFyv8jD2j51OUlc+eO79zltjVHm9ZDeV59MxC44W0/XgoJ2espf7wGGrHljMjsWO2avfpLQS1rMu2Kz91hYgeZ8+o+aXSzn69hexdZ8nedZZz3++g2bMDCO7QgPAr23hlVODqgB4ZjUimIdxAYXpuOSU1GvcREBlCi1cGl6soStL5x9Hma59aAdSOjSS4UwNni+e1HP/3Kqv7Y1P/Yu/YBey6ba7bZLi44wxbB84ibfkhtz3TlWhlYcRn24XyC2k0Xoxv7QDzdZ0+pWNRWebbo/4dscSve9CpcnmCgvPZNtMz1iWzuceHdnd5F5zP5uhriU5ZUbXv3oVk7TzDrmG2D8mqbmhlYaQoqpanRdBoqkS9WzpT98aOtHnvBsP90E741QumTm/Ddqc2715fbhsiQlCrCLpurPC2p2pD7pELJCV8WLxU3oINHaZxYvpq+3WPpTm8Ssp0THNNQSsLE8ZfEqG9m5VTUKPxTnz8fWn/6a00GBEHQLuZt9B9x6PmGYXlHo/WRoViIriDIS98SFsAApuF1ehVQIWZefh/vN98rwqKrOJPWbKp2weceH8NZ77ZwubuMzg8ebG7xPQqtIPbiJgc3PpIVU0NQnxs7xkqaZKKXjSW7F1nCelRHL6t3axbyN5zjm2DP3OpjJ7C9y/D+R2FWfmsb/kvu+XyktM5+uoygtvXA+D055tQ+UW0/vd1VuVUYRE7bphDrc4NaP3OdbaaqtZoZWGiUC+d1Vw6+NSyjq3kFxpIaE/rszV8Av1q3Ga/kuy6/Rsy/k52rLDFZt0zXyXR8s2r8fH35cSMtZyevYn6w2PI3HiczI3HqXNZc/JOZZbRWPVDKwsTeums5hIgduk9qKIiakdHEpLQlMwN9sK1XRqkJVZgpVKJWdrfTd+k+45/cvRlQ7Bsy+CJ+//xs1Pk8yb0yGjCrCz0GmxNzaV2bCQhXRojfj7ELBpL+89upcPXt1e53dbTHDO7+EUEe9VRshXBVhigjdHTHap7ZMpSzsxNcqo8SilyDp13W1gSrSxMmJWFjguluXSoe0NHIga3LbNMpx9G02BUF2IWjyN8cJtS+dG/3kWDUV3KfVaHr4aTsGeS1x4lWx5ZO89Uuu7JD9dxcNKi8gtiWEVleRiUKigi91haqXKHn/mDpF4fkfzWikrLVRG0GcqENkNpNDYJ69uCsL6GfRs+gaWHDNPg7xPsR1F26bO0AaKe7k/EVcWrq2IWj2PHzV+hbJy9falw7ocd5J/LovF9PcxpJz5cx9EpSwlJaErE1e3I2nWGlIU7Aeg4fyThA1sZyr2/htOfGULZH39nJczv43J59chookiboTSa8ijL5BE+qPSsAyD8qrY0eai3VVpI1ya0/88tTpWtOnBm3lZOf7kZgP0P/MSR5/5nPh3wyJSlHJ1iOLc8c8Nxjr2WaFYUAOe+3QrAqU83cPRV28t8XYlWFkakQM8sNJry8G9Q23wd1K4enX4oDisSbmdfRtNH+uATpI0YAAcf+YVDT/zG9uu/NKftGfktuSfSOfnhujLrKqXI2nmGw8/84WoxbaI/QRNFWlloNOXR/NmBnNx3lJgnrzGbpkw0uD2WwGZh1I6NZM+o+cVLUu24AS/l8yIy11sv13XEHJd/NosD//zFVSKVi0Mjo4j8U0TqiIFPRWSTiFzlauHcivZZaDTl4hcRTP6jHUopCjBsAAzr2wK/OkHUio00p4d0bWK7sTLiLzV7fmBVRa1WFNrx9ViSvuIwF7fYP0HR1Tg6Mo5XSqUDV2E4AvVO4A2XSeUJtLLQaJxGs2cHEjW5P/F/P2j/b6qMiUWtzg2t7jv/PMaJ0nkf266Y5WkRysVRM5RpInkdMMd4PGrNWmOqlYVG4zT8QgOJeuzyMssoGzOLpo9fTlCriFKzDvHRf5dlIXszYKBrn+HoJ7BRRP7AoCwWi0goxadW1wxMESi1stBo3EIdG0E7mz3dnwa3x1opklZvX2vX76ExEPj8Npc/w9GR8R5gMtBDKZUF+AN3u0wqT6BnFhqNW/FvUJuE/Y+RsHdS6UyLiUXkXV2t4jJpPIOjI+NlwB6l1AURGQM8D5TeUliNER1IUKNxO351gpCA0tbwoFYR1gkWuqLujR1p/9mtLpZMUxJHR8aPgCwR6QI8DhwAviy7SvVC9hkiROr14BqNe/Gt5U/radfR9qObzWm1Ojag47w76LL6AcA6LlP7T2+l7g0dafKoYddyQJNQGt7V1WbbkeO6uVDySwtHR8YCpZQSkZuBD5RSn4rIPa4UzN34bjEcq3qpR+HUaDxBw9HxpdKsdoTbsEI1e2YADcfEE9gsDBHhjHFntCWt3rqGFq8O5vRnGzny0lJzet3rO5D66x6nyO4tFF7Mc+jo3Mri6MwiQ0SewbBk9lcR8cHgt6hxFFywfXavRqPxIDZ8FiJCUPNwm9FgLfEJ9KPxg72s0lq8NoSiFtZHKfc8+hTdtj1CSPfS+0KCWtethNDuRfxdG6rIUWVxB5CLYb/FKSAKsH+0VDUm6qn+nhZBo9GUILBpnQqVb/n6VXT6bqTdfPH1oeA269VYPkF+BESGENSqtGJwJKqup3H1KZ8OtW5UEHOBMBG5AchRSpXrsxCRa0Rkj4jsF5HJNvKniUiS8d9eEblgkTdWRPYZ/42tQJ8qRVHjIAACGoW4+lEajaaC+DeoTezS8cRv+IdD5Rvdk0DYgFZ28wMiQyjq6fhsoe617ajdxbtPDXT11jdHw33cDvwNDAduB9aJyLBy6vgCM4Brgc7ASBHpbFlGKTVJKRWvlIoH3gcWGuvWBV4CegE9gZdEpMTyCCdTpFdDaTTeTO3YRgQ1D69yO00fN24W9BGavzTI0HbXxsUFSoy5fnWDCW5Xn3aXYJRcSxx1cD+HYY/FGQARaQAsARaUUacnsF8pddBYZx5wM7DTTvmRGBQEwNXA/5RSqca6/wOuAb5xUN4KI6YthlpZaDTVkohr2nH+931287usfoDURXuszo9o/EBPgjvUtz6QqcTxqSYlEdQygoZ3dbXpSL8UcFRZ+JgUhZEUyp+VNAWOWdwnY5gplEJEWgCtgD/LqNvURr37gfsBIiMjSUxMLEck+/gXFOELrF2/Dg4FVrodT5OZmVml9+BN6L54J17blxER+NZvQWH/Bvbli4N961YBhn78tXK5YRTcXBwF1u/0KauBMWnHVlThYQB881K8dmWPqz8TR5XF7yKymOJf9ncAjp0R6BgjgAVKqcKKVFJKzQRmAiQkJKiBAwdWWoA1rAegT98+BDQOrXQ7niYxMZGqvAdvQvfFO/Hqvjh2FDhgvx9pfi3Zlfi1+T6hb09qxxr8FUW98jka9hfhg1pzMekkx17/q6oSOw1XfyaOOrifxDAoxxn/zVRKPV1OteOA5XKDKGOaLUZgbWKqSF3nYDJD+eiwAhrNpUzY5S2t7mvFFIdb9wn2p+Wrgwm/ojVNJ/Ul1BjfqtmzA6jVqUFxHYsQ7TUFh7crK6W+B76vQNvrgXYi0grDQD8CGFWykIh0xBD2fI1F8mJgqoVT+yrgmQo8u+KYHdxaWWg0mmLKWmXUeeFoco6cJ7hNPSLvSeDQ44toMCIOVVDEnjHfmcs1eqAHacsOkr03xR0iu4QylYWIZGA76rwASilld/GzUqpARCZiGPh9gc+Moc1fATYopX42Fh0BzFMWx2YppVJF5FUw2obgFZOz22Xo1VAajaaCiJ8PwW3qAYaw7O1m2l4x1fLVIQCsbTjVblvdtj/Cppj3zPfxayfg16A2G9q840SJK0+ZykIpVSXjvVJqESV8G0qpF0vcT7FT9zPgs6o8v0KYV0PpmYVGozHQcEzpMCTOoPlLg0CEo1MMIUiaPHwZAQ1L7PHy88Ev1HsW2+if0SZ01FmNRmMkfLAhLlX94TFVbsuvfnFYkZZThxDSI4rIsd1oMCIW/wa1afxQb5q/cEWper4h1nGeQiyX93qASz7E6u71x/nlP5uoVTuIbnlZWlloNBo6zBlO/tmLBDSq+srIkC7FG/4a3duDRvca9nn4EkC37Y/Y9Yn417WOXeVpf+olPzJeTMtl36aTXPA1BuHSZiiN5pJHfH2coijKfY4dRWGa2ViVtRib6l7fwWUy2eOSVxZ+AQYlUWT80PTMQqPROBUn/f6sN9QQLck3LIj2n9/mnEYrwCVvhvIzRmo07QYUvc9Co9E4gbo3dyL1p100vNP2wUxlYjHj6PT9KHKPpdFwVBdqdWxAUNt6TpTScbSy8LeYWWgTlEajcRLtPhlK3kuDCIwKq3hli6EorF9L83Vor2aly7qJS97mYp5ZiGHNtEaj0TgD8ZHKKQocCzfeaWGpPc4u5ZIfHS19FtpfodFoqgthl7ckIMqwL1oFun7suuRHR5MZqhDt3NZoNJ7FJ9jgGXD0oKWOX91OaJ/m5L0U7UqxAK0s8DWanrTPQqPReJq4v+6jxWtDaPLwZQ6Vr9W5IdE/jkG1df0yX+3gNpqhCsXzm140Gs2lTVDLCKvDmbyJS35mYXJwa5+FRqPR2OeSHx21z0Kj0WjK55IfHS1nFtpnodFoNLbRPgtLn4XPJa87NRqNxiaX/OhoWg2lREArC41Go7HJJT86ikixwvDTZiiNRqOxxSWvLAD8jMqiUF0ZMyEAACAASURBVPssNBqNxiZaWVCsLIociMei0Wg0lyJaWQBSaDiAO3Nviocl0Wg0Gu9EKwtAcgsAKPKwHBqNRuOtaGUBBIQGAhDUrYmHJdFoNBrvRCsLwNd4Ol6gh06g0mg0Gm9HKwuKlUWh9m9rNBqNTVyqLETkGhHZIyL7RWSynTK3i8hOEdkhIl9bpL8pItuN/+5wpZymkFCFypVP0Wg0muqLy8J9iIgvMAMYAiQD60XkZ6XUTosy7YBngL5KqfMi0tCYfj3QDYgHAoFEEflNKZXuCllNMwu9dFaj0Whs48qZRU9gv1LqoFIqD5gH3FyizH3ADKXUeQCl1BljemdguVKqQCl1EdgKXOMqQX2NSqJI6amFRqPR2MKVyqIpcMziPtmYZkl7oL2IrBKRtSJiUghbgGtEpJaI1AeuAJq5SlCzz8JVD9BoNJoSJO9LITszz25+UWERX7+xks3LDrlRKvt4OuqsH9AOGAhEActFJFYp9YeI9ABWA2eBNdgYy0XkfuB+gMjISBITEyslRG52FgAnT5+tdBveQmZmZrXvgwndF++kpvTFk/1IOZrDH+8dJTjMj94jGnHucDbRg+siIhQWFJFyNIfstAJWLzjFXwt2MvLt9qXaKMgtIiezkJB6/m7piyuVxXGsZwNRxjRLkoF1Sql84JCI7MWgPNYrpV4DXgMwOr73lnyAUmomMBMgISFBDRw4sFKCbp1+Es5nUK9BAyrbhreQmJhY7ftgQvfFO6kpffFEP3auTeb00TRCVD5wlOy0ApZ9kgzAtsUpfLz+Pt6652cObj1NaN1gc72BAwdy7kQGh7afYe+GEwSHBrD0m+0U5BUy5bvh7DmyxeV9caWyWA+0E5FWGJTECGBUiTI/AiOBz43mpvbAQaNzPFwplSIicUAc8IerBPU1/q/NUBqNpiqknsrk9NE0OvW0trjn5RQQEOTH9ImLAOjUq6RF3sDUO3/g6O5zAGSkZpvTl327nXn/Wm2zzu71JzAsDXItLlMWSqkCEZkILMYwHn+mlNohIq8AG5RSPxvzrhKRnRjG6ieNCiIIWCEGx3M6MEYpVeAqWU3KokgvhtJoNJWkqEjxzA2G1f+TZw+lVYxhBD+6+xyvjVloVXbXupJGFsxlbWFPUQDMe2sVAD3+vIzadQIrLLejuNRnoZRaBCwqkfaixbUCHjP+syyTg2FFlFswefn1zEKj0QAsX7iLJXO38tjHNxDeoLY5/djeFJYv2MlNDyYQGlFsJsrPK2TK8Pnm+6/fWIl/oC/3vT64lKJwFcG1/V3avqcd3F6Bj3HFrN6Up9FoAOZOXQHAr//ZxOhn+5nT/2/U94BBmUxbNpbfZyex/PtdpVY1mWYIk6+b6yaJwcfXtQE5tLIAfDFoCW2G0miqN0u+3kZoRBC9rm3nlPb2bjppvr6YnmuVN+mKL5zyjOqCVhbomYVGUxNIT8niu3+vAXBYWSilKMgvYvrERWRn5pFc4kybU4cvsGX5EWqFBjDtwV+dLrOziL3K9UFQtbIAfPIN3grts9Boqi+ppzLt5imlOLLrHNkZuexef4KbJiRwYtdFJjzxn3Lb/fCxxc4U0ykE1fYn52K++T5GKwv3kLvnLESEUJivjz/SaDxJbnY+eTkFVs7j8sjJyuef/T+3Snt88JfEX9GSmx5IID+3gJeGzafA4u87vGFt/vrU9oqk6sATM2/k/0a7x3FuQisLwNdofsorYZPUaDTOo7CgiKO7z9GiU327ztjHB39Jfm4hI57qS+/r2hEcEmA2FfkH+JJ5IYdzx9OpVSeQc8cz2LkumbW/lNqvS+aFHFb+sJuVP+y2+RzTctPqxMPTr8HH14eAID+atq1Lq9iGHNp2hp7XtnXL87WyAHyMAQTPaWWh0TgNpRTGvVIUFhTxj96zALjm7v9v70zDo6iyBvyerOwQQCI7BIksAdlFQEBAZBEFZQQ3xFHBBT93BXfHGcUFhhk3ZBxFHRGRUcAFRBjCKhpUtoBAhAABZJMtYCDL/X5Udae7051OIJ3uTs77PP2k6tat2+d0VerUvffcc9ox7J4uXs/JPm0NBs98eSXLZm9i3D8G8PiQjwH465yRPDl0ZilIXnpUq1WR44etxXeJHeryx8kz3DP5CmrUqUzOmVx+XLyDeW+lcHhfJglt46lUNX8dxfj3hjp/49IIW6LJj4D9sZZ/cvpvJ4MsiaKEHtmnczh5LKtY58ya/B3jB33EqRPWC9hr9813Hls8YwNgzTFMGvsF65bt9NrG3u1HnIYCCHlDER0bWaBsSvLoAmX1msU5t1/44gYuv7ktiR3q8sDUK3nyo2uJi6+CiBAdG0XXQc15/vOR/GPZrW6GwoGUYloF7VkAR2L0Z1AUX4wfPIPMo1kkdWtIvWZx1LrI/zkOg7Dm2+30vKal24plR+9hyScb2frjPrb+uI9RT/Wk4+XNAiJ/adCudxPuerU/a5PTeethKzJR5eqxVKwSw4T3h/LiLXN44K3BNG9fl83fZ/DafQsQgeiYSIbf17XQtiOjIoiMCv57ffAlCDLGGOpl+Q4TrCjhxO+/ZfLxyys5vO+Esyz7dNEi5Rh7ODYnO5cP/7qMDSt2Adb4P8DGVbtZ+OF68nIN7zy+mPefS3Z+Z25OHh+9sJzN32d4Nur1u8Z2msbijzc69z94flmBSepwYug9nQHLaDhoe2ljAJq0rsPba8bQonN9IqMiaN2tIXdPvoIXvvAMlRfalHtjQa4hMdPqKsdWCuxyeUUpSY4fPsXRg+5Dp28++A3Js1Kd7p7rl+9kXPd3WWS/6fvihwVpPNTvA9I3HWTl3C2smPMLr9+/wGvdTx7bRsrCX1n1xVa2b9jPhCtncHfXd1j22Wam3PM1a7791Vn3oxdXMLbTNK/t5OaEtvfhA28N9lvn3n8OZGrKHdRtmj+0dMszvTi/SQ2uurOT13NEhIt6Nqbm+VVKTNbSoNyPv5icPCLtt59KVWOCLI2iFJ1HrvgPAG+uvt05TLHbXlSWse13Zk3+jnVL0wH4dPJ3xDeqTpsejby29e8n/wfAB39ZSsd+Cc7yA7uPFSrDS7fOLVA2Y+KK4ikSorToXJ8pyaOpWCWGX1L2cOrEGZI/TWVLyl4AHpx6JRd2qlfgvG5DLqTbkAtLW9yAU+57FiYnz+kNFepvOoriDc/ehYPFMzaQcyZ/qalnT2Hdsp2M7TTNbcjK5LkPG62ct6XY8pw8Vna8CitWsV4gW3SuT4c+Tbnjhb5ce9/FvPrtzV4NRVlGjUVunjNEues/lqKEC8/+6VOfxyTC3Vtmx8YDzm3HUJWrx5Hliplff3/60RKSMvi8vWaM236/expy+U1t3coG/rl9oW1UjatI/5svKtaiwbKCGguXnkWOruBWwgTjMnF8Jsv3BLbn4reJo+cU2u6+HUfZvyt/6OnnJelnJ2CQGfV0L6/lrsNw5zWtyPD7u5LUzUroWa9ZHANvbcdlI1rz2HtXl4qc4YTOWeTkOQMJ5mRrz0IJLsYYZry4ggaJteg13HdKl7xziHp54sgfPH3tLJ/HV3+17azbDjYPvDWY/TuP0f2qC7l44AWcPHaaV8d8Qd/rkwDLIDi8vByMfq43Sz5J5dJhLYitGM3IR7oHQ/SQR41Fbp6ze5WXa8jLM0REaKxyJTikpx5k2WebAQo1FsbDJTUvN4/1y3cVqHd474kCZQ9f/uE5ShkcRj7SjcSO9fjLyNlej186rAUtOtenRWcrZWlUdCTVa1fi+c9GOOsMvr0DIkKn/s34da/lIVY1rqJPzyUlHx2GyslDyA/5kau9CyVAHDt0ij1pvxcoX/zxBqY/l4wxptAhJQdfvL2G565zn6f46MUVzsVgZZE7XuzLZSOS3FZJv/LNTW51RhShRxBbMZph47rQMDHwUVrLGuXeWDiSWDh+CJ23UALFowP+w19GzubIfvdQ2rMmfcd3X2wlPfUgntEbvnrnJ8Z2muY2Mf3lv37iwO7jbvVWzPEeMK+s4JhQrlW3KpWqxtAwsRbValUiItL6wXpe05LomILhNpSSQ4eh7B5FJJCDzlsogee39KPkZOfx67rf6OKSpGfbz/to0rqOc//YoVPMm7oGsCamPb15wplRT/Wk21UXcmDXMX5ekk6fkUnEVIjiyP5M9u86xvlNarBg+lpq16/GyWNZJHasC1ihL15ZeLNz4v7pmcP57sutDLy1cC8m5dwp98YC2688GsNphKyT2eXSLU4pPabc87Vz23Xq4b//+J6Hpg1x7k8bv8jtvMyjWc5Fd6FGx34JZB7LwuQat1Skz38+gqeGfVKgfkRkBCJCfOMaDBjdzlkeF1+FuHhrZbOvieao6PweRN2mcVxz78UlpYZSCGosbGMRiyET6x/yvAbVgiuTElIs/3wz8Y2q0/DC2qxNTqdd7ybOxVqubFqdwebvMxg2rovzzXfLmr3MfGUlJ096Xzg3/dlkt/1JY75wbqet/c3t2NPXfhK0BW8d+yXw46Ltzv3LRrRmySepzv0xE/s5t/Ny8/h0ympadqlPnYbVGTC6HQumry1VeZWSp9wbC8eKVcdQ8ap5W2iaVMf3CUq5Yk/a7/znb8vdytpd1oS7XulfoO4/xlk9hoUfrmfEw924qFdjJt/5ZYnJEixD4Qgn4hrjadCf2zuNhedkcURkBCMe6ubcH3pPZ5K6N+TVO/INYa264RUXSVFj4exZHBKra7vss83c+PilwZRICSGOHTpVoGztknQ+fnklw8Z1IWPrYRbP2EDXwc3d6nzy6ipmTf6utMQsUaJiInn+sxFMG7+Idr2bOONOPf7hMFK/yyCmwRGq1arEX+eMZNPqDC69pmWh7YkIzdvX5dF/X8XRg6f4I/MMiR3LV6iMskC5NxaesXCU8sX2Dfv55Yc9DLi1vdf1NZ7rGRwkz0oleVb+MMxP/9tR8Nwwvbf+uexWIqMiGD99qFt545bn0bjlec6sbOc1qFboWhBPml10fkmKqZQyAXWdFZEBIrJFRNJEZLyPOteJyCYRSRWRGS7lL9tlm0XknxKolFA+HgZK+eClW+cy9601rFn4q9fj5fH2CIVEO0roEbC7QkQigTeAgUAr4HoRaeVRpzkwAehujGkN3G+XdwO6A22BJKAz4D3YyzkSrm9/iuWMkPJNWpHdnR29hG//s54ZL61g2oR8byPXyKseJ52znMGmz8gk5/boZ3u7HXto2hBGPdXTuf/qtzeXllhKmBHIYaguQJoxZjuAiMwErgY2udS5A3jDGHMEwBjjWHlkgApADNbcczSwPyBSqrEIWybf+SV70n5n8B0duGpsJ4wxpKcepF6zOKKiIzl5/DR/ZJ4hvlF1lsxKZebLK3225Yg4nJdnSE89QMPEWkTHRoWsrbhhfI8i5Y0Y8XA3LhvRmoQ2dcjLM1w8sDk/Ld7O+uW7aJBYi8QOdTngEjhQ3cYVXwTSWNQHdrvsZwCeDtGJACKyEmtd3LPGmAXGmO9EZAmwD8tYvG6M2ez5BSIyBhgDEB8f7xxLLQ6y7QSeadDPpp1QITMzM6zld8WfLo7QGasXbqJK8xN88qj3AHjDnk3g85e3ez3m4Mt//cSW1F/ZnnKc3GzLQgz/azNmP+l9eCrYpG33HexPIsDYgQgizj/E0qVLcdzkycl7uKBfNKZyLRI6Vyc5OZm0X/LDkBfl3ikr91hZ0QNKR5dgT3BHAc2B3kADYJmItAFqAy3tMoBvReRSY4ybD6MxZhowDaBTp06md+/exRbgROUMUnFPOXk27YQKycnJYSl/bk4e65fvJLFjPSpXs55srrpkHs3iTFYOv677jY79EuzwF1sBOLwzi2ObK/tsu1HtFkDhxgJg2yr3rHChZihGP9vbuS6jRYsW/OCjs/3g1CEc2Z9JvYQ4Gl5Y22udK1wyhlY+nUbKbCtTXlHunXC9xzwpK3pA6egSSGOxB2jost/ALnMlA/jeGJMN7BCRreQbj9XGmEwAEZkPXAIsp6Sxh6FaR+WQmhNs21l2OP1HNmuT02l7aWOvC9gO7zvBnDdSGDC6HfUvqMmC6WuZN3UNjVudx+MfDCMvz7AnNZPMdpaRmHCl0/eBd574X4H2Frzne9GXY/1DOFOrbhWSulv/TjEVorx6bk1JHk10bKTbCuei0KFvAhev2EVSd+8pVxUFAmssUoDmItIUy0iMBG7wqDMHuB54T0RqYw1LbQcSgDtE5EWsYahewJRACOmY9EyKzlVjUYLMmLiC1V9tI6l7Q+79x8ACx6eNX0R66kFSv9vN5MW3sH75TgB2bjoIwNw3U1g2fS9rZs8kspgPv7JAq0sacN9rg/hhQRo7Ug84s7NN/PpGKlaOZm1yurNu3aY1GPFwN69GuShERkXw5+f7lJDkSlklYE9HY0yOiIwDvsGaj3jXGJMqIn8B1hhj5tnH+ovIJiAXeMQYc1hEZgN9gA1Yk90LjDFfeP+mc8TuWUTanrmxFdVglASODGsbV+72etwxqXry2GmyTmVz6rj76mRHeIhTJ84ETsgQ4qFpQ4itGMXKuVto0LwmPYa2AKDLgAvoMuACZ724OtZwW3Rs/n367KfXla6wSrkkoE9GY8zXwNceZU+7bBvgQfvjWicXGBtI2Zzf5fCGsp2IT//hP5+AUpDiJo3Kdcn09sBl088p81u4M2RsRxI7WFFVG7c8r0jntOvdhDY9GtGqawP/lRWlBNDXaEdsKJc1f0cOnHS+wSn++SVlD/8Y9zW3PNObroOae62zY+MBdm85RM9rraU2ebn5eUPKq6F4e80YTh4/7ZzQLw6RURGMmzIgAFIpinfKvbFwuBi6rg/fsWE/cX0TgiNQGPLeM8nk5Rree3qJT2MxcfQcAA5mHGf98l1kn/a9kC7zaFZA5AwmIu7r+zr2s+6vszEUihIMdF2/o2fhMoSyaMYGX7XLNWeyctix8UCBeEn+ArG49iIWfrie39KPFlIbHur3wVnLWNI4HurnQq/hrRjwYGO3nsBNT2iwSiW80J6FcRiL/LLYitFBkia0+deERaxfvotRT/WkXrOabN+wnz4jk9yG8L5+92cqV4vl9KlsZ9nMV1cFQ9wS4cYJPagaV4GDe06Quip/sr7P9UnUrleVWZMKjyx716v9ade7CcnJySR1b8ig29rTuOV5VKqqPQolvCj3xsIZ7sPl7bjzFc2CI0sIkpOdS8o3v9L6kgasX74LgA+eX+Y8Xqdhdbeexdw3Uwq0sfTTTQXKwoWIyAiuf6wHAC+M+tzp2uvI19CsbTwZ237nw78ucztv9LO9ueTKRLcyEeHquzqXgtSKUvKosXAaC6Hj5Qn8+O12N7fE8s7899by5bQfiYv3PuF/MOO42xBeONMgsRYZHmlLo2Ly13i06dGInZsO0qhl/qroJq3ruEVpve/1QWxYucvN3VVRygLl/qno6jobYb8iayTafDZ/nwHAkf3e04JmbD3MoT0+IraGGUPv7szr9y+g1/BWtO3ZmNzsXKJdjMWgP7enfrM4LuzknrinQWItOl/RjLpN42jVtYG6syplknJvLFx7Fj8vsRLYrJy3pcy9GSZ/msrKeVvoMyKJS65MxBjDyrlbOL9JDS5o556UxhjD7Cmrqds0jjw/hnPlvC2BFDvg9L0+ibR1+xl+f1cSO9RlSvJonyuhI6Mi6ODFS05EuP1vfQMtqqIElXJvLIzLnEVOtuW188sPniGsQp9Zk1axd/sRLrq2UoFjmUez+PglKzz39GeT2bfjCM3axjvH2Qff3oGr7uzkrJ+eepBFH1keYVHRZcdhbtKiURw9eJK5b6ZQu0E19m0/wrBxXdyGHc82ZIailHXKvbFwOr+H+bj74o83AtC4e2O38sP7TvD7b5luZd+8v476F9R07n/1zk+06tqALWv20u/GNrx233znMYcBDVe6DLiAHxakAZYhqFKjAvf8XRezKUpxKffGIqpmRap2a8SRenmwN3wWg239cS/ZZ3JpfUlDt3LX+ZbcnDweH/Kx1/OPHnSfg3jl9nkAzJu6poQlLV0qVY1xiyfV/+a23DC+B7k5eZouVFHOgXL/31O9RxNaz7mJnOvcwzMvnR3a7p6Txn7JP++dz5ks91hWJg+OHTrFrEmr2L/T9+K3k8dO+zwWitRpVL1AWcd+CTz+4TC6DMyfX7ruoW40uyjeuR8XX8XZo1AU5ewp9z0LX8yYuIJew1v5r1gEzmTlkHUqm2o1Sz5lpevqaLAmp19/YAG7Nh/ix0X+E/6EMhGRkGdHBakaV8Et/SdYC+YqV6/Abc/3ode1rdj8wx4uHtScS65M5NCe45w6cUaNhKKUEOW+Z+FKm0sDk/zlsUEf8Uj/D0ss5tFbDy90bntGyf32td3s2nwIgKMHT5XI9wWDv827nrYDvWd5c1C5er4huKDd+QwZ09EZ+bZ2/Wo0alH4+YqiFB01Fi7c+txlAWnXkath344jZ91GTnYuxw+fYvpzyW6Jb6aNX3Su4oUktetVJbZy/hqHkY90p0LlaG58/FImLRrFlOTRwRNOUcohOgzlQqWqgXWbXL98F83b1y32eSvn/sIHzy8jOjayQLTWtLW/hf1aB1806VCNiFPVadujEY1a1GZK8mi3OFSKopQe2rNwoSQfRHl5pkB01oUfrCt2O7+k7HHGYvIV1vuDvywtvoAhxJ2vXO61PCJSGP1Mb+dCODUUihI81FgEAGMMz18/m4m3zDnndv5+11clJFXpc8mVidz21z5c2Dk/PIa3UBjtL2vKo+9ezZ8evKQ0xVMUpRjoMFQhpH63220dQ25OHgumryWpe8NC019mn85l76/W/MRuj8B0nhhjyNh6mPObxhEdE0n2mVzSft7HnrTf2WlPVIcjL355AzXqVCYiQsg6lc2WlL3ExVfmjhf7Mv/dn/lx8Q4O782PKdWsbTxNk+pwYNcxmrc/v5CWFUUJBmosCuGf987n7TVjAPgt/ShL/7uJ/328kXlT1zjLPdm4arebi+zEWz53O77oo/Wc36QGrbo2YMXcLRw9cJKv3vmJll3qc9MTl/LE1TMDp1AAuOPFvvxrwmLn/qP/voqqNStS8/wqzrIeV19ItZoVSWgbT6WqsVx7X1f2/HrEzVgAREQIN4zvUWqyK4pSdNRYFIGsU9k8M3yW33p7tx/htf+b71bmGS7j07+vBuDmJ3vy0QvLneWbf9gTdoYCKLCCvNlFBXsFEZERtOvdxK2sRed6pK7aTe36VQMpnqIoJYQaCw8iIoW8XPeJ6aku6xoKo7AV056sX76zWHIFg/oX1GRP2u8AjJnYj02rM1gx5xfn8ec/H0HFKjG8svBmFn64jksGJ/pqqgB9r29DXHyVAuG+FUUJTXSC24OnZw532z+TlcNmP1FoM49mkZuTx4Hdx4v8PeuWhraxuHtSfx5992oAomMj6dgvwW1yemrKHdRpaIXgqFazIsPv6+oWnNAfkVERdO7fLCCr2hVFKXm0Z+GB4wHo4N4e73qtd+zQKarXrsThfSd8BusLVya8P5QmresAVljvmArWbdK+T1OG39+V5h3qqhuropQzAtqzEJEBIrJFRNJEZLyPOteJyCYRSRWRGXbZZSKy1uWTJSJDAymrg4jIoj0EHx3wH9YtTXdGay1LOAwFQJUaFZzGIiJCuPymtjRp5dsTTFGUsknAehYiEgm8AVwOZAApIjLPGLPJpU5zYALQ3RhzRETqABhjlgDt7Do1gTSgaBMH5y53keu++VCpiKQoihJ0Atmz6AKkGWO2G2POADOBqz3q3AG8YYw5AmCMOeClneHAfGNM+EbFCxHGT/fdOXMN860oiuJJII1FfWC3y36GXeZKIpAoIitFZLWIeEthNhIo1UmBsuihMzXlDmrVc3dTnfB+vvEY9VQvOl6ewO0vaC5pRVEKEuwJ7iigOdAbaAAsE5E2xpijACJSF2gDfOPtZBEZA4wBiI+PJzk5+awFyczMdJ5/4uSxwiuHIUuXFowftXWXlWc7pmIEK1ctJ/GKKE6ym+Tk3QXqBgPXaxLuqC6hR1nRA0pHl0Aaiz2A64qtBnaZKxnA98aYbGCHiGzFMh4p9vHrgM/t4wUwxkwDpgF06tTJ9O7d+6yFTU5OxnH+hs/ns5eThZ9QClSoHM19rw/ipVvnnlM7z8z6E/US4gDY0O0PNq6yjEH/gX3pdkl3YipEOSexQwnXaxLuqC6hR1nRA0pHl0AOQ6UAzUWkqYjEYA0neboOzcHqVSAitbGGpVzTu11PKQ9BAWD8VykNXl5wEwlt8lOEXn5T22K3UTWugtNQAFx7f1cqVY3h+se6A+7eToqiKL4ImLEwxuQA47CGkDYDs4wxqSLyFxG5yq72DXBYRDYBS4BHjDGHAUSkCVbPpNTjb+eZ0rcWbXoUzNIXHWs9xEc+2p3Bt3dgyNiOANRpWK3Qtq645SKfx+olxDH5f7fQ+0+tz0FaRVHKGwF9pTTGfA187VH2tMu2AR60P57nplNwQrxUCMaq4qhod7vdoU9TZ4rQy67Lf7C/tuLPREZFcHfXdwCoVqsixw//4TweXSGCa+69mG/e9507QxfUKYpSXHT8wQvX3teV1V9tK9XvrF3fvbcw9mXvCYE8h4xGPdWLKjUqYIzhk1dWkdjPMnRdBl7AD/PT6DG0RWAEVhSlXKHGwgvValbkqjs7MW/qmlL5vtv/1oc2PRqRdfIMyz//xf8JLlSoHE3TJGvF9YQPhjk9IkY91Yue17R0m/NQFEU5W9RYBICX5t/IYwM/cu636dGIDSt2+axfq15VKlSO4aYnetL7utbO4afCuGF8D3ZuPsgF7bwnCoqOiTyrfN+KoijeUGPhgxrnVTqr8yYtGkWVGhWoXrsSxw5Zi87HTRnA2E7TvNZP7FjXLdZSg+a1ivQ9vYa3Oiv5FEVRzgYNUe6DroMTz8pV1RGIsFK1WK/HO/Rt6rZK+qG3hxARqZdBUZTQRnsW5qFeuwAACKhJREFUPoiMimD4/V2pWCWmWHMX/h78N4zvwcljp89VPEVRlFJFjYUfBt/egYMZx/nuy61+6zZIrEWFStEA+Jp1EBHOb1KDofd0LuABpSiKEqqosSgC0TGRbvtNk+qwY+MBbv9bH5b+dzMNL6zFiIe6Fakth+vrwFvbl7iciqIogUKNRREwHiu67558BZlHs6jbtAadryhaaO8JHwwj+3SOhtZQFCUs0SdXEfAM/hEdE+kWb8kbVeIquO1rdjlFUcIZdcMpArEevYGipF695eletLy4Pg//a0igxFIURSk1tGdRBAbd1oHdWw6z9ad9AERFR/o5wwrfcf8bgwMtmqIoSqmgxqIIVKlRgYemDWHHxgPk5eYRGaUdMkVRyhdqLIqBIwaToihKeUNfkRVFURS/qLFQFEVR/KLGQlEURfGLGgtFURTFL2osFEVRFL+osVAURVH8osZCURRF8YsaC0VRFMUvaiwURVEUv6ixUBRFUfwinrkawhUROQjsPIcmagOHSkicYFJW9ADVJVQpK7qUFT3g3HRpbIzxm0OhzBiLc0VE1hhjOgVbjnOlrOgBqkuoUlZ0KSt6QOnoosNQiqIoil/UWCiKoih+UWORz7RgC1BClBU9QHUJVcqKLmVFDygFXXTOQlEURfGL9iwURVEUv5R7YyEiA0Rki4ikicj4YMtTFEQkXUQ2iMhaEVljl9UUkW9FZJv9N84uFxH5p63fehHpEGTZ3xWRAyKy0aWs2LKLyC12/W0ickuI6PGsiOyxr8taERnkcmyCrccWEbnCpTzo95+INBSRJSKySURSReQ+uzwcr4svXcLq2ohIBRH5QUTW2Xo8Z5c3FZHvbZk+EZEYuzzW3k+zjzfxp1+xMcaU2w8QCfwKJAAxwDqgVbDlKoLc6UBtj7KXgfH29njgJXt7EDAfEKAr8H2QZe8JdAA2nq3sQE1gu/03zt6OCwE9ngUe9lK3lX1vxQJN7XsuMlTuP6Au0MHergpstWUOx+viS5ewujb2b1vF3o4Gvrd/61nASLt8KnCXvX03MNXeHgl8Uph+ZyNTee9ZdAHSjDHbjTFngJnA1UGW6Wy5Gnjf3n4fGOpS/oGxWA3UEJG6wRAQwBizDPjdo7i4sl8BfGuM+d0YcwT4FhgQeOnz8aGHL64GZhpjThtjdgBpWPdeSNx/xph9xpif7O0TwGagPuF5XXzp4ouQvDb2b5tp70bbHwP0AWbb5Z7XxHGtZgN9RUTwrV+xKe/Goj6w22U/g8JvrFDBAAtF5EcRGWOXxRtj9tnbvwHx9nY46Fhc2UNZp3H20My7jmEbwkgPe/iiPdabbFhfFw9dIMyujYhEisha4ACW4f0VOGqMyfEik1Ne+/gxoBYlqEd5NxbhSg9jTAdgIHCPiPR0PWis/mdYurmFs+zAW0AzoB2wD5gUXHGKh4hUAf4L3G+MOe56LNyuixddwu7aGGNyjTHtgAZYvYEWwZSnvBuLPUBDl/0GdllIY4zZY/89AHyOdSPtdwwv2X8P2NXDQcfiyh6SOhlj9tv/4HnAv8jv7oe8HiISjfVw/cgY85ldHJbXxZsu4XxtjDFHgSXAJVhDflFeZHLKax+vDhymBPUo78YiBWhuexjEYE0MzQuyTIUiIpVFpKpjG+gPbMSS2+F9cgsw196eB4yyPVi6AsdchhZCheLK/g3QX0Ti7OGE/nZZUPGYCxqGdV3A0mOk7bHSFGgO/ECI3H/22Pa/gc3GmMkuh8LuuvjSJdyujYicJyI17O2KwOVY8y9LgOF2Nc9r4rhWw4H/2b1BX/oVn9Ka3Q/VD5Znx1as8cAngi1PEeRNwPJuWAekOmTGGp9cDGwDFgE1Tb5XxRu2fhuATkGW/2OsYYBsrPHT285GduDPWJN1acCtIaLHh7ac6+1/0rou9Z+w9dgCDAyl+w/ogTXEtB5Ya38Ghel18aVLWF0boC3wsy3vRuBpuzwB62GfBnwKxNrlFez9NPt4gj/9ivvRFdyKoiiKX8r7MJSiKIpSBNRYKIqiKH5RY6EoiqL4RY2FoiiK4hc1FoqiKIpf1Fgo5RoRqSEid7vs1xOR2YWdU4Lf3UREbiiN71KUc0WNhVLeqYEVsRMAY8xeY8zwQuqXJE0ANRZKWKDGQinvTASa2TkOXrHf9jcCiMhoEZkjVi6HdBEZJyIPisjPIrJaRGra9ZqJyAI7sONyESkQw0dEekl+LoWf7VX4E4FL7bIH7MBxr4hIih3wbqx9bm8RWSYiX9k5CaaKSIRdf7qIbBQrv8kDpfi7KeWMKP9VFKVMMx5IMlbANkekUleSsCKXVsBaHfuYMaa9iPwdGAVMwcp/fKcxZpuIXAy8iRVK2pWHgXuMMSvtIHdZ9nc/bIy50v7uMVihMzqLSCywUkQW2ud3wcpNsBNYAFwD7ADqG2OS7PNrlMQPoijeUGOhKIWzxFh5EU6IyDHgC7t8A9DWfvB3Az61whIBVqIZT1YCk0XkI+AzY0yGS30H/e02HcNg1bFi+ZwBfjDGbAcQkY+xwlosBhJE5DXgK2ChZ4OKUlKosVCUwjntsp3nsp+H9f8TgZVjoF1hjRhjJorIV1jxhlaK9/SWAtxrjHELvicivSkYHtwYY46IyEVYSYfuBK7Dis2kKCWOzlko5Z0TWOk3zwpj5UrYISJ/Amd+6os864lIM2PMBmPMS1gRTVt4+e5vgLvsENuISKIdWRigix0BNQIYAawQkdpAhDHmv8CTWGleFSUgqLFQyjXGmMNYb/obReSVs2zmRuA2EXFEAvaWfvN++zvWY0WqnY8VUTRXRNbZk9PvAJuAn+xJ9rfJ7/2nAK9jhanegZXHpD6QLFY2tf8AE85SfkXxi0adVZQQxx6Gck6EK0ow0J6FoiiK4hftWSiKoih+0Z6FoiiK4hc1FoqiKIpf1FgoiqIoflFjoSiKovhFjYWiKIriFzUWiqIoil/+H/7Yyl2ahaA/AAAAAElFTkSuQmCC\n", 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\n", 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rueVT+l68jT1JfDvdAH+/F37fwXJfKTWNFGwOMuyUBpO9MCBCITU1lWAwSE5OjoLBA845gsEgqampfpcig8BLZ+DOEjjawdYGw4/UMHX7aZLqo9hwXXpkQITC2LFjKSsr49SpU36XckF1dXVx+4M1NTWVsWPH+l2GDGD1IfiXg/Ctw+F5CK2lB+B7U+BXT5drMNljAyIUkpKSmDRpkt9ldKmwsJB58+b5XYZIzHmzBj5aAtsq2z+3IBN+Mx3y0+HX7Z+WPqYZzSLiG+fgieMwb1v7QDDgC+PgtfnhQJD+MSDOFEQk/pxpgFX74JkOrvqOSYZfFsCVw/q/rsFOoSAi/e7ls3BHCZR1cAPRjbnw46mQk9T/dYlCQUT6UUMIHjoI3+hkMPk/L4FPjGo3R036kUJBRPrF/hq4vQS2dDCYPL95MHmqxg58p4FmEfGUc/Cz4zBve8eB8MA42DhfgRArdKYgIp452wCf3AdPdzCYPCoZfjENVmT3f13SOYWCiHjilebB5MMdDCbfkAP/NRVy22+YJj5TKIhIn2oIwcOH4JFD0HYxirQA/MclsEqDyTFLoSAifeZAbXiZ680djB3MzYTfFEBBRv/XJdFTKIhIrzkHvzoB974JVU3tn//cWHjkYkjRrS0xT6EgIr1S0Qj/sA+ePNn+uZHJ8PNp8L80mBw3FAoi0mMbKsKXiw51MJj8gRz4yVQYrsHkuKJQEJFuawzB1w7Bv3YwmJwagH+fDJ8arcHkeKRQEJFu+VtteGbyxnPtn5udEZ6ZPEODyXFLoSAiUfv1ifD4QWUHg8mfHQvfmASpCf1fl/QdhYKIdKmiET69D37dwWByXhL8bBqszOn/uqTvKRRE5IJeqwhfLjpY1/6567LhiWkwQoPJA4ZCQUQ61BiCrx+Grx2EtleLUgy+Mxk+PUaDyQONQkFE2jlYG163aEMHg8kzM+DJApiZ2f91ifcUCiIS4ckT8Kl9cK6DweR/HAPfuliDyQOZp5POzWylme01s/1m9sUOnh9vZi+Z2RtmttPMrvWyHhHp3LlGuKsEPlrSPhBGJMHaWfDoFAXCQOfZmYKZJQA/AK4ByoCtZrbGOVfcqtuDwNPOucfMbDqwFpjoVU0i0rFNzYPJb3UwmPy+bPjpNMjTYPKg4OWZwmJgv3PuLedcPbAauKFNHwcMaf56KHDMw3pEpI0mB/96EN77RvtASDF49BJ4bpYCYTDxckxhDHCk1eMy4NI2fR4C/mJm/wfIAFZ4WI/IoONceAvM7xyBtUGoZRlp6+G6HLgjD759GF7tYDB5Rjo8OR1maTB50DHnnDdvbHYTsNI594nmx3cClzrn7mvV53PNNXzXzN4D/ASY6ZwLtXmvVcAqgLy8vAWrV6/2pGavVVVVkZmp/2U9pePXPY0Y32Aar5HLeQzX6sKA4XDNX7V1I2V8krdIabeqkf/2Ha739fOzM+o4XZ3q2+fnj+/5KduVV1653Tm3sKt+Xp4pHAXGtXo8trmttXuAlQDOuY1mlgrkAhHzJp1zjwOPAyxcuNAtX77co5K9VVhYSLzWHgvi/fhdde/hfvssBxRfmkP5mDRCie2vErsOwiCprolpW4OcPR7iWx4N7a374fhevf7hfjyGHbl1SSmrN03z7fPX3dW74xcNL8cUtgJTzGySmSUDtwJr2vQ5DFwNYGYFQCrQwRbfItId57KTOw2Ejgwpr2PRX46Te7yDkWYZVDwLBedcI3Af8GeghPBdRnvM7GEzu7652z8Bf29mO4AngY87r65niQwiR/KzCAWinGrsHCk1TaTUxd7lIul/nk5ec86tJXybaeu2r7b6uhhY6mUNIoNRcHQaRBsKZuH+Ing8eU1E/BFK6N6CRN3tLwOXQkFkAAo0de8qbHf7y8ClUBAZgNLPNUTfOeTIOVbrXTESVxQKIgPM8YkZVGWnRN0/EHKM31fpYUUSTxQKIgPIiXHplC7Kjrp/oDFE7tFask77OylMYoeWzhYZIE6NSaPk0pzIXW9CDnMOZxZ5N1LIEQg5co/WUrAl2MFUNhmsFAoiA0BwZCp7luTiWv3gt5Bj+mvlpNY1cTg/i+DoNFyCYU3hMYTxeysZckZnCBJJoSAS586MSGH3Zbm41reVOkfB5iAjmgeQZ24KAv4v0yCxT2MKInHsbE4yu5YOb7ecxbStp8k7UuNTVRLPFAoicercsGR2Xj6CpqTI/8b5208z6mC1T1VJvFMoiMShqqFJ7LhiOE3Jkf+FJxedYcyBKp+qkoFAoSASZ6qzEilaNoLGlMjNkiftOqv5BtJrCgWROFKbEQ6EhtTIQBhfUsGEkg62UBPpJoWCSJyoS0+gaPkI6tMjbxocu+8cF++q0FwD6RMKBZE4cD41QNGyEdRlRAbC6AOVXFJ0VoEgfUahIBLj6lPCgVCblRTRnnewmvztZxQI0qcUCiIxrCHJ2HHFCGqGRm7YPvxINdO2ankK6XsKBZEY1ZgYDoSqYZGBkHO0humbgwS0BYJ4QKEgEoOaEoydlw+nMidyCexhb9cyY2M5AW2nLB5RKIjEmKYA7FqaS8Xw1Ij2oSfrmLWhnAQFgnhIoSASQ0IB2HPZcM6MTItoHxI8z+xXT5GgbTPFYwoFkRgRMii+NJfg6MhAyDxTz+z1J0lsVCCI9xQKIjHAAaWLcjg1Lj2iPb2injnrT5LUoECQ/qFQEPGZA/YuyObExIyI9rTKBua+fJLk8xpEkP6jUBDxkQP2zx3G8cmZEe2p1Y3MLTxJSp0CQfqXQkHEJw54a9ZQyvKzItqTaxqZW3iC1NomfwqTQU2hIOKTQwVDOFwwNKItqa6JuS+fJK1agSD+UCiI+OBwfhZ/m3VRRFvi+XAgZFQ2+lSViEJBpN8dnZzJgbnDItoS6kPMXX+SzIoGn6oSCVMoiPSj4xMz2LcgO6ItoSHEnFdOknVGgSD+UyiI9JMT49IpXRQZCIHGELNePcXQYL1PVYlEUiiI9IM/nIKSS3PA3l3s2pocM18rZ9ip8z5WJhJJoSDiseeD8JFicIFWgRByzNhYTs7bdT5WJtKeQkHEQ+vOwI17IGKVCuco2Bxk+LFa3+oS6YxCQcQjGyrg+l3QdlLytK2nyTtS409RIl1QKIh4YNs5uHYnVLcJhPztpxl1sNqfokSioFAQ6WM7q+B/7YRzbSYlTy46w5gDVf4UJRIlhYJIHyqthmt2wJk2k5K/NhHG76v0pSaR7lAoiPSRA7Vw9Q442WYO2pfGwz9P8Kcmke5SKIj0gSN1cHURHGszB+0zY+DrkyKmJ4jENIWCSC8dPw9X7YBDbeagrRoF/3GJAkHii0JBpBdO1cOKHbC/zZSDO/PgsXwFgsQfhYJID51pCN9lVNxmysHNw+GJqRBQIEgc8jQUzGylme01s/1m9sVO+txiZsVmtsfMfuNlPSJ95VwjrNwJRW3uMP1ADvyqABL165bEqUSv3tjMEoAfANcAZcBWM1vjnCtu1WcK8CVgqXPujJmN8Koekb5S0wTv3wVb2txhes0weHo6JCsQJI55+c93MbDfOfeWc64eWA3c0KbP3wM/cM6dAXDOnfSwHpFeq2uCD+6GVyoi268YCn+cCakJ/tQl0lfMOdd1r568sdlNwErn3CeaH98JXOqcu69Vnz8C+4ClQALwkHPu+Q7eaxWwCiAvL2/B6tWrPanZa1VVVWRmZvpdRtzy+/g1YPwLM9hIbkR7Aef4DjtI58L7Ku877P+eCdkZdZyuTvXt8/PHJ/fq9X4fw3g+fldeeeV259zCrvp5dvkoSonAFGA5MBZYb2aznHNnW3dyzj0OPA6wcOFCt3z58n4us28UFhYSr7XHAj+PX2MIbiuBjaci2+dmwro5QxiWdHmX7/HwvYc9qi56ty4pZfWmab59/rq7xvfq9X4fw3g/ftHw8vLRUWBcq8djm9taKwPWOOcanHN/I3zWMMXDmkS6LeTg7/bCM20CYXo6vDAbhiX5U5eIF7wMha3AFDObZGbJwK3AmjZ9/kj4LAEzywXygbc8rEmkW5yDT+2DX52IbJ+SBn+dA7m9uxoiEnM8CwXnXCNwH/BnoAR42jm3x8weNrPrm7v9GQiaWTHwEvCAcy7oVU0i3eEcfHY//Ph4ZPuEFHhxDoxK8acuES95OqbgnFsLrG3T9tVWXzvgc81/RGKGc/Dlv8H32lzwHJ0M6+bCOP/GGkU8pTuqRTrw9UPwzTZjmiOSwmcIF6f5U5NIf1AoiLTx3SPwlYORbdmJ8MIcmJbhS0ki/UahINLKD4/C5w9Etg1JgL/MgdmaYiKDgEJBpNlPj8On34xsywjA/8yGBVn+1CTS3xQKIsCTJ+CevZFtqQH40yy4bKg/NYn4QaEgg94fTsGdJdB6wZckgz/MgCuH+VaWiC+6FQpmltG8+qnIgPB8ED5STMSqRQmEVztdmeNXVSL+uWAomFnAzD5qZs+Z2UmgFDjevP/Bt83skv4pU6TvvXQGbtwDDa1OEYzwfggfHO5bWSK+6upM4SVgMuE9D0Y658Y550YA7wU2Ad8yszs8rlGkz22ogA/sgrpQZPsTU+HWPH9qEokFXc1oXuGca2jb6Jw7DfwO+J2ZaTkwiSvbzsG1O6G6TSD8cAp8fJQ/NYnEigueKbwTCGa2ou1zZvax1n1E4sHOqvC+yufabH3w3cnwD2P8qUkklkQ70PxVM3useaA5z8z+BHzAy8JE+lppNVyzA840RrZ/bSJ8blyHLxEZdKINhWXAAaAIeBX4jXPuJs+qEuljB2rh6h1wss157ZfGwz9P8KcmkVgUbSgMI7zn8gHgPDDBzMyzqkT60JE6uLoIjrXZyfEzY+Drk0D/kkXeFW0obAKed86tBBYBo4ENnlUl0keOn4erdsCh85Htq0bBf1yiQBBpK9r9FFY45w4DOOdqgX80syu8K0uk907Vw4odsL82sv3OPHgsX4Eg0pGuJq9NBHgnEFpzzq23sLHelCbSc2cawncZFddEtt88PDwXIaBAEOlQV2cK3zazAPAssB04BaQClwBXAlcD/wKUeVmkSHeca4SVO6GoKrL9Aznh2cqJWvFLpFMXDAXn3M1mNh24HbgbGAnUEt5zeS3wdedcnedVikSppgnevwu2VEa2XzMsvJ5RsgJB5IK6HFNwzhWb2b8C9xJe3sIBW4FnFAiDy1X3truK2K9uXVLPwxeooSkAu947nDMjI/fLHHqyjvO/O8W1Ta6TV0Zn3Q/H9+r1IvEg2oHmnwPngO81P/4o8AvgFi+KEumuUAD2XNY+EIYEzzP71VMk9DIQRAaLaENhpnNueqvHL5lZsRcFiXRXyKD40lyCoyMDIfNMPbPXnySxUYEgEq1or7C+bmZL3nlgZpcC27wpSSR6DihdlMOpcekR7ekV9cx5+SRJDQoEke6I9kxhAfCamb1zQXc8sNfMdgHOOTfbk+pELsABexdkc2JiRkR7WmUDc18+SXJ9qOMXikinog2FlZ5WIdJNDtg/dxjHJ2dGtKdWNzK38CQpbTdKEJGoRBUKzrlDXhciEi0HvDVrKGX5WRHtyTWNzC08QWptU8cvFJEuRXumINLvHHAuO5kjU4cQHJXKSwnjCIx2pFY1UnNRckTfpLom5r58krRqBYJIbygUJCaFDEoW51A+Jo1QwFrWpQglWrtASDwfDoSMysaO3kpEukGhIDHH0SoQulqToskxZ/1JMiu0AaBIX9Ckf4k557KTowsEIIDTcqcifUihIDHnSH5W+JJRFEJmHG4z4CwiPadQkJgTHJ0W/drWAWs3k1lEek6hIDEnlNC9y0Hd7S8inVMoSMwJdHPxuu72F5HOKRQk5uQcqwUX5Q/6kAv3F5E+oVCQmJNR0RD1HUWBkGP8vsquO4pIVBQKElMqL0riUMGQqPoGGkPkHq0l63S9x1WJDB6avCYxoz4lwK6lw3Gt5yc4F57N1vpupJAjEHLkHq2lYEsQDTOL9B2FgsSEUAB2X5bL+YzIf5ITis9Rk5VIcHQaLsGwpvAYwvi9lQw5ozMEkb6mUJCY8ObcYVQMT41oG7vvHBfvqWh5fOuSUlZvmtbfpYkMKhpTEN8duziDY5dEzkq+6EQdk3ec9akikcFLoSC+OpuTzL552RFtqVWNzNhkUqYdAAAQJklEQVRYTkDTD0T6naehYGYrzWyvme03sy9eoN+HzcyZ2UIv65HYUpeWwJ7LhuNazUgONIaYteGUttIU8YlnoWBmCcAPgPcB04HbzGx6B/2ygM8Am72qRWJPU4Kxe2ku9WkJEe0FW4JaBlvER16eKSwG9jvn3nLO1QOrgRs66Pc14FtAnYe1SAxxwN4F2VRmp0S0TyiuYESZZieL+MnLUBgDHGn1uKy5rYWZzQfGOeee87AOiTFH8rM4MTEjoi3naA2Tdld08goR6S++3ZJqZgHg34GPR9F3FbAKIC8vj8LCQk9r80pVVVXc1g5w65LezwsoTs2mcPi4iLZRDVV8IbSZtCUX3l85O6OOW5eU9rqGniosfKtXr++L49dbOoa9E+/HLxrmol14rLtvbPYe4CHn3P9ufvwlAOfcN5ofDwUOAFXNLxkJnAaud85t6+x9Fy5c6LZt6/TpmFZYWMjy5cv9LqPHrrr3cK9eX5uRyLYVeTSmvDuOkFgfYsFf3ya9quv9lf2ep7Duh+N79freHr++oGPYO/F8/Mxsu3Ouy5t5vLx8tBWYYmaTzCwZuBVY886TzrkK51yuc26ic24isIkuAkHiV2Oiseu9uRGBgHNM31QeVSCISP/wLBScc43AfcCfgRLgaefcHjN72Myu9+pzJfY4oGRxDtVDkyPaL955lpy3dX+BSCzxdEzBObcWWNum7aud9F3uZS3in4PTh1A+Nj2ibcShasbv1ZLXIrFGM5rFU6dGp3Fw5kURbZln6pm27bRWNxWJQQoF8Uz1kCRKLs2JaEuqa2LWhlMkaAtNkZikUBBPNCQH2LU0l6akd/+JWcgx87VyUmsufOupiPhHoSB9LmSwZ0kOtVlJEe1T3jjDReXnfapKRKKhUJA+99bsizgzMi2ibdSBKkYfqOrkFSISKxQK0qfeHp/OkamReywPPVVH/hsaWBaJBwoF6TPnhiWzd1HkwHJKTfPeCFoJWyQuKBSkT5xPDbB7aS6h1nsjNDlmbignpU6JIBIvFArSa6EA7HlPLufTI+dCTt0WZMgZ/xeBE5HoKRSk196cN4yK4akRbeP2nmPkoRqfKhKRnlIoSK8cnZzJsclZEW3D3q7l4p1nfapIRHpDoSA9djY3hTfnDYtoS61qYMamIAFNWBaJSwoF6ZG69AR2X5aLC7w7sJzQEGLWq+Uk1WtgWSReKRSk25oSjF1Lh9OQmhDRXrAlSOa5Bp+qEpG+oFCQbnFA6cJsqoZF7o0wcU8Fw4/W+lOUiPQZhYJ0y5GpWZyckBHRlltWw8Q9FT5VJCJ9SaEgUQuOTOXA7Mi9ETIq6inYEtQSFiIDhEJBorKvBoqX5IK9++M/8XwTs14tJ7FRtxqJDBQKBenSuUb44G5oTG71zyXkmLEpSFp1o3+FiUifUyjIBYUc3FECJW0mJ0/eeZbsE3X+FCUinlEoyAU9dBD+FIxsyztYzbh9lb7UIyLeUihIp353Cr52KLIt6/R5pm7X3ggiA5VCQTq0swo+VhLZllzbxMwN5SQ0aWBZZKBSKEg7wYbwwHJ1q9UqkgxmvHaK1Nom/woTEc8pFCRCYwhu2QN/azOG/P0pcFFQeyOIDHQKBYnwwFuwrs2q1/8wGlaN9qceEelfCgVp8fO34T/LItsuHwr/eYk/9YhI/1MoCACbz8En90a2jUuBZ2ZAsv6ViAwa+u8uHD8PH9oN51vdVJQWgD/OhBHJnb9ORAYehcIgdz4EH9oDx9qMIf9kKszP6vg1IjJwKRQGMefg0/tg07nI9v87Dm7L86cmEfGXQmEQ+8FR+MnbkW0rs+GRi/2pR0T8p1AYpArPwGf3R7ZNSYPfFECC1rAQGbQUCoPQwVq4aQ+0npuclQDPzoRhSb6VJSIxQKEwyFQ3hZewCLbZBuFXBVCQ0fFrRGTwUCgMIs7B3aWwozqy/WsT4fpcX0oSkRijUBhEvnkYnj4V2fbhXPjnCf7UIyKxR6EwSDwXhH/+W2TbrAz42bSIbZdFZJBTKAwCpdXw0WJovQtCdmJ4YDkz0beyRCQGKRQGuLMNcMNuONfqVqME4OkZMCnNt7JEJEYpFAawJge3l8C+2sj2714CVw/zpyYRiW0KhQHsK3+Dtacj2z6WB/84xp96RCT2KRQGqKdOwjcOR7YtzoIf5WtgWUQ652komNlKM9trZvvN7IsdPP85Mys2s51m9qKZ6ebIPlBUCX9XGtk2Mhn+MBNSE/ypSUTig2ehYGYJwA+A9wHTgdvMbHqbbm8AC51zs4FngH/zqp7B4lR9eMZybejdtmSD38+A0Sn+1SUi8cHLM4XFwH7n3FvOuXpgNXBD6w7OuZecczXNDzcBYz2sZ8BrCMHNe+DQ+cj2x/LhPUP9qUlE4ouXoTAGONLqcVlzW2fuAf7Hw3oGvM8dgJcrItvuGwN3j/KnHhGJP+ac67pXT97Y7CZgpXPuE82P7wQudc7d10HfO4D7gGXOufMdPL8KWAWQl5e3YPXq1Z7U7LWqqioyMzM9ee/nGMl3mBbRNpczfJudJNI33+N9h+u77uSh7Iw6Tlen+vb5+eN7tzep38cPdAx7K56P35VXXrndObewq35ehsJ7gIecc/+7+fGXAJxz32jTbwXw/xIOhJNdve/ChQvdtm3bPKjYe4WFhSxfvrzP33djBSwrgoZW38oJKbBtAeT24R7LV917uOtOHrp1SSmrN03ruqNH1v1wfK9e7/fxAx3D3orn42dmUYWCl5ePtgJTzGySmSUDtwJrWncws3nA/wdcH00gSHtHz4f3WG4dCOkB+OPMvg0EERkcPAsF51wj4UtCfwZKgKedc3vM7GEzu76527eBTOC3ZlZkZms6eTvpQF0T3Lgb3m5zRv3TaTA3y5+aRCS+ebocmnNuLbC2TdtXW329wsvPH8icg0/tg62Vke1fGg+3jPCnJhGJf5rRHKe+dxR+fiKy7bps+Nokf+oRkYFBoRCHXjwD/7Q/sm1qGvx6OiRoCQsR6QWFQpx5qxZu2QOtVsJmSAI8OwuGam8EEeklhUIcqWoM741wuvHdNgOenA5T030rS0QGEIVCnHAOPl4Ku6sj278+Ca7N8acmERl4FApx4uuH4HflkW0fGQ5f7N1cIBGRCAqFOLCmHL5yMLJtTgb8ZJr2RhCRvqVQiHHF1XBHSWRbblJ4xnKG9kYQkT6mUIhhZxrCA8uVrW41SgB+Ox0mpvlWlogMYAqFGNXk4KMlsL82sv3RKbB8mD81icjAp1CIUV9+C54/Hdl2z0i4d7Q/9YjI4DCopjv5v+xuPQ9HUcOJ8ekUL8mNaBtSfp79z5zg6lAnL4pCb5ctFpGBT2cKMaZyWBKlC7Mj2pJrGpn52ikCvQgEEZFoKBRiSH1KgF2XDSeU+O63JdDkmPVaOSl1SgQR8Z5CIUaEArD7slzOZ0Re0Zu67TRDTvu/jaOIDA4KhRjx5txhVAyP3Pt17L5zjDxU3ckrRET6nkIhBhy7OINjl0RulTbsRB2Td5z1qSIRGawUCj47m5vCvnmRA8upVY3M2FhOwHXyIhERjygUfFSXlsDuy3JxrXbGSWgIMWvDKZLqNbAsIv1PoeCTpgRj99JcGlIjFzCatiVIZkWDT1WJyGCnUPCBA/YuyKYyOyWifcKeCkYcre34RSIi/WBQzWjubw44l53MkalDCI5K5aWEcQRGO9IqG6kelhzRN/doDZP2VPhTqIhIM4WCR0IGJYtzKB+TRihgEAiPG4QSjeqLkiL6plc0ULA5iLZGEBG/KRQ84GgVCIkdXKFrtTOONTlmbjhFYqNuNRIR/2lMwQPnspM7D4R2HE3J+jaISGzQTyMPHMnPCl8yioIz43B+VtcdRUT6gULBA8HRaS1jCF0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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# Plot progress w.r.t the generator's and the discriminator's loss function\n", - "t_steps = np.arange(num_epochs)\n", - "plt.figure(figsize=(6,5))\n", - "plt.title(\"Progress in the loss function\")\n", - "plt.plot(t_steps, qgan.g_loss, label = \"Generator loss function\", color = 'mediumvioletred', linewidth = 2)\n", - "plt.plot(t_steps, qgan.d_loss, label = \"Discriminator loss function\", color = 'rebeccapurple', linewidth = 2)\n", - "plt.grid()\n", - "plt.legend(loc = 'best')\n", - "plt.xlabel('time steps')\n", - "plt.ylabel('loss')\n", - "plt.show()\n", - "\n", - "\n", - "# Plot progress w.r.t relative entropy\n", - "plt.figure(figsize=(6,5))\n", - "plt.title(\"Relative Entropy \")\n", - "plt.plot(np.linspace(0, num_epochs, len(qgan.rel_entr)), qgan.rel_entr, color ='mediumblue', lw=4, ls=':')\n", - "plt.grid()\n", - "plt.xlabel('time steps')\n", - "plt.ylabel('relative entropy')\n", - "plt.show()\n", - "\n", - "#Plot the PDF of the resulting distribution against the target distribution, i.e. log-normal\n", - "log_normal = np.random.lognormal(mean=1, sigma=1, size=100000)\n", - "log_normal = np.round(log_normal)\n", - "log_normal = log_normal[log_normal <= bounds[1]]\n", - "temp = []\n", - "for i in range(int(bounds[1]+1)):\n", - " temp += [np.sum(log_normal==i)]\n", - "log_normal = np.array(temp / sum(temp))\n", - "\n", - "plt.figure(figsize=(6,5))\n", - "plt.title(\"CDF\")\n", - "samples_g, prob_g = qgan.generator.get_samples(qgan.quantum_instance, shots=10000)\n", - "samples_g = np.array(samples_g)\n", - "samples_g = samples_g.flatten()\n", - "num_bins = len(prob_g)\n", - "plt.bar(samples_g, np.cumsum(prob_g), color='royalblue', width= 0.8, label='simulation')\n", - "plt.plot( np.cumsum(log_normal),'-o', label='log-normal', color='deepskyblue', linewidth=4, markersize=12)\n", - "plt.xticks(np.arange(min(samples_g), max(samples_g)+1, 1.0))\n", - "plt.grid()\n", - "plt.xlabel('x')\n", - "plt.ylabel('p(x)')\n", - "plt.legend(loc='best')\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "QiskitDevenv", - "language": "python", - "name": "qiskitdevenv" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.3" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/qiskit/finance/machine_learning/qgans.ipynb b/qiskit/finance/machine_learning/qgans.ipynb deleted file mode 100644 index d21327bbe..000000000 --- a/qiskit/finance/machine_learning/qgans.ipynb +++ /dev/null @@ -1,194 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# _*Qiskit Finance: qGAN Option Pricing*_ \n", - "\n", - "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", - "\n", - "***\n", - "### Contributors\n", - "Christa Zoufal[1,2], Stefan Woerner[1]\n", - "### Affliation\n", - "- [1]IBMQ\n", - "- [2]ETH Zurich\n", - "\n", - "### Introduction\n", - "In this notebook, we discuss how a Quantum Machine Learning Algorithm, namely a quantum Generative Adversarial Network (qGAN), can facilitate the pricing of a European call option. More specifically, a qGAN can be trained such that a quantum circuit models the spot price of an asset underlying a European call option. The resulting model can then be integrated into a Quantum Amplitude Estimation based algorithm to evaluate the expected payoff - see [European Call Option Pricing](../../aqua/finance/european_call_option_pricing.ipynb).
\n", - "For further details on learning and loading random distributions by training a qGAN please refer to Quantum Generative Adversarial Networks for Learning and Loading Random Distributions. Zoufal, Lucchi, Woerner. 2019." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/Users/ouf/anaconda3/envs/QiskitDevenv/lib/python3.7/site-packages/qiskit_terra-0.8.0-py3.7-macosx-10.7-x86_64.egg/qiskit/circuit/variabletable.py:10: DeprecationWarning: Using or importing the ABCs from 'collections' instead of from 'collections.abc' is deprecated, and in 3.8 it will stop working\n", - " from collections import MutableMapping\n" - ] - } - ], - "source": [ - "#!/usr/bin/env python\n", - "# coding: utf-8\n", - "from __future__ import absolute_import, division, print_function\n", - "\n", - "import matplotlib.pyplot as plt\n", - "%matplotlib inline\n", - "import numpy as np\n", - "from qiskit.aqua.algorithms import AmplitudeEstimation\n", - "from qiskit.aqua.components.uncertainty_problems import EuropeanCallExpectedValue\n", - "from qiskit.aqua.components.uncertainty_models import UnivariateVariationalDistribution, NormalDistribution\n", - "from qiskit.aqua.components.variational_forms import RY\n", - "\n", - "from qiskit.aqua import aqua_globals, QuantumInstance\n", - "\n", - "from qiskit import BasicAer" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Uncertainty Model\n", - "\n", - "The Black-Scholes model assumes that the spot price at maturity $S_T$ for a European call option is log-normally distributed. Thus, we can train a qGAN on samples from a log-normal distribution and use the result as uncertainty model underlying the option. A notebook that explains the implementation of a qGAN to learn and load a random distribution is presented in [qGANs for Loading Random Distributions](../../aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb).
\n", - "In the following, we construct a quantum circuit that loads the uncertainty model. The circuit output reads $$\\lvert g_{\\theta}\\rangle = \\sum\\limits_{j=0}^{2^n-1}\\sqrt{p_{\\theta}^{j}}\\lvert{j}\\rangle,$$ where the probabilites $p_{\\theta}^{j}$, for $j\\in \\left\\{0, \\ldots, {2^n-1} \\right\\}$, represent a model of the target distribution." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "# Set upper and lower data values\n", - "bounds = np.array([0.,7.])\n", - "# Set number of qubits used in the uncertainty model\n", - "num_qubits = [3]\n", - "\n", - "# Set entangler map\n", - "entangler_map = []\n", - "for i in range(sum(num_qubits)):\n", - " entangler_map.append([i, int(np.mod(i+1, sum(num_qubits)))])\n", - "\n", - "# Set variational form\n", - "var_form = RY(int(np.sum(num_qubits)), depth=1, entangler_map=entangler_map, entanglement_gate='cz')\n", - "# Load the trained circuit parameters\n", - "g_params = [0.29399714, 0.38853322, 0.9557694, 0.07245791, 6.02626428, 0.13537225]\n", - "# Set an initial state for the generator circuit\n", - "init_dist = NormalDistribution(int(sum(num_qubits)), mu=1., sigma=1., low=bounds[0], high=bounds[1])\n", - "# Set generator circuit\n", - "g_circuit = UnivariateVariationalDistribution(int(sum(num_qubits)), var_form, g_params,\n", - " initial_distribution=init_dist, low=bounds[0], high=bounds[1])\n", - "\n", - "# construct circuit factory for uncertainty model\n", - "uncertainty_model = g_circuit" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# plot probability distribution\n", - "x = uncertainty_model.values\n", - "y = uncertainty_model.probabilities\n", - "plt.bar(x, y, width=0.2)\n", - "plt.xticks(x, size=15, rotation=90)\n", - "plt.yticks(size=15)\n", - "plt.grid()\n", - "plt.xlabel('Spot Price at Maturity $S_T$ (\\$)', size=15)\n", - "plt.ylabel('Probability ($\\%$)', size=15)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Evaluate Expected Payoff\n", - "Now, the trained uncertainty model can be used to evaluate the expectation value of the option's payoff function with Quantum Amplitude Estimation." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Estimated value:\t1.2580\n", - "Probability: \t0.8785\n" - ] - } - ], - "source": [ - "# set the strike price (should be within the low and the high value of the uncertainty)\n", - "strike_price = 2\n", - "\n", - "# set the approximation scaling for the payoff function\n", - "c_approx = 0.25\n", - "\n", - "# construct circuit factory for payoff function\n", - "european_call = EuropeanCallExpectedValue(\n", - " uncertainty_model,\n", - " strike_price=strike_price,\n", - " c_approx=c_approx\n", - ")\n", - "# set number of evaluation qubits (samples)\n", - "m = 5\n", - "\n", - "# construct amplitude estimation \n", - "ae = AmplitudeEstimation(m, european_call)\n", - "# result = ae.run(quantum_instance=BasicAer.get_backend('qasm_simulator'), shots=100)\n", - "result = ae.run(quantum_instance=BasicAer.get_backend('statevector_simulator'))\n", - "print('Estimated value:\\t%.4f' % result['estimation'])\n", - "print('Probability: \\t%.4f' % result['max_probability'])" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "QiskitDevenv", - "language": "python", - "name": "qiskitdevenv" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.3" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} From 7365dfc1cefac004e842a2507ce08e38dc626f46 Mon Sep 17 00:00:00 2001 From: CZ Date: Sat, 20 Apr 2019 18:33:55 +0200 Subject: [PATCH 066/116] Create qgans_for_loading_random_distributions.ipynb --- ...ans_for_loading_random_distributions.ipynb | 13043 ++-------------- 1 file changed, 1030 insertions(+), 12013 deletions(-) diff --git a/qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb b/qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb index 8288dcfb8..14ed3f906 100644 --- a/qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb +++ b/qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb @@ -27,9 +27,18 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 1, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/ouf/anaconda3/envs/QiskitDevenv/lib/python3.7/site-packages/qiskit_terra-0.8.0-py3.7-macosx-10.7-x86_64.egg/qiskit/circuit/variabletable.py:10: DeprecationWarning: Using or importing the ABCs from 'collections' instead of from 'collections.abc' is deprecated, and in 3.8 it will stop working\n", + " from collections import MutableMapping\n" + ] + } + ], "source": [ "#!/usr/bin/env python\n", "# coding: utf-8\n", @@ -49,13 +58,13 @@ "start = time.time()\n", "\n", "from torch import optim\n", - "from qiskit.aqua.algorithms.adaptive.qgan.discriminator import DiscriminatorNet\n", "\n", "from qiskit.aqua.components.optimizers import ADAM\n", "from qiskit.aqua.components.uncertainty_models import UniformDistribution, UnivariateVariationalDistribution \n", "from qiskit.aqua.components.variational_forms import RY\n", "\n", - "from qiskit.aqua.algorithms.adaptive.qgan.qgan import QGAN\n", + "from qiskit.aqua.algorithms.adaptive import QGAN\n", + "from qiskit.aqua.algorithms.adaptive.qgan.discriminator import DiscriminatorNet\n", "\n", "from qiskit.aqua import aqua_globals, QuantumInstance\n", "\n", @@ -73,7 +82,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -106,7 +115,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ @@ -165,7 +174,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -173,12216 +182,1224 @@ "output_type": "stream", "text": [ "Epoch 1/3000...\n", - "Loss Discriminator: 0.6977\n", - "Loss Generator: 0.6754\n", - "Relative Entropy: 0.1783\n", - "Epoch 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"stream", - "text": [ - "Loss Discriminator: 0.6832\n", - "Loss Generator: 0.7086\n", - "Relative Entropy: 0.0728\n", - "Epoch 1970/3000...\n", - "Loss Discriminator: 0.6825\n", - "Loss Generator: 0.7112\n", - "Relative Entropy: 0.0728\n", - "Epoch 1971/3000...\n", - "Loss Discriminator: 0.683\n", - "Loss Generator: 0.7077\n", - "Relative Entropy: 0.0727\n", - "Epoch 1972/3000...\n", - "Loss Discriminator: 0.6822\n", - "Loss Generator: 0.7089\n", - "Relative Entropy: 0.0727\n", - "Epoch 1973/3000...\n", - "Loss Discriminator: 0.6832\n", - "Loss Generator: 0.7102\n", - "Relative Entropy: 0.0727\n", - "Epoch 1974/3000...\n", - "Loss Discriminator: 0.683\n", - "Loss Generator: 0.7071\n", - "Relative Entropy: 0.0726\n", - "Epoch 1975/3000...\n", - "Loss Discriminator: 0.6831\n", - "Loss Generator: 0.7096\n", - "Relative Entropy: 0.0726\n", - "Epoch 1976/3000...\n", - "Loss Discriminator: 0.6859\n", - "Loss Generator: 0.7136\n", - "Relative Entropy: 0.0725\n", - "Epoch 1977/3000...\n", - 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"Relative Entropy: 0.0377\n", - "Epoch 2973/3000...\n", - "Loss Discriminator: 0.6891\n", - "Loss Generator: 0.6977\n", - "Relative Entropy: 0.0376\n", - "Epoch 2974/3000...\n", - "Loss Discriminator: 0.6884\n", - "Loss Generator: 0.7018\n", - "Relative Entropy: 0.0376\n", - "Epoch 2975/3000...\n", - "Loss Discriminator: 0.6888\n", - "Loss Generator: 0.705\n", - "Relative Entropy: 0.0376\n", - "Epoch 2976/3000...\n", - "Loss Discriminator: 0.688\n", - "Loss Generator: 0.6991\n", - "Relative Entropy: 0.0376\n", - "Epoch 2977/3000...\n", - "Loss Discriminator: 0.688\n", - "Loss Generator: 0.6981\n", - "Relative Entropy: 0.0375\n", - "Epoch 2978/3000...\n", - "Loss Discriminator: 0.6881\n", - "Loss Generator: 0.7028\n", + "Loss Generator: 0.7026\n", "Relative Entropy: 0.0375\n", - "Epoch 2979/3000...\n", - "Loss Discriminator: 0.687\n", + "Epoch 2781/3000...\n", + "Loss Discriminator: 0.688\n", + "Loss Generator: 0.7004\n", + "Relative Entropy: 0.0372\n", + "Epoch 2791/3000...\n", + "Loss 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"Epoch 2986/3000...\n", - "Loss Discriminator: 0.6875\n", + "Relative Entropy: 0.0363\n", + "Epoch 2821/3000...\n", + "Loss Discriminator: 0.6885\n", + "Loss Generator: 0.7034\n", + "Relative Entropy: 0.036\n", + "Epoch 2831/3000...\n", + "Loss Discriminator: 0.6889\n", "Loss Generator: 0.7009\n", - "Relative Entropy: 0.0373\n", - "Epoch 2987/3000...\n", - "Loss Discriminator: 0.6884\n", - "Loss Generator: 0.6982\n", - "Relative Entropy: 0.0373\n", - "Epoch 2988/3000...\n", - "Loss Discriminator: 0.6879\n", - "Loss Generator: 0.701\n", - "Relative Entropy: 0.0372\n", - "Epoch 2989/3000...\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Loss Discriminator: 0.687\n", - "Loss Generator: 0.7023\n", - "Relative Entropy: 0.0372\n", - "Epoch 2990/3000...\n", - "Loss Discriminator: 0.6879\n", - "Loss Generator: 0.7025\n", - "Relative Entropy: 0.0372\n", - "Epoch 2991/3000...\n", - "Loss Discriminator: 0.6886\n", - "Loss Generator: 0.6976\n", - "Relative Entropy: 0.0372\n", - "Epoch 2992/3000...\n", - "Loss Discriminator: 0.6884\n", - "Loss Generator: 0.7018\n", - "Relative Entropy: 0.0371\n", - "Epoch 2993/3000...\n", - "Loss Discriminator: 0.6886\n", - "Loss Generator: 0.7024\n", - "Relative Entropy: 0.0371\n", - "Epoch 2994/3000...\n", - "Loss Discriminator: 0.6887\n", + "Relative Entropy: 0.0358\n", + "Epoch 2841/3000...\n", + "Loss Discriminator: 0.6882\n", + "Loss Generator: 0.7013\n", + "Relative Entropy: 0.0355\n", + "Epoch 2851/3000...\n", + "Loss Discriminator: 0.6898\n", + "Loss Generator: 0.7015\n", + "Relative Entropy: 0.0352\n", + "Epoch 2861/3000...\n", + "Loss Discriminator: 0.6896\n", + "Loss Generator: 0.6983\n", + "Relative Entropy: 0.0349\n", + "Epoch 2871/3000...\n", + "Loss Discriminator: 0.6885\n", + "Loss Generator: 0.6971\n", + "Relative Entropy: 0.0347\n", + "Epoch 2881/3000...\n", + "Loss Discriminator: 0.6878\n", + "Loss Generator: 0.7022\n", + "Relative Entropy: 0.0344\n", + "Epoch 2891/3000...\n", + "Loss 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3000/3000...\n", + "Loss Generator: 0.7004\n", + "Relative Entropy: 0.0333\n", + "Epoch 2931/3000...\n", + "Loss Discriminator: 0.6901\n", + "Loss Generator: 0.7039\n", + "Relative Entropy: 0.0331\n", + "Epoch 2941/3000...\n", + "Loss Discriminator: 0.6885\n", + "Loss Generator: 0.7004\n", + "Relative Entropy: 0.0328\n", + "Epoch 2951/3000...\n", + "Loss Discriminator: 0.6881\n", + "Loss Generator: 0.697\n", + "Relative Entropy: 0.0326\n", + "Epoch 2961/3000...\n", + "Loss Discriminator: 0.6873\n", + "Loss Generator: 0.7011\n", + "Relative Entropy: 0.0323\n", + "Epoch 2971/3000...\n", + "Loss Discriminator: 0.6891\n", + "Loss Generator: 0.7003\n", + "Relative Entropy: 0.032\n", + "Epoch 2981/3000...\n", "Loss Discriminator: 0.6887\n", - "Loss Generator: 0.7016\n", - "Relative Entropy: 0.0369\n", - "qGAN training runtime: 35.25595039923986 min\n" + "Loss Generator: 0.7022\n", + "Relative Entropy: 0.0318\n", + "Epoch 2991/3000...\n", + "Loss Discriminator: 0.6878\n", + "Loss Generator: 0.6988\n", + "Relative Entropy: 0.0315\n", + "qGAN training runtime: 35.40391653776169 min\n" ] } ], @@ -12406,12 +1423,12 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 5, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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XkJGhRCEi9UvJohFZtqyYrVvLEx2GiKQgJYtGIj+/kCOOyOOMMxZRWKiEISI7R8miEZg/v5BjjlnAsmUlvPXWRoYNW0RxsRKGiMQursnCzAabWZ6Z5ZvZzVXsP9rMZppZqZkNq2L/Lma23Mwejmec6e6qq5axYsX2h/TeeGMjjzyyJoERiUiqiVuyMLNMYDRwMtAbONfMelcq9jVwIfBCNW9zJ/BevGJsLJ59ths/+lGzbevDh7flyis7JDAiEUk18byyGADku/sidy8GxgJDIwu4+xJ3/wL4wT0RM+sL5ALvxDHGRmG33ZoyeXJP9tknm0suacdTT3VV11oR2Snm7vF54+C20mB3vzRc/xlwqLuPrKLsGOB1d385XM8A/gNcAPwY6FfNcSOAEQC5ubl9x44dW+t4CwoKaNmyZfSCSa6memzYYLRq5WSkSEtVunwmoLoko3SpB9StLscee+wMd+8XrVyyzmdxBTDR3ZebVf8XsLs/BjwG0K9fPx80aFCtTzh16lTqcnyySJd6gOqSrNKlLulSD2iYusTzb8xvgD0j1juH22IxEBhpZkuA+4Cfm9kf6zc8iZSXV8hVVy2jtDQ+V5oiktrieWUxHehpZt0JksQ5wHmxHOju51csm9mFBLehftCbSurH/PmFHHvsAr79toTvvivh+ee707Sp2jREZLu4XVm4eykwEngbmAuMd/fZZjbKzIYAmFl/M1sOnAk8amaz4xWPVC0/f3uiAHjppfWce+5iSkp0hSEi28W1zcLdJwITK227PWJ5OsHtqZreYwwwJg7hCcGItVlZO15F7LprJpmZCQpIRJJSivSLkXjp1i2bd9/dh732ygLg4ovb8eijXTQYoYjsQMlC6NIli3ff3Ydf/zqXxx9XohCRH0rWrrPSwDp3zuLuuzslOgwRSVK6spCYLFxYpOHNRRoxJQuJat68YHjz005byObNZYkOR0QSQMlCajR/fiHHHbeA774rZfLkTZx0Uj4bNihhiDQ2ShZSo2uuWb7tGQyAadM2M2bM9wmMSEQSQclCavTss904+ODm29Yvu6w9V1+t4c1FGhv1hpIatW/fhP/8pyennLKQHj2yGT16T2oa3FFE0pOShUTVpk0TJk3qQXZ2hp7BEGmklCwkJi1a1Dz+R1mZa0IlkTSmNgupsy+/3EqfPnP5/PMtiQ5FROIkarIws9PCmetEfmD+/EJOOGEBc+cGo9d+8snmRIckInEQSxI4G1hgZveY2b7xDkhSx6pVJRx/fPAMBsC6dWX8+McLWLSoKMGRiUh9i5os3P0C4GBgITDGzD40sxFm1iru0UlS69ChCcOG7brDtosuakf37lkJikhE4iWm20vuvhF4GRgL7AGcDsw0s6viGJskOTPj/vs7ceutuwNwySXteOCBzupaK5KGovaGCme1uwjoATwDDHD3VWaWA8wB/hrfECWZmRl33dWR/v1zOPXU1upaK5KmYuk6+1PgAXd/L3Kju28xs0viE5akmqFD2yQ6BBGJo1jaLIYD881sSNgzaveIfZPjGp2khY8/3sxNNy2nvFzzeoukqli6zl4CfAKcAQwDPjKzi+MdmKSH2bO3csop+dx33yp+9rMllJQoYYikolhuQ/0KONjdvwcws3bAB8BT8QxMUt+SJUWceGI+a9cGQ5q/8MI61q8v47XX9qZJE7VtiKSSWHpDfQ9siljfFG4TqdHmzeV4pQuJQw7JUaIQSUGxJIt84GMz+52Z/Rb4iKAN43ozuz6+4Ukq22+/5kybtg97750NBMObjxq1R4KjEpHaiOU21MLwVeG18F89lCdRde+ezX//uw8PP7yaO+7YQ89giKSoqMnC3e8AMLOW4XpBvIOS9LL77k25666OiQ5DROoglt5Q+5vZZ8BsYLaZzTCz/eIfmjQWkydvZOLEDYkOQ0RqEEubxWPA9e7e1d27AjcAj8fy5mY22MzyzCzfzG6uYv/RZjbTzErNbFjE9oPCMahmm9kXZnZ2rBWS1DJr1hZOP30RQ4Ys5O9/V78JkWQVS7Jo4e5TKlbcfSrQItpBZpYJjAZOBnoD55pZ70rFvgYuBF6otH0L8HN33w8YDDxoZnpEOM0sXlzEySfns2lTOWVlcPHFS7n77m8THZaIVCGWBu5FZnYb8Gy4fgGwKIbjBgD57r4IwMzGAkMJxpMCwN2XhPvKIw909/kRyyvMbBXQAVgfw3klRXzwweZtw5tXaNZMU6eIJCPzyh3hKxcw2xW4AzgScOB94A53XxfluGHAYHe/NFz/GXCou4+souwY4HV3f7mKfQOAp4H93L280r4RwAiA3NzcvmPHjq2xLjUpKCigZcuWtT4+WaRaPd57rwl33dWckhJj2LAirrxy+1wYqVaXmqguySdd6gF1q8uxxx47w937RS3o7tW+gEzgvprK1HDsMOCJiPWfAQ9XU3YMMKyK7XsAecBh0c7Xt29fr4spU6bU6fhkkYr1eO+9Tf7LXy71srLyHbanYl2qo7okn3Sph3vd6gJ86jF8p9d4G8rdy8zsyFqlK/gG2DNivXO4LSZmtgvwBnCru39UyxgkBRx1VEuOOio9/sITSVextFl8ZmYTgJeAbRMsu/s/ohw3HehpZt0JksQ5wHmxBGVmWcCrwDNexa0paVxee209HTs2pX//qP0qRCROYmlNbEYwFtRxwGnh69RoB7l7KTASeBuYC4x399lmNiqcUAkz629my4EzgUfNbHZ4+FnA0cCFZjYrfB20k3WTNPDRR5s555zFHHPMfF57Tf0bRBIlliuLJ9x9WuQGMzsiljd394nAxErbbo9Ynk5we6rycc8Bz8VyDklfK1YY1167kMLCoBPG6acv4sEHO3P11bslODKRxieWK4uqpk3VVKoSdx980JTVq7d3rXWHli3VtVYkEaq9sjCzgcDhQIdKo8vuQtBLSiSuhg0r5oAD9uGKK76mrAxuvXV3Lr64faLDEmmUaroNlQW0DMtEjjC7kaBbrEjcjRjRni5dmvLqqxu4804Nby6SKNUmC3d/F3jXzMa4+9IGjElkB4MHt2bw4NaJDkOkUYulgTvbzB4DukWWd/fj4hWUyM548cW1tGvXhBNP3CXRoYikrViSxUvAI8ATQFl8wxHZOVOnbmL48KWUlzsPPbQnV1zRIdEhiaSlWJJFqbv/X9wjEdlJ8+YVcvrpiygpCbrWXnnlMhYvLuLee3/QG1tE6iiWfoj/MrMrzGwPM2tb8Yp7ZCJRfPBBARs27HixO3CgnvIWiYdYriyGh//eFLHNgb3qPxyR2F18cXvat2/CeectYfPmcu66aw/OOGPXRIclkpZimYO7e0MEIlIbQ4a04YMP9uGZZ9by61/vnuhwRNJWLHNw55jZb8IeUZhZTzOLOjaUSEM54IAc7ruvM2aW6FBE0lYsbRZ/B4oJnuaGYATZu+IWkUg9e+ihVYwcuYzS0pon+hKR6sXSZrG3u59tZucCuPsW059wkiLeemsD1123nPJymD+/kHHjurPrrrH82otIpFiuLIrNrDlBozZmtjdQVPMhIok3d+5Wzj57MeXhZLyTJm3i5JPzK2ZhFJGdEEuy+C3wFrCnmT0PTAZ+FdeoROpBaSm0abP9KiIjA0aN6qi2DZFaiJos3H0ScAZwIfAi0M/dp8Y3LJG669OnOZ980ovDDw+evfjjHztpSBCRWorp5q27f08wH7ZISsnNbcrkyT159tm1XHppu0SHI5KyNJOMpL1mzTL4xS/aV3v7qbzc+frr4gaOSiS1KFlIo3f33Svp02cOb7yxIdGhiCStmJKFmR1pZheFyx3MTE91S1r417/Wc/vt37JxYzmnnbaQu+/+Vr2lRKoQyxPcvwX+F7gl3NQUeC6eQYk0hG++KeaCC5ZsW3eHBx9czXfflVZ/kEgjFcuVxenAEGAzgLuvYMdpVkVSUseOTbnjjo5khjPKZ2bCSy91Z/fdmyY2MJEkFNNDeR5cl1c8lKcxoCUtmBnXXrsb77zTk3btMrn//s4MGqS/g0SqEkvX2fFm9ijQxsx+AVwMPB7fsEQaznHHtWLOnN506KBhQESqE8tDefcBLwOvAL2A2939r/EOTKQh7bZb02q71paVOX/840o2bdKswtJ4xdLAfT0wx91vcvcbwye6Y2Jmg80sz8zyzezmKvYfbWYzzazUzIZV2jfczBaEr+GVjxVpKL/97bfccssKDj00j/nzCxMdjkhCxNJm0Qp4x8zeN7ORZpYbyxubWSYwGjgZ6A2ca2a9KxX7mmAYkRcqHduWYEyqQ4EBwG/NTFOgSYP7xz/WcffdKwGYO7eQAQPyePfdTQmOSqThxXIb6g533w+4EtgDeNfM/h3Dew8A8t19kbsXA2OBoZXee4m7fwGUVzr2JGCSu69193XAJGBwDOcUqTfuzl/+snqHbc2bGz16ZCcoIpHE2ZknuFcBK4Hvgd1iKN8JWBaxvjzcFou6HCtSL8yMN9/swfnnBxe1TZrAyy/vRadOWQmOTKThRe3+YWZXAGcBHYCXgF+4+5x4BxYLMxsBjADIzc1l6tSptX6vgoKCOh2fLNKlHpA8dbnkEmjTJousLKek5FNqE1Ky1KU+pEtd0qUe0DB1iaWv4J7Ate4+ayff+5vw2Aqdw22xHjuo0rFTKxdy98eAxwD69evngwYNqlwkZlOnTqUuxyeLdKkHJFddjj225v1lZU5mZvXzZCRTXeoqXeqSLvWAhqlLtbehzKxi4P97ga/NrG3kK4b3ng70NLPuZpYFnANMiDGut4ETzWzXsGH7xHCbSNIpLXVOOSWfUaO+pbxc40pJeqrpyuIF4FRgBsHT25F/NjmwV01v7O6lZjaS4Es+E3jK3Web2SjgU3efYGb9gVeBXYHTzOwOd9/P3dea2Z0ECQdglLuvrU0FReLt17/+hnfe2cQ772ziyy+3MmZMV1q0yEx0WCL1qtpk4e6nhv/WeoRZd58ITKy07faI5ekEt5iqOvYp4KnanlukIYwdu5Z77121bf3ll9fTqlUmTz3VNYFRidS/WB7KmxzLNpHGaPfdm9K+/fa/uTp2bMpdd+2RwIhE4qOmNotmYdtE+7DtoKK9ohvqxioCwKBBrZg+vRd9+jSjWTPjn//ci44d1bVW0k9NbRa/BK4FOhK0W1S0WWwEHo5zXCIpo1u3bKZN68XMmVvo31+DMkt6qqnN4i/AX8zsKg0cKFKzVq0yOeaY6oc337QJNm0qo1UrNXxLaor6nIW7/9XM9icY36lZxPZn4hmYSLooKXF+97sciovzmDBhb7p313AhknpinVb1r+HrWOAegpnzRCQG1123nJkzm/DVVxqIUFJXLGNDDQOOB1a6+0XAgUDruEYlkibGjl3L6NHbByNcs6aUUaNWEkw+KZI6YkkWW929HCgNn+pexY7DeIhINYYMacOZZ7bZtt6lSxYvvtit2omWRJJVLGNDfWpmbQimUp0BFAAfxjUqkTSRk5PBuHHdadHiQ15+OYcJE/Zit92aJjoskZ0WSwP3FeHiI2b2FrBLOAeFiMTAzBg+vJg//KE/u++uRCGpqdpkYWaH1LTP3WfGJySR9FRToli1qoRZs7Zy4om7VFtGJJFqurL4cw37HDiunmMRaZSKi8v56U8XMW3aZu65pxM33LCb2jQk6dT0UF6UEfxFpK7cncsvX8Z//7sZgJtu+oavvtrKo492ITt7ZyayFImvWJ6zyDGz35jZY+F6TzM7Nf6hiaS/WbO2MmbM9ztsW7ashIwMXVlIconlT5e/A8XA4eH6N8BdcYtIpBE5+OAcJk7sQevWwTAge++dzUsvdadpUyULSS6xJIu93f0eoATA3bew40RIIlIHJ520Cx9/3It+/YKutW3bxtKjXaRhxfJbWWxmzQkatTGzvYGiuEYl0sj06tWMTz7ppYZtSVqxXFn8FngL2NPMngcmA7+Ka1QijVBNiWLZsmJOP30h335b0oARiWxXY7Kw4Ld3HnAGcCHwItDP3afGPTIRAaCwsJwzzljEP/+5gX795vHRR5sTHZI0QjUmCw9GO5vo7t+7+xvu/rq7r2mg2EQaPXfnssu+5tNPtwCwYkUJxxwznxkztiQ4MmlsYrkNNdPM+sc9EhH5gcJC/8GtpxP7tbF7AAAVmElEQVRPbMXBBzdPUETSWMWSLA4FPjSzhWb2hZl9aWYaG0qkATRvnsHEiT341a9yAejVK5vnnuuu5zCkwcXSG+qkuEchItXKzDT+9KdOHHJIcw48MGfbMxkiDSmWUWeXNkQgIlKzs89uW+P+RYuK6N49S91vJS40+IxIGli0qIi+fedxzjmLKSgoS3Q4koaULERS3Natwai169eXMX78egYMyGPevMJEhyVpJq7JwswGm1memeWb2c1V7M82s3Hh/o/NrFu4vamZPR02ps81s1viGadIKrvppm+YNWvrtvW5cwuZOHFDAiOSdBS3ZGFmmcBo4GSgN3CumfWuVOwSYJ279wAeAP4Ubj8TyHb3PkBf4JcViUREdnTttR044IDtXWl/+tM2XHfdbgmMSNJRPK8sBgD57r7I3YuBscDQSmWGAk+Hyy8Dx4dPjTvQwsyaAM0JRr3dGMdYRVJWjx7N+PDDXlxwQVv23Tebv/+9qxq5pd7Fc3jLTsCyiPXlBM9sVFnG3UvNbAPQjiBxDAW+BXKA69x9bRxjFUlpOTkZPPNMV9atK6NVK3WtlfqXrGMhDwDKgI7ArsD7ZvZvd18UWcjMRgAjAHJzc5k6dWqtT1hQUFCn45NFutQDVJf69u67TfjuuwzOPLOYulx4JENd6kO61AMaqC7uHpcXMBB4O2L9FuCWSmXeBgaGy02ANQRzZYwGfhZR7ingrJrO17dvX6+LKVOm1On4ZJEu9XBXXerT/PlbvVWrzxxm+NCh+b52bUmt3yvRdakv6VIP97rVBfjUY/hOj2ebxXSgp5l1N7Ms4BxgQqUyE4Dh4fIw4D9h8F8DxwGYWQvgMILRb0VkJ23dWs6ZZy5m06ZyAF57bQOHHZZHcXF5giOTVBK3ZOHupcBIgquHucB4d59tZqPMbEhY7EmgnZnlA9cDFd1rRwMtzWw2QdL5u7trPCqRWpg7t5ClS4t32Hb11buRlaXHrCR2cW2zcPeJwMRK226PWC4k6CZb+biCqraLyM475JAcZs7cl7PPXsz06Vs466w2XHFF+0SHJSkmWRu4RaQede+ezfvv78M993zHNdfspq61stN0HSrSSGRnZ3DbbXuwyy7Vd639738LKjqViOxAyUJEABg/fh1HHTWf885bwsaNGoxQdqRkISIsWFDIpZcGsxGMHbuOQw6Zx2efaepW2U7JQqSRc3cuvnjptq61AMuXF9Okido1ZDslC5FGzsx44omu9OnTbNu2++/vTJ8+mudbtlNvKBGhV69mfPzxvtx443K+/baEyy9X11rZkZKFiADQvHkGo0d3obTUq+1au3VrOaWlDRyYJAXdhhKRHdTUVnH11cu45pocFi8uasCIJBkoWYhITMaNW8sTT3zPnDlNOOiguYwfvy7RIUkDUrIQkagWLy5ixIivt61v3FjObbetoKhIgxE2FkoWIhJVq1aZHHNMq23rWVnGuHHdyc7WV0hjoU9aRKJq374Jr722F3/5S2eaNnXuvbcTBx2Uk+iwpAGpN5SIxMTMuPrq3Wjbdh7nn9+h2nLu1femktSlKwsR2SmdO5dXmwy2bCnn8MPn88ILazUgYZpRshCRenPDDcv56KPNnH/+Es45ZzFr1+qhjHShZCEi9WLChPU88siabevjx6/nnnu+S2BEUp+ULESkXqxaVUp29vbbU/vsk81tt+2ewIikPilZiEi9uPTS9syYsS8HH9yczEx49tlutGhR/URLklrUG0pE6s1++zXno4968f77BQwY0KLacuoxlXp0ZSEi9SorK4Pjj9+l2v2ffbaFI46Yz9y5WxswKqkrJQsRaTCFheVccMESPvxwM4ccMo8HH1xFebm62KYCJQsRaTC33rqCOXMKASgsdK67bjkffLA5wVFJLJQsRKRBlJc7y5cX77DtoovaceSRLRMUkewMJQsRaRAZGcbYsd159tmutG6dSadOTbn//k6JDktipN5QItJgzIwLLmjHsce2YvnyEtq0qforqKwsaMfIzFSPqWQR1ysLMxtsZnlmlm9mN1exP9vMxoX7PzazbhH7DjCzD81stpl9aWbNKh8vIqmpU6csDj20+q6199+/imOOmc/8+YUNGJXUJG7JwswygdHAyUBv4Fwz612p2CXAOnfvATwA/Ck8tgnwHHCZu+8HDAJK4hWriCSPefMKue22FUybtpkDD5zLAw98t+1KQxInnlcWA4B8d1/k7sXAWGBopTJDgafD5ZeB4y14UudE4At3/xzA3b9397I4xioiSaCszLnooqUUFQXJobDQufPOlaxZowEJEy2eyaITsCxifXm4rcoy7l4KbADaAfsAbmZvm9lMM/tVHOMUkSRRUFBOu3Y7DhHy17/uSW5u0wRFJBWStYG7CXAk0B/YAkw2sxnuPjmykJmNAEYA5ObmMnXq1FqfsKCgoE7HJ4t0qQeoLskq3nW54Qbo06cpDz/cjAMOKKVjxy+Ix+n0mewkd4/LCxgIvB2xfgtwS6UybwMDw+UmwBrAgHOApyPK3QbcVNP5+vbt63UxZcqUOh2fLNKlHu6qS7JqqLp8802Rr1xZXOP+jRtLa/3++kwCwKcew3d6PG9DTQd6mll3M8sKE8CESmUmAMPD5WHAf8Lg3wb6mFlO2Nh9DDAnjrGKSJLp2DGr2ttP7s7Pf76U/fabwxtvbGjgyBqnuCULD9ogRhJ88c8Fxrv7bDMbZWZDwmJPAu3MLB+4Hrg5PHYdcD9BwpkFzHT3N+IVq4iklqefXsvkyZtYtqyEU09dyHnnLWbLlvJEh5XW4tpm4e4TgYmVtt0esVwInFnNsc8RdJ8VEdnmu+9KuP765TtsW7WqlObN9QBfPGm4DxFJKa1aZXLppe3ICL+9mjc3Hn20i+bHiDMlCxFJKTk5GdxzT2emT9+Xgw5qzqhRHdl77+xEh5X2krXrrIhIjQ45JIfp0/etscxLL60jJyeDn/ykdQNFlb50ZSEiKatJE6NJk6pvP61ZU8pll33Nqacu5IwzFrJsWXGV5SQ2ShYikpZ+9atvWLs2GCXo1Vc30K/fPLZuVY+p2lKyEJG0s2RJEc888/0O266/fjeaN9dXXm3pJyciaadbt2ymT9+XAQNyANhvv2Zcf31ugqNKbWrgFpG0dPDBOXzwQS8ef3wN++/fnKZNq27bWLeulJYtM6vdLwFdWYhI2srMNC67rEON83xfdtnXHHjgXP79740NGFnqUbIQkUZrypRNjB+/nrlzCznhhHx++tNFbNigqXOqomQhIo1SaSlcddWyHbYtWVJEy5b6WqyKfioi0igVF/ODecAffnhPMjPVdlEVJQsRaZRycuDJJ7vy8ce96N8/h+HD2zJwYPVtG42dkoWINGoDBrTgo4968fDDe1Zb5sUX13L22YtYtKioASNLLkoWItLoZWQYLVtmVrmvsLCcW25Zwfjx69l33zlcd91y1q4tbeAIE0/JQkSkBn/962qWLg3GlSopcUaPXq1kISIi27k7b7+94/MXV1zRnh49miUoosRRshARqYaZ8c47PXjuuW506ZJF69aZ3HbbHokOKyGULEREapCRYZx/flvy8nrzzjs9aNeu6lGS1q4t5YILFpOXV9jAETYMJQsRkRg0a5bBgAEtqt1/110ref75dey33xxGjlzG6tUlDRhd/ClZiIjU0cKFRTz88GoAyspg9OjVjBmzNsFR1S8lCxGROnrqqTWUlPi29S5dshg5skMCI6p/ShYiInV0110dGTeuO927ZwHw+993TLuJltKrNiIiCWBmnHXWrsyd25u//70r5567a7Vlr79+Oa+/vgF3r7ZMMlKyEBGpJ9nZGVx4YTsyMqoejHDatAIeeGAVp522kIED85g0aWPKJA0lCxGRBnLbbSu2LX/88RbuvHNlAqPZOXFNFmY22MzyzCzfzG6uYn+2mY0L939sZt0q7e9iZgVmdmM84xQRibevvtrKlCkFO2y76649MEuNIdHjlizMLBMYDZwM9AbONbPelYpdAqxz9x7AA8CfKu2/H3gzXjGKiDSU/fdvzqxZ+zJkSGsATjihFUcf3arKsuXlnnS3p+J5ZTEAyHf3Re5eDIwFhlYqMxR4Olx+GTjewjRrZv8DLAZmxzFGEZEGc+CBObz22t58/HEv/vznztWWe/LJ7znqqPm8807ytGnEM1l0AiLnLFwebquyjLuXAhuAdmbWEvhf4I44xicikhADBrSgT5/mVe4rKXF+//uVTJu2mZNOymfgwDxmz97awBH+UNWDnCTe74AH3L2gpvt5ZjYCGAGQm5vL1KlTa33CgoKCOh2fLNKlHqC6JKt0qUuy1uPNN5uyZMn2RDJz5mby8j5h9erqrzAapC7uHpcXMBB4O2L9FuCWSmXeBgaGy02ANYAB7wNLwtd6YC0wsqbz9e3b1+tiypQpdTo+WaRLPdxVl2SVLnVJ1npcfvlShxnbXpddtjTqMXWpC/Cpx/CdHs/bUNOBnmbW3cyygHOACZXKTACGh8vDgP+E8R/l7t3cvRvwIPB7d384jrGKiCSFv/2tC5980ovTTmtNZibceGNutWUnTtzAunUNMxFT3G5DuXupmY0kuHrIBJ5y99lmNoogk00AngSeNbN8gquHc+IVj4hIqujfvwUTJuzN0qVFdO2aXWWZlStLOOOMRTRtapx9dhaDBsU3pri2Wbj7RGBipW23RywXAmdGeY/fxSU4EZEkV12iAPjLX1ZRVOQUFTkN8aiGnuAWEUkxGzaU8be/BUOit2qVwdChxXE/p5KFiEiKycyEW27ZndzcJlx+eQdatoz/OZUsRERSTMuWmdx88+4sXrw/t966e4OcM1mfsxARkSiaN8+gedXP9tU7XVmIiEhUShYiIhKVkoWIiESlZCEiIlEpWYiISFRKFiIiEpWShYiIRKVkISIiUSlZiIhIVOZJMr9rXZnZamBpHd6iPcHkS6kuXeoBqkuySpe6pEs9oG516eruHaIVSptkUVdm9qm790t0HHWVLvUA1SVZpUtd0qUe0DB10W0oERGJSslCRESiUrLY7rFEB1BP0qUeoLokq3SpS7rUAxqgLmqzEBGRqHRlISIiUTX6ZGFmg80sz8zyzezmRMcTCzNbYmZfmtksM/s03NbWzCaZ2YLw313D7WZmD4X1+8LMDklw7E+Z2Soz+ypi207HbmbDw/ILzGx4ktTjd2b2Tfi5zDKzUyL23RLWI8/MTorYnvDfPzPb08ymmNkcM5ttZteE21Pqc6mhHin3uZhZMzP7xMw+D+tyR7i9u5l9HMY1zsyywu3Z4Xp+uL9btDruNHdvtC8gE1gI7AVkAZ8DvRMdVwxxLwHaV9p2D3BzuHwz8Kdw+RTgTcCAw4CPExz70cAhwFe1jR1oCywK/901XN41CerxO+DGKsr2Dn+3soHu4e9cZrL8/gF7AIeEy62A+WHMKfW51FCPlPtcwp9ty3C5KfBx+LMeD5wTbn8EuDxcvgJ4JFw+BxhXUx1rE1Njv7IYAOS7+yJ3LwbGAkMTHFNtDQWeDpefBv4nYvszHvgIaGNmeyQiQAB3fw9YW2nzzsZ+EjDJ3de6+zpgEjA4/tFvV009qjMUGOvuRe6+GMgn+N1Lit8/d//W3WeGy5uAuUAnUuxzqaEe1UnazyX82RaEq03DlwPHAS+H2yt/JhWf1cvA8WZmVF/HndbYk0UnYFnE+nJq/uVKFg68Y2YzzGxEuC3X3b8Nl1cCueFyKtRxZ2NP5jqNDG/NPFVx24YUqkd4++Jggr9kU/ZzqVQPSMHPxcwyzWwWsIog8S4E1rt7aRVxbYs53L8BaEc91qWxJ4tUdaS7HwKcDFxpZkdH7vTg+jMlu7mlcuzA/wF7AwcB3wJ/Tmw4O8fMWgKvANe6+8bIfan0uVRRj5T8XNy9zN0PAjoTXA3sm8h4Gnuy+AbYM2K9c7gtqbn7N+G/q4BXCX6Rvqu4vRT+uyosngp13NnYk7JO7v5d+B+8HHic7Zf7SV8PM2tK8AX7vLv/I9yccp9LVfVI5c8FwN3XA1OAgQS3/JpUEde2mMP9rYHvqce6NPZkMR3oGfYwyCJoGJqQ4JhqZGYtzKxVxTJwIvAVQdwVvU+GA6+FyxOAn4c9WA4DNkTcWkgWOxv728CJZrZreEvhxHBbQlVqCzqd4HOBoB7nhD1WugM9gU9Ikt+/8N72k8Bcd78/YldKfS7V1SMVPxcz62BmbcLl5sAJBG0wU4BhYbHKn0nFZzUM+E94NVhdHXdeQ7bwJ+OLoGfHfIL7gbcmOp4Y4t2LoHfD58DsipgJ7k9OBhYA/wba+vZeFaPD+n0J9Etw/C8S3AooIbh/ekltYgcuJmisywcuSpJ6PBvG+UX4n3SPiPK3hvXIA05Opt8/4EiCW0xfALPC1ymp9rnUUI+U+1yAA4DPwpi/Am4Pt+9F8GWfD7wEZIfbm4Xr+eH+vaLVcWdfeoJbRESiauy3oUREJAZKFiIiEpWShYiIRKVkISIiUSlZiIhIVEoW0qiZWRszuyJivaOZvVzTMfV47m5mdl5DnEukrpQspLFrQzBiJwDuvsLdh9VQvj51A5QsJCUoWUhj90dg73Ceg3vDv/a/AjCzC83snxbM5bDEzEaa2fVm9pmZfWRmbcNye5vZW+HAju+b2Q/G8DGzY2z7fAqfhU/h/xE4Ktx2XThw3L1mNj0c9O6X4bGDzOw9M3sjnJPgETPLCMuPMbOvLJjf5LoG/LlJI9MkehGRtHYzsL8HA7ZVjFYaaX+C0UubETwd+7/ufrCZPQD8HHiQYP7jy9x9gZkdCvyNYCjpSDcCV7r7tHCgu8Lw3De6+6nhuUcQDJ3R38yygWlm9k54/ACCuQmWAm8BZwCLgU7uvn94fJv6+IGIVEXJQqRmUzyYG2GTmW0A/hVu/xI4IPziPxx4KRiaCAgmmqlsGnC/mT0P/MPdl0eUr3Bi+J4Vt8FaE4zlUwx84u6LAMzsRYKhLSYDe5nZX4E3gHcqv6FIfVGyEKlZUcRyecR6OcH/nwyCOQYOqulN3P2PZvYGwZhD06zq6S0NuMrddxh8z8wG8cPhwd3d15nZgQSTDl0GnEUwNpNIvVObhTR2mwim4KwVD+ZLWGxmZ8K2+akPrFzOzPZ29y/d/U8Eo5ruW8W53wYuD4fZxsz2CUcWBhgQjoKaAZwN/NfM2gMZ7v4K8BuCaV5F4kLJQho1d/+e4C/9r8zs3lq+zfnAJWZWMRJwVVNwXhue4wuCkWrfJBhRtMzMPg8bp58A5gAzw0b2R9l+9T8deJhgmOrFBPOYdAKmWjCb2nPALbWMXyQqjTorkuTC21DbGsJFEkFXFiIiEpWuLEREJCpdWYiISFRKFiIiEpWShYiIRKVkISIiUSlZiIhIVEoWIiIS1f8Dpeb/iMaZe4MAAAAASUVORK5CYII=\n", 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\n", 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\n", 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0wU1loSnvI42uPk3RhmrSGzWRXTQNm1BwznXe8inRl2hjT5L4fn4U/moX1EX+zHeOc8tPMW3HSQL6toy6YREKaWlp1NTUkJeXp2DwgHOOmpoa0tK6PxgkEm11bfDXb8PPjnbfNqqxjcLXahhbdTr2hY0QwyIUCgoKqKyspKqqyu9Szqq5uTlhf7CmpaVRUFDgdxkyzG06BZ8oh91N3betyoOa375LSstZFlqXIRsWoZCSksL06dP9LqNPpaWlLF682O8yROJO0MF3DsJX9kLkDURpAfjXmfD5SXCZAsFzwyIURCRxHTkNn66AZ4933zYvAx4vguLuDy2LRxQKIuKbtTXwmQqo6uF5s7+aBN+ZCelJsa9rJFMoiEjMnQ7CPXvg3yq7bxubDI/NgY+Oi31dolAQkRiraICbymFrffdtF+fAfxVCQWLejzEsaJZUEYkJ5+A/j8D5W7oHQhLw9Wnw3CIFgt90piAinjvRCp/bBU/0cNf4uaPgF0VwYU73bRJ7CgUR8dQrJ+ETZbC/h+fNbhgH/z4bxqTEvi7pmUJBRDzR7uCB/fDP+yBypoqMAPzfWfAXE0CTEMQXhYKIRF1lM9xcDi+c7L5tUVbo2YM5GbGvS/qmUBCRqPptFdy6E2p7WO77CwXwrRkwSre4xC2FgohERVM7/P078Mjh7tvGpcBP5sKH8mJflwyMQkFEhmx7PdxYBjt6WOvm8rHw07kwcVTs65KB00mciAyac/DwIVj6evdASDb49gx4ZoECIZHoTEFEBqWmFW6tgKdqum+bmQa/LIKlo2NflwyNQkFEBqz0eOjuokMt3bfdMh5+MAuy9dMlIemfTUT6rS0I/7wfvrEfIlfCzEqCR2bBzRN8KU2iRKEgIv2yrym0Ktqrp7pvW5odulw0Mz32dUl0aaBZRPq0+hgs3Nw9EAz48hR4ebECYbjQmYKI9KqhHf72bXjs3e7bJqTCz+bC5bmxr0u8o1AQkR69URd69mBXU/dtV+fCj+fCuNTY1yXeUiiISJigg+9VhlZGa4kYTU41eHAm/M1kTWQ3XHk6pmBmV5rZTjPbbWb39LB9qpk9b2ZvmNlbZvYhL+sRkbM71gIf3gZffKd7IMzNgNeWwN8WKBCGM89CwcySgIeAq4Ai4CYzK4rodi/whHNuMXAj8LBX9YjI2f2xFhZsgj/Udt/2lxNh8/mwKDv2dUlseXmmsAzY7Zzb45xrAR4HVkX0ccCZZx5zgB6m0hIRL7UE4R/egQ++BUdbw7eNSYZfFcGjcyAzyZ/6JLa8HFOYDBzs8roSuCCiz33AH83sb4BM4HIP6xGRCG83hp492FzXfduK0fDzIjhXayaPKH4PNN8E/MQ59x0zex/wMzMrds4Fu3Yys9uB2wHGjx9PaWlp7CuNgvr6+oStPR7o+A2cA8rJ5gmmsIE8WtzFpJa2s5wazqWB1UzlNOGnAAEcN7OfW07tZ+8Gx15fKu/Zjct7mFcjhnIzm7lxeYVvn19ausfzzzDnIh9Wj9KOQz/k73POfbDj9T8COOe+2aXPDuBK59zBjtd7gOXOuWO97bekpMRt3rzZk5q9VlpaysqVK/0uI2El+vG79I4DMf28oEH5sjyqJ6cTDBgEuowOO9fjaPGoxjaKNtQwprqHBZWjYN3DU4f0/lgfw0g3Lq/g8Q1zffv8oRw/M9vinCvpq5+XYwqbgFlmNt3MUgkNJK+J6HMAuAzAzAqBNKDKw5pERgRHl0BIDoQHAvQYCOMqG1n6x3c9CwRJDJ5dPnLOtZnZncAzQBLwmHNuh5ndD2x2zq0B/h74DzO7i9D38WecV6cuIiPIqdzU9wKhL84xpeIUM7edRHeaiqdjCs65tcDaiLavdfm6DFjhZQ0iI9HB2dmhS0b94aA5M1mBIIAmxBMZlmompXe/ZNSbgIX6i6BQEBmWgkkD+71/oP1l+FIoiAxDgfaBDc0NtL8MXwoFkWGmPQBJrcG+O54RdOQd7mEqVBmRFAoiw0gwADsuHEdrev/vIQkEHVN39fBIs4xICgWRYSJosON9+QMaNA60Bck/1ER2rb9PCkv88HuaCxGJgqBB2fJ8qidnhLUntQRxAbo/0Rx0BIKO/ENNFG6s0e2o0kmhIJLgggblF+RRNSU8ENJPtbKo9CgtGckcmJ1NzaR0XJJh7aExhKk76xh9XGcIEk6hIJLAnEHFsjyOTc0Ma0+va2XxC8cY1RwkrbmF4g01gP9z90j805iCSIJyQEVJLkfPDQ+EtPo2FpUeY1RTuz+FSUJTKIgkIAfsLMnl3elZYe1pDW0sLj1KmgJBBkmhIJJgHLBryViOzAgPhFGNbSwqPUpaowJBBk+hIJJAHPD24rEcPi98seTUxtAlo/QGBYIMjUJBJEE4YPfCMRyaFREITe0sfuEYGfVt/hQmw4pCQSQBOGDPgjFUzhkd1p7S3M6iF46SUadAkOhQKIjEOQfsLc7hwNyIQDjdzqLSY2SeUiBI9CgUROLcvqLR7C/KCWtLPt3OwheOkXWq1aeqZLhSKIjEsX2Fo9lXPCasLbklyKIXj5F9QoEg0adQEIlTB+Zks3d+eCAktQRZ+OIxso8rEMQbCgWROHRwdjbvLBwb1pbUGmThS8cYrRlNxUMKBZE4U3leFrsXdQ+EBS9VkVOjQBBvKRRE4sihGVm8vSQ3rC3QFmT+y1WMqT7tU1UykigUROLE4emZ7CrpORDGVikQJDYUCiJx4Mi5meyMCARrdxSvryb3mAJBYkehIOKzo1MzqFiWC/be+mfW7pi/voq8o80+ViYjkUJBxEfHCjIoW5YXHghBR/Gr1eS9q0CQ2FMoiPjk2OR0ypbnha2dbEFH0avV5B9u8rEyGckUCiI+qJqUTtn78nFdAoGgo/C1Gs45pEAQ/ygURGKsemIaOyIDwTkKN9Yw/mCjf4WJoFAQiama8Wlsv3AcLik8EOZurGXCAQWC+E+hIBIjteeMYvuK/PBAAOZsrmXi/gafqhIJp1AQiYHS47Dt/eMIJof/l5u9pZZJexUIEj8UCiIee/kEfHgb3QJh1uu1TH6n3qeqRHqmUBDx0Ksn4apt0BAMbz9v63EKdisQJP4oFEQ8svEUXPkW1LeHt8988zhTdtX5U5RIHxQKIh54vQ4++BacigiE6dtOMHWnAkHil0JBJMrerIfL34QTbeHt07afYFr5KX+KEuknhYJIFG3vCITjEYHwT1NhWpkCQeKfQkEkSsob4LI3oTpi+eR/mAJfnw7W89tE4opCQSQKdjbCpW/CsYhAuKsAvjUjbBJUkbimUBAZot2NcOlWeDdi+eS/mQzfmalAkMSiUBAZgj1NcMmbcDgiED4/Cb53ngJBEo9CQWSQ9jfDJVuhMmK1zNsmwkOzFAiSmDwNBTO70sx2mtluM7unlz43mFmZme0ws194WY9ItBzsCIQDEYHw6fHw77PD1s0RSSjJXu3YzJKAh4ArgEpgk5mtcc6VdekzC/hHYIVz7riZneNVPSLRcuh0aFB5b8RqmZ88B/5zrgJBEpuXZwrLgN3OuT3OuRbgcWBVRJ+/BB5yzh0HcM4d87AekSF793RoUHl3xOJoHx8HP5kLSQoESXDmnPNmx2bXAVc6527reP0p4ALn3J1d+vwW2AWsAJKA+5xzT/ewr9uB2wHGjx9//uOPP+5JzV6rr68nKyvL7zISlt/H7zgp3MUi9pMZ1n4RVXyVMpI5+/+lXQdazro9FnIzm6ltSPPt82dPTR3S+/0+hol8/C655JItzrmSvvp5dvmon5KBWcBKoAB40czmO+dOdO3knHsUeBSgpKTErVy5MsZlRkdpaSmJWns88PP4VbeELhlFroWzKg9+NW8cKYGL+9zH/Xcc8Ki6/rtxeQWPb5jr2+evu2XqkN7v9zFM9OPXH15ePjoETOnyuqCjratKYI1zrtU5t5fQWcMsD2sSGbDaVrjiLdgWEQhX58LqeZCie/hkGPHy23kTMMvMpptZKnAjsCaiz28JnSVgZvnAbGCPhzWJDMiJVvizN2FrxNIHHxwLT86DUQoEGWY8+5Z2zrUBdwLPAOXAE865HWZ2v5ld09HtGaDGzMqA54G7nXM1XtUkMhAn20LTX2+JCITLx8J/F0Nakj91iXjJ0zEF59xaYG1E29e6fO2AL3b8EYkbdW1w1VuwMWLpg5Vj4KliSFcgyDClk1+RCPVt8KFt8GrETNfvz4HfFUOGAkGGMYWCSBeN7fCR7fDyyfD2942GtfMhy+/79UQ8plAQ6dDUDtdsg9IT4e3LsuEPCyBbgSAjgEJBBGhuh2u3w3MRgbAkC55ZADkKBBkhFAoy4p0OwnU74Jnj4e0LM+HZhTAmxZ+6RPygUJARrTUIH98Bv68Nby/OhD8thFwFgowwAwoFM8vsmP1UJOG1BuGmMngq4smYwgx4biHkD22aHpGEdNZQMLOAmX3CzH5vZseACuBIx/oHD5rZebEpUyS62oLwqXL4dXV4+5x0WLcQzlEgyAjV15nC88BMQmseTHDOTXHOnQO8H9gA/IuZ3exxjSJR1e7gMxWwuiq8/bx0WLcIJozypy6ReNDXPRWXO+daIxudc7XAr4Ffm5muukrCCDq4bSf8PGLljulpoTOESQoEGeHOeqZwJhDM7PLIbWb26a59ROJd0MHndsFP3g1vP3cUPL8Ipvg3Tb5I3OjvQPPXzOyRjoHm8Wb2O+AjXhYmEk3OwZ1vw4+OhLcXjApdMjpXgSAC9D8ULgbeAbYCLwO/cM5d51lVIlHkHPzdbnjkcHj7pFR4fiHMSPenLpF41N9QGEtozeV3gNPAuWam1Wgl7jkHf/8O/N+I5Z0mpIbOEM7L8KcukXjV31DYADztnLsSWApMAtZ7VpVIFDgH9+yB71aGt49LCT2HMEeBINJNf2d0udw5dwDAOdcE/K2ZXeRdWSJD4xx8dS98+2B4e15y6C6jokx/6hKJd309vDYN4EwgdOWce9FCCrwpTWTw7t8P34j4rh2bHJq6ojjLn5pEEkFfZwoPmlkAeArYAlQBacB5wCXAZcD/Aip73YNIjD2wH+7bF96WkxSa3G5Rti8liSSMs4aCc+56MysCPgl8FpgANBFac3kt8A3nXLPnVYr004MH4J/2hreNToI/LoTzFQgifepzoNk5Vwb8b+B3hMJgL7AJeFKBIPHkuwfhH/aEt2UlwdMLYNlof2oSSTT9HWj+f8Ap4Psdrz8B/BS4wYuiJD5deke3oaWYunF5C/f3UkPleVm8vSQ3rC2pNcisdVX80y9PR+Xz1z08NSr7EYln/Q2FYudcUZfXz5tZmRcFiQzUoRndAyHQFmT+y1WMqY5OIIiMFP19TuF1M1t+5oWZXQBs9qYkkf47PD2TXSU9B8LYKgWCyED190zhfOAVMztz7j4V2Glm2wDnnFvgSXUiZ3Hk3Ex2RgSCtTuK11eTe0yBIDIY/Q2FKz2tQmSAjk7NoGJZLnSZbcXaHfPXV5F3VPc/iAxWv0LBObff60JEIjngVG4qB+eMpmZiGs8nTSEwyZF5opW63NTwQAg6il+tJu9dBYLIUPT3TEEkpoIG5cvyqJ6cTjBgEAgFQDDZqMvrHghFr1aTf7jJr3JFhg2FgsQdR5dASO7hXoiuE/Q6x9zXajjnkAJBJBr6e/eRSMycyk3tPRAiWBAyGtpiUJXIyKBQkLhzcHZ26JJRPziDA7M1f4VItCgUJO7UTErvHEPoU8BC/UUkKhQKEneCSQNb1G+g/UWkdwoFiTuBdudpfxHpnUJB4k7e4abQ0mn9EXSh/iISFQoFiTtjqvr/AFog6Ji6q87DakRGFoWCxJWmjCT2Fo8JfxahF4G2IPmHmsiubYlBZSIjgx5ek7jRnmRsXzGOtlFJ7zU6F3qarevdSEFHIOjIP9RE4cYaNMwsEj0KBYkLDqhYmkv92NSw9knv1NOaGqBmUjouybD20BjC1J11jD6uMwSRaFMoSFw4MCebY1Mzw9rGHWxk9uvHO88EblxeweMb5sa+OJERRGMK4ruaCWnsWTAmrC3zRAtzN+nSkEisKRTEV41ZyZQtzw8bWE4+3c789dUkt+n5A5FYUyiIb9qSjW0r8mlL7fJtGHTM21BDuia5E/GFp6FgZlea2U4z222h4UFCAAAP6UlEQVRm95yl38fMzJlZiZf1SPw4Mz12Y074wPLMt06Qq5XTRHzjWSiYWRLwEHAVUATcZGZFPfTLBv4OeM2rWiT+7CsaTXVBRljb+P0NTNGDaCK+8vJMYRmw2zm3xznXAjwOrOqh39eBfwH06+EIUT0pnX3F4QPLWcdbmLO5VgPLIj7zMhQmAwe7vK7saOtkZkuAKc6533tYh8SRhuxkyi7IC2tLaW5n/voqkjSxnYjvfHtOwcwCwL8Cn+lH39uB2wHGjx9PaWmpp7V5pb6+PmFrB7hx+dAeFmu0ZL454QLaU977XSTggvztydeZveB4n+/PzWzmxuUVQ6phKEpL9wzp/UM9ftGgYzg0iX78+sNcf2ejHOiOzd4H3Oec+2DH638EcM59s+N1DvAOUN/xlglALXCNc25zb/stKSlxmzf3ujmulZaWsnLlSr/LGLRL7zgw6Pc6g7dWjKM2YkGcWa/XUrC7vpd3hfP74bV1D08d0vuHcvyiRcdwaBL5+JnZFudcnzfzeHn5aBMwy8ymm1kqcCOw5sxG59xJ51y+c26ac24asIE+AkES1955Od0CYcLeeib3MxBEJDY8CwXnXBtwJ/AMUA484ZzbYWb3m9k1Xn2uxJ9jBensL8oJa8uuOc3sLRpYFok3no4pOOfWAmsj2r7WS9+VXtYi/qjPSaF8WfjAcmpTO/NfqSYp6FNRItIrPdEsnmlNDbBtxTiCye99m1m7o/iVKkY1tftYmYj0RqEgngga7FieR3NW+Mno7Ddqyanx/y4cEemZQkE8sWfBGI5PCB9YnrS7jkl7GnyqSET6Q6EgUffu1AwOzhkd1pZT1cysrX0/iyAi/lIoSFTVjU1hZ0luWNuoxjaKX6kmoIFlkbinUJCoaRkVYNuF4QPLgXZH8fpqUk8rEUQSgUJBoiJosP19+ZzODB9YnrO5VmspiyQQhYJExe5FYzl5TlpYW8GuU0zYr4FlkUSiUJAhOzw9k0OzssPaxhxtZuabJ3yqSEQGS6EgQ3IyN5VdS8IHltPq25j3ajUBzYQtknAUCjJop9MCbF+Rj0t6bwajQFuQ+eurSG3RwLJIIlIoyKAEA7D9wnG0pIcPLM/dVEvWyVafqhKRoVIoyIA5YNeSXE7ljwprn1p+kvEHG/0pSkSiQqEgA3Z4ZhZHZmSFteUeaWLG9pM+VSQi0aJQkAE5kT+KtxePDWtLr2ulaEM1poFlkYSnUJB+a05PYvuF+bjAewPLSa1B5q+vJqVViSAyHCgUpF+a2mH7inxa05LC2gs31pB5SgPLIsOFQkH65BzcvgvqcsMHlqftOMm4Q00+VSUiXlAoSJ/+rRL+62h4W/6hRqbt0MCyyHCjUJCz+lMtfOmd8LaMU60UvlaD9fwWEUlgCgXp1d4m+HgZdH02OaklyPyXq0hu08CyyHCkUJAeNbTDR7dDbVuXRueYt6GajPq2Xt8nIolNoSDdOAd/UQFvRcx6PWPbSfLebfanKBGJieS+u8hI8y8H4FdV4W3XjYPqilP+FCQiMaMzBQnzhxr4yt7wtvmZ8OM5aGBZZARQKEintxvhprLQhHdn5CbDb4shS+eUIiOCQkEAONUGq7bDyfb32gLA6iKYke5bWSISYwoFIejglnIoj5j1+sGZcHluz+8RkeFJoSB8fT88VRPedvN4uKvAn3pExD8KhRHut1Vw377wtiVZ8OhsMI0si4w4CoURrKwBPlUR3jYuBf67GNKTen6PiAxvCoUR6kRraGC5vsvAcrLBk/Ngapp/dYmIvxQKI1C7g0+Uw+6IWa//7Ty4aIw/NYlIfFAojED37oU/1Ia33ToB7pjkTz0iEj8UCiPME8fgWwfC25aPhoc0sCwiKBRGlDfrQxPddTUhFX49D0bpO0FEUCiMGDWtoamwG7ssjpBq8Jt5MGlU7+8TkZFFoTACtAXhhh2wL2LW64dmwfty/KlJROKTQmEE+Ic9sO5EeNsdk+A2DSyLSASFwjD3s3fhu5XhbR/Ige+e5089IhLfFArD2OZT8Jc7w9sKRsGv5kGq/uVFpAf60TBMHW2Ba3fA6S6LI6QFQmsjjE/1ry4RiW8KhWGoJQjX7YDK0+Htj86G87P9qUlEEoOnoWBmV5rZTjPbbWb39LD9i2ZWZmZvmdlzZnaul/WMFHfthpdPRrQVwKcm+FOPiCQOz0LBzJKAh4CrgCLgJjMriuj2BlDinFsAPAl826t6RoofHYaHD4e3XTYGvj3Dn3pEJLF4eaawDNjtnNvjnGsBHgdWde3gnHveOXdmva8NgJZ1GYJXTsIdb4e3TUuD1fMgWRcKRaQfvPxRMRk42OV1ZUdbb24F/uBhPcPa4dPwsR3Q2mVgOaNjYDkvxb+6RCSxmHOu716D2bHZdcCVzrnbOl5/CrjAOXdnD31vBu4ELnbOne5h++3A7QDjx48///HHH/ekZq/V19eTlZUV9f22YHyBxZQzOqz9a+zgEqqi9jm7DrREbV+DkZvZTG2Df4s9zJ46tNu2/D5+oGM4VIl8/C655JItzrmSvvolD/oT+nYImNLldUFHWxgzuxz4J3oJBADn3KPAowAlJSVu5cqVUS82FkpLS4l27c7BbTuh/N3w9n+cCv88Y15UP+v+Ow703clDNy6v4PENc337/HW3TB3S+/0+fqBjOFSJfvz6w8vLR5uAWWY23cxSgRuBNV07mNli4N+Ba5xzxzysZdh6+DA8FhEIV+XC16f7U4+IJDbPQsE510boktAzQDnwhHNuh5ndb2bXdHR7EMgCfmVmW81sTS+7kx68cAK+sDu8bVY6/KIQkrQ2gogMgpeXj3DOrQXWRrR9rcvXl3v5+cPZgWa4fge0dRkSykoKDSyP0cCyiAySblRMQI3tcO12qGoNb/+vQijK9KcmERkeFAoJxjm4fSe8Xh/eft80WJXvS0kiMowoFBLMdyvh5xFD8qvy4KuaIEREokChkECerYW73wlvK8yAnxZCQAPLIhIFCoUEsacJPl4GXZZYJicJniqG0Z7eLiAiI4lCIQHUt8FHt8PxtvfaDPhlEczK8K0sERmGFApxzjn4i52wrSG8/YHpcFWePzWJyPClUIhz3zwAT0ZMX3TDOPiy90+7i8gIpFCIY7+vgXv3hrctyITH5oJpYFlEPKBQiFM7G+ETZdB1Dtvc5NATy5lJvpUlIsOcQiEOneoYWD7V/l5bAHhiHkxP960sERkBRtTNjJf6Pu1uS59T/zpg24p8aiaH31Y0Y+txvvFEHd8Ywueve1gDESJydjpTiDP75uV0C4Tx+xoo2FXnU0UiMpIoFOJI1eR09s3LCWvLrj3NnC21aFxZRGJBoRAnGkanUL4s/MGDlOZ2itdXk9TuzZKpIiKRFApxoDXF2LYin/aU9/45LOgofqWatKb2s7xTRCS6FAo+cwZly/Npyg5fGWfWG8cZU93jktUiIp5RKPhsT3EOtRPD7zOduKeeSe/U9/IOERHvKBR8dHRKBgcKwweWR1efZvbrGlgWEX8oFHxSNyaFiqW5YW2pTW0Uv1JFINjLm0REPKZQ8EFLaoDtK8YRTO4ysNzuKF5fzahmJYKI+GdEPdEcaw44lZvKwTmjqZmYxvNJUwhMciS1OVrTwicwmvN6LTm1Lf4UKiLSQaHgkaBB+bI8qienEwxY53qZwWQjGHHUJ79dx8S9DT3sRUQkthQKHnB0CYTks1+hS25qY+bW47EpTESkDxpT8MCp3NR+BQJAMCVAw9jUGFQlItI3hYIHDs7ODl0y6odgwDgwO9vjikRE+keh4IGaSemdYwh9Cliov4hIHFAoeCCYNLBHzwbaX0TEKwoFDwQGOKvpQPuLiHhFoeCBvMNNEOznD/qgC/UXEYkDCgUPTNlVR6CfoRAIOqZqVTURiRMKBQ+Mrm0h/1ATgbazT1kRaAuSf6iJbD3JLCJxQqHgAQMKN9a8FwyRZw1B1xkIhRtrNCOqiMQNPdHskYCDotdqqMtN5cDsbGompeOSDGsPjSFM3VnH6OM6QxCR+KJQ8JARupRUvKEGgBuXV/D4hrn+FiUicha6fCQiIp0UCiIi0kmhICIinRQKIiLSSaEgIiKdFAoiItJJoSAiIp0UCiIi0snTUDCzK81sp5ntNrN7etg+ysxWd2x/zcymeVmPiIicnWehYGZJwEPAVUARcJOZFUV0uxU47pw7D/gu8C9e1SMiIn3z8kxhGbDbObfHOdcCPA6siuizCvh/HV8/CVxmZpofTkTEJ16GwmTgYJfXlR1tPfZxzrUBJ4E8D2sSEZGzMOe8WQrSzK4DrnTO3dbx+lPABc65O7v02d7Rp7Lj9Tsdfaoj9nU7cHvHyznATk+K9l4+UN1nL+mNjt/Q6RgOTSIfv3Odc+P66uTlLKmHgCldXhd0tPXUp9LMkoEcoCZyR865R4FHPaozZsxss3OuxO86EpWO39DpGA7NSDh+Xl4+2gTMMrPpZpYK3AisieizBvh0x9fXAeucV6cuIiLSJ8/OFJxzbWZ2J/AMkAQ85pzbYWb3A5udc2uA/wR+Zma7gVpCwSEiIj7xdJEd59xaYG1E29e6fN0MXO9lDXEm4S+B+UzHb+h0DIdm2B8/zwaaRUQk8WiaCxER6aRQiJG+pvyQ3pnZY2Z2rOMWZhkgM5tiZs+bWZmZ7TCzv/O7pkRiZmlmttHM3uw4fv/sd01e0uWjGOiY8mMXcAWhh/g2ATc558p8LSxBmNlFQD3wU+dcsd/1JBozmwhMdM69bmbZwBbgo/r+65+OWRYynXP1ZpYCvAz8nXNug8+leUJnCrHRnyk/pBfOuRcJ3Z0mg+CcO+Kce73j6zqgnO6zC0gvXEh9x8uUjj/D9rdphUJs9GfKDxHPdcxEvBh4zd9KEouZJZnZVuAY8KxzbtgeP4WCyAhhZlnAr4EvOOdO+V1PInHOtTvnFhGamWGZmQ3by5gKhdjoz5QfIp7puBb+a+Dnzrnf+F1PonLOnQCeB670uxavKBRioz9Tfoh4omOg9D+Bcufcv/pdT6Ixs3FmNqbj63RCN4xU+FuVdxQKMdAxLfiZKT/KgSecczv8rSpxmNkvgVeBOWZWaWa3+l1TglkBfAq41My2dvz5kN9FJZCJwPNm9hahX/Cedc79j881eUa3pIqISCedKYiISCeFgoiIdFIoiIhIJ4WCiIh0UiiIiEgnhYKIiHRSKIiISCeFgsgQmdlSM3urY979zI4594ft3DgyvOnhNZEoMLP/DaQB6UClc+6bPpckMigKBZEo6JjTahPQDFzonGv3uSSRQdHlI5HoyAOygGxCZwwiCUlnCiJRYGZrCK2oN53Q0pd3+lySyKAk+12ASKIzs1uAVufcLzrW437FzC51zq3zuzaRgdKZgoiIdNKYgoiIdFIoiIhIJ4WCiIh0UiiIiEgnhYKIiHRSKIiISCeFgoiIdFIoiIhIp/8P5RNXTTn1oS8AAAAASUVORK5CYII=\n", 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" ] From c5627ab9aa5c115bf0532f8675b044ac72b8f3bc Mon Sep 17 00:00:00 2001 From: Jakub Marecek Date: Tue, 23 Apr 2019 10:58:12 +0200 Subject: [PATCH 067/116] Contributing the time_series, portfolio_diversification, and generating_random_variates notebooks. --- .../finance/generating_random_variates.ipynb | 420 ---------------- .../general/generating_random_variates.ipynb | 473 ++++++++++++++++++ qiskit/finance/data_providers/__init__.py | 20 - .../data_providers/drivers/__init__.py | 26 - .../data_providers/drivers/_basedriver.py | 154 ------ .../data_providers/drivers/algorithminput.py | 67 --- .../drivers/dataondemand/README.md | 14 - .../drivers/dataondemand/__init__.py | 21 - .../dataondemand/dataondemanddriver.py | 156 ------ .../drivers/exchangedata/README.md | 22 - .../drivers/exchangedata/__init__.py | 21 - .../exchangedata/exchangedatadriver.py | 138 ----- .../drivers/wikipedia/README.md | 11 - .../drivers/wikipedia/__init__.py | 21 - .../drivers/wikipedia/wikipediadriver.py | 136 ----- .../finance/data_providers/time_series.ipynb | 236 ++++++--- .../portfolio_diversification.ipynb | 381 +++++++------- 17 files changed, 835 insertions(+), 1482 deletions(-) delete mode 100644 qiskit/aqua/finance/generating_random_variates.ipynb create mode 100644 qiskit/aqua/general/generating_random_variates.ipynb delete mode 100644 qiskit/finance/data_providers/__init__.py delete mode 100644 qiskit/finance/data_providers/drivers/__init__.py delete mode 100644 qiskit/finance/data_providers/drivers/_basedriver.py delete mode 100644 qiskit/finance/data_providers/drivers/algorithminput.py delete mode 100644 qiskit/finance/data_providers/drivers/dataondemand/README.md delete mode 100644 qiskit/finance/data_providers/drivers/dataondemand/__init__.py delete mode 100644 qiskit/finance/data_providers/drivers/dataondemand/dataondemanddriver.py delete mode 100644 qiskit/finance/data_providers/drivers/exchangedata/README.md delete mode 100644 qiskit/finance/data_providers/drivers/exchangedata/__init__.py delete mode 100644 qiskit/finance/data_providers/drivers/exchangedata/exchangedatadriver.py delete mode 100644 qiskit/finance/data_providers/drivers/wikipedia/README.md delete mode 100644 qiskit/finance/data_providers/drivers/wikipedia/__init__.py delete mode 100644 qiskit/finance/data_providers/drivers/wikipedia/wikipediadriver.py diff --git a/qiskit/aqua/finance/generating_random_variates.ipynb b/qiskit/aqua/finance/generating_random_variates.ipynb deleted file mode 100644 index f14f562b4..000000000 --- a/qiskit/aqua/finance/generating_random_variates.ipynb +++ /dev/null @@ -1,420 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# _*Qiskit Aqua: Generating Random Variates*_ \n", - "\n", - "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", - "\n", - "***\n", - "### Contributors\n", - "Albert Akhriev[1], Jakub Marecek[1], Marco Pistoia[1]\n", - "\n", - "### Affliation\n", - "- [1]IBMQ" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Introduction\n", - "\n", - "While classical computers use only pseudo-random routines, quantum computers\n", - "can generate true random variates.\n", - "For example, the measurement of a quantum superposition is intrinsically random,\n", - "as suggested by Born's rule.\n", - "Consequently, some of the\n", - "best random-number generators are based on such quantum-mechanical effects.\n", - "Further, with a logarithmic amount of random bits, quantum computers can produce\n", - "linearly many more bits, which is known as \n", - "randomness expansion protocols. \n", - "\n", - "In practical applications, one wishes to use random variates of well-known\n", - "distributions, rather than random bits.\n", - "In this notebook, we illustrate ways of generating random variates of several popular\n", - "distributions on IBM Q.\n", - "\n", - "## Random Bits and the Bernoulli distribution\n", - "\n", - "It is clear that there are many options for generating Bernoulli-distributed scalars (i.e. either 0 or 1). Starting from a simple circuit such as a Hadamard gate followed by measurement, one can progress to\n", - "Bernoulli-distributed vectors.\n", - "\n", - "By addition of such random variates, we could get binomial distributions. \n", - "By multiplication we could get geometric distributions.\n", - "Both may lead to unacceptable circuit depth, though.\n", - "\n", - "\n", - "## Uniformly-distributed scalars and vectors\n", - "\n", - "It is clear that there are many options for approximating uniformly-distributed scalars\n", - "by the choice of an integer from a finite range uniformly at random,\n", - "e.g., by a binary-code construction from the Bernoulli-distributed vectors.\n", - "In the following snippet, we generate random bits,\n", - "which we then convert using the binary-code construction, up to the \n", - "machine precision of a classical computer." - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [], - "source": [ - "import matplotlib.pyplot as plt\n", - "%matplotlib inline\n", - "import numpy as np\n", - "import sys, math, time\n", - "import warnings\n", - "warnings.filterwarnings(\"ignore\",category=DeprecationWarning)\n", - "\n", - "from qiskit import BasicAer\n", - "from qiskit.aqua.algorithms import AmplitudeEstimation\n", - "from qiskit.aqua.components.random_distributions import MultivariateNormalDistribution\n", - "from qiskit.aqua.components.uncertainty_problems import FixedIncomeExpectedValue\n", - "from qiskit.aqua.components.random_distributions import *\n", - "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister, execute\n", - "from qiskit.tools.visualization import plot_histogram, circuit_drawer\n", - "\n", - "# In this example we use 'qasm_simulator' backend.\n", - "glo_backend = BasicAer.get_backend(\"qasm_simulator\")\n", - "\n", - "# Parameters.\n", - "glo_num_qubits = 5" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Uniform distribution over floating point numbers." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Uniform distribution of floating point numbers:\n", - "sample type: , element type: float64 , shape: (54321,)\n", - "sample min: -7.6697, max: 19.5199\n", - "time: creation: 0.00043, sampling: 6.49\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# Create uniform distribution sampler.\n", - "start_time = time.time()\n", - "uniform = UniformDistribution(glo_num_qubits, backend=glo_backend)\n", - "creation_time = time.time() - start_time\n", - "\n", - "# Draw a sample.\n", - "start_time = time.time()\n", - "sample = uniform.uniform_rand_float64(size=54321, vmin=-7.67, vmax=19.52)\n", - "sampling_time = time.time() - start_time\n", - "\n", - "# Print out some details.\n", - "print(\"Uniform distribution of floating point numbers:\")\n", - "print(\"sample type:\", type(sample), \", element type:\", sample.dtype, \", shape:\", sample.shape)\n", - "print(\"sample min: {:.4f}, max: {:.4f}\".format(np.amin(sample), np.amax(sample)))\n", - "print(\"time: creation: {:.5f}, sampling: {:.2f}\".format(creation_time, sampling_time))\n", - "\n", - "# Plotting the distribution.\n", - "plt.hist(sample.ravel(),\n", - " bins=min(int(np.ceil(np.sqrt(sample.size))), 100),\n", - " density=True, facecolor='b', alpha=0.75)\n", - "plt.xlabel(\"random variable\", size=12)\n", - "plt.ylabel(\"probability\", size=12)\n", - "plt.title(\"Uniform distribution of float64 numbers [{:.2f} ... {:.2f}]\".format(\n", - " np.amin(sample), np.amax(sample)), size=12)\n", - "plt.grid(True)\n", - "# plt.savefig(\"uniform_distrib_float.png\", bbox_inches=\"tight\")\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Uniform distribution over integers." - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Uniform distribution of integer numbers:\n", - "sample type: , element type: int64 , shape: (54321,)\n", - "sample min: 37, max: 841\n", - "time: sampling: 6.36\n" - ] - }, - { - "data": { - "image/png": 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\n", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# Draw a sample, reuse the previous instance of the sampler.\n", - "start_time = time.time()\n", - "sample = uniform.uniform_rand_int64(size=54321, vmin=37, vmax=841)\n", - "sampling_time = time.time() - start_time\n", - "\n", - "# Print out some details.\n", - "print(\"Uniform distribution of integer numbers:\")\n", - "print(\"sample type:\", type(sample), \", element type:\", sample.dtype, \", shape:\", sample.shape)\n", - "print(\"sample min: {:d}, max: {:d}\".format(np.amin(sample), np.amax(sample)))\n", - "print(\"time: sampling: {:.2f}\".format(sampling_time))\n", - "\n", - "# Plotting the distribution.\n", - "plt.hist(sample.ravel(),\n", - " bins=min(int(np.ceil(np.sqrt(sample.size))), 100),\n", - " density=True, facecolor='g', alpha=0.75)\n", - "plt.xlabel(\"random variable\", size=12)\n", - "plt.ylabel(\"probability\", size=12)\n", - "plt.title(\"Uniform distribution of int64 numbers [{:d} ... {:d}]\".format(\n", - " np.amin(sample), np.amax(sample)), size=12)\n", - "plt.grid(True)\n", - "# plt.savefig(\"uniform_distrib_int.png\", bbox_inches=\"tight\")\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Normal distribution\n", - "\n", - "To generate random variates with a standard normal distribution using two independent \n", - "samples $u_1, u_2$ of the uniform distribution on the unit interval [0, 1], one can\n", - "consider the Box-Muller transform to obtain a 2-vector:\n", - "\n", - "\\begin{align}\n", - "\\begin{bmatrix}\n", - "%R\\cos(\\Theta )=\n", - "{\\sqrt {-2\\ln u_{1}}}\\cos(2\\pi u_{2}) \\\\\n", - "% R\\sin(\\Theta )=\n", - "{\\sqrt {-2\\ln u_{1}}}\\sin(2\\pi u_{2})\n", - "\\end{bmatrix},\n", - "\\end{align}\n", - "\n", - "wherein we have two independent samples of the standard normal distribution.\n", - "In IBM Q, this is implemented as follows: " - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Normal distribution (mu=2.400, sigma=5.100):\n", - "sample type: , element type: float64 , shape: (4321,)\n", - "sample min: -14.4205, max: 20.7960\n", - "time: creation: 0.01026, sampling: 1.60\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# Create normal distribution sampler.\n", - "mu = 2.4\n", - "sigma = 5.1\n", - "start_time = time.time()\n", - "normal = NormalDistribution(glo_num_qubits, mu=mu, sigma=sigma, backend=glo_backend)\n", - "creation_time = time.time() - start_time\n", - "\n", - "# Draw a sample from the normal distribution.\n", - "start_time = time.time()\n", - "sample = normal.normal_rand_float64(size=4321)\n", - "sampling_time = time.time() - start_time\n", - "\n", - "# Print out some details.\n", - "print(\"Normal distribution (mu={:.3f}, sigma={:.3f}):\".format(mu, sigma))\n", - "print(\"sample type:\", type(sample), \", element type:\", sample.dtype, \", shape:\", sample.shape)\n", - "print(\"sample min: {:.4f}, max: {:.4f}\".format(np.amin(sample), np.amax(sample)))\n", - "print(\"time: creation: {:.5f}, sampling: {:.2f}\".format(creation_time, sampling_time))\n", - "\n", - "# Plotting the distribution.\n", - "x = np.linspace(mu - 4.0 * sigma, mu + 4.0 * sigma, 1000)\n", - "analyt = np.exp(-0.5 * ((x - mu) / sigma)**2) / (sigma * math.sqrt(2.0 * math.pi))\n", - "plt.hist(sample.ravel(),\n", - " bins=min(int(np.ceil(np.sqrt(sample.size))), 100),\n", - " density=True, facecolor='r', alpha=0.75)\n", - "plt.plot(x, analyt, '-b', lw=1)\n", - "plt.xlabel(\"random variable\", size=12)\n", - "plt.ylabel(\"probability\", size=12)\n", - "plt.title(\"Normal distribution: empirical vs analytic\", size=12)\n", - "plt.grid(True)\n", - "# plt.savefig(\"normal_distrib.png\", bbox_inches=\"tight\")\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Using basic linear algebra, we can correlate multivariate variables. Indeed, when $L$ is \n", - "the left Cholesky factor of the $n \\times n$ covariance matrix $\\Sigma= L L^T$,\n", - "and $\\mu$ is an $n$-vector,\n", - "and $x$ is an $n$-vector distributed according to the standard normal distribution,\n", - "then $\\mu + Lx$ is a random sample from $N(\\mu, \\Sigma)$.\n", - "\n", - "## Background\n", - "\n", - "In order to understand the implementation, it may be useful to see:\n", - "\n", - "Functions in the base class *UnivariateDistribution*\n", - "\n", - "```python\n", - "def uniform_rand_float64(self, size: int, vmin: float, vmax: float) -> np.ndarray:\n", - " \"\"\"\n", - " Generates a vector of random float64 values in the range [vmin, vmax].\n", - " :param size: length of the vector.\n", - " :param vmin: lower bound.\n", - " :param vmax: upper bound.\n", - " :return: vector of random values.\n", - " \"\"\"\n", - " nbits = 7 * 8 # nbits > mantissa of float64\n", - " bit_str_len = (nbits * size + self.num_target_qubits - 1) // self.num_target_qubits\n", - " job = execute(self.circuit, self.backend, shots=bit_str_len, memory=True)\n", - " bit_str = ''.join(job.result().get_memory())\n", - " scale = float(vmax - vmin) / float(2**nbits - 1)\n", - " return np.array([vmin + scale * float(int(bit_str[i:i+nbits], 2))\n", - " for i in range(0, nbits * size, nbits)], dtype=np.float64)\n", - "```\n", - "\n", - "```python\n", - "def uniform_rand_int64(self, size: int, vmin: int, vmax: int) -> np.ndarray:\n", - " \"\"\"\n", - " Generates a vector of random int64 values in the range [vmin, vmax].\n", - " :param size: length of the vector.\n", - " :param vmin: lower bound.\n", - " :param vmax: upper bound.\n", - " :return: vector of random values.\n", - " \"\"\"\n", - " return np.rint(self.uniform_rand_float64(size, float(vmin), float(vmax))).astype(np.int64)\n", - "```\n", - "\n", - "Function in the base class *NormalDistribution*:\n", - "\n", - "```python\n", - "def normal_rand_float64(self, size: int) -> np.ndarray:\n", - " \"\"\"\n", - " Draws a sample vector from standard normal distribution (mu=0, std=1)\n", - " using Box-Muller method.\n", - " \"\"\"\n", - " EPS = np.sqrt(np.finfo(np.float64).tiny)\n", - " assert isinstance(size, int) and size > 0\n", - " rand_vec = np.zeros((size,), dtype=np.float64)\n", - "\n", - " # Generate array of uniformly distributed samples.\n", - " n = 2 * size\n", - " x = np.reshape(self.uniform_rand_float64(n, float(0.0), float(1.0)), (-1, 2))\n", - "\n", - " x1 = 0.0 # first sample in a pair\n", - " c = 0 # counter\n", - " for d in range(size):\n", - " r2 = 2.0\n", - " while r2 >= 1.0 or r2 < EPS:\n", - " # Regenerate array of uniformly distributed samples upon shortage.\n", - " if c > n:\n", - " c = 0\n", - " n = max(((size // 10) // 2) * 2, 2)\n", - " x = np.reshape(self.uniform_rand_float64(n, float(0.0), float(1.0)), (-1, 2))\n", - "\n", - " x1 = 2.0 * x[c, 0] - 1.0 # first sample in a pair\n", - " x2 = 2.0 * x[c, 1] - 1.0 # second sample in a pair\n", - " r2 = x1 * x1 + x2 * x2\n", - " c += 1\n", - "\n", - " f = np.sqrt(np.abs(-2.0 * np.log(r2) / r2))\n", - " rand_vec[d] = f * x1\n", - " return rand_vec\n", - "```" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.2" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/qiskit/aqua/general/generating_random_variates.ipynb b/qiskit/aqua/general/generating_random_variates.ipynb new file mode 100644 index 000000000..7d58c353c --- /dev/null +++ b/qiskit/aqua/general/generating_random_variates.ipynb @@ -0,0 +1,473 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# _*Qiskit Aqua: Generating Random Variates*_ \n", + "\n", + "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", + "\n", + "***\n", + "### Contributors\n", + "Albert Akhriev[1], Jakub Marecek[1]\n", + "\n", + "### Affliation\n", + "- [1]IBMQ" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Introduction\n", + "\n", + "While classical computers use only pseudo-random routines, quantum computers\n", + "can generate true random variates.\n", + "For example, the measurement of a quantum superposition is intrinsically random,\n", + "as suggested by Born's rule.\n", + "Consequently, some of the\n", + "best random-number generators are based on such quantum-mechanical effects. (See the \n", + "Further, with a logarithmic amount of random bits, quantum computers can produce\n", + "linearly many more bits, which is known as \n", + "randomness expansion protocols. \n", + "\n", + "In practical applications, one wishes to use random variates of well-known\n", + "distributions, rather than random bits.\n", + "In this notebook, we illustrate ways of generating random variates of several popular\n", + "distributions on IBM Q.\n", + "\n", + "## Random Bits and the Bernoulli distribution\n", + "\n", + "It is clear that there are many options for generating random bits (i.e., Bernoulli-distributed scalars, taking values either 0 or 1). Starting from a simple circuit such as a Hadamard gate followed by measurement, one can progress to vectors of Bernoulli-distributed elements. By addition of such random variates, we could get binomial distributions. By multiplication we could get geometric distributions, although perhaps leading to a circuit depth that may be impratical at the moment, though.\n", + "\n", + "Let us start by importing the basic modules and creating a quantum circuit for generating random bits:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "import numpy as np\n", + "import sys, math, time\n", + "import warnings\n", + "warnings.filterwarnings(\"ignore\", category=DeprecationWarning)\n", + "\n", + "from qiskit import BasicAer\n", + "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister, execute\n", + "\n", + "# In this example we use 'qasm_simulator' backend.\n", + "glo_backend = BasicAer.get_backend(\"qasm_simulator\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the next step we create a quantum circuit, which will be used for generation:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Number of qubits utilised simultaneously.\n", + "glo_num_qubits = 5\n", + "\n", + "def create_circuit(num_target_qubits: int) -> QuantumCircuit:\n", + " \"\"\"\n", + " Creates and returns quantum circuit for random variate generation.\n", + " :param num_target_qubits: number of qubits to be used.\n", + " :return: quantum curcuit.\n", + " \"\"\"\n", + " assert isinstance(num_target_qubits, int) and num_target_qubits > 0\n", + " q = QuantumRegister(num_target_qubits)\n", + " c = ClassicalRegister(num_target_qubits)\n", + " circuit = QuantumCircuit(q, c)\n", + " circuit.h(q)\n", + " circuit.barrier()\n", + " circuit.measure(q, c)\n", + " return circuit\n", + "\n", + "# Create and plot generating quantum circuit.\n", + "circuit = create_circuit(glo_num_qubits)\n", + "#print(circuit)\n", + "circuit.draw(output='mpl')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Uniformly-distributed scalars and vectors\n", + "\n", + "It is clear that there are many options for approximating uniformly-distributed scalars by the choice of an integer from a finite range uniformly at random, e.g., by a binary-code construction from the Bernoulli-distributed vectors. In the following snippet, we generate random bits, which we then convert using the binary-code construction, up to the machine precision of a classical computer." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "def uniform_rand_float64(circuit: QuantumCircuit, num_target_qubits: int,\n", + " size: int, vmin: float, vmax: float) -> np.ndarray:\n", + " \"\"\"\n", + " Generates a vector of random float64 values in the range [vmin, vmax].\n", + " :param circuit: quantum circuit for random variate generation.\n", + " :param num_target_qubits: number of qubits to be used.\n", + " :param size: length of the vector.\n", + " :param vmin: lower bound.\n", + " :param vmax: upper bound.\n", + " :return: vector of random values.\n", + " \"\"\"\n", + " assert sys.maxsize == np.iinfo(np.int64).max # sizeof(int) == 64 bits\n", + " assert isinstance(size, int) and size > 0\n", + " assert isinstance(vmin, float) and isinstance(vmax, float) and vmin <= vmax\n", + " nbits = 7 * 8 # nbits > mantissa of float64\n", + " bit_str_len = (nbits * size + num_target_qubits - 1) // num_target_qubits\n", + " job = execute(circuit, glo_backend, shots=bit_str_len, memory=True)\n", + " bit_str = ''.join(job.result().get_memory())\n", + " scale = float(vmax - vmin) / float(2**nbits - 1)\n", + " return np.array([vmin + scale * float(int(bit_str[i:i+nbits], 2))\n", + " for i in range(0, nbits * size, nbits)], dtype=np.float64)\n", + "\n", + "def uniform_rand_int64(circuit: QuantumCircuit, num_target_qubits: int,\n", + " size: int, vmin: int, vmax: int) -> np.ndarray:\n", + " \"\"\"\n", + " Generates a vector of random int64 values in the range [vmin, vmax].\n", + " :param circuit: quantum circuit for random variate generation.\n", + " :param num_target_qubits: number of qubits to be used.\n", + " :param size: length of the vector.\n", + " :param vmin: lower bound.\n", + " :param vmax: upper bound.\n", + " :return: vector of random values.\n", + " \"\"\"\n", + " assert sys.maxsize == np.iinfo(np.int64).max # sizeof(int) == 64 bits\n", + " assert isinstance(size, int) and size > 0\n", + " assert isinstance(vmin, int) and isinstance(vmax, int) and vmin <= vmax\n", + " assert abs(vmin) <= 2**52 and abs(vmax) <= 2**52 # 52 == mantissa of float64\n", + " return np.rint(uniform_rand_float64(circuit, num_target_qubits,\n", + " size, float(vmin), float(vmax))).astype(np.int64)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Uniform distribution over floating point numbers.\n", + "In this example we draw a random vector of floating-point values uniformly distributed within some arbitrary selected interval:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Uniform distribution over floating point numbers:\n", + " sample type: , element type: float64 , shape: (54321,)\n", + " sample min: -7.6698, max: 19.5196\n", + " sampling time: 6.65 secs\n" + ] + }, + { + "data": { + "image/png": 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GFkvqJZ0BzWmmzGFtSEnWrq3efeALqjYW+CaC0a1tb1aNiBXAioq0cwrDTwAnDFLGuYOVaWbl6fSA0cyZTVlt7vTvut+Ye723Da/RsmGYWXs4CJmZDx6sNA5CZiUajp2/A4r164TfgoOQjUidsPEMp9Hc/tHcNmucg9Aw8u2bZlbJQfjZHIRsxPNGazZ6OQiNEpVnXSNhZz3cwaOTgtNQ6tpJ7bTG1LNuG+1R6bQeGAehJvmCspWt0d9Lu39fI+H3PBLqYANzELJteMNt3lCObNt5BNvuo+VOOzrvNJ38/ToIlayTfzytNhzfxUDdlA62NlKNpf2Cg9AYMxJ2vCOhDmY2MjgIjQFj6aiqWQ6MjSl+Xx//ePl18DrrXA5CLVbPDn+kBIVO3Ijb8d3V+l5Gwvc1Un471npjdd06CI1SnfKDnjEjvWq51psumy3TWmMkBN7RwL/J2hyErC3G4kbY3+bu7nLrMRY4WHYuB6ERqrhR1dqJjcUdu5mNLm0LQpJmAp8jvQX1qxHx6YrpE4CvA4cBDwInRsSdkg4HFvZnA86NiCvyPHcCjwJPA1siYno72mIjT5kBeSQcDIyEOjTDZzDWliAkaRxwEXA0sAG4VtLyiLilkO104KGIOFDSHOB84ETgZmB6fp33XsBvJX0vIrbk+WZExKZ2tMPGnk7duQ/FWGyzladdZ0KHA70RsQ5A0jJgFlAMQrOAc/Pw5cCFkhQRfyrk2RGI4a+uNcI7LTNrliKGf58uaTYwMyLelcdPAY6IiHmFPDfnPBvy+O05zyZJRwCLgP2AUwrdcXcAD5EC05cjYiFVSJoLzAWYNGnSYcuWLRtym9au3Tp80EHV01tl4sQ+Nm/eufUFF9RqQ6PpzWhH+1qtkfaX2b5WrqdaZe29dx8777zzkJdRLL+o0d9dq3+z/euv0WUXDcd+oVG16tbXt3X9DWTGjBnXDcclj3YFoROAN1QEocMj4gOFPGtynmIQOjwiHizkeTFwKfDaiHhC0t4RsVHSC4CfAB+IiKsHqsv06dNj9erVQ25TPf9L0ird3T0sXdrV+oLrUM//yQy1zWW2rx1G4vprZVkf/3gPXV1dQ15GPXUdSp5mv4v+9dfosotGQm9Brbr19GxdfwORNCxBqF3dcRuAfQrjU4CNNfJskDQe2A3YXMwQEbdKegw4FFgdERtz+v2SriB1+w0YhMysc42Enbm1VruC0LXANEn7A3cDc4CTKvIsB04DrgFmA1dFROR51ucbE/YDDgbulLQTsF1EPJqHjwEWDGcjRsLTj83K4t+5DYe2BKEcQOYBV5Ju0V4UEWskLSCd0SwHLgYWS+olnQHNybO/BjhT0p+BZ4D35+tEBwBXSOpvx5KI+FE72mPWKRw4bKRr2/8JRcQKYEVF2jmF4SeAE6rMtxhYXCV9HfCy1tfUirwTM2uOt536+IkJ1hRvYGbb8nbROAchMxuStWtb+wBaG1u2K7sCZmY2dvlMyMzGBHeVjUwOQmY2qjjYdBYHITMbERw8xiZfEzIzs9L4TMjMrA4+UxsePhMyM7PSOAiZmVlpHITMzKw0DkJmZlYaByEzMyuNg5CZmZXGQcjMzErjIGRmZqVxEDIzs9K0LQhJminpNkm9ks6sMn2CpMvy9FWSpub0wyXdmD+/lfTmess0M7ORrS1BSNI44CLgWOAQoFvSIRXZTgceiogDgQuA83P6zcD0iHg5MBP4sqTxdZZpZmYjWLvOhA4HeiNiXUQ8BSwDZlXkmQVcmocvB46SpIj4U0Rsyek7AtFAmWZmNoK16wGmk4H1hfENwBG18kTEFkmPAHsAmyQdASwC9gNOydPrKRMASXOBuQCTJk2ip6enqUZ0dzc125BNnNhHd3dPOQtvA7evs7l9naHWbq+vr6/pfWIrtCsIqUpa1JsnIlYBL5H0YuBSST+ss0zy/AuBhQDTp0+Prq6uOqv9bPPnNzXbkHV397B0aVc5C28Dt6+zuX2dYeXK6uk9PT00u09shXZ1x20A9imMTwE21sojaTywG7C5mCEibgUeAw6ts0wzMxvB2hWErgWmSdpf0g7AHGB5RZ7lwGl5eDZwVUREnmc8gKT9gIOBO+ss08zMRrC2dMflazjzgCuBccCiiFgjaQGwOiKWAxcDiyX1ks6A5uTZXwOcKenPwDPA+yNiE0C1MtvRHjMza422vVk1IlYAKyrSzikMPwGcUGW+xcDiess0M7PO4ScmmJlZaRyEzMysNA5CZmZWGgchMzMrjYOQmZmVxkHIzMxK4yBkZmalcRAyM7PSOAiZmVlp6g5CkvYYzoqYmdnY08iZ0HpJ35U0Oz8w1MzMbEgaCUL7AT8DPgLcK2mhpNcMT7XMzGwsqDsIRcQDEfH5iPgb4FXA/aSnXq+TtCC/ZsHMzKxuzd6Y8ML82RW4nfRq7hskndmqipmZ2ehX96scJL0EeBtwMtAHXAq8NCLuztM/AfwO+PQw1NPMzEahRt4ndDWwFJgdEb+pnBgRd0r6bMtqZmZmo14j3XFvjoh5lQFI0uH9w8WX1FWSNFPSbZJ6q3XbSZog6bI8fZWkqTn9aEnXSbop/z2yME9PLvPG/HlBA+0xM7OSNXIm9H3SNaBKPwImDjSjpHHARcDRwAbgWknLI+KWQrbTgYci4kBJc4DzgROBTcCbImKjpENJr/OeXJjv5IhY3UA7zMxshBj0TEjSdjmIKNuu8JkGbKljOYcDvRGxLiKeApYBsyryzCJdZwK4HDhKkiLihojYmNPXADtKmlBP48zMbGRTRAycQXoGqJXpGeCTEXHuIGXMBmZGxLvy+CnAERExr5Dn5pxnQx6/PefZVFHOeyPi9Xm8B9gDeBr4NnBeVGmQpLnAXIBJkyYdtmzZsgHbXMvatU3NNmQTJ/axefPO5Sy8Ddy+zub2dYaDDqqe3tfXx847D96+GTNmXBcR01tcrbq64/YHBPwceG0hPYAHIuLxOspQlbTKYDFgnnx33vnAMYXpJ0fE3ZJ2IQWhU4Cvb1NIxEJgIcD06dOjq6urjipva/78pmYbsu7uHpYu7Spn4W3g9nU2t68zrFxZPb2np4dm94mtMGgQioi78uBQ/hl1A7BPYXwKsLFGng2SxgO7AZsBJE0BrgBOjYjbC3W7O/99VNISUrffNkHIzMxGpgGDkKSFETE3D9fcuUfEqYMs51pgmqT9gbuBOcBJFXmWA6cB1wCzgasiIiTtDvwAOCsiflWo23hg94jYJGl74Djgp4PUw8zMRpDBzoTuKAzfXjPXICJii6R5pDvbxgGLImKNpAXA6ohYDlxMegxQL+kMaE6efR5wIHC2pLNz2jHAY8CVOQCNIwWgrzRbRzMza78Bg1BEfKowPKQrIhGxAlhRkXZOYfgJ4IQq850HnFej2MOGUiczMyvXYN1xRw40vV9EXNWa6piZ2VgyWHfcxXWUEcABLaiLmZmNMYN1x+3froqYmdnY0+yrHMzMzIZssGtCt0bEi/Pwemo8OSEi9h2GupmZ2Sg32DWhdxeG3zacFTEzs7FnsGtCvywM/3z4q2NmZmNJ3deEJO0gaYGk30t6LP/9hKQdh7OCZmY2ejXyPqEvAgcDHwTuIj1L7izSu33e2fqqmZnZaNdIEDoeeFFEPJzHb5G0CujFQcjMzJrQyC3a9wLPrUh7DnBP66pjZmZjSSOP7VkM/EjSf7D1tQtn4FcnmJlZk5p5bM9HK8bfQ3rZnJmZWUP82B4zMyuNH9tjZmalqfvuOEm7AucCrwP2BNQ/zY/tMTOzZjRyJvQF4BXAAmAi8AHgD8AFw1AvMzMbAxoJQscAb4mI7wJP578nAqfUM7OkmZJuk9Qr6cwq0ydIuixPXyVpak4/WtJ1km7Kf48szHNYTu+V9HlJqizXzMxGrkaC0HbAI3m4T9LupP8ROnCwGSWNAy4CjgUOAbolHVKR7XTgoYg4kHR21X/H3SbgTRHxV8BppFvF+30RmAtMy5+ZDbTHzMxK1kgQ+i3pehDAL0hB5YvA2jrmPRzojYh1EfEUsAyYVZFnFnBpHr4cOEqSIuKGiNiY09cAO+azpr2AXSPimogI0v8rHd9Ae8zMrGSNPLbn3Wy9GeGDwKeB3YFT65h3MrC+ML4BOKJWnojYIukRYA/SmVC/twA3RMSTkibncoplTq62cElzSWdMTJo0iZ6enjqqvK3u7qZmG7KJE/vo7u4pZ+Ft4PZ1NrevM9Ta7fX19TW9T2yFuoNQRKwrDD9A6j6rV7VrNZUvyBswj6SXkLrojmmgzJQYsRBYCDB9+vTo6uoapLrVzZ/f1GxD1t3dw9KlXeUsvA3cvs7m9nWGlSurp/f09NDsPrEVGvo/IUnvlPQTSWvy39PrvBmg/zE//aYAG2vlkTQe2A3YnMenAFcAp0bE7YX8UwYp08zMRrBG3if0GeAjwHeAf8x/P0x9j+y5FpgmaX9JOwBzgOUVeZaTbjwAmA1cFRGRb4D4AXBWRPyqP3NE3AM8KumVORCeCny33vaYmVn5Grkm9HbgFRHxl+swkr4PXA/800Az5ms884ArgXHAoohYI2kBsDoilpOeU7dYUi/pDGhOnn0e6Q68syWdndOOiYj7gfcBl5Ce5v3D/DEzsw7RSBB6NH8q0/5Yz8wRsQJYUZF2TmH4CeCEKvOdB5xXo8zVwKH1LN/MzEaewV7lcEBh9LPAdyR9mq3Xb/4RPzHBzMyaNNiZUC/pjrPizQczKvIcCVzYykqZmdnYMNirHPyUbTMzGzaNXBMCQNK+pH8K3RAR6wfLb2ZmVksjt2jvJennpC667wC3S7pa0t7DVjszMxvVGulu+yLp+XHPi4i9gOcBNwBfGo6KmZnZ6NdId9xrgL0i4s8AEfGYpH8C7h6WmpmZ2ajXyJnQQ6TXMBQdDDzcuuqYmdlY0siZ0GeAn0q6GLgL2A94B3D2gHOZmZnV0MhTtL8i6XbgJOClpIeFdkfEVcNVOTMzG93qCkL5zaiLgLkOOmZm1ip1XROKiKdJ7/F5ZnirY2ZmY0kjNyZcAMyXtP1wVcbMzMaWRm5M+ADwQuD/SHqArc+Ui4jYdzgqZ2Zmo1sjQehtw1YLMzMbkxrpjrsGOAr4Kum9QF8FXg+sGoZ6mZnZGNDoY3uOBD4I/E3++zrgC/XMLGmmpNsk9Uo6s8r0CZIuy9NXSZqa0/eQtFJSn6QLK+bpyWXemD8vaKA9ZmZWska6444HXhQR/U9IuEXSKtIDTd850Iz5Fu+LgKNJL8S7VtLyiLilkO104KGIOFDSHOB84ETgCdI/xB5K9beonpzfsGpmZh2mkTOhe4HnVqQ9B7injnkPB3ojYl1EPAUsA2ZV5JkFXJqHLweOkqSIeCwifkkKRmZmNoooIurLmLrQTgL+g62v9z4DWAJc25+v2j+zSpoNzIyId+XxU4AjImJeIc/NOc+GPH57zrMpj78dmF4xTw+wB/A08G3gvKjSIElzgbkAkyZNOmzZsmV1tbnS2rVNzTZkEyf2sXnzzuUsvA3cvs7m9nWGgw6qnt7X18fOOw/evhkzZlwXEdNbXK2GuuPek/9+tCL9vfkD6bbtA6rMqypplcGinjyVTo6IuyXtQgpCpwBf36aQiIXAQoDp06dHV1fXIMVWN39+U7MNWXd3D0uXdpWz8DZw+zqb29cZVq6snt7T00Oz+8RWaOTZcfsPYTn9Z079ppCePVctzwZJ44HdgM2D1Onu/PdRSUtI3X7bBCEzMxuZGrkmNBTXAtMk7S9pB2AOsLwiz3LgtDw8G7iqWtdaP0njJe2Zh7cHjgNubnnNzcxs2DTSHde0iNgiaR5wJTAOWBQRayQtAFZHxHLgYmCxpF7SGdCc/vkl3QnsCuwg6XjSc+zuAq7MAWgc8FPgK+1oj5mZtUZbghBARKwg/ZNrMe2cwvATwAk15p1ao9jDWlU/MzNrv3Z1x5mZmW3DQcjMzErjIGRmZqVxEDIzs9I4CJmZWWkchMzMrDQOQmZmVhoHITMzK42DkJmZlcZByMzMSuMgZGZmpXEQMjOz0jgImZlZaRyEzMysNA5CZmZWGgchMzMrjYOQmZmVpm1BSNJMSbdJ6pV0ZpXpEyRdlqevkjQ1p+8haaWkPkkXVsxzmKSb8jyfl6T2tMbGGSj7AAAKJUlEQVTMzFqhLUFI0jjgIuBY4BCgW9IhFdlOBx6KiAOBC4Dzc/oTwNnAh6sU/UVgLjAtf2a2vvZmZjZc2nUmdDjQGxHrIuIpYBkwqyLPLODSPHw5cJQkRcRjEfFLUjD6C0l7AbtGxDUREcDXgeOHtRVmZtZS49u0nMnA+sL4BuCIWnkiYoukR4A9gE0DlLmhoszJ1TJKmks6Y2LSpEn09PQ0WP2ku7up2YZs4sQ+urt7yll4G7h9nc3t6wy1dnt9fX1N7xNboV1BqNq1mmgiT1P5I2IhsBBg+vTp0dXVNUCxtc2f39RsQ9bd3cPSpV3lLLwN3L7O5vZ1hpUrq6f39PTQ7D6xFdrVHbcB2KcwPgXYWCuPpPHAbsDmQcqcMkiZZmY2grUrCF0LTJO0v6QdgDnA8oo8y4HT8vBs4Kp8raeqiLgHeFTSK/NdcacC32191c3MbLi0pTsuX+OZB1wJjAMWRcQaSQuA1RGxHLgYWCypl3QGNKd/fkl3ArsCO0g6HjgmIm4B3gdcAjwH+GH+mJlZh2jXNSEiYgWwoiLtnMLwE8AJNeadWiN9NXBo62ppZmbt5CcmmJlZaRyEzMysNA5CZmZWGgchMzMrjYOQmZmVxkHIzMxK4yBkZmalcRAyM7PSOAiZmVlpHITMzKw0DkJmZlYaByEzMyuNg5CZmZXGQcjMzErjIGRmZqVxEDIzs9K0LQhJminpNkm9ks6sMn2CpMvy9FWSphamnZXTb5P0hkL6nZJuknSjpNXtaYmZmbVKW96sKmkccBFwNLABuFbS8vyK7n6nAw9FxIGS5gDnAydKOoT0qu+XAHsDP5V0UEQ8neebERGb2tEOMzNrrXadCR0O9EbEuoh4ClgGzKrIMwu4NA9fDhwlSTl9WUQ8GRF3AL25PDMz63BtORMCJgPrC+MbgCNq5YmILZIeAfbI6b+umHdyHg7gx5IC+HJELKy2cElzgbkAkyZNoqenp6lGdHc3NduQTZzYR3d3TzkLbwO3r7O5fZ2h1m6vr6+v6X1iK7QrCKlKWtSZZ6B5/2dEbJT0AuAnkv47Iq7eJnMKTgsBpk+fHl1dXXVXvGj+/KZmG7Lu7h6WLu0qZ+Ft4PZ1NrevM6xcWT29p6eHZveJrdCu7rgNwD6F8SnAxlp5JI0HdgM2DzRvRPT/vR+4AnfTmZl1lHYFoWuBaZL2l7QD6UaD5RV5lgOn5eHZwFURETl9Tr57bn9gGvAbSTtJ2gVA0k7AMcDNbWiLmZm1SFu64/I1nnnAlcA4YFFErJG0AFgdEcuBi4HFknpJZ0Bz8rxrJH0TuAXYApwREU9LmgRcke5dYDywJCJ+1I72mJlZa7TrmhARsQJYUZF2TmH4CeCEGvN+EvhkRdo64GWtr6mZmbWLn5hgZmalcRAyM7PSOAiZmVlpHITMzKw0DkJmZlYaByEzMyuNg5CZmZXGQcjMzErjIGRmZqVxEDIzs9I4CJmZWWkchMzMrDQOQmZmVhoHITMzK42DkJmZlcZByMzMSuMgZGZmpWlbEJI0U9JtknolnVll+gRJl+XpqyRNLUw7K6ffJukN9ZZpZmYjW1uCkKRxwEXAscAhQLekQyqynQ48FBEHAhcA5+d5DwHmAC8BZgJfkDSuzjLNzGwEa9eZ0OFAb0Ssi4ingGXArIo8s4BL8/DlwFGSlNOXRcSTEXEH0JvLq6dMMzMbwca3aTmTgfWF8Q3AEbXyRMQWSY8Ae+T0X1fMOzkPD1YmAJLmAnPzaJ+k25poQ2l6etgT2FR2PYaL29fZ3L7OINWcVG/79mtZZQraFYSqNT/qzFMrvdpZXGWZKTFiIbBwoAqOZJJWR8T0susxXNy+zub2dbay29eu7rgNwD6F8SnAxlp5JI0HdgM2DzBvPWWamdkI1q4gdC0wTdL+knYg3WiwvCLPcuC0PDwbuCoiIqfPyXfP7Q9MA35TZ5lmZjaCtaU7Ll/jmQdcCYwDFkXEGkkLgNURsRy4GFgsqZd0BjQnz7tG0jeBW4AtwBkR8TRAtTLb0Z4SdGxXYp3cvs7m9nW2UtundLJhZmbWfn5igpmZlcZByMzMSuMg1CEknSvpbkk35s8by67TUI32xy5JulPSTXl9rS67Pq0gaZGk+yXdXEibKOknkn6f/z6vzDo2q0bbRs12J2kfSSsl3SppjaR/yOmlrj8Hoc5yQUS8PH9WlF2ZoRhDj12akdfXaPk/k0tIj88qOhP4WURMA36WxzvRJWzbNhg9290W4EMR8WLglcAZeZsrdf05CFlZ/NilDhQRV5PuXi0qPnLrUuD4tlaqRWq0bdSIiHsi4vo8/ChwK+npM6WuPwehzjJP0u9yt0FHdnkUVHuU0+QaeTtVAD+WdF1+dNRoNSki7oG0owNeUHJ9Wm00bXcA5LcU/DWwipLXn4PQCCLpp5JurvKZBXwReBHwcuAe4N9KrezQ1fMop073PyPiFaQuxzMkvbbsClnDRtt2h6SdgW8D/zsi/lh2fdr17DirQ0S8vp58kr4CfH+YqzPcRv1jlyJiY/57v6QrSF2QV5dbq2Fxn6S9IuIeSXsB95ddoVaJiPv6h0fDdidpe1IA+s+I+E5OLnX9+UyoQ+QfR783AzfXytshRvVjlyTtJGmX/mHgGDp/ndVSfOTWacB3S6xLS42m7S6/Gudi4NaI+PfCpFLXn5+Y0CEkLSZ1CQRwJ/Ce/n7cTpVvd/0sWx+79MmSq9Qykg4Arsij44Elo6F9kpYCXaTH/98HfBz4f8A3gX2BPwAnRETHXeCv0bYuRsl2J+k1wC+Am4BncvJHSdeFSlt/DkJmZlYad8eZmVlpHITMzKw0DkJmZlYaByEzMyuNg5CZmZXGQcisZJK6JG0oux5mZXAQMjOz0jgImZlZaRyEzFpE0pmSLq9I+5ykz0t6R36Z2KOS1kl6zwDlhKQDC+OXSDqvMH5cfsHaw5L+S9JLh6dFZsPPQcisdZYCb5S0K/zlxX1vBZaQHgp5HLAr8A7gAkmvaHQBeZ5FwHuAPYAvA8slTWhJC8zazEHIrEUi4i7gera+FOxI4E8R8euI+EFE3B7Jz4EfA3/bxGLeDXw5IlZFxNMRcSnwJOlNmWYdx0HIrLWWAN15+KQ8jqRjJf1a0mZJDwNvJD0os1H7AR/KXXEP57L2AfZuQd3N2s5ByKy1vgV0SZpCevT/ktxV9m3gX0lvsdwdWEH1F/sB/Al4bmH8hYXh9cAnI2L3wue5EbG05S0xawMHIbMWiogHgB7ga8AdEXErsAMwAXgA2CLpWNL7hWq5EThJ0jhJM4HXFaZ9BXivpCOU7CTp7/rfXWTWaRyEzFpvCfD6/JeIeBT4IOmdLQ+RuukGeoHfPwBvAh4GTia9r4dc1mrSdaELc1m9wNtb3QCzdvH7hMzMrDQ+EzIzs9I4CJmZWWkchMzMrDQOQmZmVhoHITMzK42DkJmZlcZByMzMSuMgZGZmpfn/QrovIPSdcl4AAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Draw a sample from uniform distribution.\n", + "start_time = time.time()\n", + "sample = uniform_rand_float64(circuit, glo_num_qubits, size=54321, vmin=-7.67, vmax=19.52)\n", + "sampling_time = time.time() - start_time\n", + "\n", + "# Print out some details.\n", + "print(\"Uniform distribution over floating point numbers:\")\n", + "print(\" sample type:\", type(sample), \", element type:\", sample.dtype, \", shape:\", sample.shape)\n", + "print(\" sample min: {:.4f}, max: {:.4f}\".format(np.amin(sample), np.amax(sample)))\n", + "print(\" sampling time: {:.2f} secs\".format(sampling_time))\n", + "\n", + "# Plotting the distribution.\n", + "plt.hist(sample.ravel(),\n", + " bins=min(int(np.ceil(np.sqrt(sample.size))), 100),\n", + " density=True, facecolor='b', alpha=0.75)\n", + "plt.xlabel(\"value\", size=12)\n", + "plt.ylabel(\"probability\", size=12)\n", + "plt.title(\"Uniform distribution over float64 numbers in [{:.2f} ... {:.2f}]\".format(\n", + " np.amin(sample), np.amax(sample)), size=12)\n", + "plt.grid(True)\n", + "# plt.savefig(\"uniform_distrib_float.png\", bbox_inches=\"tight\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Uniform distribution over integers.\n", + "Our next example is similar to the previous one, but here we generate a random vector of integers:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Uniform distribution over bounded integer numbers:\n", + " sample type: , element type: int64 , shape: (54321,)\n", + " sample min: 37, max: 841\n", + " sampling time: 6.62 secs\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Draw a sample from uniform distribution.\n", + "start_time = time.time()\n", + "sample = uniform_rand_int64(circuit, glo_num_qubits, size=54321, vmin=37, vmax=841)\n", + "sampling_time = time.time() - start_time\n", + "\n", + "# Print out some details.\n", + "print(\"Uniform distribution over bounded integer numbers:\")\n", + "print(\" sample type:\", type(sample), \", element type:\", sample.dtype, \", shape:\", sample.shape)\n", + "print(\" sample min: {:d}, max: {:d}\".format(np.amin(sample), np.amax(sample)))\n", + "print(\" sampling time: {:.2f} secs\".format(sampling_time))\n", + "\n", + "# Plotting the distribution.\n", + "plt.hist(sample.ravel(),\n", + " bins=min(int(np.ceil(np.sqrt(sample.size))), 100),\n", + " density=True, facecolor='g', alpha=0.75)\n", + "plt.xlabel(\"value\", size=12)\n", + "plt.ylabel(\"probability\", size=12)\n", + "plt.title(\"Uniform distribution over int64 numbers in [{:d} ... {:d}]\".format(\n", + " np.amin(sample), np.amax(sample)), size=12)\n", + "plt.grid(True)\n", + "# plt.savefig(\"uniform_distrib_int.png\", bbox_inches=\"tight\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Normal distribution\n", + "\n", + "To generate random variates with a standard normal distribution using two independent \n", + "samples $u_1, u_2$ of the uniform distribution on the unit interval [0, 1], one can\n", + "consider the Box-Muller transform to obtain a 2-vector:\n", + "\n", + "\\begin{align}\n", + "\\begin{bmatrix}\n", + "%R\\cos(\\Theta )=\n", + "{\\sqrt {-2\\ln u_{1}}}\\cos(2\\pi u_{2}) \\\\\n", + "% R\\sin(\\Theta )=\n", + "{\\sqrt {-2\\ln u_{1}}}\\sin(2\\pi u_{2})\n", + "\\end{bmatrix},\n", + "\\end{align}\n", + "\n", + "wherein we have two independent samples of the standard normal distribution.\n", + "In IBM Q, this is implemented as follows: " + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "def normal_rand_float64(circuit: QuantumCircuit, num_target_qubits: int,\n", + " size: int, mu: float, sigma: float) -> np.ndarray:\n", + " \"\"\"\n", + " Draws a sample vector from the normal distribution given the mean and standard\n", + " deviation, using the Box-Muller method. \n", + " \"\"\"\n", + " TINY = np.sqrt(np.finfo(np.float64).tiny)\n", + " assert isinstance(size, int) and size > 0\n", + " rand_vec = np.zeros((size,), dtype=np.float64)\n", + "\n", + " # Generate array of uniformly distributed samples, factor 1.5 longer that\n", + " # actually needed.\n", + " n = (3 * size) // 2\n", + " x = np.reshape(uniform_rand_float64(circuit, num_target_qubits,\n", + " 2*n, 0.0, 1.0), (-1, 2))\n", + "\n", + " x1 = 0.0 # first sample in a pair\n", + " c = 0 # counter\n", + " for d in range(size):\n", + " r2 = 2.0\n", + " while r2 >= 1.0 or r2 < TINY:\n", + " # Regenerate array of uniformly distributed samples upon shortage.\n", + " if c >= n:\n", + " c = 0\n", + " n = max(size // 10, 1)\n", + " x = np.reshape(uniform_rand_float64(circuit, num_target_qubits,\n", + " 2*n, 0.0, 1.0), (-1, 2))\n", + "\n", + " x1 = 2.0 * x[c, 0] - 1.0 # first sample in a pair\n", + " x2 = 2.0 * x[c, 1] - 1.0 # second sample in a pair\n", + " r2 = x1 * x1 + x2 * x2\n", + " c += 1\n", + "\n", + " f = np.sqrt(np.abs(-2.0 * np.log(r2) / r2))\n", + " rand_vec[d] = f * x1\n", + " \n", + " return (rand_vec * sigma + mu)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following example demonstrates how to draw a random vector of normally distributed variates:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Normal distribution (mu=2.400, sigma=5.100):\n", + " sample type: , element type: float64 , shape: (4321,)\n", + " sample min: -16.3332, max: 20.7365\n", + " sampling time: 1.69 secs\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Mean and standard deviation.\n", + "mu = 2.4\n", + "sigma = 5.1\n", + "\n", + "# Draw a sample from the normal distribution.\n", + "start_time = time.time()\n", + "sample = normal_rand_float64(circuit, glo_num_qubits, size=4321, mu=mu, sigma=sigma)\n", + "sampling_time = time.time() - start_time\n", + "\n", + "# Print out some details.\n", + "print(\"Normal distribution (mu={:.3f}, sigma={:.3f}):\".format(mu, sigma))\n", + "print(\" sample type:\", type(sample), \", element type:\", sample.dtype, \", shape:\", sample.shape)\n", + "print(\" sample min: {:.4f}, max: {:.4f}\".format(np.amin(sample), np.amax(sample)))\n", + "print(\" sampling time: {:.2f} secs\".format(sampling_time))\n", + "\n", + "# Plotting the distribution.\n", + "x = np.linspace(mu - 4.0 * sigma, mu + 4.0 * sigma, 1000)\n", + "analyt = np.exp(-0.5 * ((x - mu) / sigma)**2) / (sigma * math.sqrt(2.0 * math.pi))\n", + "plt.hist(sample.ravel(),\n", + " bins=min(int(np.ceil(np.sqrt(sample.size))), 100),\n", + " density=True, facecolor='r', alpha=0.75)\n", + "plt.plot(x, analyt, '-b', lw=1)\n", + "plt.xlabel(\"value\", size=12)\n", + "plt.ylabel(\"probability\", size=12)\n", + "plt.title(\"Normal distribution: empirical vs analytic\", size=12)\n", + "plt.grid(True)\n", + "# plt.savefig(\"normal_distrib.png\", bbox_inches=\"tight\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There is a substantial amount of further work needed to either certify the quality of the source of random numbers (cf. NIST SP 800-90B, Recommendation for the Entropy Sources Used for Random Bit Generation) or to use random variates within quantum algorithms (cf. uncertainty_models within Qiskit Aqua)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.2" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/qiskit/finance/data_providers/__init__.py b/qiskit/finance/data_providers/__init__.py deleted file mode 100644 index 300002f49..000000000 --- a/qiskit/finance/data_providers/__init__.py +++ /dev/null @@ -1,20 +0,0 @@ -# -*- coding: utf-8 -*- - -# Copyright 2018 IBM. -# -# Licensed under the Apache License, Version 2.0 (the "License"); -# you may not use this file except in compliance with the License. -# You may obtain a copy of the License at -# -# http://www.apache.org/licenses/LICENSE-2.0 -# -# Unless required by applicable law or agreed to in writing, software -# distributed under the License is distributed on an "AS IS" BASIS, -# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -# See the License for the specific language governing permissions and -# limitations under the License. -# ============================================================================= - -from .drivers import * - -__all__ = ['drivers'] diff --git a/qiskit/finance/data_providers/drivers/__init__.py b/qiskit/finance/data_providers/drivers/__init__.py deleted file mode 100644 index 3c737a444..000000000 --- a/qiskit/finance/data_providers/drivers/__init__.py +++ /dev/null @@ -1,26 +0,0 @@ -# -*- coding: utf-8 -*- - -# Copyright 2018 IBM. -# -# Licensed under the Apache License, Version 2.0 (the "License"); -# you may not use this file except in compliance with the License. -# You may obtain a copy of the License at -# -# http://www.apache.org/licenses/LICENSE-2.0 -# -# Unless required by applicable law or agreed to in writing, software -# distributed under the License is distributed on an "AS IS" BASIS, -# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -# See the License for the specific language governing permissions and -# limitations under the License. -# ============================================================================= - -from ._basedriver import BaseDriver, UnitsType -from .dataondemand import DataOnDemandDriver -from .exhangedata import ExchangeDataDriver -from .wikipedia import WikipediaDriver - -__all__ = ['BaseDriver', - 'DataOnDemandDriver', - 'ExchangeDataDriver', - 'WikipediaDriver'] diff --git a/qiskit/finance/data_providers/drivers/_basedriver.py b/qiskit/finance/data_providers/drivers/_basedriver.py deleted file mode 100644 index 1993d517a..000000000 --- a/qiskit/finance/data_providers/drivers/_basedriver.py +++ /dev/null @@ -1,154 +0,0 @@ -# -*- coding: utf-8 -*- - -# Copyright 2018 IBM. -# -# Licensed under the Apache License, Version 2.0 (the "License"); -# you may not use this file except in compliance with the License. -# You may obtain a copy of the License at -# -# http://www.apache.org/licenses/LICENSE-2.0 -# -# Unless required by applicable law or agreed to in writing, software -# distributed under the License is distributed on an "AS IS" BASIS, -# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -# See the License for the specific language governing permissions and -# limitations under the License. -# ============================================================================= - -""" -This module implements the abstract base class for driver modules -within Qiskit Finance. - -To create add-on driver modules subclass the BaseDriver class in this module. -Doing so requires that the required driver interface is implemented. -""" - -from abc import ABC, abstractmethod -import copy -from qiskit.aqua.parser import JSONSchema -from enum import Enum -import logging - -logger = logging.getLogger(__name__) - - -class DataType(Enum): - DAILYADJUSTED = 'Daily (adj)' - DAILY = 'Daily' - - -class BaseDriver(ABC): - """ - Base class for Drivers. - - This method should initialize the module and its configuration, and - use an exception if a component of the module is available. - - """ - @abstractmethod - def __init__(self): - self.check_driver_valid() - self._configuration = copy.deepcopy(self.CONFIGURATION) - self._work_path = None - - @property - def configuration(self): - """Return driver configuration.""" - return self._configuration - - @classmethod - def init_from_input(cls, section): - """ - Initialize via section dictionary. - - Args: - params (dict): section dictionary - - Returns: - Driver: Driver object - """ - pass - - @staticmethod - def check_driver_valid(): - """Checks if driver is ready for use. Throws an exception if not""" - pass - - def validate(self, args_dict): - schema_dict = self.CONFIGURATION.get('input_schema', None) - if schema_dict is None: - return - - jsonSchema = JSONSchema(schema_dict) - schema_property_names = jsonSchema.get_default_section_names() - json_dict = {} - for property_name in schema_property_names: - if property_name in args_dict: - json_dict[property_name] = args_dict[property_name] - - jsonSchema.validate(json_dict) - - @property - def work_path(self): - return self._work_path - - @work_path.setter - def work_path(self, new_work_path): - self._work_path = new_work_path - - @abstractmethod - def run(self): - pass - - # gets coordinates suitable for plotting - # it does not have to be overridden in non-abstract derived classes. - def get_coordinates(self): - # Coordinates for visualisation purposes - xc = np.zeros([self.n, 1]) - yc = np.zeros([self.n, 1]) - xc = (np.random.rand(self.n) - 0.5) * 1 - yc = (np.random.rand(self.n) - 0.5) * 1 - #for (cnt, s) in enumerate(self.tickers): - #xc[cnt, 1] = self.data[cnt][0] - # yc[cnt, 0] = self.data[cnt][-1] - return xc, yc - - # it does not have to be overridden in non-abstract derived classes. - def get_covariance(self): - if not self._data: return None - self.cov = np.cov(self._data, rowvar = True) - return self.cov - - # it does not have to be overridden in non-abstract derived classes. - def get_similarity_matrix(self): - if not self.data: return None - try: - import fastdtw - for ii in range(0, self._n): - self.rho[ii,ii] = 1. - for jj in range(ii + 1, self.n): - thisRho, path = fastdtw.fastdtw(self._data[ii], self._data[jj]) - self.rho[ii, jj] = thisRho - self.rho[jj, ii] = self.rho[ii, jj] - self.rho = self.rho / np.nanmax(self.rho) - for ii in range(0, self.n): - self.rho[ii,ii] = 1. - except ImportError: - print("This requires fastdtw package.") - return self.rho - - # it does not have to be overridden in non-abstract derived classes. - def plot(self): - #for (cnt, s) in enumerate(self.tickers): - # plot(self.data[cnt], grid = True, label=s) - #plt.legend() - #plt.title("Evolution of the adjusted closing price") - #plt.show() - self.get_covariance() - self.get_similarity_matrix() - print("Top: a similarity measure. Bottom: covariance matrix.") - plt.subplot(211) - plt.imshow(self.rho) - plt.subplot(212) - plt.imshow(self.cov) - plt.show() \ No newline at end of file diff --git a/qiskit/finance/data_providers/drivers/algorithminput.py b/qiskit/finance/data_providers/drivers/algorithminput.py deleted file mode 100644 index b68d5e96b..000000000 --- a/qiskit/finance/data_providers/drivers/algorithminput.py +++ /dev/null @@ -1,67 +0,0 @@ -# -*- coding: utf-8 -*- - -# Copyright 2018 IBM. -# -# Licensed under the Apache License, Version 2.0 (the "License"); -# you may not use this file except in compliance with the License. -# You may obtain a copy of the License at -# -# http://www.apache.org/licenses/LICENSE-2.0 -# -# Unless required by applicable law or agreed to in writing, software -# distributed under the License is distributed on an "AS IS" BASIS, -# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -# See the License for the specific language governing permissions and -# limitations under the License. -# ============================================================================= - -from qiskit.aqua import Pluggable -from abc import abstractmethod -import copy -from qiskit.aqua import AquaError - - -class AlgorithmInput(Pluggable): - - _PROBLEM_SET = ['portfoliodiversification', 'portfoliooptimisation'] - - @abstractmethod - def __init__(self): - super().__init__() - if 'problems' not in self.configuration or len(self.configuration['problems']) <= 0: - raise AquaError('Algorithm Input missing or empty configuration problems') - - for problem in self.configuration['problems']: - if problem not in AlgorithmInput._PROBLEM_SET: - raise AquaError('Problem {} not in known problem set {}'.format(problem, AlgorithmInput._PROBLEM_SET)) - - @property - def all_problems(self): - return copy.deepcopy(self._PROBLEM_SET) - - @property - def problems(self): - """ - Gets the set of problems that this input form supports - """ - return self.configuration.problems - - @abstractmethod - def to_params(self): - """ - Convert the derived algorithminput class fields to a dictionary where the values are in a - form that can be saved to json - Returns: - Dictionary of input fields - """ - raise NotImplementedError() - - @abstractmethod - def from_params(self, params): - """ - Load the dictionary into the algorithminput class fields. This dictionary being that as - created by to_params() - Args: - params: A dictionary as originally created by to_params() - """ - raise NotImplementedError() diff --git a/qiskit/finance/data_providers/drivers/dataondemand/README.md b/qiskit/finance/data_providers/drivers/dataondemand/README.md deleted file mode 100644 index 836eb7f04..000000000 --- a/qiskit/finance/data_providers/drivers/dataondemand/README.md +++ /dev/null @@ -1,14 +0,0 @@ -# Qiskit Finance - -## Stock market data driver for NASDAQ Data on Demand - -NASDAQ is a major vendor of stock market data. It provides data not only for NASDAQ -issues, but also for NYSE etc. - -This driver requires Data on Demand API Token. - -## Example query - -The data are obtained by running a query through the REST API. -``` -``` diff --git a/qiskit/finance/data_providers/drivers/dataondemand/__init__.py b/qiskit/finance/data_providers/drivers/dataondemand/__init__.py deleted file mode 100644 index 682ce312d..000000000 --- a/qiskit/finance/data_providers/drivers/dataondemand/__init__.py +++ /dev/null @@ -1,21 +0,0 @@ -# -*- coding: utf-8 -*- - -# Copyright 2018 IBM. -# -# Licensed under the Apache License, Version 2.0 (the "License"); -# you may not use this file except in compliance with the License. -# You may obtain a copy of the License at -# -# http://www.apache.org/licenses/LICENSE-2.0 -# -# Unless required by applicable law or agreed to in writing, software -# distributed under the License is distributed on an "AS IS" BASIS, -# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -# See the License for the specific language governing permissions and -# limitations under the License. -# ============================================================================= - -from .dataondemanddriver import DataOnDemandDriver - -__all__ = ['DataOnDemandDriver', - 'StockMarket'] diff --git a/qiskit/finance/data_providers/drivers/dataondemand/dataondemanddriver.py b/qiskit/finance/data_providers/drivers/dataondemand/dataondemanddriver.py deleted file mode 100644 index 6ef8e50d0..000000000 --- a/qiskit/finance/data_providers/drivers/dataondemand/dataondemanddriver.py +++ /dev/null @@ -1,156 +0,0 @@ -# -*- coding: utf-8 -*- - -# Copyright 2018 IBM. -# -# Licensed under the Apache License, Version 2.0 (the "License"); -# you may not use this file except in compliance with the License. -# You may obtain a copy of the License at -# -# http://www.apache.org/licenses/LICENSE-2.0 -# -# Unless required by applicable law or agreed to in writing, software -# distributed under the License is distributed on an "AS IS" BASIS, -# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -# See the License for the specific language governing permissions and -# limitations under the License. -# ============================================================================= - -from qiskit.aqua.drivers import BaseDriver, UnitsType -import importlib -from enum import Enum -import logging - -logger = logging.getLogger(__name__) - - -class StockMarket(Enum): - NASDAQ = 'NASDAQ' - NYSE = 'NYSE' - -class DataOnDemandDriver(BaseDriver): - """Python implementation of an NASDAQ Data on Demand driver.""" - - CONFIGURATION = { - "name": "DOD", - "description": "NASDAQ Data on Demand Driver", - "input_schema": { - "$schema": "http://json-schema.org/schema#", - "id": "dod_schema", - "type": "object", - "properties": { - STOCKMARKET: { - "type": "string", - "default": StockMarket.NASDAQ.value, - "oneOf": [ - {"enum": [ - StockMarket.NASDAQ.value, - StockMarket.NYSE.value, - ]} - ] - }, - DATATYPE: { - "type": "string", - "default": DataType.DAILYADJUSTED.value, - "oneOf": [ - {"enum": [ - DataType.DAILYADJUSTED.value, - DataType.DAILY.value, - DataType.BID.value, - DataType.ASK.value, - ]} - ] - }, - }, - } - } - - def __init__(self, - token, - tickers, - stockmarket = StockMarket.NASDAQ, - start = datetime.datetime(2016,1,1), - end = datetime.datetime(2016,1,30)): - """ - Initializer - Args: - token (str): quandl access token - tickers (str or list): tickers - stockmarket (StockMarket): LONDON, EURONEXT, or SINGAPORE - """ - if not isinstance(atoms, list) and not isinstance(atoms, str): - raise QiskitFinanceError("Invalid atom input for DOD Driver '{}'".format(atoms)) - - if isinstance(tickers, list): - self._tickers = ';'.join(tickers) - else: - self._tickers = tickers.replace('\n', ';') - self._n = len(self._tickers.split(";")) - - self.validate(locals()) - super().__init__() - self._stockmarket = stockmarket # .value? - self._token = token - self._start = start - self._end = end - - @staticmethod - def check_driver_valid(): - err_msg = 'quandl is not installed.' - try: - spec = importlib.util.find_spec('quandl') - if spec is not None: - return - except Exception as e: - logger.debug('quandl check error {}'.format(str(e))) - raise QiskitFinanceError(err_msg) from e - - raise QiskitFinanceError(err_msg) - - @classmethod - def init_from_input(cls, section): - """ - Initialize via section dictionary. - - Args: - params (dict): section dictionary - - Returns: - Driver: Driver object - """ - if section is None or not isinstance(section, dict): - raise QiskitFinanceError('Invalid or missing section {}'.format(section)) - - params = section - kwargs = {} - #for k, v in params.items(): - # if k == ExchangeDataDriver. ...: v = UnitsType(v) - # kwargs[k] = v - logger.debug('init_from_input: {}'.format(kwargs)) - return cls(**kwargs) - - def run(self): - import re - import urllib - import urllib2 - import json - url = 'https://dataondemand.nasdaq.com/api/v1/quotes' - self._data = [] - for ticker in self._tickers: - values = {'_Token' : self._token, - 'symbols' : [ticker] - 'start' : start.strftime("%Y-%m-%d'T'%H:%M:%S.%f'Z'") , - 'end' : end.strftime("%Y-%m-%d'T'%H:%M:%S.%f'Z'") , - 'next_cursor': 0 - #'start' : start.strftime("%m/%d/%Y %H:%M:%S.%f") , - #'end' : end.strftime("%m/%d/%Y %H:%M:%S.%f") , - } - request_parameters = urllib.urlencode(values) - req = urllib2.Request(url, request_parameters) - try: - response = urllib2.urlopen(req) - quotes = json.loads(response)["quotes"] - priceEvolution = [] - for q in quotes: priceEvolution.append(q["ask_price"]) - self._data.append(priceEvolution) - except: - raise QiskitFinanceError('Accessing Qiskit failed') diff --git a/qiskit/finance/data_providers/drivers/exchangedata/README.md b/qiskit/finance/data_providers/drivers/exchangedata/README.md deleted file mode 100644 index 31ec5e883..000000000 --- a/qiskit/finance/data_providers/drivers/exchangedata/README.md +++ /dev/null @@ -1,22 +0,0 @@ -# Qiskit Finance - -## Stock market data driver for Exchange Data International - -Exchange Data International is a major vendor of stock-market data. See -https://www.exchange-data.com/about_us.php#edi - -For samples of the data, please see: -https://www.quandl.com/data/XSES-Singapore-Exchange-Prices -https://www.quandl.com/data/XBER-Berlin-Stock-Exchange-Prices -https://www.quandl.com/data/XPAR-Euronext-Paris-Stock-Prices/documentation - -This driver requires Quandl API Token. - -## Example query - -The data are obtained by running a query through quandl. See: -https://docs.quandl.com/docs/parameters-2#section-times-series-parameters -for details. - -``` -``` diff --git a/qiskit/finance/data_providers/drivers/exchangedata/__init__.py b/qiskit/finance/data_providers/drivers/exchangedata/__init__.py deleted file mode 100644 index 26e0bf76f..000000000 --- a/qiskit/finance/data_providers/drivers/exchangedata/__init__.py +++ /dev/null @@ -1,21 +0,0 @@ -# -*- coding: utf-8 -*- - -# Copyright 2018 IBM. -# -# Licensed under the Apache License, Version 2.0 (the "License"); -# you may not use this file except in compliance with the License. -# You may obtain a copy of the License at -# -# http://www.apache.org/licenses/LICENSE-2.0 -# -# Unless required by applicable law or agreed to in writing, software -# distributed under the License is distributed on an "AS IS" BASIS, -# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -# See the License for the specific language governing permissions and -# limitations under the License. -# ============================================================================= - -from .exchangedatadriver import ExchangeDataDriver, StockMarket - -__all__ = ['ExchangeDataDriver', - 'StockMarket'] diff --git a/qiskit/finance/data_providers/drivers/exchangedata/exchangedatadriver.py b/qiskit/finance/data_providers/drivers/exchangedata/exchangedatadriver.py deleted file mode 100644 index b2458b165..000000000 --- a/qiskit/finance/data_providers/drivers/exchangedata/exchangedatadriver.py +++ /dev/null @@ -1,138 +0,0 @@ -# -*- coding: utf-8 -*- - -# Copyright 2018 IBM. -# -# Licensed under the Apache License, Version 2.0 (the "License"); -# you may not use this file except in compliance with the License. -# You may obtain a copy of the License at -# -# http://www.apache.org/licenses/LICENSE-2.0 -# -# Unless required by applicable law or agreed to in writing, software -# distributed under the License is distributed on an "AS IS" BASIS, -# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -# See the License for the specific language governing permissions and -# limitations under the License. -# ============================================================================= - -from qiskit.aqua.drivers import BaseDriver, UnitsType -import importlib -from enum import Enum -import logging - -logger = logging.getLogger(__name__) - - -class StockMarket(Enum): - LONDON = 'XLON' - EURONEXT = 'XPAR' - SINGAPORE = 'XSES' - -class ExchangeDataDriver(BaseDriver): - """Python implementation of an Exchange Data driver.""" - - CONFIGURATION = { - "name": "EDI", - "description": "Exchange Data International Driver", - "input_schema": { - "$schema": "http://json-schema.org/schema#", - "id": "edi_schema", - "type": "object", - "properties": { - STOCKMARKET: { - "type": "string", - "default": StockMarket.LONDON.value, - "oneOf": [ - {"enum": [ - StockMarket.LONDON.value, - StockMarket.EURONEXT.value, - StockMarket.SINGAPORE.value, - ]} - ] - }, - DATATYPE: { - "type": "string", - "default": DataType.LONDON.value, - "oneOf": [ - {"enum": [ - DataType.DAILYADJUSTED.value, - DataType.DAILY.value, - ]} - ] - }, - }, - } - } - - def __init__(self, - token, - tickers, - stockmarket = StockMarket.LONDON, - start = datetime.datetime(2016,1,1), - end = datetime.datetime(2016,1,30)): - """ - Initializer - Args: - token (str): quandl access token - tickers (str or list): tickers - stockmarket (StockMarket): LONDON, EURONEXT, or SINGAPORE - """ - if not isinstance(atoms, list) and not isinstance(atoms, str): - raise QiskitFinanceError("Invalid atom input for PYQUANTE Driver '{}'".format(atoms)) - - if isinstance(tickers, list): - tickers = ';'.join(tickers) - else: - tickers = tickers.replace('\n', ';') - self._n = len(self._tickers.split(";")) - - self.validate(locals()) - super().__init__() - self._stockmarket = stockmarket # .value? - self._token = token - self._tickers = tickers - self._start = start - self._end = end - - @staticmethod - def check_driver_valid(): - err_msg = 'quandl is not installed.' - try: - spec = importlib.util.find_spec('quandl') - if spec is not None: - return - except Exception as e: - logger.debug('quandl check error {}'.format(str(e))) - raise QiskitFinanceError(err_msg) from e - - raise QiskitFinanceError(err_msg) - - @classmethod - def init_from_input(cls, section): - """ - Initialize via section dictionary. - - Args: - params (dict): section dictionary - - Returns: - Driver: Driver object - """ - if section is None or not isinstance(section, dict): - raise QiskitFinanceError('Invalid or missing section {}'.format(section)) - - params = section - kwargs = {} - #for k, v in params.items(): - # if k == ExchangeDataDriver. ...: v = UnitsType(v) - # kwargs[k] = v - logger.debug('init_from_input: {}'.format(kwargs)) - return cls(**kwargs) - - def run(self): - import quandl - quandl.ApiConfig.api_key = self._token - quandl.ApiConfig.api_version = '2015-04-09' - for (cnt, s) in enumerate(self._tickers): - d = quandl.get(self._stockmarket + "/" + s, start_date=self._start, end_date=self._end) - self._data.append(d["close"]) diff --git a/qiskit/finance/data_providers/drivers/wikipedia/README.md b/qiskit/finance/data_providers/drivers/wikipedia/README.md deleted file mode 100644 index f5dc77c2f..000000000 --- a/qiskit/finance/data_providers/drivers/wikipedia/README.md +++ /dev/null @@ -1,11 +0,0 @@ -# Qiskit Finance - -## Stock market data driver for Wikipedia - -Wikipedia contains stockmarket data, that are rather reliable up until 2018. - -## Example query - -The data are obtained by running a query through quandl. -``` -``` diff --git a/qiskit/finance/data_providers/drivers/wikipedia/__init__.py b/qiskit/finance/data_providers/drivers/wikipedia/__init__.py deleted file mode 100644 index 7324d1dd5..000000000 --- a/qiskit/finance/data_providers/drivers/wikipedia/__init__.py +++ /dev/null @@ -1,21 +0,0 @@ -# -*- coding: utf-8 -*- - -# Copyright 2018 IBM. -# -# Licensed under the Apache License, Version 2.0 (the "License"); -# you may not use this file except in compliance with the License. -# You may obtain a copy of the License at -# -# http://www.apache.org/licenses/LICENSE-2.0 -# -# Unless required by applicable law or agreed to in writing, software -# distributed under the License is distributed on an "AS IS" BASIS, -# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -# See the License for the specific language governing permissions and -# limitations under the License. -# ============================================================================= - -from .wikipediadriver import WikipediaDriver, StockMarket - -__all__ = ['WikipediaDriver', - 'StockMarket'] diff --git a/qiskit/finance/data_providers/drivers/wikipedia/wikipediadriver.py b/qiskit/finance/data_providers/drivers/wikipedia/wikipediadriver.py deleted file mode 100644 index e3900cd20..000000000 --- a/qiskit/finance/data_providers/drivers/wikipedia/wikipediadriver.py +++ /dev/null @@ -1,136 +0,0 @@ -# -*- coding: utf-8 -*- - -# Copyright 2018 IBM. -# -# Licensed under the Apache License, Version 2.0 (the "License"); -# you may not use this file except in compliance with the License. -# You may obtain a copy of the License at -# -# http://www.apache.org/licenses/LICENSE-2.0 -# -# Unless required by applicable law or agreed to in writing, software -# distributed under the License is distributed on an "AS IS" BASIS, -# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -# See the License for the specific language governing permissions and -# limitations under the License. -# ============================================================================= - -from qiskit.aqua.drivers import BaseDriver, UnitsType -import importlib -from enum import Enum -import logging - -logger = logging.getLogger(__name__) - - -class StockMarket(Enum): - NASDAQ = 'NASDAQ' - NYSE = 'NYSE' - -class WikipediaDriver(BaseDriver): - """Python implementation of a Wikipedia driver.""" - - CONFIGURATION = { - "name": "WIKI", - "description": "Wikipedia Driver", - "input_schema": { - "$schema": "http://json-schema.org/schema#", - "id": "edi_schema", - "type": "object", - "properties": { - STOCKMARKET: { - "type": "string", - "default": StockMarket.NASDAQ.value, - "oneOf": [ - {"enum": [ - StockMarket.NASDAQ.value, - StockMarket.NYSE.value, - ]} - ] - }, - DATATYPE: { - "type": "string", - "default": DataType.DAILYADJUSTED.value, - "oneOf": [ - {"enum": [ - DataType.DAILYADJUSTED.value, - DataType.DAILY.value, - ]} - ] - }, - }, - } - } - - def __init__(self, - token = "", - tickers, - stockmarket = StockMarket.LONDON, - start = datetime.datetime(2016,1,1), - end = datetime.datetime(2016,1,30)): - """ - Initializer - Args: - token (str): quandl access token, which is not needed, strictly speaking - tickers (str or list): tickers - stockmarket (StockMarket): NASDAQ, NYSE - """ - if not isinstance(atoms, list) and not isinstance(atoms, str): - raise QiskitFinanceError("Invalid atom input for Wikipedia Driver '{}'".format(atoms)) - - if isinstance(tickers, list): - tickers = ';'.join(tickers) - else: - tickers = tickers.replace('\n', ';') - self._n = len(self._tickers.split(";")) - - self.validate(locals()) - super().__init__() - self._stockmarket = stockmarket # .value? - self._token = token - self._tickers = tickers - self._start = start - self._end = end - - @staticmethod - def check_driver_valid(): - err_msg = 'quandl is not installed.' - try: - spec = importlib.util.find_spec('quandl') - if spec is not None: - return - except Exception as e: - logger.debug('quandl check error {}'.format(str(e))) - raise QiskitFinanceError(err_msg) from e - - raise QiskitFinanceError(err_msg) - - @classmethod - def init_from_input(cls, section): - """ - Initialize via section dictionary. - - Args: - params (dict): section dictionary - - Returns: - Driver: Driver object - """ - if section is None or not isinstance(section, dict): - raise QiskitFinanceError('Invalid or missing section {}'.format(section)) - - params = section - kwargs = {} - #for k, v in params.items(): - # if k == ExchangeDataDriver. ...: v = UnitsType(v) - # kwargs[k] = v - logger.debug('init_from_input: {}'.format(kwargs)) - return cls(**kwargs) - - def run(self): - import quandl - quandl.ApiConfig.api_key = self._token - quandl.ApiConfig.api_version = '2015-04-09' - for (cnt, s) in enumerate(self._tickers): - d = quandl.get("WIKI/" + s, start_date=self._start, end_date=self._end) - self._data.append(d["close"]) diff --git a/qiskit/finance/data_providers/time_series.ipynb b/qiskit/finance/data_providers/time_series.ipynb index bb6641b93..8ef7b99a2 100644 --- a/qiskit/finance/data_providers/time_series.ipynb +++ b/qiskit/finance/data_providers/time_series.ipynb @@ -11,7 +11,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# _*Qiskit Finance: Loading Time Series Data*_\n", + "# _*Qiskit Finance: Loading and Processing Stock-Market Time-Series Data*_\n", "\n", "The latest version of this notebook is available on https://github.com/qiskit/qiskit-tutorial.\n", "\n", @@ -33,7 +33,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 17, "metadata": { "scrolled": true }, @@ -41,22 +41,139 @@ "source": [ "%matplotlib inline\n", "from qiskit.aqua.translators.data_providers import *\n", - "from qiskit.aqua.translators.data_providers.wikipediadataprovider import StockMarket\n", "import warnings\n", "warnings.filterwarnings(\"ignore\", category=DeprecationWarning)\n", - "import datetime" + "import datetime\n", + "import matplotlib.pyplot as plt\n", + "from pandas.plotting import register_matplotlib_converters\n", + "register_matplotlib_converters()" ] }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "stocks = [\"GOOG\", \"AAPL\"]\n", + "from qiskit.aqua.translators.data_providers.wikipediadataprovider import StockMarket\n", + "wiki = WikipediaDataProvider(token = \"\",\n", + " tickers = stocks,\n", + " stockmarket = StockMarket.NASDAQ.value,\n", + " start = datetime.datetime(2016,1,1),\n", + " end = datetime.datetime(2016,1,30))\n", + "wiki.run()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Once the data are loaded, you can run a variety of algorithms on those to aggregate the data. Notably, you can compute the covariance matrix or a variant, which would consider alternative time-series similarity measures based on dynamic time warping (DTW). In DTW, changes that vary in speed, e.g., one stock's price following another stock's price with a small delay, can be accommodated." + ] + }, + { + "cell_type": "code", + "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Evolution of the stock price:\n", + "A time-series similarity measure:\n", + "[[1.00000000e+00 8.44268222e-05]\n", + " [8.44268222e-05 1.00000000e+00]]\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A covariance matrix:\n", + "[[269.60118129 25.42252332]\n", + " [ 25.42252332 7.86304499]]\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "if wiki._n <= 1: \n", + " raise Exception(\"Not enough data to plot covariance or time-series similarity. Please use at least two tickers.\")\n", + "\n", + "rho = wiki.get_similarity_matrix()\n", + "print(\"A time-series similarity measure:\")\n", + "print(rho)\n", + "#plt.subplot(211)\n", + "plt.imshow(rho)\n", + "plt.show()\n", + "\n", + "cov = wiki.get_covariance()\n", + "print(\"A covariance matrix:\")\n", + "print(cov)\n", + "#plt.subplot(212)\n", + "plt.imshow(cov)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you wish, you can look into the internals using:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The underlying evolution of stock prices:\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ "GOOG\n", "Date\n", "2016-01-04 741.84\n", @@ -102,52 +219,19 @@ "2016-01-29 94.044912\n", "Name: Adj. Close, dtype: float64\n" ] - }, - { - "data": { - "image/png": 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\n", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "A time-series similarity measure:\n", - "[[1.00000000e+00 8.44268222e-05]\n", - " [8.44268222e-05 1.00000000e+00]]\n", - "A covariance matrix:\n", - "[[269.60118129 25.42252332]\n", - " [ 25.42252332 7.86304499]]\n" - ] - }, - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" } ], "source": [ - "wiki = WikipediaDataProvider(token = \"\",\n", - " tickers = [\"GOOG\", \"AAPL\"],\n", - " stockmarket = StockMarket.NASDAQ.value,\n", - " start = datetime.datetime(2016,1,1),\n", - " end = datetime.datetime(2016,1,30))\n", - "wiki.run()\n", - "wiki.plot()" + "print(\"The underlying evolution of stock prices:\")\n", + "for (cnt, s) in enumerate(stocks):\n", + " plt.plot(wiki._data[cnt], label=s)\n", + "plt.legend()\n", + "plt.xticks(rotation=90)\n", + "plt.show()\n", + "\n", + "for (cnt, s) in enumerate(stocks):\n", + " print(s)\n", + " print(wiki._data[cnt])" ] }, { @@ -156,22 +240,33 @@ "source": [ "### [Optional] Setup token to access recent, fine-grained time-series\n", "\n", - "If you would like to download professional data, you will have to set-up a token with one of the major providers.\n" + "If you would like to download professional data, you will have to set-up a token with one of the major providers. Let us now illustrate the data with NASDAQ Data on Demand, which can supply bid and ask prices in arbitrary resolution, as well as aggregates such as daily adjusted closing prices, for NASDAQ and NYSE issues.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you have access to NASDAQ Data on Demand you should have your own token, which you should use instead of REPLACE-ME below. \n", + "Also you should have your own means of validating NASDAQ's certificates.\n", + "If you don't you may want to run the cell below to disable the associated warnings. " + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "import urllib3\n", + "urllib3.disable_warnings(urllib3.exceptions.InsecureRequestWarning)" ] }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 13, "metadata": {}, "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/Users/jmarecek/anaconda3/envs/localqiskit/lib/python3.7/site-packages/urllib3/connectionpool.py:847: InsecureRequestWarning: Unverified HTTPS request is being made. Adding certificate verification is strongly advised. See: https://urllib3.readthedocs.io/en/latest/advanced-usage.html#ssl-warnings\n", - " InsecureRequestWarning)\n" - ] - }, { "name": "stdout", "output_type": "stream", @@ -196,15 +291,25 @@ " print(\"You need to replace REPLACE-ME with a valid token.\")" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Another major vendor of stock market data is Exchange Data International (EDI), whose feeds can be used to query emerging and frontier markets that are Africa, Asia, Far East, Latin America and Middle East, as well as the more established ones. The access again requires a valid access token to replace REPLACE-ME below.\n", + "\n", + "In the following example, we look at the prices at London Stock Exchange. " + ] + }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ + "'Cannot retrieve Exchange Data data.'\n", "You need to replace REPLACE-ME with a valid token.\n" ] } @@ -219,16 +324,17 @@ " end = datetime.datetime(2019,1,30))\n", " lse.run()\n", " lse.plot()\n", - "except QiskitFinanceError: \n", + "except QiskitFinanceError as e: \n", + " print(e)\n", " print(\"You need to replace REPLACE-ME with a valid token.\")" ] }, { - "cell_type": "code", - "execution_count": null, + "cell_type": "markdown", "metadata": {}, - "outputs": [], - "source": [] + "source": [ + "For the actual use of the data, please see the portfolio_optimization or portfolio_diversification notebooks. " + ] } ], "metadata": { diff --git a/qiskit/finance/optimization/portfolio_diversification.ipynb b/qiskit/finance/optimization/portfolio_diversification.ipynb index bcdcdca32..5b3a04b52 100644 --- a/qiskit/finance/optimization/portfolio_diversification.ipynb +++ b/qiskit/finance/optimization/portfolio_diversification.ipynb @@ -4,27 +4,41 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Portfolio diversification: classical and quantum solutions\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# _*Qiskit Finance: Portfolio diversification*_\n", + "\n", + "The latest version of this notebook is available on https://github.com/qiskit/qiskit-tutorial.\n", + "\n", + "***\n", + "### Contributors\n", + "Andrea Simonetto[1], Jakub Marecek[1], Martin Mevissen[1]\n", + "\n", + "### Affiliation\n", + "- [1]IBMQ\n", "\n", - "## Contributors\n", - "Andrea Simonetto, Jakub Marecek, Martin Mevissen; IBM Research -- Ireland\n", "\n", "## Introduction \n", "\n", "In asset management, there are broadly two approaches: active and passive investment management. Within passive investment management, there are index-tracking funds and there are approaches based on portfolio diversification, which aim at representing a portfolio with large number of assets by a smaller number of representative stocks.\n", "This notebook illustrates a portfolio diversification problem, which has recently become popular for two reasons:\n", "1. it makes it possible to mimick the performance of an index (or a similarly large set of assets) with a limited budget, at limited transaction costs. That is: traditional index-tracking may purchase all assets in the index, ideally with the same weights as in the index. This may be impractical for a number of reasons: the total of even a single round lot per asset may amount to more than the assets under management, the large scale of the index-tracking problem with integrality constraints may render the optimisation problem difficult, and the transaction costs of the frequent rebalancing to adjust the positions to the weights in the index may render the approach expensive. Thus, a popular approach is to select a portfolio of $q$ assets that represent the market with $n$ assets, where $q$ is significantly smaller than $n$, but where the portfolio replicates the behaviour of the underlying market. To determine how to group assets into $q$ clusters and how to determine which $q$ assets should represent the $q$ clusters amounts to solving a large-scale optimization problem. In the following we describe the mathematical model for the portfolio diversification problem as introduced in [Cornuejols & Tutuncu, 2006] \n", - "2. it allows for similarity measures between time-series beyond the covariance matrix. Notice that traditionally, modern portfolio theory considers the covariance matrix as measure of similarity between the assets. As such, however, covariance matrix is imperfect. Consider, for instance, a company listed both in London and New York. Although both listings should be very similar, only parts of the time series of the prices of the two listings will overlap, because of the partial overlap of the times the markets open. Instead of covariance, one ca consider, for example, dynamic time warping of [Berndt and Clifford, 1994] as a measure of similarity between two time series, which allows for the fact that for some time periods, the data are captured by only one of the time series, while for others, both time series exhibit the similarity due to the parallel evolution of the stock price.\n", + "2. it allows for similarity measures between time-series beyond the covariance matrix. Notice that traditionally, modern portfolio theory considers the covariance matrix as measure of similarity between the assets. As such, however, covariance matrix is imperfect. Consider, for instance, a company listed both in London and New York. Although both listings should be very similar, only parts of the time series of the prices of the two listings will overlap, because of the partial overlap of the times the markets open. Instead of covariance, one can consider, for example, dynamic time warping of [Berndt and Clifford, 1994] as a measure of similarity between two time series, which allows for the fact that for some time periods, the data are captured by only one of the time series, while for others, both time series exhibit the similarity due to the parallel evolution of the stock price.\n", "\n", "The overall workflow we demonstrate comprises:\n", "\n", "1. pick the ground set of assets. In our case, this is a small number of US stocks.\n", "\n", - "2. load the time series capturing the evolution of the prices of assets. In our case, this is an simplistic load of daily stock-price data from Wikipedia, whereas in a real asset management, this may come from a Reuters, Bloomberg, or similar at a much higher frequency.\n", + "2. load the time series capturing the evolution of the prices of assets. In our case, this is an simplistic load of adjusted daily closing price data from Wikipedia or Nasdaq or LSE or EuroNext, whereas in a real asset management, a much higher frequency may be considered.\n", "\n", "3. compute the pair-wise similarity among the time series. In our case, we run a linear-time approximation of the dynamic time warping, still on the classical computer.\n", "\n", - "4. compute the actual portfolio of $q$ representative assets, based on the similarity measure. This step is run twice, actually. First, we obtain a reference value by a run of an IBM solver (CPLEX) on the classical computer. Second, we run an alternative, hybrid algorithm partly on the quantum computer.\n", + "4. compute the actual portfolio of $q$ representative assets, based on the similarity measure. This step is run twice, actually. First, we obtain a reference value by a run of an IBM solver (IBM ILOG CPLEX or the Exact Eigensolver) on the classical computer. Second, we run an alternative, hybrid algorithm partly on the quantum computer.\n", "\n", "5. visualisation of the results. In our case, this is again a simplistic plot.\n", "\n", @@ -100,13 +114,13 @@ "\n", "### Construct the Ising Hamiltonian\n", "\n", - "We can now construct the Ising Hamiltonian by penalty methods (introducting a penalty coefficient $A$ for each equality constraint) as\n", + "We can now construct the Ising Hamiltonian (QUBO) by penalty methods (introducting a penalty coefficient $A$ for each equality constraint) as\n", "\n", "$$\n", "(IH) \\quad H = \\sum_{i=1}^n \\sum_{j=1}^n \\rho_{ij} x_{ij} + A\\Big( \\sum_{j=1}^n y_j - q\\Big)^2 + \\sum_{i=1}^n A\\Big( \\sum_{j=1}^n x_{ij} - 1\\Big)^2 + \\sum_{j=1}^n A (x_{jj}-y_j)^2 +\\sum_{i=1}^n \\sum_{j=1}^n A \\left(x_{ij} (1- y_j)\\right).\n", "$$\n", "\n", - "### From Hamiltonian to QP formulation \n", + "### From Hamiltonian to Quadratic Programming (QP) formulation \n", "\n", "In the vector ${\\bf z}$, the Ising Hamiltonian elements can be rewritten as follows,\n", "\n", @@ -173,45 +187,28 @@ "source": [ "## The Implementation\n", "\n", - "If everything has been installed, the following should run without any errors. \n", - "If there are errors, please refer to Installation.ipynb for details." + "First, we import the requisite modules." ] }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 7, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "localqiskit\n", - "/Users/jmarecek/anaconda3/envs/localqiskit/bin/python\n" - ] - } - ], + "outputs": [], "source": [ - "import os\n", - "print(os.environ['CONDA_DEFAULT_ENV'])\n", - "#!source activate localqiskit\n", - "#!conda list\n", - "#help(\"modules\")\n", - "# If you get errors, you can install from here using:\n", - "#!conda install -y --name localqiskit quandl\n", - "#!conda install -y -c bioconda --name localqiskit fastdtw\n", - "print(sys.executable)\n", - "\n", "# Import requisite modules\n", "import math\n", "import operator\n", "import logging\n", + "import traceback\n", "import datetime\n", "import sys\n", "import warnings\n", "warnings.filterwarnings(\"error\") \n", + "warnings.filterwarnings(\"ignore\", category=DeprecationWarning)\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", "\n", "# Import Qiskit packages\n", "warnings.filterwarnings('ignore')\n", @@ -220,7 +217,6 @@ "from qiskit.aqua import QuantumInstance\n", "from qiskit.aqua import Operator, run_algorithm\n", "from qiskit.aqua.input import EnergyInput\n", - "from qiskit.aqua.translators.ising import portfolio\n", "from qiskit.aqua.algorithms import VQE, QAOA, ExactEigensolver\n", "from qiskit.aqua.components.optimizers import COBYLA\n", "from qiskit.aqua.components.variational_forms import RY\n", @@ -228,87 +224,85 @@ "from qiskit.aqua._logging import set_logging_config, build_logging_config\n", "# set_logging_config(build_logging_config(logging.DEBUG)) # choose INFO, DEBUG to see the log\n", "\n", - "from qiskit.aqua.translators.ising import portfoliodiv" + "# The data providers of stock-market data\n", + "from qiskit.aqua.translators.data_providers import *\n", + "from qiskit.aqua.translators.data_providers.wikipediadataprovider import StockMarket\n", + "from qiskit.aqua.translators.ising import portfoliodiversification" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "We then initialize the variables" + "Next, we download price data for two stocks and compute their pair-wise similarity matrix (dynamic time warping distance normalised to (0,1] by taking the reciprocal). If this fails, e.g., due to your being offline or exeeding the daily limit for accesses to the stock-market data, we consider a constant matrix instead." ] }, { "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [], + "execution_count": 20, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Cannot load real data. This may happen with over 50 accesses per day, for instnace. Using a constant rho.\n" + ] + } + ], "source": [ - "# Initialize the problem by defining the parameters\n", + "# Generate a pairwise time-series similarity matrix\n", + "stocks = [\"GOOG\", \"AAPL\"]\n", + "n = len(stocks)\n", + "rho = np.ones((n,n))\n", + "rho[0,1] = 0.8\n", + "rho[1,0] = 0.8\n", "\n", - "n = 2 # Number of inner variables\n", - "q = 1 # Number of clusters, q less or equal than n" + "try:\n", + " wiki = WikipediaDataProvider(token = \"\",\n", + " tickers = stocks,\n", + " stockmarket = StockMarket.NASDAQ.value,\n", + " start = datetime.datetime(2016,1,1),\n", + " end = datetime.datetime(2016,1,30))\n", + " wiki.run()\n", + " rho = wiki.get_similarity_matrix()\n", + "except Exception as e:\n", + " print(\"Cannot load real data. This may happen with over 50 accesses per day, for instnace. Using a constant rho.\")\n", + "\n", + "# Actually, we consider the additive inverse to invert the direction of optimisation. \n", + "rho = -1 * rho" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "We define get data either by randomly placing the assets in a 2-D plane and computing the distance between them (the closer they are in this plane, the more similar they are), or by actually downloading stock-market price data and computing the dynamic time warping distance and normalising it to (0,1]. Either way, we obtain the `rho` matrix. " + "Now we decide on the number of clusters. This has to be smaller than the number of stocks we have loaded." ] }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 22, "metadata": {}, "outputs": [], "source": [ - "# The code for generating a random rho or obtain stock-market data\n", - "\n", - "from qiskit.aqua.input.portfoliodata import *" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[-1. -0.83591861]\n", - " [-0.83591861 -1. ]]\n" - ] - } - ], - "source": [ - "# Initialize the problem by randomly generating the similarity matrix rho\n", - "\n", - "data = RandomData(n)\n", - "xc,yc,rho = data.generate_instance()\n", - "try:\n", - " data = RealData(n, plots=True)\n", - " #data = RealData(n, plots=False)\n", - "except:\n", - " print(\"Cannot load real data, possibly due to issues with pandas.\")\n", - "print(rho)" + "q = 1 # q less or equal than wiki._n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Classical solution using IBM CPLEX\n", + "## Classical solution using IBM ILOG CPLEX\n", "\n", "For a classical solution, we use IBM CPLEX. CPLEX is able to find the exact solution of this problem. We first define a ClassicalOptimizer class that encodes the problem in a way that CPLEX can solve, and then instantiate the class and solve it. \n" ] }, { "cell_type": "code", - "execution_count": 39, + "execution_count": 23, "metadata": {}, "outputs": [], "source": [ @@ -395,7 +389,7 @@ }, { "cell_type": "code", - "execution_count": 40, + "execution_count": 24, "metadata": {}, "outputs": [ { @@ -409,7 +403,7 @@ ], "source": [ "# Instantiate the classical optimizer class\n", - "classical_optimizer = ClassicalOptimizer(rho,n,q)\n", + "classical_optimizer = ClassicalOptimizer(rho, n, q)\n", "\n", "# Compute the number of feasible solutions:\n", "print('Number of feasible combinations= ' + str(classical_optimizer.compute_allowed_combinations()))\n", @@ -420,7 +414,7 @@ }, { "cell_type": "code", - "execution_count": 41, + "execution_count": 25, "metadata": {}, "outputs": [], "source": [ @@ -446,11 +440,9 @@ " ix = ii % n\n", " plt.plot([xc[ix], xc[iy]], [yc[ix], yc[iy]], 'C2')\n", "\n", - " plt.title(title_str+' cost = ' + str(int(C * 100) / 100.))\n", + " plt.title(title_str +' cost = ' + str(int(C * 100) / 100.))\n", " plt.show()\n", - " \n", - "\n", - "# Eventually, you can runvisualize_solution(xc, yc, x, classical_cost, n, q, 'Classical')" + " " ] }, { @@ -464,101 +456,75 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Quantum solution using IBM-Q simulator\n", - "\n", - "For the quantum solution, we use Qskit. We first define a class QuantumOptimizer that encodes the quantum approach to solve the problem and then we instantiate it and solve it. We define the following methods inside the class:\n", - "- `binary_representation` : encodes the problem $(M)$ into a the Ising Hamiltonian QP (that's basically linear algebra);\n", - "- `construct_hamiltonian` : constructs the Ising Hamiltonian in terms of the $Z$ basis;\n", - "- `check_hamiltonian` : makes sure that the Ising Hamiltonian is correctly encoded in the $Z$ basis: to do this, it solves a eigenvalue-eigenvector problem for a symmetric matrix of dimension $2^N \\times 2^N$. For the problem at hand $n=3$, that is $N = 12$ seems the limit; \n", - "- `vqe_solution` : solves the problem $(M)$ via VQE by using the SPSA solver (with default parameters);\n", - "- `_q_solution` : internal routine to represent the solution in a usable format.\n" + "## Quantum Computing with IBM Q\n", + "\n", + "For the quantum solution, we use Qiskit. We first define a class QuantumOptimizer that encodes the quantum approach to solve the problem and then we instantiate it and solve it. We define the following methods inside the class:\n", + "- `construct_hamiltonian` : constructs the Ising Hamiltonian in terms of the $Z$ basis using the Ising translator provided in Qiskit Aqua;\n", + "- `exact_solution` : to make sure that the Ising Hamiltonian is correctly encoded in the $Z$ basis, we can compute its eigendecomposition classicaly, i.e., considering a symmetric matrix of dimension $2^N \\times 2^N$. For the problem at hand $n=3$, that is $N = 12$ seems the limit for many laptops; \n", + "- `vqe_solution` : solves the problem $(M)$ via the variational quantum eigensolver (VQE);\n", + "- `qaoa_solution` : solves the problem $(M)$ via a Quantum Approximate Optimization Algorithm (QAOA)." ] }, { "cell_type": "code", - "execution_count": 42, + "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "class QuantumOptimizer:\n", "\n", - " def __init__(self, rho,n,q,max_trials=1000):\n", + " def __init__(self, rho, n, q):\n", "\n", " self.rho = rho\n", " self.n = n\n", " self.q = q\n", - " self.max_trials = max_trials\n", "\n", " def construct_hamiltonian(self):\n", + " return portfoliodiversification.get_portfoliodiversification_qubitops(self.rho, self.n, self.q)\n", "\n", - " return portfoliodiv.get_portfoliodiversification_qubitops(self.rho, self.n, self.q, self.max_trials)\n", - "\n", - " def check_hamiltonian(self):\n", - "\n", - " Op = self.construct_hamiltonian()\n", - " qubitOp, offset = Op, 0\n", + " # Obtains the least eigenvalue of the Hamiltonian classically\n", + " def exact_solution(self):\n", + " qubitOp = self.construct_hamiltonian()\n", " algo_input = EnergyInput(qubitOp)\n", - "\n", - " # Making the Hamiltonian in its full form and getting the lowest eigenvalue and eigenvector\n", - "\n", " algorithm_cfg = {\n", " 'name': 'ExactEigensolver',\n", " }\n", - "\n", " params = {\n", " 'problem': {'name': 'ising'},\n", " 'algorithm': algorithm_cfg\n", " }\n", " result = run_algorithm(params, algo_input)\n", - "\n", - " quantum_solution = self._q_solution(result['eigvecs'][0],self.n*(self.n+1))\n", - " ground_level = result['energy'] + offset\n", - "\n", - " return quantum_solution, ground_level\n", + " return self.decode_result(result)\n", "\n", " def vqe_solution(self):\n", - "\n", " qubitOp = self.construct_hamiltonian()\n", - " algo_input = EnergyInput(qubitOp)\n", - "\n", " backend = BasicAer.get_backend('statevector_simulator')\n", " seed = 50\n", " cobyla = COBYLA()\n", " cobyla.set_options(maxiter=250)\n", - " ry = RY(qubitOp.num_qubits, depth=3, entanglement='full')\n", + " ry = RY(qubitOp.num_qubits, depth=5, entanglement='full')\n", " vqe = VQE(qubitOp, ry, cobyla, 'matrix')\n", " vqe.random_seed = seed\n", " quantum_instance = QuantumInstance(backend=backend, seed=seed, seed_mapper=seed)\n", - " result = vqe.run(algo_input)\n", - "\n", - " #quantum_solution = self._q_solution(result['eigvecs'][0], self.n * (self.n + 1))\n", - " quantum_solution_dict = result['eigvecs'][0]\n", - "\n", - " q_s = max(quantum_solution_dict.items(), key=operator.itemgetter(1))[0]\n", - " quantum_solution= [int(chars) for chars in q_s]\n", - " quantum_solution = np.flip(quantum_solution, axis=0)\n", - "\n", - " #_,_,_,level = self.binary_representation(x_sol=quantum_solution)\n", - " return quantum_solution_dict, quantum_solution\n", - "\n", - " def _q_solution(self, v, N):\n", - "\n", - " index_value = [x for x in range(len(v)) if v[x] == max(v)][0]\n", - " string_value = \"{0:b}\".format(index_value)\n", - "\n", - " while len(string_value)\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;31m# Check if the binary representation is correct\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mQ\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mg\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mc\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mquantum_cost\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mquantum_optimizer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvqe_solution\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 3\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0msol\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mclassical_cost\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mClassicalOptimizer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcplex_solution\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;32m\u001b[0m in \u001b[0;36mvqe_solution\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 48\u001b[0m \u001b[0mvqe\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrandom_seed\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mseed\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 49\u001b[0m \u001b[0mquantum_instance\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mQuantumInstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbackend\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mbackend\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mseed\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mseed\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mseed_mapper\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mseed\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 50\u001b[0;31m \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mvqe\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0malgo_input\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 51\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 52\u001b[0m \u001b[0;31m#quantum_solution = self._q_solution(result['eigvecs'][0], self.n * (self.n + 1))\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/qiskit_aqua/algorithms/quantum_algorithm.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self, quantum_instance, **kwargs)\u001b[0m\n\u001b[1;32m 101\u001b[0m \u001b[0mquantum_instance\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_config\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 102\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_quantum_instance\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mquantum_instance\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 103\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_run\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 104\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 105\u001b[0m \u001b[0;34m@\u001b[0m\u001b[0mabstractmethod\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/qiskit_aqua/algorithms/adaptive/vqe/vqe.py\u001b[0m in \u001b[0;36m_run\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 266\u001b[0m \u001b[0mDictionary\u001b[0m \u001b[0mof\u001b[0m \u001b[0mresults\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 267\u001b[0m \"\"\"\n\u001b[0;32m--> 268\u001b[0;31m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_quantum_instance\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mis_statevector\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_operator_mode\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'matrix'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 269\u001b[0m logger.warning('Qasm simulation does not work on {} mode, changing '\n\u001b[1;32m 270\u001b[0m 'the operator_mode to \"paulis\"'.format(self._operator_mode))\n", - "\u001b[0;31mAttributeError\u001b[0m: 'EnergyInput' object has no attribute 'is_statevector'" - ] - } - ], + "outputs": [], "source": [ - "# Check if the binary representation is correct\n", - "Q,g,c,quantum_cost = quantum_optimizer.vqe_solution()\n", - "\n", - "sol, classical_cost = ClassicalOptimizer.cplex_solution()\n", - "\n", - "print(quantum_cost, classical_cost)\n", - "if np.abs(quantum_cost - classical_cost)<0.01:\n", - " print('Binary formulation is correct')\n", - "else: print('Error in the binary formulation')" + "# Check if the binary representation is correct. This requires CPLEX\n", + "\n", + "try: \n", + " import cplex\n", + " warnings.filterwarnings('ignore')\n", + " quantum_solution, quantum_cost = quantum_optimizer.exact_solution()\n", + " classical_solution, classical_cost = classical_optimizer.cplex_solution()\n", + " print(quantum_cost, classical_cost)\n", + " if np.abs(quantum_cost - classical_cost) < 0.01:\n", + " print('Binary formulation is correct')\n", + " else: print('Error in the formulation of the Hamiltonian')\n", + "except: None" ] }, { @@ -639,17 +592,26 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 29, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0 1 0 1 0 1]\n" + ] + } + ], "source": [ - "ground_state, ground_level = quantum_optimizer.check_hamiltonian()\n", - "\n", - "print(ground_level,classical_cost)\n", + "ground_state, ground_level = quantum_optimizer.exact_solution()\n", "print(ground_state)\n", - "if np.abs(ground_level - classical_cost)<0.01:\n", + "\n", + "try:\n", + " if np.abs(ground_level - classical_cost)<0.01:\n", " print('Ising Hamiltonian in Z basis is correct')\n", - "else: print('Error in the Ising Hamiltonian formulation')" + " else: print('Error in the Ising Hamiltonian formulation')\n", + "except: None" ] }, { @@ -663,13 +625,28 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 30, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0 1 0 1 0 1]\n", + "VQE produces the same solution as the exact eigensolver.\n" + ] + } + ], "source": [ - "quantum_dictionary, quantum_solution, quantum_cost = quantum_optimizer.vqe_solution()\n", + "warnings.filterwarnings('ignore')\n", + "vqe_state, vqe_level = quantum_optimizer.vqe_solution()\n", + "print(vqe_state)\n", "\n", - "print(quantum_solution,quantum_cost)" + "try:\n", + " if np.linalg.norm(ground_state - vqe_state)<0.01:\n", + " print('VQE produces the same solution as the exact eigensolver.')\n", + " else: print('VQE does not produce the same solution as the exact eigensolver, but that is to be expected.')\n", + "except: None" ] }, { @@ -682,21 +659,45 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 31, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ - "visualize_solution(xc, yc, quantum_solution, quantum_cost, n, q, 'Quantum')\n", - "visualize_solution(xc, yc, x, classical_cost, n, q, 'Classical')" + "xc, yc = wiki.get_coordinates()\n", + "visualize_solution(xc, yc, ground_state, ground_level, n, q, 'Classical')\n", + "visualize_solution(xc, yc, vqe_state, vqe_level, n, q, 'VQE')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Solution shows the selected stocks via the stars and in green the links (via similarities) with other stocks that are represented in the fund by the linked stock. Note that in this particular case, we can find the optimal solution of the QP formulation, which happens to coincide with the optimal solution of the ILP.\n", - "\n", - "Keep in mind that VQE is an heuristic working on the QP formulation of the Ising Hamiltonian, though. For suitable choices of A, local optima of the QP formulation will be feasible solutions to the ILP. While for some small instances, as above, we can find optimal solutions of the QP formulation which coincide with optima of the ILP, finding optimal solutions of the ILP is harder than finding local optima of the QP formulation, in general. Even within the VQE, one may provide stronger guarantees, for specific variational forms (trial wave functions). " + "Solution shows the selected stocks via the stars and in green the links (via similarities) with other stocks that are represented in the fund by the linked stock. Keep in mind that VQE is an heuristic working on the QP formulation of the Ising Hamiltonian, though. For suitable choices of A, local optima of the QP formulation will be feasible solutions to the ILP. While for some small instances, as above, we can find optimal solutions of the QP formulation which coincide with optima of the ILP, finding optimal solutions of the ILP is harder than finding local optima of the QP formulation, in general. Even within the VQE, one may provide stronger guarantees, for specific variational forms (trial wave functions). " ] }, { From 558b518f433ba6cd5dfa1e29d82f3596d7070b62 Mon Sep 17 00:00:00 2001 From: stefan-woerner Date: Tue, 23 Apr 2019 11:12:34 +0200 Subject: [PATCH 068/116] update qgan tutorials --- ...ans_for_loading_random_distributions.ipynb | 17 +++--- .../qgan_option_pricing.ipynb | 54 +++++++++++++------ 2 files changed, 50 insertions(+), 21 deletions(-) diff --git a/qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb b/qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb index 14ed3f906..066e9d478 100644 --- a/qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb +++ b/qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb @@ -1,5 +1,12 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -22,7 +29,7 @@ "\n", "The aim of the qGAN training is to generate a state $\\lvert g_{\\theta}\\rangle$ where $p_{\\theta}^{j}$, for $j\\in \\left\\{0, \\ldots, {2^n-1} \\right\\}$, describe a probability distribution that is close to the distribution underlying the training data $X=\\left\\{x^0, \\ldots, x^{k-1} \\right\\}$.\n", "\n", - "For further details please refer to Quantum Generative Adversarial Networks for Learning and Loading Random Distributions. Zoufal, Lucchi, Woerner. 2019." + "For further details please refer to
Quantum Generative Adversarial Networks for Learning and Loading Random Distributions. Zoufal, Lucchi, Woerner. 2019." ] }, { @@ -49,10 +56,8 @@ "import matplotlib\n", "matplotlib.use('TkAgg')\n", "import matplotlib.pyplot as plt\n", - "\n", "%matplotlib inline\n", "\n", - "\n", "import time\n", "\n", "start = time.time()\n", @@ -1521,9 +1526,9 @@ ], "metadata": { "kernelspec": { - "display_name": "QiskitDevenv", + "display_name": "qiskit_master", "language": "python", - "name": "qiskitdevenv" + "name": "qiskit_master" }, "language_info": { "codemirror_mode": { @@ -1535,7 +1540,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.3" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/qiskit/finance/machine_learning/qgan_option_pricing.ipynb b/qiskit/finance/machine_learning/qgan_option_pricing.ipynb index d21327bbe..606ccde25 100644 --- a/qiskit/finance/machine_learning/qgan_option_pricing.ipynb +++ b/qiskit/finance/machine_learning/qgan_option_pricing.ipynb @@ -1,5 +1,12 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -16,28 +23,34 @@ "- [2]ETH Zurich\n", "\n", "### Introduction\n", - "In this notebook, we discuss how a Quantum Machine Learning Algorithm, namely a quantum Generative Adversarial Network (qGAN), can facilitate the pricing of a European call option. More specifically, a qGAN can be trained such that a quantum circuit models the spot price of an asset underlying a European call option. The resulting model can then be integrated into a Quantum Amplitude Estimation based algorithm to evaluate the expected payoff - see [European Call Option Pricing](../../aqua/finance/european_call_option_pricing.ipynb).
\n", - "For further details on learning and loading random distributions by training a qGAN please refer to Quantum Generative Adversarial Networks for Learning and Loading Random Distributions. Zoufal, Lucchi, Woerner. 2019." + "In this notebook, we discuss how a Quantum Machine Learning Algorithm, namely a quantum Generative Adversarial Network (qGAN), can facilitate the pricing of a European call option. More specifically, a qGAN can be trained such that a quantum circuit models the spot price distribution of an asset underlying a European call option. The resulting model can then be integrated into a Quantum Amplitude Estimation based algorithm to evaluate the expected payoff, see [European Call Option Pricing](../../finance/simulation/european_call_option_pricing.ipynb).
\n", + "\n", + "For a general introduction on how to train a qGAN, see [qGANs for Loading Random Distributions](../../aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb).
\n", + "\n", + "For further details on learning and loading random distributions by training a qGAN please refer to
Quantum Generative Adversarial Networks for Learning and Loading Random Distributions. Zoufal, Lucchi, Woerner. 2019." ] }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "metadata": {}, "outputs": [ { - "name": "stderr", - "output_type": "stream", - "text": [ - "/Users/ouf/anaconda3/envs/QiskitDevenv/lib/python3.7/site-packages/qiskit_terra-0.8.0-py3.7-macosx-10.7-x86_64.egg/qiskit/circuit/variabletable.py:10: DeprecationWarning: Using or importing the ABCs from 'collections' instead of from 'collections.abc' is deprecated, and in 3.8 it will stop working\n", - " from collections import MutableMapping\n" + "ename": "ImportError", + "evalue": "cannot import name 'UnivariateVariationalDistribution'", + "output_type": "error", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[1;31mImportError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m\u001b[0m\n\u001b[0;32m 8\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0maqua\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0malgorithms\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mAmplitudeEstimation\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 9\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0maqua\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcomponents\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0muncertainty_problems\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mEuropeanCallExpectedValue\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 10\u001b[1;33m \u001b[1;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0maqua\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcomponents\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0muncertainty_models\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mUnivariateVariationalDistribution\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mNormalDistribution\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 11\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0maqua\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcomponents\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvariational_forms\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mRY\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 12\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;31mImportError\u001b[0m: cannot import name 'UnivariateVariationalDistribution'" ] } ], "source": [ - "#!/usr/bin/env python\n", - "# coding: utf-8\n", - "from __future__ import absolute_import, division, print_function\n", + "# #!/usr/bin/env python\n", + "# # coding: utf-8\n", + "# from __future__ import absolute_import, division, print_function\n", "\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", @@ -70,6 +83,7 @@ "source": [ "# Set upper and lower data values\n", "bounds = np.array([0.,7.])\n", + "\n", "# Set number of qubits used in the uncertainty model\n", "num_qubits = [3]\n", "\n", @@ -80,10 +94,13 @@ "\n", "# Set variational form\n", "var_form = RY(int(np.sum(num_qubits)), depth=1, entangler_map=entangler_map, entanglement_gate='cz')\n", + "\n", "# Load the trained circuit parameters\n", "g_params = [0.29399714, 0.38853322, 0.9557694, 0.07245791, 6.02626428, 0.13537225]\n", + "\n", "# Set an initial state for the generator circuit\n", "init_dist = NormalDistribution(int(sum(num_qubits)), mu=1., sigma=1., low=bounds[0], high=bounds[1])\n", + "\n", "# Set generator circuit\n", "g_circuit = UnivariateVariationalDistribution(int(sum(num_qubits)), var_form, g_params,\n", " initial_distribution=init_dist, low=bounds[0], high=bounds[1])\n", @@ -115,7 +132,7 @@ "x = uncertainty_model.values\n", "y = uncertainty_model.probabilities\n", "plt.bar(x, y, width=0.2)\n", - "plt.xticks(x, size=15, rotation=90)\n", + "plt.xticks(x, size=15)\n", "plt.yticks(size=15)\n", "plt.grid()\n", "plt.xlabel('Spot Price at Maturity $S_T$ (\\$)', size=15)\n", @@ -168,13 +185,20 @@ "print('Estimated value:\\t%.4f' % result['estimation'])\n", "print('Probability: \\t%.4f' % result['max_probability'])" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { "kernelspec": { - "display_name": "QiskitDevenv", + "display_name": "qiskit_master", "language": "python", - "name": "qiskitdevenv" + "name": "qiskit_master" }, "language_info": { "codemirror_mode": { @@ -186,7 +210,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.3" + "version": "3.6.1" } }, "nbformat": 4, From f3fb863a5be77fd84dfa780269b7c7d5829a5d45 Mon Sep 17 00:00:00 2001 From: stefan-woerner Date: Tue, 23 Apr 2019 11:12:53 +0200 Subject: [PATCH 069/116] update qiskit finance index page --- qiskit/finance/qiskit_finance.ipynb | 1 - qiskit/finance/simulation/credit_risk_analysis.ipynb | 4 ++-- .../simulation/european_call_option_pricing.ipynb | 2 +- qiskit/finance/simulation/option_pricing.ipynb | 12 ++++++------ 4 files changed, 9 insertions(+), 10 deletions(-) diff --git a/qiskit/finance/qiskit_finance.ipynb b/qiskit/finance/qiskit_finance.ipynb index 8cb272e63..197cb4ffd 100644 --- a/qiskit/finance/qiskit_finance.ipynb +++ b/qiskit/finance/qiskit_finance.ipynb @@ -30,7 +30,6 @@ "In this notebook we provide an overview of Qiskit Finance tutorials and tutorials from other domains which might be relevant in finance.\n", "\n", "#### Machine Learning:\n", - "- Quantum Support Vector Machine for Credit Risk Rating\n", "- Quantum Generative Adversarial Networks (qGANs) for data loading in option pricing\n", "\n", "#### Optimization:\n", diff --git a/qiskit/finance/simulation/credit_risk_analysis.ipynb b/qiskit/finance/simulation/credit_risk_analysis.ipynb index c7c70ffec..c8ec89cbe 100644 --- a/qiskit/finance/simulation/credit_risk_analysis.ipynb +++ b/qiskit/finance/simulation/credit_risk_analysis.ipynb @@ -548,7 +548,7 @@ "« ░ └───┘ └───┘ ░ " ], "text/plain": [ - "" + "" ] }, "execution_count": 12, @@ -894,7 +894,7 @@ "« └───┘ └───┘ ░ " ], "text/plain": [ - "" + "" ] }, "execution_count": 21, diff --git a/qiskit/finance/simulation/european_call_option_pricing.ipynb b/qiskit/finance/simulation/european_call_option_pricing.ipynb index b11ca0a59..464abe28f 100644 --- a/qiskit/finance/simulation/european_call_option_pricing.ipynb +++ b/qiskit/finance/simulation/european_call_option_pricing.ipynb @@ -293,7 +293,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, "metadata": {}, "outputs": [ { diff --git a/qiskit/finance/simulation/option_pricing.ipynb b/qiskit/finance/simulation/option_pricing.ipynb index b69deeaf9..ab1dff8c3 100644 --- a/qiskit/finance/simulation/option_pricing.ipynb +++ b/qiskit/finance/simulation/option_pricing.ipynb @@ -28,9 +28,9 @@ "metadata": {}, "source": [ "In this notebook we provide an overview of the available Qiskit Finance tutorials on how to use Quantum Amplitude Estimation (QAE) for option pricing. We analyze different types of options with increasing complexity, featuring:\n", - "- single asset / multi asset (basket) options\n", - "- piecewise linear payoff functions (arbitrary number of break points, possibly non-continuous)\n", - "- path-dependency (sum/average, barrier, etc.)\n", + "- single asset / multi asset (basket) options,\n", + "- piecewise linear payoff functions (arbitrary number of break points, possibly non-continuous), and\n", + "- path-dependency (sum/average, barrier, etc.).\n", "\n", "The basic ideas on using QAE for option pricing and risk analysis are provided here:
\n", "Quantum Risk Analysis. Stefan Woerner, Daniel J. Egger (2019).\n", @@ -51,11 +51,11 @@ "- Basket Option (multivariate, payoff with 2 segments)\n", "- Asian Barrier Spread (multivariate, path-dependent, payoff with 3 segments)\n", "\n", - "All examples illustrate how to use the genereric Qiskit Finance framework to construct operators that can be analyzed with QAE. The same framework can be easily adjusted to estimate risk as well, for instance, the Value at Risk (VaR) or the Conditional Value at Risk (CVaR, also known as Expected Shortfall). How to use Qiskit Finance for risk analysis is illustrated in the following tutorial:\n", - "Credit Risk Analysis\n", + "All examples illustrate how to use the genereric Qiskit Finance framework to construct QAE-operators (uncertainty problems). The same framework can be easily adjusted to estimate risk as well, for instance, the Value at Risk (VaR) or the Conditional Value at Risk (CVaR, also known as Expected Shortfall). How to use Qiskit Finance for risk analysis is illustrated in the following tutorial:\n", + "Credit Risk Analysis.\n", "\n", "An example of how quantum Generative Adversarial Networks (qGANs) can be used to learn and efficiently load generic random distributions for option pricing can be found here:\n", - "QGANs to learn and load random distributions for option pricing" + "QGANs to learn and load random distributions for option pricing" ] }, { From aee18e776f62883640ada075eabb04e0d5728423 Mon Sep 17 00:00:00 2001 From: stefan-woerner Date: Tue, 23 Apr 2019 13:07:26 +0200 Subject: [PATCH 070/116] bug fix in amplitude estimation tutorial --- .../aqua/general/amplitude_estimation.ipynb | 72 ++++++++----------- 1 file changed, 30 insertions(+), 42 deletions(-) diff --git a/qiskit/aqua/general/amplitude_estimation.ipynb b/qiskit/aqua/general/amplitude_estimation.ipynb index 43d45dcef..7101c0e96 100644 --- a/qiskit/aqua/general/amplitude_estimation.ipynb +++ b/qiskit/aqua/general/amplitude_estimation.ipynb @@ -47,9 +47,7 @@ { "cell_type": "code", "execution_count": 1, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", @@ -58,9 +56,9 @@ "from qiskit.tools.visualization import plot_bloch_vector\n", "from qiskit import BasicAer\n", "from qiskit.aqua.algorithms import AmplitudeEstimation\n", - "from qiskit.aqua.algorithms.single_sample.ae.q_factory import QFactory\n", + "from qiskit.aqua.algorithms.single_sample.amplitude_estimation.q_factory import QFactory\n", "from qiskit.aqua.components.uncertainty_problems import UncertaintyProblem\n", - "from qiskit.aqua.utils.circuit_utils import cry" + "from qiskit.aqua.circuits.gates import cry" ] }, { @@ -70,7 +68,7 @@ "outputs": [ { "data": { - "image/png": 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s7+6W7qhJqFr1nMTLCYBZ8088/jheu3bt2HfgGIZSWBVZRqNeR5PFMDzfLxRP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\nrrwLIiK6J3inT0SUIgx9IqIUYegTEaUIQ5+IKEUY+kREKcLQJyJKEYY+E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\n", "text/plain": [ "
" ] @@ -92,9 +90,7 @@ { "cell_type": "code", "execution_count": 3, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "class BernoulliAFactory(UncertaintyProblem):\n", @@ -103,19 +99,17 @@ " A is used to initialize the state as well as to construct Q.\n", " \"\"\"\n", " \n", - " def __init__(self, probability=0.5, i_state=None):\n", + " def __init__(self, probability=0.5):\n", + " # \n", " super().__init__(1)\n", " self._probability = probability\n", + " self.i_state = 0\n", " self._theta_p = 2 * np.arcsin(np.sqrt(probability))\n", - " if i_state is None:\n", - " i_state = 0\n", - " self._params = {'i_state': i_state}\n", " \n", - " def build(self, qc, q, q_ancillas=None, params=None):\n", - " if params is None:\n", - " params = self._params\n", + " def build(self, qc, q, q_ancillas=None):\n", + " \n", " # A is a rotation of angle theta_p around the Y-axis\n", - " qc.ry(self._theta_p, q[params['i_state']])\n", + " qc.ry(self._theta_p, q[self.i_state])\n", "\n", "\n", "class BernoulliQFactory(QFactory):\n", @@ -126,26 +120,24 @@ " \"\"\"\n", " \n", " def __init__(self, bernoulli_expected_value):\n", - " super().__init__(bernoulli_expected_value)\n", + " super().__init__(bernoulli_expected_value, i_objective=0)\n", " \n", - " def build(self, qc, q, q_ancillas=None, params=None):\n", - " i_state = self.a_factory._params['i_state']\n", + " def build(self, qc, q, q_ancillas=None):\n", + " i_state = self.a_factory.i_state\n", " theta_p = self.a_factory._theta_p\n", " # Q is a rotation of angle 2*theta_p around the Y-axis\n", " qc.ry(q[i_state], 2*theta_p)\n", " \n", - " def build_controlled_power(self, qc, q, q_control, power, q_ancillas=None, params=None):\n", - " i_state = self.a_factory._params['i_state']\n", + " def build_controlled_power(self, qc, q, q_control, power, q_ancillas=None, use_basis_gates=True):\n", + " i_state = self.a_factory.i_state\n", " theta_p = self.a_factory._theta_p\n", - " cry(2*power*theta_p, q_control, q[i_state], qc)" + " qc.cry(2*power*theta_p, q_control, q[i_state])" ] }, { "cell_type": "code", "execution_count": 4, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# construct factories for A and Q\n", @@ -156,9 +148,7 @@ { "cell_type": "code", "execution_count": 5, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# set number of evaluation qubits\n", @@ -173,9 +163,7 @@ { "cell_type": "code", "execution_count": 6, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# result = ae.run(quantum_instance=BasicAer.get_backend('qasm_simulator'))\n", @@ -189,12 +177,14 @@ "outputs": [ { "data": { - "image/png": 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MzKySoq/hHATcmkssU0lJaO8K+73clWwAIuIB4OlsHZI+BIwE/j2371Rgz6xL\nzszMWqTohDMEmF9aEBHPAsuzdVXvl3m8ZL8dgHXLbPc4qZ471hGvmZk1SNFdagNIAwXylmTr6tlv\n+5JtKLPdktz695E0DugaS7tM0oIe4mi4k2Bz4G+17KNJTQqmgbIYa65b709c2FM/i69bHXrxb6VP\n1K9OhdetqP+z9XyfQK/j267aDVtxH06UKVM35fXsl3+vbspTYcQUoGV3DEqaExHDW3X+ZnLd+q5O\nrp/r1jpFd6ktATYpU74x5VswlfbbpGS/JSVl+W2ocHwzM2uyohPOfHLXaiRtA2xA+Ws03e6XKb22\n8ySwssx2Q4B3gCfqiNfMzBqk6IQzDThA0oYlZaOBFcDsCvttkd1nA4Ck4aTrN9MAIuIt0v03R+T2\nHQ3cGxGv9z78pujkCcBct76rk+vnurWIIipdOmngydKNn48BjwCTSAnjIuCSiJhQst1CYHZEHFtS\nNp000uwUUotlEvDXiPhcyTZ7AbOAS0k3hY7Ktj8wInwfjplZCxXawomIJcC+wNrAjaQZBi4Gzs5t\nuk62TamjSK2gXwJXAXOBL+eOfw9wOLAfcCvwX4GjnWzMzFqv0BaOmZl9cHm26CaRNFTSDEnLJb0o\n6VxJ+VZbuf02lnSFpCWSXpf0a0mbFRFzteqpm6Rds3otzPZbIOlsSesXFXc16v3cSvZfS9JcSSHp\ni82MtR69qZ+kQyX9QdIKSa9Imi5pg2bHXK1e/J8bLum2rE6vSrpD0u5FxFwtSR+XNFnSw5JWS5pV\n5X5t9X3i5+E0QckkpY+RJindAfgxKcFP6GFXSJOUfpI0SWnXtaobgM/1tFNRelG30dm2k4A/AzsD\n52WvhzUx5Kr18nPrchywVVMC7KXe1E/ScaRroxcCp5JupN6HNvkOqbdu2SjZO4B5wFey4lOB2yTt\nHBHPNDPuGuxEuiZ9H7BeDfu11/dJRHhp8AKcQbovaKOSsu+QpvDZqIf99iTdoPr5krLdsrL9Wl2v\nXtbtI2XKxmV1267V9epN3Uq2HQAsBo7N6vXFVtepQZ/d5sAbwNhW16EJdTseWA1skvscVwNfb3W9\nSmJaq+Tna4FZVezTdt8n7lJrjqZNUtoG6qpbRCwuU/xg9jqwceH1Sr2fW5fzgN8DM5oQWyPUW78j\ns9d/a1ZgDVBv3dYFVgHLSsqWZWWFzZNUSUS8U8dubfd94oTTHM2cpLTV6q1bOZ8lNfMLnb+uB3XX\nTdLOwFdJw/DbVb312530GR0r6XlJKyXdL+mzzQu1ZvXW7bpsmx9LGihpIGnk7BLgt02KtSht933i\nhNMczZiktKf9itSQGCVtAZwI93L7AAACzklEQVQF/J/o5jlILdCbuv0E+GlELGx4VI1Tb/22IF0H\nmACcBvwX4O/AdEmDGh1kneqqW0S8SHqsyWHAy9lyKHBAN63yvqTtvk+ccJqn2ZOUtlKvYpS0Hum5\nRcuA/9HAuBqh5rpJOor0hXx+s4JqoHo+u7WA/sCxEfHriJhOetT7auCbjQ+xbvV8dluSronMJXUz\nHZT9fLOkbZsRZMHa6vvECac5mjlJaavVWzcAJIl04+5OwKhINwO3i5rrJmld4Iek0T9rSdoE2Chb\nvUFuGqdWq/ezezV7ndVVkLVK5wJDGxVcL9Vbt1NJI+0Oj4jpWTI9jJRM27l7tBpt933ihNMczZyk\ntNXqrVuXi0nDVg+JiHapU5d66rYBsDVpiqYl2fJwtm4q7w2MaAf1fnaPk/4izl9EF+kaXDuot25D\ngEcjYmVXQUS8DTxKGlrdl7Xd94kTTnM0bZLSNlBv3ZB0BnAicEykaYjaTT11W0a6BlC6/Lds3ZnA\nPzUn1LrU+9ndREouI7sKske2D+O95Npq9dbtGeBTWTcv8O7j6j8FLGpCnEVqv++TVo8v78SFdEHu\nJeB20rxu40hfTOfntlsI/CJXNh14inTh8kuk0UF3t7pOva0bcDTpr+QrgD1yyxr36PSlupU5zmDa\n8z6c3vy7vCHb978DB5O+xBcDA1pdr17+uxxGeqzJzVm9vkj6Ml4J/KdW16skzg+T5ok8HLiX1ALr\nev/hHj63tvo+afkvslMXUt/2naS/sF4i3aOxdm6bRcCVubJNsi/l14ClwG+AzVtdn97WDbgy+xIu\nt4xpdZ16+7nl1rdlwunlv8v+wP8GXsn2vQP4dKvr06C67QvcRbpW9SopmY5odX26+TdVbhncQ93a\n6vvEk3eamVkhfA3HzMwK4YRjZmaFcMIxM7NCOOGYmVkhnHDMzKwQTjhmZlYIJxwzMyuEE46ZmRXi\n/wPargvhxia8vQAAAABJRU5ErkJggg==\n", 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\n", 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NuXJk+Oll/MehVfaFcg0aNNi2bdu2bdt+++23sWPHFi5ceNSoUeXLlz916pTlnStn+OFnlUvvAwAAuLwZM2bk+V00LS3t+++/t088gFPjDQUAAADIjh49mpiY2KZNG6v05unpGRUVtXPnTqv0ZoRVJn1EXpN3SmZ57DDFM3v2bCGERqPp169fjg3q1atXq1YtIcSuXbtu3LiR5dklS5bcvn1bXjbUDmZn61kbSZL27NnTtm1ba3XYrl27S5cuGco0bcRxMs0WyF6Xx/y4zEEmx4VD5iqjnLzAKAe4GI7/w25INgDuzCPPFlqtVr5fVfbrK9y4caNp06YLFy60SWhmMZx4bfghkYXhccMX9Oy6du0aEBDgFBeql29DJhT8GszeUqvVfv/992XKlAkKCgoMDKxcufLy5cuVbNTwk8bI31BYaV8oFxYWFhUVFRUV1aVLl4kTJ547dy4iIuLhw4dNmzY9e/as5f0rxA8/AAAAk/zxxx9KmuV4tRsAWfCGAgAAAGTyVaIqVKhgrQ7LlStnKA6zHUsmfQzynLxTMstj6ykerVa7cuVKIUSdOnVKliyZYxuNRvPBBx8IIXQ6Xfv27V+8zO3WrVuHDx9u+GdwcHBuG7L1rM3jx49TU1PLly9vrQ7LlSsncrnMmRU5TqbZAtnr8pgflznI5LhwyFxllJMXGOUAF8Pxf9gNyQbAnXnl2eLq1avyd+46derIj6xaterAgQMXLlzYu3evJEmdO3e2bYymMFzt3pLfD4GBgV27dl2xYsXUqVOzXLNfuYyMjGnTphm5j1V28qkL6enpylcxnGAdGRlpUktJkvr16/frr7927ty5T58+0dHRmzZt6t279+7duxcsWGD8pmYKz7e2yr4wW0hIyIIFC+rVq/f8+fNhw4bt3LnTwtv5KWTqD7+MjIxdu3bJ577DKlJSUi5fvhwREaF2IG7q8ePHO3bs+Oyzz9QOBMakp6dfvHgxIiLCPgMjzHb58uV79+7xhlJFRkbG+fPnIyIizP4qCOViYmKUNLt+/frIkSMZuByHVqs9c+ZMREREjnf+hVp4QzkUvV5/+vTpGjVqGLkcF2zn3r17Wq22VKlSagcCYyRJOnXqVLVq1Xx9fdWOBcY8fvw4Pj7eimWpEELExcU9ePCgSpUqagcC53Dq1KkqVar4+fmpHYgz2bNnj0aj+f777/P83pucnLx79+48j8CcOHEiKSlp+PDhJn1s6XS6uLg45e3NnvQRpkzeKZnlsfUUz+7du58+fSqEaNKkiZFmvXr1+umnn06cOHHhwoVq1ar16NHD39//0KFDu3btKlq0aNeuXRcvXiyEKFSoUG49mDRr8/Tp0ydPnph0OE6+nPymTZvOnTtnvOWZM2fi4uLy7FyeWJw4cWKNGjWUhxETE1OgQAHl7R0n02QDBw68fPmyJElKgs+uWLFiv/76q+GXl3tmrzzVOG/evK1bt5ryahS5du2aEGL69OlFihSxeufyoYzcLradI+bHc6TW5LgwqzB63bp1cl4pIf/REhISlIfEKCcvuNIo9+zZs8TERBtNme3du/f+/fvMx9lIcnLytWvXatasqXYgroDj/9Zy+vTpSpUq5cuXT+1AHBfJZme3bt3y9PQMDw9XOxA4gdTU1JiYGAojlTCvniF//vw5lNQ/ffr04MGDBw8evHPnzuPHj2/duiU/bvgVMWfOnKtXr1avXv3VV189ePCg5dFbkeH3Q25fu2NjY+UF478fMjIyvL29LRn0nz59+tNPP5l0wzidTieEUH50NSUl5fz580IILy+v2rVrG28s/xosV65cSEiIEGLt2rW//vrrypUre/ToITe4cOFC69atFy1a1KZNmy5duhjpSuGfxVr7wmx169aNjIw8evTo7t27jx8//vLLL9tiK1mY+ks4PT395MmTly5dslE8bkir1aakpBiuKAA7S0tLu3z58vz589UOBMbodLrk5OSjR4/y28bBPX/+PC4ujjeUKuS3ybFjx3ib2IHCCTNJkn7++WdbBwPl9Hp9UlLSsWPHOPPEofCGciiSJCUmJh49epS3iSpSU1MlSfL391c7EBgjv02OHDnCCVoOLj09XavVBgQEqB2IS8nIyMjIyNi/f7/agcAJyKPl4cOHGS1NkpSUpPB7b1pa2qlTp6Kjo/NsJoRYvHixSd/u9Hq9YSokT5ZM+ghTJu+UHO6w9RTPunXr5AXj5Xo+Pj5r1qxp3rz5zZs37927N23aNPnxtm3bzp07d9SoUfI/jRRpmTRrExsb+/z5c5MOx8l1zFu3bs3zTNrk5GS9Xp9n53LAu3btOnTokPIwkpKSlF+8yaEyTVawYEEjNZd5KlSo0Ivbcs/slU/G+OOPP7y88r6gnqnk8ty1a9farvPU1FSF7ZkfN0KVyXFhYq7KB6/27dtnqGVX2L98dUIlGOVccpS7f/9+SkqKjabMEhMTdTod83E2ItdvHD58WO1AXAHH/60lISHhn3/+scUXG5dBstlZSkqKRqPhNA8oQWGkcubVM/j7+//fx0NKSsqiRYvmzZsn/8DIzlBSv3v3bnkzn332maOV1Bt+6ly7dq1hw4bZGxhOdzZytYb4+Ph169aNGDHCkiKqokWLmnpbRvmXbVhYmML2t27dkqvww8LCjF+f5syZM/ILj4qKkh/54YcfWrdubTheIISoVq3atGnTevTo8eWXXxo/ZGC4lZjxa/BbZV9YqE6dOvIIcurUKfscNTCcH2/4KWtc/vz5//Of/0yaNMmWQQH2U6pUqTfffHP69OlqBwK4gtdee61YsWK//fab2oEAtlWjRo3cfoC8qGLFigqviAC4M95QAAAAgGzBggXvvPPOzZs387xwbGho6LvvvvvVV18Zb/bdd9+NGjXq2bNnJs3D+fj4VK1aVWFjSyZ9hCmTd0pmeWw9xbNnzx4hhIeHR46dv6hs2bLHjh2bOXPmkSNHfH19K1Wq1L1793r16mk0mosXLwoh/P39q1WrltvqJs3aVK9e/dGjRyb9XLp582aZMmWWLFny5ptvGm/51ltvXb16Nc9p71OnTtWpU2fr1q1NmzZVHka7du1yu1Zxdg6VabLvvvtOWeyKuGf2yq968+bNjRo1UvxSlPr7779btmx54MABW1xjeO3atV26dFF+9ibz48bZf3JcmJir8gAyY8aMd955R2H/iYmJQUFBFStWVNieUc4lR7nq1aufPn1avjmM1Q0aNGjfvn1cBhGOj+P/sBuSDYA7+/8l9efPn3/zzTevXLkihKhRo0aPHj1q1KhRtWrVsLCw5s2bHzlyJCAgwHAXWke+vprhl/zly5dzbGD4/WDku/uqVavS0tL69etn7eis7NGjR/KC4VdTbpYtWyYvdOvWTV4oW7Zsy5YtszR7/fXXhRAXLlzIyMjw8fHJrTeFPw6tsi8sZPiVePv2bRttIgvD30RhST0AAICb69Spk5KDMm+88YYdggGcHW8oAAAAQFasWDEhxP379/MsqVfo/v37YWFhNp0gs2TSR5gyeadklsemUzxPnjyRbwtQp04dJRfQDQkJyX5lori4uAsXLgghmjVrZuQCk7aetSlatKhGo7FihZ/clZzANuJQmWYLZK9rY37cOPtPjgvHy1VGOUY5wFVx/B92Q7IBcGceQohnz561aNHiypUrVapU2bdv35kzZ0aNGtW+ffty5cp5e3ufPn1aCFGvXj2nuKlo9erVfX19hRAnTpzIscG5c+eEEAUKFKhQoUJunSxatKhRo0ZGGjgIw2+YlJQUI82ePXsm/xps1KiR4UziH3/8UT5A8KKAgIDg4GCtVhsXF2ekQ8NPGsN5wzmyyr4wLiEhwfi9Zgw/F5Vf+99Cpl6lHgAAwM198MEHedY3BAYGDh8+3D7xAE6NNxQAAAAgq1Wrlkaj2bdvn7U63LdvX0REhLV6y5Elkz4mUTLLY9MpHsOV2hs0aGDqugbz589PT08XQgwYMMBIM1vP2vj6+sqzq9bqcN++fS+99FKZMmWs1WF2DpVptkD2ujY3nx93wMlx4Xi5yijHKAe4Ko7/w25INgDuzEMIMX369IcPHwoh1q5d27BhQ41GY3j63Llz8pfdyMhItUI0iZ+fX/v27YUQe/fuNZx/bHDnzh35N0CnTp1yO734/Pnzx44dM/7l3kFUqFBBPlf+xo0buf1OkyRpwIABjx498vHxmTlzpmHn+vv7Z//we/LkSVxcXHBwcOHChY1s13BtDOPnW1u+L/K0ZcuW8ePH5/ZsRkbG4cOH5eXGjRubtwlTGf4mxYsXt88WAQAAnFpoaOiyZcte/A2ShUajWbJkSZEiRewZFeCkeEMBAAAAsuLFi9erV2/jxo1W6e327dunTp3q1KmTVXrLjSWTPiZRMstj0ykew1V1zb7iUmZm5uzZs4UQpUuXbteunZGWdpi16dix47Zt29LS0qzS24YNG9q2bWvkUtmWc6hMswWy17W5+fy4A06OC8fLVUY5RjnAVXH8H3ZDsgFwZx5CiGPHjgkhNBpNltsISpI0YcIEedlZSuqFEH369BFCpKenT5kyJctThntO9e/fP7fVFy1aFBgY2KVLF9tFaC0BAQFt2rQRQmRmZi5dujR7A71eP3HiRPmQ8bRp0/K8gIp8Hvbbb79t/EfjSy+9JKfKrVu3jHdo3r5ITk7+6aefNm7cKEmS8f7Pnz8/adKkKVOm6HS67M/+/PPPd+7cEUJERkZWr179xadSU1PnzZu3Zs0a4+fxm8HwN6lcubJ1ewYAAHBVHTp02LRpU3BwcPanChQosGHDhjfffNP+UQFOijcUAAAAIHvjjTf+/vvv27dvW97V4sWLPT095fI127H6pE9uFM7ymDfFo2T+5erVq/JCqVKl8ow2x6miMWPG3L17VwgxY8YM49Xndpi1eeONN5KSkn7//XfLuzp48ODly5dtffKGo2WaLZC9LszN58cdcHJcOF6uMsrJC4xygEvi+D/shmQD4L4kSWrWrJm83Lt374cPH0q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"text/plain": [ - "" + "" ] }, "execution_count": 8, @@ -236,18 +226,16 @@ { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { - "display_name": "Python 3", + "display_name": "qiskit_master", "language": "python", - "name": "python3" + "name": "qiskit_master" }, "language_info": { "codemirror_mode": { @@ -259,7 +247,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.6" + "version": "3.6.1" } }, "nbformat": 4, From 1a04055b51810800b7dd863aecbf981989d5b69c Mon Sep 17 00:00:00 2001 From: stefan-woerner Date: Tue, 23 Apr 2019 13:08:04 +0200 Subject: [PATCH 071/116] update portfolio optimization and qiskit finance index --- .../optimization/portfolio_optimization.ipynb | 85 +++++++------------ qiskit/finance/qiskit_finance.ipynb | 6 +- 2 files changed, 32 insertions(+), 59 deletions(-) diff --git a/qiskit/finance/optimization/portfolio_optimization.ipynb b/qiskit/finance/optimization/portfolio_optimization.ipynb index 042776d81..9623161be 100644 --- a/qiskit/finance/optimization/portfolio_optimization.ipynb +++ b/qiskit/finance/optimization/portfolio_optimization.ipynb @@ -61,13 +61,13 @@ "outputs": [], "source": [ "from qiskit import BasicAer\n", - "from qiskit_aqua import QuantumInstance\n", - "from qiskit_aqua import Operator, run_algorithm\n", - "from qiskit_aqua.input import EnergyInput\n", - "from qiskit_aqua.translators.ising import portfolio\n", - "from qiskit_aqua.algorithms import VQE, QAOA, ExactEigensolver\n", - "from qiskit_aqua.components.optimizers import COBYLA\n", - "from qiskit_aqua.components.variational_forms import RY\n", + "from qiskit.aqua import QuantumInstance\n", + "from qiskit.aqua import Operator, run_algorithm\n", + "from qiskit.aqua.input import EnergyInput\n", + "from qiskit.aqua.translators.ising import portfolio\n", + "from qiskit.aqua.algorithms import VQE, QAOA, ExactEigensolver\n", + "from qiskit.aqua.components.optimizers import COBYLA\n", + "from qiskit.aqua.components.variational_forms import RY\n", "import numpy as np" ] }, @@ -235,27 +235,27 @@ "name": "stdout", "output_type": "stream", "text": [ - "Optimal: selection [0 0 1 1], value -0.7012\n", + "Optimal: selection [1 0 0 1], value -0.4158\n", "\n", "----------------- Full result ---------------------\n", "selection\tvalue\t\tprobability\n", "---------------------------------------------------\n", - " [0 0 1 1]\t-0.7012\t\t0.4800\n", - " [1 1 0 0]\t-0.5110\t\t0.2290\n", - " [1 0 0 1]\t-0.4158\t\t0.2173\n", - " [0 1 1 0]\t-0.5149\t\t0.0723\n", - " [1 0 1 1]\t3.0617\t\t0.0003\n", - " [0 0 1 0]\t3.4782\t\t0.0002\n", - " [1 1 0 1]\t4.6445\t\t0.0002\n", - " [0 1 0 0]\t4.5153\t\t0.0002\n", - " [1 1 1 0]\t2.6688\t\t0.0001\n", - " [0 0 0 1]\t4.0314\t\t0.0001\n", - " [0 1 0 1]\t2.1421\t\t0.0001\n", - " [1 1 1 1]\t15.6136\t\t0.0000\n", - " [1 0 1 0]\t-0.2876\t\t0.0000\n", - " [0 0 0 0]\t16.0000\t\t0.0000\n", + " [1 0 0 1]\t-0.4158\t\t0.7755\n", + " [1 0 1 0]\t-0.2876\t\t0.2241\n", + " [1 1 0 0]\t-0.5110\t\t0.0001\n", + " [0 0 1 0]\t3.4782\t\t0.0001\n", + " [1 1 1 1]\t15.6136\t\t0.0001\n", + " [1 0 1 1]\t3.0617\t\t0.0001\n", + " [0 0 1 1]\t-0.7012\t\t0.0001\n", + " [0 1 0 0]\t4.5153\t\t0.0000\n", + " [0 0 0 1]\t4.0314\t\t0.0000\n", + " [1 1 1 0]\t2.6688\t\t0.0000\n", + " [0 1 1 0]\t-0.5149\t\t0.0000\n", " [1 0 0 0]\t4.0242\t\t0.0000\n", - " [0 1 1 1]\t4.9012\t\t0.0000\n" + " [1 1 0 1]\t4.6445\t\t0.0000\n", + " [0 1 0 1]\t2.1421\t\t0.0000\n", + " [0 1 1 1]\t4.9012\t\t0.0000\n", + " [0 0 0 0]\t16.0000\t\t0.0000\n" ] } ], @@ -312,44 +312,17 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Optimal: selection [1 1 0 0], value -0.5110\n", - "\n", - "----------------- Full result ---------------------\n", - "selection\tvalue\t\tprobability\n", - "---------------------------------------------------\n", - " [1 1 0 0]\t-0.5110\t\t0.1907\n", - " [0 0 1 1]\t-0.7012\t\t0.1853\n", - " [1 0 0 1]\t-0.4158\t\t0.1839\n", - " [0 1 1 0]\t-0.5149\t\t0.1789\n", - " [0 1 0 1]\t2.1421\t\t0.1584\n", - " [1 0 1 0]\t-0.2876\t\t0.0948\n", - " [1 1 1 0]\t2.6688\t\t0.0033\n", - " [0 0 0 1]\t4.0314\t\t0.0020\n", - " [1 0 1 1]\t3.0617\t\t0.0009\n", - " [0 1 1 1]\t4.9012\t\t0.0007\n", - " [1 0 0 0]\t4.0242\t\t0.0006\n", - " [0 1 0 0]\t4.5153\t\t0.0003\n", - " [0 0 1 0]\t3.4782\t\t0.0002\n", - " [1 1 1 1]\t15.6136\t\t0.0001\n", - " [0 0 0 0]\t16.0000\t\t0.0001\n", - " [1 1 0 1]\t4.6445\t\t0.0000\n" - ] - } - ], + "outputs": [], "source": [ "backend = BasicAer.get_backend('statevector_simulator')\n", "seed = 50\n", "\n", "cobyla = COBYLA()\n", "cobyla.set_options(maxiter=250)\n", - "qaoa = QAOA(qubitOp, cobyla, 3, 'matrix')\n", + "qaoa = QAOA(qubitOp, cobyla, 3)\n", + "\n", "qaoa.random_seed = seed\n", "\n", "quantum_instance = QuantumInstance(backend=backend, seed=seed, seed_mapper=seed)\n", @@ -388,9 +361,9 @@ ], "metadata": { "kernelspec": { - "display_name": "qiskit_stable", + "display_name": "qiskit_master", "language": "python", - "name": "qiskit_stable" + "name": "qiskit_master" }, "language_info": { "codemirror_mode": { diff --git a/qiskit/finance/qiskit_finance.ipynb b/qiskit/finance/qiskit_finance.ipynb index 197cb4ffd..5ee05e65e 100644 --- a/qiskit/finance/qiskit_finance.ipynb +++ b/qiskit/finance/qiskit_finance.ipynb @@ -30,11 +30,11 @@ "In this notebook we provide an overview of Qiskit Finance tutorials and tutorials from other domains which might be relevant in finance.\n", "\n", "#### Machine Learning:\n", - "- Quantum Generative Adversarial Networks (qGANs) for data loading in option pricing\n", + "- Quantum Generative Adversarial Networks (qGANs) for data loading in option pricing\n", "\n", "#### Optimization:\n", "- Portfolio Optimization\n", - "- Portfolio Diversification\n", + "- Portfolio Diversification\n", " \n", "#### Simulation:\n", "- Option Pricing\n", @@ -42,7 +42,7 @@ "- Fixed Income Pricing\n", "\n", "#### Data Providers:\n", - "- Stock Market Time Series" + "- Stock Market Time Series" ] }, { From a63ae31407110e5e467f4a70a50de0e1706fc485 Mon Sep 17 00:00:00 2001 From: stefan-woerner Date: Tue, 23 Apr 2019 13:35:54 +0200 Subject: [PATCH 072/116] Update portfolio_optimization.ipynb --- .../optimization/portfolio_optimization.ipynb | 66 +++++++++++++------ 1 file changed, 47 insertions(+), 19 deletions(-) diff --git a/qiskit/finance/optimization/portfolio_optimization.ipynb b/qiskit/finance/optimization/portfolio_optimization.ipynb index 9623161be..3ff6db9cf 100644 --- a/qiskit/finance/optimization/portfolio_optimization.ipynb +++ b/qiskit/finance/optimization/portfolio_optimization.ipynb @@ -240,33 +240,33 @@ "----------------- Full result ---------------------\n", "selection\tvalue\t\tprobability\n", "---------------------------------------------------\n", - " [1 0 0 1]\t-0.4158\t\t0.7755\n", - " [1 0 1 0]\t-0.2876\t\t0.2241\n", - " [1 1 0 0]\t-0.5110\t\t0.0001\n", - " [0 0 1 0]\t3.4782\t\t0.0001\n", - " [1 1 1 1]\t15.6136\t\t0.0001\n", - " [1 0 1 1]\t3.0617\t\t0.0001\n", - " [0 0 1 1]\t-0.7012\t\t0.0001\n", - " [0 1 0 0]\t4.5153\t\t0.0000\n", - " [0 0 0 1]\t4.0314\t\t0.0000\n", - " [1 1 1 0]\t2.6688\t\t0.0000\n", - " [0 1 1 0]\t-0.5149\t\t0.0000\n", - " [1 0 0 0]\t4.0242\t\t0.0000\n", + " [1 0 0 1]\t-0.4158\t\t0.9322\n", + " [1 0 1 0]\t-0.2876\t\t0.0667\n", + " [1 1 0 0]\t-0.5110\t\t0.0011\n", " [1 1 0 1]\t4.6445\t\t0.0000\n", + " [0 0 1 1]\t-0.7012\t\t0.0000\n", + " [1 0 0 0]\t4.0242\t\t0.0000\n", " [0 1 0 1]\t2.1421\t\t0.0000\n", + " [0 0 1 0]\t3.4782\t\t0.0000\n", + " [0 1 1 0]\t-0.5149\t\t0.0000\n", " [0 1 1 1]\t4.9012\t\t0.0000\n", - " [0 0 0 0]\t16.0000\t\t0.0000\n" + " [0 0 0 0]\t16.0000\t\t0.0000\n", + " [0 1 0 0]\t4.5153\t\t0.0000\n", + " [1 1 1 1]\t15.6136\t\t0.0000\n", + " [0 0 0 1]\t4.0314\t\t0.0000\n", + " [1 1 1 0]\t2.6688\t\t0.0000\n", + " [1 0 1 1]\t3.0617\t\t0.0000\n" ] } ], "source": [ "backend = BasicAer.get_backend('statevector_simulator')\n", - "seed = 50\n", + "seed = 42\n", "\n", "cobyla = COBYLA()\n", - "cobyla.set_options(maxiter=250)\n", + "cobyla.set_options(maxiter=500)\n", "ry = RY(qubitOp.num_qubits, depth=3, entanglement='full')\n", - "vqe = VQE(qubitOp, ry, cobyla, 'matrix')\n", + "vqe = VQE(qubitOp, ry, cobyla)\n", "vqe.random_seed = seed\n", "\n", "quantum_instance = QuantumInstance(backend=backend, seed=seed, seed_mapper=seed)\n", @@ -281,7 +281,7 @@ "\n", "optimizer_cfg = {\n", " 'name': 'COBYLA',\n", - " 'maxiter': 250\n", + " 'maxiter': 500\n", "}\n", "\n", "var_form_cfg = {\n", @@ -312,9 +312,37 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Optimal: selection [0 0 1 1], value -0.7012\n", + "\n", + "----------------- Full result ---------------------\n", + "selection\tvalue\t\tprobability\n", + "---------------------------------------------------\n", + " [0 0 1 1]\t-0.7012\t\t0.1719\n", + " [1 0 0 1]\t-0.4158\t\t0.1714\n", + " [1 1 0 0]\t-0.5110\t\t0.1706\n", + " [0 1 1 0]\t-0.5149\t\t0.1691\n", + " [1 0 1 0]\t-0.2876\t\t0.1515\n", + " [0 1 0 1]\t2.1421\t\t0.1508\n", + " [1 1 1 0]\t2.6688\t\t0.0073\n", + " [0 0 0 1]\t4.0314\t\t0.0028\n", + " [1 0 1 1]\t3.0617\t\t0.0025\n", + " [0 1 1 1]\t4.9012\t\t0.0007\n", + " [0 1 0 0]\t4.5153\t\t0.0004\n", + " [1 0 0 0]\t4.0242\t\t0.0004\n", + " [0 0 1 0]\t3.4782\t\t0.0003\n", + " [1 1 1 1]\t15.6136\t\t0.0001\n", + " [1 1 0 1]\t4.6445\t\t0.0000\n", + " [0 0 0 0]\t16.0000\t\t0.0000\n" + ] + } + ], "source": [ "backend = BasicAer.get_backend('statevector_simulator')\n", "seed = 50\n", From d2d1326ffd1d7f1a354da49019e886c7fd9925e9 Mon Sep 17 00:00:00 2001 From: Shaohan Hu Date: Tue, 23 Apr 2019 14:01:16 -0400 Subject: [PATCH 073/116] add notebook for deutsch-jozsa --- community/aqua/general/deutsch_jozsa.ipynb | 203 +++++++++++++++++++++ 1 file changed, 203 insertions(+) create mode 100644 community/aqua/general/deutsch_jozsa.ipynb diff --git a/community/aqua/general/deutsch_jozsa.ipynb b/community/aqua/general/deutsch_jozsa.ipynb new file mode 100644 index 000000000..662dda185 --- /dev/null +++ b/community/aqua/general/deutsch_jozsa.ipynb @@ -0,0 +1,203 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "# _*Experiment with the Deutsch-Jozsa Algorithm in Aqua*_\n", + "\n", + "This notebook demonstrates how to experiment with the `Deutsch-Jozsa` algorithm in `Qiskit Aqua`.\n", + "\n", + "We first import all necessary modules." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + ], + "source": [ + "from qiskit import BasicAer\n", + "from qiskit.aqua import QuantumInstance\n", + "from qiskit.aqua import run_algorithm\n", + "from qiskit.aqua.algorithms import DeutschJozsa\n", + "from qiskit.aqua.components.oracles import TruthTableOracle" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The [Deutsch-Jozsa algorithm](https://en.wikipedia.org/wiki/Deutsch-Jozsa_algorithm) is explained in more detail in the corresponding notebook located in the directory `community/algorithms`. We can experiment with it in Aqua by feeding it oracles created using truth tables. For example, we can create a `TruthTableOracle` instance as follows." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "bitstr = '11110000'\n", + "oracle = TruthTableOracle(bitstr)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As shown, the truthtable is specified with the `bitstr` containing values of all entries in the table. It has length $8$, so the corresponding truth table is of $3$ input bits. We can of course see that this truth table represents a `'balanced'` function as half of values are $1$ and the other half $0$.\n", + "\n", + "It might seem like a moot point running Deutsch-Jozsa on a truthtable as the function outputs are literally listed as the truthtable's values. The intention is to create an oracle circuit whose groundtruth information is readily available to us but obviously not to the quantum Deutsch-Jozsa algorithm that is to act upon the oracle circuit. In more realistic situations, the oracle circuit would be provided as a blackbox to the algorihtm.\n", + "\n", + "Above said, we can inspect the circuit corresponding to the function encoded in the `TruthTableOracle` instance." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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fPnzu3LkSi0VERHz55Zc27sv5cTTgqj7++GNz+rbElnQjLMk4pBujlG6pRelGemzeW2+91aVLFzPjv3Tp0saNG81fz7DP9MaiziaUT/qm2a2/OVVnE0KULVv22Wef/eKLL8wL3xQSuj6OBlzV999/r389imkuczatxnQjnOxsOiwsrHz58qQb2XE0AEAhDLD6OBqAgf89x9fLyysiIkIIcfv2bemd2bNnp6WleXl5ff75546JznK6y4ikWwAVpTtLadiwYXGVrF+/Pjs7e/DgwXJHJ6c7d+5IL3QnZsVZu3at9KJPnz7FlcnLy/v222+FEC+++KLBR1aco0ZERAQHBxf99Oeff05NTRVCdOrUSfemVquV7ulk+1XJsnz7ZrK0pZY2U3e07XzVf9EOYJSlVzOoFEcDEHKnG1F8xiHdGKV0Sx2Vbopjn+mNdSu+yiV90+zW31y4s5HQ9XE0AOEqZ9MqTTeCs2n3GGA5GgCgEAZYfRwNwICn/v9Ij/K9c+eORqO5devWggULhBAjRoxQ0d0YGjVqJN1y8MSJE0YLSBd9BAcHS8vbRsXGxrZp08bJbx+qu5NSVlaWiWL379+XzlGfe+651q1bGy1z+/btl19+OTEx8bXXXmvVqpXBp7pzJN11ssW5fv26dLmA0VszFRYWTpgwQQjh4eExYsQI3fuXLl2Sarb9yUOyfPvmsKKlljZTd7TtfI46duzYEm/SVbp0aamBLo+jAQhZ040wmXFIN0XZoaWOSjfFsc/0xvzOJuyS9E2zT39z7c5GQtfH0QCEq5xNqzHdCM6m3WaA5WgAgEIYYPVxNAADRlZ8CwsL7969+9FHH2VnZwcHB0s3dlYLPz+/bt26CSEOHTokXRaq7+bNm9LFpC+++GJx96Y+f/780aNHhw4dqnSoNqpbt650+6lr164V96AdIcTQoUNv377t6+u7cOHCop/27du3YcOG4eHhO3fuHD58+IoVK4qWqVKlivSixKuSTT9ZZ/78+adPnxZC9OrVS/fQ6BK3sojt376ZrGippc3UHW3d8beP0NDQtWvXenp6FlfA09Pz66+/dpNnsHM0ACFTuhFmZBzSTVF2aKmj0k1x7DO9Mb+zCbskfdPs099cu7OR0PVxNADhKmfTakw3grNptxlgORoAoBAGWH0cDcCAkRVfIcS5c+dWr14thJg2bVpISIj9w7LFwIEDhRA5OTmzZ882+GjGjBlarVYIMWTIkOI2j42NLV26dK9evRQN0nYBAQExMTFCiLy8vEWLFhktM3369G3btgkh5s6d26RJk6IFsrOzAwICgoKCPDw8srOzk5OTi5YpXbq0dJr0999/mw5JdxpmUFKr1c6ePXvSpElCiODgYIObhB85ckR6YfQKXyFEVlbWsmXLtm/fbnrvEuu+fYt2IaxqaYnNNKCrWfdXaTfdunXbvn17+fLli34UHBy8bds2t7oPBkcDkCXdCDMyDummKIVaqs+B6cYo+0xvzO9sQrGk72z9zeU7GwldH0cDcI2zaTWmG8HZtDsNsBwNAFAIA6w+jgbwD1o9x48fl95s06aNEKJBgwb5+fna4klz8QULFpgoY0Lv3r2rVq1atWrVa9euWbF5165do6OjjX4knbx5eHh8+eWXujcXL14sXe7Ro0eP4urMy8urUKHC66+/bkU8touOju7evbv55U+ePOnj4yOE8PLy2rZtm/5Ht27d0j3zZvr06abr0Wg0hw4dCg0NrVChwpkzZ4oWaN++vRDC19c3JyfHRD1StxFCeHt7r1y5Mj8/v7Cw8OjRo9KVwlIN33//vcFWzZs3F0LUrFmzuGrfeOMNafNFixaZbojEim/f0l1Y0dISm2mgWbNmQogKFSqYU1i6AXtBQYGZlZvj/v37H3/8ccuWLQMDAz08PJ566qkZM2bcu3dPxl2oiO5o+Pr6+vr6uvnRgAuYOXOmv7+/+eXlSjfakjIO6cY+LdVnUbq5ePGiEGLXrl3mFLZ6E/tMb8zsbFrFkr6z9Tdn62xarbZ+/fqyz8l1Cd3T0zMgIMDNE7p0NJo2bSqEKFOmjJsfDbiA8PDw8ePHm1/eBc6m1ZhulGupPosyzrhx46pXr25mzWbSpRt/f39vb283H2B1R8PLy8vf39/NjwYAyEg3wJYpU0YI0axZM3ceYHVHIyAgwMvLi3QDt/WPFV+D2xnt3bvX9MY2rvhGR0dLO0pISLBicxMrvjdv3qxcubJUebNmzXr16qV70kyNGjWSk5OLq3PLli1CiMOHD1sRj+0sXfHVarXLly/X3VLp2Wefff/99z/44IOePXsGBAQIIQIDA7/55hszq9q6dat0uDQajcFHEydOlHZx9OjR4jYvLCwMCgoSQjz++OPVqlUTQvj4+Pj6+uq6U7ly5Xbu3GmwVXZ2tnSa3bdv3+Jqbtu2rVRDgwYNzGmIFd++RbuwoqXmNFNfbm6uVGGHDh3MKa/Eiq/OtGnTgoKClKhZjTp27BgTE+PoKABbWbriq5U13WiLzzikG/u0VMfSdGOfFV+tXaY35nQ2rZJJ36n6mxN2Nq0yK746jz322DvvvKNQ5epy5coVIURcXJyjAwFsZemKr1blZ9NqTDeKtlTH0oyjxIqvzuDBgxs3bqxQ5apTu3btMWPGODoKAHBB3377rRDCxJKHWxk9enRERISjowAc5h93dQ4KCqpatar0unv37rrLWlWnSpUqJ0+ebNeunRDi5MmTmzdvlv4to3PnzkeOHAkLCytuw9jY2Mcff7xly5b2i9U2I0eOjIuLq1mzphDi119/nTlz5vTp07du3arRaIYPH37p0qX+/fubWVW3bt1KlSp18uTJc+fOGXzUsWNH6cWxY8eK2/zChQsZGRlCiK5dux47dqx79+6FhYV5eXlCCF9f3wEDBpw5c+aFF14w2Or06dP5+fnC5PN43nvvvYoVK9apU6ewsFCr1ZbYECu+fYt2YUVLzWmmvrNnz0oVqvdvEICLkTHdiOIzDunGPi3Vcdp0Y4fpjTmdTSiZ9J2qv7lzZwPgzlR9Nq3GdKNoS3XIOAAAAHBb3gb/f+PGDbvt+8CBA8pVHhYW9uOPP546dWrfvn2pqalVq1Zt165d48aNTWySnJy8Z8+eWbNmKReVErp16xYTE3Po0KEjR46kpaWFhITUq1evc+fO0pWz5vPy8goNDb1+/fqNGzcMDlSbNm38/f1zcnJMnKPqHsYTFRVVqVKluLi4O3fuXL582dfX9/HHHy9btqzRrVq2bFniOeHzzz9/+/ZtIUTXrl01Go2Xl1eJbbH027doF1a01Jxm6tPdX71z587mbwUAipIr3YjiMw7pRp9yLdVx5nSj9PTGnM4mlEz6TtXf3LyzAXBn6j2bVmO6EZxNAwAAAEoyXPF1MZGRkZGRkWYWXrNmjYeHx4ABAxQNSQne3t7t27eXng9kjuPHj7do0cLgzdzc3Fu3bgkhGjVqZPBRQEBATEzM1q1bd+zYkZOT4+/vX7RO/TM36UXFihUrVqxofivMYc4Jqo5F3775u7BDS3fs2CGEqF27tulrFADAzixNN8LCjEO60Ue6UXR6Y05nE27T3+hsANwZZ9NGMb0BAAAAVMez5CJuIzY29oUXXqhUqZKjA1Fcr1691q9fb/DmihUrCgsLGzVqVL169aKbjB49WgiRlpa2YcMGo3VKZ24hISHSTbFkl5mZWapUKSVqtnQXSrf07t27+/btE0KMGjVKifoBwJ4szTikGx3SjaVk72zCbfobnQ0AzMfZtC27IOMAAAAAyrFmxXf37t2zZ8+ePXv24cOHhRA//PCD9L+HDh2SOzz7+e233+Lj44cOHeroQOxh2rRp/fr169Wr148//vjo0aO0tLRly5a9++673t7eq1evNrpJhw4dGjRoIIRYunRp0U+zs7Ol5xXpLtSV3TfffNOjRw+FKjd/F3Zo6cqVKwsKCoKCggYPHqzQLgDAbizNOKQbCenGCvJ2NuE2/Y3OBgAW4Wza6l2QcQAAAABFWXNX502bNumfyezcuXPnzp1CiEmTJrVp00auyOwsNja2UqVKXbp0cXQg9jBo0KDg4OBx48Z16NBB92bNmjVXr17dvHlzo5t4eHgsXry4Xbt2R48eLXobq1OnThUUFAjFztyysrI2bNggXaurEDN3oXRLs7Oz58+fL4SYMWNGaGioErsAAHuyNOOQbiSkGyvI29mE2/Q3OhsAWISzaat3QcYBAAAAFGXNiu+qVatWrVoleygOlJGRsXHjxtGjR3t7u/iDjXW6d+/+/PPPHzp06Pjx497e3s2bN2/ZsqXpuzC1bdt24MCBa9asmTlz5tatW/U/KvowHnmNGzdO6W/HzF0o3dL58+ffuXOnadOmb731lhL1A4D9WZpxSDeCdGMtGTubcJv+RmcDAEtxNm3dLsg4AAAAgKLcZYHTtE2bNmVkZAwZMsTRgdiVr69vx44dO3bsaP4mc+bM2bFjx7Zt27Zu3dqzZ0/d+4qeuZ05c6ZSpUq9e/eWvWYrdqFoS+Pj42fMmOHp6fnFF194eXnJXj8AOIqlGYd0Q7qxmlydTbhNf6OzAYAVOJu2YhdkHAAAAEBR1jzH1/WsWrXq6aefrl+/vqMDcXYVKlRYv369j4/P6NGjb9y4oXv/q6++ysjIyMjICAsLk32nTZo0+eijj2Sv1rpdKNfS7Ozs1157LScnZ86cOU8++aS8lQOAupBuSDd2U1xnE27T3+hsAGAfTG/IOAAAAICiVLziW7NmzZo1a8pSVVJS0tixY2WpyuV16tRp5cqVt2/f7tatW0ZGhvRmQEBAYGBgYGCgY2OzA4VaqtVqBw0adOzYsbfffnvChAnyVg4AakS6Id3YjdHOJtymv9HZAMBumN6QcQAAAADlqPiuzgsXLpSrqoSEBLmqcgcDBw7s27evEMLHx8fRsbgIDw+PtWvXrl271s/Pz9GxAICzIN3IjnRTHDqb7OhsAGAUGUd2ZBwAAABAouIVXzgQp1Ky45ACQFG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x2nTD9Eafa3Q24cT9zYFIN0YxAuhjBFAUnU0fnc2FkW6MYgTQxwhgB97Sf27durVgwQIhRIMGDYYMGWK06O7duw8cOCCEGD16dK1atWzf9/Lly69evSqEmDRpUkhIiO0VCiHu3bsnvahTp47RArr3jT6vt1OnTlWrVl21alWHDh1kiUdpunsClDhk2HIXeOnH6X5+fg0bNiyxcE5Ozr///W8hRFRUVJ8+fR49erRt27Y//vgjISEhLS2tefPmH3zwQZUqVQy2ysjImDZtmhCiVatW0jO6rWDjt28pK1pqZjP9/PyeeOKJkydPOuFtAewsJSVl/vz5cXFxV69e1Wq1tWrV6tat28SJE4t2IffECKCPEUBRdDZ9zt/ZhHktdc7OBrg8pjem2SHjWJRuhJJJv0T2zDhumG5cY3qjxs4m3G8u7RCkG9MYAfQxAijKNTqbcJuzaVV3Nocg3ZjGCKCPEcAetFqtVqtNS0uT/jcyMlJrzIMHDypUqCCEiIqK0mg0RstYKjo6WtppQkKCFZt37do1Ojra4M3PPvtMqvPs2bNGtzp8+LBUYN68eUYLTJkyxd/f//79+1aEZKPo6Oju3btbtEm7du2k5uzatct0yTFjxkgl4+PjLQ1Muql6VFSUOYV1R3jSpEmTJ08OCAgw6HINGzZ8+PChwVbSxQRCiCVLllgano7t375FrGip+c0cOXKkVPLu3bslRiJdrlFQUGBTe4oxbdq0oKAgJWou0YYNGwIDA4uOWgEBAWvWrHFISB07doyJiVGo8qioqFdffdWiTRgB9LntCDBz5kx/f3+LgrdiEzqbPufvbFqzW2pRZ7t48aI5fQBwfo899tg777zjkF072/TmypUrQoi4uDglKj9+/LgQ4uDBgxZtZYeMY1G60Sqc9E2zZ8ZxnnSj1WrDw8PHjx9vUfxWbOIa0xs1djatM82lx40bV716dVvaYsLgwYMbN26sUOWmOVu60Wq1tWvXHjNmjEKVh4aGTpkyxaJNGAH0ue0IMHz48AYNGlgU/Ouvv16/fn2LNnGNzqZ1m7NphTrbzp07hRCXLl2yqT3F+Pbbb4UQycnJSlRumhOmm9GjR0dERChUeb9+/Vq0aGHRJowA+tx2BNi4caMQ4vr16za1xzz//Y1v+fLlK1SokJqaKp3zFzVt2rTU1FQPD4/PP//cmR/+LP3yXQjh6+trtID0a2shxKNHj4wWGDJkyMcff7x+/fpRo0YpEKCcNBqN9M8owuyLREq8X3xR6enpycnJQojq1aubU153Ncqnn37q5eXVtm3bJ5988t69e9u3b79586YQ4vz589OmTZszZ47+VuZf7WKC7d++RaxoqfnNrFatmvTi0qVLzzzzjO3Rqs7GjRtfeeUVrVZb9KPs7OyBAwdqtdqBAwfaPzDnwQhggBFAOXQ2A87f2YTZLXW2zga4NqY3JbJDxrE03QiFk75p9sw47pZuXGZ6o8bOJtxsLm1/pJsSMQIYYARQjst0NuE2Z9Pq7Wz2R7opESOAAUYAO/jfc3wff/xxIURGRkZKSopBocuXLy9evFgI0b9//6efflqufX/wwQfr169fv359pUqV5Krz/v370osSO01GRobRAnXq1GndunVsbKxcISnn4sWLDx8+FELUrl07NDTURMnc3Fzp1udW/EFKD9MWQpQpU8ac8vr3pr9w4cLevXtnzJixZMmSs2fP6rr+xo0bDZKBtJWfn19x93A3h+3fvkWsaKn5zSxbtqz04tatW7aHqjq3b98eNmyY0RmDzqhRo9zz4OgwAhhgBFAOnc2A83c2YXZLna2zAS6M6Y057JBxLE03QuGkb5o9M467pRuXmd6osbMJN5tL2xnpxhyMAAYYAZTjMp1NuM3ZtHo7m52RbszBCGCAEcAODFd8hRDx8fEGhSZMmJCfnx8YGDhr1iz99zMyMgoLC63ed9u2bfv27du3b9+goCCrKzGQl5cnvSjuOeG69wsKCoqrZOjQoceOHfvzzz/likohuisOSry3++nTp6UjU7Rkbm6u6b8f3acWDRlhYWEHDx7UvyF7cHDwsmXLPD09hRA3btwwuLBA2ioyMlL3V20FWb5981nRUvObqRsyZLmeRXUWLFhQ4rCenZ09b948+8TjnBgBDDACKEeWziZK6m90tuIo2lJn62yAC2N6Yw47TG8sTTdC4aRvmj0zjrulG5eZS6uxswk3m0vbGenGHIwABhgBlMPZtAE6m8sg3ZiDEcAAI4AdGFnxNbix8+7du/fs2SOEmDx5svQc48LCwvnz59eqVatMmTKlS5du1aqVdLN4Z6BbPNb1HgO693VfSVG9e/cOCgpatWqV7OHJy/whw+hzv1etWtW0adNSpUqVLl26evXqn3zySU5OTtFtdV3WxBHTuX//vtR/nnrqKT8/P4NPn3jiCd2flv4fUlJSkvQ7ehvvQiPLt28mK1pqUTOddsiwjx07dphTbPv27UpH4swYAQwwAijHxs4mzOtvdDajlG6ps3U2wIUxvTGHHaY3FqUboXzSN81uGccN041rzKXV2NmE+82l7Yx0Yw5GAAOMAMrhbNoAnc1lkG7MwQhggBHADrx1r4yu+Obn50+cOFEIUaNGjbffflt6c/Dgwd9+++3LL788cODAS5cubd++/bXXXjtw4MDKlSvtGLlxpUuXll7Y0mkCAwN79+69bt26OXPmWP3Q4suXL589e9aiTVJTU729vUsu9/8VNxAUZXD/cY1G069fvw0bNnTq1Gno0KGBgYGbN2+eMmXKwYMH9+zZI13doGPRRSLHjh3T31FRtWvXln5ErvumLGqIabJ8+2ayoqUWNdOiISM3N1cIsXnzZoPvThanTp3Ky8vbtGmT7DWbUPROA0YlJiZu2LBBiVYX5/r1615eXgodjXv37mVmZppfnhHAgNuOADk5OYWFhRZ1yz///LO4i+mMsrqzCUv6G53NKKVbasUM9ddff7VosIIJly9fDg8PDwgIcHQgbicjI+PcuXNMb8T/P7n95ZdfpPmkvBITE0Xxl28bZYfpjaWXwCud9E2zW8ZxtnSTl5d35coVi/5Is7KysrKyzC/vGnNpNXY24WRzaannKJQRLl++nJqaSrqRPHjw4MKFCwodjdzcXEYAW7jtCJCZmfnw4UOLumViYqLRBf7icDZtwG07m/SDxe+//97S9QJz/P7770KIHTt2lCtXTvbKi+O06ebChQv3799XKN1cv349Ozvb/PKMAAbcdgTIz88XQuzatSskJKTEwrpNLl++3KhRIzPL66L63/pivXr1pBf6K75Lly69fPmyEGLu3Ln+/v5CiO++++6bb775z3/+88orr0hlLly40Llz56+++iomJubll1+2KALZ6b6e4g609BRrUVKnycvL8/HxsXq5Vwgxbdq0//znP5ZuZf4/oWZnZ0v3nfbx8WnatKnpwtKQUadOHalLLVq0aPPmzWvWrBkwYIBUYNiwYZ06ddq3b99//vOf/v37629r0UHQ/VVERUUZLaBrYFhYWNGtbLxIRK5v3xxWtNSiZupuH2/O8b9w4YIQQvcnqYQ+ffooV7nVNBqNoq0ujnJHw/zbYjACFOW2I8D58+fz8/Mt7Zbmf7O2dDZhSX+jsxmldEst6mzSA1c++eSTEksCzm/v3r179+51dBRGOGR6M2fOHOUql66SNod9pjeWnuIpnfRNs1vGcap0I4S4d+/erl27du3aZU5hHem0yBwuM5dWY2cTTjaXvnDhQmpqqqInvJxN6xw4cODAgQMKVc4IYAu3HQEuXbp08+ZNS/9IAwMDzSzJ2XRRbtvZ/v77byHE+PHjSyxptREjRihXudVc7x9vzV9WZwQoym1HgKtXrwohRo8eXWJJG/n7+/9vxbdGjRp+fn65ubnStdhCiPT09BkzZgghoqOjX3rpJenNRYsWPf/88/p/qA0aNJg7d27fvn0/+ugjh6/46p6AffXq1WeffbZoAengCpN/nOnp6Vu2bJF+3Gy1NWvWLFmyxKJNunfvHhwcbGbhv//+W7o4KCwsrOjP0vWdPXs2ISFBCPH8889L77zwwgt37tzRDRa6N/fv3//bb78ZzFB1v7VPT08vMSrpr8LDw6NFixZFP9VoNBcvXhRCNGrUSP/hzdJWwcHB+rdTt4Is376ZrGipRc2UHuou9I6/CZGRkV9//XVqaqqXl5fZLTDXp59+umjRohs3bsheswnPPvusOWdrderU0Q3E9tGzZ09vb2+FLhNr37697sqbEjECFOW2I0Dz5s137dqlmxKZY968eeb/474tnU1Y0t/obEYp3VKLOps0S9mwYUPHjh3NbQBMys3NNf1nBYXUr1+/d+/e06dPt+dOnXN6k5iY2KJFi2+//TYmJkb2yk+fPt2uXbvw8HAzy9tnemNRuhHKJ33T7JZxnCrdCCEqVarUtWvXmTNnmhe+EEI0btzYaPBGucxcWo2dTTjZXLpFixbXr18/c+aM2eFbYMyYMWfOnPn111+VqLw4zpluhBDNmjXr0KHDp59+qkTlERERjAC2cNsRoFmzZllZWYcPHzY7fDF+/Hjz/3Y4my7KbTtb7dq1pfpt/4MtavPmzSNGjLh06VLFihVlr7w4Tptu3nnnnYMHDx4/flyJykeMGHHt2jUzCzMCFOW2I4B0f+Vz585Jj801U15enq+vr/nlhRB+fn7/W/H18vKKiIj4888/b9++Lb0ze/bstLQ0Ly+vzz//XFesVq1aRf+Zr2vXrp6entLPjGx5dLPtGjduLL0o7sYCuk7TsGHD4ipZv359dnb24MGDbYnE29vb/OVb3SbmX5Fx584d6YXu76Q4a9eulV7orm2pU6dO0ZPntLQ0YayDWjFkREREGG37zz//nJqaKoTo1KmT7k2tViv9xN72axJl+fbNZGlLLW2m7mjr3z/BtODgYCVWfAMCAjw8PCztzDZ6+eWXzZk09OrVy86B+fr6WvGnbSZGgBLrN82dRwBL/0gtuoWsLZ1NWNLf6GxGKd1SK9JNUFCQncdeQHZeXl7+/v5Mb8T/v3Raob9rM2+brGOf6Y11K77KJX3T7JZxnC3deHh4+Pn5WdQtLbpboGvMpVXa2YTzzaU9PT0VGnj9/PyUO38sjnOmGyGEl5eXpX/X5rPo502MAEW57Qjg4eHh5eVlUbf08/Ozzz/dCM6mXauzScqUKaPEMCj97rxs2bL2HNidNt34+flZ+ndtPl9fX0YAW7j5CGCfP9J/nBRJS8137tzRaDS3bt1asGCBEGLEiBG6b0IIsWTJkq5duxrUEhAQEBgYmJ+fL93uz4EaNWok3X36xIkTRgucO3dOCBEcHBwREVFcJbGxsW3atFHiihsZ6X7YbvpRJffv35eGjOeee65169bFFcvLy/v222+FEC+++KLBR7ouq7tsoTjXr1+XLhcw+kv5wsLCCRMmCCE8PDz07zJx6dIlqWbbnzsiy7dvDitaamkzdUfb/CHDlYwdO7bEWzeULl1aOs7uiRGgKEYAhcjb2UTx/Y3OVpQdWupUnQ1wbUxvSmSf6Y356UbYJembZp+M44bpxjXm0mrsbML95tL2R7opESNAUYwACuFsuig6m8sg3ZSIEaAoRgA7MLLiW1hYePfu3Y8++ig7Ozs4OFi6sbNOQEBA0TZcvnz50aNH5cuXt+etA4zy8/Pr1q2bEOLQoUPSKr2+mzdvSmv7L774YnGXY5w/f/7o0aNDhw5VOlQb1a1bV7obwLVr10w8HXro0KG3b9/29fVduHBhcWVu37798ssvJyYmvvbaa61atTL4VPdL8xIvEjF9o/P58+efPn1aCNGrVy/9W9fK+NwR2799M1nRUkubqTvaFv3S32WEhoauXbvWxHX6np6eX3/9tcMHHAdiBCiKEUAhMnY2YbK/0dmKskNLnaqzAa6N6U2J7DO9MT/dCLskfdPsk3HcMN24xlxajZ1NuN9c2v5INyViBCiKEUAhnE0XRWdzGaSbEjECFMUIYAdGVnyFEOfOnVu9erUQYtq0abqHRZuwe/duIcTw4cPlD9ByAwcOFELk5OTMnj3b4KMZM2ZIT1QeMmRIcZvHxsaWLl26V69eigZpu4CAAOlpW3l5eYsWLTJaZvr06du2bRNCzJ07t0mTJkUL9O3bt2HDhuHh4Tt37hw+fPiKFSuKlildurTUa6UnzJug+6swKKnVamfPnj1p0iQhRHBwsP5NwsX/fyy5KP4Z2llZWcuWLdu+fbvpvUus+/Yt2oWwqqUlNtOArmbdX6W76dat2/bt28uXL1/0o+Dg4G3btvXs2dP+UTkPRgCjGAGUIEtnE2b0NzpbUQq1VJ9TdTbA5TG9Mc0+0xvz041QLOk7W8Zxw3TjGnNpNXY24X5zaYcg3ZjGCGAUI4ASOJs2is7mMkg3pjECGMUIoDitHt0Trdu0aSOEaNCgQX5+vrYkN2/eDA4Orl279v3790ssrK93795Vq1atWrXqtWvXLNpQ0rVr1+joaKMfSX9LHh4eX375pe7NxYsXS1ed9OjRo7g68/LyKlSo8Prrr1sRj+2io6O7d+9ufvmTJ09KT0328vLatm2b/ke3bt3S3YJ8+vTpxdXQrVu35s2bly9f3sPDo3///omJiUaLtW/fXgjh6+ubk5NjIh6p2wghvL29V65cmZ+fX1hYePToUenCDamG77//3mCr5s2bCyFq1qxZXLVvvPGGtPmiRYtM7F3Him/f0l1Y0dISm2mgWbNmQogKFSqYU1i6AXtBQYGZlVtk2rRpQUFBStRsjvv373/88cctW7b09/f38vJ66qmnZsyYce/ePUfF07Fjx5iYGIUqj4qKevXVV80vzwhglBuOADNnzvT39zezZus2sb2zac3rb3Q2+7RUn0Wd7eLFi0KIXbt2mVMYcGaPPfbYO++846i9S9Mb6VZRgYGBjp3eXLlyRQgRFxenROXS2eXBgwfN38Q+0xsz041WsaTvbBnH2dKNVqsNDw8fP368mYWt28QF5tJq7GzKtVSfRf1t3Lhx1atXN7NmSw0ePLhx48YKVV4i3dm0j4+Pr6+vw8+ma9euPWbMGIUqDw0NnTJlivnlGQGMcsMRYPjw4Q0aNDCzZsnrr79ev35988tzNm2UG3a2nTt3CiEuXbpkZuUWke70m5ycrETlJdKlG+lxwg5PN6NHj46IiFCo8n79+rVo0cL88owARrnhCLBx40YhxPXr182s3Bb/WPE1+HX53r17S9w+PT29SZMmFStWtGLAio6OlnaUkJBg6bZakyu+N2/erFy5slR5s2bNevXqpbvxd40aNUwMf1u2bBFCHD582Ip4bGfpiq9Wq12+fLnuF+7PPvvs+++//8EHH/Ts2TMgIEAIERgY+M0335RYiUajOXToUGhoaIUKFc6cOVO0wMSJE6VdHD16tLhKCgsLpYeEP/7449WqVRNCSCcVuu5Urly5nTt3GmyVnZ0tjXp9+/Ytrua2bdtKNZg5CbPi27doF1a01Jxm6svNzZUq7NChgznlXXjFV2fYsGENGzZ0dBTOteKrZQQwxg1HADus+Gpl6mzakvobnc0+LdWxtLOx4guX4dgVX0leXp4QYuHChY4Nw9lWfLV2md6Yk260SiZ9p8o4TphutHZZ8dWqfC6txs6maEt1LO1vLrziq9O2bdtu3bo5OgrnWvHVMgIY44YjgB1WfLWcTRvjhp3NhVd8dT755BNfX1/HxqB1shVfLSOAMW44AjhsxVer1VatWlVqtjlLj+np6U8//XT16tXj4+Ot2LdyK75arTY5Obldu3binzp37nz79m3TdT7++ONWBCMLK1Z8tVrt9u3ba9asadBSPz+/4cOH37hxw/x6tm7dKv2NaTQag4/27NkjVbtkyZLiNpeeqi2EeOedd1JSUrp37667j7+vr++AAQP+/vvvolsdPnxYKjN37tziat6zZ0/FihXr1KlTr169orEZZem3b9EurGipOc3Ud+zYMan8p59+ak55VnztxtlWfLWMAMa42whgnxVfrXydTVt8f6Oz2aelOpZ2NlZ84TJY8dVxwhVfrfLTG3PSjVbJpO9UGccJ043WXiu+WjXPpdXY2RRtqY6l/Y0VX7txthVfLSOAMe42AthnxVfL2bQx7tbZWPG1G2db8dUyAhjjbiOAPVd8vQ0O640bN4R5Hj582Llz57t37/7888/h4eFmbqXvwIEDVmxlprCwsB9//PHUqVP79u1LTU2tWrVqu3btGjdubGKT5OTkPXv2zJo1S7molNCtW7eYmJhDhw4dOXIkLS0tJCSkXr16nTt3li5ksKieUqVKnTx58ty5cwYHqk2bNv7+/jk5ObquXJTu3uhRUVGVKlWKi4u7c+fO5cuXfX19H3/88bJlyxrdqmXLllqt1nRgzz///O3bt4UQXbt21Wg0Xl5eJbbF0m/fol1Y0VJzmqlPd3/1zp07m78V3BMjQFGMAAqRq7OJ4vsbnU2fci3VcdrOBsDNKT29MSfdCCWTvlNlHDdPN+qdS6uxswn3nkvDCTECFMUIoBDOpouis8F9MAIUxQigHMMVXzOlp6d37tw5IyPjl19+CQsLkzcmGUVGRkZGRppZeM2aNR4eHgMGDFA0JCV4e3u3b99eul271by8vEJDQ69fv37jxg2Dvy7pMeNbt27dsWNHTk6Ov79/0c31/5CkFxUrVqxYsaItIRkN0vzCFn375u/CDi3dsWOHEKJ27dqmr1EAJIwARjECKEGWziaK7290Nn1u3tkAuDlFpzfmpBvhNhmHdMNc2iimN3ATjABGMQIogbNpo+hscBOMAEYxAijB04pt0tPTO3XqlJeXd/DgQWde7rVUbGzsCy+8UKlSJUcHojjdNQj6cnNzb926JYRo1KhR0U9Hjx4thEhLS9uwYYPROqU/pJCQkKL3KJBFZmZmqVKllKjZ0l0o3dK7d+/u27dPCDFq1Cgl6gcYAWzZBSOApSztb3Q2HTobAJhP9nQj3CbjkG4sxVzall3Q36B2jAC27IIRwFKcTVu9CzobXAAjgNW7cPMRwOIV3wcPHnTs2NHDw+Onn34KDQ1VIiaH+O233+Lj44cOHeroQOyhV69e69evN3hzxYoVhYWFjRo1ql69etFNOnTo0KBBAyHE0qVLi36anZ0t3R5dd92E7L755psePXooVLn5u7BDS1euXFlQUBAUFDR48GCFdgE3xwhg9S4YAaxgaX+js0nobABgEXnTjXCbjEO6sQJzaat3QX+DC2AEsHoXjABW4Gzaul3Q2eAaGAGs2wUjgMUrvkOHDj127Ji/v/+AAQO6du0a80/JyclKRGkHsbGxlSpV6tKli6MDsYdp06b169evV69eP/7446NHj9LS0pYtW/buu+96e3uvXr3a6CYeHh6LFy8WQhw9erToBSanTp0qKCgQiv0hZWVlbdiwoW/fvkpUbtEulG5pdnb2/PnzhRAzZsxwpSsq4FQYAazeBSOAFSztb3Q2CZ0NACwib7oRbpNxSDdWYC5t9S7ob3ABjABW74IRwAqcTVu3CzobXAMjgHW7YASweMU3NTVVCHHo0KGdO3fu2rXr+3/KyspSIEjFZWRkbNy4ceDAgd7eVj7YWF0GDRq0bdu2EydOdOjQoUyZMqGhoW+88UblypV//PHH5s2bF7dV27ZtBw4cKISYOXOmwUdF740ur3Hjxo0ePVrRb8fMXSjd0vnz59+5c6dp06ZvvfWWEvUDghHAhl0wAljBiv5GZxN0NgCwkLzpRrhNxiHdWIG5tNW7oL/BBTACWL0LRgArcDZt3S7obHANjADW7YIRwOLv4JdfflEiDsfatGlTRkbGkCFDHB2I/XTv3v35558/dOjQ8ePHvb29mzdv3rJlyxJvgz5nzpwdO3Zs27Zt69atPXv21L2v6B/SmTNnKlWq1Lt3b9lrtmIXirY0Pj5+xowZnp6eX3zxhUUPOQcsxQhg3S4YAaxjRX+js9HZAMBSMqYb4TYZh3RjHebS1u2C/gbXwAhg3S4YAazD2bQVu6CzwWUwAli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\n", + "text/plain": [ + "" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "oracle.circuit.draw(output='latex')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As seen, the $v_i$'s correspond to the 3 input bits; the $o_0$ is the oracle's output qubit; the $a_0$ is an ancilla qubit.\n", + "\n", + "Next we can simply create a `DeutschJozsa` instance using the oracle, and run it to check the result." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The truth table 11110000 represents a balanced function.\n" + ] + } + ], + "source": [ + "dj = DeutschJozsa(oracle)\n", + "backend = BasicAer.get_backend('qasm_simulator')\n", + "result = dj.run(QuantumInstance(backend, shots=1024))\n", + "print('The truth table {} represents a {} function.'.format(bitstr, result['result']))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The above step-by-step programatic approach can also be achieved by using a json configuration dictionary with the parameters for the algorithm and any other dependent objects it requires, as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The truth table 11110000 represents a balanced function.\n" + ] + } + ], + "source": [ + "bitstr = '11110000'\n", + "params = {\n", + " 'problem': {\n", + " 'name': 'functionevaluation',\n", + " },\n", + " 'algorithm': {\n", + " 'name': 'DeutschJozsa'\n", + " },\n", + " 'oracle': {\n", + " 'name': 'TruthTableOracle',\n", + " 'bitmaps': [bitstr]\n", + " },\n", + " 'backend': {\n", + " 'shots': 1024,\n", + " },\n", + "}\n", + "\n", + "result_dict = run_algorithm(params, backend=backend)\n", + "print('The truth table {} represents a {} function.'.format(bitstr, result_dict['result']))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can of course quickly put together another example for a `'constant'` function, as follows." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The truth table 1111111111111111 represents a constant function.\n" + ] + } + ], + "source": [ + "bitstr = '1' * 16\n", + "oracle = TruthTableOracle(bitstr)\n", + "dj = DeutschJozsa(oracle)\n", + "backend = BasicAer.get_backend('qasm_simulator')\n", + "result = dj.run(QuantumInstance(backend, shots=1024))\n", + "print('The truth table {} represents a {} function.'.format(bitstr, result['result']))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.2" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} From bed38dc101eead4ace3b1de38fc7a84ddf6a717c Mon Sep 17 00:00:00 2001 From: Shaohan Hu Date: Tue, 23 Apr 2019 14:01:33 -0400 Subject: [PATCH 074/116] add notebook for bernstein-vazirani --- .../aqua/general/bernstein_vazirani.ipynb | 213 ++++++++++++++++++ 1 file changed, 213 insertions(+) create mode 100644 community/aqua/general/bernstein_vazirani.ipynb diff --git a/community/aqua/general/bernstein_vazirani.ipynb b/community/aqua/general/bernstein_vazirani.ipynb new file mode 100644 index 000000000..24d5ae62f --- /dev/null +++ b/community/aqua/general/bernstein_vazirani.ipynb @@ -0,0 +1,213 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "# _*Experiment with the Bernstein-Vazirani Algorithm in Aqua*_\n", + "\n", + "This notebook demonstrates how to experiment with the `Bernstein-Vazirani` algorithm in `Qiskit Aqua`.\n", + "\n", + "We first import all necessary modules." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import math\n", + "from qiskit import BasicAer\n", + "from qiskit.aqua import QuantumInstance\n", + "from qiskit.aqua import run_algorithm\n", + "from qiskit.aqua.algorithms import BernsteinVazirani\n", + "from qiskit.aqua.components.oracles import TruthTableOracle" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Bernstein-Vazirani algorithm is explained in more detail in the corresponding notebook located in the directory `community/algorithms`. We can experiment with it in Aqua by feeding it oracles created using truth tables. For example, we can create a `TruthTableOracle` instance as follows." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "bitstr = '00111100'\n", + "oracle = TruthTableOracle(bitstr)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As shown, the truthtable is specified with the `bitstr` containing values of all entries in the table. It has length $8$, so the corresponding truth table is of $3$ input bits. The truthtable represents the function mappings as follows.\n", + "\n", + "- $\\mathbf{a} \\cdot 000 \\mod 2 = 0$\n", + "- $\\mathbf{a} \\cdot 001 \\mod 2 = 0$\n", + "- $\\mathbf{a} \\cdot 010 \\mod 2 = 1$\n", + "- $\\mathbf{a} \\cdot 011 \\mod 2 = 1$\n", + "- $\\mathbf{a} \\cdot 100 \\mod 2 = 1$\n", + "- $\\mathbf{a} \\cdot 101 \\mod 2 = 1$\n", + "- $\\mathbf{a} \\cdot 110 \\mod 2 = 0$\n", + "- $\\mathbf{a} \\cdot 111 \\mod 2 = 0$\n", + "\n", + "And obviously the goal is to find the bitstring $\\mathbf{a}$ that satisfies all the inner product equations.\n", + "\n", + "We can inspect the circuit corresponding to the binary function encoded in the `TruthTableOracle` instance." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "oracle.circuit.draw(output='latex')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As seen, the $v_i$'s correspond to the 3 input bits; the $o_0$ is the oracle's output qubit; the $a_0$ is an ancilla qubit.\n", + "\n", + "Let us first compute the groundtruth $\\mathbf{a}$ classically:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The groundtruth result bitstring is 110.\n" + ] + } + ], + "source": [ + "a_bitstr = \"\"\n", + "num_bits = math.log2(len(bitstr))\n", + "for i in reversed(range(3)):\n", + " bit = bitstr[2 ** i]\n", + " a_bitstr += bit\n", + "print(f'The groundtruth result bitstring is {a_bitstr}.')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we can create a `BernsteinVazirani` instance using the oracle, and run it to check the result against the groundtruth." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The result bitstring computed using Bernstein-Vazirani is 110.\n" + ] + } + ], + "source": [ + "bv = BernsteinVazirani(oracle)\n", + "backend = BasicAer.get_backend('qasm_simulator')\n", + "result = bv.run(QuantumInstance(backend, shots=1024))\n", + "print('The result bitstring computed using Bernstein-Vazirani is {}.'.format(result['result']))\n", + "assert(result['result'] == a_bitstr)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The above step-by-step programatic approach can also be achieved by using a json configuration dictionary with the parameters for the algorithm and any other dependent objects it requires, as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The result bitstring computed using Bernstein-Vazirani is 110.\n" + ] + } + ], + "source": [ + "params = {\n", + " 'problem': {\n", + " 'name': 'hiddenstringfinding',\n", + " },\n", + " 'algorithm': {\n", + " 'name': 'BernsteinVazirani'\n", + " },\n", + " 'oracle': {\n", + " 'name': 'TruthTableOracle',\n", + " 'bitmaps': [bitstr]\n", + " },\n", + " 'backend': {\n", + " 'shots': 1024,\n", + " },\n", + "}\n", + "\n", + "result_dict = run_algorithm(params, backend=backend)\n", + "print('The result bitstring computed using Bernstein-Vazirani is {}.'.format(result_dict['result']))\n", + "assert(result_dict['result'] == a_bitstr)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.2" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} From b42e98832a4435542c42dba87944d632163a9adf Mon Sep 17 00:00:00 2001 From: Shaohan Hu Date: Tue, 23 Apr 2019 14:01:43 -0400 Subject: [PATCH 075/116] add notebook for simon's --- community/aqua/general/simon.ipynb | 222 +++++++++++++++++++++++++++++ 1 file changed, 222 insertions(+) create mode 100644 community/aqua/general/simon.ipynb diff --git a/community/aqua/general/simon.ipynb b/community/aqua/general/simon.ipynb new file mode 100644 index 000000000..e5c2ac1a7 --- /dev/null +++ b/community/aqua/general/simon.ipynb @@ -0,0 +1,222 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "# _*Experiment with the Simon's Algorithm in Aqua*_\n", + "\n", + "This notebook demonstrates how to experiment with the `Simon`'s algorithm in `Qiskit Aqua`.\n", + "\n", + "We first import all necessary modules." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from qiskit import BasicAer\n", + "from qiskit.aqua import QuantumInstance\n", + "from qiskit.aqua import run_algorithm\n", + "from qiskit.aqua.algorithms import Simon\n", + "from qiskit.aqua.components.oracles import TruthTableOracle" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The [Simon's algorithm](https://en.wikipedia.org/wiki/Simon's_problem) is explained in more detail in the corresponding notebook located in the directory `community/algorithms`. We can experiment with it in Aqua by feeding it oracles created using truth tables. For example, we can create a `TruthTableOracle` instance as follows." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "bitmaps = [\n", + " '01101001', \n", + " '10011001', \n", + " '01100110'\n", + "]\n", + "oracle = TruthTableOracle(bitmaps)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As shown, the truthtable is specified with three length-8 bitstrings, each containing the values of all entries for a particular output column in the table. Each bitstring has length $8$, so the truthtable has $3$ input bits; There are $3$ bitstrings, so the truthtable has $3$ output bits.\n", + "\n", + "The function $f$ represented by the truthtable is promised to be either 1-to-1 or 2-to-1. Our goal is to determine which. For the case of 2-to-1, we also need to compute the mask $\\mathbf{s}$, which satisfies $\\forall \\mathbf{x},\\mathbf{y}$: $\\mathbf{x} \\oplus \\mathbf{y} = \\mathbf{s}$ iff $f(\\mathbf{x}) = f(\\mathbf{y})$. Apparently, if $f$ is 1-to-1, the corresponding mask $\\mathbf{s} = \\mathbf{0}$.\n", + "\n", + "Let us first compute the groundtruth mask $\\mathbf{s}$ classically:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The groundtruth mask is 011.\n" + ] + } + ], + "source": [ + "def compute_mask(input_bitmaps):\n", + " vals = list(zip(*input_bitmaps))[::-1]\n", + " def find_pair():\n", + " for i in range(len(vals)):\n", + " for j in range(i + 1, len(vals)):\n", + " if vals[i] == vals[j]:\n", + " return i, j\n", + " return 0, 0\n", + "\n", + " k1, k2 = find_pair()\n", + " return np.binary_repr(k1 ^ k2, int(np.log2(len(input_bitmaps[0]))))\n", + "\n", + "mask = compute_mask(bitmaps)\n", + "print(f'The groundtruth mask is {mask}.')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we can create a `Simon` instance using the oracle, and run it to check the result against the groundtruth." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The mask computed using Simon is 011.\n" + ] + } + ], + "source": [ + "simon = Simon(oracle)\n", + "backend = BasicAer.get_backend('qasm_simulator')\n", + "result = simon.run(QuantumInstance(backend, shots=1024))\n", + "print('The mask computed using Simon is {}.'.format(result['result']))\n", + "assert(result['result'] == mask)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The above step-by-step programatic approach can also be achieved by using a json configuration dictionary with the parameters for the algorithm and any other dependent objects it requires, as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The mask computed using Simon is 011.\n" + ] + } + ], + "source": [ + "params = {\n", + " 'problem': {\n", + " 'name': 'periodfinding',\n", + " },\n", + " 'algorithm': {\n", + " 'name': 'Simon'\n", + " },\n", + " 'oracle': {\n", + " 'name': 'TruthTableOracle',\n", + " 'bitmaps': bitmaps\n", + " },\n", + " 'backend': {\n", + " 'shots': 1024,\n", + " },\n", + "}\n", + "\n", + "result_dict = run_algorithm(params, backend=backend)\n", + "print('The mask computed using Simon is {}.'.format(result_dict['result']))\n", + "assert(result_dict['result'] == mask)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can also quickly try a truthtable that represents a 1-to-1 function (i.e., the corresponding mask is $\\mathbf{0}$), as follows." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The groundtruth mask is 000.\n", + "The mask computed using Simon is 000.\n" + ] + } + ], + "source": [ + "bitmaps = [\n", + " '00011110', \n", + " '01100110', \n", + " '10101010'\n", + "]\n", + "mask = compute_mask(bitmaps)\n", + "print(f'The groundtruth mask is {mask}.')\n", + "oracle = TruthTableOracle(bitmaps)\n", + "simon = Simon(oracle)\n", + "result = simon.run(QuantumInstance(backend, shots=1024))\n", + "print('The mask computed using Simon is {}.'.format(result['result']))\n", + "assert(result['result'] == mask)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.2" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} From 54f254116b6242376bfcde4c22ee4b9d0f35a6f5 Mon Sep 17 00:00:00 2001 From: Shaohan Hu Date: Tue, 23 Apr 2019 14:01:53 -0400 Subject: [PATCH 076/116] add notebook for shor's --- community/aqua/general/shors.ipynb | 118 +++++++++++++++++++++++++++++ 1 file changed, 118 insertions(+) create mode 100644 community/aqua/general/shors.ipynb diff --git a/community/aqua/general/shors.ipynb b/community/aqua/general/shors.ipynb new file mode 100644 index 000000000..a3d29375f --- /dev/null +++ b/community/aqua/general/shors.ipynb @@ -0,0 +1,118 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "# _*Experiment with the Shor's Algorithm in Aqua*_\n", + "\n", + "This notebook demonstrates how to experiment with the `Shor`'s algorithm in `Qiskit Aqua`.\n", + "\n", + "We first import all necessary modules." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit import BasicAer\n", + "from qiskit.aqua import QuantumInstance\n", + "from qiskit.aqua import run_algorithm\n", + "from qiskit.aqua.algorithms import Shor" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The [Shor's Factoring Algorithm](https://en.wikipedia.org/wiki/Shor's_algorithm) is explained in more detail in the corresponding notebook located in the directory `community/algorithms`. With Aqua, we can create a `Shor` instance by simply providing the target integer to be factored and run it, as follows." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The list of factors of 15 as computed by the Shor's algorithm is [3, 5].\n" + ] + } + ], + "source": [ + "N = 15\n", + "shor = Shor(N)\n", + "backend = BasicAer.get_backend('qasm_simulator')\n", + "quantum_instance = QuantumInstance(backend, shots=1024)\n", + "ret = shor.run(quantum_instance)\n", + "print(\"The list of factors of {} as computed by the Shor's algorithm is {}.\".format(N, ret['factors'][0]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The above step-by-step programatic approach can also be achieved by using a json configuration dictionary with the parameters for the algorithm and any other dependent objects it requires, as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The list of factors of 15 as computed by the Shor's algorithm is [3, 5].\n" + ] + } + ], + "source": [ + "params = {\n", + " 'problem': {\n", + " 'name': 'factoring',\n", + " },\n", + " 'algorithm': {\n", + " 'name': 'Shor',\n", + " 'N': N,\n", + " },\n", + " 'backend': {\n", + " 'shots': 1024,\n", + " },\n", + "}\n", + "result_dict = run_algorithm(params, backend=backend)\n", + "print(\"The list of factors of {} as computed by the Shor's algorithm is {}.\".format(N, result_dict['factors'][0]))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.2" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} From 5f4cbcdff10cb1f2091b3e41a10c5f14dd82dfa9 Mon Sep 17 00:00:00 2001 From: Manoel Marques Date: Fri, 26 Apr 2019 13:15:21 -0400 Subject: [PATCH 077/116] Change seed_mapper to seed_transpiler --- .../qsvm_kernel_directly.ipynb | 4 +- .../qsvm_variational.ipynb | 4 +- .../aqua/general/simulations_with_noise.ipynb | 6 +- community/aqua/general/vqe2iqpe.ipynb | 4 +- .../qsvm_kernel_classification.ipynb | 6 +- .../aqua/finance/portfolio_optimization.ipynb | 6 +- qiskit/aqua/optimization/docplex.ipynb | 4 +- qiskit/aqua/optimization/maxcut_and_tsp.ipynb | 194 ++++++++---------- 8 files changed, 98 insertions(+), 130 deletions(-) diff --git a/community/aqua/artificial_intelligence/qsvm_kernel_directly.ipynb b/community/aqua/artificial_intelligence/qsvm_kernel_directly.ipynb index 601c0fc37..23c6701ae 100644 --- a/community/aqua/artificial_intelligence/qsvm_kernel_directly.ipynb +++ b/community/aqua/artificial_intelligence/qsvm_kernel_directly.ipynb @@ -195,7 +195,7 @@ "feature_map = SecondOrderExpansion(num_qubits=feature_dim, depth=2, entangler_map=[[0, 1]])\n", "svm = QSVMKernel(feature_map, training_input, test_input, None)# the data for prediction can be fed later.\n", "svm.random_seed = random_seed\n", - "quantum_instance = QuantumInstance(backend, shots=shots, seed=random_seed, seed_mapper=random_seed)\n", + "quantum_instance = QuantumInstance(backend, shots=shots, seed=random_seed, seed_transpiler=random_seed)\n", "result = svm.run(quantum_instance)" ] }, @@ -297,7 +297,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.7" + "version": "3.6.8" } }, "nbformat": 4, diff --git a/community/aqua/artificial_intelligence/qsvm_variational.ipynb b/community/aqua/artificial_intelligence/qsvm_variational.ipynb index ed80f5fc3..9d4e15b28 100644 --- a/community/aqua/artificial_intelligence/qsvm_variational.ipynb +++ b/community/aqua/artificial_intelligence/qsvm_variational.ipynb @@ -186,7 +186,7 @@ "feature_map = SecondOrderExpansion(num_qubits=feature_dim, depth=2)\n", "var_form = RYRZ(num_qubits=feature_dim, depth=3)\n", "svm = QSVMVariational(optimizer, feature_map, var_form, training_input, test_input)\n", - "quantum_instance = QuantumInstance(backend, shots=shots, seed=random_seed, seed_mapper=random_seed)" + "quantum_instance = QuantumInstance(backend, shots=shots, seed=random_seed, seed_transpiler=random_seed)" ] }, { @@ -243,7 +243,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.7" + "version": "3.6.8" } }, "nbformat": 4, diff --git a/community/aqua/general/simulations_with_noise.ipynb b/community/aqua/general/simulations_with_noise.ipynb index 75d56803e..72d52d925 100644 --- a/community/aqua/general/simulations_with_noise.ipynb +++ b/community/aqua/general/simulations_with_noise.ipynb @@ -123,7 +123,7 @@ ], "source": [ "backend = Aer.get_backend('qasm_simulator')\n", - "quantum_instance = QuantumInstance(backend=backend, seed=167, seed_mapper=167) \n", + "quantum_instance = QuantumInstance(backend=backend, seed=167, seed_transpiler=167) \n", "\n", "counts = []\n", "values = []\n", @@ -210,7 +210,7 @@ "basis_gates = noise_model.basis_gates\n", "\n", "backend = Aer.get_backend('qasm_simulator')\n", - "quantum_instance = QuantumInstance(backend=backend, seed=167, seed_mapper=167,\n", + "quantum_instance = QuantumInstance(backend=backend, seed=167, seed_transpiler=167,\n", " coupling_map=coupling_map,\n", " noise_model=noise_model,\n", " basis_gates=basis_gates)\n", @@ -300,7 +300,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.1" + "version": "3.6.8" } }, "nbformat": 4, diff --git a/community/aqua/general/vqe2iqpe.ipynb b/community/aqua/general/vqe2iqpe.ipynb index 48fd89215..9367a2235 100644 --- a/community/aqua/general/vqe2iqpe.ipynb +++ b/community/aqua/general/vqe2iqpe.ipynb @@ -163,7 +163,7 @@ "iqpe = IQPE(algo_input.qubit_op, state_in, num_time_slices, num_iterations,\n", " expansion_mode='suzuki', expansion_order=2,\n", " shallow_circuit_concat=True)\n", - "quantum_instance = QuantumInstance(backend, shots=100, seed=random_seed, pass_manager=PassManager(), seed_mapper=random_seed)\n", + "quantum_instance = QuantumInstance(backend, shots=100, seed=random_seed, pass_manager=PassManager(), seed_transpiler=random_seed)\n", "result_iqpe = iqpe.run(quantum_instance)\n", "print(\"Continuing with VQE's result, IQPE estimated the ground energy to be {}.\".format(\n", " result_iqpe['energy']))" @@ -193,7 +193,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.7" + "version": "3.6.8" } }, "nbformat": 4, diff --git a/qiskit/aqua/artificial_intelligence/qsvm_kernel_classification.ipynb b/qiskit/aqua/artificial_intelligence/qsvm_kernel_classification.ipynb index df5c71642..eee1be33b 100644 --- a/qiskit/aqua/artificial_intelligence/qsvm_kernel_classification.ipynb +++ b/qiskit/aqua/artificial_intelligence/qsvm_kernel_classification.ipynb @@ -184,7 +184,7 @@ "qsvm = QSVMKernel(feature_map, training_input, test_input, datapoints[0])\n", "\n", "backend = BasicAer.get_backend('qasm_simulator')\n", - "quantum_instance = QuantumInstance(backend, shots=1024, seed=seed, seed_mapper=seed)\n", + "quantum_instance = QuantumInstance(backend, shots=1024, seed=seed, seed_transpiler=seed)\n", "\n", "result = qsvm.run(quantum_instance)\n", "\n", @@ -284,7 +284,7 @@ "qsvm = QSVMKernel(feature_map, training_input, test_input)\n", "\n", "backend = BasicAer.get_backend('qasm_simulator')\n", - "quantum_instance = QuantumInstance(backend, shots=1024, seed=seed, seed_mapper=seed)\n", + "quantum_instance = QuantumInstance(backend, shots=1024, seed=seed, seed_transpiler=seed)\n", "\n", "result = qsvm.run(quantum_instance)\n", "\n", @@ -324,7 +324,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.7" + "version": "3.6.8" } }, "nbformat": 4, diff --git a/qiskit/aqua/finance/portfolio_optimization.ipynb b/qiskit/aqua/finance/portfolio_optimization.ipynb index 3858359da..8b04146c1 100644 --- a/qiskit/aqua/finance/portfolio_optimization.ipynb +++ b/qiskit/aqua/finance/portfolio_optimization.ipynb @@ -270,7 +270,7 @@ "ry = RY(qubitOp.num_qubits, depth=3, entanglement='full', initial_state=init_state)\n", "vqe = VQE(qubitOp, ry, cobyla, 'matrix')\n", "vqe.random_seed = seed\n", - "quantum_instance = QuantumInstance(backend, seed=seed, seed_mapper=seed)\n", + "quantum_instance = QuantumInstance(backend, seed=seed, seed_transpiler=seed)\n", "\n", "result = vqe.run(quantum_instance)\n", "\n", @@ -324,7 +324,7 @@ "cobyla.set_options(maxiter=250)\n", "qaoa = QAOA(qubitOp, cobyla, 3, operator_mode='matrix')\n", "qaoa.random_seed = seed\n", - "quantum_instance = QuantumInstance(backend, seed=seed, seed_mapper=seed)\n", + "quantum_instance = QuantumInstance(backend, seed=seed, seed_transpiler=seed)\n", "\n", "result = qaoa.run(quantum_instance)\n", "\n", @@ -374,7 +374,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.7" + "version": "3.6.8" } }, "nbformat": 4, diff --git a/qiskit/aqua/optimization/docplex.ipynb b/qiskit/aqua/optimization/docplex.ipynb index e2570c306..7e77e94ad 100644 --- a/qiskit/aqua/optimization/docplex.ipynb +++ b/qiskit/aqua/optimization/docplex.ipynb @@ -231,7 +231,7 @@ "vqe = VQE(qubitOp, ry, spsa, 'matrix')\n", "\n", "backend = BasicAer.get_backend('statevector_simulator')\n", - "quantum_instance = QuantumInstance(backend, seed=seed, seed_mapper=seed)\n", + "quantum_instance = QuantumInstance(backend, seed=seed, seed_transpiler=seed)\n", "\n", "result = vqe.run(quantum_instance)\n", "\n", @@ -287,7 +287,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.1" + "version": "3.6.8" } }, "nbformat": 4, diff --git a/qiskit/aqua/optimization/maxcut_and_tsp.ipynb b/qiskit/aqua/optimization/maxcut_and_tsp.ipynb index 91296bd69..04cabd9db 100644 --- a/qiskit/aqua/optimization/maxcut_and_tsp.ipynb +++ b/qiskit/aqua/optimization/maxcut_and_tsp.ipynb @@ -97,7 +97,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ @@ -136,21 +136,9 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "metadata": {}, - "outputs": [ - { - "ename": "ImportError", - "evalue": "cannot import name 'IBMQ'", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mImportError\u001b[0m Traceback (most recent call last)", - "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mIBMQ\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2\u001b[0m \u001b[0;31m# IBMQ.load_accounts()\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;31mImportError\u001b[0m: cannot import name 'IBMQ'" - ] - } - ], + "outputs": [], "source": [ "from qiskit import IBMQ\n", "# IBMQ.load_accounts()" @@ -165,19 +153,17 @@ }, { "cell_type": "code", - "execution_count": 58, + "execution_count": 3, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -199,7 +185,7 @@ }, { "cell_type": "code", - "execution_count": 59, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -235,7 +221,7 @@ }, { "cell_type": "code", - "execution_count": 60, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -264,14 +250,12 @@ }, { "data": { - "image/png": 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\n", + "image/png": 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WQKVSITc3F5GRkayjPKRz586YMmUKUlNTaUqnHbDZQnZ1dcXChQuRlpaGmpoa1nGIxB06dAgDBw6Em5sb6yiNxMTEoLq6Gnv27GEdhZiZzRYyAERERKBfv360VQ5pkdSGKx7k4OCApKQkfPjhh7h9+zbrOMSMbLqQAWDOnDk4fPgwbZVDDCouLkZBQQEiIiJYRzEoJCQEL7/8MtLS0mjowobZfCF7eHhg/vz5tFUOMSgzMxMjR46Eo6Mj6yjNeu2111BSUoL09HTWUYiZ2HwhA0BkZCS6deuGzZs3s45CJIbneaaPSptCLpcjKSkJ69atQ0lJCes4xAzsopABIC4uDnv37sX58+dZRyEScvnyZajVavTp04d1FKOEhoZi3LhxWL58OQ1d2CC7KWQfHx/Mnj0bKSkp0Gg0rOMQiWjYVZrjONZRjDZt2jQUFRXh0KFDrKMQkdlNIQPA6NGjERAQgC1btrCOQiRAr9cjMzNTsrMrDFEoFEhKSqKFtGyQXRUyx3FYuHAhvvrqK1y5coV1HMLYqVOn4Ovri65du7KOYjJaSMs22VUhA0BAQMCv683qdDrWcQhD1nIzz5A333wT+fn5OHr0KOsoRCR2V8iAsN6si4sLduzYwToKYUStVuPo0aN49tlnWUdpNaVSiYSEBKxYsQIqlYp1HCICuyxkmUyG+Ph4Wm/Wjh07dgy9evWCr68v6yht0q9fPwwfPhxr165lHYWIwC4LGQA6duyIqVOnYsmSJbTerB3KzMy06uGKB7399ts4c+YMcnJyWEchbWS3hQwAL7/8MjQaDb799lvWUYgFlZeX48yZMxg+fDjrKKJwcXFBfHw80tLSUF1dzToOaQO7LuSG9WY//vhjFBcXs45DLCQrKwuDBg2Ci4sL6yiiCQ8PR0REBNavX886CmkDuy5kAOjatStiYmKwdOlSevLJTkh5Zbe2iI2NxfHjx/HDDz+wjkJaye4LGQBeffVV3Lt3D/v27WMdhZjZjRs3cO3aNQwYMIB1FNG5ublh0aJFSE1NpTXArRQVMn5btGXDhg20aIuNy8jIQFRUFORyOesoZjFo0CD069cPGzduZB2FtAIV8n0Ni7asWLGChi5sVMPKbrY4XPGgOXPm4NChQ7QGuBWiQn7AtGnTUFhYiMOHD7OOQszgwoUL0Ol06N27N+soZuXh4YG4uDhaA9wKUSE/QKFQIDExEatWrUJ5eTnrOERkDY9KW9PKbq01fPhwhIaGYtOmTayjEBNQIT+iT58+GDVqFNasWcM6ChGRTqfDgQMHEB0dzTqKxcyfPx/79u3DuXPnWEchRqJCbsJbb72Fs2fP4vjx46yjEJHk5uYiKCgIwcHBrKNYjLe3N+bOnYvk5GTU19ezjkOMQIXcBGdnZ8THx2Pp0qWoqqpiHYeIwNpXdmutqKgodOrUCZ9++inrKMQIVMgGPP300xg8eDA9+WQDamtrcezYMURFRbGOYnEcx+H999/Hrl27cPHiRdZxSAuokJvx7rvv4sSJE/Tkk5X77rvv0KdPH/j4+LCOwoSvry9iY2ORnJwMrVbLOg5pBhVyM9zc3LBw4UKkpqaitraWdRzSSunp6XY5XPGgsWPHwtfXF9u2bWMdhTSDCrkFgwcPxpNPPklPPlmp0tJSnD17FkOHDmUdhamG7ct27NiBgoIC1nGIAVTIRpg7dy4OHjyIs2fPso5CTJSVlYUhQ4bA2dmZdRTmAgMDMXPmTCxevJi2L5MoKmQjeHp6Yt68eUhJSaHpQ1YmPT3d5h+VNsW4cePg6upK25dJFBWykUaMGIGuXbvik08+YR2FGOnq1asoLi5GeHg46yiSwXEcbV8mYVTIRuI4DnFxcdi9ezfy8/NZxyFGyMjIwKhRo+Dg4MA6iqR06NABb7zxBlJSUmj7MomhQjZBw/ShlJQUmj4kcfaysltrTZw4ETzP4+uvv2YdhTyACtlENH3IOvz8889wcHBAz549WUeRJJlMhqSkJGzevBk3b95kHYfcR4VsoobpQ9u3b6fpQxJmTyu7tVZwcDCmTJmC1NRUWgNcIqiQWyEwMBBvvfUWjcFJlFarRVZWll2t7NZaMTExqK6uxu7du1lHIaBCbrXx48dDoVDgyy+/ZB2FPOLkyZPo1KkTOnTowDqK5Dk4OCApKQkbN27E7du3Wcexe1TIrSSTyRAfH49PP/0U169fZx2HPIAelTZNSEgIJk2ahLS0NBq6YIwKuQ2Cg4Px2muvITU1lYYuJKKmpgY5OTkYOXIk6yhWZcqUKSgpKUF6ejrrKHaNCrmNYmJioFarsWfPHtZRCIAjR46gf//+8PLyYh3FqjTsvL5u3TraeZ0hKuQ2apg+RGNw0kCPSrdew87ry5Yto6ELRqiQRfDYY4/hpZdewtKlS+lEZqikpATnz5/HkCFDWEexWtOmTcO1a9eQlZXFOopdokIWyWuvvYY7d+4gIyODdRS7dfDgQQwbNgxKpZJ1FKvVsPP66tWrUVZWxjqO3aFCFomjoyMSExOxbt06lJaWso5jl2i4Qhy9e/fG2LFjsWrVKtZR7A4Vsoh69uyJ559/HitWrGAdxe4UFhbi3r17CAsLYx3FJrz55pvIz8/HkSNHWEexK1TIIps+fTouX76M7Oxs1lHsSsPKbjIZndJiUCqVSEhIwMqVK6FSqVjHsRt09opMqVQiKSmJTmQL0uv1yMzMpIdBRNavXz9ERkZi7dq1rKPYDSpkM3jyyScxYsQIrFmzhnUUu3D27Fk4OTmhW7durKPYnFmzZuHMmTPIyclhHcUuUCGbyaxZs5CXl0cnsgU03Myjld3E5+Ligvj4eCxZsgRVVVWs49g8KmQzcXFxwaJFi5CWlobq6mrWcWyWRqPB4cOHaWU3MwoPD8egQYOwYcMG1lFsHhWyGT3zzDMYMGAAnchmlJOTg5CQEAQFBbGOYtNiY2Nx4sQJ5Obmso5i06iQzWz27Nn497//jdOnT7OOYpNo7rFluLm5YeHChViyZAlqampYx7FZVMhm5u7ujgULFiA1NRVqtZp1HJtSVVWFkydPYsSIEayj2IVBgwahX79++PDDD1lHsVlUyBYwZMgQ/O53v8NHH33EOopNyc7ORnh4ODw8PFhHsRtz5sxBdnY28vLyWEexSVTIFjJ37lxkZGTg559/Zh3FZtBwheV5eHggLi4OqampqKurYx3H5lAhW4i3tzfmzp2LlJQU1NfXs45j9e7cuYNLly5h8ODBrKPYnWHDhqFHjx7YtGkT6yg2hwrZgqKiotCxY0d8+umnrKNYvczMTERGRkKhULCOYpfmzZuHffv20Tc+kVEhWxDHcXj//fexa9cuXLp0iXUcq5aRkUGPSjNE3/jMgwrZwvz8/PDOO+8gJSUFOp2OdRyr9Msvv0ClUqFv376so9i1qKgoBAcH0zc+EVEhM/D888/D09MTX3zxBesoVikjIwPR0dG0shtjHMdhwYIF2LVrFy5evMg6jk2gM5oBjuOwaNEifPHFF/jf//7HOo5V0ev1NFwhIb6+voiNjUVycjK0Wi3rOFaPCpmR9u3bY8aMGUhJSYFer2cdx2rk5eXBy8sLISEhrKOQ+8aOHQtfX19s3bqVdRSrR4XM0IsvvgiZTIadO3eyjmI1GoYriHQ0fOP7xz/+gYKCAtZxrBoVMkMymQwJCQn429/+hhs3brCOI3n19fXIzs6mQpaggIAAzJw5E4sXL6ab1W1AhcxY586dMWXKFKSlpYHnedZxJO348eMIDQ2Fv78/6yikCePGjYOrqyu2b9/OOorVokKWgJiYGFRWVuKf//wn6yiSlpGRQY9KSxjHcYiPj8fWrVtRVFTEOo5VokKWAAcHByQmJuKDDz7AnTt3WMeRJJVKhdzcXERGRrKOQprRoUMHTJ8+nW5WtxIVskR069YNEyZMwLJly2joogmHDh3CwIED4ebmxjoKacGECRMAAF9//TXjJNaHCllCXn/9ddy8eRMHDhxgHUVyaLjCeshkMiQlJWHz5s10s9pEVMgS4ujoiKSkJKxduxalpaWs40hGcXExCgoKEBERwToKMVJwcDCmTJmC1NRU+sZnAipkienVqxfGjh2L1atXs44iGZmZmRg5ciQcHR1ZRyEmiImJQU1NDXbv3s06itWgQpagN998E/n5+Th69CjrKMzxPE+PSlspBwcHLF68GBs3bsTt27dZx7EKVMgSpFQqER8fjxUrVkClUrGOw9Tly5ehVqvRp08f1lFIKzz22GOYNGkSzbM3EhWyRPXv3x/Dhg3DunXrWEdhKj09HdHR0eA4jnUU0kpTpkxBSUkJ9u/fzzqK5FEhS9g777yD3NxcfP/996yjMKHX65GZmUmzK6ycXC5HUlIS1q9fj5KSEtZxJI0KWcJcXFywaNEiLF26FDU1NazjWNypU6fg6+uLrl27so5C2ig0NBTjx4+nefYtoEKWuIEDByIsLAwffPAB6ygWRzfzbMvUqVNx7do1ZGVlsY4iWVTIVuAvf/kLjhw5gry8PNZRLEatVuPo0aN49tlnWUchIlEoFEhMTMTq1atRVlbGOo4kUSFbAQ8PD8yfPx+pqamoq6tjHccijh07hl69esHX15d1FCKi3r17Y+zYsVi1ahXrKJJEhWwlhg8fjtDQUGzatIl1FIvIzMyk4Qob1TDP/siRI6yjSA4VshWZN28e9u3bh/Pnz7OOYlbl5eU4c+YMhg8fzjoKMQOlUonExESsXLnS7ufZP4oK2Yr4+PjgL3/5C5KTk6HRaFjHMZusrCwMGjQILi4urKMQM+nbty8iIyOxZs0a1lEkhQrZykRHR6N9+/b4/PPPWUcxG1rZzT7MmjULeXl5OHHiBOsokkGFbGU4jsP777+PnTt34pdffmEdR3Q3btzAtWvXMGDAANZRiJm5uLggPj4eS5cuRVVVFes4kkCFbIX8/f0xa9YspKSk2NyGkhkZGYiKioJcLmcdhVhAeHg4Bg0ahPXr17OOIglUyFbqhRdesLkNJRtWdqPhCvvy7rvvIicnB7m5uayjMEeFbKUe3FDy6tWrrOOI4sKFC9DpdOjduzfrKMSC3NzcsGjRIixZssQulwh4EBWyFevQoQOmTZtmMxtKNjwqTSu72Z+IiAj0798fH374IesoTFEhW7mXXnoJer0e33zzDesobaLT6XDgwAFER0ezjkIYee+995CdnW1XSwQ8igrZyslkMiQmJmLTpk24efMm6zitlpubi6CgIAQHB7OOQhjx8PBAXFwcUlNToVarWcdhggrZBnTp0gV/+tOfrHpXBlrZjQDAsGHD0KNHD7tZIuBRVMg2YvLkySgvL8fevXtZRzFZbW0tjh07hqioKNZRiATMmzcP+/fvx88//8w6isVRIduIhl0ZNmzYgLt377KOY5LvvvsOffr0gY+PD+soRAK8vb0xd+5cpKSkoL6+nnUci6JCtiHdu3fHH//4Ryxfvtyqhi7S09NpuII8JCoqCsHBwfjkk09YR7EoKmQbY227MpSWluLs2bMYOnQo6yhEQjiOw4IFC7B7925cvHiRdRyLoUK2MQqFAgkJCVazK8PBgwcxZMgQODs7s45CJMbX1xezZ89GcnIytFot6zgWQYVsg5544glER0dj9erVrKO0iB6VJs0ZM2YMfH19sWXLFtZRLIIK2UbNnDkT586dw7Fjx1hHMejq1asoLi5GeHg46yhEojiOw6JFi/Dll1/iypUrrOOYHRWyjXJyckJCQgKWL1+OyspK1nGalJGRgejoaDg4OLCOQiQsICAAM2fORHJyss2tbvgoKmQb9tRTT2Hw4MGSXNqwYWU3elSaGGPcuHE2t7phU6iQbVxsbCy+//57yS1t+PPPP8PBwQE9e/ZkHYVYAY7jkJCQgK1bt6KoqIh1HLOhQrZxrq6uklzakFZ2I6Zq3749pk+fbjOrGzaFCtkOREREoG/fvti4cSPrKAAArVaLrKwsGq4gJpswYQIAYOfOnYyTmAcVsp2YM2cOsrKy8N///pd1FJw8eRKdOnVChw4dWEchVkYmkyEpKQl/+9vfcOPGDdZxREeFbCc8PT0RFxcnifUB6FFp0hbBwcF47bXXkJqaalVLBBiDCtmOREZGIiQkBJs3b2aWoaamBif/IE+WAAALo0lEQVROnMDIkSOZZSDWLyYmBrW1tdi9ezfrKKKiQrYzcXFx+Ne//oULFy4w+fwjR47gqaeegpeXF5PPJ7ahYehi48aNuHXrFus4oqFCtjPt2rXD7NmzkZKSAo1GY/HPT09Pp0eliSgee+wxTJo0CUuXLrWZoQsqZDs0evRo+Pn5YevWrRb93JKSEpw/fx5Dhgyx6OcS2zVlyhSUlJRg//79rKOIggrZDj24PkBBQYHFPvfgwYMYNmwYlEqlxT6T2Da5XI7Fixdj/fr1VrcxQ1OokO1UQEAA3nrrLSQnJ1tskj0NVxBz6N69O8aPH49ly5ZZ/dAFFbIdGzduHJycnLBjxw6zf1ZhYSHu3buHsLAws38WsT9Tp07F9evXrWZjBkOokO2YTCZDQkICPv/8c1y7ds2sn5WRkYFRo0ZBJqNTjohPoVAgKSnJajZmMIT+ddi5jh074vXXX0dqaqrZhi70ej0yMzPpYRBiVr/73e/w3HPPYeXKlayjtBoVMsGkSZNQX1+PXbt2meX4Z8+ehZOTE7p162aW4xPSYMaMGbh48SKys7NZR2kVKmQCmUyGxMREfPTRR2aZZN9wM49WdiPmplQqkZiYiJUrV0KlUrGOYzIqZAJAmGT/yiuviD7JXqPR4PDhw7SyG7GYvn37YuTIkVizZg3rKCajQia/aphkn56eLtoxc3JyEBISgqCgINGOSUhLZs2ahby8PBw/fpx1FJNQIZNfyeVyJCYmYt26dbh3754ox6S5x4QFZ2dnxMfHY+nSpaiqqmIdx2hUyOQhPXr0wAsvvIAVK1a0+VhVVVU4efIkRowYIUIyQkwTHh4u2T0lDaFCJo288cYbKCgowOHDh9t0nOzsbISHh8PDw0OkZISYJjY2Fjk5OZLbU9IQKmTSiEKh+PVOdUVFRauPQ8MVhDWp7ilpCBUyaVKfPn3w7LPPtvpO9Z07d3Dp0iUMHjxY5GSEmCYiIgL9+/fHBx98wDpKi6iQiUEzZ87Ejz/+iBMnTpj83szMTERGRkKhUJghGSGmee+993DkyBHk5eWxjtIsKmRiUMOd6rS0tGbvVOt0wKNPXWdkZNCj0kQyPDw8sGDBAqSmpkKtVjf9IpUKuHEDuHkTYDS8IWfyqcRqhIeHIyIiAhs2bMDChQsBAJcuAXv3Ajk5wPnzQG2t8FpXV6BXL6Bbt7soLnZB3759GSYn5GFDhw7FgQMH8PHHH2P27NmAVgscOQJ88w1w5gxQWgrI71eiVgt06AA88wzw8stA//6ABZ405Ux5KissLIw/deqUGeMQKaqqqsLEiRPxyiur8e23vfDTT8IVsUIBODk9fA6r1cDduxWQyXgMG+aFhASgTx+2+QlpUFZWhpcnTsTm6Gh03rFDuCoGAGdnwNHxt9LleaCuTrjakMmA4GBgyRJg4MBWfS7Hcad5nm9x7VkasiAtcnR0Q/v2GzFjhjd++kkPT0/Axwdwc/utjAHhv93ceGi1dxAQ4IQffwTGjwdWrgTq69nlJ6SBt0aDLTodlElJ0KvVgKen8KNQPHwFzHHC1Ya3N+DhIQxlTJ4MLFwoXHWYCRUyaVZ1tXAeHjnSBW5uPOrq7jT7za2mpgZyuQOcnJzg6SmU9scfA1On/ja0QQgTN24AL7yAwKIiaFxdUWLsE3wcJ5zI7u7Al18K/yDMNMZMhUwM0mqBadOA06cBLy+gfXt/qFQq1NYaPhkrKioeehBELhcuMk6cAGbObHzzjxCLUKmAl14C7t4F5+2NwKAglJeVodaUq10HB+FkPn0amDHDLCczFTIx6LPPgNxcoYw5DnBwkCMgIBDFxcXg+cYnI8/rUVlZCU9Pz4d+z3HCeXzsGLB9u6XSE/KA5GSguFgYngDgKJfDPyAAxTdvQm/K6oYNJ/P335vlZKZCJk0qKADWrBG+qT04ROHh4Q6FQoGSkpJG76mqqoKTkxPkcsdGf8ZxwiyMtDTg+nVzJifkETk5wJ49v5ZxA09PT8gdHU1fSIvjABcX4WS+eVPEoFTIxIDNmwGNRrjx/DAOgYGBKCsrbzSfUxiu8Hz0Db9SKIRjfvaZ+HkJMWj9emG44ZH9HDkAQYGBKC0thbquzrRjNpzMIl8lUyGTRlQq4YLC0JpAcrkjAgL8UVx8E1ptBa5fn4v8/EEoKZkMoPmn+tzcgK++YjbvntibwkJhzNfdvck/dnR0hL+/Pz4pLMTkwkIMzM/HYmOvel1dgS++EKbHiYQKmTRy8qQwDVPezGNDnp6ecHCQo7AwCRznCH//nfDyeh+3b69EXV2Bwfc5OgpP9tF0dmIR338vnMzNTA3y8vJCO7kcLzo64v95Gv6G14hCIcznPHdOhKACKmTSyE8/GTNvmENAgCeqqo7Cw+N1VFZq0K5dBNzdh6KiYn+z7xT5HCbEsNzcFp+w4wD8sXNn9Kipgaupx9dogPz81qZrhAqZNJKXJ/yff0t4/hYcHZW4e1eGuro6uLm5Qqns1uwVMiBceUt8jRdiK86dA5TKFl+mcHSEn58fKioqYPKOkj/91KpoTaG1LEgjVVXCPZCW6PU1UCg8wXEctFotioqKUFdXDY3mFnS6QhiaTaTRKHHwYBFeffWjh35v6DF+sX5vCH2u7X7uytOn4arRQCMz7tqzvr7etPnFMpmoN0SokEkjcjkMlumDZDIX6PXV6Nq1K2prhRkX5eUKqNW+CAgINPi+6moZnnjCBQsWLDA6E2fga6dYv6fPtc3P9frjH8HdvSs8Bm0E/5IS3DOlkHneqCtwY1Ehk0a6dhWGFFxbGFBTKIIB6FBffw3OzsEAgLKy/8HVtTucnZ0Nvq+2FnjqKSV69fISMTUhTQgNBW7fbv4O9QMcZDLTrpD1eqB791aGa4zGkEkjYWGNpmw2SSZzhrt7JO7e/Rh6fS1qav6Lysrv4Ok5ttn3yeVAv34ihSWkOQMGCGsAtEDH86jX66EHoAdQr9dDZ8zXRIVCWHNWJHSFTBppKMsWZgsBAAIDF+DmzWRcuhQFBwdPBAa+D6XyMYOv53nhh5ZKJhbx9NPCDZEWTuZPS0qw+YGnT9MrKjDd1xfT/fwMH1urFY7bu7docamQSSPduws/V64ID3I0x8HBA506Gb/vXmUl8OSTQOfObQxJiDH69AE6dRLWsWhmDG66n1/z5duUykpg3DjDT1C1Ag1ZkCa99ZYwxdLEG+nN4nlhyG3GDPGOSUizOA6YNUuY/C7myazTCeN6r78u3jFBhUwMGDNGGLqoqBDvmBUVwpDeyJHiHZOQFo0bJ/7JrFIJ6yKLOH4MUCETA2QyYO1aYUaPGNMsq6uFXXJWrbLI1mSE/ObBk7m6uu3Hq6gQhkHmzm37sR5BhUwMCg4GPvlE+HbWlvO4YWOGrVuBoCBxshFikuBgYMsW4b+N3SnkUTwPlJcD7doBO3YIS3CKjAqZNGvgQGFBK6USKCszfYpmeblwL2XHDmHjXkKYefppYQsmT0/hxNTpjH+vRiO8p2dPYPduoH17s0SkQiYtCg8HsrOB6GjhxnJZWfNTO7Va4TWVlcBzzwnvpXnHRBKefBI4fBiYOPG3k7murukbfjwvjNeVlwuvWbBAWJfWjF/zOFOeCw8LC+NP0bqJdu38eWDbNuG8bJhT3FDOcrkwPsxxwIsvCvc8QkPZ5iXEoBs3gH/8A9i5E7h3T3jI48E+1GiEoY4//xn4wx8a7ThiCo7jTvM8H9bi66iQSWtotcLa3/n5wgWETCbsvdejB9Cli3GLExEiGWVlwKVLwuwJjgN8fISTWaRxYmMLmR4MIa0ilwPdugk/hFg9b2/gmWdYp6AxZEIIkQoqZEIIkQgqZEIIkQgqZEIIkQgqZEIIkQgqZEIIkQiT5iFzHHcXQJH54hBCiE3qzPN8iwsum1TIhBBCzIeGLAghRCKokAkhRCKokAkhRCKokAkhRCKokAkhRCKokAkhRCKokAkhRCKokAkhRCKokAkhRCL+PyxUNcsEcERnAAAAAElFTkSuQmCC\n", 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" ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -302,7 +286,7 @@ }, { "cell_type": "code", - "execution_count": 61, + "execution_count": 6, "metadata": {}, "outputs": [], "source": [ @@ -320,7 +304,7 @@ }, { "cell_type": "code", - "execution_count": 62, + "execution_count": 7, "metadata": {}, "outputs": [], "source": [ @@ -340,7 +324,7 @@ }, { "cell_type": "code", - "execution_count": 63, + "execution_count": 8, "metadata": {}, "outputs": [], "source": [ @@ -356,7 +340,7 @@ }, { "cell_type": "code", - "execution_count": 64, + "execution_count": null, "metadata": {}, "outputs": [ { @@ -371,14 +355,12 @@ }, { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -418,7 +400,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": null, "metadata": { "scrolled": true }, @@ -427,23 +409,21 @@ "name": "stdout", "output_type": "stream", "text": [ - "energy: -1.4919238629420386\n", - "time: 11.324347019195557\n", - "maxcut objective: -3.9919238629420386\n", - "solution: [0. 1. 0. 1.]\n", + "energy: -1.4979345138091684\n", + "time: 5.0429768562316895\n", + "maxcut objective: -3.9979345138091684\n", + "solution: [1. 0. 1. 0.]\n", "solution objective: 4.0\n" ] }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -455,7 +435,7 @@ "vqe = VQE(qubitOp, ry, spsa, 'matrix')\n", "\n", "backend = BasicAer.get_backend('statevector_simulator')\n", - "quantum_instance = QuantumInstance(backend, seed=seed, seed_mapper=seed)\n", + "quantum_instance = QuantumInstance(backend, seed=seed, seed_transpiler=seed)\n", "\n", "result = vqe.run(quantum_instance)\n", "\n", @@ -508,22 +488,20 @@ "output_type": "stream", "text": [ "energy: -1.5\n", - "time: 34.49035096168518\n", + "time: 10.28870177268982\n", "maxcut objective: -4.0\n", - "solution: [1 0 1 0]\n", + "solution: [0 1 0 1]\n", "solution objective: 4.0\n" ] }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -536,7 +514,7 @@ "vqe = VQE(qubitOp, ry, spsa, 'grouped_paulis')\n", "\n", "backend = BasicAer.get_backend('qasm_simulator')\n", - "quantum_instance = QuantumInstance(backend, shots=1024, seed=seed, seed_mapper=seed)\n", + "quantum_instance = QuantumInstance(backend, shots=1024, seed=seed, seed_transpiler=seed)\n", "\n", "result = vqe.run(quantum_instance)\n", "\n", @@ -569,7 +547,7 @@ }, { "cell_type": "code", - "execution_count": 65, + "execution_count": null, "metadata": {}, "outputs": [ { @@ -584,14 +562,12 @@ }, { "data": { - "image/png": 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\n", 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MqVOnIiUlhaZ02gGbLWRXV1csXLgQqampqKmpYR2HSNyhQ4cwcOBAuLm5sY7SSHR0NKqrq/Hdd9+xjkLMzGYLGQAiIiLQr18/elUOMUhqwxUPcnBwQGJiIj766CPcunWLdRxiRjZdyAAwZ84cHD58mF6VQ5pVXFyM/Px8REREsI7SrJCQELz88stITU2loQsbZvOF7OHhgfnz59OrckizMjIyMHLkSDg6OrKO0qLXXnsNJSUlSEtLYx2FmInNFzIAREZGolu3bti8eTPrKERieJ5n+qi0KeRyORITE7Fu3TqUlJSwjkPMwC4KGQBiY2Oxd+9enD9/nnUUIiGXL1+GWq1Gnz59WEcxSmhoKMaPH4/ly5fT0IUNsptC9vHxwezZs5GcnAyNRsM6DpGIhrdKcxzHOorRpk+fjsLCQhw6dIh1FCIyuylkABgzZgwCAgKwZcsW1lGIBOj1emRkZEh2dkVzFAoFEhMTaSEtG2RXhcxxHBYuXIivv/4aV65cYR2HMHbq1Cn4+vqia9eurKOYjBbSsk12VcgAEBAQcH+9WZ1OxzoOYchabuY156233kJeXh6OHj3KOgoRid0VMiCsN+vi4oIdO3awjkIYUavVOHr0KJ599lnWUVpNqVQiPj4eK1asgEqlYh2HiMAuC1kmkyEuLo7Wm7Vjx44dQ69eveDr68s6Spv069cPw4cPx9q1a1lHISKwy0IGgI4dO2LatGlYsmQJrTdrhzIyMqx6uOJB77zzDs6cOYPs7GzWUUgb2W0hA8DLL78MjUaDb7/9lnUUYkHl5eU4c+YMhg8fzjqKKFxcXBAXF4fU1FRUV1ezjkPawK4LuWG92U8++QTFxcWs4xALyczMxKBBg+Di4sI6imjCw8MRERGB9evXs45C2sCuCxkAunbtiujoaCxdupSefLITUl7ZrS1iYmJw/Phx/Pjjj6yjkFay+0IGgFdffRV3797Fvn37WEchZnbjxg1cu3YNAwYMYB1FdG5ubli0aBFSUlJoDXArRYWM3xZt2bBhAy3aYuPS09MxatQoyOVy1lHMYtCgQejXrx82btzIOgppBSrkexoWbVmxYgUNXdiohpXdbHG44kFz5szBoUOHaA1wK0SF/IDp06ejoKAAhw8fZh2FmMGFCxeg0+nQu3dv1lHMysPDA7GxsbQGuBWiQn6AQqFAQkICVq1ahfLyctZxiMgaHpW2ppXdWmv48OEIDQ3Fpk2bWEchJqBCfkSfPn0wevRorFmzhnUUIiKdTocDBw4gKiqKdRSLmT9/Pvbt24dz586xjkKMRIXchLfffhtnz57F8ePHWUchIsnJyUFQUBCCg4NZR7EYb29vzJ07F0lJSaivr2cdhxiBCrkJzs7OiIuLw9KlS1FVVcU6DhGBta/s1lqjRo1Cp06d8Nlnn7GOQoxAhdyMp59+GoMHD6Ynn2xAbW0tjh07hlGjRrGOYnEcx+GDDz7A7t27cfHiRdZxiAFUyC147733cOLECXryycp9//336NOnD3x8fFhHYcLX1xcxMTFISkqCVqtlHYe0gAq5BW5ubli4cCFSUlJQW1vLOg5ppbS0NLscrnjQuHHj4Ovri23btrGOQlpAhWzA4MGD8eSTT9KTT1aqtLQUZ8+exdChQ1lHYarh9WU7duxAfn4+6zikGVTIRpg7dy4OHjyIs2fPso5CTJSZmYkhQ4bA2dmZdRTmAgMDMXPmTCxevJheXyZRVMhG8PT0xLx585CcnEzTh6xMWlqazT8qbYrx48fD1dWVXl8mUVTIRhoxYgS6du2KTz/9lHUUYqSrV6+iuLgY4eHhrKNIBsdx9PoyCaNCNhLHcYiNjcWePXuQl5fHOg4xQnp6OkaPHg0HBwfWUSSlQ4cOeOONN5CcnEyvL5MYKmQTNEwfSk5OpulDEmcvK7u11qRJk8DzPHbt2sU6CnkAFbKJaPqQdfjll1/g4OCAnj17so4iSTKZDImJidi8eTOKiopYxyH3UCGbqGH60Pbt22n6kITZ08purRUcHIypU6ciJSWF1gCXCCrkVggMDMTbb79NY3ASpdVqkZmZaVcru7VWdHQ0qqursWfPHtZRCKiQW23ChAlQKBT46quvWEchjzh58iQ6deqEDh06sI4ieQ4ODkhMTMTGjRtx69Yt1nHsHhVyK8lkMsTFxeGzzz7D9evXWcchD6BHpU0TEhKCyZMnIzU1lYYuGKNCboPg4GC89tprSElJoaELiaipqUF2djZGjhzJOopVmTp1KkpKSpCWlsY6il2jQm6j6OhoqNVqfPfdd6yjEABHjhxB//794eXlxTqKVWl48/q6devozesMUSG3UcP0IRqDkwZ6VLr1Gt68vmzZMhq6YIQKWQSPPfYYXnrpJSxdupROZIZKSkpw/vx5DBkyhHUUqzV9+nRcu3YNmZmZrKPYJSpkkbz22mu4ffs20tPTWUexWwcPHsSwYcOgVCpZR7FaDW9eX716NcrKyljHsTtUyCJxdHREQkIC1q1bh9LSUtZx7BINV4ijd+/eGDduHFatWsU6it2hQhZRz5498fzzz2PFihWso9idgoIC3L17F2FhYayj2IS33noLeXl5OHLkCOsodoUKWWRvvvkmLl++jKysLNZR7ErDym4yGZ3SYlAqlYiPj8fKlSuhUqlYx7EbdPaKTKlUIjExkU5kC9Lr9cjIyKCHQUTWr18/REZGYu3atayj2A0qZDN48sknMWLECKxZs4Z1FLtw9uxZODk5oVu3bqyj2JxZs2bhzJkzyM7OZh3FLlAhm8msWbOQm5tLJ7IFNNzMo5XdxOfi4oK4uDgsWbIEVVVVrOPYPCpkM3FxccGiRYuQmpqK6upq1nFslkajweHDh2llNzMKDw/HoEGDsGHDBtZRbB4Vshk988wzGDBgAJ3IZpSdnY2QkBAEBQWxjmLTYmJicOLECeTk5LCOYtOokM1s9uzZ+Pe//43Tp0+zjmKTaO6xZbi5uWHhwoVYsmQJampqWMexWVTIZubu7o4FCxYgJSUFarWadRybUlVVhZMnT2LEiBGso9iFQYMGoV+/fvjoo49YR7FZVMgWMGTIEPzud7/Dxx9/zDqKTcnKykJ4eDg8PDxYR7Ebc+bMQVZWFnJzc1lHsUlUyBYyd+5cpKen45dffmEdxWbQcIXleXh4IDY2FikpKairq2Mdx+ZQIVuIt7c35s6di+TkZNTX17OOY/Vu376NS5cuYfDgwayj2J1hw4ahR48e2LRpE+soNocK2YJGjRqFjh074rPPPmMdxeplZGQgMjISCoWCdRS7NG/ePOzbt4++8YmMCtmCOI7DBx98gN27d+PSpUus41i19PR0elSaIfrGZx5UyBbm5+eHd999F8nJydDpdKzjWKVff/0VKpUKffv2ZR3Fro0aNQrBwcH0jU9EVMgMPP/88/D09MSXX37JOopVSk9PR1RUFK3sxhjHcViwYAF2796Nixcvso5jE+iMZoDjOCxatAhffvkl/ve//7GOY1X0ej0NV0iIr68vYmJikJSUBK1WyzqO1aNCZqR9+/aYMWMGkpOTodfrWcexGrm5ufDy8kJISAjrKOSecePGwdfXF1u3bmUdxepRITP04osvQiaTYefOnayjWI2G4QoiHQ3f+P7xj38gPz+fdRyrRoXMkEwmQ3x8PP72t7/hxo0brONIXn19PbKysqiQJSggIAAzZ87E4sWL6WZ1G1AhM9a5c2dMnToVqamp4HmedRxJO378OEJDQ+Hv7886CmnC+PHj4erqiu3bt7OOYrWokCUgOjoalZWV+Oc//8k6iqSlp6fTo9ISxnEc4uLisHXrVhQWFrKOY5WokCXAwcEBCQkJ+PDDD3H79m3WcSRJpVIhJycHkZGRrKOQFnTo0AFvvvkm3axuJSpkiejWrRsmTpyIZcuW0dBFEw4dOoSBAwfCzc2NdRRiwMSJEwEAu3btYpzE+lAhS8jrr7+OoqIiHDhwgHUUyaHhCushk8mQmJiIzZs3081qE1EhS4ijoyMSExOxdu1alJaWso4jGcXFxcjPz0dERATrKMRIwcHBmDp1KlJSUugbnwmokCWmV69eGDduHFavXs06imRkZGRg5MiRcHR0ZB2FmCA6Oho1NTXYs2cP6yhWgwpZgt566y3k5eXh6NGjrKMwx/M8PSptpRwcHLB48WJs3LgRt27dYh3HKlAhS5BSqURcXBxWrFgBlUrFOg5Tly9fhlqtRp8+fVhHIa3w2GOPYfLkyTTP3khUyBLVv39/DBs2DOvWrWMdham0tDRERUWB4zjWUUgrTZ06FSUlJdi/fz/rKJJHhSxh7777LnJycvDDDz+wjsKEXq9HRkYGza6wcnK5HImJiVi/fj1KSkpYx5E0KmQJc3FxwaJFi7B06VLU1NSwjmNxp06dgq+vL7p27co6Cmmj0NBQTJgwgebZG0CFLHEDBw5EWFgYPvzwQ9ZRLI5u5tmWadOm4dq1a8jMzGQdRbKokK3AX/7yFxw5cgS5ubmso1iMWq3G0aNH8eyzz7KOQkSiUCiQkJCA1atXo6ysjHUcSaJCtgIeHh6YP38+UlJSUFdXxzqORRw7dgy9evWCr68v6yhERL1798a4ceOwatUq1lEkiQrZSgwfPhyhoaHYtGkT6ygWkZGRQcMVNqphnv2RI0dYR5EcKmQrMm/ePOzbtw/nz59nHcWsysvLcebMGQwfPpx1FGIGSqUSCQkJWLlypd3Ps38UFbIV8fHxwV/+8hckJSVBo9GwjmM2mZmZGDRoEFxcXFhHIWbSt29fREZGYs2aNayjSAoVspWJiopC+/bt8cUXX7COYja0spt9mDVrFnJzc3HixAnWUSSDCtnKcByHDz74ADt37sSvv/7KOo7obty4gWvXrmHAgAGsoxAzc3FxQVxcHJYuXYqqqirWcSSBCtkK+fv7Y9asWUhOTra5F0qmp6dj1KhRkMvlrKMQCwgPD8egQYOwfv161lEkgQrZSr3wwgs290LJhpXdaLjCvrz33nvIzs5GTk4O6yjMUSFbqQdfKHn16lXWcURx4cIF6HQ69O7dm3UUYkFubm5YtGgRlixZYpdLBDyICtmKdejQAdOnT7eZF0o2PCpNK7vZn4iICPTv3x8fffQR6yhMUSFbuZdeegl6vR7ffPMN6yhtotPpcODAAURFRbGOQhh5//33kZWVZVdLBDyKCtnKyWQyJCQkYNOmTSgqKmIdp9VycnIQFBSE4OBg1lEIIx4eHoiNjUVKSgrUajXrOExQIduALl264E9/+pNVv5WBVnYjADBs2DD06NHDbpYIeBQVso2YMmUKysvLsXfvXtZRTFZbW4tjx45h1KhRrKMQCZg3bx7279+PX375hXUUi6NCthENb2XYsGED7ty5wzqOSb7//nv06dMHPj4+rKMQCfD29sbcuXORnJyM+vp61nEsigrZhnTv3h1//OMfsXz5cqsaukhLS6PhCvKQUaNGITg4GJ9++inrKBZFhWxjrO2tDKWlpTh79iyGDh3KOgqREI7jsGDBAuzZswcXL15kHcdiqJBtjEKhQHx8vNW8leHgwYMYMmQInJ2dWUchEuPr64vZs2cjKSkJWq2WdRyLoEK2QU888QSioqKwevVq1lEMokelSUvGjh0LX19fbNmyhXUUi6BCtlEzZ87EuXPncOzYMdZRmnX16lUUFxcjPDycdRQiURzHYdGiRfjqq69w5coV1nHMjgrZRjk5OSE+Ph7Lly9HZWUl6zhNSk9PR1RUFBwcHFhHIRIWEBCAmTNnIikpyeZWN3wUFbINe+qppzB48GBJLm3YsLIbPSpNjDF+/HibW92wKVTINi4mJgY//PCD5JY2/OWXX+Dg4ICePXuyjkKsAMdxiI+Px9atW1FYWMg6jtlQIds4V1dXSS5tSCu7EVO1b98eb775ps2sbtgUKmQ7EBERgb59+2Ljxo2sowAAtFotMjMzabiCmGzixIkAgJ07dzJOYh5UyHZizpw5yMzMxH//+1/WUXDy5El06tQJHTp0YB2FWBmZTIbExET87W9/w40bN1jHER0Vsp3w9PREbGysJNYHoEelSVsEBwfjtddeQ0pKilUtEWAMKmQ7EhkZiZCQEGzevJlZhpqaGpw4cQIjR45kloFYv+ga9GluAAALnklEQVToaNTW1mLPnj2so4iKCtnOxMbG4l//+hcuXLjA5PhHjhzBU089BS8vLybHJ7ahYehi48aNuHnzJus4oqFCtjPt2rXD7NmzkZycDI1GY/Hjp6Wl0aPSRBSPPfYYJk+ejKVLl9rM0AUVsh0aM2YM/Pz8sHXrVoset6SkBOfPn8eQIUMselxiu6ZOnYqSkhLs37+fdRRRUCHboQfXB8jPz7fYcQ8ePIhhw4ZBqVRa7JjEtsnlcixevBjr16+3uhczNIUK2U4FBATg7bffRlJSksUm2dNwBTGH7t27Y8KECVi2bJnVD11QIdux8ePHw8nJCTt27DD7sQoKCnD37l2EhYWZ/VjE/kybNg3Xr1+3mhczNIcK2Y7JZDLEx8fjiy++wLVr18x6rPT0dIwePRoyGZ1yRHwKhQKJiYlW82KG5tB/HXauY8eOeP3115GSkmK2oQu9Xo+MjAx6GISY1e9+9zs899xzWLlyJesorUaFTDB58mTU19dj9+7dZtn/2bNn4eTkhG7dupll/4Q0mDFjBi5evIisrCzWUVqFCplAJpMhISEBH3/8sVkm2TfczKOV3Yi5KZVKJCQkYOXKlVCpVKzjmIwKmQAQJtm/8sorok+y12g0OHz4MK3sRiymb9++GDlyJNasWcM6ismokMl9DZPs09LSRNtndnY2QkJCEBQUJNo+CTFk1qxZyM3NxfHjx1lHMQkVMrlPLpcjISEB69atw927d0XZJ809Jiw4OzsjLi4OS5cuRVVVFes4RqNCJg/p0aMHXnjhBaxYsaLN+6qqqsLJkycxYsQIEZIRYprw8HDJvlOyOVTIpJE33ngD+fn5OHz4cJv2k5WVhfDwcHh4eIiUjBDTxMTEIDs7W3LvlGwOFTJpRKFQ3L9TXVFR0er90HAFYU2q75RsDhUyaVKfPn3w7LPPtvpO9e3bt3Hp0iUMHjxY5GSEmCYiIgL9+/fHhx9+yDqKQVTIpFkzZ87ETz/9hBMnTpj82YyMDERGRkKhUJghGSGmef/993HkyBHk5uayjtIiKmTSrIY71ampqS3fqdbpgEceu05PT6dHpYlkeHh4YMGCBUhJSYFarW5yG5UKuHEDKCoCWI1uyNkclliL8PBwREREYMOGDVi4cKHwy0uXgL17gexs4Px5oLZW+L2rK9CrF+506waX4mL07duXXXBCHjF06FAcOHAAn3zyCWbPng2tFjhyBPjmG+DMGaC0FJDfa0StFujQAXjmGeDll4H+/QFLPGjKmfJUVlhYGH/q1CkzxiFSVFVVhUmTJmH1K6+g17ffAj//LFwRKxSAk9PDZ7FajYo7d8DLZPAaNgyIjwf69GGan5AGZWVlmDTpZURFbcaOHZ3R8HS1szPg6Phb6fI8UFcnXGvIZEBwMLBkCTBwYOuOy3HcaZ7nDa49S0MWxCA3R0dsbN8e3jNmQP/zz4CnJ+DjA7i5/VbGACCXg3dzw22tFk4BAcBPPwETJgArVwL19ez+AYTco9F4Q6fbgsREJdRqPTw9hdNZoXj4CpjjhGsNb2/Aw0MYypgyBVi4EGhmxEMUVMikZdXVwJQp6HLkiFC2dXUtfnerqamBg1wOJycn4Ux3cwM++QSYNu23oQ1CGLhxA3jhBaCwMBCurhpUVZUY9TmOE05jd3fgq6+EYjbXGDMVMmmeVgtMnw6cPg14ecG/fXuoVCrUtFCsFRUVDz8IIpcLlxknTgAzZza6+UeIJahUwEsvAXfuAN7eHIKCAlFWVg612viLBAcH4VQ+fRqYMcM8pzIVMmne558DOTmAlxfAcZA7OCAwIADFxcXQN3HvQc/zqKyshKen58N/wXHCmXzsGLB9u4XCE/KbpCSguFj40gYAcrkjAgL8UVRUDJ43vlkbTuUffjDPqUyFTJqWnw+sWSN8V3tgiMLdwwMKhQIlJY2/7lVVVcHJyQmO8iYm73CcMAsjNRW4ft2cyQl5SHY28N13v5VxA09PTzg6yk1eSIvjABcX4VQuKhIxKKiQSXM2bwY0GuHW8wM4AIGBgSgvK2s0n7OiogKeLa1boVAI+/z8czMEJqRp69cLww2NX+fIITAwCKWlpairM+1OXcOpLPZVMhUyaUylEi4pmilXR7kc/gEBKCouRoVWi7nXr2NQXh6mlJTA4DN9bm7A11+zm3lP7EpBgTDm6+7e9N87OjrC398fBQWfoqBgCvLyBqKoaLFR+3Z1Bb78UpgeJxYqZNLYyZPCRMymhh7u8fT0hNzBAYkFBXDkOOz098cHXl5YeesW8ls6Qx0dhSf7aD47sYAffhBO5ZYe6vDy8oJc3g6Oji/C0/P/Gb1vhUKYzXnunAhB76FCJo39/LPBecMcAM+AABytqsLrHh7QVFYiol07DHV3x35DK8SJfRYT0oycHGOesOPQufMfUVPTA4CrSfvXaIC8vNama4wKmTSWmyv8v38DbvI8lI6OkN25g7q6Ori6uaGbUtnyFTIgXHlLfJEXYhvOnQOUSsPbOToq4Ofnd2+5WdPeKfnzz63L1hRay4I0VlUl3AUxoEavh6dCAY7joNVqUVhYiOq6OtzUaFCg0wnfFZug1GhQePAgPn711Yd+39xj/GL9vjl0XNs97unTK6HRuEIm0xi1fX19vUnzi2UycW+HUCGTxuTyZsv0QS4yGar1enTt2hXqew+LKMrL4atWIzAgoNnPyaqr4fLEE1iwYIHRkbhmvneK9Xs6rm0e949/9MKdOxycnIzLUVLiD73e+GlwPG/cFbixqJBJY127CkMKri2PpwUrFNABuFZfj2BnZwDA/8rK0N3VFc73/tyk2loon3oKXr16iRiakMZCQ4Fbt1q8P/0QmczBpCtkvR7o3r112Zo8vni7IjYjLKypSZuNOMtkiHR3xyd37qBWr8d/a2rwfWUlxj06A/9RcjnQr59IYQlp3oABwgoAhvC8Dnp9PQA9AD30+nrwvM7g5xQKQMzrCrpCJo01lKWh+UIAFgQGIqmoCKMuXYKngwM+CAzEYy19h+N54YfWSiYW8PTTwu0QQ6dySclnKCnZfP/PFRVp8PV9E35+bzb7Ga1W2G/v3uLlpUImjXXvLvxcuSI8yNECDwcHrOnUyfh9V1YCTz4JdO7cxpCEGNanD9Cpk7CORUsjcH5+LZdvUyorgfHjm31+qlVoyII07e23hUmWJt5JbxHPC4NuM2aIt09CWsBxwKxZwtR3MU9lnU4Y1Xv9dfH2CVAhk+aMHSsMXRh6yMMUFRXCoN7IkeLtkxADxo8X/1RWqYR1kcW+L02FTJomkwFr1wpzesSYaFldLbwnZ9Uqy7ycjJB7HjyVq6vbvr+KCmEYZO7ctu/rUVTIpHnBwcCnnwrfz9pyJje8sXrrViAoSJxshJggOBjYskX4v1t6gXpLeB4oLwfatQN27BCW4BQbFTJp2cCBwpJWSiVQVmbaaxL0euEMdnUVzuD+/c2XkxADnn5aeAWTp6dwWuoMz2q7T6MRPtOzJ7BnD9C+vXkyUiETw8LDgawsICpKuLVcVtby5E6tVtimshJ47jnhszTvmEjAk08Chw8Dkyb9dirX1TV9w4/nhdG68nJhmwULhFVpzfkljzPlufCwsDD+FC2baN/Onwe2bRPOzIY5xQ3lLJcL48McB7z4onDXIzSUbV5CmnHjBvCPfwA7dwJ37woPeTxYhxqNMNTx5z8Df/hD4zeOmILjuNM8z4cZ3I4KmbSKVius/p2XJ1xCyGTCu/d69AC6dDFqcSJCpKKsDLh0SZg9wXGAj49wKos1TmxsIdODIaR15HKgWzfhhxAr5+0NPPMM6xQ0hkwIIZJBhUwIIRJBhUwIIRJBhUwIIRJBhUwIIRJBhUwIIRJh0jxkjuPuACg0XxxCCLFJnXme9zO0kUmFTAghxHxoyIIQQiSCCpkQQiSCCpkQQiSCCpkQQiSCCpkQQiSCCpkQQiSCCpkQQiSCCpkQQiSCCpkQQiTi/wNGxDXLo9qWxwAAAABJRU5ErkJggg==\n", 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" ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -646,7 +622,7 @@ }, { "cell_type": "code", - "execution_count": 66, + "execution_count": null, "metadata": {}, "outputs": [ { @@ -654,21 +630,19 @@ "output_type": "stream", "text": [ "distance\n", - " [[ 0. 61. 6.]\n", - " [61. 0. 57.]\n", - " [ 6. 57. 0.]]\n" + " [[ 0. 52. 21.]\n", + " [52. 0. 73.]\n", + " [21. 73. 0.]]\n" ] }, { "data": { - "image/png": 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\n", 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" ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -695,27 +669,25 @@ }, { "cell_type": "code", - "execution_count": 67, + "execution_count": null, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "order = (0, 1, 2) Distance = 124.0\n", - "Best order from brute force = (0, 1, 2) with total distance = 124.0\n" + "order = (0, 1, 2) Distance = 146.0\n", + "Best order from brute force = (0, 1, 2) with total distance = 146.0\n" ] }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -763,7 +735,7 @@ }, { "cell_type": "code", - "execution_count": 68, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -781,7 +753,7 @@ }, { "cell_type": "code", - "execution_count": 72, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -802,7 +774,7 @@ }, { "cell_type": "code", - "execution_count": 73, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -818,30 +790,28 @@ }, { "cell_type": "code", - "execution_count": 76, + "execution_count": null, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "energy: -600062.0\n", - "tsp objective: 124.0\n", + "energy: -600073.0\n", + "tsp objective: 146.0\n", "feasible: True\n", "solution: [0, 1, 2]\n", - "solution objective: 124.0\n" + "solution objective: 146.0\n" ] }, { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "
" ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -883,7 +853,29 @@ "cell_type": "code", "execution_count": null, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "energy: -599082.2118605649\n", + "time: 14.73941707611084\n", + "feasible: True\n", + "solution: [2, 1, 0]\n", + "solution objective: 146.0\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "seed = 10598\n", "\n", @@ -892,7 +884,7 @@ "vqe = VQE(qubitOp, ry, spsa, 'matrix')\n", "\n", "backend = BasicAer.get_backend('statevector_simulator')\n", - "quantum_instance = QuantumInstance(backend, seed=seed, seed_mapper=seed)\n", + "quantum_instance = QuantumInstance(backend, seed=seed, seed_transpiler=seed)\n", "\n", "result = vqe.run(quantum_instance)\n", "\"\"\"\n", @@ -944,10 +936,10 @@ "\n", "spsa = SPSA(max_trials=300)\n", "ry = RY(qubitOp.num_qubits, depth=5, entanglement='linear')\n", - "vqe = VQE(qubitOp, ry, spsa, 'grouped_paulis', batch_mode=True)\n", + "vqe = VQE(qubitOp, ry, spsa, 'grouped_paulis')\n", "\n", "backend = BasicAer.get_backend('qasm_simulator')\n", - "quantum_instance = QuantumInstance(backend, shots=1024, seed=seed, seed_mapper=seed)\n", + "quantum_instance = QuantumInstance(backend, shots=1024, seed=seed, seed_transpiler=seed)\n", "\n", "result = vqe.run(quantum_instance)\n", "\n", @@ -979,33 +971,9 @@ }, { "cell_type": "code", - "execution_count": 77, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "energy: -4532.0\n", - "tsp objective: 124.0\n", - "feasible: True\n", - "solution: [0, 1, 2]\n", - "solution objective: 124.0\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "ee = ExactEigensolver(qubitOp_docplex, k=1)\n", "result = ee.run()\n", @@ -1046,7 +1014,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.5" + "version": "3.6.8" } }, "nbformat": 4, From ab9a33c7d1b85b6202983ec8cc1d6a42a59c69aa Mon Sep 17 00:00:00 2001 From: stefan-woerner Date: Sun, 28 Apr 2019 11:44:58 +0200 Subject: [PATCH 078/116] merge PR --- .../finance/data_providers/time_series.ipynb | 173 +++--------------- .../portfolio_diversification.ipynb | 123 ++++--------- .../simulation/credit_risk_analysis.ipynb | 9 +- 3 files changed, 58 insertions(+), 247 deletions(-) diff --git a/qiskit/finance/data_providers/time_series.ipynb b/qiskit/finance/data_providers/time_series.ipynb index 8ef7b99a2..4580a34ce 100644 --- a/qiskit/finance/data_providers/time_series.ipynb +++ b/qiskit/finance/data_providers/time_series.ipynb @@ -33,7 +33,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": null, "metadata": { "scrolled": true }, @@ -51,11 +51,11 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ - "stocks = [\"GOOG\", \"AAPL\"]\n", + "stocks = [\"TICKER_A\", \"TICKER_B\"] # TODO\n", "from qiskit.aqua.translators.data_providers.wikipediadataprovider import StockMarket\n", "wiki = WikipediaDataProvider(token = \"\",\n", " tickers = stocks,\n", @@ -74,52 +74,9 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "A time-series similarity measure:\n", - "[[1.00000000e+00 8.44268222e-05]\n", - " [8.44268222e-05 1.00000000e+00]]\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "A covariance matrix:\n", - "[[269.60118129 25.42252332]\n", - " [ 25.42252332 7.86304499]]\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "if wiki._n <= 1: \n", " raise Exception(\"Not enough data to plot covariance or time-series similarity. Please use at least two tickers.\")\n", @@ -148,79 +105,9 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The underlying evolution of stock prices:\n" - ] - }, - { - "data": { - "image/png": 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\n", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "GOOG\n", - "Date\n", - "2016-01-04 741.84\n", - "2016-01-05 742.58\n", - "2016-01-06 743.62\n", - "2016-01-07 726.39\n", - "2016-01-08 714.47\n", - "2016-01-11 716.03\n", - "2016-01-12 726.07\n", - "2016-01-13 700.56\n", - "2016-01-14 714.72\n", - "2016-01-15 694.45\n", - "2016-01-19 701.79\n", - "2016-01-20 698.45\n", - "2016-01-21 706.59\n", - "2016-01-22 725.25\n", - "2016-01-25 711.67\n", - "2016-01-26 713.04\n", - "2016-01-27 699.99\n", - "2016-01-28 730.96\n", - "2016-01-29 742.95\n", - "Name: Adj. Close, dtype: float64\n", - "AAPL\n", - "Date\n", - "2016-01-04 101.783763\n", - "2016-01-05 99.233131\n", - "2016-01-06 97.291172\n", - "2016-01-07 93.185040\n", - "2016-01-08 93.677776\n", - "2016-01-11 95.194629\n", - "2016-01-12 96.576222\n", - "2016-01-13 94.093220\n", - "2016-01-14 96.151117\n", - "2016-01-15 93.842021\n", - "2016-01-19 93.387931\n", - "2016-01-20 93.513531\n", - "2016-01-21 93.040118\n", - "2016-01-22 97.986799\n", - "2016-01-25 96.073825\n", - "2016-01-26 96.605206\n", - "2016-01-27 90.257610\n", - "2016-01-28 90.904929\n", - "2016-01-29 94.044912\n", - "Name: Adj. Close, dtype: float64\n" - ] - } - ], + "outputs": [], "source": [ "print(\"The underlying evolution of stock prices:\")\n", "for (cnt, s) in enumerate(stocks):\n", @@ -254,7 +141,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -264,28 +151,19 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "'Accessing NASDAQ Data on Demand failed.'\n", - "You need to replace REPLACE-ME with a valid token.\n" - ] - } - ], + "outputs": [], "source": [ "from qiskit.aqua.translators.data_providers.dataondemandprovider import StockMarket\n", "try:\n", - " nasdaq = DataOnDemandProvider(token = \"REPLACE-ME\",\n", - " tickers = [\"GOOG\", \"AAPL\"],\n", + " nasdaq = DataOnDemandProvider(token = \"REPLACE-ME\",\n", + " tickers = [\"TICKER_A\", \"TICKER_B\"],\n", " stockmarket = StockMarket.NASDAQ.value,\n", " start = datetime.datetime(2016,1,1),\n", " end = datetime.datetime(2016,1,2))\n", - " nasdaq.run()\n", - " nasdaq.plot()\n", + " nasdaq.run()\n", + " nasdaq.plot()\n", "except QiskitFinanceError as e:\n", " print(e)\n", " print(\"You need to replace REPLACE-ME with a valid token.\")" @@ -302,28 +180,19 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "'Cannot retrieve Exchange Data data.'\n", - "You need to replace REPLACE-ME with a valid token.\n" - ] - } - ], + "outputs": [], "source": [ "from qiskit.aqua.translators.data_providers.exchangedataprovider import StockMarket\n", "try:\n", - " lse = ExchangeDataProvider(token = \"REPLACE-ME\",\n", - " tickers = [\"AIBGl\", \"AVSTl\"],\n", + " lse = ExchangeDataProvider(token = \"REPLACE-ME\",\n", + " tickers = [\"TICKER_A\", \"TICKER_B\"],\n", " stockmarket = StockMarket.LONDON.value,\n", " start = datetime.datetime(2019,1,1),\n", " end = datetime.datetime(2019,1,30))\n", - " lse.run()\n", - " lse.plot()\n", + " lse.run()\n", + " lse.plot()\n", "except QiskitFinanceError as e: \n", " print(e)\n", " print(\"You need to replace REPLACE-ME with a valid token.\")" @@ -353,7 +222,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.2" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/qiskit/finance/optimization/portfolio_diversification.ipynb b/qiskit/finance/optimization/portfolio_diversification.ipynb index 5b3a04b52..791e2c9ce 100644 --- a/qiskit/finance/optimization/portfolio_diversification.ipynb +++ b/qiskit/finance/optimization/portfolio_diversification.ipynb @@ -192,7 +192,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -239,37 +239,29 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": null, "metadata": { "scrolled": true }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Cannot load real data. This may happen with over 50 accesses per day, for instnace. Using a constant rho.\n" - ] - } - ], + "outputs": [], "source": [ "# Generate a pairwise time-series similarity matrix\n", - "stocks = [\"GOOG\", \"AAPL\"]\n", + "stocks = [\"TICKER_A\", \"TICKER_B\"]\n", "n = len(stocks)\n", "rho = np.ones((n,n))\n", "rho[0,1] = 0.8\n", "rho[1,0] = 0.8\n", "\n", "try:\n", - " wiki = WikipediaDataProvider(token = \"\",\n", + " wiki = WikipediaDataProvider(token = \"\",\n", " tickers = stocks,\n", " stockmarket = StockMarket.NASDAQ.value,\n", " start = datetime.datetime(2016,1,1),\n", " end = datetime.datetime(2016,1,30))\n", - " wiki.run()\n", - " rho = wiki.get_similarity_matrix()\n", + " wiki.run()\n", + " rho = wiki.get_similarity_matrix()\n", "except Exception as e:\n", - " print(\"Cannot load real data. This may happen with over 50 accesses per day, for instnace. Using a constant rho.\")\n", + " print(\"Cannot load real data. This may happen with over 50 accesses per day, for instnace. Using a constant rho.\")\n", "\n", "# Actually, we consider the additive inverse to invert the direction of optimisation. \n", "rho = -1 * rho" @@ -284,7 +276,7 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -302,7 +294,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -389,18 +381,9 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Number of feasible combinations= 2\n", - "Total number of combinations= 64\n" - ] - } - ], + "outputs": [], "source": [ "# Instantiate the classical optimizer class\n", "classical_optimizer = ClassicalOptimizer(rho, n, q)\n", @@ -414,7 +397,7 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -467,7 +450,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -540,7 +523,7 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -561,7 +544,7 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -574,7 +557,7 @@ " classical_solution, classical_cost = classical_optimizer.cplex_solution()\n", " print(quantum_cost, classical_cost)\n", " if np.abs(quantum_cost - classical_cost) < 0.01:\n", - " print('Binary formulation is correct')\n", + " print('Binary formulation is correct')\n", " else: print('Error in the formulation of the Hamiltonian')\n", "except: None" ] @@ -592,25 +575,17 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[0 1 0 1 0 1]\n" - ] - } - ], + "outputs": [], "source": [ "ground_state, ground_level = quantum_optimizer.exact_solution()\n", "print(ground_state)\n", "\n", "try:\n", - " if np.abs(ground_level - classical_cost)<0.01:\n", - " print('Ising Hamiltonian in Z basis is correct')\n", - " else: print('Error in the Ising Hamiltonian formulation')\n", + " if np.abs(ground_level - classical_cost)<0.01:\n", + " print('Ising Hamiltonian in Z basis is correct')\n", + " else: print('Error in the Ising Hamiltonian formulation')\n", "except: None" ] }, @@ -625,27 +600,18 @@ }, { "cell_type": "code", - "execution_count": 30, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[0 1 0 1 0 1]\n", - "VQE produces the same solution as the exact eigensolver.\n" - ] - } - ], + "outputs": [], "source": [ "warnings.filterwarnings('ignore')\n", "vqe_state, vqe_level = quantum_optimizer.vqe_solution()\n", "print(vqe_state)\n", "\n", "try:\n", - " if np.linalg.norm(ground_state - vqe_state)<0.01:\n", - " print('VQE produces the same solution as the exact eigensolver.')\n", - " else: print('VQE does not produce the same solution as the exact eigensolver, but that is to be expected.')\n", + " if np.linalg.norm(ground_state - vqe_state)<0.01:\n", + " print('VQE produces the same solution as the exact eigensolver.')\n", + " else: print('VQE does not produce the same solution as the exact eigensolver, but that is to be expected.')\n", "except: None" ] }, @@ -659,34 +625,9 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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7nO6MXzue01kh+ZxojHGAz81fVTOBYcBCYCMwXVXXi8hTIhLnHfYiEA3MEJG1IpJyhs2FDBGha72upMSncFPtm/j3un/TI6UHq/atcjqaMSYE+OWonqo6H5if67Ync1xu5495glGlUpUY03oMcZfE8fSKp7lj4R10rduVEc1GUK5EOafjGWOClH3DN0C0rNGS2e7Z3H7l7aRsSyEuKY552+fZcYKMMYXCmn8AKRVeiuFNh5PQOYHqUdUZ+cVI7vn0Hnb9usvpaMaYIGPNPwBdXvFyPuj0ASObj+TbA9/SNbkr7/7wLhnZGU5HM8YECWv+ASrMFUa/K/qRHJ9Mi+otGLtmLH3m9uGHgz84Hc0YEwSs+Qe4qlFVeTX2Vca1GceRU0foO68vz698nuMZx52OZowpxqz5FwMiQrva7UiKT6LXZb2YunEq7iQ3S35e4nQ0Y0wxZc2/GCkTWYZRLUYxpeMUykSW4YElD/B/S/6PAydC/ntzxphzZM2/GGpcpTHTu0znwasf5IvdX+BOcjPtx2lka7bT0YwxxYQ1/2IqwhXB4IaDSYxLpEHlBjzz9TPctuA2thzZ4nQ0Y0wxYM2/mLuw7IW83f5tnrv+OX469hO95vTi1W9e5VTmKaejGWMCmDX/ICAidLmkCynxKXS6uBNvf/823VO6s2LvCqejGWMClDX/IFKhZAWevf5Z3r7pbQCGfDKEx5c/zpFTRxxOZowJNNb8g1CLai2YFTeLIQ2HMH/7fOKS4kjZlmLHCTLG/M6af5AqGV6SB65+gOldplO7bG0eX/44QxYN4edjPzsdzRgTAKz5B7l6FeoxpeMUnmjxBOsPrqdbSjcWHl1IRpYdJ8iYUGbNPwS4xEWvy3qRHJ9M65qtmZs6l15ze7H2wFqnoxljHGLNP4RUKV2FsW3GMvSCoaRlpHHbgtt4ZsUz/Jr+q9PRjDFFzJp/CGpYuiFJ7iT6XdGPGZtn4E5ys+inRfaGsDEhxJp/iIqKiOLR5o8ytdNUKpWqxPClw3lgyQPsO77P6WjGmCJgzT/ENajcgI9u+YgRTUfw9d6vcSe5+WDDB2RlZzkdzRhTiKz5G8Jd4Qy6chCJcYk0iWnCmFVj6D+/Pz8e/tHpaMaYQmLN3/yuZpmaTGg7gRdav8Ce43voPbc3Y1eP5UTGCaejGWP8zC/NX0Q6iMgmEdkqIiPzuL+1iHwjIpki0sMfc5rCISJ0vKgjKfEpxNeN593179ItpRvLdy93Opoxxo98bv4iEgaMBzoC9YE+IlI/17CfgUHAVF/nM0WjXIlyjP7LaN69+V0iXBHc8+k9PPL5Ixw8edDpaMYYP/DHnn9zYKuqblfVdCABcOccoKo7VPU7wH5tpJhpVrUZs+Jmce9V9/LpT5/iTnKTuCXRPhZqTDEnvv5P7F3G6aCqg73XBwDXquqwPMa+B8xV1Zln2NZQYChATExM04SEBJ+y+UtaWhrR0dFOx/Cb861nX8Y+ph2axtbTW6lboi63VrqVqhFVCyHhuQu2vxEEX03BVg8EZk2xsbFrVLVZvgNV1acT0BOYmOP6AOC1M4x9D+hRkO02bdpUA8WSJUucjuBXvtSTlZ2lszbP0uumXqdNpjTRN759Q09nnvZfuPMUbH8j1eCrKdjqUQ3MmoDVWoAe649ln11ArRzXawJ7/LBdE4Bc4qJbvW6kxKfQrnY73lj3Bj3m9GDN/jVORzPGnAN/NP9VQD0RuUhEIoHeQIoftmsCWOVSlXmh9QtMaDeB9Kx0Bn08iNFfjubo6aNORzPGFIDPzV9VM4FhwEJgIzBdVdeLyFMiEgcgIteIyC48S0Rvish6X+c1geH6GteTGJfIoAaDSNqahDvJzYL/LrA3hI0JcH75nL+qzlfVS1X1ElV91nvbk6qa4r28SlVrqmqUqlZS1Qb+mNcEhtIRpRnRbAQJnROoGlWVRz5/hHsX38vutN1ORzPGnIF9w9f4zeUVL+fDTh/y6DWPsmb/Gromd+W9H94jMzvT6WjGmFys+Ru/CnOF0b9+f5LdyVxb9Vr+teZf9J3Xl/UHbaXPmEBizd8UimrR1Xj1xlcZ22YsB08epO/8voxZOcaOE2RMgLDmbwqNiNC+dnuS45PpeWlPPtz4Ie5kN0t3LnU6mjEhz5q/KXRlIsswqsUopnScQnRENPd/dj/Dlw7nlxO/OB3NmJBlzd8UmcZVGjO983QeaPIAy3YuIy4pjumbppOtdsgnY4qaNX9TpCLCIhjSaAiJ7kQaVGrA0yueZuCCgWw9stXpaMaEFGv+xhG1y9bm7Zve5pmWz7Dj2A56zu3Jq9+8yums005HMyYkWPM3jhER3HXdJMcn07FOR97+/m26p3Rn5d6VTkczJuhZ8zeOq1iyIs+1eo632r9FtmZz5yd3Mmr5KFJPpTodzZigZc3fBIzrql9HYlwigxsOZt72ecQlxTFn2xw7TpAxhcCavwkoJcNL8uDVDzKtyzRqla3FY8sf465Fd7Hz2E6noxkTVKz5m4B0aYVLmdJhCo9f+zjfHfyOrildmfj9RDKyM5yOZkxQsOZvAlaYK4zel/cm2Z1MqxqteOWbV7h17q2s+2Wd09GMKfas+ZuAFxMVw7jYcbwS+wpHTx9lwPwBPLviWdLS05yOZkyxZc3fFBs3XngjKfEp9L2iL9M2TcOd7GbxT4udjmVMsWTN3xQrURFRjGw+kg87fUiFEhV4aOlDPPjZgxzJPOJ0NGOKlXCnAxhzPhpe0JCPOn/E+xveZ8LaCXyZ/SUnNp6g92W9CXOFOR3PmIBne/6m2IpwRXDHlXeQ6E6kTok6PL/yeQYsGMCmw5ucjmZMwLPmb4q9WmVqcW+Ve3m+1fPsTtvNrXNvZdyacZzMPOl0NGMCljV/ExREhFsuvoWU+BTiLolj0g+T6JrclS93f+l0NGMCkl+av4h0EJFNIrJVREbmcX8JEZnmvf9rEanjj3mNya1ciXI81fIpJt08iQhXBHd9ehcjvxjJoZOHnI5mTEDxufmLSBgwHugI1Af6iEj9XMPuBI6oal1gHDDG13mNOZtrql7DzLiZ3H3V3SzcsRB3spvZW2bbcYKM8fLHnn9zYKuqblfVdCABcOca4wYmey/PBNqKiPhhbmPOqERYCe5rfB8zu8zkknKX8OSXT3LnJ3ey4+gOp6MZ4zjxdU9IRHoAHVR1sPf6AOBaVR2WY8wP3jG7vNe3eccczLWtocBQgJiYmKYJCQk+ZfOXtLQ0oqOjnY7hN8FWD+RfU7Zm81XaVyQfSSZDM7i53M20K9eOcAncTzsH298p2OqBwKwpNjZ2jao2y2+cP/7Lz2sPPvczSkHGoKpvAW8BNGvWTNu0aeNzOH9YunQpgZLFH4KtHihYTTdyI3edvIsxK8cwb8c8NrKRv1/3d66OubpoQp6jYPs7BVs9ULxr8seyzy6gVo7rNYE9ZxojIuFAOeCwH+Y25pxULlWZF294kfFtx3Mq8xQDPx7IP776B8fSjzkdzZgi5Y/mvwqoJyIXiUgk0BtIyTUmBRjovdwD+EztnTfjoNY1WzPbPZuB9QeSuCURd5Kbj3d8bG8Im5Dhc/NX1UxgGLAQ2AhMV9X1IvKUiMR5h70DVBKRrcBw4E8fBzWmqJWOKM3D1zzMR7d8RJXSVfjrsr8y7LNh7EnL/cLVmODjl3e7VHU+MD/XbU/muHwK6OmPuYzxt/qV6vNhpw+ZunEqr699nfjkeO5rfB/9ruhHuCtw3xA2xhf2DV9jgHBXOLc1uI0kdxLXVL2Gl1a/RN95fdlwaIPT0YwpFNb8jcmhenR1Xr/xdV664SV+OfkLfeb14cVVL3Ii44TT0YzxK2v+xuQiItxc52aS45PpXq87UzZMIT45ns93fe50NGP8xpq/MWdQNrIsT173JJM7TKZ0eGnuW3wfDy97mIMnD+b/YGMCnDV/Y/JxdczVzOgyg2GNh7Hk5yXEzY5jxuYZZGu209GMOW/W/I0pgIiwCO666i5mxc3i8kqX89RXTzHo40FsS93mdDRjzos1f2POQZ1ydXjnpnd4uuXTbD+6nR5zevD6t69zOuu009GMOSfW/I05RyJCfN14UuJT6FCnA29+9yY9Unqwat8qp6MZU2DW/I05TxVLVuSfrf7Jm+3fJDM7kzsW3sET/3mC1FOpTkczJl/W/I3x0V+q/4VEdyJ3Xnknc7bNwZ3sZu72uXacIBPQrPkb4welwkvxUNOHmNZ5GjWja/K3L/7G3Z/ezc5fdzodzZg8WfM3xo8uq3gZUzpO4W/N/8a6X9bRLbkbk36YREZ2htPRjPkDa/7G+FmYK4y+V/QlyZ1EyxotGbdmHL3n9ub7X753Opoxv7Pmb0whqRpVlZdjX+bl2JdJPZ1Kv/n9+OfX/+R4xnGnoxljzd+Ywtb2wrYku5PpfXlvPvrxI9xJbj77+TOnY5kQZ83fmCIQHRnNY9c+xgedPqBsibI8uORBHlryEPuP73c6mglR1vyNKUKNLmjEtM7TeOjqh1i+eznuZDcf/fgRWdlZTkczIcaavzFFLMIVwZ0N72R23GwaVW7Ec18/x20f38bmI5udjmZCiDV/YxxSq2wt3mz/Js9d/xw7j+3k1jm38so3r3Aq85TT0UwIsOZvjINEhC6XdCElPoVbLr6Fid9PpFtKN77a85XT0UyQs+ZvTAAoX7I8z1z/DBNvmohLXAxdNJQpB6dw+NRhp6OZIOVT8xeRiiKySES2eM8rnGHcxyKSKiJzfZnPmGB3bbVrmRU3i6GNhvLN8W9wJ7lJ3ppsxwkyfufrnv9IYLGq1gMWe6/n5UVggI9zGRMSSoSV4P4m9/NotUepU7YOo/4ziiGfDOGnYz85Hc0EEV+bvxuY7L08GYjPa5CqLgZ+9XEuY0JKtchqTO44mSdaPMGGQxvoltyNt757i4wsO06Q8Z2vzT9GVfcCeM+r+B7JGPMbl7jodVkvkuOTaVOrDa99+xq95vZi7YG1TkczxZzkt5YoIp8CVfO463FgsqqWzzH2iKqead2/DfCwqnY+y1xDgaEAMTExTRMSEvItoCikpaURHR3tdAy/CbZ6IHRq+uHED0w/PJ0jWUe4Pvp6ulToQmlXaYcSnptQ+Rs5LTY2do2qNst3oKqe9wnYBFTzXq4GbDrL2DbA3IJuu2nTphoolixZ4nQEvwq2elRDq6bj6cd1zMox2mhyI42dFqsL/7tQs7OzizbceQilv5GTgNVagB7r67JPCjDQe3kgkOzj9owx+SgdUZpHrnmEqbdMpXKpyoxYNoL7P7ufvWl7nY5mihFfm//zQHsR2QK0915HRJqJyMTfBonIF8AMoK2I7BKRm32c15iQ16BSA6beMpWHmz3Myn0rcSe7eX/D+3acIFMgPjV/VT2kqm1VtZ73/LD39tWqOjjHuFaqeoGqllLVmqq60NfgxhgId4UzsMFAZrtn0zSmKS+seoF+8/ux8dBGp6OZAGff8DUmCNSIrsEbbd/gxdYvsu/4PvrM68NLq17iRMYJp6OZAGXN35ggISJ0uKgDyfHJxNeNZ/KGyXRN7soXu75wOpoJQNb8jQky5UqUY/RfRvNeh/coGV6SexffyyPLHuHgyYNORzMBxJq/MUGqaUxTZnSZwb2N7+XTnz8lLimOWZtnka3ZTkczAcCavzFBLDIsknuuuodZcbO4rMJljP5qNLd/fDvbU7c7Hc04zJq/MSHgonIXMenmSTz1l6fYmrqV7nO688baN0jPSnc6mnGINX9jQoSI0LVeV1LiU7ip9k1MWDeB7indWbVvldPRjAOs+RsTYiqVqsSY1mP4d7t/k5GdwR0L7+DvX/6do6ePOh3NFCFr/saEqJY1WjLbPZvbr7yd5K3JxCXFMX/7fPvhmBBhzd+YEFYqvBTDmw4noXMC1aOq8+gXj3LPp/ew69ddTkczhcyavzGGyytezgedPmBk85F8e+BbuiZ35d0f3iUzO9PpaKaQWPM3xgAQ5gqj3xX9SI5PpkX1FoxdM5Y+8/rww8EfnI5mCoE1f2PMH1SNqsqrsa8yrs04Dp88TL/5/Xh+5fMczzjudDTjR9b8jTF/IiK0q92OpPgkel7ak6kbp+JOcrN051Knoxk/seZvjDmjMpFlGNViFFMvWUZJAAAP3UlEQVQ6TqFMZBnu/+x+hi8dzoETB5yOZnxkzd8Yk6/GVRozvct0Hrz6QT7f9TnuJDfTfpxmxwkqxqz5G2MKJMIVweCGg0mMS6RB5QY88/UzDFwwkC1HtjgdzZwHa/7GmHNyYdkLebv92zx3/XPsOLaDXnN68eo3r3Iq85TT0cw5sOZvjDlnIkKXS7qQEp9Cp4s78fb3b9M9pTtf7/3a6WimgKz5G2POW4WSFXj2+md5+6a3ARj8yWAeX/44R04dcTiZyY81f2OMz1pUa8GsuFkMaTiE+dvnE5cUx5xtc+w4QQHMmr8xxi9KhpfkgasfYHqX6dQuW5vHlj/GkEVD+PnYz05HM3nwqfmLSEURWSQiW7znFfIY01hEvhKR9SLynYjc6sucxpjAVq9CPaZ0nMITLZ5g/cH1dEvpxsTvJ5KlWU5HMzn4uuc/ElisqvWAxd7ruZ0AblPVBkAH4GURKe/jvMaYAOYSF70u60VyfDKta7bmlW9eYczeMaw9sNbpaMbL1+bvBiZ7L08G4nMPUNXNqrrFe3kPcAC4wMd5jTHFQJXSVRjbZiyv3fgap7JPcduC23hmxTP8mv6r09FCnvjyhoyIpKpq+RzXj6jqn5Z+ctzfHM+TRAPVP381UESGAkMBYmJimiYkJJx3Nn9KS0sjOjra6Rh+E2z1gNVUHBz69RBLM5ay7NdllA0rS4+KPbiq1FWIiNPRzlsg/o1iY2PXqGqzfAeq6llPwKfAD3mc3EBqrrFHzrKdasAmoEV+c6oqTZs21UCxZMkSpyP4VbDVo2o1FQe/1fP9L99r9+TueuV7V+qwxcN0b9peZ4P5IBD/RsBqLUCPzXfZR1XbqeqVeZySgf0iUg3Ae57n0Z5EpCwwDxilqivyfUYyxgStKytfSULnBEY0HcGKPStwJ7n5cOOHZGXbG8JFydc1/xRgoPfyQCA59wARiQRmA1NUdYaP8xljgkC4K5xBVw5itns2TWKa8PzK5+k/vz+bDm9yOlrI8LX5Pw+0F5EtQHvvdUSkmYhM9I7pBbQGBonIWu+psY/zGmOCQM0yNZnQdgJjWo1hz/E93Dr3VsauHsvJzJNORwt64b48WFUPAW3zuH01MNh7+QPgA1/mMcYELxGh08WdaFmjJWPXjOXd9e/yyU+f8ESLJ2hZo6XT8YKWfcPXGBMQypUoxz/+8g/evfldIlwR3P3p3Tz6+aMcOnnI6WhByZq/MSagNKvajFlxs7jnqntY9NMi4pLiSNySaMcJ8jNr/saYgBMZFsm9je9lZpeZ1C1fl79/+XfuWHgH/z36X6ejBQ1r/saYgHVx+Yt5t8O7jL5uNJuObKJ7SncmrJtAela609GKPWv+xpiA5hIX3S/tTkp8Cu0ubMcba9+gx5werNm/xuloxZo1f2NMsVC5VGVeuOEF3mj7BqczTzPo40GM/nI0R08fdTpasWTN3xhTrLSq2YrZ7tkMajCIpK1JuJPcfPzfj+0N4XNkzd8YU+yUjijNiGYj+OiWj4iJiuGvn/+Vexffy+603U5HKzas+Rtjiq0rKl3B1E5TefSaR1mzfw1dk7syef1kMrMznY4W8Kz5G2OKtTBXGP3r9yfZnUzzqs15afVL9J3Xl/WH1jsdLaBZ8zfGBIVq0dV47cbX+NcN/+LgyYP0ndeXMSvHcCLjhNPRApI1f2NM0BARbqpzE8nxyfS8tCcfbPyA+OR4lu1c5nS0gGPN3xgTdMpElmFUi1G83/F9oiKiGPbZMEYsHcEvJ35xOlrAsOZvjAlajas0Znrn6dzf5H6W7lyKO8nN9E3Tyf7zr8iGHGv+xpigFhEWwdBGQ0l0J3JFpSt4esXTDFwwkK1HtjodzVHW/I0xIaF22dpMvGkiz7R8hh3HdtBzbk9e+/Y1TmeddjqaI6z5G2NChojgrusmOT6ZjnU68tZ3b9E9pTsr9650OlqRs+ZvjAk5FUtW5LlWz/FW+7fI1mzu/OROnvjPE6SeSnU6WpGx5m+MCVnXVb+OxLhEBjcczNxtc4lLimPOtjkhcZwga/7GmJBWMrwkD179INO6TKNW2Vo8tvwx7lp0FzuP7XQ6WqGy5m+MMcClFS5lSocpPH7t43x38Du6pnTlne/fISM7w+lohcKn5i8iFUVkkYhs8Z5XyGNMbRFZIyJrRWS9iNzty5zGGFNYwlxh9L68N8nuZFrVaMXL37xM77m9+e6X75yO5ne+7vmPBBaraj1gsfd6bnuBv6hqY+BaYKSIVPdxXmOMKTQxUTGMix3HK7GvkHo6lf7z+/Pc18+Rlp5W+JPv3Ak9ekC5clC2LHTrBj//7PdpfG3+bmCy9/JkID73AFVNV9XfPkhbwg9zGmNMkbjxwhtJiU+h7xV9SfgxAXeym8U/Ly68CU+cgBtvhB9/hMmT4f33YcsWiI2F48f9OpX48q62iKSqavkc14+oal5LP7WAeUBd4K+qOv4M2xsKDAWIiYlpmpCQcN7Z/CktLY3o6GinY/hNsNUDVlNxUNzr2XF6BwmHEtidsZtGpRrRo2IPIk5F+LWmGjNnUnfCBFZOmcLJGjUAKLl3L9f278+2u+5iV69e+W4jNjZ2jao2y29cvs1fRD4FquZx1+PA5II0/xz3VweSgC6quv9s8zZr1kxXr1591mxFZenSpbRp08bpGH4TbPWA1VQcBEM9GdkZvL/hfSasnUCYK4yO0R0Z1XkUYa6wsz4uMyubExlZREWGE+aSMw9s2xZOnYL//OePt99wg+d8Wf5HJxWRAjX/8PwGqGq7s0yyX0SqqepeEakGHMhnW3tEZD3QCpiZ39zGGBNIIlwR3HHlHbSv3Z5nVjzDzD0z2bxgM09e9ySXVbzsD2NPZ2Yx//u9TFi6jS0H0gh3CZnZyqVVorm7zSV0aliNEuG5njTWrwe3+88TN2gAM2b4tRZf199TgIHeywOB5NwDRKSmiJTyXq4AtAQ2+TivMcY4plaZWvy73b8ZWHkgu9J20Xtub8atGcfJzJMArN2ZyrXPLmbU7B/YvD8NVcjIUlRh0/40Rs3+gWufXcy6nbm+UXz4MFTIY/GkYkU4csSvNfja/J8H2ovIFqC99zoi0kxEJnrHXAF8LSLrgGXAS6r6vY/zGmOMo0SEZlHNSIlPocslXZj0wyS6JXfjg3WL6PPWClJPZnA8PSvPxx5PzyL1ZAa931rx5ycAyWNZqBC+cexT81fVQ6raVlXrec8Pe29fraqDvZcXqWojVb3Ke/6WP4IbY0wgKFeiHE+1fIpJN0/CJWGMWTscvWAqEpb/x0JPZmQxcNJKTmd6nyQqVPDs/ed25Ejerwh8YB+7NMYYP7im6jUMrP0qergd4WW/I+risYSXWw2cfa89IyubBd/v81xp0MCz7p/bhg1Qv75f81rzN8YYP5n4+U7S9rfjxPYHyEqvQqnqMyl14dtI5Jl/PvJ4ehYTlnp/WCYuDlasgO3b/zdgxw7Pp3/i4vya1Zq/Mcb4QVa2suWAZ6knOz2Gkz8N5dTeboSV3EPURa8QWWnpGR+7+UAaWdkKQ4ZAnTqeT/wkJ0NKiudyrVpw111+zWvN3xhj/OB4eibhf/gMv4uM1OYc3zaCzF/rg5z5AHHhLuF4eiZERcFnn8Gll8KAAdCvH1x0kec2P39BLt/P+RtjjMlfVGQ4mdl/Xt/XrDKc2tMXOPOPxmdmK1GR3nZ84YUwa1Yhpfwf2/M3xhg/CHMJ9aqcbe/8zO320irRZ//mbyGw5m+MMX5yT5tLiIo8+6EecouKDOOeNnULKdGZWfM3xhg/6dSwGhFh59ZWI8JcdGyY1+HTCpc1f2OM8ZMS4WFMvqM5pSIKtvdfKsIz/k/H+CkC1vyNMcaPrqpVnoShLShfKuKMS0BRkWGULxVBwtAWXFWrfJ5jCpt92scYY/zsqlrl+frxtiz4fh8Tlm5l8x+O6lmGe9pcQseGVR3Z4/+NNX9jjCkEJcLDiG9Sg/gmNcjKVo6nZ+Z/PP8iZM3fGGMKWZhLKFsywukYf2Br/sYYE4Ks+RtjTAiy5m+MMSHImr8xxoQga/7GGBOCrPkbY0wIsuZvjDEhyJq/McaEIGv+xhgTgqz5G2NMCBLVP//sWCAQkV+An5zO4VUZOOh0CD8KtnrAaioOgq0eCMyaaqvqBfkNCtjmH0hEZLWqNnM6h78EWz1gNRUHwVYPFO+abNnHGGNCkDV/Y4wJQdb8C+YtpwP4WbDVA1ZTcRBs9UAxrsnW/I0xJgTZnr8xxoQga/7GGBOCrPnnQUQqisgiEdniPa+Qx5jaIrJGRNaKyHoRuduJrAVRwHoai8hX3lq+E5FbnchaUAWpyTvuYxFJFZG5RZ2xIESkg4hsEpGtIjIyj/tLiMg07/1fi0idok95bgpQU2sR+UZEMkWkhxMZz1UBahouIhu8/+8sFpHaTuQ8F9b88zYSWKyq9YDF3uu57QX+oqqNgWuBkSJSvQgznouC1HMCuE1VGwAdgJdFpHwRZjxXBakJ4EVgQJGlOgciEgaMBzoC9YE+IlI/17A7gSOqWhcYB4wp2pTnpoA1/QwMAqYWbbrzU8CavgWaqWojYCbwQtGmPHfW/PPmBiZ7L08G4nMPUNV0VT3tvVqCwP63LEg9m1V1i/fyHuAAkO+3BB2Ub00AqroY+LWoQp2j5sBWVd2uqulAAp66cspZ50ygrYhIEWY8V/nWpKo7VPU7INuJgOehIDUtUdUT3qsrgJpFnPGcBXLDclKMqu4F8J5XyWuQiNQSke+AncAYb9MMRAWq5zci0hyIBLYVQbbzdU41BagaeP7b+c0u7215jlHVTOAoUKlI0p2fgtRU3JxrTXcCCwo1kR+EOx3AKSLyKVA1j7seL+g2VHUn0Mi73JMkIjNVdb+/Mp4Lf9Tj3U414H1goKo6umfmr5oCWF578Lk/e12QMYGkuOUtiALXJCL9gWbADYWayA9Ctvmrarsz3Sci+0Wkmqru9TbDA/lsa4+IrAda4XlpXuT8UY+IlAXmAaNUdUUhRS0wf/6NAtQuoFaO6zWB3K8efxuzS0TCgXLA4aKJd14KUlNxU6CaRKQdnh2TG3IsCQcsW/bJWwow0Ht5IJCce4CI1BSRUt7LFYCWwKYiS3huClJPJDAbmKKqM4ow2/nKt6ZiYBVQT0Qu8v7798ZTV0456+wBfKaB/c3MgtRU3ORbk4g0Ad4E4lS1eOyIqKqdcp3wrKkuBrZ4zyt6b28GTPRebg98B6zzng91OreP9fQHMoC1OU6Nnc7uS03e618AvwAn8ezB3ex09lx1dAI243l/5XHvbU/haSIAJYEZwFZgJXCx05n9UNM13r/FceAQsN7pzH6o6VNgf47/d1KczpzfyQ7vYIwxIciWfYwxJgRZ8zfGmBBkzd8YY0KQNX9jjAlB1vyNMSYEWfM3xpgQZM3fGGNC0P8D8YEnrDImQ5IAAAAASUVORK5CYII=\n", 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "xc, yc = wiki.get_coordinates()\n", "visualize_solution(xc, yc, ground_state, ground_level, n, q, 'Classical')\n", @@ -710,9 +651,9 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3", + "display_name": "qiskit_master", "language": "python", - "name": "python3" + "name": "qiskit_master" }, "language_info": { "codemirror_mode": { @@ -724,7 +665,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.2" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/qiskit/finance/simulation/credit_risk_analysis.ipynb b/qiskit/finance/simulation/credit_risk_analysis.ipynb index c8ec89cbe..0458db2a4 100644 --- a/qiskit/finance/simulation/credit_risk_analysis.ipynb +++ b/qiskit/finance/simulation/credit_risk_analysis.ipynb @@ -30,9 +30,8 @@ "### Introduction\n", "This tutorial shows how quantum algorithms can be used for credit risk analysis.\n", "More precisecly, how Quantum Amplitude Estimation (QAE) can be used to estimate risk measures with a quadratic speed-up over classical Monte Carlo simulation.\n", - "The tutorial is based on the following two papers:\n", - "- Quantum Risk Analysis. Stefan Woerner, Daniel J. Egger. [Woerner2019]\n", - "- Quantum Credit Risk Analysis. Daniel J. Egger et al. [Egger2019]\n", + "The tutorial is based on the following paper:\n", + "Quantum Risk Analysis. Stefan Woerner, Daniel J. Egger. [Woerner2019]\n", "\n", "A general introduction to QAE can be found in the following paper and tutorial:\n", "- Quantum Amplitude Amplification and Estimation. Gilles Brassard et al.\n", @@ -101,7 +100,9 @@ "\n", "$$ \\text{CVaR}_{\\alpha}(L) = \\mathbb{E}[ L \\mid L \\geq \\text{VaR}_{\\alpha}(L) ].$$\n", "\n", - "For more details on the considered problem see [Egger2019].\n", + "For more details on the considered model, see, e.g.,
\n", + "Regulatory Capital Modelling for Credit Risk. Marek Rutkowski, Silvio Tarca.\n", + "\n", "\n", "The problem is defined by the following parameters:\n", "- number of qubits used to represent $Z$, denoted by $n_z$\n", From 9293f0614890599b2ce9e68b5bb70ed7111c32cf Mon Sep 17 00:00:00 2001 From: Shaohan Hu Date: Sun, 28 Apr 2019 07:54:23 -0400 Subject: [PATCH 079/116] edit notebooks after VQC refactor --- .../qsvm_kernel_directly.ipynb | 305 ---------------- .../qsvm_kernel_multiclass.ipynb | 124 ------- .../qsvm_variational.ipynb | 251 ------------- .../qsvm_kernel_classification.ipynb | 332 ------------------ 4 files changed, 1012 deletions(-) delete mode 100644 community/aqua/artificial_intelligence/qsvm_kernel_directly.ipynb delete mode 100644 community/aqua/artificial_intelligence/qsvm_kernel_multiclass.ipynb delete mode 100644 community/aqua/artificial_intelligence/qsvm_variational.ipynb delete mode 100644 qiskit/aqua/artificial_intelligence/qsvm_kernel_classification.ipynb diff --git a/community/aqua/artificial_intelligence/qsvm_kernel_directly.ipynb b/community/aqua/artificial_intelligence/qsvm_kernel_directly.ipynb deleted file mode 100644 index 23c6701ae..000000000 --- a/community/aqua/artificial_intelligence/qsvm_kernel_directly.ipynb +++ /dev/null @@ -1,305 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## _*Quantum SVM (quantum kernel method)*_\n", - "\n", - "### Introduction\n", - "\n", - "Please refer to [this file](https://github.com/Qiskit/qiskit-tutorials/blob/master/qiskit/aqua/artificial_intelligence/qsvm_kernel_classification.ipynb) for introduction.\n", - "\n", - "In this file, we show two ways for using the quantum kernel method: (1) the non-programming way and (2) the programming way. \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Part I: non-programming way.\n", - "In the non-programming way, we config a json-like configuration, which defines how the svm instance is internally constructed. After the execution, it returns the json-like output, which carries the important information (e.g., the details of the svm instance) and the processed results. " - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "from datasets import *\n", - "from qiskit import Aer\n", - "from qiskit.aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name\n", - "from qiskit.aqua import run_algorithm, QuantumInstance\n", - "from qiskit.aqua.input import SVMInput\n", - "from qiskit.aqua.components.feature_maps import SecondOrderExpansion\n", - "from qiskit.aqua.algorithms import QSVMKernel" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "First we prepare the dataset, which is used for training, testing and the finally prediction.\n", - "\n", - "*Note: You can easily switch to a different dataset, such as the Breast Cancer dataset, by replacing 'ad_hoc_data' to 'Breast_cancer' below.*" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{'A': 0, 'B': 1}\n" - ] - } - ], - "source": [ - "feature_dim = 2 # dimension of each data point\n", - "training_dataset_size = 20\n", - "testing_dataset_size = 10\n", - "random_seed = 10598\n", - "shots = 1024\n", - "\n", - "sample_Total, training_input, test_input, class_labels = ad_hoc_data(training_size=training_dataset_size, \n", - " test_size=testing_dataset_size, \n", - " n=feature_dim, gap=0.3, PLOT_DATA=False)\n", - "\n", - "datapoints, class_to_label = split_dataset_to_data_and_labels(test_input)\n", - "print(class_to_label)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we create the svm in the non-programming way.\n", - "In the following json, we config:\n", - "- the algorithm name \n", - "- the feature map " - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "params = {\n", - " 'problem': {'name': 'svm_classification', 'random_seed': random_seed},\n", - " 'algorithm': {\n", - " 'name': 'QSVM.Kernel'\n", - " },\n", - " 'backend': {'shots': shots},\n", - " 'feature_map': {'name': 'SecondOrderExpansion', 'depth': 2, 'entanglement': 'linear'}\n", - "}\n", - "backend = Aer.get_backend('qasm_simulator')\n", - "algo_input = SVMInput(training_input, test_input, datapoints[0])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "With everything setup, we can now run the algorithm.\n", - "\n", - "The run method includes training, testing and predict on unlabeled data.\n", - "\n", - "For the testing, the result includes the success ratio.\n", - "\n", - "For the prediction, the result includes the predicted class names for each data.\n", - "\n", - "After that the trained model is also stored in the svm instance, you can use it for future prediction." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [], - "source": [ - "result = run_algorithm(params, algo_input, backend=backend)" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "kernel matrix during the training:\n" - ] - }, - { - "data": { - "image/png": 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4FE1+RXEpmvyK4lI0+RXFpZTquK4qVYLQJba/l1YrnI9d+uBF2co7svH7NLbvgCFC+2nVIhrbPjZWaDt/k8YhAB+hNWrMMKExIw6At+xeffPVNHZov1uEduON99HYAYNuElpuDm//jEuQx7Ynk4+qerCnrFS/9+XXQjtxTLaqAkBV4og7c6wcFwYA138u269nf7uYRAKBtQKFFtE4nMY2CJF3frbulXdCdm/ldyxq1akptBHP3ktjU8h5nDBvIY015I7F0IfvpLHjv/1JaCGRfOFsxl7vuwDZOdyJmqFXfkVxKZr8iuJSNPkVxaVo8iuKSynVgl85n3KoVMW7KHTiuHQqBYDg4Aih7Ung7Z+tW5/rL+q8Zj1hXZzQ/P35DPnExHVC8ykn1807ueyy9fhOLbusuDdv3uc09h3zitBOnpAOtwAwY9xkoT34uixaAkDnzrIAdfTQUaE5zYrfECcdhAeM4EWttUlJQivI5y7KB/ceFJqfvx+NrUH8C1hx70i6g9k0aXc/1oq/RxP37hOa07k5mSd9IPYf4fvQrVNr+VwOjslpSd4jzpzOIUOv/IriUjT5FcWlaPIrikvR5FcUl1IcD78JxpgMY8yWs7RXjTH7jDEbPf/4ImZFUS5bzmvmYYzpDOAYgC/OmtX3KoBj1tr3/pcnC4uoZx97cbSX9sPEGTT24TeeFFpwDe4EW7embMlclcBn17E2y6jaV9JYZtwxjhg7sNl5AHfZ7XRbJxrbPlrOBWT7CgAxEfJOyDOvjqOx77z8qNCmLllKY+uFhQqtdpA0NFmfnEK3r0Rmzzk51Fb2k9X6OtX565uYLivd6xJk6zUArPlxjdA63S7PefcW0XR7NvNw27odNJYZqAx9bhCNXbB8vdCc7tDc31deS8dN5G3Sg+70vtN1Uc08HMZ1KYpSxinJZ/7HjTFxno8F8vKgKMplzYUm/8cA6gOIAZAGYIxT4Nmz+o4fK/5AAUVR/lguKPmttQestaestacBfAag3e/E/ndWX+UA3kmnKErpUyz3XmNMJIDZZxX8Qs9M6TXGPAWgvbW2v/NPKKJmcG17W//HvDSn549oKotav8zka6U79LpWaEPuvpnG9uku200HPvUIjW3aooF8rgZSY0UigBfmPp34HY0NCpXFLqeCEGt3HfMqHxM1aaFcI+/kX1A/RroCD+wiz+3xfNmqCvCC324H7wC27t6JXPJ8H03/nsY+dKd83cuR8ldlv4p0+/wC2R7b9/anaez4KaOF5le++B3zD9//GtVjYqVj8iMDpd8DAFzh7+/1uF3btli3bl2xCn7n3VPPuK4uAGoYY1IB/BVAF2NMDIqm86YAeKg4T6YoyuXDhY7r4itOFEUpM2iHn6K4FE1+RXEpmvyK4lJKdVZf4+bN7aTvvKvd5X18aOziZbIdMn55PI0tLCgUWodbOtDY3OzjQkvazOe+bV33m9Duf/0xoSXH8e273Sj3wel8M5fdyW99QmOXr/hWaE4tu/d2vV5oA+5+gcYyZ2HmZtu8Th26/ba0NKH1aS2NKQBgXpw0VckvlK8jwCvoTrFdGjcW2oodsj33tMPrEEgciNvU5e7M2XnSxXjjbu4KzM7ZqdOnaexX/5Ez/O7rx5fP/BznbSTz8v33IWnbNp3VpyiKM5r8iuJSNPkVxaVo8iuKSynVgl/T6Gg7bfZsLy0pI4PGsoLMgmm8vbcqGedUv0U9GnuqUBZZrmkpx2oBQAEpKk2f8qPQfHx50bLLTdcI7XpSkAKA79ZJp+A8B2fjcqRf1alld9dGqX819S0aO+3XX4XWs0ULofmU49cMtkY/+aBsRQaA6gHS5fZkIXeereovi3BTF/ECZ6doOQasXi05Eq6cg1cCY2E8LzS3JO3b+7OyaGydINm+7fRzU3ftF9odN3amsX6+3sXQG67rgo2//aYFP0VRnNHkVxSXosmvKC5Fk19RXIomv6K4lFKt9tesFWb79PN2k60WzO3/Pn3vr0Ib+f4/aexnb74jte+n0thfl24QmtP8vN3bZdvuR5OlgUPCflmdBYCIGnJW37odO2nsgz1l+yabnQcAL48bIbRdqbK1FuCz9mqSll0AuOsaeXfirc++Etr+nfx465E7LPO+kHdHAGA8uePw7ruTaGw+mXPHWpEBoHx5eedl+1rZ3rsvUc7ZA/i5efHZv9DYGYuWCc0w5xAAW1cmCG3Es/fS2Lg9e4S26hfZag4A+bne52bCP95AWmqKVvsVRXFGk19RXIomv6K4lOKM66pjjFlsjNlqjIk3xgzz6EHGmPnGmETPV/XuV5QyRHGsRgsBPGOt3WCMqQJgvTFmPoB7ASy01r5tjHkewPMAZCXqLGqFVMeTzw/20ioSx1cACG8SLrTbu/JRV1dGyXFbh4/LdfsAMPD2G4X2+RfcCTZz/yGhsf3t2pS3B4+fNVdo/bpLN1wAeO/Lr4XGinUAH6F1dVQUjZ25Ro6v6kFadgFe3HvhAWnhOPKd8XT7uCWbhPbQaO7tev9dw4UWHy8LaAAQGdlcaK27c5+Ao8fkOVv6w89C27KFP1dEhGwPHjykN409kiFbeedO4e+lvsMGCi0+lReab2gujzfzKJ95MbBTR6oXh+KM60qz1m7wfJ8DIAFAGIBbAEz2hE0G0OeC90JRlFLnf/rM7/HvbwlgNYDgM979ANIBBF/UPVMU5Q+l2MlvjAkAMBPAk9Zar7+tbFGzAG0YOHtc15HDOu9TUS4XipX8xhhfFCX+l9baMwZyB4wxoZ7/DwVA1+aePa6rGlnWqCjKpaE4E3sMioZ0JFhrx571X98DGAzgbc/XWef7WcdPnMDKLdu8tC3Lt9DYQ/tkse2eXl1pbM1AOQN+x7YUGstGSsX25GafIXXlSKkD2dlC23VAzo8HgFbRDYW2IYUbPJ44Js0gAwLlmncAWJ+cIrRqlXksM450Wo/POvdYce/NEQ/S7VvGdBMaK4oBwD8myU7Jd177jMbOnilnxCyYyv0aCvLliDM/P3+htWghjU0BwBh5brbt592TC6fPE9qQUQ/T2Ed6yTFir306gcbWJ/4DY4fx0V7PvDrO6/HUT9+lcYziVPs7AhgEYLMxZqNHG4mipJ9hjLkPwG4A/Yr9rIqiXHKKM65rOQCnXmF+KVYU5bJHO/wUxaVo8iuKS9HkVxSXUpyC30UjwN8f1zT3dq/NTM2ksWyd/+Fjx2hsgxBZld+9m1dorwoNFdqU6XzNed7RXKEFXSfXkReeOkW3Z14JrSMjaWxVMiZqQ9x2GsvuWDAN4CO0GoeF0Vi2Hp+17LKqPgD8tlGOmWrdsQuNnfLlHKE1bCvvjgDAhpX1hRZ7VyyNnTdRtlQfPLhXaNWr83OwebN0BW5d930ay1pbrm3ciEZGRbUSWucOMTQ2jdxRyszkrcA5h73bfk+d4iPAGHrlVxSXosmvKC5Fk19RXIomv6K4lFIt+GVl5+D7n7zXUaenpNPY3fGyDfae/j1p7Mw5S4TWvBUvHmXnyiJe3WaRNLZq1SpCY62xex0WLLERTfM383bmmWNnCm3ACG7gGVxVtjPvzuSF0z6t5bp3pxFazGyTrcd3atllxb1/ffgSjWWvwxc/8nFssb3lavHYdrxYtmmxLFDeOvRWoaU6GHg2ipFr6UOqynFwABDVTBb3LF/fhtq15fuxpUPx9/2p3wotPFz6DADAtXd4+0PMnzeZxjH0yq8oLkWTX1Fciia/orgUTX5FcSma/IriUkp1XFer1q3tsl9XeGnZudLEAgB8feTYpcLTvHVxD6l0t6pbl8cekiYhP69cT2MP7JYmHUOH3CG04/lynBQAJGVIc6M29fh+Hc07IbS1SUk09irSztzoSulgDAA/btwotGuuuorG5uTJ14K57DIjDoC37A5/TLrWAryd+aX3/kVjq4XIVu+QSHkOnJg7Qbb8Vqoinx8A/Cr5Ce32e/hdpoM50lF39dy1NPa+++UdhywHh2n2Pk8+QI2yMOcT73M+b+4kHD6UpuO6FEVxRpNfUVyKJr+iuJSSjOt61Rizzxiz0fNPzphWFOWypSTjugDgfWvte8V9sqzcXHy/wXvOeDeHUVdjP5Kjo0YPf4DGzlq6SmgLFq6msT1ukDPoA2vx9s0EMlN9e7psR3Yqmm6O3yk03/L8lM/+drHQCvILaGzXEfdRnZFfWCi0k4X857777iShsRFaTi67bD2+U8suK+6NfvZ+Gsucdm+6S44RA4CoVnJsWZEBtTdzZvI22M6xtwktoGJFGrs9WfoELPlBFj0BILS+9JFo2IQXf7uTcV2HHLws5s/7wuvx0WxZ0HaiOAaeaQDSPN/nGGPOjOtSFKUMU5JxXQDwuDEmzhgzQaf0KkrZoiTjuj4GUB9ADIr+MhjjsN1/x3XlHDlyEXZZUZSLwQWP67LWHrDWnrLWngbwGYB2bNuzx3VVqaZ/HCjK5UJxqv10XNeZOX0ebgXAF6orinJZUpJxXQOMMTEosjBNASBdH4rBtB9llRsA0pNkVT2/gFepA6rJOXWnCrmjblqWNKLIPijdUgEgP0+27UaROWq5J+V8OADIayzdcH1I5RngdxwO7uWmG4npsu2YtfwCgB+5u1DVn7e2suONjJSVZzY7D3Bw2SVGHABQu2FtoTnNz9u0Sb5HmrfsSGOzDsrX95cF0iglN5e/5it+kSMn+xzoTWMXTV0ktN738rsQU/72kdCGvDiUxp4md8Amvj6FxkZENPN6nJcn73w5UZJxXdzvWlGUMoF2+CmKS9HkVxSXosmvKC6lVNfzh0XUs4+OfN1L863gS2Pzc2XxaVC/HjR26ZatQtu7XbZeAsC+HdK1dczbT9HYBfHyBkYhGYfEXHoBoCFZYz99sWyXBYArqkmn4PQUWdgDgMqBlYWWdYD3UNRvKltIDx/ixS5TTpZ2Ck7IIuuCqXIsF8BHaDm57K5PShZa/Ip4GrsnYY/Qpjp4Cizdtk1oEz/4Wmi1G/Am1YbtpCPvmKGjaOyoz98W2vI5vOBWnrzPp308jsau3CjfIyt27KCx6Xu91/m/M/xJ7NmZqOv5FUVxRpNfUVyKJr+iuBRNfkVxKZr8iuJSSnVWn6+fL0LreZsaLPs3r37HxMoqcZhDVb1bTLTQQrp0prGJxIxj6z4+t+2Kiv5CY86qberJNl4A6N37CaHdOlSaRQBAA9KeW6OKvAMAAF9/KltQx7z7NI0tPCXbnDOOHqWxq7fJivLRYzK2IJ+3M8+bKF1y2ew8AOjcV74+zIgD4C27rKoPAJ0byWr9oCEvC+2kg1HKv16Wbbgz502lsVEh8m5OgYNRyjUdZIvwzyt/prHs9Xl58DAae8/T3i3Cpx3a2hl65VcUl6LJryguRZNfUVyKJr+iuJRSLfj5+JRDlSu8W1NZYQ8ADu2XI7jSyVp8APhp5TqhNawfTmMziQtqcsJuGrt9zXahvf7G40I75TBGbOBIOaoqKjiYxm7dmyq03Vv5fnW6vZPQSGcuAN4WemO0LJACwBdTZgtt6Q+yKOXnJwuhAHDwoGypvnWoHFMF8BFazGUX4Ovx847xMW+suDdlwutCa9pUnkMAOH5ctj5vSOGvQ987nxXajFW8vTcoSBYHl27i7cz3dOsitGbRfH9XzFrq9fhYFnf5ZeiVX1Fciia/orgUTX5FcSnFMfCsaIxZY4zZ5BnXNcqj1zXGrDbG7DTGfG2MqfDH766iKBeL4hT88gHEWmuPeSy8lxtjfgLwNIrGdU03xnwC4D4Uefk7P1m5cggK8DbbDGwmTR8BYM5mOZvevwL//eLjKw9jBxmlBAAdW0hzxB0b5VgtAMjcJ4uO1chcedZF50RQgFyLD/Di3pF0vkZ/yJ03Ca2yHx8pdZr4NZRzKKztS5Sdjlu2yA5MJ6PN6tXlGvlU8jMBoFIVeR6dRmgxs02n9fisc48V9+Ljl9Ptw8ObCK0+MW0FgIgmsqi8YCofT1YrTI7rujKkBo1l49TqteBdpB++OdLrcW4u795knPfKb4s4U0L09fyzAGIBfOPRJwPgNq2KolyWFHdoh4/HtjsDwHwAuwBkWWvPTIFMhc7vU5QyRbGS3zOZJwZAbRRN5pGrJxw4e1xXlo7rUpTLhv+p2m+tzQKwGEAHAIHy2b4fAAALa0lEQVTGmDMftmsDoB/uzh7XFajjuhTlsqE41f6axphAz/f+ALoDSEDRL4E7PGGDAch1poqiXLYUp9ofCmCyMcYHRb8sZlhrZxtjtgKYbowZDeA3FM3zOy/n1plXLJKtuQDATIVTDx+msTVryr8onNbC+/lKF9X0ZLnGHwAqV+WV+XPJLyyk+rHs48XaHgBq1akpRQdn5eXbZdtx71ataGwguTvhRE2yDxERsvptDL9mbN68VGiNYuS4LwDwq+QntM6x3OuAjdBiLrsAX4/PWnZZVR8A9uyRTtANQnhL9vKfpIvx0x+8QGPHPTdWaI2JuzMA5BfI99OSWXxAVqNGV3s93rp1BY1jFGdcVxyAlkRPgsNkXkVRLn+0w09RXIomv6K4FE1+RXEppTquK+TKcHv3Q8O9tOAIXky57lpZwDpE1uIDQMvISKEtczB4/M9H3wttzD+Gk0ggpGpVof2SkCA0J2NR1vb7yUczaOyIZ+8V2rETJ2js9JnzhbZ23hoe++/3hLbcYfRTu/qy1Tr18CGhbdufRrdvXTdSaCFVA2ns2iTZvh1Qkbco7zogx5a99Yhctw9ws022Ht+pZZcV9wKIkSsAJBDj12UOa/Qj68j23p4xopQGANi+X/7cqv58Hw5kexcz+/Xqhfi4OB3XpSiKM5r8iuJSNPkVxaVo8iuKS9HkVxSXUurjukIivaupy77l47qOH5WtscMfGsBj8/OFdlvbtjS2/BM+QltHKs8AbwVmVdfw6tXp9v3ueEZo3QZ1p7EpmdI4JHEvN8JI3SGdfsdPGU1js/Oky23LiAgaO2ORfC2OZEjH5IXT59Hti2wevIlqxttwuw6IFdp2BwOWRVMXCW3U52/TWDZCi7nsMiMOgLfssqo+ADQOk6vYnYxd2ra+UWirE/ldlwLSLn5Na3m+AOCBkd53qrJzit9Srld+RXEpmvyK4lI0+RXFpWjyK4pLKdWCX41qVXF/X2/n2Uf7y7nlALAiMVFoTuOcZv0qW1vTdvEW1GFD7hCaU8Fv1Qo5W75iZdmCWugwrmvEe08IrV097sI6YZ50fQ0IDCCRwNDnBgnNrzx/KVftlM7EVzo4Khky82vuFNkOPWTUw3T7axvL4p4lRUAA+PiTb4S25Ic5NLb3vbLQu3wOH4tVQJxv2QgtJ5ddth7fqWWXFffK+8iCMgBs3C1bjBcsXUtjH+13s9DiE/jx9v6/R7we5xy+iO69iqL8OdHkVxSXosmvKC5Fk19RXEpJZvVNMsYkG2M2ev7F/PG7qyjKxaIks/oA4DlrrSzbOnA0Lw8Ltmzx0qa++SWNDW8kW1DbvsIr5eFh3BCEEU9aNZ2q9Y1bXSW0yn7SddbH4S4Ea61dn5xMY9mdjJN5sm0ZABYsXy+0e27uRmOb16kjtEoOMw8nrZRGJX2HDRTaI71kNRoAoqKkAUvt2g1p7JjPXhFaaH1peAEAU/4mHXl7DuhHY6/pIO8eBQXJll82Ow/gLrsv/vNFGstadllVHwBiSEv1lKW8tX1XhjQv6diUuzOP+uQzr8dbtstWaCeK495rAbBZfYqilGEuaFaftXa157/eMMbEGWPeN8bISyK8x3UdzZKLRBRFuTRc0Kw+Y0wzAC+gaGZfWwBBAEY4bPvfcV1XBHI/N0VRSp8LndXXw1qb5hnfnQ9gInSAh6KUKc7r3muMqQmgwFqb5ZnV9zOAdwCst9ammaJK1fsATlhrn/+9nxVaO8L+5Qnv4klQCG81jW4lW0V9HVonG4bK4s289Rtp7IIvpPPteFJ8AoAK5eV6fuYKXN1hNBhb+//p59/S2KEP3ym0/Q5TjRf9IkecrZvHx569O+45oa3ZtYvGXttInvP4VOkdsGmjHBcGAJ07yBs+zFkZ4C3VTu7MSTvlOv8xz/Ei3M8rfxbaUtKee2VIDbo9G6EVFcrHarH1+EtWbKCxzKV6UOdraeyONNmafsqhKH3ue+SRfv2wPT6+WO69JZnVt8jzi8EA2AiAN3wrinJZUpJZfdxaRFGUMoF2+CmKS9HkVxSXosmvKC6lVGf1NWvRws6cO9dLY5V6ANh7SM6IW5+SQmPXLpQV1rvu6kljt5Dq9a1t2tDYNNKUFFFDVomP5/OZegay6OpkSDL+25+E1q1TaxrLzDg+mSZNN5yez68S7cdC0+ZRQruheXOhpRw8SLdPO2duHACs+JXfdelwdbTQ2KxAADhNKt1HcnNpbMZRaWbBKvgniekHAOQXSOdcp+diLrvs/QHwll0/cjcJAK4iObGKmNsAQKu6db0eX92+PdavW6ez+hRFcUaTX1Fciia/orgUTX5FcSml6t57srAQyecUi5554DUa27BNE6ENfZyP66rbv6bQnFpF25Oi0uT5i2ksc8/deUAWbpyqK6xQ1MihwHnuGDMASCTPBQAz/yPXbA8lrsQAL0qdKODFrolfSffczKM5Qhs7jL9mmZmymBoeLl9HAAipGyI0p9ds4utThHb3yLto7MuDhwmtWXQnodVrwb0hlsz6UWiz53PPCTZCy8lll63HX50g3aEBXty7ukEDGjt50RKvx4dz5OvlhF75FcWlaPIrikvR5FcUl6LJryguRZNfUVxKqVb7fcqVQ9VKlby0v08YRWNnzJKz1KpVrkxjlyVIgw3WEgoAdaoHCS0zNZPGzvt8rtDGfCJnuVWpKOf3AcC0ufIuQqtI6eIKABl7M4SWlpROYx8Y0kdoVxDjEAD4asWvQuse3YzG5udKt+CBnToK7ZlXx9Htcw7LSvO1d3DDijmfyDsL8+d9QWMjIuT+ppPzBQD3PD1UaCtmLRXah2+OpNs3anS10A6QtmUAeGDkcKGdOzvvDOe67ALOZi3MVOXcqv4ZBsd2oXpx0Cu/orgUTX5FcSma/IriUjT5FcWllOp6fmPMQQBn5hnVAMArbWUbPa6yx5/p2CKstbLfnVCqye/1xMass9ZyF40yjB5X2ePPfGy/h/7ZryguRZNfUVzKpUz+8Zfwuf9I9LjKHn/mY3Pkkn3mVxTl0qJ/9iuKSyn15DfG9DDGbDfG7DTG/O5gz8sdY8wEY0yGMWbLWVqQMWa+MSbR85VPIr2MMcbUMcYsNsZsNcbEG2OGefQyfWzGmIrGmDXGmE2e4xrl0esaY1Z73pNfG2MqXOp9LQ1KNfk9wz4/BNATQBMAA4wx3OepbDAJQI9ztOcBLLTWNgCw0PO4rFEI4BlrbRMAVwN4zPM6lfVjywcQa61tASAGQA9jzNUomjr9vrU2CsARAPddwn0sNUr7yt8OwE5rbZK19iSA6QBuKeV9uGhYa5cCOHyOfAuAyZ7vJwOQS/Auc6y1adbaDZ7vcwAkAAhDGT82W8QZo0Bfzz8LIBbANx69zB3XhVLayR8G4Oxh66ke7c9EsLX2zID1dADSmbMMYYyJRNGU5tX4ExybMcbHGLMRQAaA+QB2Aciy1p5xOv0zvicpWvD7A7FFt1LK7O0UY0wAgJkAnrTWes3BKqvHZq09Za2NAVAbRX+JysXzLqG0k38fgDpnPa7t0f5MHDDGhAKA5yt3nbjMMcb4oijxv7TWfuuR/xTHBgDW2iwAiwF0ABBojDljbPNnfE9SSjv51wJo4KmuVgDQHwCfMFl2+R7AYM/3gwHMuoT7ckGYoumenwNIsNaOPeu/yvSxGWNqGmMCPd/7A+iOonrGYgBnBh+UueO6UEq9yccY0wvABwB8AEyw1r5RqjtwETHGfAWgC4pWhR0A8FcA/wEwA0A4ilYw9rPWnlsUvKwxxnQCsAzAZgBn/NBGouhzf5k9NmNMNIoKej4ouvDNsNa+Zoyph6LicxCA3wDcba2VnmZ/MrTDT1Fcihb8FMWlaPIrikvR5FcUl6LJryguRZNfUVyKJr+iuBRNfkVxKZr8iuJS/h/l3KikFmmUawAAAABJRU5ErkJggg==\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "testing success ratio: 1.0\n", - "predicted classes: ['A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B']\n" - ] - } - ], - "source": [ - "print(\"kernel matrix during the training:\")\n", - "kernel_matrix = result['kernel_matrix_training']\n", - "img = plt.imshow(np.asmatrix(kernel_matrix),interpolation='nearest',origin='upper',cmap='bone_r')\n", - "plt.show()\n", - "\n", - "print(\"testing success ratio: \", result['testing_accuracy'])\n", - "print(\"predicted classes:\", result['predicted_classes'])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### part II: Programming way.\n", - "We construct the svm instance directly from the classes. The programming way offers the users better accessibility, e.g., the users can access the internal state of svm instance or invoke the methods of the instance. We will demonstrate this advantage soon." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we create the svm in the programming way.\n", - "- We build the svm instance by instantiating the class QSVMKernel. \n", - "- We build the feature map instance (required by the svm instance) by instantiating the class SecondOrderExpansion." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [], - "source": [ - "backend = Aer.get_backend('qasm_simulator')\n", - "feature_map = SecondOrderExpansion(num_qubits=feature_dim, depth=2, entangler_map=[[0, 1]])\n", - "svm = QSVMKernel(feature_map, training_input, test_input, None)# the data for prediction can be fed later.\n", - "svm.random_seed = random_seed\n", - "quantum_instance = QuantumInstance(backend, shots=shots, seed=random_seed, seed_transpiler=random_seed)\n", - "result = svm.run(quantum_instance)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let us check the result." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "kernel matrix during the training:\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "testing success ratio: 1.0\n" - ] - } - ], - "source": [ - "print(\"kernel matrix during the training:\")\n", - "kernel_matrix = result['kernel_matrix_training']\n", - "img = plt.imshow(np.asmatrix(kernel_matrix),interpolation='nearest',origin='upper',cmap='bone_r')\n", - "plt.show()\n", - "\n", - "print(\"testing success ratio: \", result['testing_accuracy'])" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "collapsed": true - }, - "source": [ - "Different from the non-programming way, the programming way allows the users to invoke APIs upon the svm instance directly. In the following, we invoke the API \"predict\" upon the trained svm instance to predict the labels for the newly provided data input.\n", - "\n", - "Use the trained model to evaluate data directly, and we store a `label_to_class` and `class_to_label` for helping converting between label and class name" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "ground truth: [0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1]\n", - "preduction: [0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1]\n" - ] - } - ], - "source": [ - "predicted_labels = svm.predict(datapoints[0])\n", - "\n", - "predicted_classes = map_label_to_class_name(predicted_labels, svm.label_to_class)\n", - "print(\"ground truth: {}\".format(datapoints[1]))\n", - "print(\"preduction: {}\".format(predicted_labels))" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.8" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/aqua/artificial_intelligence/qsvm_kernel_multiclass.ipynb b/community/aqua/artificial_intelligence/qsvm_kernel_multiclass.ipynb deleted file mode 100644 index 2b7c41f3f..000000000 --- a/community/aqua/artificial_intelligence/qsvm_kernel_multiclass.ipynb +++ /dev/null @@ -1,124 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## _*Quantum SVM kernel algorithm: multiclass classifier extension*_\n", - "\n", - "A multiclass extension works in conjunction with an underlying binary (two class) classifier to provide multiclass classification.\n", - "\n", - "Currently three different multiclass extensions are supported:\n", - "\n", - "* OneAgainstRest\n", - "* AllPairs\n", - "* ErrorCorrectingCode\n", - "\n", - "These use different techniques to group the data with binary classification to achieve the final multiclass classification." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "from datasets import *\n", - "from qiskit import Aer\n", - "from qiskit.aqua.input import SVMInput\n", - "from qiskit.aqua import run_algorithm\n", - "import numpy as np" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here we choose the `Wine` dataset which has 3 classes." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "n = 2 # dimension of each data point\n", - "sample_Total, training_input, test_input, class_labels = Wine(training_size=40,\n", - " test_size=10, n=n, PLOT_DATA=True)\n", - "\n", - "temp = [test_input[k] for k in test_input]\n", - "total_array = np.concatenate(temp)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we setup an Aqua configuration dictionary to use the quantum `QSVMKernel` algorithm and add a multiclass extension to classify the Wine data set, since it has 3 classes.\n", - "\n", - "Although the `AllPairs` extension is used here in the example the following multiclass extensions would also work:\n", - "\n", - " 'multiclass_extension': {'name': 'OneAgainstRest'}\n", - " 'multiclass_extension': {'name': 'ErrorCorrectingCode', 'code_size': 5}" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "aqua_dict = {\n", - " 'problem': {'name': 'svm_classification', 'random_seed': 10598},\n", - " 'algorithm': {\n", - " 'name': 'QSVM.Kernel'\n", - " },\n", - " 'feature_map': {'name': 'SecondOrderExpansion', 'depth': 2, 'entangler_map': [[0, 1]]},\n", - " 'multiclass_extension': {'name': 'AllPairs'},\n", - " 'backend': {'shots': 1024}\n", - "}\n", - "\n", - "backend = Aer.get_backend('qasm_simulator')\n", - "algo_input = SVMInput(training_input, test_input, total_array)\n", - "result = run_algorithm(aqua_dict, algo_input, backend=backend)\n", - "for k,v in result.items():\n", - " print(\"'{}' : {}\".format(k, v))\n" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.7" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/community/aqua/artificial_intelligence/qsvm_variational.ipynb b/community/aqua/artificial_intelligence/qsvm_variational.ipynb deleted file mode 100644 index 9d4e15b28..000000000 --- a/community/aqua/artificial_intelligence/qsvm_variational.ipynb +++ /dev/null @@ -1,251 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## _*Quantum SVM (variational method)*_\n", - "\n", - "The QSVMKernel notebook here demonstrates a kernel based approach. This notebook shows a variational method.\n", - "\n", - "For further information please see: [https://arxiv.org/pdf/1804.11326.pdf](https://arxiv.org/pdf/1804.11326.pdf)\n", - "\n", - "\n", - "**This notebook shows the SVM implementation based on the variational method.**\n", - "\n", - "In this file, we show two ways for using the quantum variational method: (1) the non-programming way and (2) the programming way. \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Part I: non-programming way.\n", - "In the non-programming way, we config a json-like configuration, which defines how the svm instance is internally constructed. After the execution, it returns the json-like output, which carries the important information (e.g., the details of the svm instance) and the processed results. " - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "from datasets import *\n", - "from qiskit.aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name\n", - "from qiskit import Aer\n", - "from qiskit.aqua.input import SVMInput\n", - "from qiskit.aqua import run_algorithm, QuantumInstance\n", - "from qiskit.aqua.algorithms import QSVMVariational\n", - "from qiskit.aqua.components.optimizers import SPSA\n", - "from qiskit.aqua.components.feature_maps import SecondOrderExpansion\n", - "from qiskit.aqua.components.variational_forms import RYRZ" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "First we prepare the dataset, which is used for training, testing and the finally prediction.\n", - "\n", - "*Note: You can easily switch to a different dataset, such as the Breast Cancer dataset, by replacing 'ad_hoc_data' to 'Breast_cancer' below.*" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{'A': 0, 'B': 1}\n" - ] - } - ], - "source": [ - "feature_dim = 2 # dimension of each data point\n", - "training_dataset_size = 20\n", - "testing_dataset_size = 10\n", - "random_seed = 10598\n", - "shots = 1024\n", - "\n", - "sample_Total, training_input, test_input, class_labels = ad_hoc_data(training_size=training_dataset_size, \n", - " test_size=testing_dataset_size, \n", - " n=feature_dim, gap=0.3, PLOT_DATA=True)\n", - "\n", - "datapoints, class_to_label = split_dataset_to_data_and_labels(test_input)\n", - "print(class_to_label)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we create the svm in the non-programming way.\n", - "In the following json, we config:\n", - "- the algorithm name \n", - "- the variational form\n", - "- the feature map \n", - "- the optimizer" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "params = {\n", - " 'problem': {'name': 'svm_classification', 'random_seed': 10598},\n", - " 'algorithm': {'name': 'QSVM.Variational', 'override_SPSA_params': True},\n", - " 'backend': {'shots': 1024},\n", - " 'optimizer': {'name': 'SPSA', 'max_trials': 200, 'save_steps': 1},\n", - " 'variational_form': {'name': 'RYRZ', 'depth': 3},\n", - " 'feature_map': {'name': 'SecondOrderExpansion', 'depth': 2}\n", - "}\n", - "\n", - "svm_input = SVMInput(training_input, test_input, datapoints[0])\n", - "backend = Aer.get_backend('qasm_simulator')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "With everything setup, we can now run the algorithm.\n", - "\n", - "For the testing, the result includes the details and the success ratio.\n", - "\n", - "For the prediction, the result includes the predicted labels. " - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "result = run_algorithm(params, svm_input, backend=backend)\n", - "print(\"testing success ratio: \", result['testing_accuracy'])\n", - "print(\"predicted classes:\", result['predicted_classes'])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Part II: programming way.\n", - "We construct the svm instance directly from the classes. The programming way offers the users better accessibility, e.g., the users can access the internal state of svm instance or invoke the methods of the instance. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we create the svm in the programming way.\n", - "- we build the optimizer instance (required by the svm instance) by instantiating the class SPSA.\n", - "- We build the feature map instance (required by the svm instance) by instantiating the class SecondOrderExpansion.\n", - "- We build the varitional form instance (required by the svm instance) by instantiating the class RYRZ.\n", - "- We build the svm instance by instantiating the class QSVMVariational. \n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "backend = Aer.get_backend('qasm_simulator')\n", - "optimizer = SPSA(max_trials=100, c0=4.0, skip_calibration=True)\n", - "optimizer.set_options(save_steps=1)\n", - "feature_map = SecondOrderExpansion(num_qubits=feature_dim, depth=2)\n", - "var_form = RYRZ(num_qubits=feature_dim, depth=3)\n", - "svm = QSVMVariational(optimizer, feature_map, var_form, training_input, test_input)\n", - "quantum_instance = QuantumInstance(backend, shots=shots, seed=random_seed, seed_transpiler=random_seed)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we run it." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "result = svm.run(quantum_instance)\n", - "print(\"testing success ratio: \", result['testing_accuracy'])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Different from the non-programming way, the programming way allows the users to invoke APIs upon the svm instance directly. In the following, we invoke the API \"predict\" upon the trained svm instance to predict the labels for the newly provided data input.\n", - "\n", - "Use the trained model to evaluate data directly, and we store a label_to_class and class_to_label for helping converting between label and class name" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "predicted_probs, predicted_labels = svm.predict(datapoints[0])\n", - "predicted_classes = map_label_to_class_name(predicted_labels, svm.label_to_class)\n", - "print(\"prediction: {}\".format(predicted_labels))" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.8" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/qiskit/aqua/artificial_intelligence/qsvm_kernel_classification.ipynb b/qiskit/aqua/artificial_intelligence/qsvm_kernel_classification.ipynb deleted file mode 100644 index eee1be33b..000000000 --- a/qiskit/aqua/artificial_intelligence/qsvm_kernel_classification.ipynb +++ /dev/null @@ -1,332 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# _*Qiskit Aqua: Experiment with classification problem with quantum-enhanced support vector machines*_\n", - "\n", - "The latest version of this notebook is available on https://github.com/qiskit/qiskit-tutorial.\n", - "\n", - "***\n", - "### Contributors\n", - "Vojtech Havlicek[1], Kristan Temme[1], Antonio Córcoles[1], Peng Liu[1], Richard Chen[1], Marco Pistoia[1] and Jay Gambetta[1]\n", - "### Affiliation\n", - "- [1]IBMQ" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Introduction\n", - "Classification algorithms and methods for machine learning are essential for pattern recognition and data mining applications. Well known techniques such as support vector machines and neural networks have blossomed over the last two decades as a result of the spectacular advances in classical hardware computational capabilities and speed. This progress in computer power made it possible to apply techniques, that were theoretically developed towards the middle of the 20th century, on classification problems that were becoming increasingly challenging.\n", - "\n", - "A key concept in classification methods is that of a kernel. Data cannot typically be separated by a hyperplane in its original space. A common technique used to find such a hyperplane consists on applying a non-linear transformation function to the data. This function is called a feature map, as it transforms the raw features, or measurable properties, of the phenomenon or subject under study. Classifying in this new feature space -and, as a matter of fact, also in any other space, including the raw original one- is nothing more than seeing how close data points are to each other. This is the same as computing the inner product for each pair of data in the set. So, in fact we do not need to compute the non-linear feature map for each datum, but only the inner product of each pair of data points in the new feature space. This collection of inner products is called the kernel and it is perfectly possible to have feature maps that are hard to compute but whose kernels are not.\n", - "\n", - "In this notebook we provide an example of a classification problem that requires a feature map for which computing the kernel is not efficient classically -this means that the required computational resources are expected to scale exponentially with the size of the problem. We show how this can be solved in a quantum processor by a direct estimation of the kernel in the feature space. The method we used falls in the category of what is called supervised learning, consisting of a training phase (where the kernel is calculated and the support vectors obtained) and a test or classification phase (where new unlabelled data is classified according to the solution found in the training phase).\n", - "\n", - "References and additional details:\n", - "\n", - "[1] Vojtech Havlicek, Antonio D. C´orcoles, Kristan Temme, Aram W. Harrow, Abhinav Kandala, Jerry M. Chow, and Jay M. Gambetta1, \"Supervised learning with quantum enhanced feature spaces,\" [arXiv: 1804.11326](https://arxiv.org/pdf/1804.11326.pdf)" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/Users/manoel/Documents/Quantum/qiskit-terra/qiskit/tools/qcvv/__init__.py:13: DeprecationWarning: The qiskit.tools.qcvv package is deprecated. Please use qiskit-ignis available on PIP for similar functionality and more.\n", - " 'functionality and more.', DeprecationWarning)\n" - ] - } - ], - "source": [ - "from qsvm_datasets import *\n", - "\n", - "from qiskit import BasicAer\n", - "from qiskit.aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name\n", - "from qiskit.aqua.input import SVMInput\n", - "from qiskit.aqua import run_algorithm, QuantumInstance\n", - "from qiskit.aqua.algorithms import QSVMKernel\n", - "from qiskit.aqua.components.feature_maps import SecondOrderExpansion\n", - "\n", - "# setup aqua logging\n", - "import logging\n", - "from qiskit.aqua import set_qiskit_aqua_logging\n", - "# set_qiskit_aqua_logging(logging.DEBUG) # choose INFO, DEBUG to see the log" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### [Optional] Setup token to run the experiment on a real device\n", - "If you would like to run the experiement on a real device, you need to setup your account first.\n", - "\n", - "Note: If you do not store your token yet, use `IBMQ.save_accounts()` to store it first." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "from qiskit import IBMQ\n", - "# IBMQ.load_accounts()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "First we prepare the dataset, which is used for training, testing and the finally prediction.\n", - "\n", - "*Note: You can easily switch to a different dataset, such as the Breast Cancer dataset, by replacing 'ad_hoc_data' to 'Breast_cancer' below.*" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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\n", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{'A': 0, 'B': 1}\n" - ] - } - ], - "source": [ - "feature_dim=2 # we support feature_dim 2 or 3\n", - "sample_Total, training_input, test_input, class_labels = ad_hoc_data(training_size=20, \n", - " test_size=10, \n", - " n=feature_dim, \n", - " gap=0.3, \n", - " PLOT_DATA=True)\n", - "extra_test_data = sample_ad_hoc_data(sample_Total, 10, n=feature_dim)\n", - "datapoints, class_to_label = split_dataset_to_data_and_labels(extra_test_data)\n", - "print(class_to_label)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "With the dataset ready we initialize the necessary inputs for the algorithm:\n", - "- the input dictionary (params) \n", - "- the input object containing the dataset info (algo_input).\n", - "\n", - "With everything setup, we can now run the algorithm.\n", - "\n", - "For the testing, the result includes the details and the success ratio.\n", - "\n", - "For the prediction, the result includes the predicted labels. " - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "testing success ratio: 1.0\n", - "preduction of datapoints:\n", - "ground truth: ['A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B']\n", - "prediction: ['A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B']\n" - ] - } - ], - "source": [ - "seed = 10598\n", - "\n", - "feature_map = SecondOrderExpansion(num_qubits=feature_dim, depth=2, entanglement='linear')\n", - "qsvm = QSVMKernel(feature_map, training_input, test_input, datapoints[0])\n", - "\n", - "backend = BasicAer.get_backend('qasm_simulator')\n", - "quantum_instance = QuantumInstance(backend, shots=1024, seed=seed, seed_transpiler=seed)\n", - "\n", - "result = qsvm.run(quantum_instance)\n", - "\n", - "\"\"\"declarative approach\n", - "params = {\n", - " 'problem': {'name': 'svm_classification', 'random_seed': 10598},\n", - " 'algorithm': {\n", - " 'name': 'QSVM.Kernel'\n", - " },\n", - " 'backend': {'provider': 'qiskit.BasicAer', 'name': 'qasm_simulator', 'shots': 1024},\n", - " 'feature_map': {'name': 'SecondOrderExpansion', 'depth': 2, 'entanglement': 'linear'}\n", - "}\n", - "algo_input = SVMInput(training_input, test_input, datapoints[0])\n", - "result = run_algorithm(params, algo_input)\n", - "\"\"\"\n", - "\n", - "print(\"testing success ratio: {}\".format(result['testing_accuracy']))\n", - "print(\"preduction of datapoints:\")\n", - "print(\"ground truth: {}\".format(map_label_to_class_name(datapoints[1], qsvm.label_to_class)))\n", - "print(\"prediction: {}\".format(result['predicted_classes']))" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "kernel matrix during the training:\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "print(\"kernel matrix during the training:\")\n", - "kernel_matrix = result['kernel_matrix_training']\n", - "img = plt.imshow(np.asmatrix(kernel_matrix),interpolation='nearest',origin='upper',cmap='bone_r')\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### The breast cancer dataset\n", - "Now we run our algorithm with the real-world dataset: the breast cancer dataset, we use the first two principal components as features." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "sample_Total, training_input, test_input, class_labels = Breast_cancer(training_size=20,\n", - " test_size=10,\n", - " n=2,\n", - " PLOT_DATA=True)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "seed = 10598\n", - "\n", - "feature_map = SecondOrderExpansion(num_qubits=feature_dim, depth=2, entanglement='linear')\n", - "qsvm = QSVMKernel(feature_map, training_input, test_input)\n", - "\n", - "backend = BasicAer.get_backend('qasm_simulator')\n", - "quantum_instance = QuantumInstance(backend, shots=1024, seed=seed, seed_transpiler=seed)\n", - "\n", - "result = qsvm.run(quantum_instance)\n", - "\n", - "\"\"\"declarative approach, re-use the params above\n", - "algo_input = SVMInput(training_input, test_input)\n", - "result = run_algorithm(params, algo_input)\n", - "\"\"\"\n", - "print(\"testing success ratio: \", result['testing_accuracy'])" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "print(\"kernel matrix during the training:\")\n", - "kernel_matrix = result['kernel_matrix_training']\n", - "img = plt.imshow(np.asmatrix(kernel_matrix),interpolation='nearest',origin='upper',cmap='bone_r')\n", - "plt.show()" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.8" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} From ee2860b5947f1159a5248d44e8f87851b6ecf988 Mon Sep 17 00:00:00 2001 From: Shaohan Hu Date: Sun, 28 Apr 2019 08:19:02 -0400 Subject: [PATCH 080/116] switch BasicAer -> Aer --- .../qsvm_directly.ipynb | 306 +++++++++++++++ .../qsvm_multiclass.ipynb | 136 +++++++ .../aqua/artificial_intelligence/vqc.ipynb | 276 +++++++++++++ .../qsvm_classification.ipynb | 362 ++++++++++++++++++ ...ld_a_pluggable_algorithm_components.ipynb} | 19 +- 5 files changed, 1086 insertions(+), 13 deletions(-) create mode 100644 community/aqua/artificial_intelligence/qsvm_directly.ipynb create mode 100644 community/aqua/artificial_intelligence/qsvm_multiclass.ipynb create mode 100644 community/aqua/artificial_intelligence/vqc.ipynb create mode 100644 qiskit/aqua/artificial_intelligence/qsvm_classification.ipynb rename qiskit/aqua/general/{Aqua_howto_build_a_pluggable_algorithm_components.ipynb => Aqua_how_to_build_a_pluggable_algorithm_components.ipynb} (92%) diff --git a/community/aqua/artificial_intelligence/qsvm_directly.ipynb b/community/aqua/artificial_intelligence/qsvm_directly.ipynb new file mode 100644 index 000000000..a0db62a60 --- /dev/null +++ b/community/aqua/artificial_intelligence/qsvm_directly.ipynb @@ -0,0 +1,306 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## _*Quantum SVM*_\n", + "\n", + "### Introduction\n", + "\n", + "Please refer to [this file](https://github.com/Qiskit/qiskit-tutorials/blob/master/qiskit/aqua/artificial_intelligence/qsvm_kernel_classification.ipynb) for introduction.\n", + "\n", + "In this file, we show two ways for using the quantum kernel method: (1) the non-programming way and (2) the programming way. \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Part I: non-programming way.\n", + "In the non-programming way, we config a json-like configuration, which defines how the svm instance is internally constructed. After the execution, it returns the json-like output, which carries the important information (e.g., the details of the svm instance) and the processed results. " + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "from datasets import *\n", + "from qiskit import Aer\n", + "from qiskit.aqua import run_algorithm, QuantumInstance\n", + "from qiskit.aqua.input import ClassificationInput\n", + "from qiskit.aqua.components.feature_maps import SecondOrderExpansion\n", + "from qiskit.aqua.algorithms import QSVM\n", + "from qiskit.aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First we prepare the dataset, which is used for training, testing and the finally prediction.\n", + "\n", + "*Note: You can easily switch to a different dataset, such as the Breast Cancer dataset, by replacing 'ad_hoc_data' to 'Breast_cancer' below.*" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'A': 0, 'B': 1}\n" + ] + } + ], + "source": [ + "feature_dim = 2 # dimension of each data point\n", + "training_dataset_size = 20\n", + "testing_dataset_size = 10\n", + "random_seed = 10598\n", + "shots = 1024\n", + "\n", + "sample_Total, training_input, test_input, class_labels = ad_hoc_data(\n", + " training_size=training_dataset_size, \n", + " test_size=testing_dataset_size, \n", + " n=feature_dim, gap=0.3, PLOT_DATA=False\n", + ")\n", + "datapoints, class_to_label = split_dataset_to_data_and_labels(test_input)\n", + "print(class_to_label)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we create the svm in the non-programming way.\n", + "In the following json, we config:\n", + "- the algorithm name \n", + "- the feature map " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "params = {\n", + " 'problem': {'name': 'classification', 'random_seed': random_seed},\n", + " 'algorithm': {\n", + " 'name': 'QSVM'\n", + " },\n", + " 'backend': {'shots': shots},\n", + " 'feature_map': {'name': 'SecondOrderExpansion', 'depth': 2, 'entanglement': 'linear'}\n", + "}\n", + "backend = Aer.get_backend('qasm_simulator')\n", + "algo_input = ClassificationInput(training_input, test_input, datapoints[0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With everything setup, we can now run the algorithm.\n", + "\n", + "The run method includes training, testing and predict on unlabeled data.\n", + "\n", + "For the testing, the result includes the success ratio.\n", + "\n", + "For the prediction, the result includes the predicted class names for each data.\n", + "\n", + "After that the trained model is also stored in the svm instance, you can use it for future prediction." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "result = run_algorithm(params, algo_input, backend=backend)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "kernel matrix during the training:\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "testing success ratio: 1.0\n", + "predicted classes: ['A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B']\n" + ] + } + ], + "source": [ + "print(\"kernel matrix during the training:\")\n", + "kernel_matrix = result['kernel_matrix_training']\n", + "img = plt.imshow(np.asmatrix(kernel_matrix),interpolation='nearest',origin='upper',cmap='bone_r')\n", + "plt.show()\n", + "\n", + "print(\"testing success ratio: \", result['testing_accuracy'])\n", + "print(\"predicted classes:\", result['predicted_classes'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### part II: Programming way.\n", + "We construct the svm instance directly from the classes. The programming way offers the users better accessibility, e.g., the users can access the internal state of svm instance or invoke the methods of the instance. We will demonstrate this advantage soon." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we create the svm in the programming way.\n", + "- We build the svm instance by instantiating the class QSVM. \n", + "- We build the feature map instance (required by the svm instance) by instantiating the class SecondOrderExpansion." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "backend = Aer.get_backend('qasm_simulator')\n", + "feature_map = SecondOrderExpansion(feature_dimension=feature_dim, depth=2, entangler_map=[[0, 1]])\n", + "svm = QSVM(feature_map, training_input, test_input, None)# the data for prediction can be fed later.\n", + "svm.random_seed = random_seed\n", + "quantum_instance = QuantumInstance(backend, shots=shots, seed=random_seed, seed_transpiler=random_seed)\n", + "result = svm.run(quantum_instance)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let us check the result." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "kernel matrix during the training:\n" + ] + }, + { + "data": { + "image/png": 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RXIomv6K4FJ+694aGRtheve700gJD+dilf7z6qNCOZctKPQA8OHSM0CZMf5vGtifOqO/P49Xc/j1lG+2CJbIiXq+ZrEYDvGU3siavaPduI52J2WgwAPh8hhwJddvQkpYLRTDTC9ZqCgAFhYVCa1u/vtCcTEYyyFirUOIIDAARpPX5hMNYrJlL5SpP3QZ8I2mjcGniwm4r89QpevzabXIlJaaZNPgAgGhyWyXHZ51jfZJsBf45jq841KglW3SH95Nj1wCgcgkX49iuXRGv7r2KovwamvyK4lI0+RXFpWjyK4pL8Wl7b3Sjupg09WUvLeEgnzuelStbUF9/4SMaO/OrT4Q2/t9TSCTQorOcy35dt440dvSdfxXa/K8mCs2pAMb24zu17LLiHhsNBgATFy0R2ot/4QXOGx6Q46P+MvRuGjvy8WekOLSvkJycc9kIrPGTZ9PYmpHSMblrG96S3aBRpNCa1eFtwzmkvXX0cDkibebs8fT4kM6ydfmyypVp7DbynK1YGkdjnxolN8fGREfT2DP5+UJ7bpx0JQaA554c6XW5kBRtndBPfkVxKZr8iuJSNPkVxaVo8iuKSymNh9/HxphUY8zWYtoLxphDxphNnn98KLmiKBctv9nea4zpCeAkgE+Lzep7AcBJay0vmTrQrkMHu3Cp9xyyTIeWzikfLRAaa3sEgOadZAV/9Wxu/BF7Y6zQese0o7Gsis8qtMt/+YUeX7O6rBwzIw4ASNkjjTDqt5SttQDwwA3XC+2jb5bR2PnvzBFar9ulIy8ArPtyndDe/uBvQnMy0li0caPQ/tilC41lZJMVHgB48P6XhdaqWysa26OXNGaJbdpEaImH5OMN8FWmI5l8haZXG7m64bQy8PbH8nm4rDpvsz6QeEBob417nMbuPXbM6/ItffsiYfPm8mnvdRjXpShKBacs3/nHGGO2eL4W6CgeRalgnG/yvwegCYAOAFIAvOYUWHxWX1pa2nnenKIo5c15Jb+19qi1tsBaWwjgQwCOX+yKz+qrVavW+Z6noijlzHm19xpjIotN6b0FAN+YXIKsUzlY+rN3USgnixd57h89WGivPM1HP3XoIR1quw/qRmOzM2RraiV/fxr73JhXhfbB1H8KrdChaMpGaDm57H446x2hObXssuLeff1609jXPpsrtMWT+XS1jr2uFFpqVpbQnEZl9WjRQmirEvlor7pkj30Vh2LZ+x/J9txAB0+Cn/bsEdqe1GMkktO9uSwevz/3axqbHi1fS+t37qaxrL3XqbW9Wt/uQmNty4B8HPz8Sv95/pvJ7xnXdQ2AMGNMMoDnAVxjjOmAoum8+wCMKvUtKopyUXC+47om/Q7noiiKD9EOP0VxKZr8iuJSNPkVxaX41MwjLLgGRvb3bi3dckC2MgLA59OlQ+3+JN4a26SOdHL924uyUg8ASUmbhJadLt1/AeDqwdIxNb9QOvIum89biTtfL1tN2ew8gBtkMCMOAJj12gyhsao+ADwx7I9Ce/x5vorw9stPCu2pR+8S2o87d9LjDXGuZS3OABCXKK8jrJZcAQCAiOBgoTlV+0OIWzBrR96ZmUmPL9kuCwB1G3HjkB82y7buNs250+9SMhuwQVgYjWUmIU5t+E1LvPYr/Q/Vfv3kVxSXosmvKC5Fk19RXIomv6K4FJ8W/M7m5+Ngic096xN30dghQ+We9Slv8f1DGaRYlpPD92B37ibbYHv34lsT/nDNQKENJK2XPQbKtlgAmPPOfKGdPsnbmdkILSeX3bFvvCE0p5ZdVtx7/UU5Cg0AbrhhtNC2JicLzamduVvTpkJ7+S3uohwSLot44WG84JdORmvVrsG9HbanpAjtm5nLhTb2yXvp8Wy8WIhD0XJJvPQvmP0pbwV+9fmHhZZ4mHsKNI+UbsWLl6+lsaOG3uh1+X8Zvqef/IriUjT5FcWlaPIrikvR5FcUl6LJryguxafV/oBKldCwREtjTAvprAoAc+dKw4oaNbgTUFhQkNDy8s7Q2B+/WyS01t2lCysADLrjPqEFk2rwhtWb6fFXD+kptNWz19DYAjJjjc7OA3fZZUYcAG/ZZVV9AFi06H2hfTRtnNAOpXM/1x1Hjght0B9kizQA7D56VGi1AuXzCPDH5tQZ/vyGk9fCiAf+ILQ95PYBoAWptB84fpzGBgbJVYC+g6+hsRv27pXHO7Qo7ye31+farjS2WkCA12U/0mLthH7yK4pL0eRXFJeiya8oLqU047rqG2NWGmO2GWN+Mcb8yaPXNMYsNcbs8vxU735FqUCUpuCXD+AJa+0GY0wQgHhjzFIAIwAst9aOM8aMBTAWwFO/dkWn8/LEXuXtDmOTeveX7rsxV/GxWqwF9b3PX3c8h5KwIh4AzM5bIbRI4jqbcSSDHj/kVjkWK/fkaRrbtj4ZzTW0L42t92BNoTGXXYDvx2ePF8CLe+z+Tly0hB6/aaUsfJ7J4YW52g1qC8325F4HcYvihJaVxu/vqiXS12DSV9OFNuvDhfT4KmSE1kt/4/60Cbv3Ce25P0unYQAYNGKE0Bq2akBj08nrKaV+OI3t3dG73TwzkxcyGaUZ15Vird3g+T0bQCKAegBuBnCucXsKgEGlvlVFUS44/9N3fmNMNIAYAHEA6hTz7j8CQNrpKIpy0VLq5DfGBAKYC+Axa63X31y2yGOIbigqPq4rXcd1KcpFQ6mS3xhTGUWJP81aO88jHzXGRHr+PxJAKju2+LiumjquS1EuGoyTMeB/A4pcGacASLfWPlZM/zeAtGIFv5rWWtlOVozW7drZWV9773d26tRq30AWQyZ/IwtwAODnL7uaThznBaHwKGma2CemPY2NI6OfqlSSNdKEDdxYtGaEXADxcxgN1rdTB6E57fe+slkzoTnNhWdmm0778WtUrSq0DcRv4YEbpNcCAJwmI6XGvvQfGrtzgxzj1eHqjjT2j0Nk4fR4djaNXb82QWhrv/xeaHPmvUWPXxAfL7Tv5/9AY09lSh+J5p3lyDIAeHLkUKG9NmUOjY1sIrsMX77vcRr7+TczvS7fddNN2JaQUKo2v9JU+7sDuAtAgjHmnPXtMwDGAZhljBkJYD+AIaW5QUVRLg5KM67rewBO7yTXle/pKIriK7TDT1Fciia/orgUTX5FcSk+3c9fNSAALevW9dJ+cBj9dIxUc4f06kFjWZWajV0C+B7qNIfKMRsD1iJCjm4KIrcPAN1IVX67QwU/IydHaNe15j4Ds+Nku2uPFrzKzEZoMZddgO/HZy27rKoPAJeV2FsOAIs3c6+Dzv06Cy3jKG+TnvmZdMTNz5dj0wAgtr90Yv4rqbQHVePeAXfcO1Zor41/gsbOXilXEYwfL4+Fh9UT2vwf+OoVY1OCvC0A6NLReyVkL2k5dkI/+RXFpWjyK4pL0eRXFJeiya8oLsWnBb+cM2ewcd8+L+3AMW6OGEuKUq+8O5XHXnuF0JjpIwBs37JbaI1aRdPYic9KQ8s7x8oRWmGhcvQUADz50gShRUTzWe+33SiNLsdPnk1jHx8+WGirEmW7LADUJKOmnEZoMbNNth/fqWWXFff6t+et07VrNxRax468bfjpN2RrKxtvBgDL16wX2ogJcpTZ1NUr6fEJP2wVmlML+ievvCe0I0eSaOzU5bJoWSeYv26Yv8RddzxNY4f9+SGvy++8xE1fGfrJryguRZNfUVyKJr+iuBRNfkVxKZr8iuJSfFrtvywgAJfX827v3XE4xSFakn82n+ohpKK98wB3qM04mim05m25wUZQDWnGUbuW1HZu30ePb9BSGpKczuHuvRHEJbdmpHTpdaIuOR4A4hJl+3RIOK8ysxFazGV38+oN9HjWssuq+gCQmrpfaIcPS+MQgBu7+Du00W5rJI0wKgVIo5PMtBP0+Oi2jYS2ab88VwBIStoktHr1mtNYPz/5OetU7a9epYrQTp3iLegh4d7Pu39l/lqm51TqSEVRLik0+RXFpWjyK4pLKcu4rheMMYeMMZs8/wb8/qerKEp5UZZxXQDwhrV2fGlv7ExeHvaVaOdNXMfbUtfWksWu6Da8eHSC7IVns9MBoOkVsm24S5MmNDa+u9xP/+2cVUIbfh8fVsRaTZmjL8DvQ9c2LWlsdm6u0Ko4uPeG1ZKFwPAwXhysFSj3uLMRWswjAOD78Z1adllxb/Nm3nJblfgE5OXz4m+XpvK5PHFjrNSO8YJf314yNi6Bv0bZaKxhD/K9/ympcmZFlZb8+fUjj2/vO/njGBxWw+uyf6XSF/xKY+CZAiDF83u2MebcuC5FUSowZRnXBQBjjDFbjDEf65ReRalYlGVc13sAmgDogKK/DF5zOO6/47oy0tPL4ZQVRSkPzntcl7X2qLW2wFpbCOBDANI8Dd7jukJrlr5pRVGU35fSVPsNgEkAEq21rxfTi7dS3QJAboRWFOWipTSz+noAWAMgAcA5h4xnANyOoj/5LYB9AEYVG9lNadW2rZ26cKGX1rKubMcEgBmr5Hy06ChuhHEsS87l27JazmwDgEdHSyfXWoGBNDY5XVZoI4JlpTztpJzZBgDr9+4VWut6vFb67Y9yRlwD0qoKAJ/9a6bQ3v/oORq7izjypp86RWNZW+ncqYuFdrfD6gZz2R14Kx/qxFp2WVUfAALIfMRateqSSOC6PsOENuaFe4WWkCjnMALA9nXbhfbi30fRWOYaPXPtOho7fdxnQsvK4l+DT52SLehvTOOzBT99x3ve34JZ/8Gx1EPlM6vvV8Z1yWdaUZQKg3b4KYpL0eRXFJeiya8oLsWn+/nPFhTgYIm1fjYSCwAqB8hTa1CrFo3df7h0+9ABoBopKrF2SgAIrS4Lgaz45FTwu7yuLEqxohoA1G0gH4dmdXiBs1W3VkJjY8ic9No1apBI7lKblSaLqccdxpuxEVpOLrtsP75Tyy4r7qWl8bFnR1MOCI0V5rLT+X3w85fnVcmft8wWkmJ51Sq8aMkoKMijelaWLDQ7kXHEO5/y8/gYM4Z+8iuKS9HkVxSXosmvKC5Fk19RXIomv6K4FJ9W+wsLC3Eyx9uIYs7qH2lstSA5r2xZ3EYauyteGkO0JkYcAPDLoUNCa1c/isZ+/u0qod1/ozRVGP/8h/T4B8bKVtOp0xbR2MG39hFaztmzNLZHr05C+2kPb1cNIXPftqfwLuzwIGnmsWrJXKE1jZGGKAAQ21/u7WKGJgB32WVGHABv2WVVfQD47rsZQsvKfUFojVtH0+MDQ+QKz/7jx2hsIemMnzZuOo2985m7hDbntTkkkrPrgHzdAkBurnerdmGhVvsVRfkNNPkVxaVo8iuKS9HkVxSX8pv7+cuTjh072rVxcV5aKtmLD/BRRh999S2Nva13T6G98YEs/ABAVHNZ3IuK4i3GG+N+EVpMV1lIbBgWRo+fNHGe0B56WPoJALwNd/Rwvkd/2sxXhbYnlRelapDrffNNubccAEY88AehZZC9/68/9S49ft6Cd+R13vN3GstGaMUSl10AaNOysdBYyy4AZBFn457EJdfpdT95+SqhXdu+DY2dvmCZ0IzDGLG/jLhVaNsP8xblUDJ+rnl9OUYMADbt2eF1+Za+fZGweXOp9vPrJ7+iuBRNfkVxKZr8iuJSSmPgeZkx5idjzGbPuK4XPXojY0ycMWa3MWamMab0exkVRbnglKbD7wyAXtbakx4L7++NMYsBPI6icV0zjDHvAxiJIi9/Z4wRo55WJ0rDRAAYENNBaL27xtBYtkf/oZGDaWwmKWCdzuP7qnOvkLPWr2stC37z1/MutvEvPiK0ZVu5yTHzKpg5m09CSzh4kOqMnZnSDHLsk9LQEgD2HJW+CLM+XCi0OfO4mWRQNdkhOHU1H8GVmSbHZTmN0GJmm0778VnnHivuOY0ce+zZN4V2aw9eiKxSTXozFORxT4Lmza4Q2twVX9DYY8QvIeME3+PfpVNfr8t7dknTWCd+85PfFnHOraKy558F0AvAuf7EKQC4pauiKBclpR3a4W+M2QQgFcBSAHsAZFprz73NJUPn9ylKhaJUye+ZzNMBQBSKJvPw8aKE4uO6jh/ja9GKovie/6nab63NBLASwJUAQowx52oGUQDotqPi47rCwsPLdLKKopQfpan2hxtjQjy/VwXQB0Aiit4nHT0iAAALcklEQVQEzlXVhgPg1QtFUS5KSjOuqx2KCnr+KHqzmGWtfckY0xjADAA1AWwEMMxaK+1fi9G6XTs7fZH3fvY2UXwv/RmHCjzjMKloRwRzh9q95KvH2i2JNHZgN7k/nY2/qhvKp5MfOH5caC2Joy8ALInfJLT+nWWFGAC2JScLrXtzuTIB8PvbyOEvsOzTp4X2j1cnCe3Kgbz6vWSKbL+OasZLQdFtZbtqp5bNaOxHE2YLjbnsAkCzjvJxqB4s22U3r9pMj3/zH48JLYW8vgC+OrJpq/SWAICV0+Wqxw2jbqCxTaKk10HCNu7X8OMC77F23yz6BGlpKeU2rmsLALHGZq1NgsNkXkVRLn60w09RXIomv6K4FE1+RXEpPt3P37BpM/vUeO/W0LaXc9NGdl4nSUEKAJKTZeGlTQu5BxwAAsjopU6NeWxmTo7QZq/6XmhNGvKiVhY5361xDsXFG64SWrRDYe7rjbI4eOwg76Go20iO/LqK7G8HSl+g/NsL/6HHv/TcaKGxEWAAsGn/fqGlpPD7MPjq7kJzGqHFzDaDLpN7/8OCpFEnAGSflucbGRJCY9+d+5XQ7h5wHY0tKCwU2gczvqSx7TtdLrSqlaX/AQDENvU2U+0WG4v4+Hjdz68oijOa/IriUjT5FcWlaPIrikvR5FcUl+LTcV3BgdUxoHtnL23mlyto7I3X9xDamu/iaWznbu2ElpjExzllHEkXWpCDE+x7E2YKrU5D6fRbr25tevzurUlCYwYQAK/sbyOjxQCgVxtpKJIefZJEAj9slg7ES+L52LPAINkGm7B7n9BOZfLbmr1SroR88gr3d0lKkisWmZly1QYA7s2VBiyFDqtUbIQWc9l1eh66dJKPLavqA8CYPw4UWvzoF2ls72G9hTbqthtpbBBxXH5m3Ac09kgvbwMUtkLlhH7yK4pL0eRXFJeiya8oLkWTX1Fcik8LfoyqgbzYxsYxpR3iDqapmdL1tV4kb43NOyN9AtKJoy8ArFm8WGiLVswS2vg3p9LjW3aVbbRb1yTQWD/iJrtiaRyJBFqNkGO11u/cTWPbNJety7M//ZrG9h18jdCe+7McGXbX49KVGOCjqo4ckUVPAKhXT+67H/bgEzR25tp1QqtahTvFTxs3XWidB8id504uu2w/vlPLLivuffL+8zR2wD39hJboMK4rL1+eW2Uy3gwA5r+9wOtyRir3HmDoJ7+iuBRNfkVxKZr8iuJSNPkVxaWUZVbfZGPMXmPMJs8/OV9LUZSLltK49xoA1YvP6gPwJwCjAXxlrZ3zq1dQjA4xMXbpd995aZUr8QWHnSkpQmtbvz6NZZVyp3l29WrWFBqbjQYAtWtIB2CmZeXm0uNZm+bpvLM0Nm63dGd1Mt34v/emCe2pUbfT2KVkNuD17WQ7NABs2CvnvC2cJ11nX/7rffT48DBpajJ1OV9Z8POTnzspqXw1Z95b0r3XiTufuUtot3btKjQ2Ow8AYq6QbbgfTXmJxjJTlYDK/PXMzuGDL7+hsSdPyNWnMUNvorG9e93hdXnjxmXIzk4vN/deC4DN6lMUpQJzXrP6rLXnFqBfMcZsMca8YYyhOyWKj+tKS+Pv7Iqi+J7zmtVnjGkD4GkUzezrjKLBHU85HPvfcV21yBhqRVEuDOc7q6+ftTbFM777DIBPoAM8FKVCUZqCXziAPGttpmdW37cAXgUQb61N8RQE3wBw2lo79teuKyq6sR3z7D+9tBv7yX37AHe+3e8w5fenxT8LLbQOH6E1bMj18rxq8r9I9hM32xNkv7STQ+22nfuE5l+Jv9+mH8kQ2gND5X5xAPhw1iKh9bq6E40NcHB9ZfiTwukPm6QfwInjWfT4rrFthVYnOJjGMr2KQ/G3X5+7hVZQwMe5RUREC+3FN/8stLyCAnr8xl2yHTn1QCqNZfvxnVp2E7bLgu6oG2XLLwBERclC7+fLFpBIIOmQd2H8hQdHYe+OHeVT8AMQCWCKMab4rL6vjDErPG8MBsAmFFX/FUWpIJRlVl+v3+WMFEXxCdrhpyguRZNfUVyKJr+iuBSfmnn4+fuhWo1qXppT1XXVSlnBb96hKYnkJhJ5Z3k1mM1iO5vPY/3J9XZo2FBok75eSo/vFiOdYH9JTqax+XnycThDTB0A4ECidCau1lfOswO4A3DzyEgay1Y32CpEVIsoejwjuFo1qlevInvCWJs2AJw6JQ0qsrJK3zAWWl26Eju1dDeJko9NZG2+GsTat5kRB8BbdllVHwCSk7cLzelxPJnpfb0FBXImoBP6ya8oLkWTX1Fciia/orgUTX5FcSm/2d5bnnTq1MmuX7/eS8twcM5lBaHJ3yynsf2vlK2tk2fwfeShdUKE1rS5LOIBwJ7d0hOgzeXSDTfDYURSwrptQrv5pmtobNPacuTXc+M+pLGv/v0hoeWc5T4BB0gRb/HytTS2z7Vyz/n6ROlm+69Hn6bHb0qQ47ruuoPHnjolC26975St1wDQpXMbqjN2HZAFzkdvkW7HGSd4wXDiF3KPPXvOAeDr+auE5uSy+9xjI4QWt0e2/AK8uNe+QQMa++Mu7+fn3ltuQWJCQqnae/WTX1Fciia/orgUTX5FcSma/IriUjT5FcWl+LTa3z4mxi5ZtcpL2+FgfsCq/Q3DwmhsJqm2hxOXXScyHVYcdh45IrTebWTlecKcL+nxwwf2EdrmA7I1FwBim8rW5VyHCn5qljTTCCStpgAQSirHZx1aqqsFyPl3EXXkSsg3P62mx4+4aYTQhv1ZrkwAQEi4XHUJDuPP2fJpK4SWcSSdxubmyufyrY/lTL1b+90hNABo1VaueHw8SR4PAAvi44VWcnbeOQ4nS5OQkS/wx6Zkyy4AXNGuBY3t1qyZ0Ky1Wu1XFMUZTX5FcSma/IriUjT5FcWl+LTgZ4w5BmC/52IYANl7WvHR+1XxuJTuW0NrbXhpAn2a/F43bMx6ay33m67A6P2qeFzK9+3X0D/7FcWlaPIriku5kMk/8QLe9u+J3q+Kx6V83xy5YN/5FUW5sOif/YriUnye/MaYfsaYHcaY3caYXx3sebFjjPnYGJNqjNlaTKtpjFlqjNnl+cknhl7EGGPqG2NWGmO2GWN+Mcb8yaNX6PtmjLnMGPOTMWaz53696NEbGWPiPK/JmcYYucnhEsSnye8Z9jkBQH8ArQDcboxp5ctzKGcmAyg5anUsgOXW2mYAlnsuVzTyATxhrW0FIBbAw57nqaLftzMAellr2wPoAKCfMSYWRVOn37DWNgWQAWDkBTxHn+HrT/4uAHZba5OstWcBzABws4/Podyw1q4GUHJ72c0Apnh+nwJgkE9Pqhyw1qZYazd4fs8GkAigHir4fbNFnPRcrOz5ZwH0AjDHo1e4+3W++Dr56wEo7oqZ7NEuJepYa88NTT8CoM6FPJmyYoyJRtGU5jhcAvfNGONvjNkEIBXAUgB7AGRaa8+N2rkUX5MULfj9jtiipZQKu5xijAkEMBfAY9ZaLxOBinrfrLUF1toOAKJQ9Jcon5nlAnyd/IcA1C92OcqjXUocNcZEAoDnZ+oFPp/zwhhTGUWJP81aO88jXxL3DQCstZkAVgK4EkCIMebc3MpL8TVJ8XXy/wygmae6GgDgNgALfXwOvzcLAQz3/D4cwBcX8FzOC2OMATAJQKK19vVi/1Wh75sxJtwYE+L5vSqAPiiqZ6wEMNgTVuHu1/ni8yYfY8wAAG8C8AfwsbX2FZ+eQDlijJkO4BoU7Qo7CuB5AAsAzALQAEU7GIdYa7nn1EWKMaYHgDUAEgCcG/v6DIq+91fY+2aMaYeigp4/ij74ZllrXzLGNEZR8bkmgI0Ahllr5TjnSwzt8FMUl6IFP0VxKZr8iuJSNPkVxaVo8iuKS9HkVxSXosmvKC5Fk19RXIomv6K4lP8Hv0Or98j6qc0AAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "testing success ratio: 1.0\n" + ] + } + ], + "source": [ + "print(\"kernel matrix during the training:\")\n", + "kernel_matrix = result['kernel_matrix_training']\n", + "img = plt.imshow(np.asmatrix(kernel_matrix),interpolation='nearest',origin='upper',cmap='bone_r')\n", + "plt.show()\n", + "\n", + "print(\"testing success ratio: \", result['testing_accuracy'])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "Different from the non-programming way, the programming way allows the users to invoke APIs upon the svm instance directly. In the following, we invoke the API \"predict\" upon the trained svm instance to predict the labels for the newly provided data input.\n", + "\n", + "Use the trained model to evaluate data directly, and we store a `label_to_class` and `class_to_label` for helping converting between label and class name" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ground truth: [0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1]\n", + "preduction: [0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1]\n" + ] + } + ], + "source": [ + "predicted_labels = svm.predict(datapoints[0])\n", + "\n", + "predicted_classes = map_label_to_class_name(predicted_labels, svm.label_to_class)\n", + "print(\"ground truth: {}\".format(datapoints[1]))\n", + "print(\"preduction: {}\".format(predicted_labels))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.2" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/community/aqua/artificial_intelligence/qsvm_multiclass.ipynb b/community/aqua/artificial_intelligence/qsvm_multiclass.ipynb new file mode 100644 index 000000000..80ba41c78 --- /dev/null +++ b/community/aqua/artificial_intelligence/qsvm_multiclass.ipynb @@ -0,0 +1,136 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## _*Quantum SVM algorithm: multiclass classifier extension*_\n", + "\n", + "A multiclass extension works in conjunction with an underlying binary (two class) classifier to provide multiclass classification.\n", + "\n", + "Currently three different multiclass extensions are supported:\n", + "\n", + "* OneAgainstRest\n", + "* AllPairs\n", + "* ErrorCorrectingCode\n", + "\n", + "These use different techniques to group the data with binary classification to achieve the final multiclass classification." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from datasets import *\n", + "from qiskit import Aer\n", + "from qiskit.aqua.input import ClassificationInput\n", + "from qiskit.aqua import run_algorithm" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we choose the `Wine` dataset which has 3 classes." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "n = 2 # dimension of each data point\n", + "sample_Total, training_input, test_input, class_labels = Wine(\n", + " training_size=40,\n", + " test_size=10, n=n, PLOT_DATA=True\n", + ")\n", + "temp = [test_input[k] for k in test_input]\n", + "total_array = np.concatenate(temp)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we setup an Aqua configuration dictionary to use the quantum `QSVM` algorithm and add a multiclass extension to classify the Wine data set, since it has 3 classes.\n", + "\n", + "Although the `AllPairs` extension is used here in the example the following multiclass extensions would also work:\n", + "\n", + " 'multiclass_extension': {'name': 'OneAgainstRest'}\n", + " 'multiclass_extension': {'name': 'ErrorCorrectingCode', 'code_size': 5}" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "'testing_accuracy' : 0.8260869565217391\n", + "'test_success_ratio' : 0.8260869565217391\n", + "'predicted_labels' : [0 0 0 0 0 0 1 0 0 0 2 2 1 1 1 0 1 1 1 1 2 2 2]\n", + "'predicted_classes' : ['A', 'A', 'A', 'A', 'A', 'A', 'B', 'A', 'A', 'A', 'C', 'C', 'B', 'B', 'B', 'A', 'B', 'B', 'B', 'B', 'C', 'C', 'C']\n" + ] + } + ], + "source": [ + "aqua_dict = {\n", + " 'problem': {'name': 'classification', 'random_seed': 10598},\n", + " 'algorithm': {\n", + " 'name': 'QSVM'\n", + " },\n", + " 'feature_map': {'name': 'SecondOrderExpansion', 'depth': 2, 'entangler_map': [[0, 1]]},\n", + " 'multiclass_extension': {'name': 'AllPairs'},\n", + " 'backend': {'shots': 1024}\n", + "}\n", + "\n", + "backend = Aer.get_backend('qasm_simulator')\n", + "algo_input = ClassificationInput(training_input, test_input, total_array)\n", + "result = run_algorithm(aqua_dict, algo_input, backend=backend)\n", + "for k,v in result.items():\n", + " print(\"'{}' : {}\".format(k, v))\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/community/aqua/artificial_intelligence/vqc.ipynb b/community/aqua/artificial_intelligence/vqc.ipynb new file mode 100644 index 000000000..426256fdd --- /dev/null +++ b/community/aqua/artificial_intelligence/vqc.ipynb @@ -0,0 +1,276 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## _*Variational Quantum Classifier*_\n", + "\n", + "The QSVM notebook demonstrates a kernel based approach. This notebook shows a variational method.\n", + "\n", + "For further information please see: [https://arxiv.org/pdf/1804.11326.pdf](https://arxiv.org/pdf/1804.11326.pdf)\n", + "\n", + "\n", + "**This notebook shows the variational quantum classifier method.**\n", + "\n", + "In this file, we show two ways for using the variational quantum classifier method: (1) the non-programming way and (2) the programming way. \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Part I: non-programming way.\n", + "In the non-programming way, we config a json-like configuration, which defines how the svm instance is internally constructed. After the execution, it returns the json-like output, which carries the important information (e.g., the details of the svm instance) and the processed results. " + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "from datasets import *\n", + "from qiskit import Aer\n", + "from qiskit.aqua import run_algorithm, QuantumInstance\n", + "from qiskit.aqua.algorithms import VQC\n", + "from qiskit.aqua.components.optimizers import SPSA\n", + "from qiskit.aqua.components.feature_maps import SecondOrderExpansion\n", + "from qiskit.aqua.components.variational_forms import RYRZfrom qiskit.aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name\n", + "from qiskit.aqua.input import ClassificationInput" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First we prepare the dataset, which is used for training, testing and the finally prediction.\n", + "\n", + "*Note: You can easily switch to a different dataset, such as the Breast Cancer dataset, by replacing 'ad_hoc_data' to 'Breast_cancer' below.*" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'A': 0, 'B': 1}\n" + ] + } + ], + "source": [ + "feature_dim = 2 # dimension of each data point\n", + "training_dataset_size = 20\n", + "testing_dataset_size = 10\n", + "random_seed = 10598\n", + "shots = 1024\n", + "\n", + "sample_Total, training_input, test_input, class_labels = ad_hoc_data(\n", + " training_size=training_dataset_size, \n", + " test_size=testing_dataset_size, \n", + " n=feature_dim, gap=0.3, PLOT_DATA=True\n", + ")\n", + "datapoints, class_to_label = split_dataset_to_data_and_labels(test_input)\n", + "print(class_to_label)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we create the svm in the non-programming way.\n", + "In the following json, we config:\n", + "- the algorithm name \n", + "- the variational form\n", + "- the feature map \n", + "- the optimizer" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "params = {\n", + " 'problem': {'name': 'classification', 'random_seed': 10598},\n", + " 'algorithm': {'name': 'VQC', 'override_SPSA_params': True},\n", + " 'backend': {'shots': 1024},\n", + " 'optimizer': {'name': 'SPSA', 'max_trials': 200, 'save_steps': 1},\n", + " 'variational_form': {'name': 'RYRZ', 'depth': 3},\n", + " 'feature_map': {'name': 'SecondOrderExpansion', 'depth': 2}\n", + "}\n", + "\n", + "svm_input = ClassificationInput(training_input, test_input, datapoints[0])\n", + "backend = Aer.get_backend('qasm_simulator')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With everything setup, we can now run the algorithm.\n", + "\n", + "For the testing, the result includes the details and the success ratio.\n", + "\n", + "For the prediction, the result includes the predicted labels. " + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "testing success ratio: 1.0\n", + "predicted classes: ['A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B']\n" + ] + } + ], + "source": [ + "result = run_algorithm(params, svm_input, backend=backend)\n", + "print(\"testing success ratio: \", result['testing_accuracy'])\n", + "print(\"predicted classes:\", result['predicted_classes'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Part II: programming way.\n", + "We construct the svm instance directly from the classes. The programming way offers the users better accessibility, e.g., the users can access the internal state of svm instance or invoke the methods of the instance. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we create the svm in the programming way.\n", + "- we build the optimizer instance (required by the svm instance) by instantiating the class SPSA.\n", + "- We build the feature map instance (required by the svm instance) by instantiating the class SecondOrderExpansion.\n", + "- We build the varitional form instance (required by the svm instance) by instantiating the class RYRZ.\n", + "- We build the svm instance by instantiating the class VQC. \n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "backend = Aer.get_backend('qasm_simulator')\n", + "optimizer = SPSA(max_trials=100, c0=4.0, skip_calibration=True)\n", + "optimizer.set_options(save_steps=1)\n", + "feature_map = SecondOrderExpansion(feature_dimension=feature_dim, depth=2)\n", + "var_form = RYRZ(num_qubits=feature_dim, depth=3)\n", + "svm = VQC(optimizer, feature_map, var_form, training_input, test_input)\n", + "quantum_instance = QuantumInstance(backend, shots=shots, seed=random_seed, seed_transpiler=random_seed)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we run it." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "testing success ratio: 1.0\n" + ] + } + ], + "source": [ + "result = svm.run(quantum_instance)\n", + "print(\"testing success ratio: \", result['testing_accuracy'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Different from the non-programming way, the programming way allows the users to invoke APIs upon the svm instance directly. In the following, we invoke the API \"predict\" upon the trained svm instance to predict the labels for the newly provided data input.\n", + "\n", + "Use the trained model to evaluate data directly, and we store a label_to_class and class_to_label for helping converting between label and class name" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "prediction: [0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1]\n" + ] + } + ], + "source": [ + "predicted_probs, predicted_labels = svm.predict(datapoints[0])\n", + "predicted_classes = map_label_to_class_name(predicted_labels, svm.label_to_class)\n", + "print(\"prediction: {}\".format(predicted_labels))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.2" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/qiskit/aqua/artificial_intelligence/qsvm_classification.ipynb b/qiskit/aqua/artificial_intelligence/qsvm_classification.ipynb new file mode 100644 index 000000000..d0b72e1f8 --- /dev/null +++ b/qiskit/aqua/artificial_intelligence/qsvm_classification.ipynb @@ -0,0 +1,362 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# _*Qiskit Aqua: Experiment with classification problem with quantum-enhanced support vector machines*_\n", + "\n", + "The latest version of this notebook is available on https://github.com/qiskit/qiskit-tutorial.\n", + "\n", + "***\n", + "### Contributors\n", + "Vojtech Havlicek[1], Kristan Temme[1], Antonio Córcoles[1], Peng Liu[1], Richard Chen[1], Marco Pistoia[1] and Jay Gambetta[1]\n", + "### Affiliation\n", + "- [1]IBMQ" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Introduction\n", + "Classification algorithms and methods for machine learning are essential for pattern recognition and data mining applications. Well known techniques such as support vector machines and neural networks have blossomed over the last two decades as a result of the spectacular advances in classical hardware computational capabilities and speed. This progress in computer power made it possible to apply techniques, that were theoretically developed towards the middle of the 20th century, on classification problems that were becoming increasingly challenging.\n", + "\n", + "A key concept in classification methods is that of a kernel. Data cannot typically be separated by a hyperplane in its original space. A common technique used to find such a hyperplane consists on applying a non-linear transformation function to the data. This function is called a feature map, as it transforms the raw features, or measurable properties, of the phenomenon or subject under study. Classifying in this new feature space -and, as a matter of fact, also in any other space, including the raw original one- is nothing more than seeing how close data points are to each other. This is the same as computing the inner product for each pair of data in the set. So, in fact we do not need to compute the non-linear feature map for each datum, but only the inner product of each pair of data points in the new feature space. This collection of inner products is called the kernel and it is perfectly possible to have feature maps that are hard to compute but whose kernels are not.\n", + "\n", + "In this notebook we provide an example of a classification problem that requires a feature map for which computing the kernel is not efficient classically -this means that the required computational resources are expected to scale exponentially with the size of the problem. We show how this can be solved in a quantum processor by a direct estimation of the kernel in the feature space. The method we used falls in the category of what is called supervised learning, consisting of a training phase (where the kernel is calculated and the support vectors obtained) and a test or classification phase (where new unlabelled data is classified according to the solution found in the training phase).\n", + "\n", + "References and additional details:\n", + "\n", + "[1] Vojtech Havlicek, Antonio D. C´orcoles, Kristan Temme, Aram W. Harrow, Abhinav Kandala, Jerry M. Chow, and Jay M. Gambetta1, \"Supervised learning with quantum enhanced feature spaces,\" [arXiv: 1804.11326](https://arxiv.org/pdf/1804.11326.pdf)" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "from qsvm_datasets import *\n", + "\n", + "from qiskit import Aer\n", + "from qiskit.aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name\n", + "from qiskit.aqua.input import ClassificationInput\n", + "from qiskit.aqua import run_algorithm, QuantumInstance\n", + "from qiskit.aqua.algorithms import QSVM\n", + "from qiskit.aqua.components.feature_maps import SecondOrderExpansion\n", + "\n", + "# setup aqua logging\n", + "import logging\n", + "from qiskit.aqua import set_qiskit_aqua_logging\n", + "# set_qiskit_aqua_logging(logging.DEBUG) # choose INFO, DEBUG to see the log" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### [Optional] Setup token to run the experiment on a real device\n", + "If you would like to run the experiement on a real device, you need to setup your account first.\n", + "\n", + "Note: If you do not store your token yet, use `IBMQ.save_accounts()` to store it first." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# from qiskit import IBMQ\n", + "# IBMQ.load_accounts()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First we prepare the dataset, which is used for training, testing and the finally prediction.\n", + "\n", + "*Note: You can easily switch to a different dataset, such as the Breast Cancer dataset, by replacing 'ad_hoc_data' to 'Breast_cancer' below.*" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'A': 0, 'B': 1}\n" + ] + } + ], + "source": [ + "feature_dim=2 # we support feature_dim 2 or 3\n", + "sample_Total, training_input, test_input, class_labels = ad_hoc_data(\n", + " training_size=20, \n", + " test_size=10, \n", + " n=feature_dim, \n", + " gap=0.3, \n", + " PLOT_DATA=True\n", + ")\n", + "extra_test_data = sample_ad_hoc_data(sample_Total, 10, n=feature_dim)\n", + "datapoints, class_to_label = split_dataset_to_data_and_labels(extra_test_data)\n", + "print(class_to_label)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With the dataset ready we initialize the necessary inputs for the algorithm:\n", + "- the input dictionary (params) \n", + "- the input object containing the dataset info (algo_input).\n", + "\n", + "With everything setup, we can now run the algorithm.\n", + "\n", + "For the testing, the result includes the details and the success ratio.\n", + "\n", + "For the prediction, the result includes the predicted labels. " + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "testing success ratio: 0.9\n", + "preduction of datapoints:\n", + "ground truth: ['A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B']\n", + "prediction: ['A', 'A', 'B', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'B', 'A', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B']\n" + ] + } + ], + "source": [ + "seed = 10598\n", + "\n", + "feature_map = SecondOrderExpansion(feature_dimension=feature_dim, depth=2, entanglement='linear')\n", + "qsvm = QSVM(feature_map, training_input, test_input, datapoints[0])\n", + "\n", + "backend = Aer.get_backend('qasm_simulator')\n", + "quantum_instance = QuantumInstance(backend, shots=1024, seed=seed, seed_transpiler=seed)\n", + "\n", + "result = qsvm.run(quantum_instance)\n", + "\n", + "\"\"\"declarative approach\n", + "params = {\n", + " 'problem': {'name': 'classification', 'random_seed': 10598},\n", + " 'algorithm': {\n", + " 'name': 'QSVM'\n", + " },\n", + " 'backend': {'provider': 'qiskit.Aer', 'name': 'qasm_simulator', 'shots': 1024},\n", + " 'feature_map': {'name': 'SecondOrderExpansion', 'depth': 2, 'entanglement': 'linear'}\n", + "}\n", + "algo_input = SVMInput(training_input, test_input, datapoints[0])\n", + "result = run_algorithm(params, algo_input)\n", + "\"\"\"\n", + "\n", + "print(\"testing success ratio: {}\".format(result['testing_accuracy']))\n", + "print(\"preduction of datapoints:\")\n", + "print(\"ground truth: {}\".format(map_label_to_class_name(datapoints[1], qsvm.label_to_class)))\n", + "print(\"prediction: {}\".format(result['predicted_classes']))" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "kernel matrix during the training:\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "print(\"kernel matrix during the training:\")\n", + "kernel_matrix = result['kernel_matrix_training']\n", + "img = plt.imshow(np.asmatrix(kernel_matrix),interpolation='nearest',origin='upper',cmap='bone_r')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The breast cancer dataset\n", + "Now we run our algorithm with the real-world dataset: the breast cancer dataset, we use the first two principal components as features." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "sample_Total, training_input, test_input, class_labels = Breast_cancer(\n", + " training_size=20,\n", + " test_size=10,\n", + " n=2,\n", + " PLOT_DATA=True\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "testing success ratio: 0.9\n" + ] + } + ], + "source": [ + "seed = 10598\n", + "\n", + "feature_map = SecondOrderExpansion(feature_dimension=feature_dim, depth=2, entanglement='linear')\n", + "qsvm = QSVM(feature_map, training_input, test_input)\n", + "\n", + "backend = Aer.get_backend('qasm_simulator')\n", + "quantum_instance = QuantumInstance(backend, shots=1024, seed=seed, seed_transpiler=seed)\n", + "\n", + "result = qsvm.run(quantum_instance)\n", + "\n", + "\"\"\"declarative approach, re-use the params above\n", + "algo_input = SVMInput(training_input, test_input)\n", + "result = run_algorithm(params, algo_input)\n", + "\"\"\"\n", + "print(\"testing success ratio: \", result['testing_accuracy'])" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "kernel matrix during the training:\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "print(\"kernel matrix during the training:\")\n", + "kernel_matrix = result['kernel_matrix_training']\n", + "img = plt.imshow(np.asmatrix(kernel_matrix),interpolation='nearest',origin='upper',cmap='bone_r')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.2" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/qiskit/aqua/general/Aqua_howto_build_a_pluggable_algorithm_components.ipynb b/qiskit/aqua/general/Aqua_how_to_build_a_pluggable_algorithm_components.ipynb similarity index 92% rename from qiskit/aqua/general/Aqua_howto_build_a_pluggable_algorithm_components.ipynb rename to qiskit/aqua/general/Aqua_how_to_build_a_pluggable_algorithm_components.ipynb index 57fbef38e..71b0f23a8 100644 --- a/qiskit/aqua/general/Aqua_howto_build_a_pluggable_algorithm_components.ipynb +++ b/qiskit/aqua/general/Aqua_how_to_build_a_pluggable_algorithm_components.ipynb @@ -95,7 +95,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "['QAOA.Variational', 'QSVM.Variational', 'VQE', 'ExactEigensolver', 'SVM', 'EOH', 'QSVM.Kernel', 'AmplitudeEstimation', 'BernsteinVazirani', 'DeutschJozsa', 'Grover', 'IQPE', 'QPE', 'Simon', 'EvolutionFidelity']\n" + "['QAOA.Variational', 'VQC', 'VQE', 'ExactEigensolver', 'ExactLSsolver', 'SVM', 'EOH', 'QSVM', 'AmplitudeEstimation', 'BernsteinVazirani', 'DeutschJozsa', 'Grover', 'HHL', 'IQPE', 'QPE', 'Shor', 'Simon', 'EvolutionFidelity']\n" ] } ], @@ -120,7 +120,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "0.9234907613356655\n" + "0.934847761060059\n" ] } ], @@ -185,7 +185,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "0.9234907613356655\n" + "0.9348477610600592\n" ] } ], @@ -193,20 +193,13 @@ "result = run_algorithm(params, algo_input, backend=backend)\n", "print(result['score'])" ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { "kernelspec": { - "display_name": "Quantum py37", + "display_name": "Python 3", "language": "python", - "name": "quantum-dev-37" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -218,7 +211,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.7.2" } }, "nbformat": 4, From 3dbc76dcb97ccba272909fd4502dd2377e52f607 Mon Sep 17 00:00:00 2001 From: Shaohan Hu Date: Sun, 28 Apr 2019 09:06:24 -0400 Subject: [PATCH 081/116] switch back Aer -> BasicAer --- .../aqua/artificial_intelligence/qsvm_directly.ipynb | 6 +++--- .../aqua/artificial_intelligence/qsvm_multiclass.ipynb | 4 ++-- community/aqua/artificial_intelligence/vqc.ipynb | 6 +++--- .../artificial_intelligence/qsvm_classification.ipynb | 8 ++++---- ...ua_how_to_build_a_pluggable_algorithm_components.ipynb | 4 ++-- 5 files changed, 14 insertions(+), 14 deletions(-) diff --git a/community/aqua/artificial_intelligence/qsvm_directly.ipynb b/community/aqua/artificial_intelligence/qsvm_directly.ipynb index a0db62a60..0d65df11b 100644 --- a/community/aqua/artificial_intelligence/qsvm_directly.ipynb +++ b/community/aqua/artificial_intelligence/qsvm_directly.ipynb @@ -28,7 +28,7 @@ "outputs": [], "source": [ "from datasets import *\n", - "from qiskit import Aer\n", + "from qiskit import BasicAer\n", "from qiskit.aqua import run_algorithm, QuantumInstance\n", "from qiskit.aqua.input import ClassificationInput\n", "from qiskit.aqua.components.feature_maps import SecondOrderExpansion\n", @@ -98,7 +98,7 @@ " 'backend': {'shots': shots},\n", " 'feature_map': {'name': 'SecondOrderExpansion', 'depth': 2, 'entanglement': 'linear'}\n", "}\n", - "backend = Aer.get_backend('qasm_simulator')\n", + "backend = BasicAer.get_backend('qasm_simulator')\n", "algo_input = ClassificationInput(training_input, test_input, datapoints[0])" ] }, @@ -192,7 +192,7 @@ "metadata": {}, "outputs": [], "source": [ - "backend = Aer.get_backend('qasm_simulator')\n", + "backend = BasicAer.get_backend('qasm_simulator')\n", "feature_map = SecondOrderExpansion(feature_dimension=feature_dim, depth=2, entangler_map=[[0, 1]])\n", "svm = QSVM(feature_map, training_input, test_input, None)# the data for prediction can be fed later.\n", "svm.random_seed = random_seed\n", diff --git a/community/aqua/artificial_intelligence/qsvm_multiclass.ipynb b/community/aqua/artificial_intelligence/qsvm_multiclass.ipynb index 80ba41c78..b3161ea2e 100644 --- a/community/aqua/artificial_intelligence/qsvm_multiclass.ipynb +++ b/community/aqua/artificial_intelligence/qsvm_multiclass.ipynb @@ -25,7 +25,7 @@ "source": [ "import numpy as np\n", "from datasets import *\n", - "from qiskit import Aer\n", + "from qiskit import BasicAer\n", "from qiskit.aqua.input import ClassificationInput\n", "from qiskit.aqua import run_algorithm" ] @@ -104,7 +104,7 @@ " 'backend': {'shots': 1024}\n", "}\n", "\n", - "backend = Aer.get_backend('qasm_simulator')\n", + "backend = BasicAer.get_backend('qasm_simulator')\n", "algo_input = ClassificationInput(training_input, test_input, total_array)\n", "result = run_algorithm(aqua_dict, algo_input, backend=backend)\n", "for k,v in result.items():\n", diff --git a/community/aqua/artificial_intelligence/vqc.ipynb b/community/aqua/artificial_intelligence/vqc.ipynb index 426256fdd..7e2d70a64 100644 --- a/community/aqua/artificial_intelligence/vqc.ipynb +++ b/community/aqua/artificial_intelligence/vqc.ipynb @@ -31,7 +31,7 @@ "outputs": [], "source": [ "from datasets import *\n", - "from qiskit import Aer\n", + "from qiskit import BasicAer\n", "from qiskit.aqua import run_algorithm, QuantumInstance\n", "from qiskit.aqua.algorithms import VQC\n", "from qiskit.aqua.components.optimizers import SPSA\n", @@ -130,7 +130,7 @@ "}\n", "\n", "svm_input = ClassificationInput(training_input, test_input, datapoints[0])\n", - "backend = Aer.get_backend('qasm_simulator')" + "backend = BasicAer.get_backend('qasm_simulator')" ] }, { @@ -189,7 +189,7 @@ "metadata": {}, "outputs": [], "source": [ - "backend = Aer.get_backend('qasm_simulator')\n", + "backend = BasicAer.get_backend('qasm_simulator')\n", "optimizer = SPSA(max_trials=100, c0=4.0, skip_calibration=True)\n", "optimizer.set_options(save_steps=1)\n", "feature_map = SecondOrderExpansion(feature_dimension=feature_dim, depth=2)\n", diff --git a/qiskit/aqua/artificial_intelligence/qsvm_classification.ipynb b/qiskit/aqua/artificial_intelligence/qsvm_classification.ipynb index d0b72e1f8..92b21d66a 100644 --- a/qiskit/aqua/artificial_intelligence/qsvm_classification.ipynb +++ b/qiskit/aqua/artificial_intelligence/qsvm_classification.ipynb @@ -46,7 +46,7 @@ "source": [ "from qsvm_datasets import *\n", "\n", - "from qiskit import Aer\n", + "from qiskit import BasicAer\n", "from qiskit.aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name\n", "from qiskit.aqua.input import ClassificationInput\n", "from qiskit.aqua import run_algorithm, QuantumInstance\n", @@ -176,7 +176,7 @@ "feature_map = SecondOrderExpansion(feature_dimension=feature_dim, depth=2, entanglement='linear')\n", "qsvm = QSVM(feature_map, training_input, test_input, datapoints[0])\n", "\n", - "backend = Aer.get_backend('qasm_simulator')\n", + "backend = BasicAer.get_backend('qasm_simulator')\n", "quantum_instance = QuantumInstance(backend, shots=1024, seed=seed, seed_transpiler=seed)\n", "\n", "result = qsvm.run(quantum_instance)\n", @@ -187,7 +187,7 @@ " 'algorithm': {\n", " 'name': 'QSVM'\n", " },\n", - " 'backend': {'provider': 'qiskit.Aer', 'name': 'qasm_simulator', 'shots': 1024},\n", + " 'backend': {'provider': 'qiskit.BasicAer', 'name': 'qasm_simulator', 'shots': 1024},\n", " 'feature_map': {'name': 'SecondOrderExpansion', 'depth': 2, 'entanglement': 'linear'}\n", "}\n", "algo_input = SVMInput(training_input, test_input, datapoints[0])\n", @@ -286,7 +286,7 @@ "feature_map = SecondOrderExpansion(feature_dimension=feature_dim, depth=2, entanglement='linear')\n", "qsvm = QSVM(feature_map, training_input, test_input)\n", "\n", - "backend = Aer.get_backend('qasm_simulator')\n", + "backend = BasicAer.get_backend('qasm_simulator')\n", "quantum_instance = QuantumInstance(backend, shots=1024, seed=seed, seed_transpiler=seed)\n", "\n", "result = qsvm.run(quantum_instance)\n", diff --git a/qiskit/aqua/general/Aqua_how_to_build_a_pluggable_algorithm_components.ipynb b/qiskit/aqua/general/Aqua_how_to_build_a_pluggable_algorithm_components.ipynb index 71b0f23a8..986010fd0 100644 --- a/qiskit/aqua/general/Aqua_how_to_build_a_pluggable_algorithm_components.ipynb +++ b/qiskit/aqua/general/Aqua_how_to_build_a_pluggable_algorithm_components.ipynb @@ -73,7 +73,7 @@ "metadata": {}, "outputs": [], "source": [ - "from qiskit import Aer\n", + "from qiskit import BasicAer\n", "import numpy as np\n", "from qiskit.aqua.operator import Operator\n", "from qiskit.aqua import local_pluggables, PluggableType" @@ -136,7 +136,7 @@ "\n", "algo = EvolutionFidelity(qubit_op, initial_state, expansion_order=1)\n", "\n", - "backend = Aer.get_backend('statevector_simulator')\n", + "backend = BasicAer.get_backend('statevector_simulator')\n", "quantum_instance = QuantumInstance(backend=backend)\n", "\n", "result = algo.run(quantum_instance)\n", From c2fbb6b59758adf2959eeaa2315729b76fb6cb8e Mon Sep 17 00:00:00 2001 From: Shaohan Hu Date: Sun, 28 Apr 2019 09:14:25 -0400 Subject: [PATCH 082/116] minor edits on wording --- .../artificial_intelligence/qsvm_directly.ipynb | 16 ++++++++-------- community/aqua/artificial_intelligence/vqc.ipynb | 16 ++++++++-------- 2 files changed, 16 insertions(+), 16 deletions(-) diff --git a/community/aqua/artificial_intelligence/qsvm_directly.ipynb b/community/aqua/artificial_intelligence/qsvm_directly.ipynb index 0d65df11b..3fe700da2 100644 --- a/community/aqua/artificial_intelligence/qsvm_directly.ipynb +++ b/community/aqua/artificial_intelligence/qsvm_directly.ipynb @@ -10,15 +10,15 @@ "\n", "Please refer to [this file](https://github.com/Qiskit/qiskit-tutorials/blob/master/qiskit/aqua/artificial_intelligence/qsvm_kernel_classification.ipynb) for introduction.\n", "\n", - "In this file, we show two ways for using the quantum kernel method: (1) the non-programming way and (2) the programming way. \n" + "In this file, we show two ways for using the quantum kernel method: (1) the declarative approach and (2) the programmatic approach. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Part I: non-programming way.\n", - "In the non-programming way, we config a json-like configuration, which defines how the svm instance is internally constructed. After the execution, it returns the json-like output, which carries the important information (e.g., the details of the svm instance) and the processed results. " + "### Part I: declarative approach.\n", + "In the declarative approach, we config a json-like configuration, which defines how the svm instance is internally constructed. After the execution, it returns the json-like output, which carries the important information (e.g., the details of the svm instance) and the processed results. " ] }, { @@ -78,7 +78,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Now we create the svm in the non-programming way.\n", + "Now we create the svm in the declarative approach.\n", "In the following json, we config:\n", "- the algorithm name \n", "- the feature map " @@ -173,15 +173,15 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### part II: Programming way.\n", - "We construct the svm instance directly from the classes. The programming way offers the users better accessibility, e.g., the users can access the internal state of svm instance or invoke the methods of the instance. We will demonstrate this advantage soon." + "### part II: programmatic approach.\n", + "We construct the svm instance directly from the classes. The programmatic approach offers the users better accessibility, e.g., the users can access the internal state of svm instance or invoke the methods of the instance. We will demonstrate this advantage soon." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Now we create the svm in the programming way.\n", + "Now we create the svm in the programmatic approach.\n", "- We build the svm instance by instantiating the class QSVM. \n", "- We build the feature map instance (required by the svm instance) by instantiating the class SecondOrderExpansion." ] @@ -254,7 +254,7 @@ "collapsed": true }, "source": [ - "Different from the non-programming way, the programming way allows the users to invoke APIs upon the svm instance directly. In the following, we invoke the API \"predict\" upon the trained svm instance to predict the labels for the newly provided data input.\n", + "Different from the declarative approach, the programmatic approach allows the users to invoke APIs upon the svm instance directly. In the following, we invoke the API \"predict\" upon the trained svm instance to predict the labels for the newly provided data input.\n", "\n", "Use the trained model to evaluate data directly, and we store a `label_to_class` and `class_to_label` for helping converting between label and class name" ] diff --git a/community/aqua/artificial_intelligence/vqc.ipynb b/community/aqua/artificial_intelligence/vqc.ipynb index 7e2d70a64..b2a569dcd 100644 --- a/community/aqua/artificial_intelligence/vqc.ipynb +++ b/community/aqua/artificial_intelligence/vqc.ipynb @@ -13,15 +13,15 @@ "\n", "**This notebook shows the variational quantum classifier method.**\n", "\n", - "In this file, we show two ways for using the variational quantum classifier method: (1) the non-programming way and (2) the programming way. \n" + "In this file, we show two ways for using the variational quantum classifier: (1) the declarative approach and (2) the programmatic approach. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Part I: non-programming way.\n", - "In the non-programming way, we config a json-like configuration, which defines how the svm instance is internally constructed. After the execution, it returns the json-like output, which carries the important information (e.g., the details of the svm instance) and the processed results. " + "### Part I: declarative approach.\n", + "In the declarative approach, we config a json-like configuration, which defines how the svm instance is internally constructed. After the execution, it returns the json-like output, which carries the important information (e.g., the details of the svm instance) and the processed results. " ] }, { @@ -106,7 +106,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Now we create the svm in the non-programming way.\n", + "Now we create the svm in the declarative approach.\n", "In the following json, we config:\n", "- the algorithm name \n", "- the variational form\n", @@ -168,15 +168,15 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Part II: programming way.\n", - "We construct the svm instance directly from the classes. The programming way offers the users better accessibility, e.g., the users can access the internal state of svm instance or invoke the methods of the instance. " + "### Part II: programmatic approach.\n", + "We construct the svm instance directly from the classes. The programmatic approach offers the users better accessibility, e.g., the users can access the internal state of svm instance or invoke the methods of the instance. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Now we create the svm in the programming way.\n", + "Now we create the svm in the programmatic approach.\n", "- we build the optimizer instance (required by the svm instance) by instantiating the class SPSA.\n", "- We build the feature map instance (required by the svm instance) by instantiating the class SecondOrderExpansion.\n", "- We build the varitional form instance (required by the svm instance) by instantiating the class RYRZ.\n", @@ -227,7 +227,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Different from the non-programming way, the programming way allows the users to invoke APIs upon the svm instance directly. In the following, we invoke the API \"predict\" upon the trained svm instance to predict the labels for the newly provided data input.\n", + "Different from the declarative approach, the programmatic approach allows the users to invoke APIs upon the svm instance directly. In the following, we invoke the API \"predict\" upon the trained svm instance to predict the labels for the newly provided data input.\n", "\n", "Use the trained model to evaluate data directly, and we store a label_to_class and class_to_label for helping converting between label and class name" ] From 0c3a13bff4538371644e94ff9f52847a891ddbf9 Mon Sep 17 00:00:00 2001 From: woodsp Date: Sun, 28 Apr 2019 10:43:46 -0400 Subject: [PATCH 083/116] Updates to chemistry notebooks --- .../LiH_with_qubit_tapering_and_uccsd.ipynb | 2 +- ...ipynb => ParticleHoleTransformation.ipynb} | 66 ++- ...d2end.ipynb => PySCFChemistryDriver.ipynb} | 49 ++- .../aqua/chemistry/Pyquante_end2end.ipynb | 157 ------- community/aqua/chemistry/QubitMappings.ipynb | 238 +++++++++++ .../aqua/chemistry/beh2_reductions.ipynb | 127 +++--- community/aqua/chemistry/energyplot.ipynb | 52 +-- community/aqua/chemistry/h2_basis_sets.ipynb | 22 +- .../aqua/chemistry/h2_excited_states.ipynb | 30 +- community/aqua/chemistry/h2_mappings.ipynb | 126 +++++- .../aqua/chemistry/h2_particle_hole.ipynb | 94 ++++- community/aqua/chemistry/h2_qpe.ipynb | 49 ++- community/aqua/chemistry/h2_swaprz.ipynb | 75 +++- community/aqua/chemistry/h2_uccsd.ipynb | 66 +-- community/aqua/chemistry/h2_var_forms.ipynb | 68 ++- .../aqua/chemistry/h2_vqe_initial_point.ipynb | 154 ++++++- community/aqua/chemistry/h2_vqe_spsa.ipynb | 77 ++-- community/aqua/chemistry/h2o.ipynb | 398 ++++++++++++++++-- community/aqua/chemistry/lih_dissoc.ipynb | 48 +-- community/aqua/chemistry/lih_uccsd.ipynb | 94 ++++- 20 files changed, 1427 insertions(+), 565 deletions(-) rename community/aqua/chemistry/{ParticleHole_example.ipynb => ParticleHoleTransformation.ipynb} (64%) rename community/aqua/chemistry/{PySCF_end2end.ipynb => PySCFChemistryDriver.ipynb} (58%) delete mode 100644 community/aqua/chemistry/Pyquante_end2end.ipynb create mode 100644 community/aqua/chemistry/QubitMappings.ipynb diff --git a/community/aqua/chemistry/LiH_with_qubit_tapering_and_uccsd.ipynb b/community/aqua/chemistry/LiH_with_qubit_tapering_and_uccsd.ipynb index d4d685ed4..ddb7c9f28 100644 --- a/community/aqua/chemistry/LiH_with_qubit_tapering_and_uccsd.ipynb +++ b/community/aqua/chemistry/LiH_with_qubit_tapering_and_uccsd.ipynb @@ -328,7 +328,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.7" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/community/aqua/chemistry/ParticleHole_example.ipynb b/community/aqua/chemistry/ParticleHoleTransformation.ipynb similarity index 64% rename from community/aqua/chemistry/ParticleHole_example.ipynb rename to community/aqua/chemistry/ParticleHoleTransformation.ipynb index c1b1ba1f5..e58512f7f 100644 --- a/community/aqua/chemistry/ParticleHole_example.ipynb +++ b/community/aqua/chemistry/ParticleHoleTransformation.ipynb @@ -1,5 +1,18 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## _*Particle hole transformation of FermionicOperator*_\n", + "\n", + "This notebook demonstrates carrying out a ParticleHole transformation on the FermionicOperator in Qiskit Chemistry. Here we use the FermionicOperator directly to demonstrate.\n", + "\n", + "Note: The Hamiltonian class that wraps this provides a means to use either full, or particle hole transformation. Under the covers it does what is shown here though.\n", + "\n", + "This notebook has been written to use the PYSCF chemistry driver." + ] + }, { "cell_type": "code", "execution_count": 1, @@ -7,7 +20,8 @@ "outputs": [], "source": [ "import numpy as np\n", - "from qiskit import Aer\n", + "\n", + "from qiskit import BasicAer\n", "from qiskit.transpiler import PassManager\n", "\n", "from qiskit.aqua import Operator, QuantumInstance\n", @@ -20,9 +34,16 @@ "from qiskit.chemistry.drivers import PySCFDriver, UnitsType" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll do this with H2 molecule and use the PySCF driver to create the integrals we need for the FermionicOperator." + ] + }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ @@ -31,9 +52,16 @@ "molecule = driver.run()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We first create the FermionicOperator and use ExactEigensolver with qubit operator we get from it via a jordan wigner mapping to compute the ground state energy. Here this is the electronic component of the total ground state energy (the total ground state energy would include the nuclear repulsion energy we can get from the molecule that comes from the driver)" + ] + }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -60,9 +88,16 @@ "print('The Hartree Fock Electron Energy is: {}'.format(molecule.hf_energy - molecule.nuclear_repulsion_energy))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now the same as above but with ParticleHole transformation. This removes out energy from the FermionicOperator that is equivalent to the electronic part of the Hartree Fock Energy that we also computed above. The Hartree Fock energy also comes from the driver. To get the total electronic ground state energy we need to add the part we now compute with the part that was removed by the transformation." + ] + }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -90,21 +125,28 @@ "print('The exact ground state energy in PH basis is {} (with energy_shift)'.format(ret['energy'] - energy_shift))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We run here using the quantum VQE algorithm to show the same result. The parameters printed are the optimal parameters of the variational form at the minimum energy, the ground state." + ] + }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Minimum value: -0.020307038772801052\n", - "Minimum value: -1.8572750299757856\n", - "Parameters: [ 0.6968305 -0.75469172 -0.93681376 0.90714539 -0.35663766 1.80503875\n", - " 0.36268468 0.91067094 -3.01470787 0.13268903 1.07891483 1.80043481\n", - " -2.97791979 -0.99008645 0.99278289 2.88254594 0.16418367 2.7610048\n", - " -1.98782455 -2.77533268 -2.72793504 1.146142 -0.83030385 -2.75112004]\n" + "Minimum value: -0.020307038771711697\n", + "Minimum value: -1.8572750299746963\n", + "Parameters: [-0.62024568 -0.94461634 -0.12822854 -1.33174693 -3.12835752 -2.41119768\n", + " 0.67926104 2.44344768 0.72721421 -2.76518798 -1.08251803 -1.75962366\n", + " 0.54861203 1.8995056 3.04269648 -1.75046119 0.16409288 0.68204022\n", + " -0.07661803 -0.76359574 -1.56412942 -2.02324628 1.50961019 1.31452025]\n" ] } ], @@ -119,7 +161,7 @@ "# setup VQE with operator, variational form, and optimizer\n", "vqe_algorithm = VQE(newqubitOp_jw, var_form, lbfgs, 'matrix')\n", "\n", - "backend = Aer.get_backend('statevector_simulator')\n", + "backend = BasicAer.get_backend('statevector_simulator')\n", "quantum_instance = QuantumInstance(backend, pass_manager=PassManager())\n", "\n", "results = vqe_algorithm.run(quantum_instance)\n", diff --git a/community/aqua/chemistry/PySCF_end2end.ipynb b/community/aqua/chemistry/PySCFChemistryDriver.ipynb similarity index 58% rename from community/aqua/chemistry/PySCF_end2end.ipynb rename to community/aqua/chemistry/PySCFChemistryDriver.ipynb index 878d72ab5..991697bf8 100644 --- a/community/aqua/chemistry/PySCF_end2end.ipynb +++ b/community/aqua/chemistry/PySCFChemistryDriver.ipynb @@ -1,5 +1,22 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## _*Using PySCF driver*_\n", + "\n", + "Qiskit Chemistry supports a number of different chemistry drivers, i.e chemistry programs and software libraries, which are used to compute integrals that are then used to build the second quantized Hamiltonian in the FermionicOperator.\n", + "\n", + "Drivers include Gaussian 16, PyQuante, PySCF, PSI4 and HDF5. The main Qiskit documentation has more information on [drivers](https://qiskit.org/documentation/aqua/chemistry/qiskit_chemistry_drivers.html).\n", + "\n", + "For non-Windows platforms (where PySCF has no pre-built packages), the PySCF driver is installed as a dependent when you `pip install qiskit-chemistry`. HDF5 support is built into Qiskit Chemistry. If you would like/prefer to use one of the other drivers then refer to the above link for installation and usage guidance.\n", + "\n", + "Note: drivers were written to allow existing users of them to leverage creating the molecular input in a native way for the driver. While Multiplicity (2S+1) is commonly used to specify the overall spin of the molecule, PySCF uses Spin (2S) if you are programming directly with its API and that is what is exposed here. For a singlet system, as in the example below i.e. equal numbers of alpha and beta electrons, the overall spin here is 0 and 2S is 0 (Multiplicity would have been 1).\n", + "\n", + "This notebook has been written to use the PySCF chemistry driver." + ] + }, { "cell_type": "code", "execution_count": 1, @@ -7,7 +24,8 @@ "outputs": [], "source": [ "import numpy as np\n", - "from qiskit import Aer\n", + "\n", + "from qiskit import BasicAer\n", "from qiskit.transpiler import PassManager\n", "\n", "from qiskit.aqua import Operator, QuantumInstance\n", @@ -52,7 +70,7 @@ "metadata": {}, "outputs": [], "source": [ - "# If you do not install any driver and would like to start with a random Hamiltonian\n", + "# If you do have the driver installed or would like to start with a random Hamiltonian\n", "# SIZE=4\n", "# matrix = np.random.random((SIZE,SIZE))\n", "# qubitOp = Operator(matrix=matrix)" @@ -87,15 +105,15 @@ "name": "stdout", "output_type": "stream", "text": [ - "Minimum value: -1.8543764647149892\n", - "Parameters: [-0.11491214 0.32930264 -0.88261763 1.06617404 0.40859901 -1.97440033\n", - " -1.92168204 -0.84401099 0.86926132 0.19962884 1.88259456 0.58563547\n", - " 0.2392261 -1.22095488 -1.8106901 -2.18264222 0.33053157 1.44130586\n", - " 1.16319625 3.08314583 2.86759507 1.39583915 0.89226104 -1.33970127\n", - " -0.20377285 -1.78328421 -1.13356666 2.15515282 1.72935768 -1.02814735\n", - " 0.9198738 -0.51798203 2.25275439 2.70574515 -0.7428116 2.69334082\n", - " -1.96540296 -2.06722665 0.19826459 1.29081156 0.03509571 0.55931109\n", - " 1.61732516 -0.3508986 1.62533384 -0.64622024 3.14159265 -1.78378164]\n" + "Minimum value: -1.8532124263217393\n", + "Parameters: [-2.13953054 0.70800218 -0.17157494 -2.67458466 2.43244041 0.04126769\n", + " 0.34740155 -0.04775077 -1.151147 2.76097941 -1.48948796 -0.30086504\n", + " 0.7290411 2.40033569 -2.30581555 1.06377607 -2.97789243 1.43082718\n", + " -0.91377262 -2.29316671 -0.04083006 -0.54650779 -2.43032826 -0.79940815\n", + " -1.88176584 0.05495389 2.47406188 -0.82144629 -2.44818703 -3.11585379\n", + " -2.54844951 -2.58470426 -0.99008597 -2.88926043 1.20856368 2.67069418\n", + " 2.4613227 1.22966774 -0.03176877 0.93517933 0.06694405 1.33700758\n", + " 1.49080935 -1.39533027 0.47972164 1.7949311 -3.01432916 -2.43192278]\n" ] } ], @@ -110,13 +128,20 @@ "# setup VQE with operator, variational form, and optimizer\n", "vqe_algorithm = VQE(qubitOp, var_form, lbfgs, 'matrix')\n", "\n", - "backend = Aer.get_backend('statevector_simulator')\n", + "backend = BasicAer.get_backend('statevector_simulator')\n", "quantum_instance = QuantumInstance(backend, pass_manager=PassManager())\n", "\n", "results = vqe_algorithm.run(quantum_instance)\n", "print(\"Minimum value: {}\".format(results['eigvals'][0].real))\n", "print(\"Parameters: {}\".format(results['opt_params']))" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { diff --git a/community/aqua/chemistry/Pyquante_end2end.ipynb b/community/aqua/chemistry/Pyquante_end2end.ipynb deleted file mode 100644 index adada2985..000000000 --- a/community/aqua/chemistry/Pyquante_end2end.ipynb +++ /dev/null @@ -1,157 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "from qiskit import Aer\n", - "from qiskit.transpiler import PassManager\n", - "\n", - "from qiskit.aqua import Operator, QuantumInstance\n", - "from qiskit.aqua.algorithms.adaptive import VQE\n", - "from qiskit.aqua.algorithms.classical import ExactEigensolver\n", - "from qiskit.aqua.components.optimizers import L_BFGS_B\n", - "from qiskit.aqua.components.variational_forms import RY\n", - "\n", - "from qiskit.chemistry import FermionicOperator\n", - "from qiskit.chemistry.drivers import PyQuanteDriver, UnitsType, BasisType" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "# using driver to get fermionic Hamiltonian\n", - "# PyQuante example\n", - "driver = PyQuanteDriver(atoms='H .0 .0 .0; H .0 .0 0.735', units=UnitsType.ANGSTROM,\n", - " charge=0, multiplicity=1, basis=BasisType.BSTO3G)\n", - "molecule = driver.run()\n", - "h1 = molecule.one_body_integrals\n", - "h2 = molecule.two_body_integrals" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "# convert from fermionic hamiltonian to qubit hamiltonian\n", - "ferOp = FermionicOperator(h1=h1, h2=h2)\n", - "qubitOp_jw = ferOp.mapping(map_type='JORDAN_WIGNER', threshold=0.00000001)\n", - "qubitOp_pa = ferOp.mapping(map_type='PARITY', threshold=0.00000001)\n", - "qubitOp_bi = ferOp.mapping(map_type='BRAVYI_KITAEV', threshold=0.00000001)" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "IIII\t(-0.8105479862760991+0j)\n", - "IIIZ\t(0.17218394273085635+0j)\n", - "IIZI\t(-0.22575350251540605+0j)\n", - "IIZZ\t(0.12091263358559995+0j)\n", - "IZII\t(0.17218394273085635+0j)\n", - "IZIZ\t(0.16892754048859007+0j)\n", - "IZZI\t(0.16614543338049342+0j)\n", - "IZZZ\t(-8.326672684688674e-17+0j)\n", - "XXXX\t(0.045232799794893426+0j)\n", - "XXYY\t(0.045232799794893426+0j)\n", - "YYXX\t(0.045232799794893426+0j)\n", - "YYYY\t(0.045232799794893426+0j)\n", - "ZIII\t(-0.2257535025154061+0j)\n", - "ZIIZ\t(0.16614543338049342+0j)\n", - "ZIZI\t(0.17464343142442207+0j)\n", - "ZZII\t(0.12091263358559991+0j)\n", - "ZZIZ\t(-2.42861286636753e-17+0j)\n", - "ZZZI\t(-6.938893903907228e-17+0j)\n", - "ZZZZ\t(-3.122502256758253e-17+0j)\n", - "\n", - "The exact ground state energy is: -1.8572750766378763\n" - ] - } - ], - "source": [ - "# print out qubit hamiltonian in Pauli terms and exact solution\n", - "\n", - "qubitOp_jw.to_matrix()\n", - "qubitOp_jw.chop(10**-10)\n", - "\n", - "print(qubitOp_jw.print_operators())\n", - "\n", - "# Using exact eigensolver to get the smallest eigenvalue\n", - "exact_eigensolver = ExactEigensolver(qubitOp_jw, k=1)\n", - "ret = exact_eigensolver.run()\n", - "print('The exact ground state energy is: {}'.format(ret['energy'])) " - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Minimum value: -1.857275076588138\n", - "Parameters: [ 1.72459655 1.92029571 -0.34982926 -1.49153618 2.26170073 0.1302224\n", - " 0.72586921 0.29764644 -1.401497 1.49290088 -3.09131598 0.1647657\n", - " -2.69893629 -1.46110898 -1.99677374 1.92441472 -0.94314616 2.69400524\n", - " 2.75985138 0.16260948 -2.3450682 1.46493868 1.22492389 3.03079433]\n" - ] - } - ], - "source": [ - "# setup VQE \n", - "# setup optimizer, use L_BFGS_B optimizer for example\n", - "lbfgs = L_BFGS_B(maxfun=1000, factr=10, iprint=10)\n", - "\n", - "# setup variational form generator (generate trial circuits for VQE)\n", - "var_form = RY(qubitOp_jw.num_qubits, 5, entangler_map = [[0, 1], [1, 2], [2, 3]])\n", - "\n", - "# setup VQE with operator, variational form, and optimizer\n", - "vqe_algorithm = VQE(qubitOp_jw, var_form, lbfgs, 'matrix')\n", - "\n", - "backend = Aer.get_backend('statevector_simulator')\n", - "quantum_instance = QuantumInstance(backend, pass_manager=PassManager())\n", - "\n", - "results = vqe_algorithm.run(quantum_instance)\n", - "\n", - "print(\"Minimum value: {}\".format(results['eigvals'][0]))\n", - "print(\"Parameters: {}\".format(results['opt_params']))" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/aqua/chemistry/QubitMappings.ipynb b/community/aqua/chemistry/QubitMappings.ipynb new file mode 100644 index 000000000..70b1d7878 --- /dev/null +++ b/community/aqua/chemistry/QubitMappings.ipynb @@ -0,0 +1,238 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## _*FermionicOperator and qubit mapping*_\n", + "\n", + "When we compute a FermionicOperator in Qiskit Chemistry it needs to be converted to a qubit operator to run on the simulator or real device. The FermionicOperator is built from electronn integrals where electrons behave anti-symmetrically under swap. qubits however do not exhibit this behavior and hence a mapping is needed to ensure that this is accounted for.\n", + "\n", + "Here we have the jordan wigner mapping, the bravyi-kitaev mapping and a parity.\n", + "\n", + "This notebook has been written to use the PYQUANTE chemistry driver. See the PYQUANTE chemistry driver readme if you need to install the external PyQuante2 library that this driver requires." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "\n", + "from qiskit import BasicAer\n", + "from qiskit.transpiler import PassManager\n", + "\n", + "from qiskit.aqua import Operator, QuantumInstance, aqua_globals\n", + "from qiskit.aqua.algorithms.adaptive import VQE\n", + "from qiskit.aqua.algorithms.classical import ExactEigensolver\n", + "from qiskit.aqua.components.optimizers import L_BFGS_B\n", + "from qiskit.aqua.components.variational_forms import RY\n", + "\n", + "from qiskit.chemistry import FermionicOperator\n", + "from qiskit.chemistry.drivers import PyQuanteDriver, UnitsType, BasisType\n", + "\n", + "aqua_globals.random_seed = 50" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "# using driver to get fermionic Hamiltonian\n", + "# PyQuante example\n", + "driver = PyQuanteDriver(atoms='H .0 .0 .0; H .0 .0 0.735', units=UnitsType.ANGSTROM,\n", + " charge=0, multiplicity=1, basis=BasisType.BSTO3G)\n", + "molecule = driver.run()\n", + "h1 = molecule.one_body_integrals\n", + "h2 = molecule.two_body_integrals" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "# convert from fermionic hamiltonian to qubit hamiltonian\n", + "ferOp = FermionicOperator(h1=h1, h2=h2)\n", + "qubitOp_jw = ferOp.mapping(map_type='JORDAN_WIGNER', threshold=0.00000001)\n", + "qubitOp_pa = ferOp.mapping(map_type='PARITY', threshold=0.00000001)\n", + "qubitOp_bk = ferOp.mapping(map_type='BRAVYI_KITAEV', threshold=0.00000001)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " --- jordan wigner ---\n", + "IIII\t(-0.8105479862760991+0j)\n", + "IIIZ\t(0.17218394273085635+0j)\n", + "IIZI\t(-0.22575350251540605+0j)\n", + "IIZZ\t(0.12091263358559995+0j)\n", + "IZII\t(0.17218394273085635+0j)\n", + "IZIZ\t(0.16892754048859007+0j)\n", + "IZZI\t(0.16614543338049342+0j)\n", + "IZZZ\t(-8.326672684688674e-17+0j)\n", + "XXXX\t(0.045232799794893426+0j)\n", + "XXYY\t(0.045232799794893426+0j)\n", + "YYXX\t(0.045232799794893426+0j)\n", + "YYYY\t(0.045232799794893426+0j)\n", + "ZIII\t(-0.2257535025154061+0j)\n", + "ZIIZ\t(0.16614543338049342+0j)\n", + "ZIZI\t(0.17464343142442207+0j)\n", + "ZZII\t(0.12091263358559991+0j)\n", + "ZZIZ\t(-2.42861286636753e-17+0j)\n", + "ZZZI\t(-6.938893903907228e-17+0j)\n", + "ZZZZ\t(-3.122502256758253e-17+0j)\n", + "\n", + "The exact ground state energy using jordan wigner mapping is: -1.8572750766378716\n", + "\n", + " --- parity ---\n", + "IIII\t(-0.8105479862760991+0j)\n", + "IIIZ\t(0.17218394273085635+0j)\n", + "IIZI\t(0.1209126335855999+0j)\n", + "IIZZ\t(-0.2257535025154061+0j)\n", + "IXIX\t(0.045232799794893426+0j)\n", + "IXZX\t(-0.045232799794893426+0j)\n", + "IZII\t(-6.938893903907228e-17+0j)\n", + "IZIZ\t(0.16614543338049345+0j)\n", + "IZZI\t(0.17218394273085635+0j)\n", + "IZZZ\t(0.16892754048859007+0j)\n", + "ZIII\t(-3.469446951953614e-17+0j)\n", + "ZIIZ\t(-6.245004513516506e-17+0j)\n", + "ZIZI\t(0.1209126335855999+0j)\n", + "ZIZZ\t(-2.0816681711721685e-17+0j)\n", + "ZXIX\t(0.045232799794893426+0j)\n", + "ZXZX\t(-0.045232799794893426+0j)\n", + "ZZII\t(-0.2257535025154061+0j)\n", + "ZZIZ\t(0.16614543338049342+0j)\n", + "ZZZZ\t(0.17464343142442207+0j)\n", + "\n", + "The exact ground state energy using parity mapping is: -1.8572750766378738\n", + "\n", + " --- bravyi-kitaev ---\n", + "IIII\t(-0.8105479862760991+0j)\n", + "IIIZ\t(0.17218394273085635+0j)\n", + "IIZI\t(0.1209126335855999+0j)\n", + "IIZZ\t(-0.2257535025154061+0j)\n", + "IXIX\t(0.045232799794893426+0j)\n", + "IXZX\t(-0.045232799794893426+0j)\n", + "IZII\t(0.17218394273085635+0j)\n", + "IZIZ\t(0.16892754048859007+0j)\n", + "IZZI\t(-6.938893903907228e-17+0j)\n", + "IZZZ\t(0.16614543338049345+0j)\n", + "ZIII\t(-3.469446951953614e-17+0j)\n", + "ZIIZ\t(-6.245004513516506e-17+0j)\n", + "ZIZI\t(0.1209126335855999+0j)\n", + "ZIZZ\t(-2.0816681711721685e-17+0j)\n", + "ZXIX\t(0.045232799794893426+0j)\n", + "ZXZX\t(-0.045232799794893426+0j)\n", + "ZZIZ\t(0.17464343142442207+0j)\n", + "ZZZI\t(-0.2257535025154061+0j)\n", + "ZZZZ\t(0.16614543338049342+0j)\n", + "\n", + "The exact ground state energy using bravyi-kitaev mapping is: -1.8572750766378796\n" + ] + } + ], + "source": [ + "# print out qubit hamiltonian in Pauli terms and exact solution\n", + "qubit_ops = [(qubitOp_jw, 'jordan wigner'),\n", + " (qubitOp_pa, 'parity'),\n", + " (qubitOp_bk, 'bravyi-kitaev')]\n", + "\n", + "for qubit_op, name in qubit_ops:\n", + " qubit_op.to_matrix()\n", + " qubit_op.chop(10**-10)\n", + "\n", + " print(\"\\n --- {} ---\".format(name))\n", + " print(qubit_op.print_operators())\n", + "\n", + " # Using exact eigensolver to get the smallest eigenvalue\n", + " exact_eigensolver = ExactEigensolver(qubit_op, k=1)\n", + " ret = exact_eigensolver.run()\n", + " print('The exact ground state energy using {} mapping is: {}'.format(name, ret['energy'])) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we run on quantum backend, in this case a simulator" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Ground state energy using jordan wigner: -1.8570893208672647\n", + "Ground state energy using parity: -1.8572686760592785\n", + "Ground state energy using bravyi-kitaev: -1.85727507635405\n" + ] + } + ], + "source": [ + "for qubit_op, name in qubit_ops:\n", + " # setup VQE \n", + " # setup optimizer, use L_BFGS_B optimizer for example\n", + " lbfgs = L_BFGS_B(maxfun=1000, factr=10, iprint=10)\n", + "\n", + " # setup variational form generator (generate trial circuits for VQE)\n", + " var_form = RY(qubit_op.num_qubits, 5, entanglement='full')\n", + "\n", + " # setup VQE with operator, variational form, and optimizer\n", + " vqe_algorithm = VQE(qubit_op, var_form, lbfgs, 'matrix')\n", + "\n", + " backend = BasicAer.get_backend('statevector_simulator')\n", + " quantum_instance = QuantumInstance(backend, pass_manager=PassManager())\n", + "\n", + " results = vqe_algorithm.run(quantum_instance)\n", + "\n", + " print(\"Ground state energy using {}: {}\".format(name, results['eigvals'][0]))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/community/aqua/chemistry/beh2_reductions.ipynb b/community/aqua/chemistry/beh2_reductions.ipynb index b2f247456..9d383850a 100644 --- a/community/aqua/chemistry/beh2_reductions.ipynb +++ b/community/aqua/chemistry/beh2_reductions.ipynb @@ -6,11 +6,13 @@ "source": [ "## _*BeH2 plots of various orbital reduction results*_\n", "\n", - "This notebook demonstrates using the Qiskit Chemistry to plot graphs of the ground state energy of the Beryllium Dihydride (BeH2) molecule over a range of inter-atomic distances using ExactEigensolver. Freeze core reduction is true and different virtual orbital removals are tried as a comparison.\n", + "We have notebooks showing LiH, where we often remove (discard) two unoccupied orbitals, in addition to freezing the core. While freezing of the core electrons can always be done, discarding unoccupied orbitals should be done with great care.\n", + "\n", + "This notebook demonstrates this for Beryllium Dihydride (BeH2) where we show the effect of removing different unoccupied orbitals. We use Qiskit Chemistry to plot graphs of the ground state energy of the Beryllium Dihydride (BeH2) molecule over a range of inter-atomic distances using ExactEigensolver. Freeze core reduction is true and different virtual orbital removals are tried as a comparison.\n", "\n", "This notebook populates a dictionary, that is a progammatic representation of an input file, in order to drive the Qiskit Chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here where we alter the molecule supplied to the driver in each loop as well as the orbital reductions.\n", "\n", - "This notebook has been written to use the PYSCF chemistry driver. See the PYSCF chemistry driver readme if you need to install the external PySCF library that this driver requires." + "This notebook has been written to use the PYSCF chemistry driver." ] }, { @@ -36,7 +38,7 @@ " -15.52863269 -15.5598192 -15.56723345 -15.55823699 -15.53789746\n", " -15.50975433 -15.476334 -15.43948849 -15.40061366 -15.38534487\n", " -15.30406975 -15.24876708 -15.23982192 -15.25303723 -15.27323362\n", - " -15.2904802 -15.29973676 -15.30358774]\n", + " -15.29048022 -15.29973676 -15.30358774]\n", " [-14.38085785 -14.8496625 -15.152928 -15.34484824 -15.46196656\n", " -15.52847583 -15.56042602 -15.5686254 -15.5604457 -15.54096661\n", " -15.51373779 -15.48129162 -15.44548034 -15.4076929 -15.43902234\n", @@ -51,7 +53,7 @@ " -15.53627247 -15.56808784 -15.57642757 -15.5686708 -15.54991949\n", " -15.52376812 -15.49282421 -15.45905583 -15.42402529 -15.38905694\n", " -15.31000383 -15.2593924 -15.25594154 -15.26939038 -15.28973515\n", - " -15.30706594 -15.31636055 -15.32022639]\n", + " -15.30706596 -15.31636055 -15.32022639]\n", " [-14.38815095 -14.85518765 -15.15741167 -15.34871007 -15.46542593\n", " -15.53165667 -15.56340888 -15.57146946 -15.5631985 -15.54366894\n", " -15.51642669 -15.48400243 -15.44824819 -15.41055403 -15.44242866\n", @@ -66,7 +68,7 @@ " -15.54630491 -15.58068771 -15.59206637 -15.58785438 -15.57320634\n", " -15.55177264 -15.52620548 -15.49849044 -15.47015952 -15.37198719\n", " -15.27680792 -15.18982171 -15.11557267 -15.0565821 -15.01697352\n", - " -14.99729007 -14.98854807 -14.98398255]]\n" + " -14.99729008 -14.98854807 -14.98398255]]\n" ] } ], @@ -109,25 +111,24 @@ ] }, { - "cell_type": "code", - "execution_count": 2, + "cell_type": "markdown", "metadata": {}, + "source": [ + "First we plot the ground state energy against interatomic distance for the set of reductions" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "scrolled": false + }, "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 2, - "metadata": {}, - "output_type": "execute_result" - }, { "data": { "image/png": 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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -141,29 +142,28 @@ "pylab.xlabel('Interatomic distance')\n", "pylab.ylabel('Energy')\n", "pylab.title('BeH2 Ground State Energy')\n", - "pylab.legend(loc='upper right')" + "pylab.legend(loc='upper right');" ] }, { - "cell_type": "code", - "execution_count": 3, + "cell_type": "markdown", "metadata": {}, + "source": [ + "Now the difference in energy, compared to no reduction, is plotted so it is easier to see the effect. First in one larger plot so its easier to compare, and then in individual plots." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "scrolled": false + }, "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 3, - "metadata": {}, - "output_type": "execute_result" - }, { "data": { "image/png": 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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -177,19 +177,21 @@ "pylab.xlabel('Interatomic distance')\n", "pylab.ylabel('Energy')\n", "pylab.title('Energy difference compared to no reduction []')\n", - "pylab.legend(loc='upper left')" + "pylab.legend(loc='upper left');" ] }, { "cell_type": "code", "execution_count": 4, - "metadata": {}, + "metadata": { + "scrolled": true + }, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", 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\n", 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gtWQhqQyYAJwCVALTJU0xs3mJYr8xszti+bOAHwIj47zXzazwVmHnnCt1ZrB5HWx8G959G95dEYa77AIf+nyqb53mmcURwAIzWwggaTIwCtiWLMxsfaJ8D6A0Ghecc66pahNBbQJ49+34d0XdxFC9ue5yKoP+h7fpZNEfSF4GVAkcmVtI0ljgcqAzcFJi1lBJs4D1wPVm9vcUY3XOuXRt2QgbliWSQE4yqC8R9OgLPfYMvVwPPgF69IOe/cK0nntB192hQ1nq4WfewG1mE4AJks4DrgcuAJYBg8xslaSPAH+SdHDOmQiSxgBjAAYNGtTKkTvnXD2qt8CqV2HFS7BiLqycC+verFtGHaB73/DF3/sAGHR83STQox9026NVEkEh0kwWS4GBifEBcVp9JgM/BzCzzcDmODxD0uvA/kBFcgEzmwhMBCgvL/cqLOdc6zOD9ZUhMaycG/6+Mx9qtob53XrDnofA/mfAroNCEuixJ3TvDR0y/71esDQjnQ4MkzSUkCRGA+clC0gaZmavxdHTgdfi9L7AajOrlrQPMAxYmGKszjlXmE1rYeW8eNYQzxw2rwvzOnaFPgfBIaNhz4NDkujRDzK8MbilpJYszKxK0jjgUcKls5PMbK6k8UCFmU0Bxkk6GdgKrCFUQQGcAIyXtBWoAS42s9Vpxeqcc3nlVieteAnW1zbFCnYfCkNODElhz0Ng933a1NlCU6hU7m4uLy+3ioqKxgs651x9tmyEN/6+/axh1avbq5O699meFPY8BPocCJ17ZhtvC5A0w8zKGytXminQOeea4v018OJvYO4DsPXdUJ3Ud3isTjokVCmVSHVSc3mycM61X++ugDn3wysPQdVmGHoSHHo+9D2oZKuTmsv3hnOu/Vm/FObcC/P/DFYD+42EEReGNgiXlycL51z7sWYRzP4lLHg03OdwwFnwoS/ALv2zjqzoebJwzpW+d16BWZNg0ZPQsUtoizj0/HB3tCuIJwvnXOlaPjskiSXPhCuXDvsifPA86Lpb1pG1OZ4snHOlxQyWPheSxLKZITEc/lU4+N9L4lLXrHiycM6VBqsJ90jMmhS63ejeF46+HA78FHTqlnV0bZ4nC+dc21ZTDQsfDw3XqxdAr/5w/LdCX0xlnbOOrmR4snDOtU3VW+G1qeES2HVvwm5D4WPjYd9T/R6JFPgedc61Pa8+DNN/Hp4D0fsAOPlWGPqxcDmsS4UnC+dc2zLzF1Dxc9jzg6G6aeAx7bobjtbiycI51zaYwfSfhbaJYZ+EE2/w6qZW5HvaOVf8rAb+9UN4aTIc9G9w3DVe5dTKPFk454pbTTX84/vwyp/CDXVHfcOrnTLgycI5V7xqqmDajbDgETjsIii/2BNFRjxZOOeKU/UW+Nt1sPhJOGJc6BXWZcaThXOu+FRtgseuCn06HXNF6PjPZcqThXOuuGx9Dx69HN6aASdcDweenXVEDkj1cgJJIyXNl7RA0jV55l8s6UVJsyX9Q9LwxLxr43LzJX0izTidc0Vi8waYOg6WzYKTvuuJooikliwklQETgNOA4cBnk8kg+o2ZfdDMRgD/BfwwLjscGA0cDIwEfhbX55wrVZvWwsMXw8p5cPIt4el1rmikeWZxBLDAzBaa2RZgMjAqWcDM1idGewAWh0cBk81ss5ktAhbE9TnnStF778Cfx8DaxXDqbaHrDldU0myz6A8sSYxXAkfmFpI0Frgc6AyclFj22Zxld3juoaQxwBiAQYMGtUjQzrlWtnE5PHxJSBin3Q57l2cdkcsj81sgzWyCme0LXA1c38RlJ5pZuZmV9+3rj0d0rs1ZXwlTvgyb1sDpEzxRFLE0k8VSYGBifECcVp/JQG1rVlOXdc61NWsWhUSx9X044w7od2jWEbkGpJkspgPDJA2V1JnQYD0lWUDSsMTo6cBrcXgKMFpSF0lDgWHA8ynG6pxrTateDW0UZnDmROhzYNYRuUak1mZhZlWSxgGPAmXAJDObK2k8UGFmU4Bxkk4GtgJrgAvisnMlPQDMA6qAsWZWnVaszrlWtOIlmPo16NQdzvg57OrtjW2BzKzxUm1AeXm5VVRUZB2Gc64hy2bCI5dBtz3g9J9Drw9kHVG7J2mGmTXaWJR5A7dzrp2ofDacUfToB2fe5YmijfFk4ZxL3+Kn4JFvwG6DQxtFD796sa3xZOGcS9frfw2dAvY5IFz11G33rCNyzeAdCTrn0jP/z/D0d2GvEfCJH0HnHllH5JrJzyycc+lY/BQ8dRP0PwJO+x9PFG2cn1k451rexrfhqfHh/olTb4OOXbKOyO0kP7NwzrWsmmp48tvhSXcf/09PFCXCk4VzrmXN/mW4n+K4q/2GuxLiycI513KWz4YZd8F+p8Gw07OOxrUgTxbOuZaxeT08cX242e64q0HKOiLXgryB2zm388zg6e/Buyth1CTo3DPriFwL8zML59zOe+UhWPQEHDEO9jw462hcCjxZOOd2zurX4ZnbYMBRcOjnso7GpcSThXOu+ao2wd++FW64++iNIP9KKVXeZuGca75nfwxrXofTfgLd+2QdjUuR/wxwzjXPoidh3oNw6Odh4NFZR+NS5snCOdd0G5eHDgL7DofDv5p1NK4VeLJwzjVNTRU88e3w96SboaxT1hG5VpBqspA0UtJ8SQskXZNn/uWS5kl6QdLfJA1OzKuWNDu+pqQZp3OuCWZNguWz4LhrYNeBWUfjWklqDdySyoAJwClAJTBd0hQzm5coNgsoN7P3JF0C/BfwmTjvfTMbkVZ8zrlmWDYTZt4duvIY9smso3GtKM0ziyOABWa20My2AJOBUckCZvakmb0XR58FBqQYj3NuZ2xaF6qfevWHY6/KOhrXytJMFv2BJYnxyjitPhcBf0mMd5VUIelZSWfnW0DSmFimYuXKlTsfsXMuP7PQoP3+qtDtuD/IqN0pivssJJ0PlAMnJiYPNrOlkvYBnpD0opm9nlzOzCYCEwHKy8ut1QJ2rr15+Q+weBocdRn0PSjraFwG0jyzWAokW78GxGl1SDoZuA44y8w21043s6Xx70JgGnBYirE65+qzegH864cw8Bj44HlZR+MykmaymA4MkzRUUmdgNFDnqiZJhwF3EhLFisT03SV1icN9gGOBZMO4c641bOvOo5d359HOpVYNZWZVksYBjwJlwCQzmytpPFBhZlOAHwA9gd8r9H3/ppmdBRwE3CmphpDQbsm5iso51xqeuQ3WLIRP/hS67ZF1NC5DqbZZmNlUYGrOtBsSwyfXs9wzwAfTjM0514iFj4euxz90QehR1rVrfk7pnNvRhmXw9M3Q92A4/JKso3FFwJOFc66umqrweFSrgY/fDB2K4qJJlzFPFs65umbeDW/PgeOvhV38PlkXeLJwzm33VgXM/AXsfybsNzLraFwR8WThnAs2rQ3deew6EI69MutoXJHxykjnXOjOY9pNIWGM/BF06p51RK7IFHRmIemPkk6X/I4c50rS3Afgzb/DkZdCnwOzjsYVoUK//H8GnAe8JukWSQekGJNzrjWtehWeux0GHQeHjM46GlekCkoWZva4mX0O+DCwGHhc0jOSvijJH5PlXFtVvSW0U3TuBSd+B0JPCs7toOBqJUm9gQuBLxMeWnQ7IXk8lkpkzrn0zbwb1rwOJ34buu2edTSuiBXUwC3pIeAA4H7gTDNbFmf9TlJFWsE551K08mWYfS/sf0aognKuAYVeDfU/ZvZkvhlmVt6C8TjnWkP1Fph2Y+gc8OhvZh2NawMKTRa7S/q3nGnrgBeTXYs759qI2uqnkT+GLr2yjsa1AYUmi4uAo4Has4uPAjOAoZLGm9n9KcTmnEvDynle/eSarNBk0Qk4yMzeBpDUD7gPOBJ4mtCW4Zwrdl795Jqp0KuhBtQmimgFMNDMVgNbWz4s51wqZtwVHmZ0wnVe/eSapNAzi2mSHgZ+H8fPidN6AGtTicw517JWzoM594VOAr36yTVRocliLPBvQO0Rdh/wBzMz4GNpBOaca0G11U/de8PRl2cdjWuDGq2GklQGPGFmfzCzb8TXgzFRNLbsSEnzJS2QdE2e+ZdLmifpBUl/kzQ4Me8CSa/F1wVN3jLn3Ha11U/He/WTa55Gk4WZVQM1knZtyopjkpkAnAYMBz4raXhOsVlAuZkdCjwI/Fdcdg/gO4QG9COA70jy20uda4461U/HZh2Na6MKrYbaCLwo6THg3dqJZnZpA8scASwws4UAkiYDo4B5ieWTN/o9C5wfhz8BPBYb0InvOxL4bYHxOufAq59ciyk0WfwxvpqiP7AkMV5JOFOoz0XAXxpYtn/uApLGAGMABg0a1MTwnGsHaqufRt7u1U9upxSULMzsXkndgEFmNr+lg5B0PlAOnNiU5cxsIjARoLy8vNE2FOfalRVzYc69Xv3kWkShDz86E5gNPBLHR0ia0shiS4GBifEBcVruuk8GrgPOMrPNTVnWOVePqs3w1E3QvY9XP7kWUehNeTcS2iDWApjZbGCfRpaZDgyTNFRSZ2A0UCfBSDoMuJOQKJJ9TD0KnCpp99iwfWqc5pwrxEy/+sm1rELbLLaa2TrVfTBKTUMLmFmVpHGEL/kyYJKZzZU0HqgwsynAD4CewO/jut80s7PMbLWk7xISDsD42sZu51wjVrwUrn464CyvfnItptBkMVfSeUCZpGHApcAzjS1kZlOBqTnTbkgMn9zAspOASQXG55yDWP00Hrr39eon16IKrYb6GnAwsJlw+ep64LK0gnLONVNt9dMJ10PnnllH40pIoVdDvUdohL4u3XCcc822rfppFAw8OutoXIkp9LGq+wNXAEOSy5jZSemE5ZxrkqrNMO2mWP30jayjcSWo0DaL3wN3AHcD1emF45xrlhkTYe0iOO0nXv3kUlFosqgys5+nGolzrnlWvAQv3O/VTy5VhTZw/1nSVyV9QNIeta9UI3PONa5qc+z7yaufXLoKPbOo7SL8ysQ0o/Eb85xzaZpxJ6xd7NVPLnWFXg01NO1AnHNNtOIleOFXcODZXv3kUtdgNZSkqxLD5+bM+8+0gnLONSJZ/XSU3/Lk0tdYm8XoxPC1OfNGtnAszrlC1VY/nfhtr35yraKxZKF6hvONO+daw9svxuqnT8GAo7KOxrUTjSULq2c437hzLm3buh7vC0d9PetoXDvSWAP3hyStJ5xFdIvDxPGuqUbmnNtRxR2h+umTP/XqJ9eqGkwWZlbWWoE45xrx9ovw4q+9+sllotCb8pxzWdrybrj6qceeXv3kMlHoTXnOuayYhUSxfgmc/jOvfnKZ8DML54rdrEmw+Ek48lLYuzzraFw75cnCuWL25j9Co/Z+p8EHP5d1NK4dSzVZSBopab6kBZKuyTP/BEkzJVVJ+nTOvGpJs+NrSppxOleU1r0JT1wPvYfBCdeB/NYml53U2iwklQETgFOASmC6pClmNi9R7E3gQsKDlXK9b2Yj0orPuaK25V149JvQoSOceht09CvVXbbSbOA+AlhgZgsBJE0GRgHbkoWZLY7zalKMw7m2xWpg2nfCmcXpE6DXB7KOyLlUq6H6A0sS45VxWqG6SqqQ9Kyks/MVkDQmlqlYuXLlzsTqXPGYNQkWTwuXyHqDtisSxdzAPdjMyoHzgB9L2je3gJlNNLNyMyvv27dv60foXEt74+9QcWdo0D7ks1lH49w2aSaLpcDAxPiAOK0gZrY0/l0ITAMOa8ngnCs6axeHBu0+B3iDtis6aSaL6cAwSUMldSZ0d17QVU2SdpfUJQ73AY4l0dbhXMnZshH+egWUdYJT/9sbtF3RSS1ZmFkVMA54FHgZeMDM5koaL+ksAEmHS6oEzgXulDQ3Ln4QUCFpDvAkcEvOVVTOlQ6rgSdvgHVL4ORboOdeWUfk3A5S7e7DzKYCU3Om3ZAYnk6onspd7hngg2nG5lzRmHk3vPE0HHOFN2i7olXMDdzOlb7FT8GMiTDsdDj4M1lH41y9PFk4l5W1i0P1U5+D4PhrvUHbFTVPFs5lYcvGcId2WWc49QfeoO2KnndR7lxrsxp44tuwvjJ0Oe4N2q4N8DML51rbjLvgzb/D0d+AvT+SdTTOFcSThXOtafE0mHkX7H+mN2i7NsWThXOtZc2i0KDddzgcd43W8lAzAAARSklEQVQ3aLs2xZOFc61hy0b46zdDQ/YpP4COXbKOyLkm8QZu59JmNaHPp/VL4Yw7oGe/rCNyrsn8zMK5tFXcGR6Pesw34QPeH6ZrmzxZOJemRU/ArF+EBu3h52YdjXPN5snCubSsWQjTboS+B3uDtmvzPFk4l4bNG0KX4x27xTu0vUHbtW3ewO1cS6uphieuCw3aZ94JPfbMOiLndpqfWTjX0irugCXPwLFXwl4jso7GuRbhycK5lvTyH2H2L+GAUXDQOVlH41yL8Woo51qCGcy4MzzIaOAxcNzV3qDtSoonC+d2Vk0VPH0zvPpnOOAsOP5b0MH/tVxpSbUaStJISfMlLZB0TZ75J0iaKalK0qdz5l0g6bX4uiDNOJ1rtq3vwaOXh0Tx4a/ACd/2ROFKUmpHtaQyYAJwClAJTJc0xczmJYq9CVwIXJGz7B7Ad4BywIAZcdk1acXrXJO9twoeuQxWvQonXA8Hnp11RM6lJs0ziyOABWa20My2AJOBUckCZrbYzF4AanKW/QTwmJmtjgniMWBkirE61zRr34D//RKsXQSfuM0ThSt5aSaL/sCSxHhlnNZiy0oaI6lCUsXKlSubHahzTfL2CyFRbH0PzrgTBh2XdUTOpa5NXzprZhPNrNzMyvv27Zt1OK49WDwNHr4EuuwCoybBngdnHZFzrSLNZLEUGJgYHxCnpb2sc+mY9yA8dhXssV9IFLsObHwZ50pEmsliOjBM0lBJnYHRwJQCl30UOFXS7pJ2B06N05xrfWbw/AT4xy0w8NjwTIpuu2cdlXOtKrVkYWZVwDjCl/zLwANmNlfSeElnAUg6XFIlcC5wp6S5cdnVwHcJCWc6MD5Oc651VW8NPcfO/iUc+KnQKWCnbllH5Vyrk5llHUOLKC8vt4qKiqzDcKVky7uh2mnpc1B+MRx2kd+V7UqOpBlmVt5YOb97yLl83nsH/nIprH4dTrwh3JntXDvmycK5XGsXw9Svwaa1MPJHoa8n59o5TxbOJS2fDY9+EzqUwZkToe9BWUfkXFFo0/dZONeiFj0J/zcWuu4aLo31ROHcNn5m4RzAS7+DZ/4b9jwkVD113S3riJwrKp4sXPtmNfD8T2HOfTD4RPj4zdCxa9ZROVd0PFm49qt6Kzw1Hhb8BYZ/Go65MrRVOOd24MnCtU9bNsZ7KJ6Hw8fCiAv9HgrnGuDJwrVP026Ct2bAR2+E/c/IOhrnip5fDeXan5oqqHwWDvqUJwrnCuTJwrU/qxdA1fuw12FZR+Jcm+HJwrU/y2eHv3t9KNs4nGtDPFm49mf5HOi5V3g55wriycK1L2bhzKKfn1U41xSeLFz7snEZvLcS9hqRdSTOtSmeLFz74u0VzjWLJwvXviyfA516wO77Zh2Jc22KJwvXviyfDf0O9W49nGuiVJOFpJGS5ktaIOmaPPO7SPpdnP+cpCFx+hBJ70uaHV93pBmnayc2r4c1C70KyrlmSK27D0llwATgFKASmC5pipnNSxS7CFhjZvtJGg3cCnwmznvdzLwV0rWct18AzBu3nWuGNM8sjgAWmNlCM9sCTAZG5ZQZBdwbhx8EPi55b24uJcvngMrCMyucc02SZrLoDyxJjFfGaXnLmFkVsA7oHecNlTRL0lOSjk8xTtdevD0H+hzoz6twrhmKtYF7GTDIzA4DLgd+I2mX3EKSxkiqkFSxcuXKVg/StSHVW2HFXG+vcK6Z0kwWS4GBifEBcVreMpI6ArsCq8xss5mtAjCzGcDrwP65b2BmE82s3MzK+/btm8ImuJLxzitQvdnbK5xrpjSTxXRgmKShkjoDo4EpOWWmABfE4U8DT5iZSeobG8iRtA8wDFiYYqyu1NXejOfdfDjXLKldDWVmVZLGAY8CZcAkM5sraTxQYWZTgF8A90taAKwmJBSAE4DxkrYCNcDFZrY6rVhdO/D2HNhlIHTv3XhZ59wOUn1SnplNBabmTLshMbwJODfPcn8A/pBmbK4dMQtXQg06NutInGuzirWB27mWs+5N2LTG2yuc2wmeLFzp8/YK53aaJwtX+t6eA112hd2GZB2Jc22WJwtX+mo7D/TOAZxrNk8WrrS9vya0WXh7hXM7xZOFK21vzwl//c5t53aKJwtX2pbPhrLO0Hd41pE416Z5snClbfkc6HNQSBjOuWbzZOFKV9UmeOdlb69wrgV4snCla+U8qKnyZOFcC/Bk4UrXtpvxDs02DudKgCcLV7qWz4Hd94Guu2YdiXNtnicLV5qsJjxz27v4cK5FeLJwpWnNQtiywe+vcK6FeLJwpam2vcIbt51rEZ4sXGlaPge69YZe/bOOxLmS4MnClaa354QqKO880LkWkeqT8tqELe/C7z4F3ftCjz3rf3XukXWkrlDvroANb8Ehoxsv65wriCeLmioYfGL4gtm4PFxBs3ndjuU69QiXYHbuCV12gc69wt8uveoOd+wKHbvFv3leZZ39127alsfOA/1KKOdaTKrJQtJI4HagDLjbzG7Jmd8FuA/4CLAK+IyZLY7zrgUuAqqBS83s0VSC7LornHBd3WlVm+C9d2Dj2/Deyu1/N6+HzRvC33VvhOEtG0L5gikkjA4dw986w52gQ6ft0zp0hA5l24dVVne6yrb/VYdYpkOc1mH79DovxenaPg1tn4e2z4PEfNXdhm3jufMaYAbY9r/1TaupjtNqcl7JadUh0VtNKG/V2/8umxUSc58DmvC5OOcaklqykFQGTABOASqB6ZKmmNm8RLGLgDVmtp+k0cCtwGckDQdGAwcDewOPS9rfzKrTireOjl1hlwHhVYjqLXUTR0Ovre+H8jVV4W9Dw1Xvh/GaqvBFuG24avsXpVXv+IVZ+6Xb3mxLqGWw7yfCuHOuRaT533QEsMDMFgJImgyMApLJYhRwYxx+EPipJMXpk81sM7BI0oK4vn+lGG/zlXWG7r3DqxjU/vquTRz1/lJP/GKvnb9t+cQvfquhTgKy2mGrO0wBZxjJs5cwYcdpdc6IEmdAyTOhHc6u/FoN59KUZrLoDyxJjFcCR9ZXxsyqJK0Desfpz+Ysu8M1kJLGAGPi6EZJ8+uJpQ/wTlM3IENtLV7wmFuLx5y+thYv7FzMgwsp1KbP081sIjCxsXKSKsysvBVCahFtLV7wmFuLx5y+thYvtE7MaZ67LwUGJsYHxGl5y0jqCOxKaOguZFnnnHOtJM1kMR0YJmmopM6EBuspOWWmABfE4U8DT5iZxemjJXWRNBQYBjyfYqzOOecakFo1VGyDGAc8Srh0dpKZzZU0HqgwsynAL4D7YwP2akJCIZZ7gNAYXgWM3ckroRqtqioybS1e8Jhbi8ecvrYWL7RCzDJrp5dZOuecK5hfb+icc65Rniycc841qmSShaSRkuZLWiDpmjzzL5S0UtLs+PpyFnHmxDRJ0gpJL9UzX5L+J27TC5I+3Nox5sTTWLwflbQusY9vaO0Y88Q0UNKTkuZJmivp63nKFNt+LiTmotnXkrpKel7SnBjvTXnKdJH0u7iPn5M0pPUjrRNPITEX3XcGhN4xJM2S9HCeeentZzNr8y9CA/rrwD5AZ2AOMDynzIXAT7OONSemE4APAy/VM/+TwF8It0YfBTxX5PF+FHg46/2aE9MHgA/H4V7Aq3mOjWLbz4XEXDT7Ou63nnG4E/AccFROma8Cd8Th0cDv2kDMRfedEeO6HPhNvs8/zf1cKmcW27oWMbMtQG3XIkXNzJ4mXAVWn1HAfRY8C+wm6QOtE92OCoi36JjZMjObGYc3AC+zY28AxbafC4m5aMT9tjGOdoqv3CtnRgH3xuEHgY/Hrn0yUWDMRUfSAOB04O56iqS2n0slWeTrWiTfP9c5sZrhQUkD88wvNoVuVzE5Op7a/0XSwVkHkxRPyQ8j/IpMKtr93EDMUET7OlaNzAZWAI+ZWb372MyqgNqufTJTQMxQfN8ZPwauAmrqmZ/afi6VZFGIPwNDzOxQ4DG2Z1/XcmYCg83sQ8BPgD9lHM82knoCfwAuM7P1WcdTiEZiLqp9bWbVZjaC0NvCEZIOyTKeQhQQc1F9Z0g6A1hhZjOyeP9SSRaNdg9iZqss9GIL4RTuI60U285oU92emNn62lN7M5sKdJLUJ+OwkNSJ8KX7azP7Y54iRbefG4u5WPe1ma0FngRG5syqr2ufzNUXcxF+ZxwLnCVpMaGq/SRJv8opk9p+LpVk0WjXIjl10GcR6oGL3RTgC/FqnaOAdWa2LOug6iNpr9r6UUlHEI6vTL8QYjy/AF42sx/WU6yo9nMhMRfTvpbUV9Jucbgb4Rk2r+QUq69rn0wUEnOxfWeY2bVmNsDMhhC+454ws/NziqW2n9t0r7O1rLCuRS6VdBah+5DVhCsdMiXpt4SrWvpIqgS+Q2how8zuAKYSrtRZALwHfDGbSIMC4v00cImkKuB9YHSWXwjRscDngRdj/TTAt4BBUJz7mcJiLqZ9/QHgXoUHnnUAHjCzh1VA1z4ZKiTmovvOyKe19rN39+Gcc65RpVIN5ZxzLkWeLJxzzjXKk4VzzrlGebJwzjnXKE8WzjnnGuXJwhUtSRsLKHOZpO4t+J5nSxregut7ZieW3Rj/7i3pwQbK7Sbpq819H+cK4cnCtXWXAU1KFvHa+vqcDbRYsjCzY1pgHW+Z2acbKLIbobdR51LjycIVPYVnN0yLnbm9IunX8W7rS4G9gSclPRnLnirpX5JmSvp97F8JSYsl3SppJnCupK9Imh474vuDpO6SjiHcqfsDhecX7CtphKRnY2dyD0naPa5vmqQfSaqQ9LKkwyX9UdJrkr6XiH1jYvhqSS/G97wlz3YOjbG/mLOOIYrPEJF0sMJzGGbHmIYBtwD7xmk/kNRT0t/iPnhR0qjEel6WdJfCMxz+Gu9eRtJ+kh6Psc2UtG+cfmXcTy8ozzMfXDvSUn2d+8tfLf0CNsa/HyX0njmA8APnX8Bxcd5ioE8c7gM8DfSI41cDNyTKXZVYd+/E8PeAr8Xhe4BPJ+a9AJwYh8cDP47D04Bb4/DXgbcIdwV3IfRa2ztnG04DngG6x/E98mzvFOALcXhsYtkhxGeIEDoN/Fwc7gx0S86P0zsCuyT2yQLC8xuGEO5GHhHnPQCcH4efAz4Vh7sSztZOBSbGZTsADwMnZH1c+CubV0l09+HahefNrBIgdoExBPhHTpmjCFVI/4zdJnUmJJZav0sMHxJ/ve8G9CR0FVOHpF2B3czsqTjpXuD3iSK1/Y+9CMy12J+UpIWEztySfTWdDPzSzN4DMLN8zwU5FjgnDt8P3JqnzL+A6xSea/BHM3tNOz6uQMB/SjqB0JV1f6BfnLfIzGq7EJkBDJHUC+hvZg/F2DbF7TiVkDBmxfI9gWGEhOzaGU8Wrq3YnBiuJv+xK8JzCT5bzzreTQzfA5xtZnMkXUg4e2luTDU58dXUE18hGux/x8x+I+k5wgNwpkr6D2BhTrHPAX2Bj5jZVoVeSrvmxAxhP3Zr4O0EfN/M7mxC/K5EeZuFa+s2EB49CvAscKyk/QAk9ZC0fz3L9QKWKXQF/rl86zOzdcAaScfHeZ8HnqJ5HgO+WHvllqQ98pT5J9s7fvtcnvlI2gdYaGb/A/wvcCh19wGEbqlXxETxMWBwQ4FZeBpfpaSz43t0iXE+Cnwp0e7TX9KeBW2tKzmeLFxbNxF4RNKTZraS0DPobyW9QKiyObCe5b5NqKf/J3W7pp4MXClpVmzkvYDQ4P0CMILQbtFkZvYIodqqIlajXZGn2NeBsZJepP4n9f078FJcxyGEx8GuIlS9vSTpB8CvgfK4ni+wY3fh+Xye0MvqC4S2lb3M7K+EZz3/K67rQeomJdeOeK+zzjnnGuVnFs455xrlycI551yjPFk455xrlCcL55xzjfJk4ZxzrlGeLJxzzjXKk4VzzrlG/T9kdfS0juYsrAAAAABJRU5ErkJggg==\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -259,7 +261,8 @@ "source": [ "pylab.rcParams['figure.figsize'] = (6, 4)\n", "for j in range(1, len(reductions)):\n", - " pylab.plot(distances, np.subtract(energies[j], energies[0]), color=[1.0, 0.6, 0.2], label=reductions[j])\n", + " pylab.plot(distances, np.subtract(energies[j], energies[0]), color=[1.0, 0.6, 0.2],\n", + " label=reductions[j])\n", " pylab.ylim(0, 0.4)\n", " pylab.xlabel('Interatomic distance')\n", " pylab.ylabel('Energy')\n", @@ -268,10 +271,21 @@ " pylab.show()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Frozen core\n", + "\n", + "At the start it was stated that freeze core could always be done. Here we do the computation without freezing the core, with no virtual orbitals removed, so we can compare to the same above where frozen core was used." + ] + }, { "cell_type": "code", "execution_count": 5, - "metadata": {}, + "metadata": { + "scrolled": true + }, "outputs": [ { "name": "stdout", @@ -299,16 +313,25 @@ "print(e_nofreeze)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We plot the energy with and without frozen core; the one line covers the other as they are almost identical. Plotting the energy difference we can see how small the delta is between freezing the core or not." + ] + }, { "cell_type": "code", "execution_count": 6, - "metadata": {}, + "metadata": { + "scrolled": false + }, "outputs": [ { "data": { "image/png": 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UnipFRCLTHX9dx0e7q0M6z6m5w/nBedO6HKe+vp5Zs2YBMGHCBBYvXgzABx98wJo1a8jIyOC1115j48aNLF++HOcc559/PkuXLiUrK4unn36ad999l/j4eG644Qb+8Ic/8PnPf57zzz8fgM997nOcfPLJNDc3c9NNN/HCCy8cmO7222/nkUceOaiegoICjj322A5r/fznP8/999/PySefzPe//33uuOMOfvGLXwDQ1NR0oKv7yy+/nK997WuccMIJ7NixgzPPPJP169ezYsUKHnzwQR5++OGgt+HHH3/MokWLyM/Pp6WlpdPxbr75Zr797W9z3HHHsW3bNs4991wKCgqCXk5vDLg2BGY2FPgOcDrQ1UmerwAvOueKumpMYWbXAtcC5OXlhazOHUXFFO3cytw580I2TxGRSNfZKYPTTz+djIwMAF577TVee+01jj76aABqamrYuHEja9asYeXKlcyePRvwhYvs7OwD8/jJT35CcnIyN954IwUFBRQUFHD66acD0NrayqhRo4Kus6qqisrKSk4++WQArrzySi655JIDwy+99NIDj5csWcJHH3104Hl1dTU1NTXk5+f3KAwAHHbYYeTn53c73pIlS9iwYcOB53v37qW+vp7k5OQeLa8nwhoIzGwJMLKDQbc7517oZLKFwL3OuZrO/tGbWS5wCXBKdzU45x4CHgLIz8933VcdnKK//YijC5+k9dgyYmNjQzVbEZGQ6O6bfH9LSUk58Ng5x6233sp111130Dj3338/V155JXfdddch0y9ZsoRnn32WpUuXHpjHtGnT+Ne//tXlcqdNm8bKlStZsGBBr+tta2tj2bJlJCUl9Wge3c03JiYG5/7zbynwskHnXL83QgxrGwLn3GnOuekd/HQWBgDmAj8xs23ALcBtZvaVduMcDUwCNvnHG2Jmm8KxDp2x4aNIsFbKy3b352JFRCLemWeeySOPPEJNTQ0Au3btorS0lFNPPZXnnnuO0tJSACoqKti+fTvbt2/nxhtv5Nlnnz3wDfmII46grKzsQCBobm5m3bp1hyzr1ltv5Vvf+hbFxcWA71TAww8/TGpqKunp6bz99tsAPPHEEweOFrR3xhlncP/99x943lWjyZ6IiYkhPT2djRs30tbWduD0CsBpp53Gr371q5AvsysD7pSBc+7E/Y/NbCFQ45x7oN04LxFw5MHMapxzk/qtSCAhbTQAlSU7yB45tj8XLSIS0c444wzWr1/PvHm+U65Dhw7lySefZOrUqdx5552cccYZtLW1ER8fz69+9SteffVVysvLufDCCwHIzc3l5Zdf5rnnnuPmm2+mqqqKlpYWbrnlFqZNO/jIyNlnn01JSQmnnXYazjnMjKuvvhqAxx9/nOuvv566ujomTpzIo48+2mG99913HzfeeCMzZ86kpaWFk046iQcffLBXbQja+/GPf8yZZ55JdnY2xx57LI2NjQD86le/4stf/jKPPvooLS0tzJ8//6CAEA4WeLiiP5nZRcD9QBZQCaxyzp3ZbpyF+ALBPf7nLwPXOOd2txuvJpjLDvPz893+RiJ9temDN5j04kV8eOJDHH3qpd1PICISZuvXr2fKlClelyEe6ej9N7OVzrnuGy3g7VUGi4HF3YyzsN3zszsZr9/7IEjN9jVQbKwo7O9Fi4iIhNzA6REhwqRn+04TtFUfet2riIhIpFEg6KW4hEQqSCWmptjrUkRERPpMgaAPKmMzSaov9boMERGRPlMg6IN9CVkMbS7zugwREZE+UyDog6Yh2aS1lntdhoiISJ8pEPRBW8pIMlw1jY0N3Y8sIhIFYmNjD9yIaNasWWzbts3rkli0aBHTp09nxowZHH300dxzT6c30A2ZnmyHbdu2MX369LDX1J0B1zFRJIlNHU2MOcqLd5I7brLX5YiIeC7ab3+8X3fbYSDSEYI+SMzw9VZYVbrD40pERAYu3f7YZ9u2bZx44okcc8wxHHPMMbz33nuHjLNu3boD6z9z5kw2btzY6XYJNR0h6IOhWWMAqNujzolEZIB55btQvDa08xw5Az59d5ej6PbHnW+H7OxsXn/9dZKSkti4cSOXXXYZ7XvPffDBB/nqV7/KFVdcQVNTE62traxfv77T7RJKCgR9kJ49DoDGSt3gSEQEdPvjrrZDc3MzX/nKV1i1ahWxsbF88sknh0w3b948fvjDH1JYWMjFF1/M5MmT+cc//tHldgkVBYI+SB0xkmYXC+qtUEQGmm6+yfc33f4Y7r33XnJycli9ejVtbW0dzu/yyy9n7ty5vPTSS5x99tn89re/xTnX6XYJJbUh6AOLiaUiJp24WvVWKCISrGi9/XFVVRWjRo0iJiaGJ554osN2AFu2bGHixIncfPPNXHDBBaxZs6bT7RJqOkLQR5VxI0hqUG+FIiLBitbbH99www185jOfYdGiRZx11lkHHYXY75lnnuGJJ54gPj6ekSNHctttt5GRkdHhdhk3blzQ2zwYnt3+2AuhvP3xfh/ecy7pddsY//2CkM5XRKSndPvj6NbX2x/rlEEfNSfnkKHeCkVEJMIpEPSRGzaK4VbHvupKr0sRERHpNQWCPopP83V2UVGy0+NKREREek+BoI+S/L0V7lNvhSIyAERTuzD5j1C87woEfTQsKw+AunL1Vigi3kpKSqK8vFyhIMo45ygvL+9zPwm67LCPMkb6LvtoqVLnRCLirTFjxlBYWEhZWZnXpUg/S0pKYsyYMX2ahwJBH6UMT6fOJWL71H2xiHgrPj7+wI1/RHpKpwz6yoyKmEzi69Q5kYiIRC4FghCojh9BcqMCgYiIRC4FghBoSMoirWWP12WIiIj0mgJBCDSnjCSzrYK21javSxEREekVBYIQsGEjSbJmKveqZa+IiEQmBYIQiE/zdU60tzj0t6MUERHpDwoEIZA8YiwA+8rUfbGIiEQmBYIQSMvx9VbYuHeXx5WIiIj0jgJBCGRk+44QtFapcyIREYlMCgQhkJCcQiVDiakp9roUERGRXlEgCJG9MZkk1pV4XYaIiEivKBCESG3CCFKadNmhiIhEJgWCEGlIziG1tdzrMkRERHpFgSBEWlJGkukqaW5u9roUERGRHlMgCJHY4aOIszYqSnXpoYiIRB4FghBJyPD1VlhZqs6JREQk8igQhMhQf2+FNWU7PK5ERESk5xQIQiQt29dbYXOlThmIiEjkUSAIkfTs0bQ6o62qyOtSREREekyBIERi4uKpsDRia9VboYiIRB5PAoGZXWJm68yszczyOxieZ2Y1ZvbNTqY3M/uhmX1iZuvN7ObwV929qrhMkhpKvS5DRESkx+I8Wm4BcDHw206G/xx4pYvprwLGAkc659rMLDu05fVOTUI2wxp0gyMREYk8ngQC59x6ADM7ZJiZXQhsBWq7mMWXgcudc23++Q2Ir+VNQ7LJqFvrdRkiIiI9NqDaEJjZUOA7wB3djHoYcKmZrTCzV8xschfzvNY/3oqysvDea8ANHUk6+6ivqwvrckREREItbIHAzJaYWUEHPxd0MdlC4F7nXE03s08EGpxz+cDvgEc6G9E595BzLt85l5+VldXj9eiJ2FRf50TlJeqLQEREIkvYThk4507rxWRzgc+a2U+ANKDNzBqccw+0G68Q+Iv/8WLg0d5XGjpJGbkAVJVsZ8yEIz2uRkREJHheNSrskHPuxP2PzWwhUNNBGAB4HpiPr63BycAn/VJgN4Zl+XorrKtQ50QiIhJZvLrs8CIzKwTmAS+Z2atBTPOymeX6n94NfMbM1gJ3AdeEr9rgpY8cD0DLXl1pICIikcWrqwwW4zvU39U4C9s9PzvgcSVwTliK64NhaVk0uThctQKBiIhElgF1lUGks5gYymMyiK8r8boUERGRHlEgCLGquBEkN4b38kYREZFQUyAIsbqkbIY3KxCIiEhkUSAIsZYh2WS2VeCc87oUERGRoCkQhJgblkuKNVBdtdfrUkRERIKmQBBicWm+KyMrird7XImIiEjwFAhCbEimr3OifWU7Pa5EREQkeAoEITY8awwADeqtUEREIogCQYhljhoHQEulAoGIiEQOBYIQS0pJZR/JWE2x16WIiIgETYEgDPbGZJKg3gpFRCSCKBCEwb74EaSot0IREYkgCgRhUJ+UQ2rLHq/LEBERCZoCQRi0puSQ6Spoa23zuhQREZGgKBCEgQ0fSYK1UrGnyOtSREREgqJAEAbxab6+CCpLdnhciYiISHAUCMIgZYQvENTsUW+FIiISGRQIwiAtx9d9caN6KxQRkQihQBAG6Tl5ALRW7fa4EhERkeAoEIRBfEISFQwnpladE4mISGRQIAiTythMkuoVCEREJDIoEIRJTUIWKU3qrVBERCKDAkGYNCbnkN5a7nUZIiIiQVEgCJO2lJFkuCqaGhu9LkVERKRbCgRhEpM6ihhzlJeoLwIRERn4FAjCJDFjNACVpQoEIiIy8CkQhMnQEb7OierVW6GIiEQABYIwSfN3TtRYqd4KRURk4FMgCJP0rFxaXAyuutjrUkRERLqlQBAmFhNLuaUTV6tAICIiA58CQRhVxY0gqaHU6zJERES6pUAQRnWJWQxr3uN1GSIiIt1SIAijpiE5ZKq3QhERiQAKBGHUNnQUw62W2ppqr0sRERHpkgJBGMWnjQKgvHiHx5WIiIh0TYEgjJIyxgBQrd4KRURkgFMgCKOhWb7OierLCz2uREREpGsKBGGUOWocAM2Vuz2uREREpGsKBGE0dHgG9S4B21fkdSkiIiJdUiAIJzPKYzKJryvxuhIREZEueRYIzOwSM1tnZm1mlt/B8DwzqzGzb3Yy/alm9oGZrTKzd8xsUvir7rl98SNIblRvhSIiMrB5eYSgALgYWNrJ8J8Dr3Qx/W+AK5xzs4A/At8LbXmhUZ+YRWqLeisUEZGBLc6rBTvn1gOY2SHDzOxCYCtQ29UsgOH+x6nAgGy515wykszqd3BtbViMztCIiMjA5Fkg6IyZDQW+A5wOdHi6wO8a4GUzqweqgeP6obyeGzaK5OImKveWk5aZ5XU1IiIiHQrrV1YzW2JmBR38XNDFZAuBe51zNd3M/mvA2c65McCj+E4xdFTDtWa2wsxWlJWV9Wo9+iI+LReAipJt/b5sERGRYIX1CIFz7rReTDYX+KyZ/QRIA9rMrME598D+EcwsCzjKOfe+/6Wngb93UsNDwEMA+fn5rhf19MmQEb7eCveV7oSps/t78SIiIkEZcKcMnHMn7n9sZguBmsAw4LcXSDWzw51zn+A7vbC+/6oM3nB/b4UNewdkEwcRERHA28sOLzKzQmAe8JKZvRrENC+bWa5zrgX4EvBnM1sN/A/wrfBW3DuZo3yBoK1yl8eViIiIdM7LqwwWA4u7GWdhu+dn92T6gSAxeShVpGC1xV6XIiIi0ildB9cP9sZkklCnzolERGTgUiDoBzUJI0hpUiAQEZGBS4GgH9Qn5ZDWUu51GSIiIp1SIOgHrSk5ZLq9tLS0eF2KiIhIhxQI+kHM8FzirI29Zbr0UEREBiYFgn6QkDEagMqS7R5XIiIi0jEFgn6QkunvrbCs0ONKREREOqZA0A/Sc3ydEzXtVedEIiIyMCkQ9IP0nLG0OcNVF3ldioiISIcUCPpBbFw8FZZKTI16KxQRkYFJgaCfVMZmktRQ4nUZIiIiHVIg6Cc1idkMbdrjdRkiIiIdUiDoJ03J2WS07cE553UpIiIih1Ag6C8Zh5HOPir2qB2BiIgMPAoE/SQ5dyoARZvXeFyJiIjIoRQI+knWxBkA1BSu87gSERGRQykQ9JPs0ZNocPG40g1elyIiInIIBYJ+EhMXx+64MSRXb/G6FBERkUMoEPSjyiHjyWrUDY5ERGTgUSDoR80ZkxnVVkptzT6vSxERETmIAkE/Shg5hRhz7N5c4HUpIiIiB1Eg6EcZ46YBULlDgUBERAYWBYJ+NGriDFqd0VzysdeliIiIHESBoB8lJA2hOCaHhL2bvC5FRETkIAoE/aw8eRwZ9Vu9LkNEROQgCgT9rD51EqNbd9PS3Ox1KSIiIgcoEPSz2OwjSbRmdm1Xj4UiIjJwKBD0s+FjfVcalG9d63ElIiIi/6FA0M9GTZoJQEPReo8rERER+Q8Fgn42LC2LctK69lGIAAAgAElEQVSIrdjodSkiIiIHBBUIzOwvZnaOmSlAhEBJYh6pNbrSQEREBo5g/8H/Grgc2Ghmd5vZEWGsadCrHTaRUc07cG1tXpciIiICBBkInHNLnHNXAMcA24AlZvaemX3BzOLDWeCgNOJwUq2WsuJCrysREREBetCGwMwygauAa4APgV/iCwivh6WyQWzIaN+VBiVb1nhciYiIiE+wbQgWA28DQ4DznHPnO+eeds7dBAwNZ4GDUc7EGQDU7vrI40pERER84oIc7z7n3D87GuCcyw9hPVEhc9QEaknClX3idSkiIiJA8IEg3cwubvdaFbDWOVca4poGPYuJYXfcWFL2bfa6FBERESD4QPBFYB6w/yjBKcBKYIKZ/a9z7okw1DaoVadMYEzVSq/LEBERAYJvVBgPTHHOfcY59xlgKuCAucB3wlXcYNaSMZkcyqmuqvC6FBERkaADwRjnXEnA81JgrHOuAtBt+3ohcdQUAHZv1j0NRETEe8EGgjfN7G9mdqWZXQm84H8tBagMX3mD14jxvisNqnYUeFyJiIhI8IHgRuBRYJb/ZxFwo3Ou1jk3v6cLNbNLzGydmbWZWX7A6+PNrN7MVvl/Huxk+gwze93MNvp/p/e0Bq+NHD+FZhdLS6lugywiIt7rtlGhmcUCS/z/+P8couUWABcDv+1g2Gbn3Kxupv8u8A/n3N1m9l3/84hqyxCXkMiO2FEkV+pKAxER8V63Rwicc61Am5mlhmqhzrn1zrm+fDW+AHjc//hx4MK+V9X/KpLHkVm/zesyREREgr7ssAZYa2avA7X7X3TO3RyGmiaY2YdANfA959zbHYyT45wr8j8uBnLCUEfYNaZNJrdmGY2NDSQmJnldjoiIRLFgA8Ff/D9BM7MlwMgOBt3unHuhk8mKgDznXLmZHQs8b2bTnHPVnS3HOefMzHVRx7XAtQB5eXnBr0A/iMs5kvhdrWzdup4JRx7tdTkiIhLFggoEzrnHzSwZ3z/roA71O+dO62kxzrlGoNH/eKWZbQYOB1a0G7XEzEY554rMbBS+yyA7m+dDwEMA+fn5nQYHL6TlTYMPoGLbWgUCERHxVLA3NzoPWAX83f98lpm9GOpizCzL34gRM5sITAa2dDDqi8CV/sf7L4OMOLmHzQSgsfhjjysREZFoF+xlhwuBOfj7HHDOrQIm9nahZnaRmRXi6w75JTN71T/oJGCNma0CngOu93d+hJk9HHCJ4t3A6Wa2ETjN/zziJA9Lo4RM4io2el2KiIhEuWDbEDQ756rMLPC1tt4u1Dm3GFjcwet/ppNLG51z1wQ8LgdO7e3yB5KypHGk1W71ugwREYlywR4hWGdmlwOxZjbZzO4H3gtjXVGjbvhhjG7ZSVtrr/OViIhInwUbCG4CpuFr8PcUvksCbwlXUVFlxBGkWAMluzpqKiEiItI/ggoEzrk659ztzrnZzrl8/+OGcBcXDYaNnQZA6ZY1HlciIiLRLKg2BGZ2OPBNYHzgNM65BeEpK3qMnOi7yVHt7vUeVyIiItEs2EaFzwIPAg8DreErJ/qkZ4+hmhRiyj/xuhQREYliwQaCFufcb8JaSbQyoyg+j6H71IZARES8E2yjwr+a2Q1mNsp/6+EMM8sIa2VRZN/QCeQ07fC6DBERiWLBHiHY3yvgtwJec/ShcyL5j9bMw8na+zJ7y8tIz8zyuhwREYlCwd7LYEK4C4lmyblTYBMUbV5NemaPbwEhIiLSZ12eMjCzbwc8vqTdsB+Fq6hokzXed6VB9c51HlciIiLRqrs2BP8V8PjWdsPOCnEtUSsn7wgaXTxtpUHdSFJERCTkugsE1snjjp5LL8XExbE7bjRDqjd7XYqIiESp7gKB6+RxR8+lDyqHjCezYbvXZYiISJTqrlHhUWZWje9oQLL/Mf7nSWGtLMo0pU8mt/ot6utqSR6S4nU5IiISZbo8QuCci3XODXfODXPOxfkf738e319FRoP4nCOJNceuLQVelyIiIlEo2I6JJMwyxk0HYO92BQIREel/CgQDxKjDptPmjObij70uRUREopACwQCRmDyU4phsEvZu8roUERGJQgoEA0h50jjS6rZ5XYaIiEQhBYIBpC71MEa3FtLS0uJ1KSIiEmUUCAaQmOwjSLYminds9LoUERGJMgoEA8jwMdMAKNu61uNKREQk2igQDCCjJh0FQP3u9R5XIiIi0UaBYAAZnpFDBcOJLf/E61JERCTKKBAMMCUJeQyv3eJ1GSIiEmUUCAaYmmGHMbJ5J87p3lEiItJ/FAgGGJc5mXT2sad0l9eliIhIFFEgGGCGjPZdaVCyeY3HlYiISDRRIBhgsifOAKCm8COPKxERkWiiQDDAZI2eSJ1LxO3RlQYiItJ/FAgGGIuJZXfcGFKqNntdioiIRBEFggGoKmUCWY3bvS5DRESiiALBANScMZlRlFGzr8rrUkREJEooEAxASaOmALB7k640EBGR/qFAMABljJsOQOWOdR5XIiIi0UKBYAAaNXEaLS6GltKPvS5FRESihALBABSfkERR7CgSKzd5XYqIiEQJBYIBqiJpHJl1W70uQ0REooQCwQDVOPJoxrtCykp3e12KiIhEAQWCASpj2gIAtq183eNKREQkGigQDFDjZ5xAnUukefNSr0sREZEo4EkgMLNLzGydmbWZWX7A6+PNrN7MVvl/Huxk+p+a2cdmtsbMFptZWv9V3z/iEpLYkjydkRX/9roUERGJAl4dISgALgY6+vq72Tk3y/9zfSfTvw5Md87NBD4Bbg1TnZ6qyz2OiW3bKSvZ5XUpIiIyyHkSCJxz651zG/ow/WvOuRb/02XAmNBUNrCoHYGIiPSXgdiGYIKZfWhmb5nZiUGMfzXwSriL8sKBdgRb3va6FBERGeTiwjVjM1sCjOxg0O3OuRc6mawIyHPOlZvZscDzZjbNOVfdyTJuB1qAP3RRx7XAtQB5eXk9WQXPxSUk8bHaEYiISD8IWyBwzp3Wi2kagUb/45Vmthk4HFjRflwzuwo4FzjVOee6mOdDwEMA+fn5nY43UNXlzmP6lgcoK9lFVs5or8sREZFBakCdMjCzLDOL9T+eCEwGtnQw3lnAt4HznXN1/Vtl/1I7AhER6Q9eXXZ4kZkVAvOAl8zsVf+gk4A1ZrYKeA643jlX4Z/m4YBLFB8AhgGvd3V54mCgdgQiItIfwnbKoCvOucXA4g5e/zPw506muSbg8aTwVTewxCUk8nHydHLUjkBERMJoQJ0ykI7V5c7jMPVHICIiYaRAEAHUjkBERMJNgSAC7G9H0KL7GoiISJgoEESAuIREtiRPJ2fvIVdfioiIhIQCQYSoy53nu69BcaHXpYiIyCCkQBAhMqedCsC2D5Z4XImIiAxGCgQRYvxMtSMQEZHwUSCIELHxCWpHICIiYaNAEEHUjkBERMJFgSCCZEz33S9K7QhERCTUFAgiyIQZn1I7AhERCQsFgggSG5/A5uQZakcgIiIhp0AQYer97QhK1Y5ARERCSIEgwmRM9/dHoPsaiIhICCkQRJj97Qhat6gdgYiIhI4CQYTZ345gpNoRiIhICCkQRKD63HlMaNtBafFOr0sREZFBQoEgAqkdgYiIhJoCQQSaMONT1JFI65a3vS5FREQGCQWCCOS7r4HaEYiISOgoEESoOrUjEBGREFIgiFCZ09SOQEREQkeBIEKNn/EpaklSOwIREQkJBYIIpXYEIiISSgoEEexAfwRFakcgIiJ9o0AQwTL390fwgdoRiIhI3ygQRLDx04/3tyPQfQ1ERKRv4rwuQHpvfzuCUWpHIBLxnHM0tzpa2tp8v1taaW5upqW5kZaWZlqbm2hpbqC1uRlwB6YJ/B342Gg75LXA8ehiWgJfC5hPe4YBdvBrBi7gNQscAJgdOn4g55/rweO0f2X/gE6+03Yy/qFz3j+bTubfyfjB6LTmbiQmJjFx4qReL7cvFAgiXH3uPGZsvo/Sop1kjxrrdTkig1J9Ywsle8qoLN5O7Z6dNO0tpK26CGuqxdqasbYWrK2ZmLZmzLUc+B3b1kKM8/3EuhZiXTOxrtX3mBbiXAtxtBBLK3G0kkALcbSSTAsJ1ur1aosHNsdOhP/3oSfLViCIcJnTT4XN97H9g9fIPueLXpcjElHa2hx7qmuoKC6kumwH9eU7aancTcy+3cTXlzK0sZS01j1kuQrGW+Mh07cQSzNxtBJHi8X6f8fRZnG0+n/aLI7WmDhcTBxtlkJbTDwtFk9TTBwuJh4XEw8xcbjYeIiJ9/+Ow2LjITYBi43HYuMgNoGYOP/zwG/G+7+JBn4j3f9tnI5eC5y23Tw6He/Qb7sOsMAjDoDDsf/oxYGRDn4QMMwd8qq5/fM4eLyOHDp178Zvvw7/mU0n8w9GH6aNS8no/XL7SIEgwo2ffjy1LyTRsuVtQIFAZL+6xmZKy0rZW7Kduj07aazYBdW7ia0tJrmhlGHNe8hsK2cEVWTbwR/gzcRREZPBvvgsaoZNoTJlJDGpuSSmjyYlayxpOXkMzRxLXMIQfYjKoKF9OcKpHYFEs6qaWtYte5X6wjXE7Csmoa6YoU1lpLaWk+3/Vj++/TQ2jKq4EdQOyaJ4yDSKho8iLm00yRljSM0ZR2p2HvFDR5ATE0OOFysl4hEFgkFA7QgkmmzdsZ3t/3qexK2vM71+BcdbPQBNxFERM4J9CVnUDJtK5dCRxAzPJTFjNEOz8kjPGceQzDGkxieR6vE6iAxECgSDgNoRyGDW1NzKR6uWUbHqRbKL3mRq6wYmmKPC0tmScwYp089h/Kz5JAzLYqQZI70uWCRCKRAMAmpHIINNeWUV6997mdYNrzC58l1m2R4AtiZMZu2E6xg5+wJyDj+OjBh1pSISKgoEg0BsfAJbhhzFuPJ3aG5uJj4+3uuSRHrEOcfmLRvZ8f4LDN22hOmNH3KCNVJPIltSZ1N5+FlMmHchEzJ1SkwkXBQIBotZl5P73ldZ8eZfyD/9Uq+rEelWQ1MzBSuWUr36b+SWvsWRbjOTgNKYLD7JPZ/Umecx7tgzmJaQ7HWpIlFBgWCQmDr/Msrf+wExKx8BBQIZoErKy/nkvb/iNrzKkfv+Rb7tpc0ZW5Kmsmb8Vxk99yKyJ8wiu5e9vIlI7ykQDBKx8YlsGXsxx+x4lB1bN5A34QivSxKhrc2xYcM6iv79PKk732B60xpOtGZqGMLW9OMoP/LTTJh3IZNSs70uVSTqKRAMIhPOvAH73aPseP1B8q691+tyJErVNTRS8P4SagteYmzZ20xhB1OA3bGjWT/2c2QcfT5jj1rAjLgEr0sVkQAKBIPIiDGTWZsylyN2L6ah4S6SkpK8LkmiRGtrG+//8wXcB08ytfZ95tg+ml0sW4bMZO3ESxl73GfIHTuFXK8LFZFOeRIIzOwSYCEwBZjjnFvhf308sB7Y4B91mXPu+i7m8w3gHiDLObcnjCVHjNg5XyTrzS+x/B9PMeecL3hdjgxyLS2tLFvyLGnL7+X4to+pYhjbR3yK0qlnM/G48zkiJd3rEkUkSF4dISgALgZ+28Gwzc65Wd3NwMzGAmcAO0JcW0Q78oSLKX7rNhJXPw4KBBImzS2tLPv7HxnxwS85oW0jpTaCgqO+z9RzbmCmrgoQiUieBALn3Hro/f2i/e4Fvg28EIqaBouYuDh2Tvgcs7f8is0fr+awI4/yuiQZRBqbm1n20iJGrn6AE90WimNyWHfsnUw561qy4xO9Lk9E+mAgdvM1wcw+NLO3zOzEjkYwswuAXc651d3NzMyuNbMVZrairKws5MUORJPP/DLNLpbiN37jdSkySDQ0NvHmnx9k54+O4eRVX2doTAPr5/6YnNsKmHbeTcQoDIhEvLAdITCzJdBht+K3O+c6+1ZfBOQ558rN7FjgeTOb5pyrDpjvEOA2fKcLuuWcewh4CCA/P78PN7iOHGk5Y1k1/ESmlfyV2tp7SEkZ6nVJEqHqGhpY/uLvGPfRbziFXRTGjuXjuT/niFOvZHSs2iSLDCZh+4t2zp3Wi2kagUb/45Vmthk4HAi8t+9hwARgtf+UwxjgAzOb45wr7nPhg8SQ479E2qtv8q/XHmfeRTd6XY5EmJq6ev79wq+ZtOEhTqGY7XET2HD8Axx+yuVYTKzX5YlIGAyoiG9mWUCFc67VzCYCk4EtgeM459YC2QHTbAPydZXBwSbPPZvC10eTuu4J3IU39LW9hkSJqn01rHzhAY7Y9DDzKWNr/GQ2nXAHk078HOhGQiKDmid/4WZ2kZkVAvOAl8zsVf+gk4A1ZrYKeA643jlX4Z/mYTPL96LeSGQxMRRPvoypLev5ZM0yr8uRAa6yqoo3Hv9f6n82kwWb7qIhIZPNZzzKhNv+zaST/0thQCQKmHNRcVod8LUhWLFiRfcjDhL79paS8IuprMw8h+NvftzrcmQAKq+oYPULv2DGtsfJsko2Jk0nbv53mTDnXNBRJZGIZ2YrnXNBfZkeUKcMJLSGpWfzQcapzCx/larKvaSmqZMY8Skr38PaxT/jqJ1PssCq2TDkaOpPu5XJx5yhICASpXQccJBLPfE6hlo9Ba8+7HUpMgCUlJbyxm+/Sdx9R7Gg8NeUDj2SwosWc8R33iTv2DMVBkSimI4QDHKHHT2frS9NIHvDH3Ft38B0Ljgq7SraxYbnf0J+8TMssDo+GnY8dZ++nSnTTvC6NBEZIBQIBjszKqb+N8eu/T8KVrzJ9DkLvK5I+tHOwh1sev5uZpf9mQXWQEHqSYw4+3amHnmc16WJyACjQBAFpp5xDbVrf8q+dx4CBYKosG3bFra+eDdzy59nNE2sS19AzrnfY/qkY7wuTUQGKAWCKJA8LI0VI85iVtnLlO8pIXNEjtclSZiUle+h4KnvM6/sGcbSwrrMM8k973ZmTJjpdWkiMsDphHKUyF5wA8nWxPq/P+R1KRIGDY1N/POpn2H3HcP8PX/gk8wFVF3zL2be/DQjFAZEJAg6QhAl8qbO5ZP4Ixmz+SnaWm8nJlZZcDBwzrH8ny+S/vZC5rstbEqaSuN5f2Dm9A7vCyYi0in9V4gitTOuZLzbxZp3X/K6FAmBDevX8P6Pz2Xu0s+TRjUff+oXTPrue4xWGBCRXlAgiCLTTr+SKobS9L76JIhkZXvK+OcDNzD+T/M5quHfrJr8FTK+s5ojT/+C+hEQkV7TKYMokpCcwuqR5zGr6BlKdu8gJzfP65KkBxoam/jXX+5jxsf3Md+qWDPi04y/9CfMytb7KCJ9pyMEUWbM6TeQYK188uqDXpciQXLO8f4bL7Dj7rnM3/B/VCaNYdclLzPzpj8xXGFAREJERwiizKjDZvJR4iwO2/4szc13EB8f73VJ0oVNG9dT9udvMa/hbUosiw0n/JIjTr1SpwZEJOR0hCAKtRzzBXIpZfWbf/G6FOlEZVUVbzz4dUY/eRKzGt5n1aQbGPHdNRxx2lUKAyISFgoEUWjagssoJ43E5ffT0tLidTkSoLW1jaUv/J66e49lQfHv2ZR+Ak3Xv8+s/76L2MQhXpcnIoOYAkEUio1PpHDWLcxoXsu7f/iR1+WIX8Gq91lz13xO+vDrNMelsP28Z5hxy2JSR070ujQRiQJqQxCljrrgFgo2vcZxW+5j/arTmTJrntclRa2SkhLW/+k2Tqj4C3U2hLVHfY/p59+Cxap9h4j0Hx0hiFZmjPvC76m1ISS8cB21tTVeVxR1Gpub+edT9xD363xOqvgz60ZeQNwtHzDjom8pDIhIv1MgiGLDMnMpXfBzDnPbWfnI170uJ2o45/j3239n613HMX/D/7E3KY+Sy17lqC8/xpA03XhKRLyhUwZR7siTPssH617mpJKn+fc/zmL2qRd7XdKgtnXLJ+x67lZOqFvCHstg/fE/Z8rpV+vKARHxnI4QCNOvuo+dsWMY9/bXKS3Z7XU5g1JlVRVv/Pab5Dx+ArPr3mLVuKtJ/fZqppzxRYUBERkQFAiEhOShcPHDpLlqtj32Jdpa27wuadBoaWnlrcUP+S4jLPodW9LmUXfNe8z6wr3EJw/3ujwRkQMUCASAsdPmUXDETcypf4d3/3Kf1+UMCh++/xYf3XUiJ6/+Fs1xQ9l+3jNM/9oLpI853OvSREQOoUAgBxx96f/j48SZHF1wF1s+KfC6nIi1Y8c2lt5zGUe9fAF5rTtZd8wd5N26gnHHnul1aSIinVIgkAMsNo7sKx/DWQwNT3+RxqZGr0uKKPtqa/nH779Hxu+PY96+V1kz9nKSvrGaaeffgsWq/a6IDGwKBHKQjNzD2DHvTqa2fsyyx27zupyI0Nraxtt/W8Tenx7DqTvvZ8ewWVR/YSmzrvk1ScMyvC5PRCQo+toih5h25hdZ/fHf+dSuR1i97NMcddxpXpc0IDnnWL70FZKX3smJresojB3LltMeZ+q8C70uTUSkxxQIpEOHf+G3lN87h4y/f4XKI98jLU3fdAOtWfkeDa/ewdymZVRYGgVHfZ9p592ExSV4XZqISK/olIF0KHl4BrXn/JrRrph1j9yIc87rkgaETzas452ffpbpL57N1KY1rD78JoZ/u4DpF31DYUBEIpoCgXRqYv4ZfDjuKj5V/TL/eulxr8vx1M7CHbz5y6sZ98eTmF37Jmvz/pu4r63hqMvvJC55mNfliYj0mUXTN7/8/Hy3YsUKr8uIKK3NjWz/8fGkN5dQd/VSRo+LrlvxlpXvYe2zP2JO0R9IppF12ecx/rP/x/Cc8V6XJiLSLTNb6ZzLD2ZcHSGQLsXGJ5Jy+aMkWSMNj11AwYf/8rqkflFdU8M/HltI7H2zWFD8e7alzaXyqqXMvPEJhQERGZQUCKRbORNnsuvM35Puqpj0/Hm8sehOWlpavS4rLMr27OEfjy2k5p6jOHXbvexJmcSuS15i+tdeJHPCTK/LExEJG50ykKDVlO9mx6NfYGrNMlYkzGbk/zzCmLF5XpcVEhs3bqDw7/dy7J4XGG51bEqcRtyCWxk/51zdfEhEIlZPThkoEEjPOMeaxfdwxJofU+OG8PFxP+b4s/4Li8B/ms45Vi57k8alv2RO3VJiaOOj9PmMOO1rjJp+ktfliYj0mQJBJxQIQqd44wc0Pv0FxrVs4620i5n1xftIHRYZre0bmpr592tPMezDh5jVupZaktg4+mImnvsNho+a5HV5IiIho0DQCQWC0Gptqmft419j1q6n2Gx51J//ENOPnud1WZ0q37uX1X97kMM2L2Icuym1LIqnXMWRZ99IwtB0r8sTEQk5BYJOKBCEx6b3FpP++i0Mbavl3Yk3c+IVtxMfF+t1WQA0Nbey9oN3qFrxLEeXPk+67WNrwuE0zbmBw0+5Qp0JicigpkDQCQWC8KmtKGL7I1czteY9Vibkk/0/v2fs2PGe1FK1r5aC916mef1LHL73bXJtD23OWJ/6KVIXfI0xR52qhoIiEhUUCDqhQBBmzrH2+Z8xefXd1LpkVo27kuFHnMThM08gddiQsC66sKiITe8uJmHT35lRv5xhVk8DCWwePoeYI89hwvEXk5Q2Mqw1iIgMNAoEnVAg6B8lmz+k9unrmNi0AYA6l8gncUdQMeIYEid+ivFHnUxuTnafrkxoa3N8/HEBRcsXk1G4hOnNBcRbK3stlZ0jTiblqPOZMPtsYhJTQrVaIiIRZ8AHAjO7BFgITAHmOOdW+F8fD6wHNvhHXeacu76TedwE3Ai0Ai85577d3XIVCPpXfXkhO1b/k/pN75C6ZyV5jZuINUerMzbFjKco9Whs3HGMmj6fww6bTGyM0dTSRnlVNVVlu6kp3019ZREt1SW07Ssjtr6MhIZyhjSVk9a6h/EUAVAYl8ee0aeSM/siRk09EWLU35aICERGIJgCtAG/Bb7ZLhD8zTk3vZvp5wO3A+c45xrNLNs5V9rdchUIvNVaX83OtUup2vA2SUXLyatbRzKNABS6LFosjgxXxXCr63D6WpKpjk2nNj6DhsRM2kbPZtzxnyV1zJT+XA0RkYjRk0AQF+5iOuKcWw/05ZDxl4G7nXON/vl1GwbEe7HJw309/805FwDX0kTJphWUFryFFS4HoCp5BAzNJm54DknpIxmakUvqiNEkpY8kJT4ZnQAQEQkPTwJBNyaY2YdANfA959zbHYxzOHCimf0QaMB3lOHfHc3MzK4FrgXIyxsc3ewOFhaXQM6Rx5Nz5PFelyIiEvXCFgjMbAnQUbPu251zL3QyWRGQ55wrN7NjgefNbJpzrrrdeHFABnAcMBt4xswmug7OfzjnHgIeAt8pg16ujoiIyKAWtkDgnDutF9M0AvtPA6w0s834jga0P/FfCPzFHwCWm1kbMAIo61vVIiIi0WlANcc2sywzi/U/nghMBrZ0MOrzwHz/eIcDCcCe/qpTRERksPEkEJjZRWZWCMwDXjKzV/2DTgLWmNkq4DngeudchX+ah81sf0vJR4CJZlYA/Am4sqPTBSIiIhIcdUwkIiIySPXkssMBdcpAREREvKFAICIiIgoEIiIiokAgIiIiKBCIiIgICgQiIiKCAoGIiIigQCAiIiJEWcdEZlYGbO9ilBFEVxfIWt/BK5rWFbS+g1k0rSuEfn3HOeeyghkxqgJBd8xsRbA9Og0GWt/BK5rWFbS+g1k0rSt4u746ZSAiIiIKBCIiIqJA0N5DXhfQz7S+g1c0rStofQezaFpX8HB91YZAREREdIRAREREojQQmNlZZrbBzDaZ2Xc7GH6VmZWZ2Sr/zzVe1BkKZvaImZWaWUEnw83M7vNvizVmdkx/1xhKQazvKWZWFfDefr+/awwVMxtrZv80s4/MbJ2ZfbWDcQbN+xvk+g6m9zfJzJab2Wr/+t7RwTiJZva0//1938zG93+lfRfkug6az+X9zCzWzD40s791MKz/31vnXFT9wP9v7/xjtarrOP56J6Ag5E2wRKiuIq0pM9JiJEX0i1U2oEmNhiC2tZaWspa6atVyrg3/W4gAAAd0SURBVGRs5bI/zLREA38hFjH8QQm6EFC85r0wXBKxRbLRsBCyLOTTH9/v1cPj81weLs+9D8+579d2dj/nnM/5ns/nfJ77vZ/7Pd/n++EE4M/AWcAQ4FngnAqdBcBPm21rg/ydCpwPbKlx/tPAg4CAycCmZtvcx/5OA1Y1284G+ToaOD/LI4A/Vfkslya+dfpbpvgKGJ7lwcAmYHKFzuXAzVmeA9zTbLv70NfS9MsFn74OLKv2mW1GbAfiCMEkYHtE7IiI/wJ3AzObbFOfERGPAy/2oDITuCMSG4E2SaP7x7rGU4e/pSEidkdER5b3A9uAMRVqpYlvnf6WhhyzA3l3cN4qJ33NBJZkeTnwMUnqJxMbRp2+lgpJY4GLgFtrqPR7bAdiQjAG+GthfxfVO5WL8xDrcklv7x/TmkK9z6NMfCAPTT4o6dxmG9MI8nDie0n/WRUpZXx78BdKFN88pPxHYA+wJiJqxjciDgL7gJH9a2VjqMNXKFe/fCNwDXCoxvl+j+1ATAjq4bdAe0ScB6zh9SzNtD4dpKU83wPcBPy6yfYcM5KGA/cDCyPipWbb09ccwd9SxTciXo2IicBYYJKkCc22qa+ow9fS9MuSPgPsiYinm21LkYGYEPwNKGaWY/Ox14iIvRHxSt69Fbign2xrBkd8HmUiIl7qHpqMiNXAYEmjmmxWr5E0mPTHcWlErKiiUqr4HsnfssW3m4j4J7AW+GTFqdfiK2kQcAqwt3+tayy1fC1ZvzwFmCFpJ+m19Ucl/apCp99jOxATgqeA8ZLOlDSENFljZVGh4h3rDNK7yrKyEpifZ6NPBvZFxO5mG9VXSDq9+z2cpEmk34GW7ECzH7cB2yLiRzXUShPfevwtWXxPk9SW5aHAJ4DnKtRWApdmeTbwaORZaK1EPb6WqV+OiG9GxNiIaCf9DXo0Ii6pUOv32A7qy8aPRyLioKSvAg+TvnHwi4jYKuk6YHNErASulDQDOEiaoLagaQYfI5LuIs28HiVpF/A90oQdIuJmYDVpJvp24GXgsuZY2hjq8Hc28BVJB4F/A3NasQPNTAHmAV353SvAt4B3QCnjW4+/ZYrvaGCJpBNIic29EbGqoq+6DbhT0nZSXzWneeYeE/X4Wpp+uRbNjq1XKjTGGGPMgHxlYIwxxpgKnBAYY4wxxgmBMcYYY5wQGGOMMQYnBMYYY4zBCYExxzWSDtShs1DSsAbec5akcxrY3hPHcO2B/PMMSct70GuTdHlv72OMcUJgTBlYCBxVQpC/712LWUDDEoKIuLABbbwQEbN7UGkjVYczxvQSJwTGtACSpklal4u6PCdpaV598ErgDGCtpLVZd7qkDZI6JN2X1/5H0k5JiyR1AJ+T9CVJT+VCQPdLGibpQtIqcIuVas6PkzRR0sZcVOYBSW/J7a2T9GNJmyVtk/R+SSskPS/p+oLtBwrytZK68j1vqOLnmdn2roo22iVtyfK5kp7M9nVKGg/cAIzLxxZLGi7p9/kZdEmaWWhnm6SfS9oq6ZG8Mh6Szpb0u2xbh6Rx+fjV+Tl1Svp+QwNrzPFEX9dX9ubNW+834ED+OY1U7WwsKZHfAHwwn9sJjMryKOBx4OS8fy3w3YLeNYW2Rxbk64GvZfl2YHbhXCfw4SxfB9yY5XXAoixfBbxAWnHuRFJVxZEVPnwKeAIYlvdPreLvSmB+lq8oXNsObMnyTcDcLA8BhhbP5+ODgDcXnsl2QFnvIDAxn7sXuCTLm4DPZvkk0qjLdOCWfO2bgFXA1GZ/Lrx564ttwC1dbEwL82RE7ALIS/e2A3+o0JlMGu5fn5f0H0JKHrq5pyBPyP+FtwHDSct5H4akU4C2iHgsH1oC3FdQ6a4D0gVsjVwnQdIOUmGWYh2BjwO/jIiXASLixSo+TgEuzvKdwKIqOhuAbyvVk18REc/rjWXiBfxA0lRSedkxwNvyub9ERPfSx08D7ZJGAGMi4oFs23+yH9NJScEzWX84MJ6UdBlTKpwQGNM6vFKQX6X6769IteS/UKONfxXk24FZEfGspAWkUYje2nSowr5DNeyrhx7XU4+IZZI2ARcBqyV9GdhRoTYXOA24ICL+p1RV7qQKmyE9x6E93E7ADyPiZ0dhvzEtiecQGNP67AdGZHkjMEXS2QCSTpb0rhrXjQB2K5UUnlutvYjYB/xD0ofyuXnAY/SONcBl3d+IkHRqFZ31vF7EZW6V80g6C9gRET8BfgOcx+HPAFKp2D05GfgI8M6eDIuI/cAuSbPyPU7Mdj4MfLEwD2OMpLfW5a0xLYYTAmNan1uAhyStjYi/k6rA3SWpkzS8/u4a132H9N58PYeXmr0buFrSM3li3aWkSYadwETSPIKjJiIeIr1i2JxfeXyjitpVwBWSukjD/NX4PLAltzEBuCMi9pJek2yRtBhYCrwvtzOfN5YNrsY8UkW9TtJch9Mj4hFgGbAht7WcwxMPY0qDqx0aY4wxxiMExhhjjHFCYIwxxhicEBhjjDEGJwTGGGOMwQmBMcYYY3BCYIwxxhicEBhjjDEGJwTGGGOMAf4Pv5bCTsnsJIkAAAAASUVORK5CYII=\n", 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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -338,6 +361,16 @@ "pylab.plot(distances, np.subtract(energies[0], e_nofreeze), label='Freeze Core: False')\n", "pylab.show()" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true, + "scrolled": true + }, + "outputs": [], + "source": [] } ], "metadata": { @@ -356,7 +389,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/community/aqua/chemistry/energyplot.ipynb b/community/aqua/chemistry/energyplot.ipynb index 9e3042680..60a1eaa56 100644 --- a/community/aqua/chemistry/energyplot.ipynb +++ b/community/aqua/chemistry/energyplot.ipynb @@ -10,10 +10,9 @@ "\n", "This notebook demonstrates using Qiskit Chemistry to plot graphs of the ground state energy and dipole moments of a Lithium Hydride (LiH) molecule over a range of inter-atomic distances.\n", "\n", - "This notebook populates a dictionary, which is a progammatic representation of an input file, in order to drive the Qiskit Chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here where we alter the molecule supplied to the driver in each loop.\n", + "This notebook populates a dictionary, which is a progammatic representation of an input file, in order to drive the Qiskit Chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here where we alter the molecule supplied to the driver in each loop. The main goal of this notebook is to show this technique and to keep things simpler and quicker a classical algorithm, the ExactEigensolver, is used here.\n", " \n", - "This notebook has been written to use the PYSCF chemistry driver. See the PYSCF chemistry driver readme if you need to install the external PySCF library that this driver requires.\n", - " " + "This notebook has been written to use the PYSCF chemistry driver. " ] }, { @@ -47,8 +46,9 @@ "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", "# Note: In order to allow this to run reasonably quickly it takes advantage\n", "# of the ability to freeze core orbitals and remove unoccupied virtual\n", - "# orbitals to reduce the size of the problem. The result without this\n", - "# will be more accurate but it takes rather longer to run.\n", + "# orbitals to reduce the size of the problem. Freeze core can always\n", + "# be used, but be very cautious when removing unoccupied orbitals.\n", + "# \n", "qiskit_chemistry_dict = {\n", " 'driver': {'name': 'PYSCF'},\n", " 'PYSCF': {'atom': '', 'basis': 'sto3g'},\n", @@ -88,24 +88,12 @@ "outputs": [ { "data": { + "image/png": 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zmx3cK69S2E+dyUHcMLwHRSVlPPHhqrBLERE5YgqaeqjXUZmcc0xbnpixml3FJWGXIyJyRBQ09dSEET0oLC7lmZka7llE4puCpp4a2LE5p/ZqzWMfrKS4pCzsckREDpuCph67cURPtu7ez6RZ68IuRUTksClo6rETu7Xk+C4t+Ou7KykpKw+7HBGRw6KgqcfMjO+M6Mn6nUVM+Wx92OWIiBwWBU09N7xPNv3aNePhd1dQVq7vPIlI/FHQ1HNmxo0jerAyfw+vL9wUdjkiIjWmoIkD5/ZvR/fWTfjztOWoJwcRiTcKmjiQnGRcP7wHCzcUMn1p+GPniIjUhIImTowe3IH2Wek8NE0Do4lIfFHQxIm0lCTGn9adT1fv4JNV28MuR0Sk2hQ0ceTyEzrTqkkaf9ZZjYjEEQVNHGmclsx1p3Tj3aX5zM8rCLscEZFqUdDEmauGdSEzPYWHpuusRkTig4ImzjRLT+Xrw7ryn4WbWL5lV9jliIgckoImDl17clfSU5J54G2d1YhI/aegiUOtmjbi2pO78srcDczL2xl2OSIiVVLQxKnrh/egZZM07py6SL0FiEi9pqCJU83SU7llZC9mrtzOO4u3hF2OiEilFDRxbNyQznRv3YQ7py6iVOPViEg9paCJY6nJSfzwnL6syN/DRI3CKSL1lIImzp19zFHkdGnBH95cxu59pWGXIyLyJQqaOGdm/OSr/di6ex+PvLcy7HJERL5EQZMAjuvcgq8ObMej761kc2Fx2OWIiHyBgiZB3H52X0rLy/n9G0vDLkVE5AsUNAmic6sMrhralednr2PJJnVNIyL1h4Imgdx0Rk+aNErhrtcWhV2KiMh/KWgSSIsmaXxnRE+mL8nnw+Vbwy5HRARQ0CScr5/UlQ7NG/PbVxdRXq6uaUQkfAqaBJOemswPz+nD5xsLeemz9WGXIyKioElEFwxsz4AOWdz3xhKKS8rCLkdEGrhqBY2ZTTazr5qZgikOJCUZPzmvHxsKivn7h6vCLkdEGrjqBsdDwBXAMjO728z6xLAmqQXDerTizL5teHjaCrbt3hd2OSLSgFUraNz9LXf/GnAcsBp4y8xmmNm1ZpYaywLl8P34vL7sLSnjwXc0EqeIhKfal8LMrBVwDfBN4DPgj0SC582YVCZHrGebTC4/oRPPzFzDqq17wi5HRBqo6t6jeQl4H8gALnD3C919orvfBDSt6Zua2UQzyw2m1WaWW0m7W81soZktMLNnzSw9WP5+1PYbzGxKsNzM7AEzW25m88zsuJrWlmhuGdmLtJQk7nltcdiliEgDlVLNdg+4+7SDrXD3nJq+qbtffmDezO4DCiq2MbMOwM3A0e5eZGaTgLHAE+5+alS7F4GXg5fnAr2C6UTg4eC/DVabzHS+fVoP/vDWUmat3k5O15ZhlyQiDUx1L521MLOLK0xnmlmbI3lzMzNgDPBsJU1SgMZmlkLkbGpDhe2bAWcAU4JFo4CnPGIm0NzM2h1JjYngW6d1o01mI+6cugh3fYlTROpWdYPmG8DfgK8F06PA7cCHZnbVEbz/qcBmd19WcYW7rwfuBdYCG4ECd3+jQrPRwNvuXhi87gBEDzWZFyz7EjMbb2azzGxWfn7+ERxC/ZeRlsL3z+rNnLU7eW3BprDLEZEGprpBkwr0c/dL3P0S4GjAiVyWuv1gG5jZW8G9lYrTqKhm46jkbMbMWhA5Q+kGtAeamNmVFZpVuv2huPsj7p7j7jnZ2dmHs4u4cunxnehzVCb3/Gcx+0vLwy5HRBqQ6gZNR3ffHPV6C9DJ3bcDJQfbwN1Hunv/g0wvAwSXwy4GJlbyniOBVe6e7+4lwGTgpAMrzaw1MAR4NWqb9UCn6LqDZQ1ecpLxo/P6smbbXp6ZuSbsckSkAalu0Ew3s3+b2dfN7OtEbr5PN7MmwM7DfO+RwGJ3z6tk/VpgqJllBPdyzgSi+7+/FPi3u0cPKfkKcHXw9NlQIpfbNh5mfQlneO9sTu7ZigfeWUZB0UH/PhARqXXVDZobgceBwcH0FHCju+9x9xGH+d5jqXDZy8zam9lUAHf/GHgBmAPMD2p9pKrtganASmA5kftIEw6ztoRkFumapqCohIem6UucIlI37FBPIZlZMvDWEQRKvZeTk+OzZs0Ku4w684Pn5/Jy7nr+fdOp9GmbGXY5IhKnzGx2db7icsgzGncvA8rNLKtWKpPQ/eS8fmSmp3L7i/Mo05g1IhJj1b10thuYb2aPBd+8f8DMHohlYRI7LZuk8YsLjiZ33U6emLE67HJEJMFVt2eAycEkCeLCQe2Z8tl67n19CWcdfRSdWmaEXZKIJKjq9t78JDAJmOnuTx6YYluaxJKZ8ZuLBpBk8JOX5qvHABGJmep2qnkBkAv8J3g92MxeiWVhEnsdmjfmh+f05f1lW5k8R183EpHYqO49ml8S+XLkTgB3zwW6x6gmqUNXDe3C8V1a8OtXP2erBkgTkRiobtCUuHvFHpbVj0kCSEoy7rlkAHv3lfHLVxaGXY6IJKDqBs1CM7sCSDazXmb2IDAjhnVJHerZJpPvnNGTf8/byFufbz70BiIiNVDdoLkJOAbYR+Tb+IXALbEqSure9af3oM9RmfzflAXsKlb3NCJSe6r71Nled/+pu58Q9Hj80wp9jEmcS0tJ4p5LB7J5VzH3/EejcYpI7anuU2e9zewRM3vDzN45MMW6OKlbgzs159qTuvHMzLV8smp72OWISIKo7qWz54HPgP8DbouaJMH84OzedGzRmB+9OI/ikrKwyxGRBFDdoCl194fd/RN3n31gimllEoqMtBTuvGgAK7fu4cF3vjTwqYhIjVU3aP5lZhPMrJ2ZtTwwxbQyCc1pvbO55LiO/PXdlXy+ofDQG4iIVKG6QfN1IpfKZgCzg6nh9KvfAP3s/H40z0jlR5PnUVqmr0yJyOGr7lNn3Q4yqWeABNY8I41fXngM8/IKePzD1WGXIyJxrMqgMbMfRs1fVmHdnbEqSuqHrw5ox8h+bbjvzSWs2bYn7HJEJE4d6oxmbNT8jyusO6eWa5F6xsz49ej+pCQl8ePJ6uFZRA7PoYLGKpk/2GtJQO2yGvOjc/syY8U2np+VF3Y5IhKHDhU0Xsn8wV5LgrpiSGeGdGvJb179nC271CGEiNTMoYJmkJkVmtkuYGAwf+D1gDqoT+qBpCTjrosHUFxarh6eRaTGqgwad09292bununuKcH8gdepdVWkhK9HdlO+e2Yvps7fxOsLN4VdjojEkep+j0aE8ad1p1+7ZvxsygK2aZA0EakmBY1UW2pyEvdeNpCdRSXcOmku5eW6TScih6agkRo5pn0Wv7zgGN5bms+fpi0PuxwRiQMKGqmxcUM6cdGxHfjDW0v5cPnWsMsRkXpOQSM1Zmb89qL+9Mxuynef+4xNBXrkWUQqp6CRw5KRlsLDVx7H3v1l3PTsHErU8aaIVEJBI4etZ5tM7rp4AJ+u3sG9ry8JuxwRqacUNHJERg3uwNdO7Mxf31vJm59vDrscEamHFDRyxH52/tH079CM70/KZd32vWGXIyL1jIJGjlh6ajIPXXE8Dkz4xxyKS8rCLklE6hEFjdSKzq0yuO+yQcxfX8BvXv087HJEpB5R0EitOeuYtow/rTvPzFzLy7nrwy5HROoJBY3UqtvO7sMJXVvw48nzWb5lV9jliEg9oKCRWpWanMSD446jcWoyNzwzh737S8MuSURCpqCRWtc2K50/jj2W5fm7+b+XFmgIaJEGTkEjMXFKr9Z898xeTP5sPc99ui7sckQkRKEEjZlNNLPcYFptZrmVtLvVzBaa2QIze9bM0oPl70dtv8HMpgTLh5tZQdS6n9flcckX3XRGL07t1ZpfvLKQBesLwi5HREISStC4++XuPtjdBwMvApMrtjGzDsDNQI679weSgbHB9qdGbf9Rhe3fP7DO3e+I+cFIpZKTjPsvH0zLjDRu/OccCotLwi5JREIQ6qUzMzNgDPBsJU1SgMZmlgJkABsqbN8MOAOYEss65fC1atqIP11xLOt3FHHb83N1v0akAQr7Hs2pwGZ3X1ZxhbuvB+4F1gIbgQJ3f6NCs9HA2+5eGLVsmJnNNbPXzOyYyt7YzMab2Swzm5Wfn3/kRyKVyunakh+d25fXF27msQ9WhV2OiNSxmAWNmb0V3FupOI2KajaOSs5mzKwFMAroBrQHmpjZlRWaVdx+DtDF3QcBD1LFmY67P+LuOe6ek52dXfMDlBr5xindOPuYo7j7tcUaLE2kgYlZ0Lj7SHfvf5DpZYDgctjFwMRKdjESWOXu+e5eQuQ+zEkHVppZa2AI8GrUexa6++5gfiqQGrSTkJkZ/+/SQfTIbsr4p2YxP08PB4g0FGFeOhsJLHb3vErWrwWGmllGcC/nTGBR1PpLgX+7+3+HdzSztkFbzGwIkePbFpPqpcayGqfy5HVDaJ6RxjWPf8LK/N1hlyQidSDMoBlLhctmZtbezKYCuPvHwAtELofNJ1LrI1VtTyR8FpjZXOABYKzr7nO90jYrnWe+eSIAVz32iYaBFmkATL+HIScnx2fNmhV2GQ3KgvUFjH1kJu2y0nn++mE0z0gLuyQRqSEzm+3uOYdqF/ZTZ9JA9e+QxSNXH8+abXu57olP1SeaSAJT0EhoTurRmgfGDSZ33U4m/GMOJWXlYZckIjGgoJFQndO/Hb+9aADTl+Tzg+fnUl6uS7kidWVTQXGdjIiroJHQjRvSmdvO7sPLuRu449+fq/cAkTrw2vyNnH3/e9z7+pKYv1dKzN9BpBomDO/B9j37eeyDVbRqksZNZ/YKuySRhLRnXym/+tdCJs3KY2DHLK44sXPM31NBI/WCmfHT8/qxY89+7ntzKS2bpvG1E7uEXZZIQvls7Q5umZjLuu17+c6Innx3ZC9Sk2N/YUtBI/VGUpJxz6UD2VlUwv9NWUCLjDTOG9Au7LJE4l5pWTkPTV/BH99eRttm6Tw3fhhDurWss/dX0Ei9kpqcxJ+vOI6rHvuYW57LJatxKif3VC9CIodr3fa93DIxl9lrdjB6cHvuGN2fZumpdVqDHgaQeqdxWjKPff0Eumc3YfxTs5iXtzPskkTijrszeU4e5/7xfZZu2sUfxw7m/rHH1nnIgIJG6qmsjEi/aC2apHHN45+yQv2iiVRbQVEJNz+Xy/cmzaVfu0ymfvdURg3uEFo9Chqpt45qls7T3ziRJIOrH/uEjQVFYZckUu/NXLmNc+9/j9fmb+S2s/vw3PhhdGqZEWpNChqp17q1bsIT1w6hoKiEqx/7hB179oddkki9tL+0nHv+s5hxj86kUWoyL95wEjeO6ElykoVdmoJG6r/+HbJ49Ooc1mzfy2V//Yi8HXvDLkmkXlmRv5tLHp7Bw9NXcHlOJ/590ykM6tQ87LL+S0EjcWFYj1Y8ee0QNhcWc/FDM1i4QQOnibg7//h4DV994H3W7djLX648nrsvGUiTRvXrgWIFjcSNYT1a8eINJ5GcZFz+15m8vyw/7JJEQrNm2x6ufOxjfvrSAnK6tOT1W07jnP5twy7roBQ0Eld6H5XJSxNOpmOLxlz7+Ke8OLuyAVpFElNpWTl/eXcFZ9//HnPXFfDr0f156rohHNUsPezSKlW/zq9EqqFtVjqTrh/G9U/P5vvPz2VTYTEThvcgGMVbJGEtWF/A7S/OY+GGQr5y9FH8elR/2mbV34A5QEEjcalZeipPXDuEH74wl9+9voT1O4u448JjSKmDfptE6lrR/jL+8NZSHvtgFS2bpPHw147jnP5t4+aPKwWNxK20lCR+P2Yw7Zo35uHpK9hSWMwD444lI03/rCVxfLBsKz95aT5rt+9l3JBO/OicfmRl1P23+4+E/o+UuJaUZNx+Tl/aZ6Xzi1cWMu7Rj3ns6zm0btoo7NJEjsiOPfv5zauLeHFOHt1aN+G58UMZ2r1V2GUdFgWNJISrhnXlqGbp3PzcZ1zy8AyevHYIXVs3CbsskRpzd16Zu4E7/vU5BUUl3DiiBzed0Yv01OSwSztsuqAtCeOsY9ryz28NpbCohIsfnsFna3eEXZJIjazfWcR1T3zKd5/LpWPLDP510yncdnbfuA4ZUNBIgjmucwtevOEkmjRKZtyjM3nr881hlySQOskrAAASMklEQVRySGXlzuMfruIrv3+Xj1dt5+fnH83kG06iX7tmYZdWKxQ0knC6Zzdl8g0n0/uoTMY/PYt/fLwm7JJEKrVgfQGXPDyDX/3rc4Z0a8kbt57Gdad0qxd9lNUW3aORhJSd2Yjnxg/lxn/M4acvLWDjzmK+f1bvuHkcVBLfpoJifvf6EiZ/lkfLjDT+OHYwFw5qn5D/RhU0krAy0lJ49OocfvbyAv40bTmrtu7hzosGxN2joZJY9u4v5a/vruSR91ZSVu58+7QeTBjRI5QByeqKgkYSWkpyEndeNIAurZpw7+tLmL1mB/deNohTeml4aKlb5eXOi3Py+N3rS9iyax/nD2zH7ef0DX2smLqgoJGEZ2Zcf3oPTu7RmlsmfsaVj33MNSd15Ufnxv/TPBIfZqzYym9fXcTCDYUM7tSch688juO7tAy7rDqjoJEGY0DHLF69+VTufm0xT8xYzfvL8rn/8mMZ0DEr7NIkQa3M382dUxfz1qLNdGjemAfGHcsFA9sl5H2Yqpi7h11D6HJycnzWrFlhlyF16P1l+dz2/Dy27t7HLSN7cf3pPdRPmtSaHXv288e3l/HMzDWkpyYzYUQPrju5W8KdQZvZbHfPOWQ7BY2CpqEq2FvCz15ewCtzN3Bs5+b8Ycxg9SYgR2R/aTlPfbSaB95exu59pYwd0plbR/YmOzMxu0RS0NSAgqZhezl3PT+bsoCSMudn5x/NuCGdGtylDTky7s7rCzdz92uLWL1tL6f1zuan5/WjT9vMsEuLqeoGje7RSIM3anAHhnRryW3Pz+MnL83nrUWbufuSAbTJrP/jfEi43J23F23hT9OWk7tuJ73aNOWJa09geJ82YZdWr+iMBp3RSER5ufPUR6u567XFZKQlc9fFA+vt0LgSrrJy59X5G3lo2nIWb9pFxxaNmTC8J2NyOjaoe326dFYDChqJtnzLLm6ZmMuC9YVcenxHfnHB0WQm8JfppPr2l5bz0md5PDx9Bau37aVnm6ZMGN6DCwa1J7UBBcwBunQmcph6tslk8g0n8+A7y/jztOV8tGIb9142iGE94nMsEDlyRfvLeO7TtTzy3ko2FhQzoEMWf7nyOM46ui1JCdQnWazojAad0UjlZq/Zwfcm5bJm215G9Mnm+2f1oX8Hfe+moSgsLuHpj9bw2Aer2L5nP0O6teTGET05rVdrPTBCHFw6M7OJQJ/gZXNgp7sPPki7W4FvAg7MB65192IzOxP4HZEeqHcD17j7cjNrBDwFHA9sAy5399VV1aKgkaoU7S/jiRmr+cu7KygoKuG8AW353ld607NNYj9R1JBt272Pv3+4iqdmrGHXvlKG98nmxhE9OaFrw/k2f3XU+6D5QhFm9wEF7n5HheUdgA+Ao929yMwmAVPd/QkzWwqMcvdFZjYBGOLu1wTzA939ejMbC1zk7pdX9f4KGqmOwuIS/vb+Kh57fyVFJWWMPrYDt5zZm86tEr+vqoZiY0ERj7y3kmc/Wcu+0nLO7d+WCcN76iy2EnFzj8Yi559jgDMqaZICNDazEiAD2BAsd+DAqEBZUctHAb8M5l8A/mRm5vUhUSWuNUtP5Xtf6c01J3XlL++u4MkZq3kldwNjTujETWf0pF1W47BLlMPg7sxes4PnPl3Hy7nrKXcYPbgDNwzvQc82TcMuLyGEfkZjZqcBv68sFc3su8BvgSLgDXf/WrD8VGBKsLwQGOruhWa2ADjH3fOCdiuAE919a4X9jgfGA3Tu3Pn4NWs0OJbUzJbCYv40bTnPfrIWM+PKE7swYUQPWjdNzG+BJ5r8XfuYPCePSbPWsSJ/D03Skrn4uI6MP617g+hRuTbUi0tnZvYWcLAvIvzU3V8O2jwMLHf3+w6yfQvgReByYCfwPPCCuz9jZpOBe9z9YzO7Dejj7t+sbtBE06UzORLrtu/lwXeW8cLsPNJTk7n25K6MP7WHxr2ph0rLynl3aT4TP13HO4u3UFru5HRpwZicTnx1YDuaNAr9Ik9cqReXztx9ZFXrzSwFuJjIjfuDGQmscvf8oP1k4CQzex0Y5O4fB+0mAv8J5tcDnYC8YP9ZRB4KEImJTi0z+H+XDuL603vwh7eW8edpK3jqozWMP7U7157Sjab65RW61Vv3MGnWOl6YnceWXfto3TSNb5zSjctyOunyWB0I+/+AkcDiA2cfB7EWGGpmGUQukZ0JzAJ2AFlm1tvdlwJfARYF27wCfB34CLgUeEf3Z6QudM9uyoPjjmXC8B7c98ZS7ntzKY/PWM31p3fnkuM60kqX1OpU0f4yps7fyKRZ6/h41XaSDEb0acOYEzpxRt82DfILlmEJ9R6NmT0BzHT3v0Qtaw/8zd3PC17/isils1LgM+Cb7r7PzC4C7gDKiQTPde6+0szSgaeBY4HtwFh3X1lVHbp0JrGQu24n972xhPeXbSUlyTi1V2tGH9uBrxx9FBlpYf+Nl5jcnXl5BUyctY5/5W5g175SurbK4LKcTlx6fEeOaqb+62pTvbhHEy8UNBJLizYWMiV3Pa/kbmBjQTEZacmcfUxbRg1uzyk9WzeovrFiobSsnDlrdzJtyRbeXrSZpZt3k56axHn92zHmhE6c2K2lvlwZIwqaGlDQSF0oL3c+Wb2dl3PX8+q8jRQWl9K6aRrnD2zPqMHtGdypuX4hVtOWwmKmL83n3SX5vLcsn13FpaQkGcd3acEFg9pz4eD2NFP/dDGnoKkBBY3UtX2lZUxbnM/Luet5e/EW9peW07VVBhcO7sDowe3pnq0b1NFKy8rJXbeT6UvymbZkCws3FALQJrMRI/q0YXifbE7u1VrhUscUNDWgoJEwFRSV8PqCTUzJXc9HK7fhDoM6ZjFqcAfOH9SuwY6Lk79rH+8uzWf6ki28v2wrBUUlJCcZx3duwel9shnRpw392mXqLDBECpoaUNBIfbGpoJhX5q5nymcb+HxjIWbQq01TBnZszqCOWQzo2Jx+7TJplJJYY8+XlzvrdxaxaGMh8/IKeHdpPvPXFwCQndmI4b2zGd6nDaf0ak1WY5211BcKmhpQ0Eh9tGzzLqbO30Tuuh3Myytg2579AKQmG33bNmNgxywGdWzOgI5Z9GrTNG4eKigoKmHJpl0s3lTIoo27WLKpkCWbdrFnfxkASQbHdW7B8D6RcDm6XTN1xV9PKWhqQEEj9Z175C/++XkFzM0rYF7eTubnFbBrXykAjVOTOaZ9s8iZT6csBnTIomurJqH+gi4pK2fV1j0s2ljI4k27IuGysZANBcX/bZPVOJW+bTPp164Zfdpm0rdtJr2PytQ39OOEgqYGFDQSj8rLndXb9jAvr4C5QfAs2FBAcUk5AJnpKXRo3pisxqk0z0glq/EXp2aNU2mekfbFZekpXzozcnf27i+jsLiEXcWlFBYF/y0uobDC613FpewqLmFTQTEr8/ewvyxSS0qS0bNNU/q2zaRP22b0bZdJv7bNOKpZI91jiWP1ogsaEYmdpCSje3ZTumc3ZfSxHYDI01nLtuxmfl4B89bvZHPhPgr2lrB6614KikooKCqhqKSsyv1mNkqhWeNUkpIIgqOUsvKq/yBNS06iWeMUMtMjYdUuK53T+2TTLwiV7q2bkpYSH5f2pPYpaEQSSEpyEv3aNaNfu2aMOaHTQdvsKy2joKiEwiB4CopK2Ln3f/MFRSUU7C2h3J1mjVNplp5KZnokfDLTUw76Oj01sR5OkNqloBFpYBqlJNMmM7nBPjYtdU/nsiIiElMKGhERiSkFjYiIxJSCRkREYkpBIyIiMaWgERGRmFLQiIhITCloREQkptTXGWBm+cCasOs4DK2BrWEXUcd0zImvoR0vxO8xd3H37EM1UtDEMTObVZ0O7RKJjjnxNbTjhcQ/Zl06ExGRmFLQiIhITClo4tsjYRcQAh1z4mtoxwsJfsy6RyMiIjGlMxoREYkpBY2IiMSUgqaeM7O/m9kWM1tQyfpRZjbPzHLNbJaZnVLXNda2Qx1zVLsTzKzUzC6tq9pipRqf83AzKwg+51wz+3ld11jbqvM5B8eda2YLzezduqyvtlXjM74t6vNdYGZlZtayruuMBd2jqefM7DRgN/CUu/c/yPqmwB53dzMbCExy9751XWdtOtQxB22SgTeBYuDv7v5CHZZY66rxOQ8HfuDu59d1bbFSjWNuDswAznH3tWbWxt231HWdtaU6/66j2l4A3OruZ9RJcTGmM5p6zt3fA7ZXsX63/++vhSZA3P/lcKhjDtwEvAjE7S+eaNU85oRSjWO+Apjs7muD9nH9WdfwMx4HPBvDcuqUgiYBmNlFZrYYeBW4Lux6Ys3MOgAXAQ+HXUsdG2Zmc83sNTM7Juxi6kBvoIWZTTez2WZ2ddgF1QUzywDOIfKHVEJICbsAOXLu/hLwUnBq/mtgZMglxdr9wO3uXm5mYddSV+YQ6Vdqt5mdB0wBeoVcU6ylAMcDZwKNgY/MbKa7Lw23rJi7APjQ3RPmDFdBk0Dc/T0z625mrd09Hjvoq64c4LkgZFoD55lZqbtPCbes2HH3wqj5qWb2UAP4nPOAbe6+B9hjZu8Bg4BED5qxJNBlM9Cls7hnZj0t+I1rZscBjYBt4VYVW+7ezd27untX4AVgQiKHDICZtY36nIcQ+X83oT9n4GXgFDNLCS4nnQgsCrmmmDKzLOB0IseeMHRGU8+Z2bPAcKC1meUBvwBSAdz9L8AlwNVmVgIUAZdHPRwQl6pxzAmnGsd8KXCDmZUS+ZzHJvrn7O6LzOw/wDygHPibu1f5yHt9Vs1/1xcBbwRncQlDjzeLiEhM6dKZiIjElIJGRERiSkEjIiIxpaAREZGYUtCIiEhMKWgkIZnZ7mq0uSX4fkZtvedoMzu6Fvc34wi23R38t72ZVdrhqJk1N7MJh/s+ItWhoJGG7BagRkET9BpdmdFArQWNu59UC/vY4O5VDaPQHFDQSEwpaCShBeOZTDezF8xssZn9wyJuBtoD08xsWtD2LDP7yMzmmNnzwRAMmNlqM7vHzOYAl5nZt8zs06CDyxfNLMPMTgIuBH4XjCfSw8wGm9lMi4wX9JKZtQj2N93M/mCR8YMWWWRcnclmtszMfhNV++6o+dvNbH7wnncf5Di7BbXPr7CPrgfGPzGzY8zsk6C+eWbWC7gb6BEs+52ZNTWzt4OfwXwzGxW1n0Vm9qhFxoZ5w8waB+t6mtlbQW1zzKxHsPy24Oc0z8x+VasfrMQXd9ekKeEmYHfw3+FAAdCRyB9WHwGnBOtWA62D+dbAe0CT4PXtwM+j2v0wat+touZ/A9wUzD8BXBq1bh5wejB/B3B/MD8duCeY/y6wAWhHpPugvAP7jzqGc4mMy5IRvG55kON9Bbg6mL8xatuuwIJg/kHga8F8GpGOKv+7PlieAjSL+pksByxoVwoMDtZNAq4M5j8GLgrm04mcJZ4FPBJsmwT8Gzgt7H8XmsKZ1AWNNASfuHsegJnlEvml+UGFNkOJXPb6MOhSLI1IKB0wMWq+f3DW0BxoCrxe8Q2DPquau/uBUSGfBJ6PavJK8N/5wEJ33xhstxLoxBf7MRsJPO7uewH84L36nkykOyKAp4F7DtLmI+CnZtaRyDgvy+zLvV8bcKdFegIvBzoARwXrVrl7bjA/G+hqZplAB4/0II67FwfHcRaRsPksaN+USG/T7x2kLklwChppCPZFzZdx8H/3Brzp7uMq2Ud031NPAKPdfa6ZXUPkrOlwayqvUF95JfVVR5X9Sbn7P83sY+CrwFQz+zawskKzrwHZwPHuXmJmq4mcpUTXDJGfY+Mq3s6Au9z9rzWoXxKU7tFIQ7YLyAzmZwInm1lPADNrYma9K9kuE9hoZqlEfjF/aX/uXgDsMLNTg3VXAYc75v2bwLUHnpCzg48j/yGR7uWpUNN/mVl3YKW7P0Ckd+CBfPFnAJAFbAlCZgTQparC3H0XkGdmo4P3aBTU+TpwXdR9rg5m1qZaRysJR0EjDdkjwH/MbJq75wPXAM+a2Twil5n6VrLdz4jcl/gQWBy1/DngNjP7LLgh/nUiDwfMAwYTuU9TY+7+HyKX2mYFl/5+cJBm3wVuNLP5RC53HcwYYEGwj/5Exq7fRuRy4QIz+x3wDyAn2M/VFY6vMlcBNwfHOQNo6+5vAP8kMljZfCLDOWRWsQ9JYOq9WUREYkpnNCIiElMKGhERiSkFjYiIxJSCRkREYkpBIyIiMaWgERGRmFLQiIhITP1/AI/OIczCUVQAAAAASUVORK5CYII=\n", "text/plain": [ - "Text(0.5, 1.0, 'LiH Ground State Energy')" + "" ] }, - "execution_count": 2, "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, "output_type": "display_data" } ], @@ -113,7 +101,7 @@ "pylab.plot(distances, energies)\n", "pylab.xlabel('Interatomic distance')\n", "pylab.ylabel('Energy')\n", - "pylab.title('LiH Ground State Energy')" + "pylab.title('LiH Ground State Energy');" ] }, { @@ -123,24 +111,12 @@ "outputs": [ { "data": { + "image/png": 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\n", "text/plain": [ - "Text(0.5, 1.0, 'LiH Dipole Moment')" + "" ] }, - "execution_count": 3, "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, "output_type": "display_data" } ], @@ -148,7 +124,7 @@ "pylab.plot(distances, dipoles)\n", "pylab.xlabel('Interatomic distance')\n", "pylab.ylabel('Moment a.u')\n", - "pylab.title('LiH Dipole Moment')" + "pylab.title('LiH Dipole Moment');" ] }, { @@ -161,9 +137,9 @@ ], "metadata": { "kernelspec": { - "display_name": "Quantum py37", + "display_name": "Python 3", "language": "python", - "name": "quantum-dev-37" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -175,7 +151,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/community/aqua/chemistry/h2_basis_sets.ipynb b/community/aqua/chemistry/h2_basis_sets.ipynb index 10a097850..110b79e08 100644 --- a/community/aqua/chemistry/h2_basis_sets.ipynb +++ b/community/aqua/chemistry/h2_basis_sets.ipynb @@ -17,7 +17,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "metadata": {}, "outputs": [ { @@ -54,7 +54,7 @@ " 'algorithm': {'name': 'ExactEigensolver'},\n", "}\n", "# PSI4 config here is a multi-line string that we update using format()\n", - "# To do so all other curly brackets from PSI4 config must be doubled\n", + "# To do so all other curly brackets that are required in the PSI4 config must be doubled\n", "psi4_cfg = \"\"\"\n", "molecule h2 {{\n", " 0 1\n", @@ -92,24 +92,14 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 3, "metadata": {}, "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 2, - "metadata": {}, - "output_type": "execute_result" - }, { "data": { "image/png": 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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -122,7 +112,7 @@ "pylab.xlabel('Interatomic distance')\n", "pylab.ylabel('Energy')\n", "pylab.title('H2 Ground State Energy in different basis sets')\n", - "pylab.legend(loc='upper right')" + "pylab.legend(loc='upper right');" ] }, { @@ -149,7 +139,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/community/aqua/chemistry/h2_excited_states.ipynb b/community/aqua/chemistry/h2_excited_states.ipynb index 7bd30e4c6..eee73d724 100644 --- a/community/aqua/chemistry/h2_excited_states.ipynb +++ b/community/aqua/chemistry/h2_excited_states.ipynb @@ -12,7 +12,7 @@ "\n", "This notebook populates a dictionary, that is a progammatic representation of an input file, in order to drive the Qiskit Chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here where we alter the molecule supplied to the driver in each loop.\n", "\n", - "This notebook has been written to use the PYSCF chemistry driver. See the PYSCF chemistry driver readme if you need to install the external PySCF library that this driver requires." + "This notebook has been written to use the PYSCF chemistry driver." ] }, { @@ -85,14 +85,14 @@ "cell_type": "code", "execution_count": 2, "metadata": { - "scrolled": true + "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -111,6 +111,13 @@ "pylab.show()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The above plot has all the states. Below we plot them individually. With each plot having its own y-axis scale the energy change over distance change is more evident, particularly the ground state curve which is very flattened above by the scale." + ] + }, { "cell_type": "code", "execution_count": 3, @@ -120,7 +127,7 @@ "data": { "image/png": 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\n", 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\n", 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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -170,6 +177,13 @@ " pylab.legend(loc='upper right')\n", " pylab.show()" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { @@ -188,7 +202,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/community/aqua/chemistry/h2_mappings.ipynb b/community/aqua/chemistry/h2_mappings.ipynb index 6a3a3ad6c..2c21b217e 100644 --- a/community/aqua/chemistry/h2_mappings.ipynb +++ b/community/aqua/chemistry/h2_mappings.ipynb @@ -12,19 +12,57 @@ "\n", "This notebook populates a dictionary, that is a progammatic representation of an input file, in order to drive the Qiskit Chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here where we alter the molecule supplied to the driver in each loop.\n", "\n", - "This notebook has been written to use the PYSCF chemistry driver. See the PYSCF chemistry driver readme if you need to install the external PySCF library that this driver requires." + "This notebook has been written to use the PYSCF chemistry driver." ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Processing step __\b\b 0" + "Processing step 20 --- complete\n", + "Distances: [0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.675 0.7 0.725 0.75 0.775\n", + " 0.8 0.825 0.85 0.875 0.9 0.925 0.95 0.975 1. ]\n", + "Energies: [[[-1.0550072 -1.07448988 -1.0924703 -1.10560872 -1.11617561\n", + " -1.12411068 -1.12989951 -1.13377934 -1.13618819 -1.13718219\n", + " -1.13693919 -1.11393966 -1.13361768 -1.10702409 -1.10251126\n", + " -1.09745433 -1.11822278 -1.08595587 -1.09165606 -1.10587795\n", + " -1.1011269 ]\n", + " [-1.05515979 -1.07591366 -1.09262991 -1.10591805 -1.11628601\n", + " -1.12416092 -1.12990478 -1.13382622 -1.13618945 -1.13722138\n", + " -1.13711707 -1.13604436 -1.13414767 -1.13155121 -1.12836188\n", + " -1.12467175 -1.12056028 -1.11609624 -1.11133942 -1.10634211\n", + " -1.10115033]]\n", + "\n", + " [[-1.05515979 -1.07591366 -1.09262991 -1.10591805 -1.11628601\n", + " -1.12416092 -1.12990478 -1.13382622 -1.13618945 -1.13720975\n", + " -1.1370938 -1.13602101 -1.13411334 -1.13150719 -1.12831842\n", + " -1.1246409 -1.12051863 -1.11605095 -1.11129941 -1.10631446\n", + " -1.10113394]\n", + " [-1.05515979 -1.07591366 -1.09262991 -1.10591805 -1.11628601\n", + " -1.12416092 -1.12990478 -1.13382622 -1.13618945 -1.13722138\n", + " -1.13711707 -1.13604436 -1.13414767 -1.13155121 -1.12836188\n", + " -1.12467175 -1.12056028 -1.11609624 -1.11133942 -1.10634211\n", + " -1.10115033]]\n", + "\n", + " [[-1.05455947 -1.07579394 -1.09245568 -1.1057838 -1.11595615\n", + " -1.12392843 -1.12915081 -1.13217365 -1.13590692 -1.1371984\n", + " -1.13674928 -1.13514718 -1.13336169 -1.13069373 -1.12796665\n", + " -1.1244492 -1.12029028 -1.11595806 -1.11131729 -1.10626288\n", + " -1.10100739]\n", + " [-1.05515979 -1.07591366 -1.09262991 -1.10591805 -1.11628601\n", + " -1.12416092 -1.12990478 -1.13382622 -1.13618945 -1.13722138\n", + " -1.13711707 -1.13604436 -1.13414767 -1.13155121 -1.12836188\n", + " -1.12467175 -1.12056028 -1.11609624 -1.11133942 -1.10634211\n", + " -1.10115033]]]\n", + "Hartree-Fock energies: [-1.04299627 -1.06306214 -1.07905074 -1.0915705 -1.10112824 -1.10814999\n", + " -1.11299655 -1.11597526 -1.11734903 -1.11734327 -1.11615145 -1.11393966\n", + " -1.1108504 -1.10700581 -1.10251055 -1.09745432 -1.09191404 -1.08595587\n", + " -1.07963693 -1.07300676 -1.06610865]\n" ] } ], @@ -84,9 +122,20 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "pylab.rcParams['figure.figsize'] = (12, 8)\n", "pylab.ylim(-1.14, -1.04)\n", @@ -103,9 +152,70 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", 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\n", 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\n", 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "pylab.rcParams['figure.figsize'] = (6, 4)\n", "for k in range(len(mappings)):\n", @@ -153,7 +263,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.7" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/community/aqua/chemistry/h2_particle_hole.ipynb b/community/aqua/chemistry/h2_particle_hole.ipynb index b130f635a..942387945 100644 --- a/community/aqua/chemistry/h2_particle_hole.ipynb +++ b/community/aqua/chemistry/h2_particle_hole.ipynb @@ -15,16 +15,47 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": { - "scrolled": true + "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Processing step 9" + "Processing step 20 --- complete\n", + "Distances: [0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.675 0.7 0.725 0.75 0.775\n", + " 0.8 0.825 0.85 0.875 0.9 0.925 0.95 0.975 1. ]\n", + "Energies: [[[-1.05515973 -1.07591359 -1.09262986 -1.105918 -1.11628597\n", + " -1.12416088 -1.12990475 -1.1338262 -1.13618942 -1.13722134\n", + " -1.13711707 -1.13604434 -1.13414766 -1.1315512 -1.12836187\n", + " -1.12467173 -1.12056027 -1.11609624 -1.11133942 -1.10634211\n", + " -1.10115033]\n", + " [-1.05515974 -1.07591361 -1.09262987 -1.10591802 -1.11628599\n", + " -1.12416089 -1.12990476 -1.1338262 -1.13618944 -1.13722136\n", + " -1.13711707 -1.13604436 -1.13414767 -1.13155121 -1.12836188\n", + " -1.12467175 -1.12056028 -1.11609624 -1.11133943 -1.10634212\n", + " -1.10115034]]\n", + "\n", + " [[-1.05515973 -1.07591359 -1.09262987 -1.105918 -1.11628598\n", + " -1.12416087 -1.12990474 -1.13382619 -1.13618943 -1.13722134\n", + " -1.13711704 -1.13604435 -1.13414766 -1.13155119 -1.12836186\n", + " -1.12467175 -1.12056028 -1.11609624 -1.11133942 -1.1063421\n", + " -1.10115033]\n", + " [-1.05515974 -1.07591361 -1.09262987 -1.10591802 -1.11628599\n", + " -1.12416089 -1.12990476 -1.1338262 -1.13618944 -1.13722136\n", + " -1.13711707 -1.13604436 -1.13414767 -1.13155121 -1.12836188\n", + " -1.12467175 -1.12056028 -1.11609624 -1.11133943 -1.10634212\n", + " -1.10115034]]]\n", + "Hartree-Fock energies: [-1.04299622 -1.0630621 -1.0790507 -1.09157046 -1.10112822 -1.10814997\n", + " -1.11299652 -1.11597525 -1.11734902 -1.11734325 -1.11615145 -1.11393966\n", + " -1.1108504 -1.10700581 -1.10251056 -1.09745432 -1.09191405 -1.08595588\n", + " -1.07963694 -1.07300677 -1.06610866]\n", + "VQE num evaluations: [[45. 51. 51. 51. 43. 54. 50. 47. 51. 46. 42. 57. 49. 53. 49. 55. 50. 46.\n", + " 51. 56. 55.]\n", + " [49. 49. 50. 51. 47. 52. 47. 48. 52. 46. 52. 56. 45. 49. 48. 52. 47. 49.\n", + " 54. 58. 60.]]\n" ] } ], @@ -92,9 +123,20 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "pylab.plot(distances, hf_energies, label='Hartree-Fock')\n", "for j in range(len(algorithms)):\n", @@ -103,14 +145,25 @@ "pylab.xlabel('Interatomic distance')\n", "pylab.ylabel('Energy')\n", "pylab.title('H2 Ground State Energy')\n", - "pylab.legend(loc='upper right')" + "pylab.legend(loc='upper right');" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "pylab.plot(distances, np.subtract(hf_energies, energies[0][1]), label='Hartree-Fock')\n", "for k in range(len(transformations)):\n", @@ -118,27 +171,40 @@ "pylab.xlabel('Interatomic distance')\n", "pylab.ylabel('Energy')\n", "pylab.title('Energy difference from ExactEigensolver')\n", - "pylab.legend(loc='upper left')" + "pylab.legend(loc='upper left');" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "for k in range(len(transformations)):\n", " pylab.plot(distances, eval_counts[k], '-o', label='VQE + ' + transformations[k])\n", "pylab.xlabel('Interatomic distance')\n", "pylab.ylabel('Evaluations')\n", "pylab.title('VQE number of evaluations')\n", - "pylab.legend(loc='upper left')" + "pylab.legend(loc='upper left');" ] }, { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "scrolled": true + }, "outputs": [], "source": [] } @@ -159,7 +225,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.7" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/community/aqua/chemistry/h2_qpe.ipynb b/community/aqua/chemistry/h2_qpe.ipynb index ff7148d0c..fc7e2b1e0 100644 --- a/community/aqua/chemistry/h2_qpe.ipynb +++ b/community/aqua/chemistry/h2_qpe.ipynb @@ -8,7 +8,7 @@ "\n", "This notebook demonstrates using Qiskit Chemistry to compute ground state energy of the Hydrogen (H2) molecule using QPE (Quantum Phase Estimation) algorithm. Let's first look at how to carry out such computation programmatically. Afterwards, we will illustrate how the computation can also be carried out using json configuration dictionaries.\n", "\n", - "This notebook has been written to use the PYSCF chemistry driver. See the PYSCF chemistry driver readme if you need to install the external PySCF library that this driver requires." + "This notebook has been written to use the PYSCF chemistry driver." ] }, { @@ -25,6 +25,8 @@ "outputs": [], "source": [ "from collections import OrderedDict\n", + "import time\n", + "\n", "from qiskit import BasicAer\n", "from qiskit.transpiler import PassManager\n", "from qiskit.aqua import AquaError\n", @@ -34,24 +36,14 @@ "from qiskit.aqua.components.iqfts import Standard\n", "from qiskit.chemistry import FermionicOperator\n", "from qiskit.chemistry import QiskitChemistry\n", - "from qiskit.chemistry.drivers import get_driver_class\n", "from qiskit.chemistry.aqua_extensions.components.initial_states import HartreeFock\n", - "import time\n", + "from qiskit.chemistry.drivers import PySCFDriver, UnitsType\n", "\n", "distance = 0.735\n", - "pyscf_cfg = OrderedDict([\n", - " ('atom', 'H .0 .0 .0; H .0 .0 {}'.format(distance)),\n", - " ('unit', 'Angstrom'),\n", - " ('charge', 0),\n", - " ('spin', 0),\n", - " ('basis', 'sto3g')\n", - "])\n", - "try:\n", - " driver = get_driver_class('PYSCF').init_from_input(pyscf_cfg)\n", - "except ModuleNotFoundError:\n", - " raise AquaError('PYSCF driver does not appear to be installed')\n", - "\n", + "driver = PySCFDriver(atom='H .0 .0 .0; H .0 .0 {}'.format(distance),\n", + " unit=UnitsType.ANGSTROM, charge=0, spin=0, basis='sto3g')\n", "molecule = driver.run()\n", + "\n", "qubit_mapping = 'parity'\n", "fer_op = FermionicOperator(h1=molecule.one_body_integrals, h2=molecule.two_body_integrals)\n", "qubit_op = fer_op.mapping(map_type=qubit_mapping,threshold=1e-10).two_qubit_reduced_operator(2)" @@ -73,7 +65,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "The exact ground state energy is: -1.8572750302023824\n" + "The exact ground state energy is: -1.8572750302023817\n" ] } ], @@ -100,7 +92,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "The ground state energy as computed by QPE is: -1.857136875325887\n" + "The ground state energy as computed by QPE is: -1.8571368753258866\n" ] } ], @@ -180,9 +172,19 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The groundtruth total ground state energy is -1.857275030202381.\n", + "The total ground state energy as computed by QPE is -1.857136875325887.\n", + "In comparison, the Hartree-Fock ground state energy is -1.8369679912029842.\n" + ] + } + ], "source": [ "result_qpe = QiskitChemistry().run(qiskit_chemistry_qpe_dict, backend=backend)\n", "result_ees = QiskitChemistry().run(qiskit_chemistry_ees_dict)\n", @@ -197,6 +199,13 @@ " result_ees['hf_energy'] - result_ees['nuclear_repulsion_energy']\n", "))" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { @@ -215,7 +224,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.7" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/community/aqua/chemistry/h2_swaprz.ipynb b/community/aqua/chemistry/h2_swaprz.ipynb index da46c7db6..3bb2e2fc6 100644 --- a/community/aqua/chemistry/h2_swaprz.ipynb +++ b/community/aqua/chemistry/h2_swaprz.ipynb @@ -6,7 +6,7 @@ "source": [ "## _*H2 energy plot computed using SWAPRZ variational form*_\n", "\n", - "This notebook demonstrates using Qiskit Chemistry to plot graphs of the ground state energy of the Hydrogen (H2) molecule over a range of inter-atomic distances using VQE and SWAPRZ. It is compared to the same energies as computed by the ExactEigensolver\n", + "This notebook demonstrates using Qiskit Chemistry to plot graphs of the ground state energy of the Hydrogen (H2) molecule over a range of inter-atomic distances using VQE and SWAPRZ. It is compared to the same energies as computed by the ExactEigensolver. `SWAPRZ` is a particle preserving variational form and should be used in conjunction with operator `jordan_wigner mapping` and `HarteeFock` initial state.\n", "\n", "This notebook populates a dictionary, that is a progammatic representation of an input file, in order to drive the Qiskit Chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here where we alter the molecule supplied to the driver in each loop.\n", "\n", @@ -15,7 +15,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": { "scrolled": true }, @@ -24,7 +24,23 @@ "name": "stdout", "output_type": "stream", "text": [ - "Processing step __\b\b 0" + "Processing step 20 --- complete\n", + "Distances: [0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.675 0.7 0.725 0.75 0.775\n", + " 0.8 0.825 0.85 0.875 0.9 0.925 0.95 0.975 1. ]\n", + "Energies: [[-1.05515972 -1.07591361 -1.09262986 -1.10591801 -1.11628597 -1.12416089\n", + " -1.12990475 -1.1338262 -1.13618944 -1.13722135 -1.13711706 -1.13604435\n", + " -1.13414767 -1.1315512 -1.12836187 -1.12467172 -1.12056028 -1.11609624\n", + " -1.11133942 -1.10634211 -1.10115033]\n", + " [-1.05515974 -1.07591361 -1.09262987 -1.10591802 -1.11628599 -1.12416089\n", + " -1.12990476 -1.1338262 -1.13618944 -1.13722136 -1.13711707 -1.13604436\n", + " -1.13414767 -1.13155121 -1.12836188 -1.12467175 -1.12056028 -1.11609624\n", + " -1.11133943 -1.10634212 -1.10115034]]\n", + "Hartree-Fock energies: [-1.04299622 -1.0630621 -1.0790507 -1.09157046 -1.10112822 -1.10814997\n", + " -1.11299652 -1.11597525 -1.11734902 -1.11734325 -1.11615145 -1.11393966\n", + " -1.1108504 -1.10700581 -1.10251056 -1.09745432 -1.09191405 -1.08595588\n", + " -1.07963694 -1.07300677 -1.06610866]\n", + "VQE num evaluations: [ 737. 710. 734. 793. 919. 804. 695. 731. 619. 727. 637. 743.\n", + " 708. 782. 701. 1032. 1051. 1119. 1141. 995. 884.]\n" ] } ], @@ -86,9 +102,20 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "pylab.plot(distances, hf_energies, label='Hartree-Fock')\n", "for j in range(len(algorithms)):\n", @@ -96,14 +123,25 @@ "pylab.xlabel('Interatomic distance')\n", "pylab.ylabel('Energy')\n", "pylab.title('H2 Ground State Energy')\n", - "pylab.legend(loc='upper right')" + "pylab.legend(loc='upper right');" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "pylab.plot(distances, np.subtract(hf_energies, energies[1]), label='Hartree-Fock')\n", "pylab.plot(distances, np.subtract(energies[0], energies[1]), label='VQE')\n", @@ -111,20 +149,31 @@ "pylab.ylabel('Energy')\n", "pylab.yscale('log')\n", "pylab.title('Energy difference from ExactEigensolver')\n", - "pylab.legend(loc='center right')" + "pylab.legend(loc='center right');" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "pylab.plot(distances, eval_counts, '-o', color=[0.8500, 0.3250, 0.0980], label='VQE')\n", "pylab.xlabel('Interatomic distance')\n", "pylab.ylabel('Evaluations')\n", "pylab.title('VQE number of evaluations')\n", - "pylab.legend(loc='upper left')" + "pylab.legend(loc='upper left');" ] }, { @@ -151,7 +200,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.7" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/community/aqua/chemistry/h2_uccsd.ipynb b/community/aqua/chemistry/h2_uccsd.ipynb index dbde1be85..881f9d0de 100644 --- a/community/aqua/chemistry/h2_uccsd.ipynb +++ b/community/aqua/chemistry/h2_uccsd.ipynb @@ -6,7 +6,7 @@ "source": [ "## _*H2 dissociation curve using VQE with UCCSD*_\n", "\n", - "This notebook demonstrates using Qiskit Chemistry to plot graphs of the ground state energy of the Hydrogen (H2) molecule over a range of inter-atomic distances using VQE and UCCSD. It is compared to the same energies as computed by the ExactEigensolver\n", + "This notebook demonstrates using Qiskit Chemistry to plot graphs of the ground state energy of the Hydrogen (H2) molecule over a range of inter-atomic distances using VQE and UCCSD. It is compared to the same energies as computed by the ExactEigensolver. `UCCSD` should be used together with `HartreeFock` initial state.\n", "\n", "This notebook populates a dictionary, that is a progammatic representation of an input file, in order to drive the Qiskit Chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here where we alter the molecule supplied to the driver in each loop.\n", "\n", @@ -27,9 +27,9 @@ "Processing step 20 --- complete\n", "Distances: [0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.675 0.7 0.725 0.75 0.775\n", " 0.8 0.825 0.85 0.875 0.9 0.925 0.95 0.975 1. ]\n", - "Energies: [[-1.05515973 -1.0759136 -1.09262986 -1.105918 -1.11628597 -1.12416089\n", - " -1.12990475 -1.1338262 -1.13618942 -1.13722134 -1.13711706 -1.13604434\n", - " -1.13414766 -1.1315512 -1.12836186 -1.12467174 -1.12056028 -1.11609624\n", + "Energies: [[-1.05515973 -1.07591359 -1.09262986 -1.105918 -1.11628597 -1.12416088\n", + " -1.12990475 -1.1338262 -1.13618942 -1.13722134 -1.13711707 -1.13604434\n", + " -1.13414766 -1.1315512 -1.12836187 -1.12467173 -1.12056027 -1.11609624\n", " -1.11133942 -1.10634211 -1.10115033]\n", " [-1.05515974 -1.07591361 -1.09262987 -1.10591802 -1.11628599 -1.12416089\n", " -1.12990476 -1.1338262 -1.13618944 -1.13722136 -1.13711707 -1.13604436\n", @@ -39,7 +39,7 @@ " -1.11299652 -1.11597525 -1.11734902 -1.11734325 -1.11615145 -1.11393966\n", " -1.1108504 -1.10700581 -1.10251056 -1.09745432 -1.09191405 -1.08595588\n", " -1.07963694 -1.07300677 -1.06610866]\n", - "VQE num evaluations: [45. 52. 50. 50. 43. 50. 47. 47. 51. 46. 42. 57. 45. 47. 44. 54. 53. 49.\n", + "VQE num evaluations: [45. 51. 51. 51. 43. 54. 50. 47. 51. 46. 42. 57. 49. 53. 49. 55. 50. 46.\n", " 51. 56. 55.]\n" ] } @@ -106,24 +106,12 @@ "outputs": [ { "data": { + "image/png": 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yhCVLltyzbcmSJTzxxBP06dOH8ePHEx4ezpEjR9i3bx/ffvttWrn008kHBQXRoEGDvA6/SNAJJRf8vd05FXmHI5eirB2KphV6AwYMYP369SQmGhe6O3v2LJcvX+bkyZNpMwIDODs7M3PmTL788ktrhlsk6ckhc6Fn40pMWn2UlYcu4eVRytrhaFre2TAerhwx7zkrNoYen2W6u0yZMvj6+rJhwwb69u3LkiVLGDRoEEePHqV58+b3lK1VqxZ3797l9u3bwL3TyQPs2bMny9mHtYejayi54FrMns71y7P28GWSUwzWDkfTCr30zV5LlixhyJAhOTru/iYvnUwsQ9dQcsnf250NIVfYceI6HeuVt3Y4mpY3sqhJWFLfvn159dVXOXjwIHFxcTRv3pxDhw6xffv2e8qdPn2asmXLUqqUbjnIS7qGkkuPeJanlLO9nopF0/JAiRIl6NixI88++2xa7WTYsGHs3LmTrVu3AsZVHV955RUmT55szVCLJJ1QcsnBzobeXpXYHHqF2IRka4ejaYXekCFDOHz4cFpCKVasGGvWrGHKlCnUrVuXcuXK4efnx7Bhw9KOSV1DPvWxe/dua4VfqOnp683gwLmb9P9uD1MHNmFAcw+zn1/T8oOCMn39qlWreO211/j777+pVq2atcMpcPT09XkgOupCpvuaVS1NtbLOrDx0MQ8j0jQtI/369eP06dM6mViBTig5MGVpTwat6IkyZHwnl4jQr6k7u0/d4EpUfB5Hp2malj/ohJIDjdy8uGQLwaHLMi3Tz9sdpfRULJqmFV06oeRA5xbjcFCKgNAFmZapUa443lVL6bu9NE0rsnRCyYESLpXoYFuKTbFnSU7KvEnL39udY1diCIuIzsPoNE3T8gedUHKoR42e3LAV9h3+OdMyvb0qY2cjupaiaVqRpBNKDrVrPpoSBsWG439kWqZMcQce8XRjddAlUgxF53ZsTcsrtra294wn+ewz843YDwoKIiAgIO11ZtPeX758mQEDBpjtug/j7NmzNGrUyKoxZERPvZJDTsVK08mxAlsTrvB+fBSOTq4ZlvP39mBr2DX2nLpB2zrl8jhKTSvcihUrRlBQkEXOHRQURGBgID179kzbNnjwYGbOnPmfssuXL7dIDHktOTkZOzvzpQFdQ3kAPev4E2sj7DzwXaZlOtcvj4ujnW720rQ8EhUVhaenJ+Hh4YBxJP3cuXMBGD16ND4+PjRs2JBJkyalHbN//37atGlDkyZN8PX1JSoqiokTJ6aNqF+6dGmm10tfO4iLi2PQoEE0aNAAf39/WrZsSerg6c2bN9O6dWuaNWvGwIEDiY2NBaB69epMmjSJZs2a0bhxY44dOwbAP//8k1YT8vb2JiYmBqUUb775Jo0aNaJx48YZxtWqVSuOHj2a9vqRRx4hMDCQO3fu8Oyzz+Lr64u3tzerV68GjDWvPn360KlTJzp37vzQn3tGrFJDEZGBwAdAfcBXKZXh8HUR6Q58C9gCPyqlPjNtF+BjYCCQAnynlJpu6bhbNh1JmZDvWX96PZ39xmdYxsnelp6NK7Eu+DIf92tEMQdbS4elaXnu832fc+zmMbOes16Zerzt+3aWZe7evUvTpk3TXr/zzjtptYjhw4czbtw4bt26xfPPPw/AlClTKFOmDCkpKXTu3Jng4GDq1avH4MGDWbp0KS1atCA6OhpnZ2c+/PBDAgMD02ok8+bNy3Da+/Rmz55N6dKlCQ0NJSQkJC2269ev8/HHH7N161aKFy/O559/zrRp05g4cSIA5cqV4+DBg8yePZupU6fy448/MnXqVGbNmoWfnx+xsbE4OTnxxx9/EBQUxOHDh7l+/TotWrSgffv298QwePBgli1bxuTJk4mIiCAiIgIfHx/effddOnXqxM8//8zt27fx9fWlS5cuABw8eJDg4GDKlCnzMH+qTFmrySsEeBz4IbMCImILzAK6AheB/SKyRikVCgwHqgD1lFIGEcmTaX7t7J141LkqK+POExsTQQmXShmW82/mztLAC2wOvZK2VLCmabmXWZNX165d+f333xkzZgyHDx9O275s2TLmzJlDcnIyERERhIaGIiJUqlSJFi1aAFCyZMlMr5dZk1eqnTt3Mm7cOAAaNWqEl5cXAHv37iU0NBQ/Pz8AEhMTad26ddpxjz/+OADNmzfnjz+M/bJ+fn689tprDBs2jMcffxwPDw927tzJkCFDsLW1pUKFCnTo0IH9+/enXQdg0KBBPProo0yePJlly5al9e9s3ryZNWvWMHXqVADi4+M5f/582udl7mQCVkooSqkwMI4wz4IvcFIpddpUdgnQFwgFRgNDlVIG0/muWTTgdHo1GMaSg5/x1/4Z9On0SYZlfKuXwb1UMVYeuqQTilYoZVeTyGsGg4GwsDCcnZ25desWHh4enDlzhqlTp7J//35Kly7N8OHDiY/Pm5kslFJ07dqVxYsXZ7jf0dERMN5kkJxsnFR2/Pjx9OrVi4CAAPz8/Ni0aVOOruXu7k7ZsmUJDg5m6dKlfP/992kxrFixAk9Pz3vK//vvvxQvXvxh31qW8nMfijuQfgKti6ZtALWAwSISKCIbRKROZicRkVGmcoGRkZG5DqpJwyFUToGAC39mWsbGRujbtDI7TlwnMiYh19fUNC1rX3/9NfXr12fRokWMGDGCpKQkoqOjKV68OK6urly9epUNGzYA4OnpSUREBPv37wcgJiaG5ORkXFxciImJeaDr+vn5sWyZcQaN0NBQjhwxrmLZqlUrdu3axcmTJwG4c+cOx48fz/Jcp06donHjxrz99tu0aNGCY8eO0a5dO5YuXUpKSgqRkZFs374dX1/f/xw7ePBgvvjiC6KiotJqL926dWPGjBmkTgB86NChB3pvD8NiCUVEtopISAaPvmY4vSMQb5r9ci6Q6eAQpdQcpZSPUsrHzc0t1xcWGxt6uHqyV93h5s2TmZbz93YnxaBYe/hyrq+paZpRah9K6mP8+PGEh4fz448/8tVXX9GuXTvat2/Pxx9/TJMmTfD29qZevXoMHTo0rfnJwcGBpUuXMnbsWJo0aULXrl2Jj4+nY8eOhIaG3tMpn9209y+99BKRkZE0aNCA999/n4YNG+Lq6oqbmxvz5s1jyJAheHl50bp167TO98x88803ac1m9vb29OjRA39/f7y8vGjSpAmdOnXiiy++oGLFiv85dsCAAWlLIqeaMGECSUlJeHl50bBhQyZMmJDbjz9bVp2+XkS2AW9k1CkvIq2BD5RS3Uyv3wFQSn0qIseAHkqpM6YO+ttKqYzv403HXNPXh59Yz4Dd43mvwiM80X1GpuV6z9iBIKwd2zbX19Q0ayso09fnpZSUFJKSknBycuLUqVN06dKF8PBwHBwcrB3aQyus09fvB+qISA0RcQCeANaY9q0COpqedwCyrkuaWd1aPaidIgRcyXqRnn5N3TlyKYqT1x6sGq1pWsEQFxdH27ZtadKkCf7+/syePbtAJ5PcskpCERF/EbkItAbWi8gm0/bKIhIAoJRKBl4GNgFhwDKlVOrN1p8B/UXkCPApMDJP47exoUe5JhySRC5fzrzG06dpZWwEPSZF0wopFxcXAgMDOXz4MMHBwfTo0cPaIVmVVRKKUmqlUspDKeWolKqQ2qyllLqslOqZrlyAUqquUqqWUmpKuu23lVK9lFKNlVKtlVKHM7qOJfXwfgmADQdmZVqmvIsTbeu4serQZQx6KhatEChKK7wWRbn9++bnJq98rUqV1ngZ7Nhw/WCW5fo3c+fS7bv8cyL3d5hpmjU5OTlx48YNnVQKKaUUN27cwMnJ6aHPoefyyoWeFVvx2bWdnDq1hVq1umZYpkejSnxa8hg/7jhNR888GX+paRbh4eHBxYsXMcft91r+5OTkhIeHx0MfrxNKLnTzeYUv1u8gIPhHxmaSUBzsbBjhV51PNxwj5FIUjdyzvRlN0/Ile3t7atSoYe0wtHxMN3nlQjm3+viKMwG3QjNdbx5gSMuqlHC0Y+6O03kYnaZpWt7SCSWXerp34KIthIStyLRMSSd7nmhRhXXBEVy6fTcPo9M0Tcs7OqHkUucWr2CvFAFHf82y3Ii2xqaCX3aeyYuwNE3T0kRE5c0PWZ1QcqmkaxXa2bqyMfYMKcmJmZZzL1WM3l6VWLzvPFF3k/IwQk3TirK1hy/T4YttbA29avFr6YRiBj2rd+e6rRAYPC/Lcs+3q8mdxBSW7DufN4FpmlakLQu8wLglh2hapRQta5p/uvr76YRiBh18XsbZoAgI/z3Lco3cXfGrXZZfdp0lMTnzTnxN07TcmrfrDG8tD8avdjnmP+uLi5O9xa+pE4oZOBUrTWeH8myJjyAxIet5u55vV5Mr0fF6FmJN0yxm1t8n+WBtKN0aVuDHZ3zybOVYnVDMpEedfsRks948QIe6bnhWcGHujtN6xLGmaWallOKLjcf4clM4/ZpWZtbQZjja5d0y5DqhmEkr75GUNig2nF6XZTkRYWS7Ghy7EsOOE9fzKDpN0wo7g0ExeW0os7edYohvVaYNaoqdbd5+xeuEYib29s48WqwK25JuEheb9YrEfZpWpryLox7oqGmaWaQYFG+tCGbe7rOMbFuDT/wbYWOT5RLrFqETihn1rD+EeBvhr8DMF90CcLSzZbhfdXacuE7o5eg8ik7TtMIoMdnAK0sOsfzARcZ1rsN7vepjXHcw7+mEYkZNGw2lYooi4PyWbMsO862Gs4MtP+paiqZpDyk+KYXRCw6wPjiC93rW59Wuda2WTEAnFLOysbWjh2td9hhiuXXzVJZlXZ3teaJFVdYcvpxno1g1TSs87iQk8+y8/fwVfo2P+zXi+fY1rR2STijm1rPRcJJF2LJ/erZlR/hVRwG/7Dpr8bg0TSs8ou4m8dRP/7L39A2+GtiEJ1tVs3ZIgE4oZudZpzc1U4SAiF3Zlq1SxpmejSux6N/zRMfr6Vg0TcvejdgEhszZy5FLUcwe1ozHmz38+iXmphOKmYmNDT3KenFAErgScSjb8s+3q0FsQjJL913Ig+g0TSvIrkTFM3jOXk5FxjL3aR+6N6pk7ZDuoROKBfT0fhGAjVmsN5/Ky6MUrWqW4eddZ0hK0dOxaJqWsQs34xj4w24ibt9l/rO+PJIPV4DVCcUCqlZtSyODHQGRgTkqP6p9TSKi4lkfHGHhyDRNK4hOXotl4Pd7iL6bzMLnW9GqZllrh5QhnVAspGcFX8JsUjh95q9syz5Stzy1y5dgznY9HYumafcKunCbgd/vJtlgYMmoVjStUsraIWVKJxQL6dZ8LKIUG4LmZlvWxkYY1a4moRHR7D51Iw+i0zStINh+PJKhc/fi4mTPitFtqF+ppLVDypJOKBZSvkIjfKUYG26FZLnefKq+3pUpV8KRH7brgY6apsGaw5d5bv5+qpUtzvIXW1OtbHFrh5QtnVAsqEfl9pyzhdDwldmWdbSzZYRfdbYfjyQsQk/HomlF2fzdZxm35BDeVUuzZFQrypd0snZIOaITigV18R2HnVIEhGS93nyqYS2rUszelh936HXnNa0oUkoxbctxJq05Spf6Ffj1WV9ci1l+YSxz0QnFglxdq9LWpiQbY05lud58qlLODgxuUYU1hy9xJSo+DyLUNC2/SDEo3l8VwvQ/TzDIx4PvhjXDyT7v1jIxB51QLKx3jR5csxV25WBMCsCzfjVIMSjm7T5r2cA0Tcs3EpJTGLv4IAv/Pc/oR2rxeX+vPF/LxBwKXsQFTKdWr1M+RbHg2OIcla9a1pkejSqx8N9zxCYkWzg6TdOsLTYhmRG/7CfgyBXe71Wft7vXs+qMwbmhE4qF2ds7M7icN3u4y6lT2U9rD8aBjjHxySzdr6dj0bTC7LppXq5/z9xk2qAmjGxn/RmDc0MnlDwwoO0kHJRi4f6vclS+SZVS+NYow8879XQsmlZYXbgZx8Dv93DiWgxzn26eryZ5fFg6oeSBMmVq08uxImvvXiTq9tkcHTOqXU0u3b5LwBE9HYumFTbHrkTT/7vd3IhNYOHIlnSqV8HaIZmFTih5ZJjPq8TbCCt2fJij8p3qlaemW3Hm7tDTsWhaYRJ49iaDvt+DCPz+YhuaVytj7ZDMxmoJRUQGishRETEtduupAAAgAElEQVSIiE8W5bqLSLiInBSR8em2dxaRgyISJCI7RaR23kT+cDzr9KKFcmRx5D6Sk7K/JdjGRni+XU1CLkWz8+T1PIhQ0zRL+zPsKsN+/JdyJRxZMboNnhVdrB2SWVmzhhICPA5sz6yAiNgCs4AeQANgiIg0MO3+DhimlGoKLALet2y4ufdk3UFcsRX+2js1R+X9vd3xKF2MKevDSNZ9KZpWoP0eeIFRvx3As6ILv7/YGo/SztYOyeysllCUUmFKqfBsivkCJ5VSp5VSicASoG/qKYDUmdJcgcuWidR8Ovj+D/cUWHgq+6lYAJzsbXmvZ32OXYlhsb7jS9MKJKUU32w9zpvLg2ldsyyLnm9F2RKO1g7LIvJ7H4o7kP6b9KJpG8BIIEBELgJPAZ9ldAIRGSUigSISGBkZadFgs2Nr58DQiq05KImEHluVo2O6N6pIq5plmLY5nNtx2Y+21zQt/0hMNvDm8mC+2XqCAc09+Hl4C0o42lk7LIuxaEIRka0iEpLBo2/2R2frVaCnUsoD+AWYllEhpdQcpZSPUsrHzc3NDJfNHf+2k3A2KBYenJ6j8iLCxN4NibqbxDdbT1g4Ok3TzCU6PokR8/ax/MBFXu1Sly8HeOFgl99/w+eORVOlUqpLLk9xCaiS7rUHcElE3IAmSql/TduXAhtzea084VLSnb7O1Vh+9xyvXj9GuXL1sj2mQeWSDPGtym97zzG0ZVXqVihcHXmaVthcun2XEb/s43TkHaYObMKA5gV/jElO5Pd0uR+oIyI1RMQBeAJYA9wCXEWkrqlcVyDMSjE+sKEt3yJJhN935uwWYoDXH/WkuIMtH60L1bcRa1o+FnIpCv9Zu4i4Hc/8Z32LTDIB69427G/q/2gNrBeRTabtlUUkAEAplQy8DGzCmDCWKaWOmrY/D6wQkcMY+1DetMb7eBjVq3egnRRn6c1gEhNicnRMmeIOvNq1LjtOXGdr2DULR6hp2sP4O/wag37Yg52NsHx0G/xql7N2SHlKitKvXR8fHxUYGGjtMADYvX8WL4R+z5Qqj9Gn0yc5OiYpxUDPb3eQmGJg86vtcbQrWFNba1phtujf80xYHUK9ii78PLwFFQrIolg5ISIHlFKZjhdMlaMaioj8ISK9RCS/N5EVGK2bj6ZmirDgXECOlggGsLe1YeJjDTh3I46fd561bICapuWIwaD4fOMx3l15hPZ1yrHshdaFKpk8iJwmiNnAUOCEiHwmIp4WjKlIEBsbhrl3JMwmhUNHFuT4uHZ13OhSvwIz/zrBtWi9CJemWVNCcgrjlgbx3bZTDG1ZlblP+1C8EN8WnJ0cJRSl1Fal1DCgGXAW2Coiu0VkhIgUnPUp85ne7SZQ0qBYEDz3gY57v1d9ElMMfL4xu3GhmqZZyu24RJ76cR9rD19mfI96TOnXqEAuimVOOX73IlIWGI5xQOEh4FuMCSZni3xo/+HsXI7+JevyV8otIi4fyPFx1csV59m2NVhx8CJBF25bMEJN0zJy/kYcj3+3m6ALt5k+xJsXO9QqsItimVNO+1BWAjsAZ+AxpVQfpdRSpdRYoIQlAyzshrR+D4DFe6Y80HFjO9XBzcWRD9YcxWAoOjdWaJq1BV24jf/sXdyITWTByJb0aVLZ2iHlGzmtoUxXSjVQSn2qlLpngY6c9PxrmatUuTmdbEuzIvo4cXE5n1W4hKMdb3XzJOjCbVYFXbJghJqmpdp09ApPzNmDs6Mtf7zUBt8ahWfqeXPIaUIpLSKP3/foLCLlLRpdEfGk1/NE2wjrdn78QMf1b+ZBEw9XPttwjDt6/XlNsxilFLP+PsmLCw7gWbEkK1/yo5abbpy5X04TynPAj8Aw02Mu8DawS0SeslBsRYZ34yepb7Bl0cW/cnwLMRjXTJn4WEOuxSQwe9tJC0aoaUXX3cQUXlkSxJebwnnMqzJLR7WiXCGdLTi3cppQ7IH6Sqn+Sqn+GNcmUUBLjIlFywWxseHJaj05ZavYc/D7Bzq2ebXS+Hu7M3fHGc7fiLNQhJpWNEVE3WXQD3tYF3yZt7p78u0TTXGy1wOKM5PThOKhlLqa7vU1oIpS6iaQZP6wip7ufu9QNkWxMPS3Bz727e71sLMRpgSEWiAyTSuaDp6/RZ+ZuzgdGcvcp3x46ZHa+k6ubOQ0oWwTkXUi8oyIPAOsNm0rDuj7Vs3AwdGFQaUbs13Fcu7cjgc6tqKrE2M61mbT0avs0ssFa1quLT9wkSd+2Esxe1tWjvGjS4MK1g6pQMhpQhmDcc2RpqbHr8AYpdQdpVRHSwVX1AxqOxE7pVj07+cPfOxzbWvgUboYH64N1csFa9pDSjEopqwP5Y3fD9O8WmlWj/HTy0U8gGwTimld97+UUiuUUq+aHstVUZpVMo+Uc6tPT4fyrLpzlpjoB7sV2Mnelvd71Sf8agyL9p23UISaVnhF3U3i2Xn7mbvjDM+0rsavz/lSuriDtcMqULJNKEqpFMAgIq55EE+RN6zZK8TZCCt3Tn7gY7s1rEjrmmX5avNxbt3RywVrWk6diozFf9Yudp28zif+jZnctxH2RXwalYeR008sFjgiIj+JyPTUhyUDK6oa1OtHM+XAoit7SEl+sKQgIkzq04CY+CS+2XrcQhFqWuHyz/FI+s3axe27SSwc2ZKhLataO6QCK6cJ5Q9gArAdOJDuoVnAsFr+XLKFf/Z988DH1qtYkmEtq7Hg3/OEX8nZ4l2aVhQppfhxx2lG/LIP91LFWD3Gj5Y1y1o7rAItp7MNzweWAXuVUvNTH5YNrejq1OoNKqUoFh5f9lDHv9a1LiUc7Zi89qheLljTMpCQnMKby4P5eH0YXRtUYMXoNlQp42ztsAq8nE4O+RgQBGw0vW4qImssGVhRZmfvxBNuvuyTBMJPrH/g40sXd+C1rnXZfeoGG0OuWCBCTSu4rsXEM2TOXpYfuMgrnevw3bDmRXoNE3PKaZPXB4AvpjEnSqkgoKaFYtKA/u0m4mRQLAp88GYvgGEtq1K/UkneXXmEy7fvmjk6TSuYDpy7Rd+ZuwiNiGbW0Ga81rUuNjZ6sKK55DShJCmlou7bpgc7WJBrqeo8VsyD9fER3Lp56oGPt7O1YdZQbxKTDby86CBJemyKVoQppfh55xkG/7AHWxth+Ytt6OVVydphFTo5TShHRWQoYCsidURkBrDbgnFpwJMt3yRRYN7fbz3U8TXdSvD5AC8Onr/N5xuOmTk6TSsYYuKTeGnhQT5cF8ojnuVZP7Ydjdz1KAhLyGlCGQs0BBKAxUA08D9LBaUZ1azRmV72biyMDudKxKGHOkdvr8o807oaP+48o/tTtCInLCKaPjN3sTn0Ku/0qMfcp5vj6qxXLbeUnN7lFaeUek8p1UIp5WN6Hm/p4DQY2/FLDAIz/37zoc/xbq/6eHm48ubyw3pGYq3IWBZ4gX6zdnEnIZlFI1vygl6m1+JyepdXXRGZIyKbReSv1Ielg9OgcmUfhpWow5rEKxw/ueGhzuFoZ8usoc0Q4KVFB4hPSjFvkJqWj8QnpfDW8sO8tTyYZlVLs/6Vdnp8SR7JaZPX78Ah4H3gzXQPLQ+M7PotLgq+3vXg07GkqlLGma8GNSXkUjQfr9fT3GuF05nrd+g3axfLAi/ycsfaLBjZEjcXvRhWXslpQklWSn2nlNqnlDqQ+rBoZFoaV9eqPO/Wip3cYe+BHx76PF0bVOCF9jVZsPc8q/U69Fohs+FIBI/N2MmV6Hh+GdGCN7p5YqtvCc5TOU0oa0XkJRGpJCJlUh8WjUy7x5AuX1EpRTEt+DsMKQ+/fvwb3TzxqVaad/44wslrsWaMUNOsIzHZwIdrQxm98CC1ypdg/Svt6OhZ3tphFUk5TSjPYGzi2s3/z+MVaKmgtP9ydHJlbI1+hNmksHHnRw99HntbG2YM9cbJ3paXFh7gbqLuT9EKrsu37/LEnD38vOsMw9tU5/cXWuNeqpi1wyqycnqXV40MHnqkfB7r1f4D6hlsmH7qDxITHn7ix0quxfhmcFNOXItlwuoQM0aoaXnnn+OR9Jq+g/ArMcwc6s0HfRriYKennLemLD99EXkr3fOB9+37xFJBaRmzsbXj1cYvcMkWlvz5eq7O1b6uG2M71WH5gYss23/BTBFqmuWlGBTTthxn+C/7KO/ixJqxbentVdnaYWlkX0N5It3zd+7b193MsWg50MbnJdpQjDlXdxMdlbtEMK5zHfxql2XC6hDCIqLNFKGmWc6Fm3EM/mEP0/88wePeHqwa40cttxLWDkszyS6hSCbPM3qt5ZFXW71PtMBPW3M3WYGtjfDNYG9ci9nz0sKDxMQnmSlCTTMvpRTLAi/Q/ZvthF+JYdqgJkwd6EUxB1trh6alk11CUZk8z+i1lkfqefbhMYfyLIgJJ+Jy7u7ednNxZMYQb87duMM7fxzR66do+c6N2AReXHCAt5YH08jdlQ3/a8fjzTz0qPd8KLuE0kREokUkBvAyPU993fhhLyoiA0XkqIgYRMQni3I/i8g1EQm5b3sZEdkiIidM/y39sLEUVC8/8iUAM7c93MSR6bWsWZY3unmyLjiC3/aey/X5NM1c/jp2lW7f7ODvY5G827Mei55vhUdpvRBWfpVlQlFK2SqlSiqlXJRSdqbnqa9zM8NaCPA4xiWFszKPjPtqxgN/KqXqAH+aXhcplSo3Z1iJOqxNvEr48XW5Pt+L7WvRqV55PloXyuELt80QoaY9vLjEZN5beYRn5wVSroQDq1/2Y1T7WnqgYj5nlXvslFJhSqnwHJTbDtzMYFdfIHUJ4vlAPzOGV2A8lzoly56HH5eSysZG+GpgE8q7ODFm0UGi4nR/imYdh87fotf0nSzad55R7Wuyaowf9SuVtHZYWg4U1Ju2KyilIkzPrwAVMisoIqNEJFBEAiMjI/Mmujzi6lqVUeXbsIs49hz4PtfnK13cgZlDvbkaHc/rvx/W/SlankpKMfD1luMM+H4PickGFo1sxbs96+NkrzveCwqLJRQR2SoiIRk8+przOsr4rZfpN59Sao5pyn0fNzc3c146XxjS5Ssqp8DXwd/nakqWVN5VS/NOj/psDbvKd/88+EqRmvYwTkXGMuC73Xz75wn6NqnMhv+1o3UtPUOwOURHXeCzZY8RGxORfeFcslhCUUp1UUo1yuCx2gynvyoilQBM/71mhnMWSA6OLoytaZySJWDHw89GnN4Iv+r09qrEFxvD+WnnGbOcU9MyopTit73n6DV9B2dvxDFraDOmDW5KSSe9CJY5HDg8nwErerA07gyBRxdZ/HoFtclrDcb5xTD91xxJqsDq2W4S9Q22zDi9KldTsqQSEaYNakqPRhX5aF0os7edNEOUmnava9HxjJi3nwmrQmhRvQyb/tder/NuJklJccxYOZhnD32JPcJvvpN4pFXuZtfICaskFBHxF5GLQGtgvYhsMm2vLCIB6cotBvYAniJyUUSeM+36DOgqIieALqbXRZaNrR2veY3msi0s3mqefzQOdjbMGOJN36aV+WJjOF9vOa77VDSzUEqxOugS3b7Zzp5TN5jcpyG/PutLRVcna4dWKFy4sIfhC9oyJzqUxxwqsmzQFho1GJj9gWYgRelLwsfHRwUGFt5Jkl+c35IjhjsEPB6Aq2tVs5wzxaAYvyKY3w9c5MUOtXi7u6ceUKY9tLPX7zBhdQg7TlzHy8OVaYOaULu8i7XDKhSUwcC6fyYw5exqbICJtQbRvf1Es5xbRA4opTIdM5jKzixX0/KFV1tPYODu8fy0ZRyvDVhplnPa2gif9/fCwc6G7/85RUJyChN7N9BJRXsgCckpzPnnNDP+PomDrQ0fPNaAp1pX1+NKzCQm+hIfrRnKhpSbNBNHPnt0DpUqN8/zOHRCKUQ86/bmscCvWRh7giGXD5jtH5SNjfBxv0Y42tny864zJCYb+KhvI2z0l4GWA3tP3+C9lUc4FXmHXo0rMaF3A928ZUaHghcwPvBzrtooXi7tzcheP2Fr52CVWHRCKWTGdpzKxk1PMXPbm0wZ+pfZzisiTOhdH0d7G77bdoqEZAOf9/fSvzC1TN28k8iU9WGsOHgRj9LF+GV4CzrW0yspmktyUjxz1o3gh6gjVEaY7/M+TRo9kf2BFqQTSiFTsZI3w1zqMi/mOE+Fr6GeZx+znVtEeKubJ052tny99TiJyQamDWqCnW1BvVlQswSDQbH8wEU+2RBGbHwyLz1Si7Gd6uiZgc3o4sW9vLP1JYIkiT4O5XnnsYWUcLH+HXI6oRRCI7t8yx9/9ODrvR/zgxkTChiTyrgudXCws+HzjcdITDYwfYi3XilPA+D41RjeXxnCvrM3aVG9NFP8G1O3gu50N6d12yYw5Yyxj/TzGv3p2cE848/MQSeUQqikaxVGVWjDl5F72B04mzY+L5n9GqMfqYWjnQ0frgvlxQUHmD2smZ4iowi7m5jCjL9OMGf7aUo42fFFfy8GNPfQ/WxmFBsTwZQ1Q1mXfB1vceTTrt/h7u5r7bDuoW8bLqQSE2Lot7ANClg+aAvFS1S0yHUW7D3H+6tCaFenHHOe8tHNGkXQ3+HXmLg6hAs379K/mQfv9qxH2RKO1g6rUAk6spDx+z/jio3ihVJNeL7XT9jZ592NDTm9bVi3UxRSDo4uTPF5m8s2is/XPmmx6zzZqhpfDvBi58nrjJi3jzsJuZ9PTCsYrkbHM2bhQUb8sh8HWxsWP9+KrwY10cnEjBITYvhmxQCeOfApAPOav8PofgvzNJk8CJ1QCjFvryd5rmR9ViZe5c/dn1vsOgN9qvDN4KbsP3uLp3/eR7ReSrhQi7qbxBcbj9Hhy7/ZEnaV17vWJWCcnszR3MJPrGfIorb8FBuOv2NlVgzaQtPGw6wdVpZ0k1chl5Rwh2GL/IggmT96LcWtfEOLXWtjSARjFx+ifqWS/PqsL6WcrXMvvGYZdxNTmLf7LN9tO0lMQjJ9mlTm9a6eVC2rV1A0p5TkROZveJGZN/ZR0gCTGzxLh1avWTWmnDZ56YRSBJw+8yeDto2jhU0JZj+1G7GxXMX0z7CrjF5wkBrlijN9iDeeFfUdPgVdUoqBpfsvMP3PE1yLSaBTvfK88agnDSrrRa/M7cKFXbz35ysckkS62Lgyodc8ypSpbe2wdB+K9v9q1ujMa5U6sJM7LN08zqLX6ly/Ar+MaMH12AQem7GTWX+fJDnFYNFrapZhMBgncewy7R/eXxVC1TLO/P5ia34e3kInEzNTBgO/b36V/ltf4KRK4JOqfZk2bHu+SCYPQtdQighlMDD6t9YcMNxhWceZ1Kj+iEWvd/NOIhNXh7AuOAIvD1emDmyixyMUEEopth2P5IuN4YRFRFOvogtvdfeko2d5PYebBUReO8qkjc+xQ92hJU58/OgcKlbytnZY99BNXhkoygkF4NrVEB4PeAIP7Pjtyd3Y21u+7TvgSAQTVoUQE5/MuC51eKF9TT2yPh8LPHuTLzaGs+/sTaqWceb1R+vymFdlPZ7EQjbt+IiPTi4lHni1YjuGPDoDG9v8NzxQJ5QMFPWEArB156e8emoRo0o2YKz/0jy55o3YBCauPsr6IxE0MdVW6ujaSr4SFhHN1E3h/HnsGm4ujrzSuQ6DfaroGRAsJCrqPJ+ue4b1yddpaLDlk0emUbNGJ2uHlSmdUDKgE4rR+4u6sDbxCvObv5OntyGuD45gwuoQYuOT+V/XOoxqp2sr1nb+Rhxfbz3OqqBLlHC048UOtRjhVx1nh/z3K7mw2B04mwnBs7lhAy+U8mJkrx/zpLUgN3RCyYBOKEaxMREM+P1RBMuOos/I9dgEJq4OIeDIFV1bsRKlFHtO32D+7rNsCb2Kva0NI/xq8GKHmvpWbwu6G3eTr9c+xeL489RIET5tPYmG9ftbO6wc0QklAzqh/L+Dh39lxKEv6OdYiclDtuT59dcFX2bi6qPExifzate6PN+uhq6tWFhcYjIrD13i193nCL8aQ2lne57wrcrwNtWpUDJ/jrwuLAKD5jHp4Fect4UnnWswrvd8nIqVtnZYOaYTSgZ0QrnXtysG8GNsON/UeZLObd7O8+tfj01gwqoQNoRcoUmVUnw10EsvB2sB52/E8euesywLvEB0fDINKpVkeJvq9GlaWU/oaWF3Yq/w9fpnWRp/AfcU+NB7HL7eI60d1gPTCSUDOqHcK3UU/RWS+aP375Rzq5/nMSilWBccwcTVIdxJTOG1rnV5vl1NvXBXLiml2HHiOvN3n+Wv8GvYiNC9UUWGt6mOT7XS+vbfPLB7/yw+OPIdV2xgmHMNxvb+BWfnctYO66HohJIBnVD+Ky9H0WclMsZYW9l41FhbGduxNh3rldeJ5QHFJiSz4sBF5u85y+nIO5Qr4cAQ36oMa1lNL7ubR6KjLjA1YAQrE69SPUX4qMXb+X4OruzohJIBnVAytnDDS3x2bQfvV+zI4G7TrRaHUoq1wRF8vC6UazEJuJcqxtCWVRnkUwU3Fz2DbVZOR8by655zLD9wkdiEZJp4uPJMm+r08qqEo51u1sorf++Zysdh87hhA8Nd6jG61084OrlaO6xc0wklAzqhZMyQksxLC/zybBR9dpJSDGwJvcqCvefYfeoG9rZCt4YVebJVNVrWKKOba0wiYxL469hV1gVHsOPEdexthV6NK/FMm+p4Vy04Hb6Fwa2bp/hsw3MEJN+gjsGGj1pNLDB3cOWETigZ0Aklc9YYRZ8TpyJjWbj3PMsPGDuU65QvwbCWVXm8uQclneytHV6eUkpx4losW0KvsjXsKkEXbqMUuJcqxkAfD4a2rEp5F92slZeUwcDmXVP45ORSogVGlfJiZI+52DsWt3ZoZqUTSgZ0Qsnalp2f8NqpxbxQsiEv+y+xdjj3uJuYwtrgyyzce47DF6MoZm9LP+/KDGtZjUbuBb9JITNJKQb2n73J1tBrbA27yvmbcQB4ebjSpX4FutSvQP1KLrrWZgXXI8P4eONI/jRE09Bgy4ftPqVu7R7WDssidELJgE4o2XtvUWfWJV5lvs+7NG001NrhZCj44m0W7D3HmsOXiU8y0LRKKZ5sVY3eXpUKxW2w0fFJ/BMeydawq/x97BrR8ck42NngV6ssXRpUoHO9CrqD3YqUwcDabe/z+bk1xAuMKevL091n59tVFM1BJ5QM6ISSPWuOon9QUXFJrDh4kQX/nuN05B1KOdszoJkHHTzdaFCpZIFaivbCzTj+DLvK1rBr7D19g2SDokxxBzrVK0+X+hVoV6ccxR31dCjWdiXiEJM3j2Ynd2iq7PnwkWlW73PMCzqhZEAnlJw5cHg+Iw59SW/78kwZstVqtxLnVOpUIgv3nmfT0SskG4z/piuWdKJB5ZI0rFySBpVK0rCyK1XKFLNa85BSiuuxiZy4FsPJa7GcuBqb9vx6bCIANd2K07V+Bbo0qECzqqX1bdP5RHJSPIu3jGPm1V0oYFzFdjzR9Vts7YrGVDU6oWRAJ5Sc+27VUGZHHWFkCU/G9V9u7XByLCouiZDLUYRejubo5ShCI6I5eS0WU47BxdGO+mkJpiQNKpekTnkXs86qq5TiWkxCWsI4cS2Wk6bnt+KS0sq5ONpRp0IJ6pR3wbOiCx083ajlVsJscWjmEXx0KR/t+4RjNgbaUpx3O31NlSqtrR1WntIJJQM6oeScMhj4cFkPlidc5o1yrXmm1xxrh/TQ4pNSCL8Sw9HL0YRGRHH0cjTHImK4m5QCgL2tUKe8Cw0rl6RcBuNdMvpfRPHfjbfvJKUlkJj45LTtrsXsqVuhBLXLu1CnfAnqVChB3QoulHdx1J3p+VhU1HmmbxjF7/EXcTPA+LpD6dJmfL6vsVuCTigZ0AnlwaQkJ/Lm4s5sMdzm4yq96NvpM2uHZDYpBsWZ63cIjTDVZC5HExYRTfTd5P8WzuQ7//7NLk521C5vrHHUqVAi7Xm5Eg46cRQgymBg3T8TmXp2FVECQ4vXYkyPH/J1f6Kl6YSSAZ1QHlxiQgxjlnRmv4rja8/hdGz9hrVD0jSLOX3mL6b88xb7JAEvgx0T2kymnmcfa4dldTlNKEWv7qY9EAdHF77tv44Gyp43wuexP+hna4ekaWYXf/cW0/8YRP9/XiFMxTOhUmd+e3q/TiYPyCoJRUQGishRETGISKZZT0R+FpFrIhJy3/YvReSYiASLyEoRKWX5qIsu5xLlmdV3OR4GG145NI2w8NXWDknTzGb7v9/Sb3F75saE0cO+PGsf+4NBj36TL9d2z++sVUMJAR4HtmdTbh7QPYPtW4BGSikv4Djwjlmj0/6jdJla/NDzV1wUvLj7Pc6d22HtkDQtV65cCeK139oy5tiPOCD85DWOT4b9Rdlyda0dWoFllYSilApTSoXnoNx24GYG2zcrpVJ7T/cCHmYOUctAxYpN+aHTTBTwwp8vce1qSLbHaFp+k5wUz68Bo+i74Um2J9/mldLerBi2p0AufJXfFIY+lGeBDZntFJFRIhIoIoGRkZF5GFbhVKP6I3zXajK3RPFCwDCibp+1dkialmP7g37miQUt+TJyD81sSrCyy1ye7/NroZvM0VosllBEZKuIhGTw6GvGa7wHJAMLMyujlJqjlPJRSvm4ubmZ69JFWsP6/Zne5BXOSQpjVj5OXNx1a4ekaVk6f34n//vNj2cPf02USuGrmoOZ/dTuIjdA0dIs1uuklOpiqXMDiMhwoDfQWRWle5/ziZbNRvFF3A1eP7mQ137vxYwn/tK/8rR8JzrqAnM2j2XhnZPYKxhb1punu07HqZheL8YSCmSTl4h0B94C+iil4qwdT1HVpe07TPLozi7ieO/3nhhSMhgUqGlWkJwUz5KNY+n9Rw9+vXOSxxwrsr7XUkb1+U0nEwuy1m3D/iJyEWgNrBeRTabtlUUkIF25xcAewFNELorIc6ZdMwEXYIuIBInI93n8FjSTx7tM5dUyLdiQcpNPl/dBGXfBZ3EAABH4SURBVAzWDkkr4nbtn8mA33yZcnUbtcWJpa2n8OGQrbiVb2jt0Ao9PVJeM4uvlvsz785JXnJtzOh+i6wdjlYEnT7zJ19uf4+d3KFKCrxe70k6tXqzSM69ZW45HSmvR+5oZvHa4yu4veRRZkcdwXXjGIZ2n2XtkLQi4tbNU8zeMpbf757HWcEb5VszpMs0HBxdrB1akaMTimYWYmPDpIHriFrcmU+vbsd120R6PfKhtcPSCrGkhDss2voqP1zbTZzAgGJVeanrdMqUqW3t0IosXRfUzMbO3okvBwXgoxx59+wf/LLuOd2nopmdMhj4a/cX9FvYiqnX9+BlU5zl7abx/uAAnUysTCcUzawcnVyZNSCALnalmXZjH28s6kBc7DVrh6UVAspgYM+B73lqvg/jTvyGHcJ39Ufx/TP/UrvWo9YOT0MnFM0CnEuUZ+rQf3itrC9bk28xdFkXPfeXliv7D/3E8F9b/F979x4dVXnucfz7S4LcIchFQCDhZpEqIsrFGyICtdKKF2prFaXW2mN7vB1be1rb2uNx1QtrVY+ttWKPtVIFW9Qj1htgQS2FAAYIQaAiDfdLBKSAEJPZz/ljb+wQBxhgkp1Jns9as/Jm9p49zzszmV/23jPvy42lj7LFPuGnnUbw/Lj5nDvo5rhLc0n8U16uRs199zfcWfIrqoD7T76e84f8R9wluSxSvORpHl30CPNVQYeEcUPnYVxxwX1+wr2W+QRbKXigxGPDhvncPv1GluckuKnVKfzbJZN8aHB3SEtKp/Drd3/B39hL24RxQ6dzGTvsPv9SYkw8UFLwQInPvr07+O8XxzKtcivnqwU/H/NHWrXuGndZro5Ztvx5Hl0wgXdsD20C45sdzuLKCx6gabPj4y6tQfNAScEDJV4WBEyZfgsPbp5N50A8PHQCvXulmu7GNTQrVk7j0aL7mW27aB0Y49udydcveJBmLTrEXZrDAyUlD5S6oXjJ09zx7oPsEdzT80ouGvrTuEtyMXl/1es8NvdeZgQ7aRkY1x1/OlcPf5AWLTvFXZpL4oGSggdK3bF1Syl3vHYti1XJN5r34pYxk8lr1CTuslwt+fuq13hi3n28UbWd5gbj8k/lmuEP+mHQOsoDJQUPlLqlsmIPD7w4lucq1jOYJkz48hTaHN8z7rJcDQkSVbyz4BEmrZxMEftoGhjXtD6Z64ZPoHV+YdzluUPwQEnBA6VuevHNO7l33au0DeChs+/h830uj7skl0Ef797KS3+9h2c2vsWaXOiQML7efiBjz7vbgyRLeKCk4IFSdy1b/jy3zb2b7Tnwk66jGXPBfT5KbJbbvGkRz865h6m73mdXjjg1yGNcjzGMOPtOGjVqFnd57gh4oKTggVK3bd++ijtfvooi9jGYJtw++Ie+t5KFlpRO4Q+Lf82Mqu0YMCKvDeP638Rpfb/m/yRkKQ+UFDxQ6r6qyn08N/N2Ht/8DjtyxBdzj+fm839O167nxF2aO4Sqyn3MnPsAkz54iZKcSloGxhUte3PV2XfRufNh34dcHeeBkoIHSvbYvWsTv5t5G5M+Wkal4Mpmhdw4/Be0bXdS3KW5JDt3ruX5t3/G5PL5bM4V3RJwdeehXHru3f4dknrEAyUFD5TsU751GY/95Q5e2Leexgbj25zGdSMe8jerGAWJKoqX/oE/L3+WV/dtZG+OGGSNGdfnKoYOvNWH1amHPFBS8EDJXv8om80v3/kxM4KdtE0YN504nMuH3+8nd2vRqg+m88riibyycwWbckXTwBjVuCPXnHELfT53SdzluRrkgZKCB0r2W1I6hV8snECxPqEgAbf0/iojz/mRn+ytIVu3lPLawv/hz1vnsyInINeMs9SC0QUjGX7mzb6n2EB4oKTggVI/WBDw9vyHefi9p1iVa5wa5HH76TczsP/1cZdWL+zetYkZ8x/ilfWzmG97MYUf+R3dcQhfGHgr7dr1ibtEV8s8UFLwQKlfElWfMO2tH/PomlfZkivOU3NuO/tuTur1xbhLyzqVFXv4a/FjvPLBNGZXbqciR3RNwJfanMLoAd+hoOC8uEt0MfJAScEDpX7at3cHk9/8Hk+UF7FbMEhNGdnxLC4ccBPt2p8cd3l1VmXFHhYvf443VvyJ1/euY2eOaBMYFzUrYPTnx9Gv75V+KNEBHigpeaDUbzs/KuMPs37I6ztKKcsFmXE6jRl5wkBG9P82HTudHneJsQoSVaxc9QpF77/MvG1LKQ72sDdHNAmMCxq15Uu9L+esAd/yDzq4z/BAScEDpWGwIGDV6unMLH2a6TuWsSonAKBfkMfI9mcwov8NdOkyJOYqa54FAWvXzaFoxVTmbS1mQdUOPsoRAN0TYnDzLgzpMpQhp42neYuOMVfr6jIPlBQ8UBqmsrK3mFnyJNO3LWF5TgKAk4NcRrbtx4h+19O9cFi8BWbQ1i2lFL03haJN8yjat5nNuWGAdEwYg5t0ZHCnwQzq+1VOOKFfzJW6bOKBkoIHilu/fh4zF/+WGeXFlORUAtAryGFkfl9GnnodvXqMyprzBpUVe1i3sYgPNsxjwYY5FO1Zx+rc8O+5dWAMymvDkA4DGNxnLN26npM1/XJ1jwdKCh4oLtnmzYt5c9HjzNiygGL2YRKtA6OARnQ9Lp+C5p3omt+Tbu1PoeDEwbEMtR4kqti8ZTFlG+ez5sP3WPvPNZTtLWdNYg8bcoxA4R5I08AYkNOcIW1PZXDvL/O5XqP9G+suYzxQUvBAcQfzYflyZi2ayIrty1lbsZ21ib1syjEsesMGaBUY3WhEt+Na061ZJ7pFYdOt80Dy87sf0R6ABQGJxCcEQSVViQo+/vhD1m1cSFl5CWs+Ws2ajzdTVrWLdSSoyPlXDU0Do5A8Chq1oqB5Zwrye1HY4TT69LqYRo2bZ/QxcW4/D5QUPFDckfikYhfrN85n7ZbFrNm2knW71rGmYhvrEnvZWC1sWgZGW8shwEgAVRgBkBBUQdgGqhS1k25bXZ4ZXYMcCvJaUNjsBLq1KqSw/SkUdB5M+/Z9/dCVq3XpBorvEzt3EMc1bkmP7hfSo/uFn1kWhs0C1m5ZxNrtK1n7z3XsqNpNLjnkKZdc5SRdcv/1M2d/O++AduO8JnRr24fCTmfQqeMZ5DVqEkOPnTs2HijOHYUwbIbTo/vwuEtxrs7wfWfnnHMZEUugSPqKpGWSAkkHPS4n6UlJWyWVHmT5HZJMUruaq9Y551w64tpDKQUuB94+zHpPARelWiCpKzAKWJvRypxzzh2VWALFzJab2co01nsb2H6QxQ8BdwIN52NqzjlXh2XlORRJY4ANZrYkjXVvlLRQ0sLy8vJaqM455xqmGvuUl6SZQKoR5+4ys5eOYbvNgB8RHu46LDObCEyE8HsoR3u/zjnnDq3GAsXMRtTQpnsC3YElCr8c1gUoljTIzDbX0H0655w7jKz7HoqZLQU+nchaUhlwppl9GFtRzjnn4hl6RdJlwC+B9sBHwGIz+4KkzsBvzeziaL3JwDCgHbAFuNvM/rfatspIM1AklQNrjrLsdkBDCy3vc8PgfW4YjqXPBWbW/nArNaixvI6FpIXpjGVTn3ifGwbvc8NQG33Oyk95Oeecq3s8UJxzzmWEB0r6JsZdQAy8zw2D97lhqPE++zkU55xzGeF7KM455zLCA8U551xGeKBUI+kiSSslrZL0nymWj5dULmlxdLkhjjoz6XB9jta5UtJ70bQDz9Z2jZmWxvP8UNJz/HdJH8VRZyal0edukmZJWiSpRNLFcdSZKWn0t0DSm1FfZ0vqEkedmZTGlB+S9Ej0mJRIGpDRAszML9EFyAU+AHoAxwFLgL7V1hkP/CruWmu5z72BRUCb6PcOcddd032utv7NwJNx110Lz/NE4Kao3Rcoi7vuGu7vn4DrovZwYFLcdWeg30OBAUDpQZZfDLwGCBgCFGXy/n0P5UCDgFVmttrMPgGmAGNirqmmpdPnbwGPmtkOADPbWss1ZtqRPs9XAZNrpbKak06fDWgVtVsDG2uxvkxLp799gb9E7VkplmcdO/SUHxD28WkLzQPyJXXK1P17oBzoRGBd0u/ro+uquyLaXZwaTfSVzdLp80nASZLmSJonKeWkZ1kk3ecZSQWEg5H+JdXyLJJOn38GXCNpPfAq4Z5Ztkqnv0sIJ/oDuAxoKaltLdQWp7Rf+0fDA+XIvQwUmlk/YAbw+5jrqQ15hIe9hhH+t/6EpPxYK6o9XwOmmlki7kJqwVXAU2bWhfDQyCRJ9fk94nvA+ZIWAecDG4CG8DzXmPr8YjkaG4DkPY4u0XWfMrNtZlYR/fpb4Ixaqq2mHLbPhP/FTDOzSjP7B/B3woDJVun0eb+vkf2HuyC9Pn8T+COAmc0FmhAOKJiN0vlb3mhml5vZ6cBd0XVZ/+GLwziS1/4R80A50AKgt6Tuko4jfDOZlrxCteONlwDLa7G+mnDYPgP/R7h3gqR2hIfAVtdmkRmWTp+R1AdoA8yt5fpqQjp9XgtcCCDpZMJAydZpTtP5W26XtAf2Q+DJWq4xDtOAa6NPew0BdprZpkxtPOvmQ6lJZlYl6d+BNwg/JfKkmS2TdA+w0MymAbdIugSoIjz5NT62gjMgzT6/AYyS9B7hIYHvm9m2+Ko+Nmn2GcI3oSkWfTwmm6XZ5zsID2feTniCfny29j3N/g4D7pNkwNvAd2MrOEOSp/yIzoXdDTQCMLPfEJ4buxhYBXwMfCOj95+lrxfnnHN1jB/ycs45lxEeKM455zLCA8U551xGeKA455zLCA8U55xzGeGB4rKapN1prHObpGYZvM9LJfXN4Pb+dgy33R397Cxp6iHWy5f0naO9H+fS4YHiGoLbgCMKFEm5h1h8KeHAghlhZmdnYBsbzWzsIVbJBzxQXI3yQHH1gqRh0ZwWUyWtkPRM9G3gW4DOwCxJs6J1R0maK6lY0p8ktYiuL5P0gKRi4CuSviVpgaQlkp6X1EzS2YQjJEyI5krpKal/NGhmiaQXJbWJtjdb4bwqCyUtlzRQ0guS3pd0b1Ltu5PaP5C0NLrP+1P0s3tU+9Jq2yjcPweGpM9Lmh/VVyKpN3A/0DO6boKkFgrnAimOtjUmaTvLJT2hcO6b6ZKaRst6SZoZ1VYsqWd0/fejx6lE0n9l9Il12SXu8fv94pdjuQC7o5/DgJ2EYxPlEA6Xcm60rAxoF7XbEX4runn0+w+Anyatd2fSttsmte8Fbo7aTwFjk5aVAOdH7XuAh6P2bOCBqH0r4XDwnYDGhOOjta3Why8CfwOaRb8fn6K/04Bro/Z3k25bSDQHBvBL4OqofRzQNHl5dH0e0CrpMVlFOEdGIeEoEP2jZX8EronaRcBlUbsJ4V7fKMJ5VBQ97n8Ghsb9uvBLPBcfesXVJ/PNbD2ApMWEb45/rbbOEMLDVXMkQfiGmzxW13NJ7VOivYB8oAXhMB4HkNQayDezt6Krfk84cdN++4dxWQoss2jcJEmrCQfpSx7CZgTwOzP7GMDMUs1rcQ5wRdSeBDyQYp25wF0KZyB8wczej/p6QOnAzyUNBQLCIcxPiJb9w8wWR+13gUJJLYETzezFqLZ9UT9GEYbKomj9FoQDh76doi5Xz3mguPqkIqmdIPXrW8AMM7vqINvYk9R+CrjUzJZIGk80QOZR1hRUqy84SH3pOOR4SWb2rKQiYDTwqqRv89nBPK8G2gNnmFmlpDLCvY7kmiF8HJse4u4E3Gdmjx9B/a6e8nMoriHYBbSM2vOAcyT1ApDUXNJJB7ldS2CTpEaEb8Cf2Z6Z7QR2SDovWjYOeIujMwP4xv5PpEk6PsU6cwgHraRaTZ+S1ANYbWaPAC8B/TjwMYBwRsatUZhcABQcqjAz2wWsl3RpdB+NozrfAK5POg91oqQOafXW1TseKK4hmAi8LmmWmZUTjhA9WVIJ4eGhPge53U8IzxvMAVYkXT8F+L6kRdGJ6esIT9KXAP0Jz6McMTN7nfAQ2cLokN33Uqx2K/BdSUs5+Ex7VwKl0TZOIZzydRvhYb5SSROAZ4Azo+1cW61/BzOOcLTtEsJzPR3NbDrwLDA32tZUDgwu14D4aMPOOecywvdQnHPOZYQHinPOuYzwQHHOOZcRHijOOecywgPFOedcRnigOOecywgPFOeccxnx/8N/bkLxDnv5AAAAAElFTkSuQmCC\n", "text/plain": [ - "" + "" ] }, - "execution_count": 2, "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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yhCVLltyzbcmSJTzxxBP06dOH8ePHEx4ezpEjR9i3bx/ffvttWrn008kHBQXRoEGDvA6/SNAJJRf8vd05FXmHI5eirB2KphV6AwYMYP369SQmGhe6O3v2LJcvX+bkyZNpMwIDODs7M3PmTL788ktrhlsk6ckhc6Fn40pMWn2UlYcu4eVRytrhaFre2TAerhwx7zkrNoYen2W6u0yZMvj6+rJhwwb69u3LkiVLGDRoEEePHqV58+b3lK1VqxZ3797l9u3bwL3TyQPs2bMny9mHtYejayi54FrMns71y7P28GWSUwzWDkfTCr30zV5LlixhyJAhOTru/iYvnUwsQ9dQcsnf250NIVfYceI6HeuVt3Y4mpY3sqhJWFLfvn159dVXOXjwIHFxcTRv3pxDhw6xffv2e8qdPn2asmXLUqqUbjnIS7qGkkuPeJanlLO9nopF0/JAiRIl6NixI88++2xa7WTYsGHs3LmTrVu3AsZVHV955RUmT55szVCLJJ1QcsnBzobeXpXYHHqF2IRka4ejaYXekCFDOHz4cFpCKVasGGvWrGHKlCnUrVuXcuXK4efnx7Bhw9KOSV1DPvWxe/dua4VfqOnp683gwLmb9P9uD1MHNmFAcw+zn1/T8oOCMn39qlWreO211/j777+pVq2atcMpcPT09XkgOupCpvuaVS1NtbLOrDx0MQ8j0jQtI/369eP06dM6mViBTig5MGVpTwat6IkyZHwnl4jQr6k7u0/d4EpUfB5Hp2malj/ohJIDjdy8uGQLwaHLMi3Tz9sdpfRULJqmFV06oeRA5xbjcFCKgNAFmZapUa443lVL6bu9NE0rsnRCyYESLpXoYFuKTbFnSU7KvEnL39udY1diCIuIzsPoNE3T8gedUHKoR42e3LAV9h3+OdMyvb0qY2cjupaiaVqRpBNKDrVrPpoSBsWG439kWqZMcQce8XRjddAlUgxF53ZsTcsrtra294wn+ewz843YDwoKIiAgIO11ZtPeX758mQEDBpjtug/j7NmzNGrUyKoxZERPvZJDTsVK08mxAlsTrvB+fBSOTq4ZlvP39mBr2DX2nLpB2zrl8jhKTSvcihUrRlBQkEXOHRQURGBgID179kzbNnjwYGbOnPmfssuXL7dIDHktOTkZOzvzpQFdQ3kAPev4E2sj7DzwXaZlOtcvj4ujnW720rQ8EhUVhaenJ+Hh4YBxJP3cuXMBGD16ND4+PjRs2JBJkyalHbN//37atGlDkyZN8PX1JSoqiokTJ6aNqF+6dGmm10tfO4iLi2PQoEE0aNAAf39/WrZsSerg6c2bN9O6dWuaNWvGwIEDiY2NBaB69epMmjSJZs2a0bhxY44dOwbAP//8k1YT8vb2JiYmBqUUb775Jo0aNaJx48YZxtWqVSuOHj2a9vqRRx4hMDCQO3fu8Oyzz+Lr64u3tzerV68GjDWvPn360KlTJzp37vzQn3tGrFJDEZGBwAdAfcBXKZXh8HUR6Q58C9gCPyqlPjNtF+BjYCCQAnynlJpu6bhbNh1JmZDvWX96PZ39xmdYxsnelp6NK7Eu+DIf92tEMQdbS4elaXnu832fc+zmMbOes16Zerzt+3aWZe7evUvTpk3TXr/zzjtptYjhw4czbtw4bt26xfPPPw/AlClTKFOmDCkpKXTu3Jng4GDq1avH4MGDWbp0KS1atCA6OhpnZ2c+/PBDAgMD02ok8+bNy3Da+/Rmz55N6dKlCQ0NJSQkJC2269ev8/HHH7N161aKFy/O559/zrRp05g4cSIA5cqV4+DBg8yePZupU6fy448/MnXqVGbNmoWfnx+xsbE4OTnxxx9/EBQUxOHDh7l+/TotWrSgffv298QwePBgli1bxuTJk4mIiCAiIgIfHx/effddOnXqxM8//8zt27fx9fWlS5cuABw8eJDg4GDKlCnzMH+qTFmrySsEeBz4IbMCImILzAK6AheB/SKyRikVCgwHqgD1lFIGEcmTaX7t7J141LkqK+POExsTQQmXShmW82/mztLAC2wOvZK2VLCmabmXWZNX165d+f333xkzZgyHDx9O275s2TLmzJlDcnIyERERhIaGIiJUqlSJFi1aAFCyZMlMr5dZk1eqnTt3Mm7cOAAaNWqEl5cXAHv37iU0NBQ/Pz8AEhMTad26ddpxjz/+OADNmzfnjz+M/bJ+fn689tprDBs2jMcffxwPDw927tzJkCFDsLW1pUKFCnTo0IH9+/enXQdg0KBBPProo0yePJlly5al9e9s3ryZNWvWMHXqVADi4+M5f/582udl7mQCVkooSqkwMI4wz4IvcFIpddpUdgnQFwgFRgNDlVIG0/muWTTgdHo1GMaSg5/x1/4Z9On0SYZlfKuXwb1UMVYeuqQTilYoZVeTyGsGg4GwsDCcnZ25desWHh4enDlzhqlTp7J//35Kly7N8OHDiY/Pm5kslFJ07dqVxYsXZ7jf0dERMN5kkJxsnFR2/Pjx9OrVi4CAAPz8/Ni0aVOOruXu7k7ZsmUJDg5m6dKlfP/992kxrFixAk9Pz3vK//vvvxQvXvxh31qW8nMfijuQfgKti6ZtALWAwSISKCIbRKROZicRkVGmcoGRkZG5DqpJwyFUToGAC39mWsbGRujbtDI7TlwnMiYh19fUNC1rX3/9NfXr12fRokWMGDGCpKQkoqOjKV68OK6urly9epUNGzYA4OnpSUREBPv37wcgJiaG5ORkXFxciImJeaDr+vn5sWyZcQaN0NBQjhwxrmLZqlUrdu3axcmTJwG4c+cOx48fz/Jcp06donHjxrz99tu0aNGCY8eO0a5dO5YuXUpKSgqRkZFs374dX1/f/xw7ePBgvvjiC6KiotJqL926dWPGjBmkTgB86NChB3pvD8NiCUVEtopISAaPvmY4vSMQb5r9ci6Q6eAQpdQcpZSPUsrHzc0t1xcWGxt6uHqyV93h5s2TmZbz93YnxaBYe/hyrq+paZpRah9K6mP8+PGEh4fz448/8tVXX9GuXTvat2/Pxx9/TJMmTfD29qZevXoMHTo0rfnJwcGBpUuXMnbsWJo0aULXrl2Jj4+nY8eOhIaG3tMpn9209y+99BKRkZE0aNCA999/n4YNG+Lq6oqbmxvz5s1jyJAheHl50bp167TO98x88803ac1m9vb29OjRA39/f7y8vGjSpAmdOnXiiy++oGLFiv85dsCAAWlLIqeaMGECSUlJeHl50bBhQyZMmJDbjz9bVp2+XkS2AW9k1CkvIq2BD5RS3Uyv3wFQSn0qIseAHkqpM6YO+ttKqYzv403HXNPXh59Yz4Dd43mvwiM80X1GpuV6z9iBIKwd2zbX19Q0ayso09fnpZSUFJKSknBycuLUqVN06dKF8PBwHBwcrB3aQyus09fvB+qISA0RcQCeANaY9q0COpqedwCyrkuaWd1aPaidIgRcyXqRnn5N3TlyKYqT1x6sGq1pWsEQFxdH27ZtadKkCf7+/syePbtAJ5PcskpCERF/EbkItAbWi8gm0/bKIhIAoJRKBl4GNgFhwDKlVOrN1p8B/UXkCPApMDJP47exoUe5JhySRC5fzrzG06dpZWwEPSZF0wopFxcXAgMDOXz4MMHBwfTo0cPaIVmVVRKKUmqlUspDKeWolKqQ2qyllLqslOqZrlyAUqquUqqWUmpKuu23lVK9lFKNlVKtlVKHM7qOJfXwfgmADQdmZVqmvIsTbeu4serQZQx6KhatEChKK7wWRbn9++bnJq98rUqV1ngZ7Nhw/WCW5fo3c+fS7bv8cyL3d5hpmjU5OTlx48YNnVQKKaUUN27cwMnJ6aHPoefyyoWeFVvx2bWdnDq1hVq1umZYpkejSnxa8hg/7jhNR888GX+paRbh4eHBxYsXMcft91r+5OTkhIeHx0MfrxNKLnTzeYUv1u8gIPhHxmaSUBzsbBjhV51PNxwj5FIUjdyzvRlN0/Ile3t7atSoYe0wtHxMN3nlQjm3+viKMwG3QjNdbx5gSMuqlHC0Y+6O03kYnaZpWt7SCSWXerp34KIthIStyLRMSSd7nmhRhXXBEVy6fTcPo9M0Tcs7OqHkUucWr2CvFAFHf82y3Ii2xqaCX3aeyYuwNE3T0kRE5c0PWZ1QcqmkaxXa2bqyMfYMKcmJmZZzL1WM3l6VWLzvPFF3k/IwQk3TirK1hy/T4YttbA29avFr6YRiBj2rd+e6rRAYPC/Lcs+3q8mdxBSW7DufN4FpmlakLQu8wLglh2hapRQta5p/uvr76YRiBh18XsbZoAgI/z3Lco3cXfGrXZZfdp0lMTnzTnxN07TcmrfrDG8tD8avdjnmP+uLi5O9xa+pE4oZOBUrTWeH8myJjyAxIet5u55vV5Mr0fF6FmJN0yxm1t8n+WBtKN0aVuDHZ3zybOVYnVDMpEedfsRks948QIe6bnhWcGHujtN6xLGmaWallOKLjcf4clM4/ZpWZtbQZjja5d0y5DqhmEkr75GUNig2nF6XZTkRYWS7Ghy7EsOOE9fzKDpN0wo7g0ExeW0os7edYohvVaYNaoqdbd5+xeuEYib29s48WqwK25JuEheb9YrEfZpWpryLox7oqGmaWaQYFG+tCGbe7rOMbFuDT/wbYWOT5RLrFqETihn1rD+EeBvhr8DMF90CcLSzZbhfdXacuE7o5eg8ik7TtMIoMdnAK0sOsfzARcZ1rsN7vepjXHcw7+mEYkZNGw2lYooi4PyWbMsO862Gs4MtP+paiqZpDyk+KYXRCw6wPjiC93rW59Wuda2WTEAnFLOysbWjh2td9hhiuXXzVJZlXZ3teaJFVdYcvpxno1g1TSs87iQk8+y8/fwVfo2P+zXi+fY1rR2STijm1rPRcJJF2LJ/erZlR/hVRwG/7Dpr8bg0TSs8ou4m8dRP/7L39A2+GtiEJ1tVs3ZIgE4oZudZpzc1U4SAiF3Zlq1SxpmejSux6N/zRMfr6Vg0TcvejdgEhszZy5FLUcwe1ozHmz38+iXmphOKmYmNDT3KenFAErgScSjb8s+3q0FsQjJL913Ig+g0TSvIrkTFM3jOXk5FxjL3aR+6N6pk7ZDuoROKBfT0fhGAjVmsN5/Ky6MUrWqW4eddZ0hK0dOxaJqWsQs34xj4w24ibt9l/rO+PJIPV4DVCcUCqlZtSyODHQGRgTkqP6p9TSKi4lkfHGHhyDRNK4hOXotl4Pd7iL6bzMLnW9GqZllrh5QhnVAspGcFX8JsUjh95q9syz5Stzy1y5dgznY9HYumafcKunCbgd/vJtlgYMmoVjStUsraIWVKJxQL6dZ8LKIUG4LmZlvWxkYY1a4moRHR7D51Iw+i0zStINh+PJKhc/fi4mTPitFtqF+ppLVDypJOKBZSvkIjfKUYG26FZLnefKq+3pUpV8KRH7brgY6apsGaw5d5bv5+qpUtzvIXW1OtbHFrh5QtnVAsqEfl9pyzhdDwldmWdbSzZYRfdbYfjyQsQk/HomlF2fzdZxm35BDeVUuzZFQrypd0snZIOaITigV18R2HnVIEhGS93nyqYS2rUszelh936HXnNa0oUkoxbctxJq05Spf6Ffj1WV9ci1l+YSxz0QnFglxdq9LWpiQbY05lud58qlLODgxuUYU1hy9xJSo+DyLUNC2/SDEo3l8VwvQ/TzDIx4PvhjXDyT7v1jIxB51QLKx3jR5csxV25WBMCsCzfjVIMSjm7T5r2cA0Tcs3EpJTGLv4IAv/Pc/oR2rxeX+vPF/LxBwKXsQFTKdWr1M+RbHg2OIcla9a1pkejSqx8N9zxCYkWzg6TdOsLTYhmRG/7CfgyBXe71Wft7vXs+qMwbmhE4qF2ds7M7icN3u4y6lT2U9rD8aBjjHxySzdr6dj0bTC7LppXq5/z9xk2qAmjGxn/RmDc0MnlDwwoO0kHJRi4f6vclS+SZVS+NYow8879XQsmlZYXbgZx8Dv93DiWgxzn26eryZ5fFg6oeSBMmVq08uxImvvXiTq9tkcHTOqXU0u3b5LwBE9HYumFTbHrkTT/7vd3IhNYOHIlnSqV8HaIZmFTih5ZJjPq8TbCCt2fJij8p3qlaemW3Hm7tDTsWhaYRJ49iaDvt+DCPz+YhuaVytj7ZDMxmoJRUQGishRETEtduupAAAgAElEQVSIiE8W5bqLSLiInBSR8em2dxaRgyISJCI7RaR23kT+cDzr9KKFcmRx5D6Sk7K/JdjGRni+XU1CLkWz8+T1PIhQ0zRL+zPsKsN+/JdyJRxZMboNnhVdrB2SWVmzhhICPA5sz6yAiNgCs4AeQANgiIg0MO3+DhimlGoKLALet2y4ufdk3UFcsRX+2js1R+X9vd3xKF2MKevDSNZ9KZpWoP0eeIFRvx3As6ILv7/YGo/SztYOyeysllCUUmFKqfBsivkCJ5VSp5VSicASoG/qKYDUmdJcgcuWidR8Ovj+D/cUWHgq+6lYAJzsbXmvZ32OXYlhsb7jS9MKJKUU32w9zpvLg2ldsyyLnm9F2RKO1g7LIvJ7H4o7kP6b9KJpG8BIIEBELgJPAZ9ldAIRGSUigSISGBkZadFgs2Nr58DQiq05KImEHluVo2O6N6pIq5plmLY5nNtx2Y+21zQt/0hMNvDm8mC+2XqCAc09+Hl4C0o42lk7LIuxaEIRka0iEpLBo2/2R2frVaCnUsoD+AWYllEhpdQcpZSPUsrHzc3NDJfNHf+2k3A2KBYenJ6j8iLCxN4NibqbxDdbT1g4Ok3TzCU6PokR8/ax/MBFXu1Sly8HeOFgl99/w+eORVOlUqpLLk9xCaiS7rUHcElE3IAmSql/TduXAhtzea084VLSnb7O1Vh+9xyvXj9GuXL1sj2mQeWSDPGtym97zzG0ZVXqVihcHXmaVthcun2XEb/s43TkHaYObMKA5gV/jElO5Pd0uR+oIyI1RMQBeAJYA9wCXEWkrqlcVyDMSjE+sKEt3yJJhN935uwWYoDXH/WkuIMtH60L1bcRa1o+FnIpCv9Zu4i4Hc/8Z32LTDIB69427G/q/2gNrBeRTabtlUUkAEAplQy8DGzCmDCWKaWOmrY/D6wQkcMY+1DetMb7eBjVq3egnRRn6c1gEhNicnRMmeIOvNq1LjtOXGdr2DULR6hp2sP4O/wag37Yg52NsHx0G/xql7N2SHlKitKvXR8fHxUYGGjtMADYvX8WL4R+z5Qqj9Gn0yc5OiYpxUDPb3eQmGJg86vtcbQrWFNba1phtujf80xYHUK9ii78PLwFFQrIolg5ISIHlFKZjhdMlaMaioj8ISK9RCS/N5EVGK2bj6ZmirDgXECOlggGsLe1YeJjDTh3I46fd561bICapuWIwaD4fOMx3l15hPZ1yrHshdaFKpk8iJwmiNnAUOCEiHwmIp4WjKlIEBsbhrl3JMwmhUNHFuT4uHZ13OhSvwIz/zrBtWi9CJemWVNCcgrjlgbx3bZTDG1ZlblP+1C8EN8WnJ0cJRSl1Fal1DCgGXAW2Coiu0VkhIgUnPUp85ne7SZQ0qBYEDz3gY57v1d9ElMMfL4xu3GhmqZZyu24RJ76cR9rD19mfI96TOnXqEAuimVOOX73IlIWGI5xQOEh4FuMCSZni3xo/+HsXI7+JevyV8otIi4fyPFx1csV59m2NVhx8CJBF25bMEJN0zJy/kYcj3+3m6ALt5k+xJsXO9QqsItimVNO+1BWAjsAZ+AxpVQfpdRSpdRYoIQlAyzshrR+D4DFe6Y80HFjO9XBzcWRD9YcxWAoOjdWaJq1BV24jf/sXdyITWTByJb0aVLZ2iHlGzmtoUxXSjVQSn2qlLpngY6c9PxrmatUuTmdbEuzIvo4cXE5n1W4hKMdb3XzJOjCbVYFXbJghJqmpdp09ApPzNmDs6Mtf7zUBt8ahWfqeXPIaUIpLSKP3/foLCLlLRpdEfGk1/NE2wjrdn78QMf1b+ZBEw9XPttwjDt6/XlNsxilFLP+PsmLCw7gWbEkK1/yo5abbpy5X04TynPAj8Aw02Mu8DawS0SeslBsRYZ34yepb7Bl0cW/cnwLMRjXTJn4WEOuxSQwe9tJC0aoaUXX3cQUXlkSxJebwnnMqzJLR7WiXCGdLTi3cppQ7IH6Sqn+Sqn+GNcmUUBLjIlFywWxseHJaj05ZavYc/D7Bzq2ebXS+Hu7M3fHGc7fiLNQhJpWNEVE3WXQD3tYF3yZt7p78u0TTXGy1wOKM5PThOKhlLqa7vU1oIpS6iaQZP6wip7ufu9QNkWxMPS3Bz727e71sLMRpgSEWiAyTSuaDp6/RZ+ZuzgdGcvcp3x46ZHa+k6ubOQ0oWwTkXUi8oyIPAOsNm0rDuj7Vs3AwdGFQaUbs13Fcu7cjgc6tqKrE2M61mbT0avs0ssFa1quLT9wkSd+2Esxe1tWjvGjS4MK1g6pQMhpQhmDcc2RpqbHr8AYpdQdpVRHSwVX1AxqOxE7pVj07+cPfOxzbWvgUboYH64N1csFa9pDSjEopqwP5Y3fD9O8WmlWj/HTy0U8gGwTimld97+UUiuUUq+aHstVUZpVMo+Uc6tPT4fyrLpzlpjoB7sV2Mnelvd71Sf8agyL9p23UISaVnhF3U3i2Xn7mbvjDM+0rsavz/lSuriDtcMqULJNKEqpFMAgIq55EE+RN6zZK8TZCCt3Tn7gY7s1rEjrmmX5avNxbt3RywVrWk6diozFf9Yudp28zif+jZnctxH2RXwalYeR008sFjgiIj+JyPTUhyUDK6oa1OtHM+XAoit7SEl+sKQgIkzq04CY+CS+2XrcQhFqWuHyz/FI+s3axe27SSwc2ZKhLataO6QCK6cJ5Q9gArAdOJDuoVnAsFr+XLKFf/Z988DH1qtYkmEtq7Hg3/OEX8nZ4l2aVhQppfhxx2lG/LIP91LFWD3Gj5Y1y1o7rAItp7MNzweWAXuVUvNTH5YNrejq1OoNKqUoFh5f9lDHv9a1LiUc7Zi89qheLljTMpCQnMKby4P5eH0YXRtUYMXoNlQp42ztsAq8nE4O+RgQBGw0vW4qImssGVhRZmfvxBNuvuyTBMJPrH/g40sXd+C1rnXZfeoGG0OuWCBCTSu4rsXEM2TOXpYfuMgrnevw3bDmRXoNE3PKaZPXB4AvpjEnSqkgoKaFYtKA/u0m4mRQLAp88GYvgGEtq1K/UkneXXmEy7fvmjk6TSuYDpy7Rd+ZuwiNiGbW0Ga81rUuNjZ6sKK55DShJCmlou7bpgc7WJBrqeo8VsyD9fER3Lp56oGPt7O1YdZQbxKTDby86CBJemyKVoQppfh55xkG/7AHWxth+Ytt6OVVydphFTo5TShHRWQoYCsidURkBrDbgnFpwJMt3yRRYN7fbz3U8TXdSvD5AC8Onr/N5xuOmTk6TSsYYuKTeGnhQT5cF8ojnuVZP7Ydjdz1KAhLyGlCGQs0BBKAxUA08D9LBaUZ1azRmV72biyMDudKxKGHOkdvr8o807oaP+48o/tTtCInLCKaPjN3sTn0Ku/0qMfcp5vj6qxXLbeUnN7lFaeUek8p1UIp5WN6Hm/p4DQY2/FLDAIz/37zoc/xbq/6eHm48ubyw3pGYq3IWBZ4gX6zdnEnIZlFI1vygl6m1+JyepdXXRGZIyKbReSv1Ielg9OgcmUfhpWow5rEKxw/ueGhzuFoZ8usoc0Q4KVFB4hPSjFvkJqWj8QnpfDW8sO8tTyYZlVLs/6Vdnp8SR7JaZPX78Ah4H3gzXQPLQ+M7PotLgq+3vXg07GkqlLGma8GNSXkUjQfr9fT3GuF05nrd+g3axfLAi/ycsfaLBjZEjcXvRhWXslpQklWSn2nlNqnlDqQ+rBoZFoaV9eqPO/Wip3cYe+BHx76PF0bVOCF9jVZsPc8q/U69Fohs+FIBI/N2MmV6Hh+GdGCN7p5YqtvCc5TOU0oa0XkJRGpJCJlUh8WjUy7x5AuX1EpRTEt+DsMKQ+/fvwb3TzxqVaad/44wslrsWaMUNOsIzHZwIdrQxm98CC1ypdg/Svt6OhZ3tphFUk5TSjPYGzi2s3/z+MVaKmgtP9ydHJlbI1+hNmksHHnRw99HntbG2YM9cbJ3paXFh7gbqLuT9EKrsu37/LEnD38vOsMw9tU5/cXWuNeqpi1wyqycnqXV40MHnqkfB7r1f4D6hlsmH7qDxITHn7ix0quxfhmcFNOXItlwuoQM0aoaXnnn+OR9Jq+g/ArMcwc6s0HfRriYKennLemLD99EXkr3fOB9+37xFJBaRmzsbXj1cYvcMkWlvz5eq7O1b6uG2M71WH5gYss23/BTBFqmuWlGBTTthxn+C/7KO/ixJqxbentVdnaYWlkX0N5It3zd+7b193MsWg50MbnJdpQjDlXdxMdlbtEMK5zHfxql2XC6hDCIqLNFKGmWc6Fm3EM/mEP0/88wePeHqwa40cttxLWDkszyS6hSCbPM3qt5ZFXW71PtMBPW3M3WYGtjfDNYG9ci9nz0sKDxMQnmSlCTTMvpRTLAi/Q/ZvthF+JYdqgJkwd6EUxB1trh6alk11CUZk8z+i1lkfqefbhMYfyLIgJJ+Jy7u7ednNxZMYQb87duMM7fxzR66do+c6N2AReXHCAt5YH08jdlQ3/a8fjzTz0qPd8KLuE0kREokUkBvAyPU993fhhLyoiA0XkqIgYRMQni3I/i8g1EQm5b3sZEdkiIidM/y39sLEUVC8/8iUAM7c93MSR6bWsWZY3unmyLjiC3/aey/X5NM1c/jp2lW7f7ODvY5G827Mei55vhUdpvRBWfpVlQlFK2SqlSiqlXJRSdqbnqa9zM8NaCPA4xiWFszKPjPtqxgN/KqXqAH+aXhcplSo3Z1iJOqxNvEr48XW5Pt+L7WvRqV55PloXyuELt80QoaY9vLjEZN5beYRn5wVSroQDq1/2Y1T7WnqgYj5nlXvslFJhSqnwHJTbDtzMYFdfIHUJ4vlAPzOGV2A8lzoly56HH5eSysZG+GpgE8q7ODFm0UGi4nR/imYdh87fotf0nSzad55R7Wuyaowf9SuVtHZYWg4U1Ju2KyilIkzPrwAVMisoIqNEJFBEAiMjI/Mmujzi6lqVUeXbsIs49hz4PtfnK13cgZlDvbkaHc/rvx/W/SlankpKMfD1luMM+H4PickGFo1sxbs96+NkrzveCwqLJRQR2SoiIRk8+przOsr4rZfpN59Sao5pyn0fNzc3c146XxjS5Ssqp8DXwd/nakqWVN5VS/NOj/psDbvKd/88+EqRmvYwTkXGMuC73Xz75wn6NqnMhv+1o3UtPUOwOURHXeCzZY8RGxORfeFcslhCUUp1UUo1yuCx2gynvyoilQBM/71mhnMWSA6OLoytaZySJWDHw89GnN4Iv+r09qrEFxvD+WnnGbOcU9MyopTit73n6DV9B2dvxDFraDOmDW5KSSe9CJY5HDg8nwErerA07gyBRxdZ/HoFtclrDcb5xTD91xxJqsDq2W4S9Q22zDi9KldTsqQSEaYNakqPRhX5aF0os7edNEOUmnava9HxjJi3nwmrQmhRvQyb/tder/NuJklJccxYOZhnD32JPcJvvpN4pFXuZtfICaskFBHxF5GLQGtgvYhsMm2vLCIB6cotBvYAniJyUUSeM+36DOgqIieALqbXRZaNrR2veY3msi0s3mqefzQOdjbMGOJN36aV+WJjOF9vOa77VDSzUEqxOugS3b7Zzp5TN5jcpyG/PutLRVcna4dWKFy4sIfhC9oyJzqUxxwqsmzQFho1GJj9gWYgRelLwsfHRwUGFt5Jkl+c35IjhjsEPB6Aq2tVs5wzxaAYvyKY3w9c5MUOtXi7u6ceUKY9tLPX7zBhdQg7TlzHy8OVaYOaULu8i7XDKhSUwcC6fyYw5exqbICJtQbRvf1Es5xbRA4opTIdM5jKzixX0/KFV1tPYODu8fy0ZRyvDVhplnPa2gif9/fCwc6G7/85RUJyChN7N9BJRXsgCckpzPnnNDP+PomDrQ0fPNaAp1pX1+NKzCQm+hIfrRnKhpSbNBNHPnt0DpUqN8/zOHRCKUQ86/bmscCvWRh7giGXD5jtH5SNjfBxv0Y42tny864zJCYb+KhvI2z0l4GWA3tP3+C9lUc4FXmHXo0rMaF3A928ZUaHghcwPvBzrtooXi7tzcheP2Fr52CVWHRCKWTGdpzKxk1PMXPbm0wZ+pfZzisiTOhdH0d7G77bdoqEZAOf9/fSvzC1TN28k8iU9WGsOHgRj9LF+GV4CzrW0yspmktyUjxz1o3gh6gjVEaY7/M+TRo9kf2BFqQTSiFTsZI3w1zqMi/mOE+Fr6GeZx+znVtEeKubJ052tny99TiJyQamDWqCnW1BvVlQswSDQbH8wEU+2RBGbHwyLz1Si7Gd6uiZgc3o4sW9vLP1JYIkiT4O5XnnsYWUcLH+HXI6oRRCI7t8yx9/9ODrvR/zgxkTChiTyrgudXCws+HzjcdITDYwfYi3XilPA+D41RjeXxnCvrM3aVG9NFP8G1O3gu50N6d12yYw5Yyxj/TzGv3p2cE848/MQSeUQqikaxVGVWjDl5F72B04mzY+L5n9GqMfqYWjnQ0frgvlxQUHmD2smZ4iowi7m5jCjL9OMGf7aUo42fFFfy8GNPfQ/WxmFBsTwZQ1Q1mXfB1vceTTrt/h7u5r7bDuoW8bLqQSE2Lot7ANClg+aAvFS1S0yHUW7D3H+6tCaFenHHOe8tHNGkXQ3+HXmLg6hAs379K/mQfv9qxH2RKO1g6rUAk6spDx+z/jio3ihVJNeL7XT9jZ592NDTm9bVi3UxRSDo4uTPF5m8s2is/XPmmx6zzZqhpfDvBi58nrjJi3jzsJuZ9PTCsYrkbHM2bhQUb8sh8HWxsWP9+KrwY10cnEjBITYvhmxQCeOfApAPOav8PofgvzNJk8CJ1QCjFvryd5rmR9ViZe5c/dn1vsOgN9qvDN4KbsP3uLp3/eR7ReSrhQi7qbxBcbj9Hhy7/ZEnaV17vWJWCcnszR3MJPrGfIorb8FBuOv2NlVgzaQtPGw6wdVpZ0k1chl5Rwh2GL/IggmT96LcWtfEOLXWtjSARjFx+ifqWS/PqsL6WcrXMvvGYZdxNTmLf7LN9tO0lMQjJ9mlTm9a6eVC2rV1A0p5TkROZveJGZN/ZR0gCTGzxLh1avWTWmnDZ56YRSBJw+8yeDto2jhU0JZj+1G7GxXMX0z7CrjF5wkBrlijN9iDeeFfUdPgVdUoqBpfsvMP3PE1yLSaBTvfK88agnDSrrRa/M7cKFXbz35ysckkS62Lgyodc8ypSpbe2wdB+K9v9q1ujMa5U6sJM7LN08zqLX6ly/Ar+MaMH12AQem7GTWX+fJDnFYNFrapZhMBgncewy7R/eXxVC1TLO/P5ia34e3kInEzNTBgO/b36V/ltf4KRK4JOqfZk2bHu+SCYPQtdQighlMDD6t9YcMNxhWceZ1Kj+iEWvd/NOIhNXh7AuOAIvD1emDmyixyMUEEopth2P5IuN4YRFRFOvogtvdfeko2d5PYebBUReO8qkjc+xQ92hJU58/OgcKlbytnZY99BNXhkoygkF4NrVEB4PeAIP7Pjtyd3Y21u+7TvgSAQTVoUQE5/MuC51eKF9TT2yPh8LPHuTLzaGs+/sTaqWceb1R+vymFdlPZ7EQjbt+IiPTi4lHni1YjuGPDoDG9v8NzxQJ5QMFPWEArB156e8emoRo0o2YKz/0jy55o3YBCauPsr6IxE0MdVW6ujaSr4SFhHN1E3h/HnsGm4ujrzSuQ6DfaroGRAsJCrqPJ+ue4b1yddpaLDlk0emUbNGJ2uHlSmdUDKgE4rR+4u6sDbxCvObv5OntyGuD45gwuoQYuOT+V/XOoxqp2sr1nb+Rhxfbz3OqqBLlHC048UOtRjhVx1nh/z3K7mw2B04mwnBs7lhAy+U8mJkrx/zpLUgN3RCyYBOKEaxMREM+P1RBMuOos/I9dgEJq4OIeDIFV1bsRKlFHtO32D+7rNsCb2Kva0NI/xq8GKHmvpWbwu6G3eTr9c+xeL489RIET5tPYmG9ftbO6wc0QklAzqh/L+Dh39lxKEv6OdYiclDtuT59dcFX2bi6qPExifzate6PN+uhq6tWFhcYjIrD13i193nCL8aQ2lne57wrcrwNtWpUDJ/jrwuLAKD5jHp4Fect4UnnWswrvd8nIqVtnZYOaYTSgZ0QrnXtysG8GNsON/UeZLObd7O8+tfj01gwqoQNoRcoUmVUnw10EsvB2sB52/E8euesywLvEB0fDINKpVkeJvq9GlaWU/oaWF3Yq/w9fpnWRp/AfcU+NB7HL7eI60d1gPTCSUDOqHcK3UU/RWS+aP375Rzq5/nMSilWBccwcTVIdxJTOG1rnV5vl1NvXBXLiml2HHiOvN3n+Wv8GvYiNC9UUWGt6mOT7XS+vbfPLB7/yw+OPIdV2xgmHMNxvb+BWfnctYO66HohJIBnVD+Ky9H0WclMsZYW9l41FhbGduxNh3rldeJ5QHFJiSz4sBF5u85y+nIO5Qr4cAQ36oMa1lNL7ubR6KjLjA1YAQrE69SPUX4qMXb+X4OruzohJIBnVAytnDDS3x2bQfvV+zI4G7TrRaHUoq1wRF8vC6UazEJuJcqxtCWVRnkUwU3Fz2DbVZOR8by655zLD9wkdiEZJp4uPJMm+r08qqEo51u1sorf++Zysdh87hhA8Nd6jG61084OrlaO6xc0wklAzqhZMyQksxLC/zybBR9dpJSDGwJvcqCvefYfeoG9rZCt4YVebJVNVrWKKOba0wiYxL469hV1gVHsOPEdexthV6NK/FMm+p4Vy04Hb6Fwa2bp/hsw3MEJN+gjsGGj1pNLDB3cOWETigZ0Aklc9YYRZ8TpyJjWbj3PMsPGDuU65QvwbCWVXm8uQclneytHV6eUkpx4losW0KvsjXsKkEXbqMUuJcqxkAfD4a2rEp5F92slZeUwcDmXVP45ORSogVGlfJiZI+52DsWt3ZoZqUTSgZ0Qsnalp2f8NqpxbxQsiEv+y+xdjj3uJuYwtrgyyzce47DF6MoZm9LP+/KDGtZjUbuBb9JITNJKQb2n73J1tBrbA27yvmbcQB4ebjSpX4FutSvQP1KLrrWZgXXI8P4eONI/jRE09Bgy4ftPqVu7R7WDssidELJgE4o2XtvUWfWJV5lvs+7NG001NrhZCj44m0W7D3HmsOXiU8y0LRKKZ5sVY3eXpUKxW2w0fFJ/BMeydawq/x97BrR8ck42NngV6ssXRpUoHO9CrqD3YqUwcDabe/z+bk1xAuMKevL091n59tVFM1BJ5QM6ISSPWuOon9QUXFJrDh4kQX/nuN05B1KOdszoJkHHTzdaFCpZIFaivbCzTj+DLvK1rBr7D19g2SDokxxBzrVK0+X+hVoV6ccxR31dCjWdiXiEJM3j2Ynd2iq7PnwkWlW73PMCzqhZEAnlJw5cHg+Iw59SW/78kwZstVqtxLnVOpUIgv3nmfT0SskG4z/piuWdKJB5ZI0rFySBpVK0rCyK1XKFLNa85BSiuuxiZy4FsPJa7GcuBqb9vx6bCIANd2K07V+Bbo0qECzqqX1bdP5RHJSPIu3jGPm1V0oYFzFdjzR9Vts7YrGVDU6oWRAJ5Sc+27VUGZHHWFkCU/G9V9u7XByLCouiZDLUYRejubo5ShCI6I5eS0WU47BxdGO+mkJpiQNKpekTnkXs86qq5TiWkxCWsI4cS2Wk6bnt+KS0sq5ONpRp0IJ6pR3wbOiCx083ajlVsJscWjmEXx0KR/t+4RjNgbaUpx3O31NlSqtrR1WntIJJQM6oeScMhj4cFkPlidc5o1yrXmm1xxrh/TQ4pNSCL8Sw9HL0YRGRHH0cjTHImK4m5QCgL2tUKe8Cw0rl6RcBuNdMvpfRPHfjbfvJKUlkJj45LTtrsXsqVuhBLXLu1CnfAnqVChB3QoulHdx1J3p+VhU1HmmbxjF7/EXcTPA+LpD6dJmfL6vsVuCTigZ0AnlwaQkJ/Lm4s5sMdzm4yq96NvpM2uHZDYpBsWZ63cIjTDVZC5HExYRTfTd5P8WzuQ7//7NLk521C5vrHHUqVAi7Xm5Eg46cRQgymBg3T8TmXp2FVECQ4vXYkyPH/J1f6Kl6YSSAZ1QHlxiQgxjlnRmv4rja8/hdGz9hrVD0jSLOX3mL6b88xb7JAEvgx0T2kymnmcfa4dldTlNKEWv7qY9EAdHF77tv44Gyp43wuexP+hna4ekaWYXf/cW0/8YRP9/XiFMxTOhUmd+e3q/TiYPyCoJRUQGishRETGISKZZT0R+FpFrIhJy3/YvReSYiASLyEoRKWX5qIsu5xLlmdV3OR4GG145NI2w8NXWDknTzGb7v9/Sb3F75saE0cO+PGsf+4NBj36TL9d2z++sVUMJAR4HtmdTbh7QPYPtW4BGSikv4Djwjlmj0/6jdJla/NDzV1wUvLj7Pc6d22HtkDQtV65cCeK139oy5tiPOCD85DWOT4b9Rdlyda0dWoFllYSilApTSoXnoNx24GYG2zcrpVJ7T/cCHmYOUctAxYpN+aHTTBTwwp8vce1qSLbHaFp+k5wUz68Bo+i74Um2J9/mldLerBi2p0AufJXfFIY+lGeBDZntFJFRIhIoIoGRkZF5GFbhVKP6I3zXajK3RPFCwDCibp+1dkialmP7g37miQUt+TJyD81sSrCyy1ye7/NroZvM0VosllBEZKuIhGTw6GvGa7wHJAMLMyujlJqjlPJRSvm4ubmZ69JFWsP6/Zne5BXOSQpjVj5OXNx1a4ekaVk6f34n//vNj2cPf02USuGrmoOZ/dTuIjdA0dIs1uuklOpiqXMDiMhwoDfQWRWle5/ziZbNRvFF3A1eP7mQ137vxYwn/tK/8rR8JzrqAnM2j2XhnZPYKxhb1punu07HqZheL8YSCmSTl4h0B94C+iil4qwdT1HVpe07TPLozi7ieO/3nhhSMhgUqGlWkJwUz5KNY+n9Rw9+vXOSxxwrsr7XUkb1+U0nEwuy1m3D/iJyEWgNrBeRTabtlUUkIF25xcAewFNELorIc6ZdMwEXYIuIBInI93n8FjSTx7tM5dUyLdiQcpNPl/dBGXfBZ3EAABH4SURBVAzWDkkr4nbtn8mA33yZcnUbtcWJpa2n8OGQrbiVb2jt0Ao9PVJeM4uvlvsz785JXnJtzOh+i6wdjlYEnT7zJ19uf4+d3KFKCrxe70k6tXqzSM69ZW45HSmvR+5oZvHa4yu4veRRZkcdwXXjGIZ2n2XtkLQi4tbNU8zeMpbf757HWcEb5VszpMs0HBxdrB1akaMTimYWYmPDpIHriFrcmU+vbsd120R6PfKhtcPSCrGkhDss2voqP1zbTZzAgGJVeanrdMqUqW3t0IosXRfUzMbO3okvBwXgoxx59+wf/LLuOd2nopmdMhj4a/cX9FvYiqnX9+BlU5zl7abx/uAAnUysTCcUzawcnVyZNSCALnalmXZjH28s6kBc7DVrh6UVAspgYM+B73lqvg/jTvyGHcJ39Ufx/TP/UrvWo9YOT0MnFM0CnEuUZ+rQf3itrC9bk28xdFkXPfeXliv7D/3E8F9b/F979x4dVXnucfz7S4LcIchFQCDhZpEqIsrFGyICtdKKF2prFaXW2mN7vB1be1rb2uNx1QtrVY+ttWKPtVIFW9Qj1htgQS2FAAYIQaAiDfdLBKSAEJPZz/ljb+wQBxhgkp1Jns9as/Jm9p49zzszmV/23jPvy42lj7LFPuGnnUbw/Lj5nDvo5rhLc0n8U16uRs199zfcWfIrqoD7T76e84f8R9wluSxSvORpHl30CPNVQYeEcUPnYVxxwX1+wr2W+QRbKXigxGPDhvncPv1GluckuKnVKfzbJZN8aHB3SEtKp/Drd3/B39hL24RxQ6dzGTvsPv9SYkw8UFLwQInPvr07+O8XxzKtcivnqwU/H/NHWrXuGndZro5Ztvx5Hl0wgXdsD20C45sdzuLKCx6gabPj4y6tQfNAScEDJV4WBEyZfgsPbp5N50A8PHQCvXulmu7GNTQrVk7j0aL7mW27aB0Y49udydcveJBmLTrEXZrDAyUlD5S6oXjJ09zx7oPsEdzT80ouGvrTuEtyMXl/1es8NvdeZgQ7aRkY1x1/OlcPf5AWLTvFXZpL4oGSggdK3bF1Syl3vHYti1XJN5r34pYxk8lr1CTuslwt+fuq13hi3n28UbWd5gbj8k/lmuEP+mHQOsoDJQUPlLqlsmIPD7w4lucq1jOYJkz48hTaHN8z7rJcDQkSVbyz4BEmrZxMEftoGhjXtD6Z64ZPoHV+YdzluUPwQEnBA6VuevHNO7l33au0DeChs+/h830uj7skl0Ef797KS3+9h2c2vsWaXOiQML7efiBjz7vbgyRLeKCk4IFSdy1b/jy3zb2b7Tnwk66jGXPBfT5KbJbbvGkRz865h6m73mdXjjg1yGNcjzGMOPtOGjVqFnd57gh4oKTggVK3bd++ijtfvooi9jGYJtw++Ie+t5KFlpRO4Q+Lf82Mqu0YMCKvDeP638Rpfb/m/yRkKQ+UFDxQ6r6qyn08N/N2Ht/8DjtyxBdzj+fm839O167nxF2aO4Sqyn3MnPsAkz54iZKcSloGxhUte3PV2XfRufNh34dcHeeBkoIHSvbYvWsTv5t5G5M+Wkal4Mpmhdw4/Be0bXdS3KW5JDt3ruX5t3/G5PL5bM4V3RJwdeehXHru3f4dknrEAyUFD5TsU751GY/95Q5e2Leexgbj25zGdSMe8jerGAWJKoqX/oE/L3+WV/dtZG+OGGSNGdfnKoYOvNWH1amHPFBS8EDJXv8om80v3/kxM4KdtE0YN504nMuH3+8nd2vRqg+m88riibyycwWbckXTwBjVuCPXnHELfT53SdzluRrkgZKCB0r2W1I6hV8snECxPqEgAbf0/iojz/mRn+ytIVu3lPLawv/hz1vnsyInINeMs9SC0QUjGX7mzb6n2EB4oKTggVI/WBDw9vyHefi9p1iVa5wa5HH76TczsP/1cZdWL+zetYkZ8x/ilfWzmG97MYUf+R3dcQhfGHgr7dr1ibtEV8s8UFLwQKlfElWfMO2tH/PomlfZkivOU3NuO/tuTur1xbhLyzqVFXv4a/FjvPLBNGZXbqciR3RNwJfanMLoAd+hoOC8uEt0MfJAScEDpX7at3cHk9/8Hk+UF7FbMEhNGdnxLC4ccBPt2p8cd3l1VmXFHhYvf443VvyJ1/euY2eOaBMYFzUrYPTnx9Gv75V+KNEBHigpeaDUbzs/KuMPs37I6ztKKcsFmXE6jRl5wkBG9P82HTudHneJsQoSVaxc9QpF77/MvG1LKQ72sDdHNAmMCxq15Uu9L+esAd/yDzq4z/BAScEDpWGwIGDV6unMLH2a6TuWsSonAKBfkMfI9mcwov8NdOkyJOYqa54FAWvXzaFoxVTmbS1mQdUOPsoRAN0TYnDzLgzpMpQhp42neYuOMVfr6jIPlBQ8UBqmsrK3mFnyJNO3LWF5TgKAk4NcRrbtx4h+19O9cFi8BWbQ1i2lFL03haJN8yjat5nNuWGAdEwYg5t0ZHCnwQzq+1VOOKFfzJW6bOKBkoIHilu/fh4zF/+WGeXFlORUAtAryGFkfl9GnnodvXqMyprzBpUVe1i3sYgPNsxjwYY5FO1Zx+rc8O+5dWAMymvDkA4DGNxnLN26npM1/XJ1jwdKCh4oLtnmzYt5c9HjzNiygGL2YRKtA6OARnQ9Lp+C5p3omt+Tbu1PoeDEwbEMtR4kqti8ZTFlG+ez5sP3WPvPNZTtLWdNYg8bcoxA4R5I08AYkNOcIW1PZXDvL/O5XqP9G+suYzxQUvBAcQfzYflyZi2ayIrty1lbsZ21ib1syjEsesMGaBUY3WhEt+Na061ZJ7pFYdOt80Dy87sf0R6ABQGJxCcEQSVViQo+/vhD1m1cSFl5CWs+Ws2ajzdTVrWLdSSoyPlXDU0Do5A8Chq1oqB5Zwrye1HY4TT69LqYRo2bZ/QxcW4/D5QUPFDckfikYhfrN85n7ZbFrNm2knW71rGmYhvrEnvZWC1sWgZGW8shwEgAVRgBkBBUQdgGqhS1k25bXZ4ZXYMcCvJaUNjsBLq1KqSw/SkUdB5M+/Z9/dCVq3XpBorvEzt3EMc1bkmP7hfSo/uFn1kWhs0C1m5ZxNrtK1n7z3XsqNpNLjnkKZdc5SRdcv/1M2d/O++AduO8JnRr24fCTmfQqeMZ5DVqEkOPnTs2HijOHYUwbIbTo/vwuEtxrs7wfWfnnHMZEUugSPqKpGWSAkkHPS4n6UlJWyWVHmT5HZJMUruaq9Y551w64tpDKQUuB94+zHpPARelWiCpKzAKWJvRypxzzh2VWALFzJab2co01nsb2H6QxQ8BdwIN52NqzjlXh2XlORRJY4ANZrYkjXVvlLRQ0sLy8vJaqM455xqmGvuUl6SZQKoR5+4ys5eOYbvNgB8RHu46LDObCEyE8HsoR3u/zjnnDq3GAsXMRtTQpnsC3YElCr8c1gUoljTIzDbX0H0655w7jKz7HoqZLQU+nchaUhlwppl9GFtRzjnn4hl6RdJlwC+B9sBHwGIz+4KkzsBvzeziaL3JwDCgHbAFuNvM/rfatspIM1AklQNrjrLsdkBDCy3vc8PgfW4YjqXPBWbW/nArNaixvI6FpIXpjGVTn3ifGwbvc8NQG33Oyk95Oeecq3s8UJxzzmWEB0r6JsZdQAy8zw2D97lhqPE++zkU55xzGeF7KM455zLCA8U551xGeKBUI+kiSSslrZL0nymWj5dULmlxdLkhjjoz6XB9jta5UtJ70bQDz9Z2jZmWxvP8UNJz/HdJH8VRZyal0edukmZJWiSpRNLFcdSZKWn0t0DSm1FfZ0vqEkedmZTGlB+S9Ej0mJRIGpDRAszML9EFyAU+AHoAxwFLgL7V1hkP/CruWmu5z72BRUCb6PcOcddd032utv7NwJNx110Lz/NE4Kao3Rcoi7vuGu7vn4DrovZwYFLcdWeg30OBAUDpQZZfDLwGCBgCFGXy/n0P5UCDgFVmttrMPgGmAGNirqmmpdPnbwGPmtkOADPbWss1ZtqRPs9XAZNrpbKak06fDWgVtVsDG2uxvkxLp799gb9E7VkplmcdO/SUHxD28WkLzQPyJXXK1P17oBzoRGBd0u/ro+uquyLaXZwaTfSVzdLp80nASZLmSJonKeWkZ1kk3ecZSQWEg5H+JdXyLJJOn38GXCNpPfAq4Z5Ztkqnv0sIJ/oDuAxoKaltLdQWp7Rf+0fDA+XIvQwUmlk/YAbw+5jrqQ15hIe9hhH+t/6EpPxYK6o9XwOmmlki7kJqwVXAU2bWhfDQyCRJ9fk94nvA+ZIWAecDG4CG8DzXmPr8YjkaG4DkPY4u0XWfMrNtZlYR/fpb4Ixaqq2mHLbPhP/FTDOzSjP7B/B3woDJVun0eb+vkf2HuyC9Pn8T+COAmc0FmhAOKJiN0vlb3mhml5vZ6cBd0XVZ/+GLwziS1/4R80A50AKgt6Tuko4jfDOZlrxCteONlwDLa7G+mnDYPgP/R7h3gqR2hIfAVtdmkRmWTp+R1AdoA8yt5fpqQjp9XgtcCCDpZMJAydZpTtP5W26XtAf2Q+DJWq4xDtOAa6NPew0BdprZpkxtPOvmQ6lJZlYl6d+BNwg/JfKkmS2TdA+w0MymAbdIugSoIjz5NT62gjMgzT6/AYyS9B7hIYHvm9m2+Ko+Nmn2GcI3oSkWfTwmm6XZ5zsID2feTniCfny29j3N/g4D7pNkwNvAd2MrOEOSp/yIzoXdDTQCMLPfEJ4buxhYBXwMfCOj95+lrxfnnHN1jB/ycs45lxEeKM455zLCA8U551xGeKA455zLCA8U55xzGeGB4rKapN1prHObpGYZvM9LJfXN4Pb+dgy33R397Cxp6iHWy5f0naO9H+fS4YHiGoLbgCMKFEm5h1h8KeHAghlhZmdnYBsbzWzsIVbJBzxQXI3yQHH1gqRh0ZwWUyWtkPRM9G3gW4DOwCxJs6J1R0maK6lY0p8ktYiuL5P0gKRi4CuSviVpgaQlkp6X1EzS2YQjJEyI5krpKal/NGhmiaQXJbWJtjdb4bwqCyUtlzRQ0guS3pd0b1Ltu5PaP5C0NLrP+1P0s3tU+9Jq2yjcPweGpM9Lmh/VVyKpN3A/0DO6boKkFgrnAimOtjUmaTvLJT2hcO6b6ZKaRst6SZoZ1VYsqWd0/fejx6lE0n9l9Il12SXu8fv94pdjuQC7o5/DgJ2EYxPlEA6Xcm60rAxoF7XbEX4runn0+w+Anyatd2fSttsmte8Fbo7aTwFjk5aVAOdH7XuAh6P2bOCBqH0r4XDwnYDGhOOjta3Why8CfwOaRb8fn6K/04Bro/Z3k25bSDQHBvBL4OqofRzQNHl5dH0e0CrpMVlFOEdGIeEoEP2jZX8EronaRcBlUbsJ4V7fKMJ5VBQ97n8Ghsb9uvBLPBcfesXVJ/PNbD2ApMWEb45/rbbOEMLDVXMkQfiGmzxW13NJ7VOivYB8oAXhMB4HkNQayDezt6Krfk84cdN++4dxWQoss2jcJEmrCQfpSx7CZgTwOzP7GMDMUs1rcQ5wRdSeBDyQYp25wF0KZyB8wczej/p6QOnAzyUNBQLCIcxPiJb9w8wWR+13gUJJLYETzezFqLZ9UT9GEYbKomj9FoQDh76doi5Xz3mguPqkIqmdIPXrW8AMM7vqINvYk9R+CrjUzJZIGk80QOZR1hRUqy84SH3pOOR4SWb2rKQiYDTwqqRv89nBPK8G2gNnmFmlpDLCvY7kmiF8HJse4u4E3Gdmjx9B/a6e8nMoriHYBbSM2vOAcyT1ApDUXNJJB7ldS2CTpEaEb8Cf2Z6Z7QR2SDovWjYOeIujMwP4xv5PpEk6PsU6cwgHraRaTZ+S1ANYbWaPAC8B/TjwMYBwRsatUZhcABQcqjAz2wWsl3RpdB+NozrfAK5POg91oqQOafXW1TseKK4hmAi8LmmWmZUTjhA9WVIJ4eGhPge53U8IzxvMAVYkXT8F+L6kRdGJ6esIT9KXAP0Jz6McMTN7nfAQ2cLokN33Uqx2K/BdSUs5+Ex7VwKl0TZOIZzydRvhYb5SSROAZ4Azo+1cW61/BzOOcLTtEsJzPR3NbDrwLDA32tZUDgwu14D4aMPOOecywvdQnHPOZYQHinPOuYzwQHHOOZcRHijOOecywgPFOedcRnigOOecywgPFOeccxnx/8N/bkLxDnv5AAAAAElFTkSuQmCC\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, "output_type": "display_data" } ], @@ -134,7 +122,7 @@ "pylab.xlabel('Interatomic distance')\n", "pylab.ylabel('Energy')\n", "pylab.title('H2 Ground State Energy')\n", - "pylab.legend(loc='upper right')" + "pylab.legend(loc='upper right');" ] }, { @@ -144,24 +132,12 @@ "outputs": [ { "data": { + "image/png": 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\n", "text/plain": [ - "" + "" ] }, - "execution_count": 3, "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, "output_type": "display_data" } ], @@ -171,7 +147,7 @@ "pylab.xlabel('Interatomic distance')\n", "pylab.ylabel('Energy')\n", "pylab.title('Energy difference from ExactEigensolver')\n", - "pylab.legend(loc='upper left')" + "pylab.legend(loc='upper left');" ] }, { @@ -181,24 +157,12 @@ "outputs": [ { "data": { + "image/png": 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\n", "text/plain": [ - "" + "" ] }, - "execution_count": 4, "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, "output_type": "display_data" } ], @@ -207,7 +171,7 @@ "pylab.xlabel('Interatomic distance')\n", "pylab.ylabel('Evaluations')\n", "pylab.title('VQE number of evaluations')\n", - "pylab.legend(loc='upper left')" + "pylab.legend(loc='upper left');" ] }, { @@ -234,7 +198,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.7" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/community/aqua/chemistry/h2_var_forms.ipynb b/community/aqua/chemistry/h2_var_forms.ipynb index 9f5aefd11..f386f756f 100644 --- a/community/aqua/chemistry/h2_var_forms.ipynb +++ b/community/aqua/chemistry/h2_var_forms.ipynb @@ -10,7 +10,7 @@ "\n", "This notebook populates a dictionary, that is a progammatic representation of an input file, in order to drive the Qiskit Chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here. \n", "\n", - "This notebook has been written to use the PYSCF chemistry driver. See the PYSCF chemistry driver readme if you need to install the external PySCF library that this driver requires." + "This notebook has been written to use the PYSCF chemistry driver." ] }, { @@ -22,8 +22,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "Hartree-Fock energy: -1.1173432691225826\n", - "FCI energy: -1.1372213770723034\n" + "Hartree-Fock energy: -1.1173432691225829\n", + "FCI energy: -1.1372213770723014\n" ] } ], @@ -67,7 +67,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": { "scrolled": true }, @@ -76,7 +76,22 @@ "name": "stdout", "output_type": "stream", "text": [ - "Processing step __\b\b 0" + "Processing step 7 --- complete\n", + "Depths: [3, 4, 5, 6, 7, 8, 9, 10]\n", + "Energies: [[[-1.11734306 -1.13720243 -1.13720372 -1.13722021 -1.13722135\n", + " -1.13722136 -1.13722136 -1.13722136]\n", + " [-1.13722127 -1.13722069 -1.13722133 -1.13711301 -1.13715782\n", + " -1.13717939 -1.13722016 -1.13717511]]\n", + "\n", + " [[-1.13722034 -1.13722128 -1.13722094 -1.13722098 -1.13722135\n", + " -1.13722136 -1.13722137 -1.13722136]\n", + " [-1.1372213 -1.13722138 -1.13722136 -1.13722137 -1.13722137\n", + " -1.13722137 -1.13722137 -1.13722137]]]\n", + "Num evaluations: [[[ 8011. 10000. 10000. 10000. 4405. 3554. 3410. 3097.]\n", + " [ 5603. 10000. 5328. 10000. 10000. 10000. 10000. 10000.]]\n", + "\n", + " [[ 7455. 2840. 4351. 3553. 1145. 1944. 1053. 1052.]\n", + " [ 1956. 380. 1052. 841. 1024. 1016. 675. 702.]]]\n" ] } ], @@ -107,9 +122,20 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "for k in range(len(var_forms)):\n", " for j in range(len(entanglements)):\n", @@ -118,14 +144,32 @@ "pylab.ylabel('Energy difference')\n", "pylab.yscale('log')\n", "pylab.title('H2 Ground State Energy Difference from Reference')\n", - "pylab.legend(loc='upper right')" + "pylab.legend(loc='upper right');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The above plot shows how close the ground state energy result from VQE was to the reference. The next plot shows how many evaluations (calls to the objective/cost function) were needed by the optimizer before it stopped and returned. Note that the optimzer was configured with a maximum number of iterations of 10,000. The COBYLA optimizer makes one evaluation per iteration and it can be seen that for some points that the iteration limit was reached which caused the optimizer to return." ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "for k in range(len(var_forms)):\n", " for j in range(len(entanglements)):\n", @@ -133,7 +177,7 @@ "pylab.xlabel('Variational form depth')\n", "pylab.ylabel('Evaluations')\n", "pylab.title('VQE number of evaluations')\n", - "pylab.legend(loc='upper right')" + "pylab.legend(loc='upper right');" ] }, { @@ -160,7 +204,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.7" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/community/aqua/chemistry/h2_vqe_initial_point.ipynb b/community/aqua/chemistry/h2_vqe_initial_point.ipynb index e74286c0b..2e83c3549 100644 --- a/community/aqua/chemistry/h2_vqe_initial_point.ipynb +++ b/community/aqua/chemistry/h2_vqe_initial_point.ipynb @@ -15,16 +15,40 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": { - "scrolled": true + "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Processing step 16" + "Processing step 20 --- complete\n", + "Distances: [0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.675 0.7 0.725 0.75 0.775\n", + " 0.8 0.825 0.85 0.875 0.9 0.925 0.95 0.975 1. ]\n", + "Energies: [[-1.05515974 -1.07591361 -1.09262987 -1.10591801 -1.11628598 -1.12416089\n", + " -1.12990476 -1.1338262 -1.13618944 -1.13722136 -1.13711707 -1.13604436\n", + " -1.13414767 -1.1315512 -1.12836188 -1.12467175 -1.12056028 -1.11609624\n", + " -1.11133942 -1.10634212 -1.10115033]\n", + " [-1.05515974 -1.07591361 -1.09262987 -1.10591801 -1.11628598 -1.12416089\n", + " -1.12990476 -1.1338262 -1.13618944 -1.13722135 -1.13711706 -1.13604436\n", + " -1.13414767 -1.1315512 -1.12836188 -1.12467175 -1.12056028 -1.11609624\n", + " -1.11133942 -1.10634212 -1.10115033]\n", + " [-1.05515974 -1.07591361 -1.09262987 -1.10591802 -1.11628599 -1.12416089\n", + " -1.12990476 -1.1338262 -1.13618944 -1.13722136 -1.13711707 -1.13604436\n", + " -1.13414767 -1.13155121 -1.12836188 -1.12467175 -1.12056028 -1.11609624\n", + " -1.11133943 -1.10634212 -1.10115034]]\n", + "Hartree-Fock energies: [-1.04299622 -1.0630621 -1.0790507 -1.09157046 -1.10112822 -1.10814997\n", + " -1.11299652 -1.11597525 -1.11734902 -1.11734325 -1.11615145 -1.11393966\n", + " -1.1108504 -1.10700581 -1.10251056 -1.09745432 -1.09191405 -1.08595588\n", + " -1.07963694 -1.07300677 -1.06610866]\n", + "VQE num evaluations: [[377 418 377 357 374 380 361 376 365 353 350 353 351 360 378 342 345 365\n", + " 344 341 349]\n", + " [377 300 262 263 281 293 286 273 292 259 288 266 265 241 301 280 283 273\n", + " 296 291 266]\n", + " [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n", + " 0 0 0]]\n" ] } ], @@ -87,11 +111,29 @@ "print('VQE num evaluations:', eval_counts)\n" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The plot of ground energies from VQE, whether starting from a random initial point or the optimal solution from the prior point are indistinguisable here." + ] + }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "pylab.plot(distances, hf_energies, label='Hartree-Fock')\n", "for j in range(len(algorithms)):\n", @@ -99,14 +141,25 @@ "pylab.xlabel('Interatomic distance')\n", "pylab.ylabel('Energy')\n", "pylab.title('H2 Ground State Energy')\n", - "pylab.legend(loc='upper right')" + "pylab.legend(loc='upper right');" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "for i in range(2):\n", " pylab.plot(distances, np.subtract(energies[i], energies[2]), label=titles[i])\n", @@ -114,21 +167,96 @@ "pylab.xlabel('Interatomic distance')\n", "pylab.ylabel('Energy')\n", "pylab.title('Energy difference from ExactEigensolver')\n", - "pylab.legend(loc='upper left')" + "pylab.legend(loc='upper left');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Lets plot the difference of the VQE ground state energies from the ExactEigensolver. They are both in the same ballpark and both very small." ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 10, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for i in range(len(algorithms)-1):\n", + " pylab.plot(distances, np.subtract(energies[i], energies[2]), label=titles[i])\n", + "pylab.xlabel('Interatomic distance')\n", + "pylab.ylabel('Energy')\n", + "pylab.yscale('log')\n", + "pylab.title('H2 Ground State Energy')\n", + "pylab.legend(loc='upper right');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally lets plot the number of evaluations taken at each point. Both start out at the same number since we start them the same. But we can see, as we step along small distances, that the prior solution is a better guess as the starting point for the next step leading to fewer evaluations." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "for i in range(2):\n", " pylab.plot(distances, eval_counts[i], '-o', label=titles[i])\n", "pylab.xlabel('Interatomic distance')\n", "pylab.ylabel('Evaluations')\n", "pylab.title('VQE number of evaluations')\n", - "pylab.legend(loc='center left')" + "pylab.legend(loc='center left');" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Total evaluations for 'VQE Random Seed' = 7616\n", + "Total evaluations for 'VQE + Initial Point' = 5936\n", + "\n", + "Total evaluations for 'VQE + Initial Point' are 77.94% of 'VQE Random Seed'\n" + ] + } + ], + "source": [ + "for i in range(2):\n", + " print(\"Total evaluations for '{}' = {}\".format(titles[i], np.sum(eval_counts[i])))\n", + "\n", + "percent = np.sum(eval_counts[1])*100/np.sum(eval_counts[0])\n", + "print(\"\\nTotal evaluations for '{}' are {:.2f}% of '{}'\".format(titles[1], percent, titles[0]))" ] }, { @@ -155,7 +283,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.7" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/community/aqua/chemistry/h2_vqe_spsa.ipynb b/community/aqua/chemistry/h2_vqe_spsa.ipynb index 880884406..a8538f625 100644 --- a/community/aqua/chemistry/h2_vqe_spsa.ipynb +++ b/community/aqua/chemistry/h2_vqe_spsa.ipynb @@ -10,7 +10,7 @@ "\n", "This notebook populates a dictionary, that is a progammatic representation of an input file, in order to drive the qiskit.chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here where we alter the molecule supplied to the driver in each loop.\n", "\n", - "This notebook has been written to use the PYSCF chemistry driver. See the PYSCF chemistry driver readme if you need to install the external PySCF library that this driver requires." + "This notebook has been written to use the PYSCF chemistry driver." ] }, { @@ -25,10 +25,10 @@ "Processing step 20 --- complete\n", "Distances: [0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.675 0.7 0.725 0.75 0.775\n", " 0.8 0.825 0.85 0.875 0.9 0.925 0.95 0.975 1. ]\n", - "Energies: [[-1.04791876 -1.07420635 -1.08779346 -1.10880279 -1.11899652 -1.12671817\n", - " -1.13457894 -1.13277581 -1.1344774 -1.1347043 -1.13293985 -1.14356835\n", - " -1.14347015 -1.12904676 -1.14013816 -1.12672765 -1.12100335 -1.1174054\n", - " -1.1043725 -1.10428366 -1.09728721]\n", + "Energies: [[-1.06086904 -1.07138175 -1.09113875 -1.10744489 -1.11953674 -1.13116184\n", + " -1.13320145 -1.13667867 -1.13892688 -1.13662612 -1.13536438 -1.13603326\n", + " -1.13339153 -1.1308772 -1.12739979 -1.12469779 -1.12047399 -1.11336415\n", + " -1.11008319 -1.10846154 -1.10181643]\n", " [-1.05515979 -1.07591366 -1.09262991 -1.10591805 -1.11628601 -1.12416092\n", " -1.12990478 -1.13382622 -1.13618945 -1.13722138 -1.13711707 -1.13604436\n", " -1.13414767 -1.13155121 -1.12836188 -1.12467175 -1.12056028 -1.11609624\n", @@ -47,19 +47,20 @@ "\n", "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", "qiskit_chemistry_dict = {\n", + " 'problem': {'random_seed': 750},\n", " 'driver': {'name': 'PYSCF'},\n", " 'PYSCF': {'atom': '', 'basis': 'sto3g'},\n", " 'operator': {'name': 'hamiltonian', 'transformation': 'full', \n", " 'qubit_mapping': 'parity', 'two_qubit_reduction': True},\n", - " 'algorithm': {'name': 'VQE'},\n", - " 'optimizer': {'name': 'SPSA', 'max_trials': 350},\n", - " 'variational_form': {'name': 'RYRZ', 'depth': 3, 'entanglement': 'full'}\n", + " 'algorithm': {},\n", "}\n", "molecule = 'H .0 .0 -{0}; H .0 .0 {0}'\n", - "algorithms = ['VQE', 'ExactEigensolver']\n", - "backends = [{'name': 'qasm_simulator', 'shots': 1024},\n", - " None\n", - " ]\n", + "algorithms = [{'name': 'VQE', 'operator_mode': 'paulis'},\n", + " {'name': 'ExactEigensolver'}\n", + " ]\n", + "optimizer = {'name': 'SPSA', 'max_trials': 200}\n", + "variational_form = {'name': 'RYRZ', 'depth': 3, 'entanglement': 'full'}\n", + "backend = {'provider': 'qiskit.BasicAer', 'name': 'qasm_simulator', 'shots': 1024}\n", "\n", "start = 0.5 # Start distance\n", "by = 0.5 # How much to increase distance by\n", @@ -74,10 +75,14 @@ " d = start + i*by/steps\n", " qiskit_chemistry_dict['PYSCF']['atom'] = molecule.format(d/2) \n", " for j in range(len(algorithms)):\n", - " qiskit_chemistry_dict['algorithm']['name'] = algorithms[j]\n", - " if backends[j] is not None:\n", - " qiskit_chemistry_dict['backend'] = backends[j]\n", + " qiskit_chemistry_dict['algorithm'] = algorithms[j]\n", + " if algorithms[j]['name'] == 'VQE':\n", + " qiskit_chemistry_dict['optimizer'] = optimizer\n", + " qiskit_chemistry_dict['variational_form'] = variational_form\n", + " qiskit_chemistry_dict['backend'] = backend\n", " else:\n", + " qiskit_chemistry_dict.pop('optimizer')\n", + " qiskit_chemistry_dict.pop('variational_form')\n", " qiskit_chemistry_dict.pop('backend')\n", " solver = QiskitChemistry()\n", " result = solver.run(qiskit_chemistry_dict)\n", @@ -100,19 +105,9 @@ "outputs": [ { "data": { + "image/png": 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\n", "text/plain": [ - "" - ] - }, - "execution_count": 2, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -126,7 +121,7 @@ "pylab.xlabel('Interatomic distance (Angstrom)')\n", "pylab.ylabel('Energy (Hartree)')\n", "pylab.title('H2 Ground State Energy')\n", - "pylab.legend(loc='upper right')" + "pylab.legend(loc='upper right');" ] }, { @@ -136,19 +131,9 @@ "outputs": [ { "data": { + "image/png": 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\n", "text/plain": [ - "" - ] - }, - "execution_count": 3, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -161,24 +146,22 @@ "pylab.xlabel('Interatomic distance (Angstrom)')\n", "pylab.ylabel('Energy (Hartree)')\n", "pylab.title('Energy difference from ExactEigensolver')\n", - "pylab.legend(loc='upper left')" + "pylab.legend(loc='upper left');" ] }, { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { - "display_name": "Quantum", + "display_name": "Python 3", "language": "python", - "name": "quantum" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -190,7 +173,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.3" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/community/aqua/chemistry/h2o.ipynb b/community/aqua/chemistry/h2o.ipynb index c2c25e0d1..f028e74d7 100644 --- a/community/aqua/chemistry/h2o.ipynb +++ b/community/aqua/chemistry/h2o.ipynb @@ -8,40 +8,63 @@ "\n", "This notebook demonstrates how to use Qiskit Chemistry to compute the ground state energy of a water (H2O) molecule using VQE and UCCSD.\n", "\n", - "This notebook has been written to use the PYSCF chemistry driver. See the PYSCF chemistry driver readme if you need to install the external PySCF library that this driver requires." + "While the molecule has been input below to the driver in xyz format, the Z-matrix format is also support. H2O in Z-matrix format would look like this \n", + "```\n", + "H; O 1 1.08; H 2 1.08 1 104.5\n", + "```\n", + "and is convenient when the goal is to change bond angle, or plot the energy changing distance(s) while preserving the angle.\n", + "\n", + "This notebook has been written to use the PYSCF chemistry driver. " ] }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ + "# imports needed by declarative approach here. List is short as classes are dynamically\n", + "# loaded based on dictionary names which are registered to our pluggable framework.\n", + "# The name of a given algorithm or component can be found in its CONFIGURATION dictonary\n", "from qiskit.chemistry import QiskitChemistry\n", "\n", - "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", - "qiskit_chemistry_dict = {\n", - " 'problem': {'random_seed': 50},\n", - " 'driver': {'name': 'PYSCF'},\n", - " 'PYSCF': {'atom': 'O 0.0 0.0 0.0; H 0.757 0.586 0.0; H -0.757 0.586 0.0', 'basis': 'sto-3g'},\n", - " 'operator': {'name': 'hamiltonian', 'freeze_core': True},\n", - " 'algorithm': {'name': 'ExactEigensolver'}\n", - "}" + "# imports needed by programmatic approach\n", + "from qiskit import BasicAer\n", + "\n", + "from qiskit.aqua import Operator, QuantumInstance\n", + "from qiskit.aqua.algorithms.adaptive import VQE\n", + "from qiskit.aqua.algorithms.classical import ExactEigensolver\n", + "from qiskit.aqua.components.optimizers import SLSQP\n", + "\n", + "from qiskit.chemistry.drivers import PySCFDriver, UnitsType\n", + "from qiskit.chemistry.core import Hamiltonian, TransformationType, QubitMappingType \n", + "from qiskit.chemistry.aqua_extensions.components.variational_forms import UCCSD\n", + "from qiskit.chemistry.aqua_extensions.components.initial_states import HartreeFock" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "With the above input problem dictionary for water we now create an `QiskitChemistry` object and call `run` on it passing in the dictionary to get a result. We use ExactEigensolver first as a reference." + "#### Using a declarative dictionary approach with QiskitChemistry\n", + "\n", + "Lets format up a dictionary and run the experiment this way. The operator will default to `parity` mapping and `two_qubit_reduction` of True.\n", + "\n", + "With the input problem dictionary for water we now create an QiskitChemistry object and call run on it passing in the dictionary to get a result. We use ExactEigensolver first as a reference." ] }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 12, "metadata": {}, "outputs": [], "source": [ + "qiskit_chemistry_dict = {\n", + " 'driver': {'name': 'PYSCF'},\n", + " 'PYSCF': {'atom': 'O 0.0 0.0 0.0; H 0.757 0.586 0.0; H -0.757 0.586 0.0', 'basis': 'sto-3g'},\n", + " 'operator': {'name': 'hamiltonian', 'freeze_core': True},\n", + " 'algorithm': {'name': 'ExactEigensolver'}\n", + "}\n", "solver = QiskitChemistry()\n", "result = solver.run(qiskit_chemistry_dict)" ] @@ -55,14 +78,14 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Ground state energy: -75.01235928580498\n" + "Ground state energy: -75.0123592858051\n" ] } ], @@ -79,26 +102,32 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "* Electronic ground state energy: -84.20627244642836\n", - " - computed part: -23.544497240436005\n", - " - frozen energy part: -60.661775205992356\n", + "=== GROUND STATE ENERGY ===\n", + " \n", + "* Electronic ground state energy (Hartree): -84.206272446428\n", + " - computed part: -23.544497240436\n", + " - frozen energy part: -60.661775205992\n", " - particle hole part: 0.0\n", - "~ Nuclear repulsion energy: 9.193913160623385\n", - "> Total ground state energy: -75.01235928580498\n", + "~ Nuclear repulsion energy (Hartree): 9.193913160623\n", + "> Total ground state energy (Hartree): -75.012359285805\n", " Measured:: Num particles: 8.000, S: 0.000, M: 0.00000\n", - "* Electronic dipole moment: [0. 1.57867263 0. ]\n", - " - computed part: [0. 1.57778798 0. ]\n", - " - frozen energy part: [0. 0.00088465 0. ]\n", - " - particle hole part: [0. 0. 0.]\n", - "~ Nuclear dipole moment: [0. 2.21475902 0. ]\n", - "> Dipole moment: [0. 0.63608639 0. ] Total: 0.6360863875724845\n" + " \n", + "=== DIPOLE MOMENT ===\n", + " \n", + "* Electronic dipole moment (a.u.): [0.0 1.57867263 0.0]\n", + " - computed part: [0.0 1.57778798 0.0]\n", + " - frozen energy part: [0.0 0.00088465 0.0]\n", + " - particle hole part: [0.0 0.0 0.0]\n", + "~ Nuclear dipole moment (a.u.): [0.0 2.21475902 0.0]\n", + "> Dipole moment (a.u.): [0.0 0.63608639 0.0] Total: 0.63608639\n", + " (debye): [0.0 1.61677018 0.0] Total: 1.61677018\n" ] } ], @@ -111,38 +140,166 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We update the dictionary, for VQE with UCCSD, and run the computation again." + "#### Lets do the same programmatically\n", + "\n", + "First we create and run a driver to produce our molecule object. The molecule object holds data from the drivers in a common way so it can then be used independently of which specific driver created it.\n", + "\n", + "And let's print some of fields it has. You can refer to qiskit.aqua.qmolecule.py for more information or look at the API documentation." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Hartree-Fock energy: -74.96294665653834\n", + "Nuclear repulsion energy: 9.193913160623385\n", + "Number of molecular orbitals: 7\n", + "Number of alpha electrons: 5\n", + "Number of beta electrons: 5\n" + ] + } + ], + "source": [ + "driver = PySCFDriver(atom='O 0.0 0.0 0.0; H 0.757 0.586 0.0; H -0.757 0.586 0.0',\n", + " unit=UnitsType.ANGSTROM, charge=0, spin=0, basis='sto3g')\n", + "molecule = driver.run()\n", + "\n", + "print('Hartree-Fock energy: {}'.format(molecule.hf_energy))\n", + "print('Nuclear repulsion energy: {}'.format(molecule.nuclear_repulsion_energy))\n", + "print('Number of molecular orbitals: {}'.format(molecule.num_orbitals))\n", + "print('Number of alpha electrons: {}'.format(molecule.num_alpha))\n", + "print('Number of beta electrons: {}'.format(molecule.num_beta))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We now need to create a qubit operator as input to compute the ground state energy. The Hamilitonian object can be used. This wraps a `FermionicOperator` class, which can be used directly but entails more steps. Other tutorials here show FermionicOperator being used.\n", + "\n", + "The Hamiltonian class not only gives us a qubit operator for the main Hamiltonian but also auxilliary operators including dipole operators and others to measure spin and num particles. The algorithm, if it supports aux_ops, which ExactEignesolver and VQE both do, will evaluate these at the ground state where the minimum energy is found." ] }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Ground state energy: -75.01136277625662\n", - "* Electronic ground state energy: -84.20527593688\n", - " - computed part: -23.543500730887647\n", - " - frozen energy part: -60.661775205992356\n", + "Representation: paulis, qubits: 10, size: 551\n" + ] + } + ], + "source": [ + "core = Hamiltonian(transformation=TransformationType.FULL, qubit_mapping=QubitMappingType.PARITY, \n", + " two_qubit_reduction=True, freeze_core=True)\n", + "qubit_op, aux_ops = core.run(molecule)\n", + "\n", + "print(qubit_op)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We now pass these to the ExactEigensolver and run it to produce a result. This result will include the computed electronic part of the ground state energy. We can pass this result back to the Hamiltonian object from above and it will combine it with values it stored such as the frozen core energy to form a complete result for the molecule. As can be seen this matches the result from the declarative approach above.\n", + "\n", + "Note: the num particles printed here is that which is observed from the spin operator that is in the aux_ops. It says 8 which matches what we expect; the molecule has 10 (5 alpha and 5 beta) but the operator was left with 8 after we took away 2 from freezing the core. The molecule has a core_orbitals property which lists the orbitals comprising the core ones that can be frozen so we can easily figure how many electrons that is (2 per orbital in that list)." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "=== GROUND STATE ENERGY ===\n", + " \n", + "* Electronic ground state energy (Hartree): -84.206272446429\n", + " - computed part: -23.544497240436\n", + " - frozen energy part: -60.661775205992\n", " - particle hole part: 0.0\n", - "~ Nuclear repulsion energy: 9.193913160623385\n", - "> Total ground state energy: -75.01136277625662\n", - " Measured:: Num particles: 8.000, S: 0.002, M: 0.00000\n", - "* Electronic dipole moment: [-3.30862414e-06 1.57868676e+00 -1.64045876e-05]\n", - " - computed part: [-3.30862414e-06 1.57780210e+00 -1.64045876e-05]\n", - " - frozen energy part: [0. 0.00088465 0. ]\n", - " - particle hole part: [0. 0. 0.]\n", - "~ Nuclear dipole moment: [0. 2.21475902 0. ]\n", - "> Dipole moment: [3.30862414e-06 6.36072265e-01 1.64045876e-05] Total: 0.6360722651436584\n" + "~ Nuclear repulsion energy (Hartree): 9.193913160623\n", + "> Total ground state energy (Hartree): -75.012359285805\n", + " Measured:: Num particles: 8.000, S: 0.000, M: 0.00000\n", + " \n", + "=== DIPOLE MOMENT ===\n", + " \n", + "* Electronic dipole moment (a.u.): [0.0 1.57867263 0.0]\n", + " - computed part: [0.0 1.57778798 0.0]\n", + " - frozen energy part: [0.0 0.00088465 0.0]\n", + " - particle hole part: [0.0 0.0 0.0]\n", + "~ Nuclear dipole moment (a.u.): [0.0 2.21475902 0.0]\n", + "> Dipole moment (a.u.): [0.0 0.63608639 0.0] Total: 0.63608639\n", + " (debye): [0.0 1.61677018 0.0] Total: 1.61677018\n" + ] + } + ], + "source": [ + "ee = ExactEigensolver(qubit_op, aux_operators=aux_ops)\n", + "algo_result = ee.run()\n", + "result = core.process_algorithm_result(algo_result)\n", + "for line in result[0]:\n", + " print(line)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Using VQE. First declaratively with the dictionary.\n", + "\n", + "We update the dictionary, for VQE with UCCSD, and run the computation again. By default, if a backend is not explicitly provided, as is the case here, it will use the `statevector_simulator` from `BasicAer`. \n", + "\n", + "_*Please note that with 10 qubits the simulation can take a while.*_" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Ground state energy: -75.0122585919439\n", + "=== GROUND STATE ENERGY ===\n", + " \n", + "* Electronic ground state energy (Hartree): -84.206171752567\n", + " - computed part: -23.544396546575\n", + " - frozen energy part: -60.661775205992\n", + " - particle hole part: 0.0\n", + "~ Nuclear repulsion energy (Hartree): 9.193913160623\n", + "> Total ground state energy (Hartree): -75.012258591944\n", + " Measured:: Num particles: 8.000, S: 0.000, M: 0.00000\n", + " \n", + "=== DIPOLE MOMENT ===\n", + " \n", + "* Electronic dipole moment (a.u.): [-0.00000112 1.57887918 0.00000014]\n", + " - computed part: [-0.00000112 1.57799453 0.00000014]\n", + " - frozen energy part: [0.0 0.00088465 0.0]\n", + " - particle hole part: [0.0 0.0 0.0]\n", + "~ Nuclear dipole moment (a.u.): [0.0 2.21475902 0.0]\n", + "> Dipole moment (a.u.): [0.00000112 0.63587984 -0.00000014] Total: 0.63587984\n", + " (debye): [0.00000284 1.61624518 -0.00000036] Total: 1.61624518\n" ] } ], "source": [ "qiskit_chemistry_dict['algorithm']['name'] = 'VQE'\n", - "qiskit_chemistry_dict['optimizer'] = {'name': 'COBYLA', 'maxiter': 25000}\n", + "qiskit_chemistry_dict['optimizer'] = {'name': 'SLSQP', 'maxiter': 2500}\n", "qiskit_chemistry_dict['variational_form'] = {'name': 'UCCSD'}\n", "qiskit_chemistry_dict['initial_state'] = {'name': 'HartreeFock'}\n", "\n", @@ -157,14 +314,14 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Actual VQE evaluations taken: 2422\n" + "Actual VQE evaluations taken: 666\n" ] } ], @@ -172,6 +329,157 @@ "print('Actual VQE evaluations taken: {}'.format(result['algorithm_retvals']['eval_count']))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Using VQE, programmatically\n", + "\n", + "The solver above, with the complete dictionary, will recompute the molecule internally again with the driver. Here we will start with the qubit operator that we computed above. We need to setup an optimizer, variational form and initial state for use with VQE.\n", + "\n", + "The variational form and UCCSD are a little more complex since they need information about numbers of orbitals and numbers of electrons, as well as what qubit mapping etc was used for the qubit operator. However we have some help from the Hamiltonian class that we can use (which internally is what the declarative form takes advantage of too). \n", + "\n", + "Note: If you use FermionicOperator directly to make a qubit operator then you need to keep track of electrons removed etc. The molecule object from the driver has the original values but if you freeze out orbitals then the electrons remaining in the operator is what is required." + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Ground state energy: -75.0122585919439\n", + "=== GROUND STATE ENERGY ===\n", + " \n", + "* Electronic ground state energy (Hartree): -84.206171752567\n", + " - computed part: -23.544396546575\n", + " - frozen energy part: -60.661775205992\n", + " - particle hole part: 0.0\n", + "~ Nuclear repulsion energy (Hartree): 9.193913160623\n", + "> Total ground state energy (Hartree): -75.012258591944\n" + ] + } + ], + "source": [ + "init_state = HartreeFock(num_qubits=qubit_op.num_qubits, \n", + " num_orbitals=core._molecule_info['num_orbitals'],\n", + " num_particles=core._molecule_info['num_particles'],\n", + " qubit_mapping=core._qubit_mapping,\n", + " two_qubit_reduction=core._two_qubit_reduction)\n", + "\n", + "var_form = UCCSD(num_qubits=qubit_op.num_qubits,\n", + " depth=1,\n", + " num_orbitals=core._molecule_info['num_orbitals'], \n", + " num_particles=core._molecule_info['num_particles'],\n", + " qubit_mapping=core._qubit_mapping,\n", + " two_qubit_reduction=core._two_qubit_reduction, \n", + " initial_state=init_state)\n", + "\n", + "optimizer = SLSQP(maxiter=2500)\n", + "\n", + "# setup backend on which we will run\n", + "backend = BasicAer.get_backend('statevector_simulator')\n", + "quantum_instance = QuantumInstance(backend=backend)\n", + "\n", + "vqe = VQE(qubit_op, var_form, optimizer, 'matrix')\n", + "algo_result = vqe.run(quantum_instance)\n", + "lines, result = core.process_algorithm_result(algo_result)\n", + "\n", + "print('Ground state energy: {}'.format(result['energy']))\n", + "\n", + "for line in lines:\n", + " print(line)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Internally the core, when processing the algorithm result, stores the result dictionary from the algorithm under the `algorithm_retvals` key. We used this above in declarative approach, to get the eval count, and since we process the result the same way here, using the core, we can do this here too. But here we have direct access to the algorithm result since we ran it. Hence we can access the count directly from the above algo_result. To show these are the same they are both printed below." + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Actual VQE evaluations taken: 666\n", + "Actual VQE evaluations taken: 666\n" + ] + } + ], + "source": [ + "print('Actual VQE evaluations taken: {}'.format(result['algorithm_retvals']['eval_count']))\n", + "\n", + "print('Actual VQE evaluations taken: {}'.format(algo_result['eval_count']))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Z-matrix format\n", + "\n", + "Z-matrix was mentioned in the introduction. Lets show it in use in a quick final example here. We'll use ExactEigensolver as the goal here is just to show the technique. We will keep the bond angle between the Hydrogen atoms and Oxygen constant while varying the interatomic distance of one the Hydrogen atoms. This is simple to do in Z-matrix format, though can of course be done using xyz format but that needs more work to compute the coordinates each time." + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pylab\n", + "\n", + "h2o = 'H; O 1 1.08; H 2 {} 1 104.5'\n", + "qiskit_chemistry_dict = {\n", + " 'driver': {'name': 'PYSCF'},\n", + " 'PYSCF': {'atom': '', 'basis': 'sto-3g'},\n", + " 'operator': {'name': 'hamiltonian', 'freeze_core': True},\n", + " 'algorithm': {'name': 'ExactEigensolver'}\n", + "}\n", + "\n", + "distances = [x * 0.01 + 1.00 for x in range(17)]\n", + "energies = np.empty(len(distances))\n", + "\n", + "for i, distance in enumerate(distances):\n", + " qiskit_chemistry_dict['PYSCF']['atom'] = h2o.format(distance)\n", + " solver = QiskitChemistry()\n", + " result = solver.run(qiskit_chemistry_dict)\n", + " energies[i] = result['energy']" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pylab.plot(distances, energies)\n", + "pylab.xlabel('Distance of Hydrogen atom')\n", + "pylab.ylabel('Energy')\n", + "pylab.title('H2O molecule, one H atom distance varied');" + ] + }, { "cell_type": "code", "execution_count": null, @@ -196,7 +504,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/community/aqua/chemistry/lih_dissoc.ipynb b/community/aqua/chemistry/lih_dissoc.ipynb index 45b6c4804..9dc711a73 100644 --- a/community/aqua/chemistry/lih_dissoc.ipynb +++ b/community/aqua/chemistry/lih_dissoc.ipynb @@ -12,8 +12,7 @@ "\n", "This notebook populates a dictionary, which is a progammatic representation of an input file, in order to drive the qiskit.chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here where we alter the molecule supplied to the driver in each loop.\n", " \n", - "This notebook has been written to use the PYSCF chemistry driver. See the PYSCF chemistry driver readme if you need to install the external PySCF library that this driver requires.\n", - " " + "This notebook has been written to use the PYSCF chemistry driver. " ] }, { @@ -36,23 +35,24 @@ "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", "# Note: In order to allow this to run reasonably quickly it takes advantage\n", "# of the ability to freeze core orbitals and remove unoccupied virtual\n", - "# orbitals to reduce the size of the problem. The result without this\n", - "# will be more accurate but it takes rather longer to run.\n", + "# orbitals to reduce the size of the problem.\n", "\n", - "# qiskit_chemistry_dict_eigen uses classical approach to produce the reference ground state energy.\n", + "# dict using a classical approach to produce the reference ground state energy.\n", "qiskit_chemistry_dict_eigen = {\n", " 'driver': {'name': 'PYSCF'},\n", " 'PYSCF': {'atom': '', 'basis': 'sto3g'},\n", " 'algorithm': {'name': 'ExactEigensolver'},\n", - " 'operator': {'name':'hamiltonian','freeze_core': True, 'orbital_reduction': [-3, -2], 'qubit_mapping': 'parity', 'two_qubit_reduction': True},\n", + " 'operator': {'name':'hamiltonian','freeze_core': True, 'orbital_reduction': [-3, -2],\n", + " 'qubit_mapping': 'parity', 'two_qubit_reduction': True},\n", "}\n", "\n", - "# qiskit_chemistry_dict_vqe uses quantum approach to evaluate the ground state energy.\n", + "# dict using a quantum approach to evaluate the ground state energy.\n", "qiskit_chemistry_dict_vqe = {\n", " 'driver': {'name': 'PYSCF'},\n", " 'PYSCF': {'atom': '', 'basis': 'sto3g'},\n", " 'algorithm': {'name': 'VQE', 'operator_mode': 'matrix'},\n", - " 'operator': {'name':'hamiltonian','freeze_core': True, 'orbital_reduction': [-3, -2], 'qubit_mapping': 'parity', 'two_qubit_reduction': True},\n", + " 'operator': {'name':'hamiltonian','freeze_core': True, 'orbital_reduction': [-3, -2],\n", + " 'qubit_mapping': 'parity', 'two_qubit_reduction': True},\n", " 'optimizer': {'name': 'COBYLA', 'maxiter': 20000},\n", " 'variational_form': {'name': 'RYRZ', 'depth': 10},\n", " 'backend': {'name': 'statevector_simulator'}\n", @@ -95,7 +95,7 @@ "Dipole moments: [5.3479565 5.05436846 4.89154649 4.80824206 4.76423166 4.73775921\n", " 4.71893511 4.70394304 4.69125691 4.67959192 4.66694467 4.65022445\n", " 4.62517401 4.5864183 4.52758314 4.24518851 3.69244462 2.8795465\n", - " 1.99991673 1.27228084 0.76878114 0.45190607 0.26134837]\n" + " 1.99991673 1.27228084 0.76878114 0.45190607 0.26134836]\n" ] } ], @@ -134,21 +134,11 @@ "scrolled": true }, "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" - }, { "data": { "image/png": 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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -161,7 +151,7 @@ "pylab.xlabel('Interatomic distance')\n", "pylab.ylabel('Energy')\n", "pylab.title('LiH Ground State Energy')\n", - "pylab.legend(loc='upper right')" + "pylab.legend(loc='upper right');" ] }, { @@ -169,21 +159,11 @@ "execution_count": 6, "metadata": {}, "outputs": [ - { - "data": { - "text/plain": [ - "Text(0.5,1,'LiH Dipole Moment')" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" - }, { "data": { "image/png": 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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -194,7 +174,7 @@ "pylab.plot(distances, dipoles)\n", "pylab.xlabel('Interatomic distance')\n", "pylab.ylabel('Moment debye')\n", - "pylab.title('LiH Dipole Moment')" + "pylab.title('LiH Dipole Moment');" ] }, { @@ -221,7 +201,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/community/aqua/chemistry/lih_uccsd.ipynb b/community/aqua/chemistry/lih_uccsd.ipynb index 66b200343..c5b8cbd1b 100644 --- a/community/aqua/chemistry/lih_uccsd.ipynb +++ b/community/aqua/chemistry/lih_uccsd.ipynb @@ -10,12 +10,12 @@ "\n", "This notebook populates a dictionary, that is a progammatic representation of an input file, in order to drive the Qiskit Chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here where we alter the molecule supplied to the driver in each loop.\n", "\n", - "This notebook has been written to use the PYSCF chemistry driver. See the PYSCF chemistry driver readme if you need to install the external PySCF library that this driver requires." + "This notebook has been written to use the PYSCF chemistry driver." ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": { "scrolled": true }, @@ -24,7 +24,23 @@ "name": "stdout", "output_type": "stream", "text": [ - "Processing step __\b\b 0" + "Processing step 22 --- complete\n", + "Distances: [0.6 0.7 0.8 0.9 1. 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9\n", + " 2. 2.25 2.5 2.75 3. 3.25 3.5 3.75 4. ]\n", + "Energies: [[-7.3133458 -7.50092206 -7.63097823 -7.7208124 -7.78224239 -7.82359927\n", + " -7.85069837 -7.86756328 -7.87700148 -7.8810157 -7.88107203 -7.87826815\n", + " -7.87344011 -7.86723367 -7.86015319 -7.84104235 -7.82307636 -7.80861236\n", + " -7.79836328 -7.79175303 -7.78771683 -7.7853196 -7.78391829]\n", + " [-7.31334583 -7.50092209 -7.63097825 -7.72081241 -7.7822424 -7.82359928\n", + " -7.85069838 -7.86756329 -7.87700149 -7.88101572 -7.88107204 -7.87826817\n", + " -7.87344029 -7.86723396 -7.86015321 -7.84104271 -7.82307664 -7.8086124\n", + " -7.79836343 -7.79175325 -7.78771697 -7.78531972 -7.78391847]]\n", + "Hartree-Fock energies: [-7.29954105 -7.48594487 -7.61577016 -7.70575334 -7.76736214 -7.80874318\n", + " -7.83561583 -7.85195386 -7.86053866 -7.86335762 -7.86186477 -7.85714496\n", + " -7.8500187 -7.84111204 -7.83090558 -7.80193896 -7.77087367 -7.74000074\n", + " -7.7108299 -7.68437642 -7.6612016 -7.64145387 -7.62497563]\n", + "VQE num evaluations: [71. 62. 71. 71. 71. 71. 71. 71. 71. 71. 71. 62. 60. 60. 61. 60. 70. 71.\n", + " 70. 80. 90. 90. 90.]\n" ] } ], @@ -41,7 +57,7 @@ " 'operator': {'name': 'hamiltonian', 'qubit_mapping': 'parity',\n", " 'two_qubit_reduction': True, 'freeze_core': True, 'orbital_reduction': [-3, -2]},\n", " 'algorithm': {'name': ''},\n", - " 'optimizer': {'name': 'COBYLA', 'maxiter': 10000 },\n", + " 'optimizer': {'name': 'SLSQP', 'maxiter': 1000},\n", " 'variational_form': {'name': 'UCCSD'},\n", " 'initial_state': {'name': 'HartreeFock'}\n", "}\n", @@ -86,11 +102,22 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": { "scrolled": true }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "pylab.plot(distances, hf_energies, label='Hartree-Fock')\n", "for j in range(len(algorithms)):\n", @@ -98,48 +125,81 @@ "pylab.xlabel('Interatomic distance')\n", "pylab.ylabel('Energy')\n", "pylab.title('LiH Ground State Energy')\n", - "pylab.legend(loc='upper right')" + "pylab.legend(loc='upper right');" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "pylab.plot(distances, np.subtract(hf_energies, energies[1]), label='Hartree-Fock')\n", "pylab.plot(distances, np.subtract(energies[0], energies[1]), label='VQE')\n", "pylab.xlabel('Interatomic distance')\n", "pylab.ylabel('Energy')\n", "pylab.title('Energy difference from ExactEigensolver')\n", - "pylab.legend(loc='upper left')" + "pylab.legend(loc='upper left');" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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eeYVnn33Wybh+yZv98OsBn7nvwxgEfKiq33hxe8ct6YIbSO94JunJd5C07X2CkiexPrAFGS0uplX/kdRp0NTpiMZUzIz74M/llbvO+h3h3LLvYBUXF0ePHj2YMWMGF1100eGhBFasWEG3bt2OWLZly5bk5eWRmZkJUOowx+Hh4ZWb33jvCF9VN6hqZ/fUXlWf8Na2KkODpidzyj3Tybx1OfNOvocigui59nlqv96ZZU8NIGXaf8nNyXI6pjE+rWSzzuTJkxk+fLhH7zu6SceKvXfU6Cttj0edeonUufL/gP9j85olbJvzLs22f03DxfeRu+gRUmLPQJueTu1WSTRp3Y2QMPuPaXxQOUfi3nTRRRdx5513snjxYnJzc+nWrRtLlixhzpw5Ryy3YcMG4uPjqVWrliM5/ZUV/HI0bd2Vpq27Ulz0HCsWfE/Owg9os+cHYpd/D8uhQANZH9SEPdGtKa7XkZhm3UhsdyrRsZV/4wJjqoOoqCj69evHqFGjDh/djxgxgieffJKZM2dy1llnkZeXx+23386jjz7qcFr/YwXfAwGBgbTvNQh6DaK4qIgtG1aQsTaF/LRUIvaspHnmPOpkfgNrgG9hm9Rjb0hD8sIbUhTdkMDajQmv05SY+s1IaNiC8Kiy7+BjTHU3fPhwLrnkksNNO+Hh4UybNo3Ro0dz6623sm3bNh588EFGjPjfbUiPbsN/7bXXOO2006o8e01XY4dHrkqqyq70LWxfPY/czUsI2b2K6APbqV2YQbxmEiBH7uNMotgdmEBuUG0OhsZRGBYHEXUIiKpDcExdwmPrElm7HrHxDYmKjSOgEu9ab2qu6jI88ueff87YsWOZNWsWTZtah4iKsOGRfYCIkNCwKQkNmwLDjph38GAeu7ZtJnPHRvIyNlGwdysB2dsIzf2TiII9xO/bRmxWFpFS9q3dsolgv0SSGxDNgcBo8oOjKQiOoTg0Fg2LRcJiCQyPITA8lpCIGEIiaxEWXYuIqNpExNQiPDwKCfCbUTSMj7v44ou5+OKLnY7hl6zge1loaDiNWrShUYs25S53IG8/mbvSydmzg9zMHRzM2knhvgw4kIUcyCQwP4vg/GxCC/dRO28LEftziNYcwuXYVwgXagC5Ek4u4RwICOdgQAQFgeEUBEZSGBxJUXAkGhwNYdFIaAyBYTEERsYSEh5LaFQsoZG1CI+pRXRMPGHhEZW1a4wxVcwKvo8IC4+kfuNW0LhVhd538EAuufuyyN2XyYGcvRzcn0V+bhaFuVkU5WWjB7LRg9kE5OcQULCfwIL9BBXtJ6Qol8iCvYTl5RKueURqHsFSdMzt5Woo2RJNTmAMeYEx5IfEUhBSi+LwOCS8NgFRCe7zFS2o07AZURHWi6kqqSrua19MDVMZze9W8Ku50LAIQsMiqJ3Q4MRWpMrBg7nsz9pDXk4mefsyyc/NomC/+4/HgWyK8zKRvL0EHswkOD+TsIIsYnPXEZ2zjxjdR+BR5yqKVdhBbXYF1WVfSD0ORDakOCaR4Lim1G7WiaYt2xAdHnpiuc1hYWFh7N69m/j4eCv6NYyqsnv3bsLCTuwGTlbwjYsIoWGRhIZFQr3GFX67FheRsy+TrIw0sv/cxIHdmynau5XA7DTC89Jpkr+WOnm/ErKrEDYAKZCnIawJaMTu8BYcrN2K4AbtiG/WiSYt2xEZbncmq6jExETS0tLw9qizxhlhYWEkJiae0Dqsl46pOsXFFO7bya4tq9iz+Xfy01cRmvkH8XmbqFv8vyJ1UIPYFNiEnbWTCG51Ji27DyShTl0HgxvjuyrSS8cKvvEJRXnZ/LlhOXs2LSM/fSURu5bR4sAKQimgSIV1gS3IiO9B6Eln0jJpIHFx8U5HNsYnWME3NUJRfh6blv7E3hU/EJU+jxYHVhIiha4/AEGt2NWgH20uGkv8iZ6/MKYas4JvaqSCA/vZkDqb7JU/Ev3nXNrkr2C/hrKs/hBOuuh+6jS0i3iM/7GCb/zCltWLyJjxb7pkzqSQIJYlXEDTwfdTt0lrp6MZU2UqUvDt8ktTbTVp041ud37Cn9f+SmrcIDpnTKP2W71Y9J8rSF+/zOl4xvgcK/im2mvUoj2njnmf3dcvYEHCENrt+YF6k85g6fMXs331fKfjGeMzrOCbGqNBk1b0/vsEsm9exK/1r6Zl1jwaTh7IinGDSFv+k9PxjHGcFXxT49Rr0IQ+t7xM3m2pzG54A432LSfx08GseaYfWxd9Az503sqYqmQF39RYCXXr0/fGcRSOWcaPTW4nbv8GGn85jA1PncbmuZ9a4Td+xwq+qfHqxMXTf9S/CBq7nJkt7iH0QAZNvx3Fln93Y/Oc96H42IPGGVMTWLdM43eycnKZ/8UbnLR2PM3ZTnpQYw72vJ1m/a6DwGCn4xlTIdYP3xgP7Ms9wG9fvU2zlW/Qmk1kBNYjp9utND/7Zgi2wdtM9WAF35gKyD1YwM9ff0CDZa/SiT/YExBH4dBJ1G3Xx+loxhyTXXhlTAVEhAZzzpCRnPzAXL7pNp6c4mAip1xG+vLZTkczplJZwTfGLSwkiEEXDiP3yi/ZRS1iPh3G1iUznY5lTKWxgm/MUdqc3JrCa74igzjivxjBxpRvnY5kTKWwgm9MKVq2aEXAddPZIXWo/9VVrJ33tdORjDlhVvCNKUOTps0J/dsM0qU+jWdcy6pfPnc6kjEnxAq+MeVo2KgJkTfOYHtgQ1p8/zeWz/7U6UjGHDevF3wRCRSRJSLylbe3ZYw31GuQSOzN35AW1JiTZ93Ekh+SnY5kzHGpiiP8McCqKtiOMV4TX7chdW79hq1BTWg/51bmf/OB05GMqTCvFnwRSQTOByZ4czvGVIXY+HrUG/0tW4Kb03XuaH79epLTkYypEG8f4b8I3AMUe3k7xlSJ6FoJNLz9W7aEnkSPBXcw+/O3nI5kjMe8VvBF5AJgp6ouOsZyN4pIioikZGRkeCuOMZUmIiaexNHfsDmsNacvuYuZn7zhdCRjPOLNI/zewGAR2QRMBvqLyPtHL6Sq41U1SVWTEhISvBjHmMoTFl2bJrd/w+bwdvRdfh8zPnoFXxqXypjSeK3gq+r9qpqoqs2AK4AfVfUqb23PmKoWEhlL0zEz2BzZkYGrH+TL9/9jRd/4NOuHb8wJCAqPofnt09kc1YXz1/2Tzyc+R3GxFX3jmzwq+CLSVETOcj8OF5HoimxEVWer6gXHE9AYXxcQFkXzMV+zOaYbF216nE/feooiK/rGBx2z4IvIDcAnwKEzU4mAXWNuTAkSEknz0V+ypXYPLk17minjH6egyDqnGd/iyRH+bbhOwGYDqOpaoK43QxlTHUlIBM1um8bWuF4M/3Mcyf99lIOFdr9c4zs8KfgHVTX/0BMRCQLs+6oxpQkOo+mtn7GlTh+u2vUiya8+zIECK/rGN3hS8H8SkQeAcBE5G/gY+NK7sYypxoLDaHLzp6TV7cs1e19h8sv/x/6DhU6nMsajgn8fkAEsB24CpgMPejOUMdVeUCiJN37M9voDGJn9X5Jfvo+svAKnUxk/50nBPx94S1UvU9WhqvqmWmdjY44tKISGNyTzZ6OBjMp5k09evoe9+/OP/T5jvMSTgj8MWCsiz4hIG28HMqZGCQym/qgP2dH4PK7PfZvPX3/Iumwaxxyz4Luvju0KrAcmishc9/g3FeqLb4zfCgym3sj32F6vH1dlv8mnX9mtIYwzPLrwSlWzcfXFnww0AC4BFovIaC9mM6bmCAyiwbVvkxMcR9Kiu1m+cbvTiYwf8uTCq8Ei8hkwGwgGeqjquUBn4B/ejWdMzSERcQQPfZNm8iebP7id3HzruWOqlidH+JcCL6hqR1V9VlV3AqhqLnC9V9MZU8NEtelHevubuKDwe6Z+8JrTcYyf8aQN/1rgD/eR/oUiUr/EvB+8ms6YGqjRJf8iPbItF2x6ip8WLnE6jvEjnjTpXA8sAIYAQ4F5IjLK28GMqbGCQoi/9j1CpYiIr29jR+Z+pxMZP+FJk849QFdVHek+2u8G3OvdWMbUbCF1TyK735N0ZwWz33nQhlQ2VcKTgr8b2Ffi+T73a8aYE1DvjFFsrj+QIZnv8uUM66ppvK/Mgi8iY0VkLLAOmC8i/xSRR4B5wB9VFdCYGkuEJteMJzsojs4L7mL1lnSnE5karrwj/Gj3tB7X+PeHvnN+AWz0ci5j/IJE1CZo6Js0kR1sfu/vNrKm8aqgsmao6qMln4tIhLsrpjGmEsW27cfm9jdzzor/MuXD17j8Wrue0XiHJ710eonISmC1+3lnEbEOxMZUoqZD/kVaRHvO2fAkcxenOh3H1FCenLR9ETgH94laVV0KnOHNUMb4ncBgEkZOIliUkGm3sDvbvkybyufpWDpbj3rJGhqNqWShdVuR2fcJurGSn975P2wUclPZPCn4W0XkNEBFJFhE7gJWeTmXMX6p4ZmjWF93IIP3TOTb76yrpqlcnhT8m3HdyLwRsA3o4n5ujKlsIjQfOZ7MoDq0+20s69P+dDqRqUE8GUtnl6qOUNV6qlpXVa9SVbvwyhgvCYioTcDQCTSSDDa+dyv5hcVORzI1RJndMkXkZf7X9/4vVPV2ryQyxhDX9kzWtb2Fs1a9xheTX+Wiq6yrpjlx5R3hpwCLgDDgFGCte+oChHg/mjH+rdXQf7E5vD391j7JoqXLnI5jaoAyC76qvquq7wKdgL6q+rKqvgwMwFX0jTHeFBhEwrWTCBQl8PMbycrJczqRqeY8OWlbG4gp8TzK/Zoxxssi6rdi15lP0kVX8fM791tXTXNCPCn4TwFLRGSiiLwLLAae9G4sY8whTfuNYk3CIAbtepeffvja6TimGvOkl847wKnAZ8BUoJe7qccYU0VaXfcGe4ISaPnznaSl73A6jqmmPL3S9k9V/cI9edQxWETCRGSBiCwVkRUi8uix32WMKU1gRC0YMp6GZLDu3VsoLLKumqbiPCr4x+kg0F9VO+M6yTtIRHp6cXvG1Gh12/dlbZtb6HvgB2Ymv+p0HFMNea3gq0uO+2mwe7IzTsacgDaX/4sN4R3oveYJfl9hXTVNxXhU8EUkUEQaikiTQ1MF3pcK7AS+V9X5pSxzo4ikiEhKRkZGxdIb428Cg6hz7SREBP30BnLyDjidyFQjnoyHPxrYAXwPfO2ePBrVSVWLVLULkAj0EJEOpSwzXlWTVDUpISGhQuGN8Ucx9Vuyo8+TdCxezW9v3+d0HFONeHKEPwZorartVbWje+pUkY2oaiYwCxh0PCGNMUdqOeA6VtQZxICdE5k7y7pqGs94NDwykFXRFYtIgojUcj8OB87GfdcsY8yJO3nUG2QE1qXJT2P4c6d11TTH5knB3wDMFpH7RWTsocmD9zUAZonIMmAhrjZ8G+DbmEoSHFGLokvGU093s/6dmygutj4RpnyeFPwtuNrvQ4DoElO5VHWZqnZV1U6q2kFVHzuxqMaYozXq2JeVJ91M77xZzJn2ttNxjI8TXxqbIykpSVNSUpyOYUy1ooX5bHq6F9H5GeTf9BsNGyY6HclUIRFZpKpJnixb5hG+iLzo/vmliEw7eqqssMaYEyNBIYQP/S+x5LDh/TE2wJopU5k3QAHec/8cVxVBjDHHr37rHixteT2nbxjPz9M/oM/5Vzkdyfgga9IxpoYozj9A2jM9CC3ch9w2n7oJdZ2OZKpApTTpGGOql4CQMAIvfo06upfVk+6wph3zF1bwjalBGnU4neVNr+GMfV8zb+anTscxPsaToRUu8+Q1Y4xv6HDlv9kW2Iimv97H7j27nY5jfIgnR/j3e/iaMcYHBIVFUnTBK9TXXfw+6R9OxzE+pMxeOiJyLnAe0EhEXioxKwYo9HYwY8zxa9K1P0sWDOPM9MksmD2UHn0vcDqS8QHlHeFvB1KAA8CiEtM04BzvRzPGnIj2V48jPaAe9Wf/g6ysCg+HZWqgMgu+qi5137u2laq+W2Kaqqp7qzCjMeY4hEREkzfoRZrwJ0sm3eN0HOMDPGnD7yEi34vIHyKyQUQ2isgGryczxpywFj3OI7XuJfTZlczi3753Oo5xmCcF/y3geeB0oDuQ5P5pjKkG2lzzArsD4qj9/Z3k7N/vdBzjIE8KfpaqzlDVnaq6+9A8jVJfAAAVyElEQVTk9WTGmEoRFlWbrLPG0Vy3kjLJOtj5M08K/iwReVZEeonIKYcmryczxlSak3oPITX+PE7/8z2WLZzjdBzjkPIGTzvkVPfPkmM1KNC/8uMYY7zl5GteIuuF7kTMGE1eh/mEh4c5HclUsWMe4atqv1ImK/bGVDMRsQlknPkkrYo3Mf/9h5yOYxzgydAK9UTkLRGZ4X7eTkSu9340Y0xla9PvSpbWGsBpaW+xcul8p+OYKuZJG/5E4Fugofv5H8Ad3gpkjPGulte8yn6JJOCL2ziYf9DpOKYKeVLw66jqFKAYQFULgSKvpjLGeE1UXAO2n/YYbYrXMu+Dfzkdx1QhTwr+fhGJx3WiFhHpCdh12sZUY+3PHsny6NPpuel1/lix2Ok4pop4UvDH4ho/p6WI/ApMAkZ7NZUxxrtEaHL1fzkoIRRMvY2CQhsP0R940ktnMXAmcBpwE9BeVZd5O5gxxrti6zZhU9JDtC9aydzJTzkdx1QBT3rpBOIaJnkAMBAYLSJjvR3MGON9nc6/mRURp5K09iU2rl3hdBzjZZ406XwJjATigegSkzGmuhOhwVWvUywB7JtyC0VFxU4nMl7kyZW2iarayetJjDGOiGvYgtQu99Il9Z/8/PFz9LnibqcjGS/x5Ah/hogM9HoSY4xjOg8ew6qwrnRd9RxbN/7hdBzjJZ4U/HnAZyKSJyLZIrJPRLK9HcwYU3UkIIA6w18nQIrZNflWiq1pp0bypOA/D/QCIlQ1RlWjVTXGy7mMMVUsoWkbVre7k64HFzL381edjmO8wJOCvxX4XVXV22GMMc7qOvQe1oS0p8Oyf5O+bZPTcUwl86TgbwBmi8j9IjL20HSsN4lIYxGZJSIrRWSFiIw58bjGGG+SgEBihr1BKPlse/9WtNiadmoSTwr+RuAHIISKdcssBP6hqu2AnsBtItLueIMaY6pGg5YdWdH67yTl/cq8ryY4HcdUIvG0pUZEogBUNee4NiTyBfCKqpZ5J+WkpCRNSUk5ntUbYypRcWEBG54+jbiCdApvnkfd+olORzJlEJFFqpp07CU9u9K2g4gsAVYAK0RkkYi0r2CgZkBX4C8DcIvIjSKSIiIpGRkZFVmtMcZLAoKCCRv6OlGaR/rbV1NQUOB0JFMJPGnSGQ+MVdWmqtoU+AfwpqcbcH8z+BS4Q1X/0p1TVcerapKqJiUkJHi6WmOMlyW27saKrg/TOX8x8ybYaCo1gScFP1JVZx16oqqzgUhPVi4iwbiK/QeqOvW4EhpjHNP14jEsqnMRfXZMYt5X7zgdx5wgj3rpiMhDItLMPT2Iq+dOuUREgLeAVar6/IkGNcY4o/MNb7AuuDUdF97H2t/tHFt15knBHwUkAFPdU4L7tWPpDVwN9BeRVPd03nEnNcY4Iig0nLhRyRyUEEI+vYa9e3Y7HckcJ4976VQF66VjjO9au+Abmn89nNSInnS96ysCAwOdjmSoWC+dMkfLFJFp5b1RVQdXNJgxpvo6qccglmy6i6SVz/DTO//HmX+zm6ZUN+UNj9wL17AKH+HqTilVksgY47O6XvYAS/+zmD5bX2fh96fQ/ezLnY5kKqC8Nvz6wANAB+A/wNnALlX9SVV/qopwxhgfI0KbG99hc3AzTv7lDrtLVjVTZsFX1SJV/UZVr8U1NMI6XGPq/L3K0hljfE5oRAxRV09GBAo/GkH2viynIxkPldtLR0RCRWQI8D5wG/AS8FlVBDPG+K6Epm1IH/AKLYs2seL1UTZ+fjVRZsEXkUnAXOAU4FFV7a6q/1LVbVWWzhjjs1r3GUJqq1votX8mcz54wuk4xgPlHeFfBZwEjAF+c9/tyu54ZYw5rOuIx/k9qje917/AojlfOR3HHEN5bfgB7rtbRbvvdHVosjteGWMA1/j5rW76gJ2B9Wj6461s3bTe6UimHJ5caWuMMWUKi65NwPAPieAA+967kv25uU5HMmWwgm+MOWENTurK5tOfpV3Raha9cRO+dAW/+R8r+MaYStH2rGtZ0vgazsiaxpzkF52OY0phBd8YU2m6jHye1eGn0HPVEyydP+vYbzBVygq+MabSSGAwiTd+RGZALerO+Bvp6WlORzIlWME3xlSqqNr1KRj6LnGaxY63r+TAwYNORzJuVvCNMZUusX1v1vV4jC4FS5k7foydxPURVvCNMV7R/vxbSa1/Kf12f8ScLyY4HcdgBd8Y40Wdrv8v60LakrTk/1ixdL7TcfyeFXxjjNcEBIdS9/opHAgIJ+qza8nI2Ol0JL9mBd8Y41Ux9Zqwf/BbNNSdbJpwNfkFhU5H8ltW8I0xXtek61ms6XIf3Q/O4+e373M6jt+ygm+MqRIdLr6b5fGD6Ld9Ar9M/8jpOH7JCr4xpmqI0PaGt9gS0pyO8//BmpVLnU7kd6zgG2OqTFBYFLHXTkZECJ9yOSt+T3U6kl+xgm+MqVK1E1uTc+mHxLCf+h9fyLyfv3M6kt+wgm+MqXINO56JjvqOgsAIOs8cwczP3nE6kl+wgm+McUTtJu2IHf0Tf4Y1p1/qncx4+zGKi20IBm+ygm+McUx47fo0ufNH1tbqzblbnmPmSzdxIL/A6Vg1lhV8Y4yjAsOiaDNmGisTL2dgZjIpzw1hd2aW07FqJCv4xhjnBQTS7vrxrO54N6cfnMPWl85lS5qNpV/ZrOAbY3yDCG0ufZCNfV+iXfEaCicMZPnvy5xOVaN4reCLyNsislNEfvfWNowxNU/zvtey+5IpJJBJ/Y8v4Nc53zsdqcbw5hH+RGCQF9dvjKmhGnQeQNGo79DAULr8MIJvP5/kdKQawWsFX1XnAHu8tX5jTM1Wq0kHYv4+m91hTRiwZAxfvv0ERdZt84Q43oYvIjeKSIqIpGRkZDgdxxjjQ8LiGpF45yw21erJhVue4duXbiXvoA2vfLwcL/iqOl5Vk1Q1KSEhwek4xhgfExAWTavbv2RNoyGcl/kh854fyq6sfU7HqpYcL/jGGHNMgUG0/tvbrO1wJ/0OzmLLf85lY9o2p1NVO1bwjTHVgwgnDf0nm898gY7FqyiacA5LV1gnwIrwZrfMj4C5QGsRSROR6721LWOM/2jabxR7Lv6I+uym/pQL+HnOj05Hqja82UtnuKo2UNVgVU1U1be8tS1jjH+p12UgRSNnEBgYSJcfruTrz95H1XrwHIs16RhjqqXYZl2Ium02WaENGJh6O5+/84x12zwGK/jGmGorLL4xDe+cTVpsNy7Z8iRfvzSa3IM22mZZrOAbY6q1gPBYmo+ZzrqGgxmc+R5znx/G6k3bnY7lk6zgG2Oqv8BgWt0wiQ3t/s6Agz9Q551T+fT1f7J9d7bTyXyKFXxjTM0gQovLnyDnmu/YH9OSS/98gYMv9WDqh6+TnZfvdDqfYAXfGFOjRLU4laZjZ7HrwkmEh4Yw5I97Wf/06Xz19efkFxY7Hc9RVvCNMTWPCHW6XUT9exezrc9TNAvI4IKF1/Lbv89n9tx5ftuF0wq+MabmCgyi0YBbqHXvMjZ2uJ1TixbT+5vzmP7MNaSuXut0uipnBd8YU+NJaDTNh/6LkLFL2dx0COfkfUWLj/rw2Utj2ZjuP6P0WsE3xviNwJj6tBo1gYIbf2FXfHcu2fMWYa/3YOpbT7MrO9fpeF5nBd8Y43fCG7anxe1fkjnsCwoj6zFk65Psfq4n0z6ZRF5+kdPxvMYKvjHGb9Vq25fGd8/lz4GvERecz+DfR7Ps3/34bub3NXKYBiv4xhj/JkL900aQcN9SNnd/iLZs4KyfL+PHfw9h7uLUGtWjxwq+McYABIXS9Py7iL5nORtaj+KMgp855Yuz+PL5G1m5cavT6SqFFXxjjClBwmvT6srnkdGL2NrgHC7Y9zH1J/bks/8+yJq0ndX6iF98KXxSUpKmpKQ4HcMYYw7bt2kRu6beQ/PsFHI0jPnBPchpcT4nn34JbRrXRUQczScii1Q1yaNlreAbY8wxqJK1ahY7f3ufettnElOcRa6GsiA4iazm53FS7yG0bdrAkeJvBd8YY7ylqJCsNbPZMW8KddO+o1bxXg5oMAuCupHZ7Dxa9r6Uds0bVVnxt4JvjDFVobiI7D9+5s+5ydRJ+5a4ot0c1CAWBnVlb9NzaX7aUNq3bOLV4m8F3xhjqlpxMdnrfiN9bjJ1tswgviiDfA1kUWBndjc5hyanXUbHk1pUevG3gm+MMU5SJWfDArb99hFxm2eQUPgnhRrA4oAOZDQZRGKvy+l4cisCAk68+FvBN8YYX6HKvs2L2fbrZGpt/Jr6hdsoUiE1oD07Es+hYa/L6dSm9XEXfyv4xhjji1TJ2bqMtF8/ImbDdBoWbKZYhaWBbelw32yCQ0IrvMqKFPygCq/dGGPM8REhqkln2jTpDDzF/m2/s+XnyYRkbj2uYl9RVvCNMcYhkY060PaKx6tseza0gjHG+Akr+MYY4yes4BtjjJ+wgm+MMX7CCr4xxvgJrxZ8ERkkImtEZJ2I3OfNbRljjCmf1wq+iAQCrwLnAu2A4SLSzlvbM8YYUz5vHuH3ANap6gZVzQcmAxd5cXvGGGPK4c0LrxoBJW8EmQacevRCInIjcKP7aY6IrCllXXWAXZWe0LuqW+bqlhcsc1WpbpmrW144scxNPV3Q8SttVXU8ML68ZUQkxdOxInxFdctc3fKCZa4q1S1zdcsLVZfZm00624DGJZ4nul8zxhjjAG8W/IXASSLSXERCgCuAaV7cnjHGmHJ4rUlHVQtF5O/At0Ag8LaqrjjO1ZXb5OOjqlvm6pYXLHNVqW6Zq1teqKLMPjUevjHGGO+xK22NMcZPWME3xhg/4VMF/1hDMYjISBHJEJFU9/Q3J3KWyPO2iOwUkd/LmC8i8pL78ywTkVOqOuNReY6Vt6+IZJXYvw9XdcZSMjUWkVkislJEVojImFKW8bX97Elmn9nXIhImIgtEZKk776OlLBMqIsnufTxfRJpVfdIj8niS2afqxSEiEigiS0Tkq1LmeXc/q6pPTLhO7K4HWgAhwFKg3VHLjARecTpriTxnAKcAv5cx/zxgBiBAT2C+j+ftC3zl9H49KlMD4BT342jgj1L+X/jafvYks8/sa/d+i3I/DgbmAz2PWuZW4HX34yuA5GqQ2afqRYlcY4EPS/v39/Z+9qUj/Go3FIOqzgH2lLPIRcAkdZkH1BKRBlWT7q88yOtzVDVdVRe7H+8DVuG6irskX9vPnmT2Ge79luN+Guyeju7NcRHwrvvxJ8AAEZEqivgXHmb2OSKSCJwPTChjEa/uZ18q+KUNxVDaL8ml7q/tn4hI41Lm+xJPP5Mv6eX+mjxDRNo7HaYk99fbrriO5kry2f1cTmbwoX3tbmZIBXYC36tqmftYVQuBLCC+alMeyYPM4Hv14kXgHqC4jPle3c++VPA98SXQTFU7Ad/zv7+EpnIsBpqqamfgZeBzh/McJiJRwKfAHaqa7XQeTxwjs0/ta1UtUtUuuK6I7yEiHZzM4wkPMvtUvRCRC4CdqrrIqQy+VPCPORSDqu5W1YPupxOAblWU7XhVq+ElVDX70NdkVZ0OBItIHYdjISLBuArnB6o6tZRFfG4/Hyuzr+5rVc0EZgGDjpp1eB+LSBAQC+yu2nSlKyuzD9aL3sBgEdmEq8m6v4i8f9QyXt3PvlTwjzkUw1HtsoNxtY36smnANe5eJD2BLFVNdzpUWUSk/qH2QhHpgev/h6O/1O48bwGrVPX5Mhbzqf3sSWZf2tcikiAitdyPw4GzgdVHLTYNuNb9eCjwo7rPLDrBk8y+Vi9U9X5VTVTVZrjq24+qetVRi3l1Pzs+WuYhWsZQDCLyGJCiqtOA20VkMFCI6+TjSMcCAyLyEa7eFnVEJA14BNfJI1T1dWA6rh4k64Bc4Dpnkrp4kHcocIuIFAJ5wBVO/lK79QauBpa722sBHgCagG/uZzzL7Ev7ugHwrrhuWhQATFHVr4763XsLeE9E1uH63bvCoayHeJLZp+pFWapyP9vQCsYY4yd8qUnHGGOMF1nBN8YYP2EF3xhj/IQVfGOM8RNW8I0xxk9YwTdeIyI5Hixzh4hEVOI2LxaRdpW4vt9O4L057p8NReSTcparJSK3Hu92jPGUFXzjtDuAChV8d9/rslwMVFrBV9XTKmEd21V1aDmL1MI1SqIxXmUF33iduMZ+n+0ewGq1iHzgvir2dqAhMEtEZrmXHSgic0VksYh87B6PBhHZJCJPi8hi4DIRuUFEFroHH/tURCJE5DRcV1Q+K67xz1uKSBcRmeceQOszEantXt9sEXlBRFJEZJWIdBeRqSKyVkQeL5E9p8Tje0VkuXubT5XyOZu7sy8/ah3NxH0PAhFpL65x3FPdmU4CngJaul97VkSiROQH9z5YLiIXlVjPKhF5U1xjwH/nvsoUEWklIjPd2RaLSEv363e799MyKWXMeONnKnOsZZtsKjkBOe6ffXGN+peI6yBjLnC6e94moI77cR1gDhDpfn4v8HCJ5e4pse74Eo8fB0a7H08EhpaYtww40/34MeBF9+PZwNPux2OA7biu3gzFNdpm/FGf4VzgNyDC/TyulM87DbjG/fi2Eu9thvseBLgGShvhfhwChJec7349CIgpsU/W4Rr/vRmuq0a7uOdNAa5yP54PXOJ+HIbrW9NAXDfHFvd+/wo4w+n/FzY5N/nM0AqmxlugqmkA7uEGmgG/HLVMT1zNMb+6h5kJwfXH4ZDkEo87uI+iawFRuIbkOIKIxAK1VPUn90vvAh+XWOTQWE3LgRXqHn9HRDbgGsCq5Ng2ZwHvqGougKqWdl+B3sCl7sfvAU+Xssxc4P/ENS76VFVdK38d7lyAJ0XkDFzD6DYC6rnnbVTVQ8M1LAKaiUg00EhVP3NnO+D+HANxFf0l7uWjgJNw/VE1fsgKvqkqB0s8LqL0/3uCa1zz4WWsY3+JxxOBi1V1qYiMxPUt4ngzFR+Vr7iMfJ4od6wSVf1QRObjugnGdBG5Cdhw1GIjgASgm6oWiGt0xbCjMoNrP4aXszkB/q2qb1Qgv6nBrA3fOG0frtsAAswDeotIKwARiRSRk8t4XzSQLq5hiEeUtj5VzQL2ikgf97yrgZ84Pt8D1x3qUSQicaUs8yv/G+xqRCnzEZEWwAZVfQn4AujEkfsAXEPi7nQX+35A0/KCqeuuWmkicrF7G6HunN8Co0qcB2kkInU9+rSmRrKCb5w2HvhGRGapagauEQ0/EpFluJo/2pTxvodwtVv/ypHD4k4G7hbXTaJb4hpq9ln3+rrgasevMFX9BlcTUIq7SequUhYbA9wmIssp+45blwO/u9fRAdetGXfjasb6XUSeBT4AktzruYa/DlVcmqtxjQ65DNe5hvqq+h2ue6fOda/rE478w2L8jI2WaYwxfsKO8I0xxk9YwTfGGD9hBd8YY/yEFXxjjPETVvCNMcZPWME3xhg/YQXfGGP8xP8DIcKLYC5W7lgAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "for j in reversed(range(len(algorithms))):\n", " pylab.plot(distances, dipoles[j], label=algorithms[j])\n", "pylab.xlabel('Interatomic distance')\n", "pylab.ylabel('Moment in debye')\n", "pylab.title('LiH Dipole Moment')\n", - "pylab.legend(loc='upper right')" + "pylab.legend(loc='upper right');" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "pylab.plot(distances, eval_counts, '-o', color=[0.8500, 0.3250, 0.0980], label='VQE')\n", "pylab.xlabel('Interatomic distance')\n", "pylab.ylabel('Evaluations')\n", "pylab.title('VQE number of evaluations')\n", - "pylab.legend(loc='upper left')" + "pylab.legend(loc='upper left');" ] }, { @@ -166,7 +226,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.7" + "version": "3.6.1" } }, "nbformat": 4, From 219890dd05e265636934ff2b6d55a91537bdc227 Mon Sep 17 00:00:00 2001 From: woodsp Date: Sun, 28 Apr 2019 13:45:33 -0400 Subject: [PATCH 084/116] Update chemistry notebooks --- community/aqua/chemistry/nah_uccsd.ipynb | 109 +++++++++++++++++++---- 1 file changed, 91 insertions(+), 18 deletions(-) diff --git a/community/aqua/chemistry/nah_uccsd.ipynb b/community/aqua/chemistry/nah_uccsd.ipynb index ce3c7da82..f0ce1246e 100644 --- a/community/aqua/chemistry/nah_uccsd.ipynb +++ b/community/aqua/chemistry/nah_uccsd.ipynb @@ -6,16 +6,18 @@ "source": [ "## _*NaH dissociation curve using VQE with UCCSD*_\n", "\n", - "This notebook demonstrates using the Qiskit Chemistry to plot graphs of the ground state energy of the Sodium Hydride (NaH) molecule over a range of inter-atomic distances using VQE and UCCSD. It is compared to the same energies as computed by the ExactEigensolver\n", + "This notebook demonstrates using the Qiskit Chemistry to plot graphs of the ground state energy of the Sodium Hydride (NaH) molecule over a range of inter-atomic distances using VQE and UCCSD. It is compared to the same energies as computed by the ExactEigensolver.\n", "\n", "This notebook populates a dictionary, that is a progammatic representation of an input file, in order to drive the Qiskit Chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here where we alter the molecule supplied to the driver in each loop.\n", "\n", - "This notebook has been written to use the PYSCF chemistry driver. See the PYSCF chemistry driver readme if you need to install the external PySCF library that this driver requires." + "_*Note: this molecule is larger than the similar LiH and this notebook can take a while to run.*_\n", + "\n", + "This notebook has been written to use the PYSCF chemistry driver." ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": { "scrolled": false }, @@ -24,7 +26,34 @@ "name": "stdout", "output_type": "stream", "text": [ - "Processing step __\b\b 0" + "Processing step 23 --- complete\n", + "Distances: [1. 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2. 2.1 2.2 2.3\n", + " 2.4 2.5 2.75 3. 3.25 3.5 3.75 4. 4.25 4.5 ]\n", + "Energies: [[-160.05849063 -160.15699836 -160.22568735 -160.27202139 -160.30172252\n", + " -160.31895083 -160.32675432 -160.32741528 -160.32269878 -160.31400273\n", + " -160.30245852 -160.28899051 -160.27435538 -160.2591661 -160.2439109\n", + " -160.2289718 -160.19475711 -160.16708758 -160.14746338 -160.13627128\n", + " -160.13114984 -160.12788151 -160.12587996 -160.06078205]\n", + " [-160.05849084 -160.15699856 -160.22568741 -160.2720216 -160.30172261\n", + " -160.31895199 -160.32675458 -160.32741545 -160.32269886 -160.31400297\n", + " -160.30245861 -160.28899063 -160.27435552 -160.25916618 -160.24391112\n", + " -160.22897222 -160.19475719 -160.16708762 -160.14746354 -160.13627173\n", + " -160.13150727 -160.12988489 -160.12941537 -160.12738873]]\n", + "Hartree-Fock energies: [-160.04320295 -160.14360744 -160.21336733 -160.26022033 -160.29007462\n", + " -160.30721237 -160.31476208 -160.31507193 -160.30995602 -160.30085169\n", + " -160.28891892 -160.2751014 -160.26016389 -160.24471683 -160.2292359\n", + " -160.21408033 -160.17913095 -160.14978812 -160.12634274 -160.10810649\n", + " -160.09400858 -160.08298959 -160.07419396 -160.0607817 ]\n", + "Dipoles: [[ 2.97124996 3.47605491 3.89545827 4.26391121 4.59602643 4.90977845\n", + " 5.21848651 5.52130528 5.82181265 6.11915269 6.41401426 6.70106614\n", + " 6.97515248 7.2256667 7.44609665 7.6264232 7.7960656 7.18509199\n", + " 5.30076748 2.68452589 1.70805451 1.77404721 1.76460865 21.57731566]\n", + " [ 2.97335246 3.47789485 3.89561999 4.26006188 4.59374084 4.91025573\n", + " 5.21772576 5.52078168 5.82151088 6.11992744 6.41423476 6.70095324\n", + " 6.97491033 7.22906568 7.45413201 7.63797444 7.80073442 7.19343854\n", + " 5.31627389 2.65735429 0.91782198 0.26885135 0.07470177 0.0219034 ]]\n", + "VQE num evaluations: [211. 211. 186. 185. 160. 159. 211. 236. 212. 186. 186. 184. 184. 186.\n", + " 211. 211. 236. 262. 286. 338. 391. 339. 364. 28.]\n" ] } ], @@ -41,7 +70,7 @@ " 'operator': {'name': 'hamiltonian', 'qubit_mapping': 'parity',\n", " 'two_qubit_reduction': True, 'freeze_core': True, 'orbital_reduction': []},\n", " 'algorithm': {'name': ''},\n", - " 'optimizer': {'name': 'COBYLA', 'maxiter': 10000 },\n", + " 'optimizer': {'name': 'SLSQP', 'maxiter': 2500 },\n", " 'variational_form': {'name': 'UCCSD'},\n", " 'initial_state': {'name': 'HartreeFock'}\n", "}\n", @@ -87,9 +116,20 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "pylab.plot(distances, hf_energies, label='Hartree-Fock')\n", "for j in range(len(algorithms)):\n", @@ -97,48 +137,81 @@ "pylab.xlabel('Interatomic distance')\n", "pylab.ylabel('Energy')\n", "pylab.title('NaH Ground State Energy')\n", - "pylab.legend(loc='upper right')" + "pylab.legend(loc='upper right');" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "pylab.plot(distances, np.subtract(hf_energies, energies[1]), label='Hartree-Fock')\n", "pylab.plot(distances, np.subtract(energies[0], energies[1]), label='VQE')\n", "pylab.xlabel('Interatomic distance')\n", "pylab.ylabel('Energy')\n", "pylab.title('Energy difference from ExactEigensolver')\n", - "pylab.legend(loc='upper left')" + "pylab.legend(loc='upper left');" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "for j in reversed(range(len(algorithms))):\n", " pylab.plot(distances, dipoles[j], label=algorithms[j])\n", "pylab.xlabel('Interatomic distance')\n", "pylab.ylabel('Moment in debye')\n", "pylab.title('NaH Dipole Moment')\n", - "pylab.legend(loc='upper right')" + "pylab.legend(loc='upper right');" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "pylab.plot(distances, eval_counts, '-o', color=[0.8500, 0.3250, 0.0980], label='VQE')\n", "pylab.xlabel('Interatomic distance')\n", "pylab.ylabel('Evaluations')\n", "pylab.title('VQE number of evaluations')\n", - "pylab.legend(loc='upper left')" + "pylab.legend(loc='upper left');" ] }, { @@ -165,7 +238,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.7" + "version": "3.6.1" } }, "nbformat": 4, From 20c4217e84eace8fc83bcf8b599507728636df34 Mon Sep 17 00:00:00 2001 From: Shaohan Hu Date: Sun, 28 Apr 2019 14:41:17 -0400 Subject: [PATCH 085/116] more updates for vqc refactor --- .../{qsvm_kernel.json => qsvm.json} | 6 +- .../input_files/svm_classical.json | 4 +- .../{qsvm_variational.json => vqc.json} | 6 +- .../qsvm_directly.ipynb | 2 +- .../svm_classical.ipynb | 37 +- .../svm_classical_multiclass.ipynb | 8 +- .../aqua/artificial_intelligence/vqc.ipynb | 30 +- community/aqua/index.ipynb | 6 +- .../.ipynb_checkpoints/w8_02-checkpoint.ipynb | 338 ++++++++++++++++++ .../exercises/w8_02.ipynb | 18 +- .../latex/main.tex | 14 +- .../aqua/artificial_intelligence/index.ipynb | 8 +- .../qsvm_classification.ipynb | 4 +- 13 files changed, 413 insertions(+), 68 deletions(-) rename community/aqua/artificial_intelligence/input_files/{qsvm_kernel.json => qsvm.json} (97%) rename community/aqua/artificial_intelligence/input_files/{qsvm_variational.json => vqc.json} (97%) create mode 100644 community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/.ipynb_checkpoints/w8_02-checkpoint.ipynb diff --git a/community/aqua/artificial_intelligence/input_files/qsvm_kernel.json b/community/aqua/artificial_intelligence/input_files/qsvm.json similarity index 97% rename from community/aqua/artificial_intelligence/input_files/qsvm_kernel.json rename to community/aqua/artificial_intelligence/input_files/qsvm.json index a0dc7592c..5673fc17c 100644 --- a/community/aqua/artificial_intelligence/input_files/qsvm_kernel.json +++ b/community/aqua/artificial_intelligence/input_files/qsvm.json @@ -1,11 +1,11 @@ { "algorithm": { - "name": "QSVM.Kernel"}, - "problem": {"name": "svm_classification"}, + "name": "QSVM"}, + "problem": {"name": "classification"}, "backend": {"provider": "qiskit.BasicAer", "name": "qasm_simulator", "shots":1000}, "input": { - "name": "SVMInput", + "name": "ClassificationInput", "training_dataset": {"A": [[6.220353454107791, 4.1469023027385274], [3.204424506661589, 4.335397861953915], [3.5185837720205684, 3.7699111843077513], [2.4504422698000385, 5.717698629533423], [4.39822971502571, 2.324778563656447], [2.9530970943744057, 1.8221237390820801], [2.8902652413026093, 4.838052686528282], [3.015928947446201, 4.1469023027385274], [1.4451326206513047, 2.827433388230814], [0.0, 4.335397861953915], [3.5185837720205684, 2.4504422698000385], [1.7592918860102842, 2.6389378290154264], [5.717698629533423, 1.9477874452256716], [3.330088212805181, 1.2566370614359172], [1.382300767579509, 0.6911503837897545], [3.015928947446201, 2.324778563656447], [5.780530482605219, 0.9424777960769378], [0.06283185307179587, 5.0893800988154645], [2.9530970943744057, 4.9637163926718735], [3.7699111843077513, 4.084070449666731]], "B": [[1.4451326206513047, 5.277875658030853], [1.5079644737231006, 5.0893800988154645], [0.8168140899333463, 5.277875658030853], [1.0053096491487339, 0.25132741228718347], [0.3141592653589793, 6.220353454107791], [4.335397861953915, 3.4557519189487724], [3.4557519189487724, 6.031857894892402], [5.592034923389832, 0.5026548245743669], [0.3141592653589793, 5.654866776461628], [0.5654866776461628, 1.5079644737231006], [5.277875658030853, 3.141592653589793], [4.272566008882119, 0.5026548245743669], [2.0106192982974678, 4.461061568097507], [4.0212385965949355, 4.71238898038469], [1.4451326206513047, 4.900884539600077], [1.8849555921538756, 3.204424506661589], [5.592034923389832, 1.4451326206513047], [2.3876104167282426, 4.335397861953915], [4.084070449666731, 2.3876104167282426], [4.084070449666731, 4.649557127312894]]}, "test_dataset": diff --git a/community/aqua/artificial_intelligence/input_files/svm_classical.json b/community/aqua/artificial_intelligence/input_files/svm_classical.json index febf4bb4e..de6744777 100644 --- a/community/aqua/artificial_intelligence/input_files/svm_classical.json +++ b/community/aqua/artificial_intelligence/input_files/svm_classical.json @@ -2,9 +2,9 @@ "algorithm": { "name": "SVM" }, - "problem": {"name": "svm_classification"}, + "problem": {"name": "classification"}, "input": { - "name": "SVMInput", + "name": "ClassificationInput", "training_dataset": {"A": [[6.220353454107791, 4.1469023027385274], [3.204424506661589, 4.335397861953915], [3.5185837720205684, 3.7699111843077513], [2.4504422698000385, 5.717698629533423], [4.39822971502571, 2.324778563656447], [2.9530970943744057, 1.8221237390820801], [2.8902652413026093, 4.838052686528282], [3.015928947446201, 4.1469023027385274], [1.4451326206513047, 2.827433388230814], [0.0, 4.335397861953915], [3.5185837720205684, 2.4504422698000385], [1.7592918860102842, 2.6389378290154264], [5.717698629533423, 1.9477874452256716], [3.330088212805181, 1.2566370614359172], [1.382300767579509, 0.6911503837897545], [3.015928947446201, 2.324778563656447], [5.780530482605219, 0.9424777960769378], [0.06283185307179587, 5.0893800988154645], [2.9530970943744057, 4.9637163926718735], [3.7699111843077513, 4.084070449666731]], "B": [[1.4451326206513047, 5.277875658030853], [1.5079644737231006, 5.0893800988154645], [0.8168140899333463, 5.277875658030853], [1.0053096491487339, 0.25132741228718347], [0.3141592653589793, 6.220353454107791], [4.335397861953915, 3.4557519189487724], [3.4557519189487724, 6.031857894892402], [5.592034923389832, 0.5026548245743669], [0.3141592653589793, 5.654866776461628], [0.5654866776461628, 1.5079644737231006], [5.277875658030853, 3.141592653589793], [4.272566008882119, 0.5026548245743669], [2.0106192982974678, 4.461061568097507], [4.0212385965949355, 4.71238898038469], [1.4451326206513047, 4.900884539600077], [1.8849555921538756, 3.204424506661589], [5.592034923389832, 1.4451326206513047], [2.3876104167282426, 4.335397861953915], [4.084070449666731, 2.3876104167282426], [4.084070449666731, 4.649557127312894]]}, "test_dataset": diff --git a/community/aqua/artificial_intelligence/input_files/qsvm_variational.json b/community/aqua/artificial_intelligence/input_files/vqc.json similarity index 97% rename from community/aqua/artificial_intelligence/input_files/qsvm_variational.json rename to community/aqua/artificial_intelligence/input_files/vqc.json index 36ee9663a..e7eb30e9d 100644 --- a/community/aqua/artificial_intelligence/input_files/qsvm_variational.json +++ b/community/aqua/artificial_intelligence/input_files/vqc.json @@ -1,12 +1,12 @@ { "algorithm": { - "name": "QSVM.Variational" + "name": "VQC" }, - "problem": {"name": "svm_classification"}, + "problem": {"name": "classification"}, "backend": {"provider": "qiskit.BasicAer", "name": "qasm_simulator", "shots": 1000}, "optimizer": {"name": "SPSA", "max_trials": 100, "save_steps": 10}, "input": { - "name": "SVMInput", + "name": "ClassificationInput", "training_dataset": {"A": [[6.220353454107791, 4.1469023027385274], [3.204424506661589, 4.335397861953915], [3.5185837720205684, 3.7699111843077513], [2.4504422698000385, 5.717698629533423], [4.39822971502571, 2.324778563656447], [2.9530970943744057, 1.8221237390820801], [2.8902652413026093, 4.838052686528282], [3.015928947446201, 4.1469023027385274], [1.4451326206513047, 2.827433388230814], [0.0, 4.335397861953915], [3.5185837720205684, 2.4504422698000385], [1.7592918860102842, 2.6389378290154264], [5.717698629533423, 1.9477874452256716], [3.330088212805181, 1.2566370614359172], [1.382300767579509, 0.6911503837897545], [3.015928947446201, 2.324778563656447], [5.780530482605219, 0.9424777960769378], [0.06283185307179587, 5.0893800988154645], [2.9530970943744057, 4.9637163926718735], [3.7699111843077513, 4.084070449666731]], "B": [[1.4451326206513047, 5.277875658030853], [1.5079644737231006, 5.0893800988154645], [0.8168140899333463, 5.277875658030853], [1.0053096491487339, 0.25132741228718347], [0.3141592653589793, 6.220353454107791], [4.335397861953915, 3.4557519189487724], [3.4557519189487724, 6.031857894892402], [5.592034923389832, 0.5026548245743669], [0.3141592653589793, 5.654866776461628], [0.5654866776461628, 1.5079644737231006], [5.277875658030853, 3.141592653589793], [4.272566008882119, 0.5026548245743669], [2.0106192982974678, 4.461061568097507], [4.0212385965949355, 4.71238898038469], [1.4451326206513047, 4.900884539600077], [1.8849555921538756, 3.204424506661589], [5.592034923389832, 1.4451326206513047], [2.3876104167282426, 4.335397861953915], [4.084070449666731, 2.3876104167282426], [4.084070449666731, 4.649557127312894]]}, "test_dataset": {"A": [[4.900884539600077, 5.780530482605219], [1.6336281798666925, 2.199114857512855], [6.094689747964199, 0.6283185307179586], [5.340707511102648, 3.8327430373795477], [3.015928947446201, 0.6911503837897545], [0.6911503837897545, 4.71238898038469], [3.267256359733385, 0.8796459430051421], [0.18849555921538758, 5.403539364174444], [0.18849555921538758, 0.8168140899333463], [3.4557519189487724, 1.4451326206513047]], "B": [[0.6911503837897545, 5.215043804959057], [1.9477874452256716, 1.3194689145077132], [2.6389378290154264, 3.204424506661589], [1.5079644737231006, 0.8168140899333463], [2.701769682087222, 3.3929200658769765], [4.523893421169302, 3.5185837720205684], [2.261946710584651, 4.39822971502571], [4.71238898038469, 2.827433388230814], [2.199114857512855, 1.1938052083641213], [2.764601535159018, 3.707079331235956]]}, diff --git a/community/aqua/artificial_intelligence/qsvm_directly.ipynb b/community/aqua/artificial_intelligence/qsvm_directly.ipynb index 3fe700da2..adf51dcb2 100644 --- a/community/aqua/artificial_intelligence/qsvm_directly.ipynb +++ b/community/aqua/artificial_intelligence/qsvm_directly.ipynb @@ -8,7 +8,7 @@ "\n", "### Introduction\n", "\n", - "Please refer to [this file](https://github.com/Qiskit/qiskit-tutorials/blob/master/qiskit/aqua/artificial_intelligence/qsvm_kernel_classification.ipynb) for introduction.\n", + "Please refer to [this file](https://github.com/Qiskit/qiskit-tutorials/blob/master/qiskit/aqua/artificial_intelligence/qsvm_classification.ipynb) for introduction.\n", "\n", "In this file, we show two ways for using the quantum kernel method: (1) the declarative approach and (2) the programmatic approach. \n" ] diff --git a/community/aqua/artificial_intelligence/svm_classical.ipynb b/community/aqua/artificial_intelligence/svm_classical.ipynb index 3e5e40ed2..293a30ab9 100644 --- a/community/aqua/artificial_intelligence/svm_classical.ipynb +++ b/community/aqua/artificial_intelligence/svm_classical.ipynb @@ -6,7 +6,7 @@ "source": [ "## _*SVM with a classical RBF kernel*_\n", "\n", - "We have shown here a QSVM_Kernel notebook with the classification problem solved using a quantum algorithm. By comparison this shows the problem solved classically.\n", + "We have shown here a QSVM notebook with the classification problem solved using a quantum algorithm. By comparison this shows the problem solved classically.\n", "\n", "**This notebook shows the SVM implementation based on the classical RBF kernel.**" ] @@ -19,7 +19,7 @@ "source": [ "from datasets import *\n", "from qiskit.aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name\n", - "from qiskit.aqua.input import SVMInput\n", + "from qiskit.aqua.input import ClassificationInput\n", "from qiskit.aqua import run_algorithm" ] }, @@ -39,7 +39,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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\n", 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\n", "text/plain": [ "
" ] @@ -74,10 +74,11 @@ "training_dataset_size = 20\n", "testing_dataset_size = 10\n", "\n", - "sample_Total, training_input, test_input, class_labels = ad_hoc_data(training_size=training_dataset_size, \n", - " test_size=testing_dataset_size, \n", - " n=feature_dim, gap=0.3, PLOT_DATA=True)\n", - "\n", + "sample_Total, training_input, test_input, class_labels = ad_hoc_data(\n", + " training_size=training_dataset_size, \n", + " test_size=testing_dataset_size, \n", + " n=feature_dim, gap=0.3, PLOT_DATA=True\n", + ")\n", "datapoints, class_to_label = split_dataset_to_data_and_labels(test_input)\n", "print(class_to_label)" ] @@ -98,13 +99,13 @@ "outputs": [], "source": [ "params = {\n", - " 'problem': {'name': 'svm_classification'},\n", + " 'problem': {'name': 'classification'},\n", " 'algorithm': {\n", " 'name': 'SVM'\n", " }\n", "}\n", "\n", - "algo_input = SVMInput(training_input, test_input, datapoints[0])" + "algo_input = ClassificationInput(training_input, test_input, datapoints[0])" ] }, { @@ -132,7 +133,7 @@ }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -146,8 +147,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "testing success ratio: 0.7\n", - "predicted classes: ['A', 'B', 'A', 'A', 'A', 'B', 'B', 'A', 'A', 'A', 'B', 'B', 'B', 'A', 'B', 'A', 'A', 'B', 'B', 'B']\n" + "testing success ratio: 0.6\n", + "predicted classes: ['A', 'B', 'A', 'A', 'A', 'A', 'B', 'A', 'A', 'B', 'A', 'A', 'A', 'B', 'B', 'B', 'A', 'B', 'B', 'A']\n" ] } ], @@ -155,7 +156,7 @@ "result = run_algorithm(params, algo_input)\n", "print(\"kernel matrix during the training:\")\n", "kernel_matrix = result['kernel_matrix_training']\n", - "img = plt.imshow(np.asmatrix(kernel_matrix),interpolation='nearest',origin='upper',cmap='bone_r')\n", + "img = plt.imshow(np.asmatrix(kernel_matrix), interpolation='nearest', origin='upper', cmap='bone_r')\n", "plt.show()\n", "\n", "print(\"testing success ratio: \", result['testing_accuracy'])\n", @@ -196,7 +197,9 @@ } ], "source": [ - "sample_Total, training_input, test_input, class_labels = Breast_cancer(training_size=20, test_size=10, n=2, PLOT_DATA=True)\n", + "sample_Total, training_input, test_input, class_labels = Breast_cancer(\n", + " training_size=20, test_size=10, n=2, PLOT_DATA=True\n", + ")\n", "# n =2 is the dimension of each data point\n", "\n", "datapoints, class_to_label = split_dataset_to_data_and_labels(test_input)\n", @@ -239,7 +242,7 @@ } ], "source": [ - "algo_input = SVMInput(training_input, test_input, datapoints[0])\n", + "algo_input = ClassificationInput(training_input, test_input, datapoints[0])\n", "result = run_algorithm(params, algo_input)\n", "# print(result)\n", "print(\"kernel matrix during the training:\")\n", @@ -270,7 +273,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.7.2" } }, "nbformat": 4, diff --git a/community/aqua/artificial_intelligence/svm_classical_multiclass.ipynb b/community/aqua/artificial_intelligence/svm_classical_multiclass.ipynb index 717ea81e1..1a5cb2b7a 100644 --- a/community/aqua/artificial_intelligence/svm_classical_multiclass.ipynb +++ b/community/aqua/artificial_intelligence/svm_classical_multiclass.ipynb @@ -25,7 +25,7 @@ "source": [ "from datasets import *\n", "from qiskit.aqua.utils import split_dataset_to_data_and_labels\n", - "from qiskit.aqua.input import SVMInput\n", + "from qiskit.aqua.input import ClassificationInput\n", "from qiskit.aqua import run_algorithm\n", "import numpy as np" ] @@ -106,14 +106,14 @@ ], "source": [ "aqua_dict = {\n", - " 'problem': {'name': 'svm_classification'},\n", + " 'problem': {'name': 'classification'},\n", " 'algorithm': {\n", " 'name': 'SVM'\n", " },\n", " 'multiclass_extension': {'name': 'OneAgainstRest'}\n", "}\n", "\n", - "algo_input = SVMInput(training_input, test_input, total_array)\n", + "algo_input = ClassificationInput(training_input, test_input, total_array)\n", "\n", "extensions = [\n", " {'name': 'OneAgainstRest'},\n", @@ -146,7 +146,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.7.2" } }, "nbformat": 4, diff --git a/community/aqua/artificial_intelligence/vqc.ipynb b/community/aqua/artificial_intelligence/vqc.ipynb index b2a569dcd..aa8929e6e 100644 --- a/community/aqua/artificial_intelligence/vqc.ipynb +++ b/community/aqua/artificial_intelligence/vqc.ipynb @@ -21,7 +21,7 @@ "metadata": {}, "source": [ "### Part I: declarative approach.\n", - "In the declarative approach, we config a json-like configuration, which defines how the svm instance is internally constructed. After the execution, it returns the json-like output, which carries the important information (e.g., the details of the svm instance) and the processed results. " + "In the declarative approach, we config a json-like configuration, which defines how the vqc instance is internally constructed. After the execution, it returns the json-like output, which carries the important information (e.g., the details of the vqc instance) and the processed results. " ] }, { @@ -106,7 +106,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Now we create the svm in the declarative approach.\n", + "Now we create the vqc in the declarative approach.\n", "In the following json, we config:\n", "- the algorithm name \n", "- the variational form\n", @@ -129,7 +129,7 @@ " 'feature_map': {'name': 'SecondOrderExpansion', 'depth': 2}\n", "}\n", "\n", - "svm_input = ClassificationInput(training_input, test_input, datapoints[0])\n", + "classification_input = ClassificationInput(training_input, test_input, datapoints[0])\n", "backend = BasicAer.get_backend('qasm_simulator')" ] }, @@ -159,7 +159,7 @@ } ], "source": [ - "result = run_algorithm(params, svm_input, backend=backend)\n", + "result = run_algorithm(params, classification_input, backend=backend)\n", "print(\"testing success ratio: \", result['testing_accuracy'])\n", "print(\"predicted classes:\", result['predicted_classes'])" ] @@ -169,18 +169,18 @@ "metadata": {}, "source": [ "### Part II: programmatic approach.\n", - "We construct the svm instance directly from the classes. The programmatic approach offers the users better accessibility, e.g., the users can access the internal state of svm instance or invoke the methods of the instance. " + "We construct the vqc instance directly from the classes. The programmatic approach offers the users better accessibility, e.g., the users can access the internal state of vqc instance or invoke the methods of the instance. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Now we create the svm in the programmatic approach.\n", - "- we build the optimizer instance (required by the svm instance) by instantiating the class SPSA.\n", - "- We build the feature map instance (required by the svm instance) by instantiating the class SecondOrderExpansion.\n", - "- We build the varitional form instance (required by the svm instance) by instantiating the class RYRZ.\n", - "- We build the svm instance by instantiating the class VQC. \n" + "Now we create the vqc in the programmatic approach.\n", + "- we build the optimizer instance (required by the vqc instance) by instantiating the class SPSA.\n", + "- We build the feature map instance (required by the vqc instance) by instantiating the class SecondOrderExpansion.\n", + "- We build the varitional form instance (required by the vqc instance) by instantiating the class RYRZ.\n", + "- We build the vqc instance by instantiating the class VQC. \n" ] }, { @@ -194,7 +194,7 @@ "optimizer.set_options(save_steps=1)\n", "feature_map = SecondOrderExpansion(feature_dimension=feature_dim, depth=2)\n", "var_form = RYRZ(num_qubits=feature_dim, depth=3)\n", - "svm = VQC(optimizer, feature_map, var_form, training_input, test_input)\n", + "vqc = VQC(optimizer, feature_map, var_form, training_input, test_input)\n", "quantum_instance = QuantumInstance(backend, shots=shots, seed=random_seed, seed_transpiler=random_seed)" ] }, @@ -219,7 +219,7 @@ } ], "source": [ - "result = svm.run(quantum_instance)\n", + "result = vqc.run(quantum_instance)\n", "print(\"testing success ratio: \", result['testing_accuracy'])" ] }, @@ -227,7 +227,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Different from the declarative approach, the programmatic approach allows the users to invoke APIs upon the svm instance directly. In the following, we invoke the API \"predict\" upon the trained svm instance to predict the labels for the newly provided data input.\n", + "Different from the declarative approach, the programmatic approach allows the users to invoke APIs upon the vqc instance directly. In the following, we invoke the API \"predict\" upon the trained vqc instance to predict the labels for the newly provided data input.\n", "\n", "Use the trained model to evaluate data directly, and we store a label_to_class and class_to_label for helping converting between label and class name" ] @@ -246,8 +246,8 @@ } ], "source": [ - "predicted_probs, predicted_labels = svm.predict(datapoints[0])\n", - "predicted_classes = map_label_to_class_name(predicted_labels, svm.label_to_class)\n", + "predicted_probs, predicted_labels = vqc.predict(datapoints[0])\n", + "predicted_classes = map_label_to_class_name(predicted_labels, vqc.label_to_class)\n", "print(\"prediction: {}\".format(predicted_labels))" ] } diff --git a/community/aqua/index.ipynb b/community/aqua/index.ipynb index 4f74d1ecd..415db6024 100644 --- a/community/aqua/index.ipynb +++ b/community/aqua/index.ipynb @@ -60,8 +60,8 @@ "\n", "Qiskit Aqua Artificial Intelligence is a set of tools, algorithms and software for use with quantum computers to carry out research and investigate how to take advantage of quantum computing power to solve artificial intelligence problems. \n", "\n", - "* [Quantum SVM kernel algorithm: multiclass classifier extension](artificial_intelligence/qsvm_kernel_multiclass.ipynb)\n", - "* [Quantum SVM (variational method)](artificial_intelligence/qsvm_variational.ipynb)\n", + "* [Quantum SVM algorithm: multiclass classifier extension](artificial_intelligence/qsvm_multiclass.ipynb)\n", + "* [Variational Quantum Classifier (vqc)](artificial_intelligence/vqc.ipynb)\n", "\n", "The repository here may be viewed for the\n", "[full listing](https://github.com/Qiskit/qiskit-tutorial/tree/master/artificial_intelligence).\n", @@ -116,7 +116,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.7.2" } }, "nbformat": 4, diff --git a/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/.ipynb_checkpoints/w8_02-checkpoint.ipynb b/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/.ipynb_checkpoints/w8_02-checkpoint.ipynb new file mode 100644 index 000000000..3b9c29e80 --- /dev/null +++ b/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/.ipynb_checkpoints/w8_02-checkpoint.ipynb @@ -0,0 +1,338 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# _*Qiskit Aqua: Experiment with classification problem with quantum-enhanced support vector machines*_\n", + "\n", + "This notebook is based on an official notebook by Qiskit team, available at https://github.com/qiskit/qiskit-tutorial under the [Apache License 2.0](https://github.com/Qiskit/qiskit-tutorial/blob/master/LICENSE) license. \n", + "The original notebook was developed by Vojtech Havlicek[1], Kristan Temme[1], Antonio Córcoles[1], Peng Liu[1], Richard Chen[1], Marco Pistoia[1] and Jay Gambetta[1] ([1]IBMQ)\n", + "\n", + "Your **TASK** is to execute every step of this notebook while learning to use qiskit-aqua and also understanding how this SVM implementation can be used for classifying breast cancer analysis." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Introduction\n", + "Classification algorithms and methods for machine learning are essential for pattern recognition and data mining applications. Well known techniques such as support vector machines and neural networks have blossomed over the last two decades as a result of the spectacular advances in classical hardware computational capabilities and speed. This progress in computer power made it possible to apply techniques, that were theoretically developed towards the middle of the 20th century, on classification problems that were becoming increasingly challenging.\n", + "\n", + "A key concept in classification methods is that of a kernel. Data cannot typically be separated by a hyperplane in its original space. A common technique used to find such a hyperplane consists on applying a non-linear transformation function to the data. This function is called a feature map, as it transforms the raw features, or measurable properties, of the phenomenon or subject under study. Classifying in this new feature space -and, as a matter of fact, also in any other space, including the raw original one- is nothing more than seeing how close data points are to each other. This is the same as computing the inner product for each pair of data in the set. So, in fact we do not need to compute the non-linear feature map for each datum, but only the inner product of each pair of data points in the new feature space. This collection of inner products is called the kernel and it is perfectly possible to have feature maps that are hard to compute but whose kernels are not.\n", + "\n", + "In this notebook we provide an example of a classification problem that requires a feature map for which computing the kernel is not efficient classically -this means that the required computational resources are expected to scale exponentially with the size of the problem. We show how this can be solved in a quantum processor by a direct estimation of the kernel in the feature space. The method we used falls in the category of what is called supervised learning, consisting of a training phase (where the kernel is calculated and the support vectors obtained) and a test or classification phase (where new unlabelled data is classified according to the solution found in the training phase).\n", + "\n", + "References and additional details:\n", + "\n", + "[1] Vojtech Havlicek, Antonio D. C´orcoles, Kristan Temme, Aram W. Harrow, Abhinav Kandala, Jerry M. Chow, and Jay M. Gambetta1, \"Supervised learning with quantum enhanced feature spaces,\" [arXiv: 1804.11326](https://arxiv.org/pdf/1804.11326.pdf)" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "from qsvm_datasets import *\n", + "from qiskit.aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name\n", + "from qiskit.aqua.input import get_input_instance\n", + "from qiskit.aqua import run_algorithm\n", + "\n", + "# setup aqua logging\n", + "import logging\n", + "from qiskit.aqua._logging import set_logging_config, build_logging_config\n", + "# set_logging_config(build_logging_config(logging.DEBUG)) # choose INFO, DEBUG to see the log" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### [Optional] Setup token to run the experiment on a real device\n", + "If you would like to run the experiement on a real device, you need to setup your account first.\n", + "\n", + "Note: If you do not store your token yet, use `IBMQ.save_accounts()` to store it first." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit import IBMQ\n", + "IBMQ.load_accounts()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First we prepare the dataset, which is used for training, testing and the finally prediction.\n", + "\n", + "*Note: You can easily switch to a different dataset, such as the Breast Cancer dataset, by replacing 'ad_hoc_data' to 'Breast_cancer' below.*" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'A': 0, 'B': 1}\n" + ] + } + ], + "source": [ + "feature_dim=2 # we support feature_dim 2 or 3\n", + "sample_Total, training_input, test_input, class_labels = ad_hoc_data(\n", + " training_size=20, test_size=10, n=feature_dim, gap=0.3, PLOT_DATA=True\n", + ")\n", + "\n", + "datapoints, class_to_label = split_dataset_to_data_and_labels(test_input)\n", + "print(class_to_label)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With the dataset ready we initialize the necessary inputs for the algorithm:\n", + "- the input dictionary (params) \n", + "- the input object containing the dataset info (algo_input)." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "params = {\n", + " 'problem': {'name': 'classification', 'random_seed': 10598},\n", + " 'algorithm': {\n", + " 'name': 'QSVM'\n", + " },\n", + " 'backend': {'name': 'qasm_simulator', 'shots': 1024},\n", + " 'feature_map': {'name': 'SecondOrderExpansion', 'depth': 2, 'entanglement': 'linear'}\n", + "}\n", + "\n", + "algo_input = get_input_instance('ClassificationInput')\n", + "algo_input.training_dataset = training_input\n", + "algo_input.test_dataset = test_input\n", + "algo_input.datapoints = datapoints[0] # 0 is data, 1 is labels" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With everything setup, we can now run the algorithm.\n", + "\n", + "For the testing, the result includes the details and the success ratio.\n", + "\n", + "For the prediction, the result includes the predicted labels. " + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "testing success ratio: 1.0\n", + "predicted classes: ['A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B']\n" + ] + } + ], + "source": [ + "result = run_algorithm(params, algo_input)\n", + "print(\"testing success ratio: \", result['testing_accuracy'])\n", + "print(\"predicted classes:\", result['predicted_classes'])" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "kernel matrix during the training:\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "print(\"kernel matrix during the training:\")\n", + "kernel_matrix = result['kernel_matrix_training']\n", + "img = plt.imshow(np.asmatrix(kernel_matrix),interpolation='nearest',origin='upper',cmap='bone_r')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The breast cancer dataset\n", + "Now we run our algorithm with the real-world dataset: the breast cancer dataset, we use the first two principal components as features." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'A': 0, 'B': 1} {0: 'A', 1: 'B'}\n" + ] + } + ], + "source": [ + "sample_Total, training_input, test_input, class_labels = Breast_cancer(\n", + " training_size=20, test_size=10, n=2, PLOT_DATA=True\n", + ")\n", + "# n =2 is the dimension of each data point\n", + "\n", + "datapoints, class_to_label = split_dataset_to_data_and_labels(test_input)\n", + "label_to_class = {label:class_name for class_name, label in class_to_label.items()}\n", + "print(class_to_label, label_to_class)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "testing success ratio: 0.95\n", + "ground truth: ['A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B']\n", + "predicted: ['A', 'B', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B']\n" + ] + } + ], + "source": [ + "algo_input = get_input_instance('ClassificationInput')\n", + "algo_input.training_dataset = training_input\n", + "algo_input.test_dataset = test_input\n", + "algo_input.datapoints = datapoints[0]\n", + "result = run_algorithm(params, algo_input)\n", + "print(\"testing success ratio: \", result['testing_accuracy'])\n", + "print(\"ground truth: {}\".format(map_label_to_class_name(datapoints[1], label_to_class)))\n", + "print(\"predicted: {}\".format(result['predicted_classes']))" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "kernel matrix during the training:\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "print(\"kernel matrix during the training:\")\n", + "kernel_matrix = result['kernel_matrix_training']\n", + "img = plt.imshow(np.asmatrix(kernel_matrix),interpolation='nearest',origin='upper',cmap='bone_r')\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.2" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_02.ipynb b/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_02.ipynb index 73058409b..3b9c29e80 100644 --- a/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_02.ipynb +++ b/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_02.ipynb @@ -116,7 +116,9 @@ ], "source": [ "feature_dim=2 # we support feature_dim 2 or 3\n", - "sample_Total, training_input, test_input, class_labels = ad_hoc_data(training_size=20, test_size=10, n=feature_dim, gap=0.3, PLOT_DATA=True)\n", + "sample_Total, training_input, test_input, class_labels = ad_hoc_data(\n", + " training_size=20, test_size=10, n=feature_dim, gap=0.3, PLOT_DATA=True\n", + ")\n", "\n", "datapoints, class_to_label = split_dataset_to_data_and_labels(test_input)\n", "print(class_to_label)" @@ -138,15 +140,15 @@ "outputs": [], "source": [ "params = {\n", - " 'problem': {'name': 'svm_classification', 'random_seed': 10598},\n", + " 'problem': {'name': 'classification', 'random_seed': 10598},\n", " 'algorithm': {\n", - " 'name': 'QSVM.Kernel'\n", + " 'name': 'QSVM'\n", " },\n", " 'backend': {'name': 'qasm_simulator', 'shots': 1024},\n", " 'feature_map': {'name': 'SecondOrderExpansion', 'depth': 2, 'entanglement': 'linear'}\n", "}\n", "\n", - "algo_input = get_input_instance('SVMInput')\n", + "algo_input = get_input_instance('ClassificationInput')\n", "algo_input.training_dataset = training_input\n", "algo_input.test_dataset = test_input\n", "algo_input.datapoints = datapoints[0] # 0 is data, 1 is labels" @@ -245,7 +247,9 @@ } ], "source": [ - "sample_Total, training_input, test_input, class_labels = Breast_cancer(training_size=20, test_size=10, n=2, PLOT_DATA=True)\n", + "sample_Total, training_input, test_input, class_labels = Breast_cancer(\n", + " training_size=20, test_size=10, n=2, PLOT_DATA=True\n", + ")\n", "# n =2 is the dimension of each data point\n", "\n", "datapoints, class_to_label = split_dataset_to_data_and_labels(test_input)\n", @@ -269,7 +273,7 @@ } ], "source": [ - "algo_input = get_input_instance('SVMInput')\n", + "algo_input = get_input_instance('ClassificationInput')\n", "algo_input.training_dataset = training_input\n", "algo_input.test_dataset = test_input\n", "algo_input.datapoints = datapoints[0]\n", @@ -326,7 +330,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.4" + "version": "3.7.2" } }, "nbformat": 4, diff --git a/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/latex/main.tex b/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/latex/main.tex index b5b20e31a..ada7f3810 100755 --- a/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/latex/main.tex +++ b/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/latex/main.tex @@ -15,14 +15,14 @@ \begin{document} \begin{frame} - \titlepage + \titlepage \end{frame} \begin{frame}{Table of contents} - \begin{card} - \tableofcontents - \end{card} + \begin{card} + \tableofcontents + \end{card} \end{frame} @@ -172,14 +172,14 @@ \section{\ai} \end{frame} \begin{frame}[fragile]{\ai (SVM)} -\small{Here's an example of a configuration for an SVM classification model:}\begin{minted}{python} +\small{Here's an example of a configuration for an classification model:}\begin{minted}{python} params = { 'problem': { - 'name': 'svm_classification', + 'name': 'classification', 'random_seed': 1219 # same seed ensures reproducibility }, 'algorithm': { - 'name': 'QSVM.Kernel' + 'name': 'QSVM' }, 'backend': { 'name': 'qasm_simulator', diff --git a/qiskit/aqua/artificial_intelligence/index.ipynb b/qiskit/aqua/artificial_intelligence/index.ipynb index b0c063914..5537442db 100644 --- a/qiskit/aqua/artificial_intelligence/index.ipynb +++ b/qiskit/aqua/artificial_intelligence/index.ipynb @@ -12,7 +12,7 @@ "\n", "## Contents\n", "\n", - "* [Quantum SVM for Classification](qsvm_kernel_classification.ipynb)\n", + "* [Quantum SVM for Classification](qsvm_classification.ipynb)\n", "* More examples can be found in [commuity/aqua/artificial_intelligence](../../../community/aqua/artificial_intelligence)" ] }, @@ -28,9 +28,9 @@ ], "metadata": { "kernelspec": { - "display_name": "quantum-dev", + "display_name": "Python 3", "language": "python", - "name": "quantum-dev" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -42,7 +42,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.5" + "version": "3.7.2" } }, "nbformat": 4, diff --git a/qiskit/aqua/artificial_intelligence/qsvm_classification.ipynb b/qiskit/aqua/artificial_intelligence/qsvm_classification.ipynb index 92b21d66a..7f6620745 100644 --- a/qiskit/aqua/artificial_intelligence/qsvm_classification.ipynb +++ b/qiskit/aqua/artificial_intelligence/qsvm_classification.ipynb @@ -190,7 +190,7 @@ " 'backend': {'provider': 'qiskit.BasicAer', 'name': 'qasm_simulator', 'shots': 1024},\n", " 'feature_map': {'name': 'SecondOrderExpansion', 'depth': 2, 'entanglement': 'linear'}\n", "}\n", - "algo_input = SVMInput(training_input, test_input, datapoints[0])\n", + "algo_input = ClassificationInput(training_input, test_input, datapoints[0])\n", "result = run_algorithm(params, algo_input)\n", "\"\"\"\n", "\n", @@ -292,7 +292,7 @@ "result = qsvm.run(quantum_instance)\n", "\n", "\"\"\"declarative approach, re-use the params above\n", - "algo_input = SVMInput(training_input, test_input)\n", + "algo_input = ClassificationInput(training_input, test_input)\n", "result = run_algorithm(params, algo_input)\n", "\"\"\"\n", "print(\"testing success ratio: \", result['testing_accuracy'])" From 3f4a76c48b3dbde678f412d7681f3391c267dfa4 Mon Sep 17 00:00:00 2001 From: woodsp Date: Sun, 28 Apr 2019 17:07:55 -0400 Subject: [PATCH 086/116] Update optimization notebooks --- community/aqua/optimization/clique.ipynb | 141 +++++++++++----- community/aqua/optimization/exact_cover.ipynb | 152 ++++++++++++------ .../aqua/optimization/graph_partition.ipynb | 133 +++++++++------ community/aqua/optimization/set_packing.ipynb | 148 +++++++++++------ .../aqua/optimization/vertex_cover.ipynb | 145 +++++++++++------ 5 files changed, 478 insertions(+), 241 deletions(-) diff --git a/community/aqua/optimization/clique.ipynb b/community/aqua/optimization/clique.ipynb index e43a53568..802bbeb8e 100644 --- a/community/aqua/optimization/clique.ipynb +++ b/community/aqua/optimization/clique.ipynb @@ -10,8 +10,10 @@ "\n", "The problem is defined as follows. A clique in a graph $G$ is a complete subgraph of $G$. That is, it is a subset $K$ of the vertices such that every two vertices in $K$ are the two endpoints of an edge in $G$. A maximal clique is a clique to which no more vertices can be added. A maximum clique is a clique that includes the largest possible number of vertices. \n", "\n", - "We will go through three examples to show (1) how to run the optimization in the non-programming way, (2) how to run the optimization in the programming way, (3) how to run the optimization with the VQE.\n", - "We will omit the details for the support of CPLEX, which are explained in other notebooks such as maxcut.\n", + "We will go through three examples to show:\n", + "1. How to run the optimization using the declarative approach\n", + "2. How to run the optimization using the programmatic approach\n", + "3. How how to run the optimization with the VQE.\n", "\n", "Note that the solution may not be unique." ] @@ -20,7 +22,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### The problem and a brute-force method." + "#### The problem and a brute-force method." ] }, { @@ -31,7 +33,7 @@ "source": [ "import numpy as np\n", "\n", - "from qiskit import Aer\n", + "from qiskit import BasicAer\n", "\n", "from qiskit.aqua import run_algorithm\n", "from qiskit.aqua.input import EnergyInput\n", @@ -87,7 +89,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "solution is [1, 0, 0, 1, 1]\n" + "Solution is [1, 0, 0, 1, 1]\n" ] } ], @@ -111,16 +113,22 @@ "\n", "has_sol, sol = brute_force()\n", "if has_sol:\n", - " print(\"solution is \", sol)\n", + " print(\"Solution is \", sol)\n", "else:\n", - " print(\"no solution found for K=\", K)" + " print(\"No solution found for K=\", K)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Part I: run the optimization in the non-programming way" + "#### Part I: Run the optimization using the declarative approach\n", + "\n", + "Here the steps are:\n", + "* Create the qubit operator i.e. Ising Hamiltonian, using clique ising translator\n", + "* Create an EnergyInput object and a dictionary describing the algorithm and the components for Aqua to solve the problem\n", + "* Run the algorithm and get the result\n", + "* Use the result with the clique object to determine a solution" ] }, { @@ -132,31 +140,35 @@ "name": "stdout", "output_type": "stream", "text": [ - "solution is [1. 0. 1. 1. 0.]\n" + "Solution is [1. 0. 1. 1. 0.]\n" ] } ], "source": [ "qubit_op, offset = clique.get_clique_qubitops(w, K)\n", + "\n", "algo_input = EnergyInput(qubit_op)\n", "params = {\n", " 'problem': {'name': 'ising'},\n", " 'algorithm': {'name': 'ExactEigensolver'}\n", "}\n", "result = run_algorithm(params, algo_input)\n", + "\n", "x = clique.sample_most_likely(len(w), result['eigvecs'][0])\n", "ising_sol = clique.get_graph_solution(x)\n", "if clique.satisfy_or_not(ising_sol, w, K):\n", - " print(\"solution is\", ising_sol)\n", + " print(\"Solution is\", ising_sol)\n", "else:\n", - " print(\"no solution found for K=\", K)" + " print(\"No solution found for K=\", K)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Part II: run the optimization in the programming way" + "#### Part II: Run the optimization using the programmatic approach\n", + "\n", + "The main difference here is running the Aqua algorithm. Here we directly construct the algorithm and then run() it to get the result. The post computation on the result is identical." ] }, { @@ -168,27 +180,33 @@ "name": "stdout", "output_type": "stream", "text": [ - "solution is [1. 0. 1. 1. 0.]\n" + "Solution is [1. 0. 1. 1. 0.]\n" ] } ], "source": [ + "# We will use the qubit_op and offset from above and not re-compute them here\n", "\n", - "algo = ExactEigensolver(algo_input.qubit_op, k=1, aux_operators=[])\n", + "algo = ExactEigensolver(qubit_op)\n", "result = algo.run()\n", + "\n", "x = clique.sample_most_likely(len(w), result['eigvecs'][0])\n", "ising_sol = clique.get_graph_solution(x)\n", "if clique.satisfy_or_not(ising_sol, w, K):\n", - " print(\"solution is\", ising_sol)\n", + " print(\"Solution is\", ising_sol)\n", "else:\n", - " print(\"no solution found for K=\", K) " + " print(\"No solution found for K=\", K) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Part III: run the optimization with the VQE" + "#### Part III: Run the optimization with the VQE\n", + "\n", + "##### Declarative\n", + "\n", + "We reuse the EnergyInput object we created above. VQE algorithm needs an optimizer and a variational form. Then also we need a quantum backend on which the algorithm will run." ] }, { @@ -200,49 +218,88 @@ "name": "stdout", "output_type": "stream", "text": [ - "solution is [1. 0. 1. 1. 0.]\n" + "Solution is [1. 0. 1. 1. 0.]\n" ] } ], "source": [ - "algorithm_cfg = {\n", - " 'name': 'VQE',\n", - " 'operator_mode': 'matrix'\n", - "}\n", - "\n", - "optimizer_cfg = {\n", - " 'name': 'COBYLA'\n", - "}\n", - "\n", - "var_form_cfg = {\n", - " 'name': 'RY',\n", - " 'depth': 5,\n", - " 'entanglement': 'linear'\n", - "}\n", - "\n", "params = {\n", " 'problem': {'name': 'ising', 'random_seed': 10598},\n", - " 'algorithm': algorithm_cfg,\n", - " 'optimizer': optimizer_cfg,\n", - " 'variational_form': var_form_cfg\n", + " 'algorithm': {'name': 'VQE'},\n", + " 'optimizer': {'name': 'COBYLA'},\n", + " 'variational_form': {'name': 'RY', 'depth': 5, 'entanglement': 'linear'}\n", "}\n", - "backend = Aer.get_backend('statevector_simulator')\n", + "backend = BasicAer.get_backend('statevector_simulator')\n", "result = run_algorithm(params, algo_input, backend=backend)\n", + "\n", "x = clique.sample_most_likely(len(w), result['eigvecs'][0])\n", "ising_sol = clique.get_graph_solution(x)\n", "\n", "if clique.satisfy_or_not(ising_sol, w, K):\n", - " print(\"solution is\", ising_sol)\n", + " print(\"Solution is\", ising_sol)\n", "else:\n", - " print(\"no solution found for K=\", K)" + " print(\"No solution found for K=\", K)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Programmatic\n", + "\n", + "We can create the objects directly ourselves too and run VQE for the result" ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Solution is [1. 0. 1. 1. 0.]\n" + ] + } + ], + "source": [ + "from qiskit.aqua import aqua_globals\n", + "from qiskit.aqua.algorithms import VQE\n", + "from qiskit.aqua.components.optimizers import COBYLA\n", + "from qiskit.aqua.components.variational_forms import RY\n", + "\n", + "aqua_globals.random_seed = 10598\n", + "\n", + "optimizer = COBYLA()\n", + "var_form = RY(qubit_op.num_qubits, depth=5, entanglement='linear')\n", + "vqe = VQE(qubit_op, var_form, optimizer)\n", + "\n", + "backend = BasicAer.get_backend('statevector_simulator')\n", + "result = vqe.run(backend)\n", + "\n", + "x = clique.sample_most_likely(len(w), result['eigvecs'][0])\n", + "ising_sol = clique.get_graph_solution(x)\n", + "\n", + "if clique.satisfy_or_not(ising_sol, w, K):\n", + " print(\"Solution is\", ising_sol)\n", + "else:\n", + " print(\"No solution found for K=\", K)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { "kernelspec": { - "display_name": "mykernel", + "display_name": "Python 3", "language": "python", - "name": "mykernel" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -254,7 +311,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/community/aqua/optimization/exact_cover.ipynb b/community/aqua/optimization/exact_cover.ipynb index aa8b5b169..23473db08 100644 --- a/community/aqua/optimization/exact_cover.ipynb +++ b/community/aqua/optimization/exact_cover.ipynb @@ -9,22 +9,19 @@ "In mathematics, given a collection $S$ of subsets of a set $X$.\n", "An exact cover is a subcollection $S_{ec} \\subseteq S$ such that each element in $X$ is contained in exactly one subset $\\in S_{ec}$. \n", "\n", - "We will go through three examples to show (1) how to run the optimization in the non-programming way, (2) how to run the optimization in the programming way, (3) how to run the optimization with the VQE.\n", - "We will omit the details for the support of CPLEX, which are explained in other notebooks such as maxcut." + "We will go through three examples to show:\n", + "1. How to run the optimization using the declarative approach\n", + "2. How to run the optimization using the programmatic approach\n", + "3. How how to run the optimization with the VQE." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### The problem and the brute-force method." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "first, let us take a look at the list of subsets." + "#### The problem and the brute-force method.\n", + "\n", + "First, let us take a look at the list of subsets." ] }, { @@ -43,7 +40,8 @@ "source": [ "import numpy as np\n", "import json\n", - "from qiskit import Aer\n", + "\n", + "from qiskit import BasicAer\n", "from qiskit.aqua import run_algorithm\n", "from qiskit.aqua.input import EnergyInput\n", "from qiskit.aqua.translators.ising import exactcover\n", @@ -52,9 +50,7 @@ "input_file = 'sample.exactcover'\n", "with open(input_file) as f:\n", " list_of_subsets = json.load(f)\n", - " print(list_of_subsets)\n", - " qubitOp, offset = exactcover.get_exactcover_qubitops(list_of_subsets)\n", - " algo_input = EnergyInput(qubitOp)" + " print(list_of_subsets)" ] }, { @@ -73,7 +69,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "solution is [0, 1, 1, 0]\n" + "Solution is [0, 1, 1, 0]\n" ] } ], @@ -98,16 +94,22 @@ "\n", "has_sol, cur = brute_force()\n", "if has_sol:\n", - " print(\"solution is\", cur)\n", + " print(\"Solution is\", cur)\n", "else:\n", - " print(\"no solution is found\")" + " print(\"No solution is found\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Part I: run the optimization in the non-programming way" + "#### Part I: Run the optimization using the declarative approach\n", + "\n", + "Here the steps are:\n", + "* Create the qubit operator i.e. Ising Hamiltonian, using exactcover ising translator\n", + "* Create an EnergyInput object and a dictionary describing the algorithm and the components for Aqua to solve the problem\n", + "* Run the algorithm and get the result\n", + "* Use the result with the exactcover object to determine a solution" ] }, { @@ -119,30 +121,36 @@ "name": "stdout", "output_type": "stream", "text": [ - "solution is [0. 1. 1. 0.]\n" + "Solution is [0. 1. 1. 0.]\n" ] } ], "source": [ + "qubit_op, offset = exactcover.get_exactcover_qubitops(list_of_subsets)\n", + "algo_input = EnergyInput(qubit_op)\n", + "\n", "params = {\n", " 'problem': {'name': 'ising'},\n", " 'algorithm': {'name': 'ExactEigensolver'}\n", "}\n", "result = run_algorithm(params, algo_input)\n", + "\n", "x = exactcover.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", "ising_sol = exactcover.get_solution(x)\n", "np.testing.assert_array_equal(ising_sol, [0, 1, 1, 0])\n", "if exactcover.check_solution_satisfiability(ising_sol, list_of_subsets):\n", - " print(\"solution is\", ising_sol)\n", + " print(\"Solution is\", ising_sol)\n", "else:\n", - " print(\"no solution is found\")" + " print(\"No solution is found\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Part II: run the optimization in the programming way" + "#### Part II: Run the optimization using the programmatic approach\n", + "\n", + "The main difference here is running the Aqua algorithm. Here we directly construct the algorithm and then run() it to get the result. The post computation on the result is identical." ] }, { @@ -154,28 +162,33 @@ "name": "stdout", "output_type": "stream", "text": [ - "solution is [0. 1. 1. 0.]\n" + "Solution is [0. 1. 1. 0.]\n" ] } ], "source": [ "algo = ExactEigensolver(algo_input.qubit_op, k=1, aux_operators=[])\n", "result = algo.run()\n", + "\n", "x = exactcover.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", "ising_sol = exactcover.get_solution(x)\n", "np.testing.assert_array_equal(ising_sol, [0, 1, 1, 0])\n", "\n", "if exactcover.check_solution_satisfiability(ising_sol, list_of_subsets):\n", - " print(\"solution is\", ising_sol)\n", + " print(\"Solution is\", ising_sol)\n", "else:\n", - " print(\"no solution is found\")" + " print(\"No solution is found\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Part III: run the optimization with VQE" + "#### Part III: Run the optimization with the VQE\n", + "\n", + "##### Declarative\n", + "\n", + "We reuse the EnergyInput object we created above. VQE algorithm needs an optimizer and a variational form. Then also we need a quantum backend on which the algorithm will run." ] }, { @@ -187,47 +200,86 @@ "name": "stdout", "output_type": "stream", "text": [ - "solution is [0. 1. 1. 0.]\n" + "Solution is [0. 1. 1. 0.]\n" ] } ], "source": [ - "algorithm_cfg = {\n", - " 'name': 'VQE',\n", - " 'operator_mode': 'matrix'\n", - "}\n", - "\n", - "optimizer_cfg = {\n", - " 'name': 'COBYLA'\n", - "}\n", - "\n", - "var_form_cfg = {\n", - " 'name': 'RYRZ',\n", - " 'depth': 5\n", - "}\n", - "\n", "params = {\n", " 'problem': {'name': 'ising', 'random_seed': 10598},\n", - " 'algorithm': algorithm_cfg,\n", - " 'optimizer': optimizer_cfg,\n", - " 'variational_form': var_form_cfg\n", + " 'algorithm': {'name': 'VQE'},\n", + " 'optimizer': {'name': 'COBYLA'},\n", + " 'variational_form': {'name': 'RYRZ', 'depth': 5}\n", "}\n", - "backend = Aer.get_backend('statevector_simulator')\n", + "backend = BasicAer.get_backend('statevector_simulator')\n", "result = run_algorithm(params, algo_input, backend=backend)\n", + "\n", "x = exactcover.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", "ising_sol = exactcover.get_solution(x)\n", "if exactcover.check_solution_satisfiability(ising_sol, list_of_subsets):\n", - " print(\"solution is\", ising_sol)\n", + " print(\"Solution is\", ising_sol)\n", "else:\n", - " print(\"no solution is found\")" + " print(\"No solution is found\")" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Programmatic\n", + "\n", + "We can create the objects directly ourselves too and run VQE for the result" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Solution is [0. 1. 1. 0.]\n" + ] + } + ], + "source": [ + "from qiskit.aqua import aqua_globals\n", + "from qiskit.aqua.algorithms import VQE\n", + "from qiskit.aqua.components.optimizers import COBYLA\n", + "from qiskit.aqua.components.variational_forms import RY\n", + "\n", + "aqua_globals.random_seed = 10598\n", + "\n", + "optimizer = COBYLA()\n", + "var_form = RY(qubit_op.num_qubits, depth=5, entanglement='linear')\n", + "vqe = VQE(qubit_op, var_form, optimizer)\n", + "\n", + "backend = BasicAer.get_backend('statevector_simulator')\n", + "result = vqe.run(backend)\n", + "\n", + "x = exactcover.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", + "ising_sol = exactcover.get_solution(x)\n", + "if exactcover.check_solution_satisfiability(ising_sol, list_of_subsets):\n", + " print(\"Solution is\", ising_sol)\n", + "else:\n", + " print(\"No solution is found\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { "kernelspec": { - "display_name": "mykernel", + "display_name": "Python 3", "language": "python", - "name": "mykernel" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -239,7 +291,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/community/aqua/optimization/graph_partition.ipynb b/community/aqua/optimization/graph_partition.ipynb index 9fe476ba5..81500f48b 100644 --- a/community/aqua/optimization/graph_partition.ipynb +++ b/community/aqua/optimization/graph_partition.ipynb @@ -11,8 +11,10 @@ "The objective of graph partition is to partition $G$ into two sets of the same size (let us assume we have even number of vertices), \n", "while minimizing the capacity of the edges across the two sets.\n", "\n", - "We will go through three examples to show (1) how to run the optimization in the non-programming way, (2) how to run the optimization in the programming way, (3) how to run the optimization with the VQE.\n", - "We will omit the details for the support of CPLEX, which are explained in other notebooks such as maxcut.\n", + "We will go through three examples to show:\n", + "1. How to run the optimization using the declarative approach\n", + "2. How to run the optimization using the programmatic approach\n", + "3. How how to run the optimization with the VQE.\n", "\n", "Note the objective_value below is defined as the the number of crossing edges. The goal is to minimize this value.\n" ] @@ -21,14 +23,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### The problem and the brute-force method" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "the graph involved in our example is as follows. The graph is in the adjacent matrix form." + "#### The problem and the brute-force method\n", + "\n", + "The graph involved in our example is as follows. The graph is in the adjacent matrix form." ] }, { @@ -49,7 +46,7 @@ ], "source": [ "import numpy as np\n", - "from qiskit import Aer\n", + "from qiskit import BasicAer\n", "from qiskit.aqua import run_algorithm\n", "from qiskit.aqua.input import EnergyInput\n", "from qiskit.aqua.translators.ising import graphpartition\n", @@ -65,7 +62,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "the brute-force method is as follows. Basically, we exhaustively try all the binary assignments. In each binary assignment, the entry of a vertex is either 0 (meaning the vertex is in the first partition) or 1 (meaning the vertex is in the second partition). We print the binary assignment that satisfies the definition of the graph partition and corresponds to the minimial number of crossing edges." + "The brute-force method is as follows. Basically, we exhaustively try all the binary assignments. In each binary assignment, the entry of a vertex is either 0 (meaning the vertex is in the first partition) or 1 (meaning the vertex is in the second partition). We print the binary assignment that satisfies the definition of the graph partition and corresponds to the minimial number of crossing edges." ] }, { @@ -77,7 +74,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "objective value computed by the brute-force method is 3\n" + "Objective value computed by the brute-force method is 3\n" ] } ], @@ -104,14 +101,14 @@ " return minimal_v\n", "\n", "sol = brute_force()\n", - "print(\"objective value computed by the brute-force method is\", sol)" + "print(\"Objective value computed by the brute-force method is\", sol)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Part I: run the optimization in the non-programming way" + "#### Part I: Run the optimization using the declarative approach" ] }, { @@ -123,7 +120,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "objective value computed by ExactEigensolver is 3.0\n" + "Objective value computed by ExactEigensolver is 3.0\n" ] } ], @@ -136,18 +133,19 @@ " 'algorithm': {'name': 'ExactEigensolver'}\n", "}\n", "result = run_algorithm(params, algo_input)\n", + "\n", "x = graphpartition.sample_most_likely(result['eigvecs'][0])\n", "# check against the oracle\n", "ising_sol = graphpartition.get_graph_solution(x)\n", "np.testing.assert_array_equal(ising_sol, [0, 1, 0, 1])\n", - "print(\"objective value computed by ExactEigensolver is\", graphpartition.objective_value(x, w))" + "print(\"Objective value computed by ExactEigensolver is\", graphpartition.objective_value(x, w))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Part II: run the optimization in the programming way" + "#### Part II: Run the optimization using the programmatic approach" ] }, { @@ -159,25 +157,30 @@ "name": "stdout", "output_type": "stream", "text": [ - "objective value computed by the ExactEigensolver is 3.0\n" + "Objective value computed by the ExactEigensolver is 3.0\n" ] } ], "source": [ "algo = ExactEigensolver(algo_input.qubit_op, k=1, aux_operators=[])\n", "result = algo.run()\n", + "\n", "x = graphpartition.sample_most_likely(result['eigvecs'][0])\n", "# check against the oracle\n", "ising_sol = graphpartition.get_graph_solution(x)\n", "np.testing.assert_array_equal(ising_sol, [0, 1, 0, 1])\n", - "print(\"objective value computed by the ExactEigensolver is\", graphpartition.objective_value(x, w))" + "print(\"Objective value computed by the ExactEigensolver is\", graphpartition.objective_value(x, w))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Part III: run the optimization with VQE" + "#### Part III: Run the optimization with the VQE\n", + "\n", + "##### Declarative\n", + "\n", + "We reuse the EnergyInput object we created above. VQE algorithm needs an optimizer and a variational form. Then also we need a quantum backend on which the algorithm will run." ] }, { @@ -189,48 +192,84 @@ "name": "stdout", "output_type": "stream", "text": [ - "objective value computed by VQE is 3.0\n" + "Objective value computed by VQE is 3.0\n" ] } ], "source": [ - "algorithm_cfg = {\n", - " 'name': 'VQE',\n", - " 'operator_mode': 'matrix'\n", - "}\n", - "\n", - "optimizer_cfg = {\n", - " 'name': 'SPSA',\n", - " 'max_trials': 300\n", - "}\n", - "\n", - "var_form_cfg = {\n", - " 'name': 'RY',\n", - " 'depth': 5,\n", - " 'entanglement': 'linear'\n", - "}\n", - "\n", "params = {\n", " 'problem': {'name': 'ising', 'random_seed': 10598},\n", - " 'algorithm': algorithm_cfg,\n", - " 'optimizer': optimizer_cfg,\n", - " 'variational_form': var_form_cfg\n", + " 'algorithm': {'name': 'VQE'},\n", + " 'optimizer': {'name': 'COBYLA'},\n", + " 'variational_form': {'name': 'RY', 'depth': 5, 'entanglement': 'linear'}\n", "}\n", - "backend = Aer.get_backend('statevector_simulator')\n", + "backend = BasicAer.get_backend('statevector_simulator')\n", "result = run_algorithm(params, algo_input, backend=backend)\n", + "\n", + "x = graphpartition.sample_most_likely(result['eigvecs'][0])\n", + "# check against the oracle\n", + "ising_sol = graphpartition.get_graph_solution(x)\n", + "np.testing.assert_array_equal(ising_sol, [1, 0, 1, 0])\n", + "print(\"Objective value computed by VQE is\", graphpartition.objective_value(x, w))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Programmatic\n", + "\n", + "We can create the objects directly ourselves too and run VQE for the result." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Objective value computed by VQE is 3.0\n" + ] + } + ], + "source": [ + "from qiskit.aqua import aqua_globals\n", + "from qiskit.aqua.algorithms import VQE\n", + "from qiskit.aqua.components.optimizers import COBYLA\n", + "from qiskit.aqua.components.variational_forms import RY\n", + "\n", + "aqua_globals.random_seed = 10598\n", + "\n", + "optimizer = COBYLA()\n", + "var_form = RY(qubit_op.num_qubits, depth=5, entanglement='linear')\n", + "vqe = VQE(qubit_op, var_form, optimizer)\n", + "\n", + "backend = BasicAer.get_backend('statevector_simulator')\n", + "result = vqe.run(backend)\n", + "\n", "x = graphpartition.sample_most_likely(result['eigvecs'][0])\n", "# check against the oracle\n", "ising_sol = graphpartition.get_graph_solution(x)\n", - "np.testing.assert_array_equal(ising_sol, [1, 0, 0, 1])\n", - "print(\"objective value computed by VQE is\", graphpartition.objective_value(x, w))" + "np.testing.assert_array_equal(ising_sol, [1, 0, 1, 0])\n", + "print(\"Objective value computed by VQE is\", graphpartition.objective_value(x, w))" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { "kernelspec": { - "display_name": "mykernel", + "display_name": "Python 3", "language": "python", - "name": "mykernel" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -242,7 +281,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.7" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/community/aqua/optimization/set_packing.ipynb b/community/aqua/optimization/set_packing.ipynb index b2d539e74..f73752c6b 100644 --- a/community/aqua/optimization/set_packing.ipynb +++ b/community/aqua/optimization/set_packing.ipynb @@ -8,23 +8,19 @@ "\n", "Given a collection $S$ of subsets of a set $X$, the set packing problem tries to find the subsets that are pairwise disjoint (in other words, no two of them share an element). The goal is to maximize the number of such subsets.\n", "\n", - "We will go through three examples to show (1) how to run the optimization in the non-programming way, (2) how to run the optimization in the programming way, (3) how to run the optimization with the VQE.\n", - "We will omit the details for the support of CPLEX, which are explained in other notebooks such as maxcut.\n", - "\n" + "We will go through three examples to show:\n", + "1. How to run the optimization using the declarative approach\n", + "2. How to run the optimization using the programmatic approach\n", + "3. How how to run the optimization with the VQE." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### The problem and the brute-force method." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "the problem is as follows. First, let us print the list of subsets." + "#### The problem and the brute-force method.\n", + "\n", + "The problem is as follows. First, let us print the list of subsets." ] }, { @@ -44,7 +40,7 @@ "import numpy as np\n", "import json\n", "\n", - "from qiskit import Aer\n", + "from qiskit import BasicAer\n", "\n", "from qiskit.aqua import run_algorithm\n", "from qiskit.aqua.input import EnergyInput\n", @@ -55,16 +51,14 @@ "input_file = 'sample.setpacking'\n", "with open(input_file) as f:\n", " list_of_subsets = json.load(f)\n", - " print(list_of_subsets)\n", - " qubitOp, offset = setpacking.get_setpacking_qubitops(list_of_subsets)\n", - " algo_input = EnergyInput(qubitOp)" + " print(list_of_subsets)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "the brute-force method is as follows. Basically, we exhaustively try all the binary assignments. In each binary assignment, the entry of a subset is either 0 (meaning the subset is not taken) or 1 (meaning the subset is taken). We print the binary assignment that satisfies the definition of the set packing. " + "The brute-force method is as follows. Basically, we exhaustively try all the binary assignments. In each binary assignment, the entry of a subset is either 0 (meaning the subset is not taken) or 1 (meaning the subset is taken). We print the binary assignment that satisfies the definition of the set packing. " ] }, { @@ -76,7 +70,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "size of set packing 2\n" + "Size of set packing 2\n" ] } ], @@ -99,14 +93,20 @@ " return max_v\n", "\n", "size = brute_force()\n", - "print(\"size of set packing\", size)" + "print(\"Size of set packing\", size)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Part I: run the optimization in the non-programming way" + "#### Part I: Run the optimization using the declarative approach\n", + "\n", + "Here the steps are:\n", + "* Create the qubit operator i.e. Ising Hamiltonian, using setpacking ising translator\n", + "* Create an EnergyInput object and a dictionary describing the algorithm and the components for Aqua to solve the problem\n", + "* Run the algorithm and get the result\n", + "* Use the result with the setpacking object to determine a solution" ] }, { @@ -118,27 +118,33 @@ "name": "stdout", "output_type": "stream", "text": [ - "size of set packing 2\n" + "Size of set packing 2\n" ] } ], "source": [ + "qubit_op, offset = setpacking.get_setpacking_qubitops(list_of_subsets)\n", + "\n", + "algo_input = EnergyInput(qubit_op)\n", "params = {\n", " 'problem': {'name': 'ising'},\n", " 'algorithm': {'name': 'ExactEigensolver'}\n", "}\n", "result = run_algorithm(params, algo_input)\n", + "\n", "x = setpacking.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", "ising_sol = setpacking.get_solution(x)\n", "np.testing.assert_array_equal(ising_sol, [0, 1, 1])\n", - "print(\"size of set packing\", np.count_nonzero(ising_sol))" + "print(\"Size of set packing\", np.count_nonzero(ising_sol))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Part II: run the optimization in the programming way" + "#### Part II: Run the optimization using the programmatic approach\n", + "\n", + "The main difference here is running the Aqua algorithm. Here we directly construct the algorithm and then run() it to get the result. The post computation on the result is identical." ] }, { @@ -150,25 +156,30 @@ "name": "stdout", "output_type": "stream", "text": [ - "size of set packing 2\n" + "Size of set packing 2\n" ] } ], "source": [ - "algo = ExactEigensolver(algo_input.qubit_op, k=1, aux_operators=[])\n", + "algo = ExactEigensolver(qubit_op)\n", "result = algo.run()\n", + "\n", "x = setpacking.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", "ising_sol = setpacking.get_solution(x)\n", "np.testing.assert_array_equal(ising_sol, [0, 1, 1])\n", "oracle = brute_force()\n", - "print(\"size of set packing\", np.count_nonzero(ising_sol))" + "print(\"Size of set packing\", np.count_nonzero(ising_sol))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Part III: run the optimization with VQE" + "#### Part III: Run the optimization with the VQE\n", + "\n", + "##### Declarative\n", + "\n", + "We reuse the EnergyInput object we created above. VQE algorithm needs an optimizer and a variational form. Then also we need a quantum backend on which the algorithm will run." ] }, { @@ -180,47 +191,80 @@ "name": "stdout", "output_type": "stream", "text": [ - "size of set packing 2\n" + "Size of set packing 2\n" ] } ], "source": [ - "algorithm_cfg = {\n", - " 'name': 'VQE',\n", - " 'operator_mode': 'paulis'\n", - "\n", - "}\n", - "\n", - "optimizer_cfg = {\n", - " 'name': 'SPSA',\n", - " 'max_trials': 200\n", - "}\n", - "\n", - "var_form_cfg = {\n", - " 'name': 'RY',\n", - " 'depth': 5,\n", - " 'entanglement': 'linear'\n", - "}\n", - "\n", "params = {\n", " 'problem': {'name': 'ising', 'random_seed': 100},\n", - " 'algorithm': algorithm_cfg,\n", - " 'optimizer': optimizer_cfg,\n", - " 'variational_form': var_form_cfg\n", + " 'algorithm': {'name': 'VQE'},\n", + " 'optimizer': {'name': 'COBYLA'},\n", + " 'variational_form': {'name': 'RY', 'depth': 5, 'entanglement': 'linear'}\n", "}\n", - "backend = Aer.get_backend('qasm_simulator')\n", + "backend = BasicAer.get_backend('statevector_simulator')\n", "result = run_algorithm(params, algo_input, backend=backend)\n", + "\n", "x = setpacking.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", "ising_sol = setpacking.get_solution(x)\n", - "print(\"size of set packing\", np.count_nonzero(ising_sol))" + "print(\"Size of set packing\", np.count_nonzero(ising_sol))" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Programmatic\n", + "\n", + "We can create the objects directly ourselves too and run VQE for the result" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Size of set packing 2\n" + ] + } + ], + "source": [ + "from qiskit.aqua import aqua_globals\n", + "from qiskit.aqua.algorithms import VQE\n", + "from qiskit.aqua.components.optimizers import COBYLA\n", + "from qiskit.aqua.components.variational_forms import RY\n", + "\n", + "aqua_globals.random_seed = 100\n", + "\n", + "optimizer = COBYLA()\n", + "var_form = RY(qubit_op.num_qubits, depth=5, entanglement='linear')\n", + "vqe = VQE(qubit_op, var_form, optimizer)\n", + "\n", + "backend = BasicAer.get_backend('statevector_simulator')\n", + "result = vqe.run(backend)\n", + "\n", + "x = setpacking.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", + "ising_sol = setpacking.get_solution(x)\n", + "print(\"Size of set packing\", np.count_nonzero(ising_sol))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { "kernelspec": { - "display_name": "mykernel", + "display_name": "Python 3", "language": "python", - "name": "mykernel" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -232,7 +276,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.7" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/community/aqua/optimization/vertex_cover.ipynb b/community/aqua/optimization/vertex_cover.ipynb index 31e0869cd..951af3f08 100644 --- a/community/aqua/optimization/vertex_cover.ipynb +++ b/community/aqua/optimization/vertex_cover.ipynb @@ -8,23 +8,19 @@ "\n", "A vertex cover of a graph is a set of vertices such that each edge of the graph is incident to at least one vertex of the set. The goal of NPC problem is to minimize the size of the vertex cover. \n", "\n", - "\n", - "We will go through three examples to show (1) how to run the optimization in the non-programming way, (2) how to run the optimization in the programming way, (3) how to run the optimization with the VQE.\n", - "We will omit the details for the support of CPLEX, which are explained in other notebooks such as maxcut.\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### The problem and the brute-force method" + "We will go through three examples to show:\n", + "1. How to run the optimization using the declarative approach\n", + "2. How to run the optimization using the programmatic approach\n", + "3. How how to run the optimization with the VQE." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "the problem is as follows. the graph is in the adjacent matrix form." + "#### The problem and the brute-force method\n", + "\n", + "The problem is as follows. the graph is in the adjacent matrix form." ] }, { @@ -44,7 +40,7 @@ ], "source": [ "import numpy as np\n", - "from qiskit import Aer\n", + "from qiskit import BasicAer\n", "from qiskit.aqua import run_algorithm\n", "from qiskit.aqua.input import EnergyInput\n", "from qiskit.aqua.translators.ising import vertexcover\n", @@ -53,16 +49,14 @@ "np.random.seed(100)\n", "num_nodes = 3\n", "w = vertexcover.random_graph(num_nodes, edge_prob=0.8, weight_range=10)\n", - "print(w)\n", - "qubit_op, offset = vertexcover.get_vertexcover_qubitops(w)\n", - "algo_input = EnergyInput(qubit_op)" + "print(w)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "the brute-force method is as follows. Basically, we exhaustively try all the binary assignments. In each binary assignment, the entry of a vertex is either 0 (meaning the vertex is not in the cover) or 1 (meaning the vertex is in the cover). We print the binary assignment that satisfies the definition of the vertex cover and corresponds to the minimial size. " + "The brute-force method is as follows. Basically, we exhaustively try all the binary assignments. In each binary assignment, the entry of a vertex is either 0 (meaning the vertex is not in the cover) or 1 (meaning the vertex is in the cover). We print the binary assignment that satisfies the definition of the vertex cover and corresponds to the minimial size. " ] }, { @@ -74,7 +68,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "size of the vertex cover 2\n" + "Size of the vertex cover 2\n" ] } ], @@ -100,14 +94,20 @@ " return minimal_v\n", "\n", "size = brute_force()\n", - "print('size of the vertex cover', size)" + "print('Size of the vertex cover', size)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Part I: run the optimization in the non-programming way" + "#### Part I: Run the optimization using the declarative approach\n", + "\n", + "Here the steps are:\n", + "* Create the qubit operator i.e. Ising Hamiltonian, using vertexcover ising translator\n", + "* Create an EnergyInput object and a dictionary describing the algorithm and the components for Aqua to solve the problem\n", + "* Run the algorithm and get the result\n", + "* Use the result with the vertexcover object to determine a solution" ] }, { @@ -119,11 +119,14 @@ "name": "stdout", "output_type": "stream", "text": [ - "size of the vertex cover 2\n" + "Size of the vertex cover 2\n" ] } ], "source": [ + "qubit_op, offset = vertexcover.get_vertexcover_qubitops(w)\n", + "\n", + "algo_input = EnergyInput(qubit_op)\n", "params = {\n", " 'problem': {'name': 'ising'},\n", " 'algorithm': {'name': 'ExactEigensolver'}\n", @@ -133,14 +136,16 @@ "x = vertexcover.sample_most_likely(len(w), result['eigvecs'][0])\n", "sol = vertexcover.get_graph_solution(x)\n", "np.testing.assert_array_equal(sol, [0, 1, 1])\n", - "print('size of the vertex cover', np.count_nonzero(sol))" + "print('Size of the vertex cover', np.count_nonzero(sol))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Part II: run the optimization in the programming way" + "#### Part II: Run the optimization using the programmatic approach\n", + "\n", + "The main difference here is running the Aqua algorithm. Here we directly construct the algorithm and then run() it to get the result. The post computation on the result is identical." ] }, { @@ -152,24 +157,29 @@ "name": "stdout", "output_type": "stream", "text": [ - "size of the vertex cover 2\n" + "Size of the vertex cover 2\n" ] } ], "source": [ - "algo = ExactEigensolver(algo_input.qubit_op, k=1, aux_operators=[])\n", + "algo = ExactEigensolver(qubit_op)\n", "result = algo.run()\n", + "\n", "x = vertexcover.sample_most_likely(len(w), result['eigvecs'][0])\n", "sol = vertexcover.get_graph_solution(x)\n", "np.testing.assert_array_equal(sol, [0, 1, 1])\n", - "print('size of the vertex cover', np.count_nonzero(sol))" + "print('Size of the vertex cover', np.count_nonzero(sol))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Part III: run the optimization with VQE" + "#### Part III: Run the optimization with the VQE\n", + "\n", + "##### Declarative\n", + "\n", + "We reuse the EnergyInput object we created above. VQE algorithm needs an optimizer and a variational form. Then also we need a quantum backend on which the algorithm will run." ] }, { @@ -181,45 +191,80 @@ "name": "stdout", "output_type": "stream", "text": [ - "size of the vertex cover 2\n" + "Size of the vertex cover 2\n" ] } ], "source": [ - "algorithm_cfg = {\n", - " 'name': 'VQE',\n", - " 'operator_mode': 'paulis'\n", - "}\n", - "\n", - "optimizer_cfg = {\n", - " 'name': 'SPSA',\n", - " 'max_trials': 200\n", - "}\n", - "\n", - "var_form_cfg = {\n", - " 'name': 'RYRZ',\n", - " 'depth': 3,\n", - "}\n", - "\n", "params = {\n", " 'problem': {'name': 'ising', 'random_seed': 100},\n", - " 'algorithm': algorithm_cfg,\n", - " 'optimizer': optimizer_cfg,\n", - " 'variational_form': var_form_cfg\n", + " 'algorithm': {'name': 'VQE', 'operator_mode': 'paulis'},\n", + " 'optimizer': {'name': 'SPSA', 'max_trials': 200},\n", + " 'variational_form': {'name': 'RYRZ', 'depth': 3}\n", "}\n", - "backend = Aer.get_backend('qasm_simulator')\n", + "backend = BasicAer.get_backend('qasm_simulator')\n", "result = run_algorithm(params, algo_input, backend=backend)\n", + "\n", + "x = vertexcover.sample_most_likely(len(w), result['eigvecs'][0])\n", + "sol = vertexcover.get_graph_solution(x)\n", + "print('Size of the vertex cover', np.count_nonzero(sol))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Programmatic\n", + "\n", + "We can create the objects directly ourselves too and run VQE for the result" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Size of the vertex cover 2\n" + ] + } + ], + "source": [ + "from qiskit.aqua import aqua_globals\n", + "from qiskit.aqua.algorithms import VQE\n", + "from qiskit.aqua.components.optimizers import SPSA\n", + "from qiskit.aqua.components.variational_forms import RYRZ\n", + "\n", + "aqua_globals.random_seed = 100\n", + "\n", + "optimizer = SPSA(max_trials=200)\n", + "var_form = RYRZ(qubit_op.num_qubits, depth=3)\n", + "vqe = VQE(qubit_op, var_form, optimizer, operator_mode='paulis')\n", + "\n", + "backend = BasicAer.get_backend('qasm_simulator')\n", + "result = vqe.run(backend)\n", + "\n", "x = vertexcover.sample_most_likely(len(w), result['eigvecs'][0])\n", "sol = vertexcover.get_graph_solution(x)\n", - "print('size of the vertex cover', np.count_nonzero(sol))" + "print('Size of the vertex cover', np.count_nonzero(sol))" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { "kernelspec": { - "display_name": "mykernel", + "display_name": "Python 3", "language": "python", - "name": "mykernel" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -231,7 +276,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.7" + "version": "3.6.1" } }, "nbformat": 4, From bbfc55ff334e2af0c108cd5212786d4c7bce2539 Mon Sep 17 00:00:00 2001 From: stefan-woerner Date: Mon, 29 Apr 2019 10:29:43 +0200 Subject: [PATCH 087/116] adjust tutorials index --- index.ipynb | 9 +++++++-- qiskit/finance/{qiskit_finance.ipynb => index.ipynb} | 0 2 files changed, 7 insertions(+), 2 deletions(-) rename qiskit/finance/{qiskit_finance.ipynb => index.ipynb} (100%) diff --git a/index.ipynb b/index.ipynb index d03034999..3a9fc0911 100644 --- a/index.ipynb +++ b/index.ipynb @@ -79,7 +79,12 @@ " * [Chemistry](qiskit/aqua/chemistry/index.ipynb) - using variational quantum eigensolver to experiment with molecular ground-state energy on a quantum computer\n", " * [Optimization](qiskit/aqua/optimization/index.ipynb) - using variational quantum eigensolver to experiment with optimization problems (maxcut and traveling salesman problem) on a quantum computer \n", " * [Artificial Intelligence](qiskit/aqua/artificial_intelligence/index.ipynb) - using quantum-enhanced support vector machine to experiment with classification problems on a quantum computer\n", - " * [Finance](qiskit/aqua/finance/index.ipynb) - using variational quantum eigensolver to optimize portfolio on a quantum computer \n", + "\n", + "#### 1.7 Qiskit Finance\n", + "\n", + "[Qiskit Finance]() provides a colleaction of applications of quantum algorithms to use cases relevant in finance.\n", + "This includes use cases like portfolio management, derivative pricing, or credit risk analysis.\n", + "\n", "\n", "### 2. Community Notebooks\n", "\n", @@ -245,7 +250,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.0" + "version": "3.7.3" } }, "nbformat": 4, diff --git a/qiskit/finance/qiskit_finance.ipynb b/qiskit/finance/index.ipynb similarity index 100% rename from qiskit/finance/qiskit_finance.ipynb rename to qiskit/finance/index.ipynb From 3e8c4940b86c21e4f7a40d0e12496da22b98d1e3 Mon Sep 17 00:00:00 2001 From: Shaohan Hu Date: Mon, 29 Apr 2019 11:20:03 -0400 Subject: [PATCH 088/116] along with https://github.com/Qiskit/qiskit-aqua/pull/496 --- community/aqua/general/vqe2iqpe.ipynb | 20 +- community/aqua/index.ipynb | 2 +- community/aqua/optimization/exact_cover.ipynb | 36 +- .../aqua/optimization/graph_partition.ipynb | 41 +- .../{maxcut.ipynb => max_cut.ipynb} | 54 +- community/aqua/optimization/set_packing.ipynb | 35 +- .../{stableset.ipynb => stable_set.ipynb} | 30 +- .../aqua/optimization/vertex_cover.ipynb | 39 +- .../.ipynb_checkpoints/w8_03-checkpoint.ipynb | 504 ++++++++ .../.ipynb_checkpoints/w8_04-checkpoint.ipynb | 478 ++++++++ .../exercises/w8_03.ipynb | 111 +- .../exercises/w8_04.ipynb | 14 +- .../08_Sampling a Thermal State.ipynb | 27 +- ...timization and Unsupervised Learning.ipynb | 22 +- index.ipynb | 4 +- qiskit/aqua/optimization/docplex.ipynb | 8 +- qiskit/aqua/optimization/index.ipynb | 8 +- .../aqua/optimization/max_cut_and_tsp.ipynb | 1060 +++++++++++++++++ qiskit/aqua/optimization/maxcut_and_tsp.ipynb | 1022 ---------------- 19 files changed, 2260 insertions(+), 1255 deletions(-) rename community/aqua/optimization/{maxcut.ipynb => max_cut.ipynb} (81%) rename community/aqua/optimization/{stableset.ipynb => stable_set.ipynb} (90%) create mode 100644 community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/.ipynb_checkpoints/w8_03-checkpoint.ipynb create mode 100644 community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/.ipynb_checkpoints/w8_04-checkpoint.ipynb create mode 100644 qiskit/aqua/optimization/max_cut_and_tsp.ipynb delete mode 100644 qiskit/aqua/optimization/maxcut_and_tsp.ipynb diff --git a/community/aqua/general/vqe2iqpe.ipynb b/community/aqua/general/vqe2iqpe.ipynb index 9367a2235..3949bb4b0 100644 --- a/community/aqua/general/vqe2iqpe.ipynb +++ b/community/aqua/general/vqe2iqpe.ipynb @@ -26,7 +26,7 @@ "from qiskit.aqua.algorithms import IQPE\n", "from qiskit.aqua.components.variational_forms import RYRZ\n", "from qiskit.aqua.components.optimizers import SPSA\n", - "from qiskit.aqua.components.initial_states.varformbased import VarFormBased" + "from qiskit.aqua.components.initial_states.var_form_based import VarFormBased" ] }, { @@ -70,7 +70,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "The reference ground energy level is -1.8572750302023793.\n" + "The reference ground energy level is -1.857275030202379.\n" ] } ], @@ -137,7 +137,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ @@ -153,9 +153,17 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Continuing with VQE's result, IQPE estimated the ground energy to be -1.8531516030612387.\n" + ] + } + ], "source": [ "num_time_slices = 50\n", "num_iterations = 11\n", @@ -193,7 +201,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.8" + "version": "3.7.2" } }, "nbformat": 4, diff --git a/community/aqua/index.ipynb b/community/aqua/index.ipynb index 415db6024..6e9a52e53 100644 --- a/community/aqua/index.ipynb +++ b/community/aqua/index.ipynb @@ -72,7 +72,7 @@ "\n", "* [Using Grover Search for 3SAT problems](optimization/grover.ipynb)\n", "* [Using Aqua for partition problems](optimization/partition.ipynb)\n", - "* [Using Aqua for stableset problems](optimization/stableset.ipynb)\n", + "* [Using Aqua for stable-set problems](optimization/stable_set.ipynb)\n", "\n", "The repository here may be viewed for the\n", "[full listing](https://github.com/Qiskit/qiskit-tutorial/tree/master/community/aqua/optimization).\n", diff --git a/community/aqua/optimization/exact_cover.ipynb b/community/aqua/optimization/exact_cover.ipynb index 23473db08..172b6110a 100644 --- a/community/aqua/optimization/exact_cover.ipynb +++ b/community/aqua/optimization/exact_cover.ipynb @@ -44,7 +44,7 @@ "from qiskit import BasicAer\n", "from qiskit.aqua import run_algorithm\n", "from qiskit.aqua.input import EnergyInput\n", - "from qiskit.aqua.translators.ising import exactcover\n", + "from qiskit.aqua.translators.ising import exact_cover\n", "from qiskit.aqua.algorithms import ExactEigensolver\n", "\n", "input_file = 'sample.exactcover'\n", @@ -86,7 +86,7 @@ " max = 2**L\n", " for i in range(max):\n", " cur = bitfield(i, L)\n", - " cur_v = exactcover.check_solution_satisfiability(cur, list_of_subsets)\n", + " cur_v = exact_cover.check_solution_satisfiability(cur, list_of_subsets)\n", " if cur_v:\n", " has_sol = True\n", " break\n", @@ -106,10 +106,10 @@ "#### Part I: Run the optimization using the declarative approach\n", "\n", "Here the steps are:\n", - "* Create the qubit operator i.e. Ising Hamiltonian, using exactcover ising translator\n", + "* Create the qubit operator i.e. Ising Hamiltonian, using `exact_cover` ising translator\n", "* Create an EnergyInput object and a dictionary describing the algorithm and the components for Aqua to solve the problem\n", "* Run the algorithm and get the result\n", - "* Use the result with the exactcover object to determine a solution" + "* Use the result with the `exact_cover` object to determine a solution" ] }, { @@ -126,7 +126,7 @@ } ], "source": [ - "qubit_op, offset = exactcover.get_exactcover_qubitops(list_of_subsets)\n", + "qubit_op, offset = exact_cover.get_exact_cover_qubitops(list_of_subsets)\n", "algo_input = EnergyInput(qubit_op)\n", "\n", "params = {\n", @@ -135,10 +135,10 @@ "}\n", "result = run_algorithm(params, algo_input)\n", "\n", - "x = exactcover.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", - "ising_sol = exactcover.get_solution(x)\n", + "x = exact_cover.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", + "ising_sol = exact_cover.get_solution(x)\n", "np.testing.assert_array_equal(ising_sol, [0, 1, 1, 0])\n", - "if exactcover.check_solution_satisfiability(ising_sol, list_of_subsets):\n", + "if exact_cover.check_solution_satisfiability(ising_sol, list_of_subsets):\n", " print(\"Solution is\", ising_sol)\n", "else:\n", " print(\"No solution is found\")" @@ -170,11 +170,11 @@ "algo = ExactEigensolver(algo_input.qubit_op, k=1, aux_operators=[])\n", "result = algo.run()\n", "\n", - "x = exactcover.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", - "ising_sol = exactcover.get_solution(x)\n", + "x = exact_cover.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", + "ising_sol = exact_cover.get_solution(x)\n", "np.testing.assert_array_equal(ising_sol, [0, 1, 1, 0])\n", "\n", - "if exactcover.check_solution_satisfiability(ising_sol, list_of_subsets):\n", + "if exact_cover.check_solution_satisfiability(ising_sol, list_of_subsets):\n", " print(\"Solution is\", ising_sol)\n", "else:\n", " print(\"No solution is found\")" @@ -214,9 +214,9 @@ "backend = BasicAer.get_backend('statevector_simulator')\n", "result = run_algorithm(params, algo_input, backend=backend)\n", "\n", - "x = exactcover.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", - "ising_sol = exactcover.get_solution(x)\n", - "if exactcover.check_solution_satisfiability(ising_sol, list_of_subsets):\n", + "x = exact_cover.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", + "ising_sol = exact_cover.get_solution(x)\n", + "if exact_cover.check_solution_satisfiability(ising_sol, list_of_subsets):\n", " print(\"Solution is\", ising_sol)\n", "else:\n", " print(\"No solution is found\")" @@ -259,9 +259,9 @@ "backend = BasicAer.get_backend('statevector_simulator')\n", "result = vqe.run(backend)\n", "\n", - "x = exactcover.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", - "ising_sol = exactcover.get_solution(x)\n", - "if exactcover.check_solution_satisfiability(ising_sol, list_of_subsets):\n", + "x = exact_cover.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", + "ising_sol = exact_cover.get_solution(x)\n", + "if exact_cover.check_solution_satisfiability(ising_sol, list_of_subsets):\n", " print(\"Solution is\", ising_sol)\n", "else:\n", " print(\"No solution is found\")" @@ -291,7 +291,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.1" + "version": "3.7.2" } }, "nbformat": 4, diff --git a/community/aqua/optimization/graph_partition.ipynb b/community/aqua/optimization/graph_partition.ipynb index 81500f48b..e64c44514 100644 --- a/community/aqua/optimization/graph_partition.ipynb +++ b/community/aqua/optimization/graph_partition.ipynb @@ -49,12 +49,12 @@ "from qiskit import BasicAer\n", "from qiskit.aqua import run_algorithm\n", "from qiskit.aqua.input import EnergyInput\n", - "from qiskit.aqua.translators.ising import graphpartition\n", + "from qiskit.aqua.translators.ising import graph_partition\n", "from qiskit.aqua.algorithms import ExactEigensolver\n", "\n", "np.random.seed(100)\n", "num_nodes = 4\n", - "w = graphpartition.random_graph(num_nodes, edge_prob=0.8, weight_range=10)\n", + "w = graph_partition.random_graph(num_nodes, edge_prob=0.8, weight_range=10)\n", "print(w)" ] }, @@ -95,7 +95,7 @@ " if how_many_nonzero * 2 != L: # not balanced\n", " continue\n", "\n", - " cur_v = graphpartition.objective_value(np.array(cur), w)\n", + " cur_v = graph_partition.objective_value(np.array(cur), w)\n", " if cur_v < minimal_v:\n", " minimal_v = cur_v\n", " return minimal_v\n", @@ -125,7 +125,7 @@ } ], "source": [ - "qubit_op, offset = graphpartition.get_graphpartition_qubitops(w)\n", + "qubit_op, offset = graph_partition.get_graph_partition_qubitops(w)\n", "algo_input = EnergyInput(qubit_op)\n", "\n", "params = {\n", @@ -134,11 +134,11 @@ "}\n", "result = run_algorithm(params, algo_input)\n", "\n", - "x = graphpartition.sample_most_likely(result['eigvecs'][0])\n", + "x = graph_partition.sample_most_likely(result['eigvecs'][0])\n", "# check against the oracle\n", - "ising_sol = graphpartition.get_graph_solution(x)\n", + "ising_sol = graph_partition.get_graph_solution(x)\n", "np.testing.assert_array_equal(ising_sol, [0, 1, 0, 1])\n", - "print(\"Objective value computed by ExactEigensolver is\", graphpartition.objective_value(x, w))" + "print(\"Objective value computed by ExactEigensolver is\", graph_partition.objective_value(x, w))" ] }, { @@ -165,11 +165,11 @@ "algo = ExactEigensolver(algo_input.qubit_op, k=1, aux_operators=[])\n", "result = algo.run()\n", "\n", - "x = graphpartition.sample_most_likely(result['eigvecs'][0])\n", + "x = graph_partition.sample_most_likely(result['eigvecs'][0])\n", "# check against the oracle\n", - "ising_sol = graphpartition.get_graph_solution(x)\n", + "ising_sol = graph_partition.get_graph_solution(x)\n", "np.testing.assert_array_equal(ising_sol, [0, 1, 0, 1])\n", - "print(\"Objective value computed by the ExactEigensolver is\", graphpartition.objective_value(x, w))" + "print(\"Objective value computed by the ExactEigensolver is\", graph_partition.objective_value(x, w))" ] }, { @@ -206,11 +206,11 @@ "backend = BasicAer.get_backend('statevector_simulator')\n", "result = run_algorithm(params, algo_input, backend=backend)\n", "\n", - "x = graphpartition.sample_most_likely(result['eigvecs'][0])\n", + "x = graph_partition.sample_most_likely(result['eigvecs'][0])\n", "# check against the oracle\n", - "ising_sol = graphpartition.get_graph_solution(x)\n", + "ising_sol = graph_partition.get_graph_solution(x)\n", "np.testing.assert_array_equal(ising_sol, [1, 0, 1, 0])\n", - "print(\"Objective value computed by VQE is\", graphpartition.objective_value(x, w))" + "print(\"Objective value computed by VQE is\", graph_partition.objective_value(x, w))" ] }, { @@ -250,19 +250,12 @@ "backend = BasicAer.get_backend('statevector_simulator')\n", "result = vqe.run(backend)\n", "\n", - "x = graphpartition.sample_most_likely(result['eigvecs'][0])\n", + "x = graph_partition.sample_most_likely(result['eigvecs'][0])\n", "# check against the oracle\n", - "ising_sol = graphpartition.get_graph_solution(x)\n", + "ising_sol = graph_partition.get_graph_solution(x)\n", "np.testing.assert_array_equal(ising_sol, [1, 0, 1, 0])\n", - "print(\"Objective value computed by VQE is\", graphpartition.objective_value(x, w))" + "print(\"Objective value computed by VQE is\", graph_partition.objective_value(x, w))" ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { @@ -281,7 +274,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.1" + "version": "3.7.2" } }, "nbformat": 4, diff --git a/community/aqua/optimization/maxcut.ipynb b/community/aqua/optimization/max_cut.ipynb similarity index 81% rename from community/aqua/optimization/maxcut.ipynb rename to community/aqua/optimization/max_cut.ipynb index daa003ba2..fcc88a02c 100644 --- a/community/aqua/optimization/maxcut.ipynb +++ b/community/aqua/optimization/max_cut.ipynb @@ -6,7 +6,7 @@ "collapsed": true }, "source": [ - "## _*Using Qiskit Aqua for maxcut problems*_\n", + "## _*Using Qiskit Aqua for max-cut problems*_\n", "\n", "This Qiskit Aqua Optimization notebook demonstrates how to use the VQE quantum algorithm to compute the max cut of a given graph. \n", "\n", @@ -25,7 +25,7 @@ "\n", "from qiskit.aqua import Operator, run_algorithm\n", "from qiskit.aqua.input import EnergyInput\n", - "from qiskit.aqua.translators.ising import maxcut\n", + "from qiskit.aqua.translators.ising import max_cut\n", "from qiskit.aqua.algorithms.classical.cplex.cplex_ising import CPLEX_Ising\n", "from qiskit import Aer" ] @@ -34,7 +34,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Here an Operator instance is created for our Hamiltonian. In this case the paulis are from an Ising Hamiltonian translated from the max cut problem. We load a small sample instance of the maxcut problem." + "Here an Operator instance is created for our Hamiltonian. In this case the paulis are from an Ising Hamiltonian translated from the max-cut problem. We load a small sample instance of the max-cut problem." ] }, { @@ -43,8 +43,8 @@ "metadata": {}, "outputs": [], "source": [ - "w = maxcut.parse_gset_format('sample.maxcut')\n", - "qubitOp, offset = maxcut.get_maxcut_qubitops(w)\n", + "w = max_cut.parse_gset_format('sample.maxcut')\n", + "qubitOp, offset = max_cut.get_max_cut_qubitops(w)\n", "algo_input = EnergyInput(qubitOp)" ] }, @@ -74,8 +74,8 @@ "source": [ "if True:\n", " np.random.seed(8123179)\n", - " w = maxcut.random_graph(4, edge_prob=0.5, weight_range=10)\n", - " qubitOp, offset = maxcut.get_maxcut_qubitops(w)\n", + " w = max_cut.random_graph(4, edge_prob=0.5, weight_range=10)\n", + " qubitOp, offset = max_cut.get_max_cut_qubitops(w)\n", " algo_input.qubit_op = qubitOp\n", "print(w)" ] @@ -84,7 +84,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Here we test for the presence of algorithms we want to use in this notebook. If Aqua is installed correctly `ExactEigensolver` and `VQE` will always be found. `CPLEX.Ising` is dependent on IBM CPLEX being installed (see introduction above). CPLEX is *not required* but if installed then this notebook will demonstrate the `CPLEX.Ising` algorithm , that uses CPLEX, to compute maxcut as well." + "Here we test for the presence of algorithms we want to use in this notebook. If Aqua is installed correctly `ExactEigensolver` and `VQE` will always be found. `CPLEX.Ising` is dependent on IBM CPLEX being installed (see introduction above). CPLEX is *not required* but if installed then this notebook will demonstrate the `CPLEX.Ising` algorithm , that uses CPLEX, to compute max-cut as well." ] }, { @@ -122,7 +122,7 @@ "output_type": "stream", "text": [ "energy: -20.5\n", - "maxcut objective: -24.0\n", + "max-cut objective: -24.0\n", "solution: [1. 0. 1. 1.]\n", "solution objective: 24.0\n" ] @@ -138,12 +138,12 @@ " 'algorithm': algorithm_cfg\n", "}\n", "result = run_algorithm(params,algo_input)\n", - "# print('objective function:', maxcut.maxcut_obj(result, offset))\n", - "x = maxcut.sample_most_likely(result['eigvecs'][0])\n", + "# print('objective function:', max_cut.max_cut_obj(result, offset))\n", + "x = max_cut.sample_most_likely(result['eigvecs'][0])\n", "print('energy:', result['energy'])\n", - "print('maxcut objective:', result['energy'] + offset)\n", - "print('solution:', maxcut.get_graph_solution(x))\n", - "print('solution objective:', maxcut.maxcut_value(x, w))" + "print('max-cut objective:', result['energy'] + offset)\n", + "print('solution:', max_cut.get_graph_solution(x))\n", + "print('solution objective:', max_cut.max_cut_value(x, w))" ] }, { @@ -154,7 +154,7 @@ "\n", "We change the configuration parameters to solve it with the CPLEX backend. The CPLEX backend can deal with a particular type of Hamiltonian called Ising Hamiltonian, which consists of only Pauli Z at most second order and often for combinatorial optimization problems that can be formulated as quadratic unconstrained binary optimization problems, such as the max-cut problem.\n", "\n", - "Note that for a maxcut problem, since we are computing a bipartition of the graph, every binary vector $x$ and its complement (i.e., the vector $y$ such that $y_j = 1 - x_j$ for all $j$) represent exactly the same solution, and will have the same objective function value. Different solution methods may return solutions that look different, but in fact have the same objective function value." + "Note that for a max-cut problem, since we are computing a bipartition of the graph, every binary vector $x$ and its complement (i.e., the vector $y$ such that $y_j = 1 - x_j$ for all $j$) represent exactly the same solution, and will have the same objective function value. Different solution methods may return solutions that look different, but in fact have the same objective function value." ] }, { @@ -174,7 +174,7 @@ "CPXPARAM_MIP_Display 0\n", "energy: -20.5\n", "time: 0.026632682000126806\n", - "maxcut objective: -24.0\n", + "max-cut objective: -24.0\n", "solution: [1 0 1 1]\n", "solution objective: 24.0\n" ] @@ -204,10 +204,10 @@ " x_dict = result['x_sol']\n", " print('energy:', result['energy'])\n", " print('time:', result['eval_time'])\n", - " print('maxcut objective:', result['energy'] + offset)\n", + " print('max-cut objective:', result['energy'] + offset)\n", " x = np.array([x_dict[i] for i in sorted(x_dict.keys())])\n", - " print('solution:', maxcut.get_graph_solution(x))\n", - " print('solution objective:', maxcut.maxcut_value(x, w))" + " print('solution:', max_cut.get_graph_solution(x))\n", + " print('solution objective:', max_cut.max_cut_value(x, w))" ] }, { @@ -226,9 +226,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "energy: -20.499999999996096\n", - "time: 48.52856922149658\n", - "maxcut objective: -23.999999999996096\n", + "energy: -20.499999999997623\n", + "time: 12.321285724639893\n", + "max-cut objective: -23.999999999997623\n", "solution: [1. 0. 1. 1.]\n", "solution objective: 24.0\n" ] @@ -261,12 +261,12 @@ "backend = Aer.get_backend('statevector_simulator')\n", "result = run_algorithm(params, algo_input, backend=backend)\n", "\n", - "x = maxcut.sample_most_likely(result['eigvecs'][0])\n", + "x = max_cut.sample_most_likely(result['eigvecs'][0])\n", "print('energy:', result['energy'])\n", "print('time:', result['eval_time'])\n", - "print('maxcut objective:', result['energy'] + offset)\n", - "print('solution:', maxcut.get_graph_solution(x))\n", - "print('solution objective:', maxcut.maxcut_value(x, w))" + "print('max-cut objective:', result['energy'] + offset)\n", + "print('solution:', max_cut.get_graph_solution(x))\n", + "print('solution objective:', max_cut.max_cut_value(x, w))" ] } ], @@ -286,7 +286,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.7" + "version": "3.7.2" } }, "nbformat": 4, diff --git a/community/aqua/optimization/set_packing.ipynb b/community/aqua/optimization/set_packing.ipynb index f73752c6b..4d435e1e2 100644 --- a/community/aqua/optimization/set_packing.ipynb +++ b/community/aqua/optimization/set_packing.ipynb @@ -44,7 +44,7 @@ "\n", "from qiskit.aqua import run_algorithm\n", "from qiskit.aqua.input import EnergyInput\n", - "from qiskit.aqua.translators.ising import setpacking\n", + "from qiskit.aqua.translators.ising import set_packing\n", "from qiskit.aqua.algorithms import ExactEigensolver\n", "\n", "\n", @@ -86,7 +86,7 @@ " max_v = -np.inf\n", " for i in range(max):\n", " cur = bitfield(i, L)\n", - " cur_v = setpacking.check_disjoint(cur, list_of_subsets)\n", + " cur_v = set_packing.check_disjoint(cur, list_of_subsets)\n", " if cur_v:\n", " if np.count_nonzero(cur) > max_v:\n", " max_v = np.count_nonzero(cur)\n", @@ -103,10 +103,10 @@ "#### Part I: Run the optimization using the declarative approach\n", "\n", "Here the steps are:\n", - "* Create the qubit operator i.e. Ising Hamiltonian, using setpacking ising translator\n", + "* Create the qubit operator i.e. Ising Hamiltonian, using `set_packing` ising translator\n", "* Create an EnergyInput object and a dictionary describing the algorithm and the components for Aqua to solve the problem\n", "* Run the algorithm and get the result\n", - "* Use the result with the setpacking object to determine a solution" + "* Use the result with the `set_packing` object to determine a solution" ] }, { @@ -123,7 +123,7 @@ } ], "source": [ - "qubit_op, offset = setpacking.get_setpacking_qubitops(list_of_subsets)\n", + "qubit_op, offset = set_packing.get_set_packing_qubitops(list_of_subsets)\n", "\n", "algo_input = EnergyInput(qubit_op)\n", "params = {\n", @@ -132,8 +132,8 @@ "}\n", "result = run_algorithm(params, algo_input)\n", "\n", - "x = setpacking.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", - "ising_sol = setpacking.get_solution(x)\n", + "x = set_packing.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", + "ising_sol = set_packing.get_solution(x)\n", "np.testing.assert_array_equal(ising_sol, [0, 1, 1])\n", "print(\"Size of set packing\", np.count_nonzero(ising_sol))" ] @@ -164,8 +164,8 @@ "algo = ExactEigensolver(qubit_op)\n", "result = algo.run()\n", "\n", - "x = setpacking.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", - "ising_sol = setpacking.get_solution(x)\n", + "x = set_packing.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", + "ising_sol = set_packing.get_solution(x)\n", "np.testing.assert_array_equal(ising_sol, [0, 1, 1])\n", "oracle = brute_force()\n", "print(\"Size of set packing\", np.count_nonzero(ising_sol))" @@ -205,8 +205,8 @@ "backend = BasicAer.get_backend('statevector_simulator')\n", "result = run_algorithm(params, algo_input, backend=backend)\n", "\n", - "x = setpacking.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", - "ising_sol = setpacking.get_solution(x)\n", + "x = set_packing.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", + "ising_sol = set_packing.get_solution(x)\n", "print(\"Size of set packing\", np.count_nonzero(ising_sol))" ] }, @@ -247,17 +247,10 @@ "backend = BasicAer.get_backend('statevector_simulator')\n", "result = vqe.run(backend)\n", "\n", - "x = setpacking.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", - "ising_sol = setpacking.get_solution(x)\n", + "x = set_packing.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", + "ising_sol = set_packing.get_solution(x)\n", "print(\"Size of set packing\", np.count_nonzero(ising_sol))" ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { @@ -276,7 +269,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.1" + "version": "3.7.2" } }, "nbformat": 4, diff --git a/community/aqua/optimization/stableset.ipynb b/community/aqua/optimization/stable_set.ipynb similarity index 90% rename from community/aqua/optimization/stableset.ipynb rename to community/aqua/optimization/stable_set.ipynb index c2229f33a..dfe91fa4f 100644 --- a/community/aqua/optimization/stableset.ipynb +++ b/community/aqua/optimization/stable_set.ipynb @@ -6,7 +6,7 @@ "collapsed": true }, "source": [ - "## _*Using Qiskit Aqua for stableset problems*_\n", + "## _*Using Qiskit Aqua for stable-set problems*_\n", "\n", "This Qiskit Aqua Optimization notebook demonstrates how to use the VQE algorithm to compute the maximum stable set of a given graph. \n", "\n", @@ -24,7 +24,7 @@ "import numpy as np\n", "\n", "from qiskit.aqua import Operator, run_algorithm\n", - "from qiskit.aqua.translators.ising import stableset\n", + "from qiskit.aqua.translators.ising import stable_set\n", "from qiskit.aqua.input import EnergyInput\n", "from qiskit.aqua.algorithms.classical.cplex.cplex_ising import CPLEX_Ising\n", "from qiskit import Aer" @@ -43,8 +43,8 @@ "metadata": {}, "outputs": [], "source": [ - "w = stableset.parse_gset_format('sample.maxcut')\n", - "qubitOp, offset = stableset.get_stableset_qubitops(w)\n", + "w = stable_set.parse_gset_format('sample.maxcut')\n", + "qubitOp, offset = stable_set.get_stable_set_qubitops(w)\n", "algo_input = EnergyInput(qubitOp)" ] }, @@ -75,8 +75,8 @@ "source": [ "if True:\n", " np.random.seed(8123179)\n", - " w = stableset.random_graph(5, edge_prob=0.5)\n", - " qubitOp, offset = stableset.get_stableset_qubitops(w)\n", + " w = stable_set.random_graph(5, edge_prob=0.5)\n", + " qubitOp, offset = stable_set.get_stable_set_qubitops(w)\n", " algo_input.qubit_op = qubitOp\n", "print(w)" ] @@ -140,11 +140,11 @@ "}\n", "result = run_algorithm(params,algo_input)\n", "\n", - "x = stableset.sample_most_likely(result['eigvecs'][0])\n", + "x = stable_set.sample_most_likely(result['eigvecs'][0])\n", "print('energy:', result['energy'])\n", "print('stable set objective:', result['energy'] + offset)\n", - "print('solution:', stableset.get_graph_solution(x))\n", - "print('solution objective and feasibility:', stableset.stableset_value(x, w))" + "print('solution:', stable_set.get_graph_solution(x))\n", + "print('solution objective and feasibility:', stable_set.stable_set_value(x, w))" ] }, { @@ -205,8 +205,8 @@ " print('time:', result['eval_time'])\n", " print('stable set objective:', result['energy'] + offset)\n", " x = np.array([x_dict[i] for i in sorted(x_dict.keys())])\n", - " print('solution:', stableset.get_graph_solution(x))\n", - " print('solution objective and feasibility:', stableset.stableset_value(x, w))" + " print('solution:', stable_set.get_graph_solution(x))\n", + " print('solution objective and feasibility:', stable_set.stable_set_value(x, w))" ] }, { @@ -260,12 +260,12 @@ "backend = Aer.get_backend('statevector_simulator')\n", "result = run_algorithm(params, algo_input, backend=backend)\n", "\n", - "x = stableset.sample_most_likely(result['eigvecs'][0])\n", + "x = stable_set.sample_most_likely(result['eigvecs'][0])\n", "print('energy:', result['energy'])\n", "print('time:', result['eval_time'])\n", "print('stable set objective:', result['energy'] + offset)\n", - "print('solution:', stableset.get_graph_solution(x))\n", - "print('solution objective and feasibility:', stableset.stableset_value(x, w))" + "print('solution:', stable_set.get_graph_solution(x))\n", + "print('solution objective and feasibility:', stable_set.stable_set_value(x, w))" ] } ], @@ -285,7 +285,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.7" + "version": "3.7.2" } }, "nbformat": 4, diff --git a/community/aqua/optimization/vertex_cover.ipynb b/community/aqua/optimization/vertex_cover.ipynb index 951af3f08..00aec67c9 100644 --- a/community/aqua/optimization/vertex_cover.ipynb +++ b/community/aqua/optimization/vertex_cover.ipynb @@ -4,7 +4,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## _*Using Qiskit Aqua for the vertex cover problems*_\n", + "## _*Using Qiskit Aqua for the vertex-cover problems*_\n", "\n", "A vertex cover of a graph is a set of vertices such that each edge of the graph is incident to at least one vertex of the set. The goal of NPC problem is to minimize the size of the vertex cover. \n", "\n", @@ -43,12 +43,12 @@ "from qiskit import BasicAer\n", "from qiskit.aqua import run_algorithm\n", "from qiskit.aqua.input import EnergyInput\n", - "from qiskit.aqua.translators.ising import vertexcover\n", + "from qiskit.aqua.translators.ising import vertex_cover\n", "from qiskit.aqua.algorithms import ExactEigensolver\n", "\n", "np.random.seed(100)\n", "num_nodes = 3\n", - "w = vertexcover.random_graph(num_nodes, edge_prob=0.8, weight_range=10)\n", + "w = vertex_cover.random_graph(num_nodes, edge_prob=0.8, weight_range=10)\n", "print(w)" ] }, @@ -85,7 +85,7 @@ " for i in range(max):\n", " cur = bitfield(i, L)\n", "\n", - " cur_v = vertexcover.check_full_edge_coverage(np.array(cur), w)\n", + " cur_v = vertex_cover.check_full_edge_coverage(np.array(cur), w)\n", " if cur_v:\n", " nonzerocount = np.count_nonzero(cur)\n", " if nonzerocount < minimal_v:\n", @@ -104,10 +104,10 @@ "#### Part I: Run the optimization using the declarative approach\n", "\n", "Here the steps are:\n", - "* Create the qubit operator i.e. Ising Hamiltonian, using vertexcover ising translator\n", + "* Create the qubit operator i.e. Ising Hamiltonian, using `vertex_cover` ising translator\n", "* Create an EnergyInput object and a dictionary describing the algorithm and the components for Aqua to solve the problem\n", "* Run the algorithm and get the result\n", - "* Use the result with the vertexcover object to determine a solution" + "* Use the result with the `vertex_cover` object to determine a solution" ] }, { @@ -124,7 +124,7 @@ } ], "source": [ - "qubit_op, offset = vertexcover.get_vertexcover_qubitops(w)\n", + "qubit_op, offset = vertex_cover.get_vertex_cover_qubitops(w)\n", "\n", "algo_input = EnergyInput(qubit_op)\n", "params = {\n", @@ -133,8 +133,8 @@ "}\n", "result = run_algorithm(params, algo_input)\n", "\n", - "x = vertexcover.sample_most_likely(len(w), result['eigvecs'][0])\n", - "sol = vertexcover.get_graph_solution(x)\n", + "x = vertex_cover.sample_most_likely(len(w), result['eigvecs'][0])\n", + "sol = vertex_cover.get_graph_solution(x)\n", "np.testing.assert_array_equal(sol, [0, 1, 1])\n", "print('Size of the vertex cover', np.count_nonzero(sol))" ] @@ -165,8 +165,8 @@ "algo = ExactEigensolver(qubit_op)\n", "result = algo.run()\n", "\n", - "x = vertexcover.sample_most_likely(len(w), result['eigvecs'][0])\n", - "sol = vertexcover.get_graph_solution(x)\n", + "x = vertex_cover.sample_most_likely(len(w), result['eigvecs'][0])\n", + "sol = vertex_cover.get_graph_solution(x)\n", "np.testing.assert_array_equal(sol, [0, 1, 1])\n", "print('Size of the vertex cover', np.count_nonzero(sol))" ] @@ -205,8 +205,8 @@ "backend = BasicAer.get_backend('qasm_simulator')\n", "result = run_algorithm(params, algo_input, backend=backend)\n", "\n", - "x = vertexcover.sample_most_likely(len(w), result['eigvecs'][0])\n", - "sol = vertexcover.get_graph_solution(x)\n", + "x = vertex_cover.sample_most_likely(len(w), result['eigvecs'][0])\n", + "sol = vertex_cover.get_graph_solution(x)\n", "print('Size of the vertex cover', np.count_nonzero(sol))" ] }, @@ -247,17 +247,10 @@ "backend = BasicAer.get_backend('qasm_simulator')\n", "result = vqe.run(backend)\n", "\n", - "x = vertexcover.sample_most_likely(len(w), result['eigvecs'][0])\n", - "sol = vertexcover.get_graph_solution(x)\n", + "x = vertex_cover.sample_most_likely(len(w), result['eigvecs'][0])\n", + "sol = vertex_cover.get_graph_solution(x)\n", "print('Size of the vertex cover', np.count_nonzero(sol))" ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { @@ -276,7 +269,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.1" + "version": "3.7.2" } }, "nbformat": 4, diff --git a/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/.ipynb_checkpoints/w8_03-checkpoint.ipynb b/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/.ipynb_checkpoints/w8_03-checkpoint.ipynb new file mode 100644 index 000000000..7e4bf44be --- /dev/null +++ b/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/.ipynb_checkpoints/w8_03-checkpoint.ipynb @@ -0,0 +1,504 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# _*Qiskit Aqua: Experimenting with Max-Cut problem with variational quantum eigensolver*_ \n", + "\n", + "\n", + "This notebook is based on an official notebook by Qiskit team, available at https://github.com/qiskit/qiskit-tutorial under the [Apache License 2.0](https://github.com/Qiskit/qiskit-tutorial/blob/master/LICENSE) license. \n", + "The original notebook was developed by Antonio Mezzacapo[1], Jay Gambetta[1], Kristan Temme[1], Ramis Movassagh[1], Albert Frisch[1], Takashi Imamichi[1], Giacomo Nannicni[1], Richard Chen[1], Marco Pistoia[1], Stephen Wood[1]([1]IBMQ)\n", + "\n", + "Your **TASK** is to execute every step of this notebook while learning to use qiskit-aqua and also how to leverage general problem modeling into know problems that qiskit-aqua can solve, namely the [Maximum Cut problem](https://en.wikipedia.org/wiki/Maximum_cut) problem." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Introduction\n", + "\n", + "Many problems in quantitative fields such as finance and engineering are optimization problems. Optimization problems lay at the core of complex decision-making and definition of strategies. \n", + "\n", + "Optimization (or combinatorial optimization) means searching for an optimal solution in a finite or countably infinite set of potential solutions. Optimality is defined with respect to some criterion function, which is to be minimized or maximized. This is typically called cost function or objective function. \n", + "\n", + "**Typical optimization problems**\n", + "\n", + "Minimization: cost, distance, length of a traversal, weight, processing time, material, energy consumption, number of objects\n", + "\n", + "Maximization: profit, value, output, return, yield, utility, efficiency, capacity, number of objects \n", + "\n", + "We consider here max-cut problem of practical interest in many fields, and show how they can mapped on quantum computers.\n", + "\n", + "\n", + "### Weighted Max-Cut\n", + "\n", + "Max-Cut is an NP-complete problem, with applications in clustering, network science, and statistical physics. To grasp how practical applications are mapped into given Max-Cut instances, consider a system of many people that can interact and influence each other. Individuals can be represented by vertices of a graph, and their interactions seen as pairwise connections between vertices of the graph, or edges. With this representation in mind, it is easy to model typical marketing problems. For example, suppose that it is assumed that individuals will influence each other's buying decisions, and knowledge is given about how strong they will influence each other. The influence can be modeled by weights assigned on each edge of the graph. It is possible then to predict the outcome of a marketing strategy in which products are offered for free to some individuals, and then ask which is the optimal subset of individuals that should get the free products, in order to maximize revenues.\n", + "\n", + "The formal definition of this problem is the following:\n", + "\n", + "Consider an $n$-node undirected graph *G = (V, E)* where *|V| = n* with edge weights $w_{ij}>0$, $w_{ij}=w_{ji}$, for $(i, j)\\in E$. A cut is defined as a partition of the original set V into two subsets. The cost function to be optimized is in this case the sum of weights of edges connecting points in the two different subsets, *crossing* the cut. By assigning $x_i=0$ or $x_i=1$ to each node $i$, one tries to maximize the global profit function (here and in the following summations run over indices 0,1,...n-1)\n", + "\n", + "$$\\tilde{C}(\\textbf{x}) = \\sum_{i,j} w_{ij} x_i (1-x_j).$$\n", + "\n", + "In our simple marketing model, $w_{ij}$ represents the probability that the person $j$ will buy a product after $i$ gets a free one. Note that the weights $w_{ij}$ can in principle be greater than $1$, corresponding to the case where the individual $j$ will buy more than one product. Maximizing the total buying probability corresponds to maximizing the total future revenues. In the case where the profit probability will be greater than the cost of the initial free samples, the strategy is a convenient one. An extension to this model has the nodes themselves carry weights, which can be regarded, in our marketing model, as the likelihood that a person granted with a free sample of the product will buy it again in the future. With this additional information in our model, the objective function to maximize becomes \n", + "\n", + "$$C(\\textbf{x}) = \\sum_{i,j} w_{ij} x_i (1-x_j)+\\sum_i w_i x_i. $$\n", + " \n", + "In order to find a solution to this problem on a quantum computer, one needs first to map it to an Ising Hamiltonian. This can be done with the assignment $x_i\\rightarrow (1-Z_i)/2$, where $Z_i$ is the Pauli Z operator that has eigenvalues $\\pm 1$. Doing this we find that \n", + "\n", + "$$C(\\textbf{Z}) = \\sum_{i,j} \\frac{w_{ij}}{4} (1-Z_i)(1+Z_j) + \\sum_i \\frac{w_i}{2} (1-Z_i) = -\\frac{1}{2}\\left( \\sum_{i" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Generating a graph of 4 nodes \n", + "\n", + "n=4 # Number of nodes in graph\n", + "G=nx.Graph()\n", + "G.add_nodes_from(np.arange(0,n,1))\n", + "elist=[(0,1,1.0),(0,2,1.0),(0,3,1.0),(1,2,1.0),(2,3,1.0)]\n", + "# tuple is (i,j,weight) where (i,j) is the edge\n", + "G.add_weighted_edges_from(elist)\n", + "\n", + "colors = ['r' for node in G.nodes()]\n", + "pos = nx.spring_layout(G)\n", + "default_axes = plt.axes(frameon=True)\n", + "nx.draw_networkx(G, node_color=colors, node_size=600, alpha=.8, ax=default_axes, pos=pos)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0. 1. 1. 1.]\n", + " [1. 0. 1. 0.]\n", + " [1. 1. 0. 1.]\n", + " [1. 0. 1. 0.]]\n" + ] + } + ], + "source": [ + "# Computing the weight matrix from the random graph\n", + "w = np.zeros([n,n])\n", + "for i in range(n):\n", + " for j in range(n):\n", + " temp = G.get_edge_data(i,j,default=0)\n", + " if temp != 0:\n", + " w[i,j] = temp['weight'] \n", + "print(w)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Brute force approach\n", + "\n", + "Try all possible $2^n$ combinations. For $n = 4$, as in this example, one deals with only 16 combinations, but for n = 1000, one has 1.071509e+30 combinations, which is impractical to deal with by using a brute force approach. " + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "case = [0, 0, 0, 0] cost = 0.0\n", + "case = [1, 0, 0, 0] cost = 3.0\n", + "case = [0, 1, 0, 0] cost = 2.0\n", + "case = [1, 1, 0, 0] cost = 3.0\n", + "case = [0, 0, 1, 0] cost = 3.0\n", + "case = [1, 0, 1, 0] cost = 4.0\n", + "case = [0, 1, 1, 0] cost = 3.0\n", + "case = [1, 1, 1, 0] cost = 2.0\n", + "case = [0, 0, 0, 1] cost = 2.0\n", + "case = [1, 0, 0, 1] cost = 3.0\n", + "case = [0, 1, 0, 1] cost = 4.0\n", + "case = [1, 1, 0, 1] cost = 3.0\n", + "case = [0, 0, 1, 1] cost = 3.0\n", + "case = [1, 0, 1, 1] cost = 2.0\n", + "case = [0, 1, 1, 1] cost = 3.0\n", + "case = [1, 1, 1, 1] cost = 0.0\n", + "\n", + "Best solution = [1, 0, 1, 0] cost = 4.0\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "best_cost_brute = 0\n", + "for b in range(2**n):\n", + " x = [int(t) for t in reversed(list(bin(b)[2:].zfill(n)))]\n", + " cost = 0\n", + " for i in range(n):\n", + " for j in range(n):\n", + " cost = cost + w[i,j]*x[i]*(1-x[j])\n", + " if best_cost_brute < cost:\n", + " best_cost_brute = cost\n", + " xbest_brute = x \n", + " print('case = ' + str(x)+ ' cost = ' + str(cost))\n", + "\n", + "colors = ['r' if xbest_brute[i] == 0 else 'b' for i in range(n)]\n", + "nx.draw_networkx(G, node_color=colors, node_size=600, alpha=.8, pos=pos)\n", + "print('\\nBest solution = ' + str(xbest_brute) + ' cost = ' + str(best_cost_brute)) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Mapping to the Ising problem" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "qubitOp, offset = max_cut.get_max_cut_qubitops(w)\n", + "algo_input = EnergyInput(qubitOp)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Checking that the full Hamiltonian gives the right cost " + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "energy: -1.5\n", + "max-cut objective: -4.0\n", + "solution: [0. 1. 0. 1.]\n", + "solution objective: 4.0\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#Making the Hamiltonian in its full form and getting the lowest eigenvalue and eigenvector\n", + "\n", + "algorithm_cfg = {\n", + " 'name': 'ExactEigensolver',\n", + "}\n", + "\n", + "params = {\n", + " 'problem': {'name': 'ising'},\n", + " 'algorithm': algorithm_cfg\n", + "}\n", + "result = run_algorithm(params,algo_input)\n", + "x = max_cut.sample_most_likely(result['eigvecs'][0])\n", + "print('energy:', result['energy'])\n", + "print('max-cut objective:', result['energy'] + offset)\n", + "print('solution:', max_cut.get_graph_solution(x))\n", + "print('solution objective:', max_cut.max_cut_value(x, w))\n", + "\n", + "colors = ['r' if max_cut.get_graph_solution(x)[i] == 0 else 'b' for i in range(n)]\n", + "nx.draw_networkx(G, node_color=colors, node_size=600, alpha = .8, pos=pos)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Running it on quantum computer\n", + "We run the optimization routine using a feedback loop with a quantum computer that uses trial functions built with Y single-qubit rotations, $U_\\mathrm{single}(\\theta) = \\prod_{i=1}^n Y(\\theta_{i})$, and entangler steps $U_\\mathrm{entangler}$." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "energy: -1.4995485513056617\n", + "time: 8.994375944137573\n", + "max-cut objective: -3.9995485513056614\n", + "solution: [0. 1. 0. 1.]\n", + "solution objective: 4.0\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "algorithm_cfg = {\n", + " 'name': 'VQE',\n", + " 'operator_mode': 'matrix'\n", + "}\n", + "\n", + "optimizer_cfg = {\n", + " 'name': 'SPSA',\n", + " 'max_trials': 300\n", + "}\n", + "\n", + "var_form_cfg = {\n", + " 'name': 'RY',\n", + " 'depth': 5,\n", + " 'entanglement': 'linear'\n", + "}\n", + "\n", + "params = {\n", + " 'problem': {'name': 'ising', 'random_seed': 10598},\n", + " 'algorithm': algorithm_cfg,\n", + " 'optimizer': optimizer_cfg,\n", + " 'variational_form': var_form_cfg,\n", + " 'backend': {'name': 'statevector_simulator'}\n", + "}\n", + "\n", + "result = run_algorithm(params, algo_input)\n", + "\n", + "x = max_cut.sample_most_likely(result['eigvecs'][0])\n", + "print('energy:', result['energy'])\n", + "print('time:', result['eval_time'])\n", + "print('max-cut objective:', result['energy'] + offset)\n", + "print('solution:', max_cut.get_graph_solution(x))\n", + "print('solution objective:', max_cut.max_cut_value(x, w))\n", + "\n", + "colors = ['r' if max_cut.get_graph_solution(x)[i] == 0 else 'b' for i in range(n)]\n", + "nx.draw_networkx(G, node_color=colors, node_size=600, alpha = .8, pos=pos)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "energy: -1.5\n", + "time: 18.19207787513733\n", + "max-cut objective: -4.0\n", + "solution: [1 0 1 0]\n", + "solution objective: 4.0\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# run quantum algorithm with shots\n", + "params['algorithm']['operator_mode'] = 'grouped_paulis'\n", + "params['backend']['name'] = 'qasm_simulator'\n", + "params['backend']['shots'] = 1024\n", + "\n", + "result = run_algorithm(params, algo_input)\n", + "x = max_cut.sample_most_likely(result['eigvecs'][0])\n", + "print('energy:', result['energy'])\n", + "print('time:', result['eval_time'])\n", + "print('max-cut objective:', result['energy'] + offset)\n", + "print('solution:', max_cut.get_graph_solution(x))\n", + "print('solution objective:', max_cut.max_cut_value(x, w))\n", + "plot_histogram(result['eigvecs'][0])\n", + "\n", + "colors = ['r' if max_cut.get_graph_solution(x)[i] == 0 else 'b' for i in range(n)]\n", + "nx.draw_networkx(G, node_color=colors, node_size=600, alpha = .8, pos=pos)" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.2" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/.ipynb_checkpoints/w8_04-checkpoint.ipynb b/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/.ipynb_checkpoints/w8_04-checkpoint.ipynb new file mode 100644 index 000000000..dc0b353e9 --- /dev/null +++ b/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/.ipynb_checkpoints/w8_04-checkpoint.ipynb @@ -0,0 +1,478 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# _*Qiskit Aqua: Experimenting with Traveling Salesman problem with variational quantum eigensolver*_ \n", + "\n", + "\n", + "This notebook is based on an official notebook by Qiskit team, available at https://github.com/qiskit/qiskit-tutorial under the [Apache License 2.0](https://github.com/Qiskit/qiskit-tutorial/blob/master/LICENSE) license. \n", + "The original notebook was developed by Antonio Mezzacapo[1], Jay Gambetta[1], Kristan Temme[1], Ramis Movassagh[1], Albert Frisch[1], Takashi Imamichi[1], Giacomo Nannicni[1], Richard Chen[1], Marco Pistoia[1], Stephen Wood[1]([1]IBMQ)\n", + "\n", + "Your **TASK** is to execute every step of this notebook while learning to use qiskit-aqua and also how to leverage general problem modeling into know problems that qiskit-aqua can solve, namely the [Travelling salesman problem](https://en.wikipedia.org/wiki/Travelling_salesman_problem)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Introduction\n", + "\n", + "Many problems in quantitative fields such as finance and engineering are optimization problems. Optimization problems lay at the core of complex decision-making and definition of strategies. \n", + "\n", + "Optimization (or combinatorial optimization) means searching for an optimal solution in a finite or countably infinite set of potential solutions. Optimality is defined with respect to some criterion function, which is to be minimized or maximized. This is typically called cost function or objective function. \n", + "\n", + "**Typical optimization problems**\n", + "\n", + "Minimization: cost, distance, length of a traversal, weight, processing time, material, energy consumption, number of objects\n", + "\n", + "Maximization: profit, value, output, return, yield, utility, efficiency, capacity, number of objects \n", + "\n", + "We consider here max-cut problem of practical interest in many fields, and show how they can mapped on quantum computers.\n", + "\n", + "\n", + "### Weighted Max-Cut\n", + "\n", + "Max-Cut is an NP-complete problem, with applications in clustering, network science, and statistical physics. To grasp how practical applications are mapped into given Max-Cut instances, consider a system of many people that can interact and influence each other. Individuals can be represented by vertices of a graph, and their interactions seen as pairwise connections between vertices of the graph, or edges. With this representation in mind, it is easy to model typical marketing problems. For example, suppose that it is assumed that individuals will influence each other's buying decisions, and knowledge is given about how strong they will influence each other. The influence can be modeled by weights assigned on each edge of the graph. It is possible then to predict the outcome of a marketing strategy in which products are offered for free to some individuals, and then ask which is the optimal subset of individuals that should get the free products, in order to maximize revenues.\n", + "\n", + "The formal definition of this problem is the following:\n", + "\n", + "Consider an $n$-node undirected graph *G = (V, E)* where *|V| = n* with edge weights $w_{ij}>0$, $w_{ij}=w_{ji}$, for $(i, j)\\in E$. A cut is defined as a partition of the original set V into two subsets. The cost function to be optimized is in this case the sum of weights of edges connecting points in the two different subsets, *crossing* the cut. By assigning $x_i=0$ or $x_i=1$ to each node $i$, one tries to maximize the global profit function (here and in the following summations run over indices 0,1,...n-1)\n", + "\n", + "$$\\tilde{C}(\\textbf{x}) = \\sum_{i,j} w_{ij} x_i (1-x_j).$$\n", + "\n", + "In our simple marketing model, $w_{ij}$ represents the probability that the person $j$ will buy a product after $i$ gets a free one. Note that the weights $w_{ij}$ can in principle be greater than $1$, corresponding to the case where the individual $j$ will buy more than one product. Maximizing the total buying probability corresponds to maximizing the total future revenues. In the case where the profit probability will be greater than the cost of the initial free samples, the strategy is a convenient one. An extension to this model has the nodes themselves carry weights, which can be regarded, in our marketing model, as the likelihood that a person granted with a free sample of the product will buy it again in the future. With this additional information in our model, the objective function to maximize becomes \n", + "\n", + "$$C(\\textbf{x}) = \\sum_{i,j} w_{ij} x_i (1-x_j)+\\sum_i w_i x_i. $$\n", + " \n", + "In order to find a solution to this problem on a quantum computer, one needs first to map it to an Ising Hamiltonian. This can be done with the assignment $x_i\\rightarrow (1-Z_i)/2$, where $Z_i$ is the Pauli Z operator that has eigenvalues $\\pm 1$. Doing this we find that \n", + "\n", + "$$C(\\textbf{Z}) = \\sum_{i,j} \\frac{w_{ij}}{4} (1-Z_i)(1+Z_j) + \\sum_i \\frac{w_i}{2} (1-Z_i) = -\\frac{1}{2}\\left( \\sum_{i0,$$ \n", + "\n", + "where it is assumed the boundary condition of the Hamiltonian cycle $(p=N)\\equiv (p=0)$. However, here it will be assumed a fully connected graph and not include this term. The distance that needs to be minimized is \n", + "\n", + "$$C(\\textbf{x})=\\sum_{i,j}w_{ij}\\sum_{p} x_{i,p}x_{j,p+1}.$$\n", + "\n", + "Putting this all together in a single objective function to be minimized, we get the following:\n", + "\n", + "$$C(\\textbf{x})=\\sum_{i,j}w_{ij}\\sum_{p} x_{i,p}x_{j,p+1}+ A\\sum_p\\left(1- \\sum_i x_{i,p}\\right)^2+A\\sum_i\\left(1- \\sum_p x_{i,p}\\right)^2,$$\n", + "\n", + "where $A$ is a free parameter. One needs to ensure that $A$ is large enough so that these constraints are respected. One way to do this is to choose $A$ such that $A > \\mathrm{max}(w_{ij})$.\n", + "\n", + "Once again, it is easy to map the problem in this form to a quantum computer, and the solution will be found by minimizing a Ising Hamiltonian. " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "distance\n", + " [[ 0. 91. 55.]\n", + " [91. 0. 39.]\n", + " [55. 39. 0.]]\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Generating a graph of 3 nodes\n", + "\n", + "n = 3\n", + "num_qubits = n ** 2\n", + "ins = tsp.random_tsp(n)\n", + "G = nx.Graph()\n", + "G.add_nodes_from(np.arange(0, n, 1))\n", + "colors = ['r' for node in G.nodes()]\n", + "pos = {k: v for k, v in enumerate(ins.coord)}\n", + "default_axes = plt.axes(frameon=True)\n", + "nx.draw_networkx(G, node_color=colors, node_size=600, alpha=.8, ax=default_axes, pos=pos)\n", + "print('distance\\n', ins.w)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Brute force approach" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "order = (0, 1, 2) Distance = 185.0\n", + "Best order from brute force = (0, 1, 2) with total distance = 185.0\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from itertools import permutations\n", + "\n", + "def brute_force_tsp(w, N):\n", + " a=list(permutations(range(1,N)))\n", + " last_best_distance = 1e10\n", + " for i in a:\n", + " distance = 0\n", + " pre_j = 0\n", + " for j in i:\n", + " distance = distance + w[j,pre_j]\n", + " pre_j = j\n", + " distance = distance + w[pre_j,0]\n", + " order = (0,) + i\n", + " if distance < last_best_distance:\n", + " best_order = order\n", + " last_best_distance = distance\n", + " print('order = ' + str(order) + ' Distance = ' + str(distance))\n", + " return last_best_distance, best_order\n", + " \n", + "best_distance, best_order = brute_force_tsp(ins.w, ins.dim)\n", + "print('Best order from brute force = ' + str(best_order) + ' with total distance = ' + str(best_distance))\n", + "\n", + "def draw_tsp_solution(G, order, colors, pos):\n", + " G2 = G.copy()\n", + " n = len(order)\n", + " for i in range(n):\n", + " j = (i + 1) % n\n", + " G2.add_edge(order[i], order[j])\n", + " default_axes = plt.axes(frameon=True)\n", + " nx.draw_networkx(G2, node_color=colors, node_size=600, alpha=.8, ax=default_axes, pos=pos)\n", + "\n", + "draw_tsp_solution(G, best_order, colors, pos)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Mapping to the Ising problem" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "qubitOp, offset = tsp.get_tsp_qubitops(ins)\n", + "algo_input = get_input_instance('EnergyInput')\n", + "algo_input.qubit_op = qubitOp" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Checking that the full Hamiltonian gives the right cost " + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "energy: -600092.5\n", + "feasible: True\n", + "solution: [0, 1, 2]\n", + "solution objective: 185.0\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#Making the Hamiltonian in its full form and getting the lowest eigenvalue and eigenvector\n", + "\n", + "algorithm_cfg = {\n", + " 'name': 'ExactEigensolver',\n", + "}\n", + "\n", + "params = {\n", + " 'problem': {'name': 'ising'},\n", + " 'algorithm': algorithm_cfg\n", + "}\n", + "\n", + "result = run_algorithm(params,algo_input)\n", + "print('energy:', result['energy'])\n", + "#print('tsp objective:', result['energy'] + offset)\n", + "x = tsp.sample_most_likely(result['eigvecs'][0])\n", + "print('feasible:', tsp.tsp_feasible(x))\n", + "z = tsp.get_tsp_solution(x)\n", + "print('solution:', z)\n", + "print('solution objective:', tsp.tsp_value(z, ins.w))\n", + "draw_tsp_solution(G, z, colors, pos)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Running it on quantum computer\n", + "We run the optimization routine using a feedback loop with a quantum computer that uses trial functions built with Y single-qubit rotations, $U_\\mathrm{single}(\\theta) = \\prod_{i=1}^n Y(\\theta_{i})$, and entangler steps $U_\\mathrm{entangler}$." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "energy: -598732.7787240263\n", + "time: 88.01577425003052\n", + "feasible: True\n", + "solution: [1, 2, 0]\n", + "solution objective: 185.0\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "algorithm_cfg = {\n", + " 'name': 'VQE',\n", + " 'operator_mode': 'matrix'\n", + "}\n", + "\n", + "optimizer_cfg = {\n", + " 'name': 'SPSA',\n", + " 'max_trials': 300\n", + "}\n", + "\n", + "var_form_cfg = {\n", + " 'name': 'RY',\n", + " 'depth': 5,\n", + " 'entanglement': 'linear'\n", + "}\n", + "\n", + "params = {\n", + " 'problem': {'name': 'ising', 'random_seed': 10598},\n", + " 'algorithm': algorithm_cfg,\n", + " 'optimizer': optimizer_cfg,\n", + " 'variational_form': var_form_cfg,\n", + " 'backend': {'name': 'statevector_simulator'}\n", + "}\n", + "\n", + "result = run_algorithm(params,algo_input)\n", + "print('energy:', result['energy'])\n", + "print('time:', result['eval_time'])\n", + "#print('tsp objective:', result['energy'] + offset)\n", + "x = tsp.sample_most_likely(result['eigvecs'][0])\n", + "print('feasible:', tsp.tsp_feasible(x))\n", + "z = tsp.get_tsp_solution(x)\n", + "print('solution:', z)\n", + "print('solution objective:', tsp.tsp_value(z, ins.w))\n", + "draw_tsp_solution(G, z, colors, pos)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# run quantum algorithm with shots\n", + "params['algorithm']['operator_mode'] = 'grouped_paulis'\n", + "params['backend']['name'] = 'qasm_simulator'\n", + "params['backend']['shots'] = 1024\n", + "result = run_algorithm(params,algo_input)\n", + "print('energy:', result['energy'])\n", + "print('time:', result['eval_time'])\n", + "#print('tsp objective:', result['energy'] + offset)\n", + "x = tsp.sample_most_likely(result['eigvecs'][0])\n", + "print('feasible:', tsp.tsp_feasible(x))\n", + "z = tsp.get_tsp_solution(x)\n", + "print('solution:', z)\n", + "print('solution objective:', tsp.tsp_value(z, ins.w))\n", + "plot_histogram(result['eigvecs'][0])\n", + "draw_tsp_solution(G, z, colors, pos)" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.2" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_03.ipynb b/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_03.ipynb index 6c6b8ba22..7e4bf44be 100644 --- a/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_03.ipynb +++ b/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_03.ipynb @@ -11,7 +11,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# _*Qiskit Aqua: Experimenting with MaxCut problem with variational quantum eigensolver*_ \n", + "# _*Qiskit Aqua: Experimenting with Max-Cut problem with variational quantum eigensolver*_ \n", "\n", "\n", "This notebook is based on an official notebook by Qiskit team, available at https://github.com/qiskit/qiskit-tutorial under the [Apache License 2.0](https://github.com/Qiskit/qiskit-tutorial/blob/master/LICENSE) license. \n", @@ -36,12 +36,12 @@ "\n", "Maximization: profit, value, output, return, yield, utility, efficiency, capacity, number of objects \n", "\n", - "We consider here maxcut problem of practical interest in many fields, and show how they can mapped on quantum computers.\n", + "We consider here max-cut problem of practical interest in many fields, and show how they can mapped on quantum computers.\n", "\n", "\n", - "### Weighted MaxCut\n", + "### Weighted Max-Cut\n", "\n", - "MaxCut is an NP-complete problem, with applications in clustering, network science, and statistical physics. To grasp how practical applications are mapped into given MaxCut instances, consider a system of many people that can interact and influence each other. Individuals can be represented by vertices of a graph, and their interactions seen as pairwise connections between vertices of the graph, or edges. With this representation in mind, it is easy to model typical marketing problems. For example, suppose that it is assumed that individuals will influence each other's buying decisions, and knowledge is given about how strong they will influence each other. The influence can be modeled by weights assigned on each edge of the graph. It is possible then to predict the outcome of a marketing strategy in which products are offered for free to some individuals, and then ask which is the optimal subset of individuals that should get the free products, in order to maximize revenues.\n", + "Max-Cut is an NP-complete problem, with applications in clustering, network science, and statistical physics. To grasp how practical applications are mapped into given Max-Cut instances, consider a system of many people that can interact and influence each other. Individuals can be represented by vertices of a graph, and their interactions seen as pairwise connections between vertices of the graph, or edges. With this representation in mind, it is easy to model typical marketing problems. For example, suppose that it is assumed that individuals will influence each other's buying decisions, and knowledge is given about how strong they will influence each other. The influence can be modeled by weights assigned on each edge of the graph. It is possible then to predict the outcome of a marketing strategy in which products are offered for free to some individuals, and then ask which is the optimal subset of individuals that should get the free products, in order to maximize revenues.\n", "\n", "The formal definition of this problem is the following:\n", "\n", @@ -57,7 +57,7 @@ "\n", "$$C(\\textbf{Z}) = \\sum_{i,j} \\frac{w_{ij}}{4} (1-Z_i)(1+Z_j) + \\sum_i \\frac{w_i}{2} (1-Z_i) = -\\frac{1}{2}\\left( \\sum_{i" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -248,12 +250,14 @@ }, { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -288,9 +292,8 @@ "metadata": {}, "outputs": [], "source": [ - "qubitOp, offset = maxcut.get_maxcut_qubitops(w)\n", - "algo_input = get_input_instance('EnergyInput')\n", - "algo_input.qubit_op = qubitOp" + "qubitOp, offset = max_cut.get_max_cut_qubitops(w)\n", + "algo_input = EnergyInput(qubitOp)" ] }, { @@ -310,19 +313,21 @@ "output_type": "stream", "text": [ "energy: -1.5\n", - "maxcut objective: -4.0\n", + "max-cut objective: -4.0\n", "solution: [0. 1. 0. 1.]\n", "solution objective: 4.0\n" ] }, { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -338,13 +343,13 @@ " 'algorithm': algorithm_cfg\n", "}\n", "result = run_algorithm(params,algo_input)\n", - "x = maxcut.sample_most_likely(result['eigvecs'][0])\n", + "x = max_cut.sample_most_likely(result['eigvecs'][0])\n", "print('energy:', result['energy'])\n", - "print('maxcut objective:', result['energy'] + offset)\n", - "print('solution:', maxcut.get_graph_solution(x))\n", - "print('solution objective:', maxcut.maxcut_value(x, w))\n", + "print('max-cut objective:', result['energy'] + offset)\n", + "print('solution:', max_cut.get_graph_solution(x))\n", + "print('solution objective:', max_cut.max_cut_value(x, w))\n", "\n", - "colors = ['r' if maxcut.get_graph_solution(x)[i] == 0 else 'b' for i in range(n)]\n", + "colors = ['r' if max_cut.get_graph_solution(x)[i] == 0 else 'b' for i in range(n)]\n", "nx.draw_networkx(G, node_color=colors, node_size=600, alpha = .8, pos=pos)" ] }, @@ -367,21 +372,23 @@ "name": "stdout", "output_type": "stream", "text": [ - "energy: -1.4998924230468886\n", - "time: 45.33000445365906\n", - "maxcut objective: -3.9998924230468886\n", - "solution: [1. 0. 1. 0.]\n", + "energy: -1.4995485513056617\n", + "time: 8.994375944137573\n", + "max-cut objective: -3.9995485513056614\n", + "solution: [0. 1. 0. 1.]\n", "solution objective: 4.0\n" ] }, { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -412,14 +419,14 @@ "\n", "result = run_algorithm(params, algo_input)\n", "\n", - "x = maxcut.sample_most_likely(result['eigvecs'][0])\n", + "x = max_cut.sample_most_likely(result['eigvecs'][0])\n", "print('energy:', result['energy'])\n", "print('time:', result['eval_time'])\n", - "print('maxcut objective:', result['energy'] + offset)\n", - "print('solution:', maxcut.get_graph_solution(x))\n", - "print('solution objective:', maxcut.maxcut_value(x, w))\n", + "print('max-cut objective:', result['energy'] + offset)\n", + "print('solution:', max_cut.get_graph_solution(x))\n", + "print('solution objective:', max_cut.max_cut_value(x, w))\n", "\n", - "colors = ['r' if maxcut.get_graph_solution(x)[i] == 0 else 'b' for i in range(n)]\n", + "colors = ['r' if max_cut.get_graph_solution(x)[i] == 0 else 'b' for i in range(n)]\n", "nx.draw_networkx(G, node_color=colors, node_size=600, alpha = .8, pos=pos)" ] }, @@ -432,31 +439,23 @@ "name": "stdout", "output_type": "stream", "text": [ - "energy: -1.4970703125\n", - "time: 52.9637291431427\n", - "maxcut objective: -3.9970703125\n", + "energy: -1.5\n", + "time: 18.19207787513733\n", + "max-cut objective: -4.0\n", "solution: [1 0 1 0]\n", "solution objective: 4.0\n" ] }, { "data": { - "image/png": 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\n", 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\n", 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\n", 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" - ] + "metadata": { + "needs_background": "light" }, - "metadata": {}, "output_type": "display_data" } ], @@ -467,15 +466,15 @@ "params['backend']['shots'] = 1024\n", "\n", "result = run_algorithm(params, algo_input)\n", - "x = maxcut.sample_most_likely(result['eigvecs'][0])\n", + "x = max_cut.sample_most_likely(result['eigvecs'][0])\n", "print('energy:', result['energy'])\n", "print('time:', result['eval_time'])\n", - "print('maxcut objective:', result['energy'] + offset)\n", - "print('solution:', maxcut.get_graph_solution(x))\n", - "print('solution objective:', maxcut.maxcut_value(x, w))\n", + "print('max-cut objective:', result['energy'] + offset)\n", + "print('solution:', max_cut.get_graph_solution(x))\n", + "print('solution objective:', max_cut.max_cut_value(x, w))\n", "plot_histogram(result['eigvecs'][0])\n", "\n", - "colors = ['r' if maxcut.get_graph_solution(x)[i] == 0 else 'b' for i in range(n)]\n", + "colors = ['r' if max_cut.get_graph_solution(x)[i] == 0 else 'b' for i in range(n)]\n", "nx.draw_networkx(G, node_color=colors, node_size=600, alpha = .8, pos=pos)" ] } @@ -497,7 +496,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.4" + "version": "3.7.2" } }, "nbformat": 4, diff --git a/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_04.ipynb b/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_04.ipynb index f687a4973..dc0b353e9 100644 --- a/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_04.ipynb +++ b/community/awards/teach_me_quantum_2018/TeachMeQ/Week_8-High_Level_Quantum_Programming/exercises/w8_04.ipynb @@ -36,12 +36,12 @@ "\n", "Maximization: profit, value, output, return, yield, utility, efficiency, capacity, number of objects \n", "\n", - "We consider here maxcut problem of practical interest in many fields, and show how they can mapped on quantum computers.\n", + "We consider here max-cut problem of practical interest in many fields, and show how they can mapped on quantum computers.\n", "\n", "\n", - "### Weighted MaxCut\n", + "### Weighted Max-Cut\n", "\n", - "MaxCut is an NP-complete problem, with applications in clustering, network science, and statistical physics. To grasp how practical applications are mapped into given MaxCut instances, consider a system of many people that can interact and influence each other. Individuals can be represented by vertices of a graph, and their interactions seen as pairwise connections between vertices of the graph, or edges. With this representation in mind, it is easy to model typical marketing problems. For example, suppose that it is assumed that individuals will influence each other's buying decisions, and knowledge is given about how strong they will influence each other. The influence can be modeled by weights assigned on each edge of the graph. It is possible then to predict the outcome of a marketing strategy in which products are offered for free to some individuals, and then ask which is the optimal subset of individuals that should get the free products, in order to maximize revenues.\n", + "Max-Cut is an NP-complete problem, with applications in clustering, network science, and statistical physics. To grasp how practical applications are mapped into given Max-Cut instances, consider a system of many people that can interact and influence each other. Individuals can be represented by vertices of a graph, and their interactions seen as pairwise connections between vertices of the graph, or edges. With this representation in mind, it is easy to model typical marketing problems. For example, suppose that it is assumed that individuals will influence each other's buying decisions, and knowledge is given about how strong they will influence each other. The influence can be modeled by weights assigned on each edge of the graph. It is possible then to predict the outcome of a marketing strategy in which products are offered for free to some individuals, and then ask which is the optimal subset of individuals that should get the free products, in order to maximize revenues.\n", "\n", "The formal definition of this problem is the following:\n", "\n", @@ -57,7 +57,7 @@ "\n", "$$C(\\textbf{Z}) = \\sum_{i,j} \\frac{w_{ij}}{4} (1-Z_i)(1+Z_j) + \\sum_i \\frac{w_i}{2} (1-Z_i) = -\\frac{1}{2}\\left( \\sum_{i" ] @@ -191,7 +191,7 @@ "from qiskit.aqua.operator import Operator\n", "from qiskit.aqua.components.optimizers import COBYLA\n", "from qiskit.aqua.algorithms import VQE\n", - "from qiskit.aqua.algorithms.adaptive.qaoa.varform import QAOAVarForm" + "from qiskit.aqua.algorithms.adaptive.qaoa.var_form import QAOAVarForm" ] }, { @@ -463,17 +463,16 @@ "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 11\u001b[0m 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242\u001b[0;31m \u001b[0mf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 243\u001b[0m \u001b[0mi\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 244\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0msize\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mizip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcons_lengths\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mconstraints\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/qiskit/aqua/qiskit/aqua/algorithms/adaptive/vqe/vqe.py\u001b[0m in \u001b[0;36m_energy_evaluation\u001b[0;34m(self, parameters)\u001b[0m\n\u001b[1;32m 317\u001b[0m \u001b[0;32mfor\u001b[0m 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202\u001b[0m \"\"\"\n\u001b[0;32m--> 203\u001b[0;31m \u001b[0minput_circuit\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_var_form\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconstruct_circuit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mparameter\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 204\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mbackend\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 205\u001b[0m \u001b[0mwarning_msg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m\"Circuits used in VQE depends on the backend type, \"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/qiskit/aqua/qiskit/aqua/algorithms/adaptive/qaoa/var_form.py\u001b[0m in \u001b[0;36mconstruct_circuit\u001b[0;34m(self, angles)\u001b[0m\n\u001b[1;32m 58\u001b[0m \u001b[0mcircuit\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mQuantumCircuit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 59\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_initial_state\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 60\u001b[0;31m \u001b[0mcircuit\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_initial_state\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconstruct_circuit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'circuit'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 61\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcircuit\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mqregs\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 62\u001b[0m \u001b[0mq\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mQuantumRegister\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_cost_operator\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnum_qubits\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'q'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mTypeError\u001b[0m: construct_circuit() missing 1 required positional argument: 'qr'" ] } @@ -610,7 +609,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.7" + "version": "3.7.2" } }, "nbformat": 4, diff --git a/community/awards/teach_me_quantum_2018/qml_mooc/10_Discrete Optimization and Unsupervised Learning.ipynb b/community/awards/teach_me_quantum_2018/qml_mooc/10_Discrete Optimization and Unsupervised Learning.ipynb index f19f08a76..e30ad729f 100644 --- a/community/awards/teach_me_quantum_2018/qml_mooc/10_Discrete Optimization and Unsupervised Learning.ipynb +++ b/community/awards/teach_me_quantum_2018/qml_mooc/10_Discrete Optimization and Unsupervised Learning.ipynb @@ -23,7 +23,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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ywe12Izk5GampqUhOTobb7YbL5YKqquHP30AggEAgAL/fD03TBjQQieD1eqUNXXa6BhEFBf3PK9O0/uDt6ICYN+/bt7OzpWFcClyCqqhwqf1ftDPcGejo7YBf8yMlKcW0usayYDeW8YTMna4tQleGcBJXXw39llugvvVW/xMd8vMRvOceLpLRiExOm4wkNQnd/m5kJmfizKUzmJo11dTAjcaIRyex06XYFAX6nXdCX7q0f/fCFVdAuN1cJKMRyU7Nxl0L78KOozvQ6m3FtKxpuG3ebWaXFZdEPjpJ1rt0AUCJMROS5kIDn89ndgkjxlECjZYQAkE9CLdrZNsNZRStI45000034c0337TygymjvqDZ6RqIYUtjpSiKrQMXGH5O3NfXh40bN+LUqVNISbHeaGUkbPP9rJXDizsSiMZGVVUcPnwYS5cuRVpaGlpaWnj3Al0u8sw7F8mIRsfn82H9+vWoq6vDli1bsHDhQrNLGhN2uuMk1N2GFgTY2RLF7+DBg6iursaECROwZ88e6QMXYKebcJzbEo2dz+fDunXr8NFHH2Hr1q2YP3++2SUlDDvdBOHcligxmpqacOONNyInJwcffvihrQIXYKc7ZuxsiRKjr68Pa9euxb59+7Bt2zaUlZWZXdK4sE2na7TIS6HZ2RKNTWNjI6qrq5GXl4e6ujrbBi5go07XyLDjdYtEidHb24va2lo0NjZi+/btmDt3rtkljTumRRwi57bcAkY0NvX19aipqcGUKVPw/vvvOyJwAXa6I8K5LVHi9Pb2Ys2aNThw4ABeeeUVzJ492+ySDMVOdxjckUCUWPv27UN1dTWmTZuG999/33GBC7DTHRJPkhElVk9PD1avXo3Dhw9jx44dKC0tNbsk07DTHYQnyYgSRwiBjz/+GNXV1SgpKcF7773n6MAFbNTpjhXntkSJdenSJaxatQpHjx7Fq6++ipKSErNLsgTbdLqjDUjObYkSSwiBvXv3orq6GnPmzMHu3bsZuBFs1ekqijLiB/WxsyVKvO7ubjz22GNobm7Ga6+9hquuusrskizHNp3uSPEkGVHiCSGwZ88e1NTUYMGCBdi9ezcDNwpHdbpWOUmmnDgBpa0NorAQgp+YJLmuri48+uijOHHiBHbu3IkZM2aYXZKlOaLTtdJJMtcbbyD5Zz+D+4knkPzzn8P1t7+ZUgfRWAkhUFdXh5qaGpSXl+Odd95h4I6AbR5MCQCBQGDAQ+wsN7e9eBEpd9wBkZMDJCcDgQCUjg74Xn4ZmDzZvLqI4tTV1YWVK1eitbUVf/zjHzF9+nSzS7KaqEFjq043FKhW3ZGgeL39P0hO7v+32w0oChSPx7yiiOIghMAHH3yAmpoaLFmyBG+//TYDN062mulGdrZmjxGGIvLzIbKygAsXgNxcoLMTIjMTorDQ7NKIYvJ6vVi5ciVOnz6Nv//975g2bZrZJUnJVp3uihUrwg+w6+7uNrucy6WlIbB2LZCdDeX0aSAzE4HaWiA93ezKiKISQuC9995DTU0NrrnmGuzatYuBOwa2mukeO3YM+/fvR319PQ4cOAC/34/58+ejsrISixcvRllZGdxut9llAkIAPh+QkgJYqBMnGszj8WDFihU4e/Ysnn/+eUydOtXskmQR9YVtq9AdrK+vD4cOHcL+/fvR2NiIzz//HOnp6aisrERVVRWqqqowffp0XkJONIgQArt378ajjz6KBx98EHfeeSdfJ/FxZugOJoTAhQsX0NjYGA7ir776CldeeSUWL14cDuOcnBxLzYKJjNTZ2YmHH34YFy5cwPPPP4+ioiKzS5IRQzcaXddx8uRJ1NfXo76+Hp988gm6urowd+7ccAgvWrQIqampZpdKNK6EEHjnnXfw+OOP46GHHsKPf/xjdrejx9CNRyAQwJEjR8JBfPjwYSQlJaGiogIVFRWoqqrCrFmz4HK5zC6VKCEuXryIX//61/B6vXjuuecwZcoUs0uSHUN3LIQQ6OrqwieffIL6+no0NDTg+PHjyM/PHzAfLigo4FiCpCKEwNtvv41Vq1Zh+fLl+NGPfsTuNjEYuokmhEBbW1u4G25oaMD58+cxa9YsVFVVobKyEhUVFUhPT2cQkyVduHABy5cvR29vLzZv3oxC7hdPJIauETRNw7/+9S/U19ejsbERBw4cgKZpWLhwYbgbnjt3LpKSbHUmhSQjhMCuXbvwxBNPYMWKFbj99tvZGCQeQ9cMQgj09vaiqakJDQ0NqK+vxxdffIGJEyeG9w5XVVWhqKiI39KRITo6OvDLX/4SwWAQmzdvRkFBgdkl2RVD1yqEEDh//vyAscTp06cxY8aMcDdcUVGBiRMnsvughBFC4M0330RtbS0eeeQR3Hbbbfz8Gl8MXSvTdR3Hjx8Ph3BTUxN6enpQVlYWDuL58+cjJSXF7FJJQufPn8eyZcugKAqeffZZ5Ofnm12SEzB0ZeP3+3Ho0KFwEH/22WdITU1FeXl5OIhnzpzJsQRFJYTAzp07sW7dOvzmN7/BD3/4Q3a3xmHoyk4Igc7OTjQ2NoYX6k6cOIGioiJUVFSET9RNnjyZLyzC2bNnsWzZMrjdbvzhD39AXl6e2SU5DUPXjnRdx6lTp7B//340NDSgsbERnZ2dmD17dnihbtGiRUhLS2MQO4QQAq+//jrWr1+Pxx9/HLfeeiv/7s3B0HWKYDCIzz//PHy3xKFDh6AoCq6++urwQY7Zs2fzNJ0NffPNN1i2bBnS0tKwadMmTObTSMzE0HUqIQS6u7vR1NQUHks0Nzdj0qRJqKysRGVlJZYsWYIrrriCHZGkdF3Ha6+9hqeeegqrV6/GD37wA/5dmo+hS98SQqC9vR0NDQ3hjri9vR0lJSXhsUR5eTkyMzP54rW49vZ2PPjgg5gwYQKeeeYZTJo0yeySqB9Dl4anaRqam5vD8+GDBw/C7/djwYIF4SCeN2+eNS6BJ+i6jr/+9a94+umnsWbNGtx88838AmktDF2KX19fHw4ePDjgEvjMzMwBl/xMmzaN29YM1t7ejgceeAC5ubl4+umnkZuba3ZJdDmGLo2dEAIdHR0DLoFvbW3FtGnTwpf8VFZW8hL4caLrOnbs2IHf//73qK2txU033cQ/Z+ti6NL40HUdLS0tAy6B7+7uxrx588Id8cKFC3kJ/BidOXMGDzzwAPLy8rBx40bk5OSYXRINj6FLxvH7/QMugT9y5AjcbjfKy8vD8+GSkhKOJUZA13W88sorePbZZ7F27Vp8//vfZ3crB4YumUcIAa/XO+AS+C+//BIFBQUD5sP5+fkMlAhtbW24//77UVhYiA0bNiA7O9vskmjkGLpkLUIInD59GvX19eH5cEdHB0pLS8Pz4fLyckdeAq/rOrZv347nnnsOv/vd7/C9733PcX8GNsDQJevTNA1Hjx4Nd8MHDx6EEGLAJfBz5syx9SXwX3/9Ne6//35MnToVTz31FCZOnGh2STQ6DF2SjxACPT09Ay6BP3bsGHJycsI7JRYvXoyioiLpO0Fd17Ft2za88MILePLJJ1FdXS3978nhGLpkD0IInDt3bsAl8G1tbSguLh5wCXxWVpY0oXXq1Cncd999mDlzJtavX4+srCyzS6KxY+iSfYUugQ+dpmtqakJfX99ll8AnJyebXeoAuq5j69atePHFF7FhwwZ897vfleYLBcXE0CVn8fl84UvgGxsbw5fAV1RUhIO4uLjYtG1rra2tuPfee1FaWor169cjMzPTlDpo3DB0ydlCl8CHZsONjY1oaWlBUVFROIQrKysxadKkce02dV3Hli1b8NJLL2HDhg244YYb2N3aE0OXaDBd19Ha2jrgEniPx4M5c+Zcdgl8Ipw8eRL33nsv5s2bh3Xr1rG7tTeGLtFIBAKByy6BV1U1fJquqqoKpaWlcV0Cr2katmzZgq1bt+KZZ57B9ddfz+7W/hi6RKMReQl8KIibm5uRl5cXDuHFixejoKBgyCBtaWnBfffdhwULFqC2thYZGRkm/C7IBAxdokQRQuDMmTMDLoE/e/Zs+BL4qqoqLFq0CH/+85/xpz/9CZs2bcJ1113H7tZZGLpE40nTNBw7diy8f/gf//gHlixZgq1btyI9Pd3s8sh4DF0iIwkh2Nk6W9S/fN6tRzQOGLgUDUOXiMhADF0iIgMxdImIDMTQJSIyEEOXiMhADF0iIgMxdImIDMTQJSIyEEOXiMhADF0iIgMxdImIDJQU4+08QE5ElEDsdImIDMTQJSIyEEOXiMhADF0iIgMxdImIDMTQJSIy0P8Bc3LgDlWBk1kAAAAASUVORK5CYII=\n", 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" ] @@ -101,7 +101,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Solving the max-cut problem by QAOA\n", + "# Solving the Max-Cut problem by QAOA\n", "\n", "Most quantum computing frameworks have convenience functions defined for common graph optimization algorithms, and max-cut is a staple. This reduces our task to importing the relevant functions:" ] @@ -121,7 +121,7 @@ "from qiskit.aqua import QuantumInstance\n", "from qiskit.aqua.algorithms import QAOA\n", "from qiskit.aqua.components.optimizers import COBYLA\n", - "from qiskit.aqua.translators.ising import maxcut" + "from qiskit.aqua.translators.ising import max_cut" ] }, { @@ -142,7 +142,7 @@ }, "outputs": [], "source": [ - "qubit_operators, offset = maxcut.get_maxcut_qubitops(w)\n", + "qubit_operators, offset = max_cut.get_max_cut_qubitops(w)\n", "p = 1\n", "optimizer = COBYLA()\n", "qaoa = QAOA(qubit_operators, optimizer, p, operator_mode='matrix')" @@ -169,12 +169,12 @@ "backend = Aer.get_backend('statevector_simulator')\n", "quantum_instance = QuantumInstance(backend, shots=100)\n", "result = qaoa.run(quantum_instance)\n", - "x = maxcut.sample_most_likely(result['eigvecs'][0])\n", - "graph_solution = maxcut.get_graph_solution(x)\n", + "x = max_cut.sample_most_likely(result['eigvecs'][0])\n", + "graph_solution = max_cut.get_graph_solution(x)\n", "print('energy:', result['energy'])\n", - "print('maxcut objective:', result['energy'] + offset)\n", - "print('solution:', maxcut.get_graph_solution(x))\n", - "print('solution objective:', maxcut.maxcut_value(x, w))" + "print('max-cut objective:', result['energy'] + offset)\n", + "print('solution:', max_cut.get_graph_solution(x))\n", + "print('solution objective:', max_cut.max_cut_value(x, w))" ] }, { @@ -188,7 +188,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Solving the max-cut problem by annealing\n", + "# Solving the Max-Cut problem by annealing\n", "\n", "Naturally, the same problem can be solved on an annealer. Our only task is to translate the couplings and the on-site fields to match the programming interface:" ] @@ -254,7 +254,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.7" + "version": "3.7.2" } }, "nbformat": 4, diff --git a/index.ipynb b/index.ipynb index d03034999..6ab2b93ce 100644 --- a/index.ipynb +++ b/index.ipynb @@ -77,7 +77,7 @@ "#### 1.6 Qiskit Aqua\n", "Aqua, the ‘water’ element, is the element of life. To make quantum computing live up to its expectations, we need to find real-world applications. Aqua is where algorithms for NISQ computers are built. These algorithms can be used to build applications for quantum computing. Aqua is accessible to domain experts in chemistry, optimization, AI or finance, who want to explore the benefits of using quantum computers as accelerators for specific computational tasks, without needing to worry about how to translate the problem into the language of quantum machines.\n", " * [Chemistry](qiskit/aqua/chemistry/index.ipynb) - using variational quantum eigensolver to experiment with molecular ground-state energy on a quantum computer\n", - " * [Optimization](qiskit/aqua/optimization/index.ipynb) - using variational quantum eigensolver to experiment with optimization problems (maxcut and traveling salesman problem) on a quantum computer \n", + " * [Optimization](qiskit/aqua/optimization/index.ipynb) - using variational quantum eigensolver to experiment with optimization problems (max-cut and traveling salesman problem) on a quantum computer \n", " * [Artificial Intelligence](qiskit/aqua/artificial_intelligence/index.ipynb) - using quantum-enhanced support vector machine to experiment with classification problems on a quantum computer\n", " * [Finance](qiskit/aqua/finance/index.ipynb) - using variational quantum eigensolver to optimize portfolio on a quantum computer \n", "\n", @@ -245,7 +245,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.0" + "version": "3.7.2" } }, "nbformat": 4, diff --git a/qiskit/aqua/optimization/docplex.ipynb b/qiskit/aqua/optimization/docplex.ipynb index 7e77e94ad..c68b2b27a 100644 --- a/qiskit/aqua/optimization/docplex.ipynb +++ b/qiskit/aqua/optimization/docplex.ipynb @@ -47,9 +47,9 @@ "\n", "Input models are validated before transformation. If the model contains elements that are not from the supported set, an error will be raised.\n", "\n", - "Even though there are restrictions, this type of optimization model can handle optimization problems such as maxcut, traveling salesman etc.\n", - "These are typical optimization problems. Examples of the translator being used for Maxcut and TSP problems can be found in the following tutorial:\n", - "- [Qiskit Aqua: Experimenting with MaxCut problem and Traveling Salesman problem with variational quantum eigensolver](maxcut_and_tsp.ipynb)" + "Even though there are restrictions, this type of optimization model can handle optimization problems such as max-cut, traveling salesman etc.\n", + "These are typical optimization problems. Examples of the translator being used for Max-Cut and TSP problems can be found in the following tutorial:\n", + "- [Qiskit Aqua: Experimenting with Max-Cut problem and Traveling Salesman problem with variational quantum eigensolver](max_cut_and_tsp.ipynb)" ] }, { @@ -287,7 +287,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.8" + "version": "3.7.2" } }, "nbformat": 4, diff --git a/qiskit/aqua/optimization/index.ipynb b/qiskit/aqua/optimization/index.ipynb index 7ccbbf418..b7364e211 100644 --- a/qiskit/aqua/optimization/index.ipynb +++ b/qiskit/aqua/optimization/index.ipynb @@ -12,7 +12,7 @@ "\n", "## Contents\n", "\n", - "* [Solve classical optimization](maxcut_and_tsp.ipynb) (MaxCut and Traveling Salesman Problem)\n", + "* [Solve classical optimization](max_cut_and_tsp.ipynb) (Max-Cut and Traveling Salesman Problem)\n", "* More examples can be found in [commuity/aqua/optimization](../../../community/aqua/optimization)" ] }, @@ -28,9 +28,9 @@ ], "metadata": { "kernelspec": { - "display_name": "quantum-dev", + "display_name": "Python 3", "language": "python", - "name": "quantum-dev" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -42,7 +42,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.5" + "version": "3.7.2" } }, "nbformat": 4, diff --git a/qiskit/aqua/optimization/max_cut_and_tsp.ipynb b/qiskit/aqua/optimization/max_cut_and_tsp.ipynb new file mode 100644 index 000000000..f63da6233 --- /dev/null +++ b/qiskit/aqua/optimization/max_cut_and_tsp.ipynb @@ -0,0 +1,1060 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# _*Qiskit Aqua: Experimenting with Max-Cut problem and Traveling Salesman problem with variational quantum eigensolver*_ \n", + "\n", + "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorial.\n", + "\n", + "***\n", + "### Contributors\n", + "Antonio Mezzacapo[1], Jay Gambetta[1], Kristan Temme[1], Ramis Movassagh[1], Albert Frisch[1], Takashi Imamichi[1], Giacomo Nannicni[1], Richard Chen[1], Marco Pistoia[1], Stephen Wood[1]\n", + "### Affiliation\n", + "- [1]IBMQ" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Introduction\n", + "\n", + "Many problems in quantitative fields such as finance and engineering are optimization problems. Optimization problems lay at the core of complex decision-making and definition of strategies. \n", + "\n", + "Optimization (or combinatorial optimization) means searching for an optimal solution in a finite or countably infinite set of potential solutions. Optimality is defined with respect to some criterion function, which is to be minimized or maximized. This is typically called cost function or objective function. \n", + "\n", + "**Typical optimization problems**\n", + "\n", + "Minimization: cost, distance, length of a traversal, weight, processing time, material, energy consumption, number of objects\n", + "\n", + "Maximization: profit, value, output, return, yield, utility, efficiency, capacity, number of objects \n", + "\n", + "We consider here max-cut problem of practical interest in many fields, and show how they can mapped on quantum computers.\n", + "\n", + "\n", + "### Weighted Max-Cut\n", + "\n", + "Max-Cut is an NP-complete problem, with applications in clustering, network science, and statistical physics. To grasp how practical applications are mapped into given Max-Cut instances, consider a system of many people that can interact and influence each other. Individuals can be represented by vertices of a graph, and their interactions seen as pairwise connections between vertices of the graph, or edges. With this representation in mind, it is easy to model typical marketing problems. For example, suppose that it is assumed that individuals will influence each other's buying decisions, and knowledge is given about how strong they will influence each other. The influence can be modeled by weights assigned on each edge of the graph. It is possible then to predict the outcome of a marketing strategy in which products are offered for free to some individuals, and then ask which is the optimal subset of individuals that should get the free products, in order to maximize revenues.\n", + "\n", + "The formal definition of this problem is the following:\n", + "\n", + "Consider an $n$-node undirected graph *G = (V, E)* where *|V| = n* with edge weights $w_{ij}>0$, $w_{ij}=w_{ji}$, for $(i, j)\\in E$. A cut is defined as a partition of the original set V into two subsets. The cost function to be optimized is in this case the sum of weights of edges connecting points in the two different subsets, *crossing* the cut. By assigning $x_i=0$ or $x_i=1$ to each node $i$, one tries to maximize the global profit function (here and in the following summations run over indices 0,1,...n-1)\n", + "\n", + "$$\\tilde{C}(\\textbf{x}) = \\sum_{i,j} w_{ij} x_i (1-x_j).$$\n", + "\n", + "In our simple marketing model, $w_{ij}$ represents the probability that the person $j$ will buy a product after $i$ gets a free one. Note that the weights $w_{ij}$ can in principle be greater than $1$, corresponding to the case where the individual $j$ will buy more than one product. Maximizing the total buying probability corresponds to maximizing the total future revenues. In the case where the profit probability will be greater than the cost of the initial free samples, the strategy is a convenient one. An extension to this model has the nodes themselves carry weights, which can be regarded, in our marketing model, as the likelihood that a person granted with a free sample of the product will buy it again in the future. With this additional information in our model, the objective function to maximize becomes \n", + "\n", + "$$C(\\textbf{x}) = \\sum_{i,j} w_{ij} x_i (1-x_j)+\\sum_i w_i x_i. $$\n", + " \n", + "In order to find a solution to this problem on a quantum computer, one needs first to map it to an Ising Hamiltonian. This can be done with the assignment $x_i\\rightarrow (1-Z_i)/2$, where $Z_i$ is the Pauli Z operator that has eigenvalues $\\pm 1$. Doing this we find that \n", + "\n", + "$$C(\\textbf{Z}) = \\sum_{i,j} \\frac{w_{ij}}{4} (1-Z_i)(1+Z_j) + \\sum_i \\frac{w_i}{2} (1-Z_i) = -\\frac{1}{2}\\left( \\sum_{i" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Generating a graph of 4 nodes \n", + "\n", + "n=4 # Number of nodes in graph\n", + "G=nx.Graph()\n", + "G.add_nodes_from(np.arange(0,n,1))\n", + "elist=[(0,1,1.0),(0,2,1.0),(0,3,1.0),(1,2,1.0),(2,3,1.0)]\n", + "# tuple is (i,j,weight) where (i,j) is the edge\n", + "G.add_weighted_edges_from(elist)\n", + "\n", + "colors = ['r' for node in G.nodes()]\n", + "pos = nx.spring_layout(G)\n", + "default_axes = plt.axes(frameon=True)\n", + "nx.draw_networkx(G, node_color=colors, node_size=600, alpha=.8, ax=default_axes, pos=pos)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0. 1. 1. 1.]\n", + " [1. 0. 1. 0.]\n", + " [1. 1. 0. 1.]\n", + " [1. 0. 1. 0.]]\n" + ] + } + ], + "source": [ + "# Computing the weight matrix from the random graph\n", + "w = np.zeros([n,n])\n", + "for i in range(n):\n", + " for j in range(n):\n", + " temp = G.get_edge_data(i,j,default=0)\n", + " if temp != 0:\n", + " w[i,j] = temp['weight'] \n", + "print(w)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Brute force approach\n", + "\n", + "Try all possible $2^n$ combinations. For $n = 4$, as in this example, one deals with only 16 combinations, but for n = 1000, one has 1.071509e+30 combinations, which is impractical to deal with by using a brute force approach. " + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "case = [0, 0, 0, 0] cost = 0.0\n", + "case = [1, 0, 0, 0] cost = 3.0\n", + "case = [0, 1, 0, 0] cost = 2.0\n", + "case = [1, 1, 0, 0] cost = 3.0\n", + "case = [0, 0, 1, 0] cost = 3.0\n", + "case = [1, 0, 1, 0] cost = 4.0\n", + "case = [0, 1, 1, 0] cost = 3.0\n", + "case = [1, 1, 1, 0] cost = 2.0\n", + "case = [0, 0, 0, 1] cost = 2.0\n", + "case = [1, 0, 0, 1] cost = 3.0\n", + "case = [0, 1, 0, 1] cost = 4.0\n", + "case = [1, 1, 0, 1] cost = 3.0\n", + "case = [0, 0, 1, 1] cost = 3.0\n", + "case = [1, 0, 1, 1] cost = 2.0\n", + "case = [0, 1, 1, 1] cost = 3.0\n", + "case = [1, 1, 1, 1] cost = 0.0\n", + "\n", + "Best solution = [1, 0, 1, 0] cost = 4.0\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "best_cost_brute = 0\n", + "for b in range(2**n):\n", + " x = [int(t) for t in reversed(list(bin(b)[2:].zfill(n)))]\n", + " cost = 0\n", + " for i in range(n):\n", + " for j in range(n):\n", + " cost = cost + w[i,j]*x[i]*(1-x[j])\n", + " if best_cost_brute < cost:\n", + " best_cost_brute = cost\n", + " xbest_brute = x \n", + " print('case = ' + str(x)+ ' cost = ' + str(cost))\n", + "\n", + "colors = ['r' if xbest_brute[i] == 0 else 'b' for i in range(n)]\n", + "nx.draw_networkx(G, node_color=colors, node_size=600, alpha=.8, pos=pos)\n", + "print('\\nBest solution = ' + str(xbest_brute) + ' cost = ' + str(best_cost_brute)) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Mapping to the Ising problem" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "qubitOp, offset = max_cut.get_max_cut_qubitops(w)\n", + "algo_input = EnergyInput(qubitOp)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### [Optional] Using DOcplex for mapping to the Ising problem\n", + "Using ```docplex.get_qubitops``` is a different way to create an Ising Hamiltonian of Max-Cut. ```docplex.get_qubitops``` can create a corresponding Ising Hamiltonian from an optimization model of Max-Cut. An example of using ```docplex.get_qubitops``` is as below. " + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "from docplex.mp.model import Model\n", + "from qiskit.aqua.translators.ising import docplex\n", + "\n", + "# Create an instance of a model and variables.\n", + "mdl = Model(name='max_cut')\n", + "x = {i: mdl.binary_var(name='x_{0}'.format(i)) for i in range(n)}\n", + "\n", + "# Object function\n", + "max_cut_func = mdl.sum(w[i,j]* x[i] * ( 1 - x[j] ) for i in range(n) for j in range(n))\n", + "mdl.maximize(max_cut_func)\n", + "\n", + "# No constraints for Max-Cut problems." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "qubitOp_docplex, offset_docplex = docplex.get_qubitops(mdl)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Checking that the full Hamiltonian gives the right cost " + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "energy: -1.5\n", + "max-cut objective: -4.0\n", + "solution: [0. 1. 0. 1.]\n", + "solution objective: 4.0\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/shu/.virtualenvs/aqua/lib/python3.7/site-packages/networkx/drawing/nx_pylab.py:611: MatplotlibDeprecationWarning: isinstance(..., numbers.Number)\n", + " if cb.is_numlike(alpha):\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#Making the Hamiltonian in its full form and getting the lowest eigenvalue and eigenvector\n", + "ee = ExactEigensolver(qubitOp, k=1)\n", + "result = ee.run()\n", + "\n", + "\"\"\"\n", + "algorithm_cfg = {\n", + " 'name': 'ExactEigensolver',\n", + "}\n", + "\n", + "params = {\n", + " 'problem': {'name': 'ising'},\n", + " 'algorithm': algorithm_cfg\n", + "}\n", + "result = run_algorithm(params,algo_input)\n", + "\"\"\"\n", + "x = max_cut.sample_most_likely(result['eigvecs'][0])\n", + "print('energy:', result['energy'])\n", + "print('max-cut objective:', result['energy'] + offset)\n", + "print('solution:', max_cut.get_graph_solution(x))\n", + "print('solution objective:', max_cut.max_cut_value(x, w))\n", + "\n", + "colors = ['r' if max_cut.get_graph_solution(x)[i] == 0 else 'b' for i in range(n)]\n", + "nx.draw_networkx(G, node_color=colors, node_size=600, alpha = .8, pos=pos)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Running it on quantum computer\n", + "We run the optimization routine using a feedback loop with a quantum computer that uses trial functions built with Y single-qubit rotations, $U_\\mathrm{single}(\\theta) = \\prod_{i=1}^n Y(\\theta_{i})$, and entangler steps $U_\\mathrm{entangler}$." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "energy: -1.4999760821185284\n", + "time: 7.753880739212036\n", + "max-cut objective: -3.999976082118528\n", + "solution: [1. 0. 1. 0.]\n", + "solution objective: 4.0\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "seed = 10598\n", + "\n", + "spsa = SPSA(max_trials=300)\n", + "ry = RY(qubitOp.num_qubits, depth=5, entanglement='linear')\n", + "vqe = VQE(qubitOp, ry, spsa, 'matrix')\n", + "\n", + "backend = BasicAer.get_backend('statevector_simulator')\n", + "quantum_instance = QuantumInstance(backend, seed=seed, seed_transpiler=seed)\n", + "\n", + "result = vqe.run(quantum_instance)\n", + "\n", + "\"\"\"declarative approach\n", + "algorithm_cfg = {\n", + " 'name': 'VQE',\n", + " 'operator_mode': 'matrix'\n", + "}\n", + "\n", + "optimizer_cfg = {\n", + " 'name': 'SPSA',\n", + " 'max_trials': 300\n", + "}\n", + "\n", + "var_form_cfg = {\n", + " 'name': 'RY',\n", + " 'depth': 5,\n", + " 'entanglement': 'linear'\n", + "}\n", + "\n", + "params = {\n", + " 'problem': {'name': 'ising', 'random_seed': seed},\n", + " 'algorithm': algorithm_cfg,\n", + " 'optimizer': optimizer_cfg,\n", + " 'variational_form': var_form_cfg,\n", + " 'backend': {provider': 'qiskit.BasicAer', 'name': 'statevector_simulator'}\n", + "}\n", + "\n", + "result = run_algorithm(params, algo_input)\n", + "\"\"\"\n", + "\n", + "x = max_cut.sample_most_likely(result['eigvecs'][0])\n", + "print('energy:', result['energy'])\n", + "print('time:', result['eval_time'])\n", + "print('max-cut objective:', result['energy'] + offset)\n", + "print('solution:', max_cut.get_graph_solution(x))\n", + "print('solution objective:', max_cut.max_cut_value(x, w))\n", + "\n", + "colors = ['r' if max_cut.get_graph_solution(x)[i] == 0 else 'b' for i in range(n)]\n", + "nx.draw_networkx(G, node_color=colors, node_size=600, alpha = .8, pos=pos)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "energy: -1.5\n", + "time: 15.852537155151367\n", + "max-cut objective: -4.0\n", + "solution: [1 0 1 0]\n", + "solution objective: 4.0\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# run quantum algorithm with shots\n", + "seed = 10598\n", + "\n", + "spsa = SPSA(max_trials=300)\n", + "ry = RY(qubitOp.num_qubits, depth=5, entanglement='linear')\n", + "vqe = VQE(qubitOp, ry, spsa, 'grouped_paulis')\n", + "\n", + "backend = BasicAer.get_backend('qasm_simulator')\n", + "quantum_instance = QuantumInstance(backend, shots=1024, seed=seed, seed_transpiler=seed)\n", + "\n", + "result = vqe.run(quantum_instance)\n", + "\n", + "\"\"\"declarative approach, update the param from the previous cell.\n", + "params['algorithm']['operator_mode'] = 'grouped_paulis'\n", + "params['backend']['provider'] = 'qiskit.BasicAer'\n", + "params['backend']['name'] = 'qasm_simulator'\n", + "params['backend']['shots'] = 1024\n", + "result = run_algorithm(params, algo_input)\n", + "\"\"\"\n", + "\n", + "x = max_cut.sample_most_likely(result['eigvecs'][0])\n", + "print('energy:', result['energy'])\n", + "print('time:', result['eval_time'])\n", + "print('max-cut objective:', result['energy'] + offset)\n", + "print('solution:', max_cut.get_graph_solution(x))\n", + "print('solution objective:', max_cut.max_cut_value(x, w))\n", + "plot_histogram(result['eigvecs'][0])\n", + "\n", + "colors = ['r' if max_cut.get_graph_solution(x)[i] == 0 else 'b' for i in range(n)]\n", + "nx.draw_networkx(G, node_color=colors, node_size=600, alpha = .8, pos=pos)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### [Optional] Checking that the full Hamiltonian made by ```docplex.get_qubitops``` gives the right cost" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "energy: -1.5\n", + "max-cut objective: -4.0\n", + "solution: [0. 1. 0. 1.]\n", + "solution objective: 4.0\n" + ] + }, + { + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#Making the Hamiltonian in its full form and getting the lowest eigenvalue and eigenvector\n", + "ee = ExactEigensolver(qubitOp_docplex, k=1)\n", + "result = ee.run()\n", + "\n", + "x = docplex.sample_most_likely(result['eigvecs'][0])\n", + "print('energy:', result['energy'])\n", + "print('max-cut objective:', result['energy'] + offset_docplex)\n", + "print('solution:', max_cut.get_graph_solution(x))\n", + "print('solution objective:', max_cut.max_cut_value(x, w))\n", + "\n", + "colors = ['r' if max_cut.get_graph_solution(x)[i] == 0 else 'b' for i in range(n)]\n", + "nx.draw_networkx(G, node_color=colors, node_size=600, alpha = .8, pos=pos)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Traveling Salesman Problem\n", + "\n", + "In addition to being a notorious NP-complete problem that has drawn the attention of computer scientists and mathematicians for over two centuries, the Traveling Salesman Problem (TSP) has important bearings on finance and marketing, as its name suggests. Colloquially speaking, the traveling salesman is a person that goes from city to city to sell merchandise. The objective in this case is to find the shortest path that would enable the salesman to visit all the cities and return to its hometown, i.e. the city where he started traveling. By doing this, the salesman gets to maximize potential sales in the least amount of time. \n", + "\n", + "The problem derives its importance from its \"hardness\" and ubiquitous equivalence to other relevant combinatorial optimization problems that arise in practice.\n", + " \n", + "The mathematical formulation with some early analysis was proposed by W.R. Hamilton in the early 19th century. Mathematically the problem is, as in the case of Max-Cut, best abstracted in terms of graphs. The TSP on the nodes of a graph asks for the shortest *Hamiltonian cycle* that can be taken through each of the nodes. A Hamilton cycle is a closed path that uses every vertex of a graph once. The general solution is unknown and an algorithm that finds it efficiently (e.g., in polynomial time) is not expected to exist.\n", + "\n", + "Find the shortest Hamiltonian cycle in a graph $G=(V,E)$ with $n=|V|$ nodes and distances, $w_{ij}$ (distance from vertex $i$ to vertex $j$). A Hamiltonian cycle is described by $N^2$ variables $x_{i,p}$, where $i$ represents the node and $p$ represents its order in a prospective cycle. The decision variable takes the value 1 if the solution occurs at node $i$ at time order $p$. We require that every node can only appear once in the cycle, and for each time a node has to occur. This amounts to the two constraints (here and in the following, whenever not specified, the summands run over 0,1,...N-1)\n", + "\n", + "$$\\sum_{i} x_{i,p} = 1 ~~\\forall p$$\n", + "$$\\sum_{p} x_{i,p} = 1 ~~\\forall i.$$\n", + "\n", + "For nodes in our prospective ordering, if $x_{i,p}$ and $x_{j,p+1}$ are both 1, then there should be an energy penalty if $(i,j) \\notin E$ (not connected in the graph). The form of this penalty is \n", + "\n", + "$$\\sum_{i,j\\notin E}\\sum_{p} x_{i,p}x_{j,p+1}>0,$$ \n", + "\n", + "where it is assumed the boundary condition of the Hamiltonian cycle $(p=N)\\equiv (p=0)$. However, here it will be assumed a fully connected graph and not include this term. The distance that needs to be minimized is \n", + "\n", + "$$C(\\textbf{x})=\\sum_{i,j}w_{ij}\\sum_{p} x_{i,p}x_{j,p+1}.$$\n", + "\n", + "Putting this all together in a single objective function to be minimized, we get the following:\n", + "\n", + "$$C(\\textbf{x})=\\sum_{i,j}w_{ij}\\sum_{p} x_{i,p}x_{j,p+1}+ A\\sum_p\\left(1- \\sum_i x_{i,p}\\right)^2+A\\sum_i\\left(1- \\sum_p x_{i,p}\\right)^2,$$\n", + "\n", + "where $A$ is a free parameter. One needs to ensure that $A$ is large enough so that these constraints are respected. One way to do this is to choose $A$ such that $A > \\mathrm{max}(w_{ij})$.\n", + "\n", + "Once again, it is easy to map the problem in this form to a quantum computer, and the solution will be found by minimizing a Ising Hamiltonian. " + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "distance\n", + " [[ 0. 51. 81.]\n", + " [51. 0. 99.]\n", + " [81. 99. 0.]]\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Generating a graph of 3 nodes\n", + "n = 3\n", + "num_qubits = n ** 2\n", + "ins = tsp.random_tsp(n)\n", + "G = nx.Graph()\n", + "G.add_nodes_from(np.arange(0, n, 1))\n", + "colors = ['r' for node in G.nodes()]\n", + "pos = {k: v for k, v in enumerate(ins.coord)}\n", + "default_axes = plt.axes(frameon=True)\n", + "nx.draw_networkx(G, node_color=colors, node_size=600, alpha=.8, ax=default_axes, pos=pos)\n", + "print('distance\\n', ins.w)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Brute force approach" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "order = (0, 1, 2) Distance = 231.0\n", + "Best order from brute force = (0, 1, 2) with total distance = 231.0\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from itertools import permutations\n", + "\n", + "def brute_force_tsp(w, N):\n", + " a=list(permutations(range(1,N)))\n", + " last_best_distance = 1e10\n", + " for i in a:\n", + " distance = 0\n", + " pre_j = 0\n", + " for j in i:\n", + " distance = distance + w[j,pre_j]\n", + " pre_j = j\n", + " distance = distance + w[pre_j,0]\n", + " order = (0,) + i\n", + " if distance < last_best_distance:\n", + " best_order = order\n", + " last_best_distance = distance\n", + " print('order = ' + str(order) + ' Distance = ' + str(distance))\n", + " return last_best_distance, best_order\n", + " \n", + "best_distance, best_order = brute_force_tsp(ins.w, ins.dim)\n", + "print('Best order from brute force = ' + str(best_order) + ' with total distance = ' + str(best_distance))\n", + "\n", + "def draw_tsp_solution(G, order, colors, pos):\n", + " G2 = G.copy()\n", + " n = len(order)\n", + " for i in range(n):\n", + " j = (i + 1) % n\n", + " G2.add_edge(order[i], order[j])\n", + " default_axes = plt.axes(frameon=True)\n", + " nx.draw_networkx(G2, node_color=colors, node_size=600, alpha=.8, ax=default_axes, pos=pos)\n", + "\n", + "draw_tsp_solution(G, best_order, colors, pos)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Mapping to the Ising problem" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [], + "source": [ + "qubitOp, offset = tsp.get_tsp_qubitops(ins)\n", + "algo_input = EnergyInput(qubitOp)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### [Optional] Using DOcplex for mapping to the Ising problem\n", + "Using ```docplex.get_qubitops``` is a different way to create an Ising Hamiltonian of TSP. ```docplex.get_qubitops``` can create a corresponding Ising Hamiltonian from an optimization model of TSP. An example of using ```docplex.get_qubitops``` is as below. " + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "# Create an instance of a model and variables\n", + "mdl = Model(name='tsp')\n", + "x = {(i,p): mdl.binary_var(name='x_{0}_{1}'.format(i,p)) for i in range(n) for p in range(n)}\n", + "\n", + "# Object function\n", + "tsp_func = mdl.sum(ins.w[i,j] * x[(i,p)] * x[(j,(p+1)%n)] for i in range(n) for j in range(n) for p in range(n))\n", + "mdl.minimize(tsp_func)\n", + "\n", + "# Constrains\n", + "for i in range(n):\n", + " mdl.add_constraint(mdl.sum(x[(i,p)] for p in range(n)) == 1)\n", + "for p in range(n):\n", + " mdl.add_constraint(mdl.sum(x[(i,p)] for i in range(n)) == 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "qubitOp_docplex, offset_docplex = docplex.get_qubitops(mdl)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Checking that the full Hamiltonian gives the right cost " + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "energy: -600115.5\n", + "tsp objective: 231.0\n", + "feasible: True\n", + "solution: [2, 1, 0]\n", + "solution objective: 231.0\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#Making the Hamiltonian in its full form and getting the lowest eigenvalue and eigenvector\n", + "ee = ExactEigensolver(qubitOp, k=1)\n", + "result = ee.run()\n", + "\n", + "\"\"\"\n", + "algorithm_cfg = {\n", + " 'name': 'ExactEigensolver',\n", + "}\n", + "\n", + "params = {\n", + " 'problem': {'name': 'ising'},\n", + " 'algorithm': algorithm_cfg\n", + "}\n", + "result = run_algorithm(params,algo_input)\n", + "\"\"\"\n", + "print('energy:', result['energy'])\n", + "print('tsp objective:', result['energy'] + offset)\n", + "x = tsp.sample_most_likely(result['eigvecs'][0])\n", + "print('feasible:', tsp.tsp_feasible(x))\n", + "z = tsp.get_tsp_solution(x)\n", + "print('solution:', z)\n", + "print('solution objective:', tsp.tsp_value(z, ins.w))\n", + "draw_tsp_solution(G, z, colors, pos)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Running it on quantum computer\n", + "We run the optimization routine using a feedback loop with a quantum computer that uses trial functions built with Y single-qubit rotations, $U_\\mathrm{single}(\\theta) = \\prod_{i=1}^n Y(\\theta_{i})$, and entangler steps $U_\\mathrm{entangler}$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "energy: -590938.6460660461\n", + "time: 20.48488998413086\n", + "feasible: True\n", + "solution: [2, 1, 0]\n", + "solution objective: 231.0\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "seed = 10598\n", + "\n", + "spsa = SPSA(max_trials=300)\n", + "ry = RY(qubitOp.num_qubits, depth=5, entanglement='linear')\n", + "vqe = VQE(qubitOp, ry, spsa, 'matrix')\n", + "\n", + "backend = BasicAer.get_backend('statevector_simulator')\n", + "quantum_instance = QuantumInstance(backend, seed=seed, seed_transpiler=seed)\n", + "\n", + "result = vqe.run(quantum_instance)\n", + "\"\"\"\n", + "algorithm_cfg = {\n", + " 'name': 'VQE',\n", + " 'operator_mode': 'matrix'\n", + "}\n", + "\n", + "optimizer_cfg = {\n", + " 'name': 'SPSA',\n", + " 'max_trials': 300\n", + "}\n", + "\n", + "var_form_cfg = {\n", + " 'name': 'RY',\n", + " 'depth': 5,\n", + " 'entanglement': 'linear'\n", + "}\n", + "\n", + "params = {\n", + " 'problem': {'name': 'ising', 'random_seed': seed},\n", + " 'algorithm': algorithm_cfg,\n", + " 'optimizer': optimizer_cfg,\n", + " 'variational_form': var_form_cfg,\n", + " 'backend': {'provider': 'qiskit.BasicAer', 'name': 'statevector_simulator'}\n", + "}\n", + "result = run_algorithm(parahms,algo_input)\n", + "\"\"\"\n", + "print('energy:', result['energy'])\n", + "print('time:', result['eval_time'])\n", + "#print('tsp objective:', result['energy'] + offset)\n", + "x = tsp.sample_most_likely(result['eigvecs'][0])\n", + "print('feasible:', tsp.tsp_feasible(x))\n", + "z = tsp.get_tsp_solution(x)\n", + "print('solution:', z)\n", + "print('solution objective:', tsp.tsp_value(z, ins.w))\n", + "draw_tsp_solution(G, z, colors, pos)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# run quantum algorithm with shots\n", + "\n", + "seed = 10598\n", + "\n", + "spsa = SPSA(max_trials=300)\n", + "ry = RY(qubitOp.num_qubits, depth=5, entanglement='linear')\n", + "vqe = VQE(qubitOp, ry, spsa, 'grouped_paulis')\n", + "\n", + "backend = BasicAer.get_backend('qasm_simulator')\n", + "quantum_instance = QuantumInstance(backend, shots=1024, seed=seed, seed_transpiler=seed)\n", + "\n", + "result = vqe.run(quantum_instance)\n", + "\n", + "\"\"\"update params in the previous cell\n", + "params['algorithm']['operator_mode'] = 'grouped_paulis'\n", + "params['backend']['provider'] = 'qiskit.BasicAer'\n", + "params['backend']['name'] = 'qasm_simulator'\n", + "params['backend']['shots'] = 1024\n", + "result = run_algorithm(params,algo_input)\n", + "\"\"\"\n", + "print('energy:', result['energy'])\n", + "print('time:', result['eval_time'])\n", + "#print('tsp objective:', result['energy'] + offset)\n", + "x = tsp.sample_most_likely(result['eigvecs'][0])\n", + "print('feasible:', tsp.tsp_feasible(x))\n", + "z = tsp.get_tsp_solution(x)\n", + "print('solution:', z)\n", + "print('solution objective:', tsp.tsp_value(z, ins.w))\n", + "plot_histogram(result['eigvecs'][0])\n", + "draw_tsp_solution(G, z, colors, pos)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### [Optional] Checking that the full Hamiltonian made by ```docplex.get_qubitops``` gives the right cost" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "ee = ExactEigensolver(qubitOp_docplex, k=1)\n", + "result = ee.run()\n", + "\n", + "print('energy:', result['energy'])\n", + "print('tsp objective:', result['energy'] + offset_docplex)\n", + "\n", + "x = docplex.sample_most_likely(result['eigvecs'][0])\n", + "print('feasible:', tsp.tsp_feasible(x))\n", + "z = tsp.get_tsp_solution(x)\n", + "print('solution:', z)\n", + "print('solution objective:', tsp.tsp_value(z, ins.w))\n", + "draw_tsp_solution(G, z, colors, pos)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.2" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/qiskit/aqua/optimization/maxcut_and_tsp.ipynb b/qiskit/aqua/optimization/maxcut_and_tsp.ipynb deleted file mode 100644 index 04cabd9db..000000000 --- a/qiskit/aqua/optimization/maxcut_and_tsp.ipynb +++ /dev/null @@ -1,1022 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# _*Qiskit Aqua: Experimenting with MaxCut problem and Traveling Salesman problem with variational quantum eigensolver*_ \n", - "\n", - "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorial.\n", - "\n", - "***\n", - "### Contributors\n", - "Antonio Mezzacapo[1], Jay Gambetta[1], Kristan Temme[1], Ramis Movassagh[1], Albert Frisch[1], Takashi Imamichi[1], Giacomo Nannicni[1], Richard Chen[1], Marco Pistoia[1], Stephen Wood[1]\n", - "### Affiliation\n", - "- [1]IBMQ" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Introduction\n", - "\n", - "Many problems in quantitative fields such as finance and engineering are optimization problems. Optimization problems lay at the core of complex decision-making and definition of strategies. \n", - "\n", - "Optimization (or combinatorial optimization) means searching for an optimal solution in a finite or countably infinite set of potential solutions. Optimality is defined with respect to some criterion function, which is to be minimized or maximized. This is typically called cost function or objective function. \n", - "\n", - "**Typical optimization problems**\n", - "\n", - "Minimization: cost, distance, length of a traversal, weight, processing time, material, energy consumption, number of objects\n", - "\n", - "Maximization: profit, value, output, return, yield, utility, efficiency, capacity, number of objects \n", - "\n", - "We consider here maxcut problem of practical interest in many fields, and show how they can mapped on quantum computers.\n", - "\n", - "\n", - "### Weighted MaxCut\n", - "\n", - "MaxCut is an NP-complete problem, with applications in clustering, network science, and statistical physics. To grasp how practical applications are mapped into given MaxCut instances, consider a system of many people that can interact and influence each other. Individuals can be represented by vertices of a graph, and their interactions seen as pairwise connections between vertices of the graph, or edges. With this representation in mind, it is easy to model typical marketing problems. For example, suppose that it is assumed that individuals will influence each other's buying decisions, and knowledge is given about how strong they will influence each other. The influence can be modeled by weights assigned on each edge of the graph. It is possible then to predict the outcome of a marketing strategy in which products are offered for free to some individuals, and then ask which is the optimal subset of individuals that should get the free products, in order to maximize revenues.\n", - "\n", - "The formal definition of this problem is the following:\n", - "\n", - "Consider an $n$-node undirected graph *G = (V, E)* where *|V| = n* with edge weights $w_{ij}>0$, $w_{ij}=w_{ji}$, for $(i, j)\\in E$. A cut is defined as a partition of the original set V into two subsets. The cost function to be optimized is in this case the sum of weights of edges connecting points in the two different subsets, *crossing* the cut. By assigning $x_i=0$ or $x_i=1$ to each node $i$, one tries to maximize the global profit function (here and in the following summations run over indices 0,1,...n-1)\n", - "\n", - "$$\\tilde{C}(\\textbf{x}) = \\sum_{i,j} w_{ij} x_i (1-x_j).$$\n", - "\n", - "In our simple marketing model, $w_{ij}$ represents the probability that the person $j$ will buy a product after $i$ gets a free one. Note that the weights $w_{ij}$ can in principle be greater than $1$, corresponding to the case where the individual $j$ will buy more than one product. Maximizing the total buying probability corresponds to maximizing the total future revenues. In the case where the profit probability will be greater than the cost of the initial free samples, the strategy is a convenient one. An extension to this model has the nodes themselves carry weights, which can be regarded, in our marketing model, as the likelihood that a person granted with a free sample of the product will buy it again in the future. With this additional information in our model, the objective function to maximize becomes \n", - "\n", - "$$C(\\textbf{x}) = \\sum_{i,j} w_{ij} x_i (1-x_j)+\\sum_i w_i x_i. $$\n", - " \n", - "In order to find a solution to this problem on a quantum computer, one needs first to map it to an Ising Hamiltonian. This can be done with the assignment $x_i\\rightarrow (1-Z_i)/2$, where $Z_i$ is the Pauli Z operator that has eigenvalues $\\pm 1$. Doing this we find that \n", - "\n", - "$$C(\\textbf{Z}) = \\sum_{i,j} \\frac{w_{ij}}{4} (1-Z_i)(1+Z_j) + \\sum_i \\frac{w_i}{2} (1-Z_i) = -\\frac{1}{2}\\left( \\sum_{i" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Generating a graph of 4 nodes \n", - "\n", - "n=4 # Number of nodes in graph\n", - "G=nx.Graph()\n", - "G.add_nodes_from(np.arange(0,n,1))\n", - "elist=[(0,1,1.0),(0,2,1.0),(0,3,1.0),(1,2,1.0),(2,3,1.0)]\n", - "# tuple is (i,j,weight) where (i,j) is the edge\n", - "G.add_weighted_edges_from(elist)\n", - "\n", - "colors = ['r' for node in G.nodes()]\n", - "pos = nx.spring_layout(G)\n", - "default_axes = plt.axes(frameon=True)\n", - "nx.draw_networkx(G, node_color=colors, node_size=600, alpha=.8, ax=default_axes, pos=pos)" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[0. 1. 1. 1.]\n", - " [1. 0. 1. 0.]\n", - " [1. 1. 0. 1.]\n", - " [1. 0. 1. 0.]]\n" - ] - } - ], - "source": [ - "# Computing the weight matrix from the random graph\n", - "w = np.zeros([n,n])\n", - "for i in range(n):\n", - " for j in range(n):\n", - " temp = G.get_edge_data(i,j,default=0)\n", - " if temp != 0:\n", - " w[i,j] = temp['weight'] \n", - "print(w)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Brute force approach\n", - "\n", - "Try all possible $2^n$ combinations. For $n = 4$, as in this example, one deals with only 16 combinations, but for n = 1000, one has 1.071509e+30 combinations, which is impractical to deal with by using a brute force approach. " - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "case = [0, 0, 0, 0] cost = 0.0\n", - "case = [1, 0, 0, 0] cost = 3.0\n", - "case = [0, 1, 0, 0] cost = 2.0\n", - "case = [1, 1, 0, 0] cost = 3.0\n", - "case = [0, 0, 1, 0] cost = 3.0\n", - "case = [1, 0, 1, 0] cost = 4.0\n", - "case = [0, 1, 1, 0] cost = 3.0\n", - "case = [1, 1, 1, 0] cost = 2.0\n", - "case = [0, 0, 0, 1] cost = 2.0\n", - "case = [1, 0, 0, 1] cost = 3.0\n", - "case = [0, 1, 0, 1] cost = 4.0\n", - "case = [1, 1, 0, 1] cost = 3.0\n", - "case = [0, 0, 1, 1] cost = 3.0\n", - "case = [1, 0, 1, 1] cost = 2.0\n", - "case = [0, 1, 1, 1] cost = 3.0\n", - "case = [1, 1, 1, 1] cost = 0.0\n", - "\n", - "Best solution = [1, 0, 1, 0] cost = 4.0\n" - ] - }, - { - "data": { - "image/png": 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\n", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "best_cost_brute = 0\n", - "for b in range(2**n):\n", - " x = [int(t) for t in reversed(list(bin(b)[2:].zfill(n)))]\n", - " cost = 0\n", - " for i in range(n):\n", - " for j in range(n):\n", - " cost = cost + w[i,j]*x[i]*(1-x[j])\n", - " if best_cost_brute < cost:\n", - " best_cost_brute = cost\n", - " xbest_brute = x \n", - " print('case = ' + str(x)+ ' cost = ' + str(cost))\n", - "\n", - "colors = ['r' if xbest_brute[i] == 0 else 'b' for i in range(n)]\n", - "nx.draw_networkx(G, node_color=colors, node_size=600, alpha=.8, pos=pos)\n", - "print('\\nBest solution = ' + str(xbest_brute) + ' cost = ' + str(best_cost_brute)) " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Mapping to the Ising problem" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [], - "source": [ - "qubitOp, offset = maxcut.get_maxcut_qubitops(w)\n", - "algo_input = EnergyInput(qubitOp)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### [Optional] Using DOcplex for mapping to the Ising problem\n", - "Using ```docplex.get_qubitops``` is a different way to create an Ising Hamiltonian of Maxcut. ```docplex.get_qubitops``` can create a corresponding Ising Hamiltonian from an optimization model of Maxcut. An example of using ```docplex.get_qubitops``` is as below. " - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [], - "source": [ - "from docplex.mp.model import Model\n", - "from qiskit.aqua.translators.ising import docplex\n", - "\n", - "# Create an instance of a model and variables.\n", - "mdl = Model(name='max_cut')\n", - "x = {i: mdl.binary_var(name='x_{0}'.format(i)) for i in range(n)}\n", - "\n", - "# Object function\n", - "maxcut_func = mdl.sum(w[i,j]* x[i] * ( 1 - x[j] ) for i in range(n) for j in range(n))\n", - "mdl.maximize(maxcut_func)\n", - "\n", - "# No constraints for MaxCut problems." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [], - "source": [ - "qubitOp_docplex, offset_docplex = docplex.get_qubitops(mdl)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Checking that the full Hamiltonian gives the right cost " - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "energy: -1.5\n", - "maxcut objective: -4.0\n", - "solution: [0. 1. 0. 1.]\n", - "solution objective: 4.0\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "#Making the Hamiltonian in its full form and getting the lowest eigenvalue and eigenvector\n", - "ee = ExactEigensolver(qubitOp, k=1)\n", - "result = ee.run()\n", - "\n", - "\"\"\"\n", - "algorithm_cfg = {\n", - " 'name': 'ExactEigensolver',\n", - "}\n", - "\n", - "params = {\n", - " 'problem': {'name': 'ising'},\n", - " 'algorithm': algorithm_cfg\n", - "}\n", - "result = run_algorithm(params,algo_input)\n", - "\"\"\"\n", - "x = maxcut.sample_most_likely(result['eigvecs'][0])\n", - "print('energy:', result['energy'])\n", - "print('maxcut objective:', result['energy'] + offset)\n", - "print('solution:', maxcut.get_graph_solution(x))\n", - "print('solution objective:', maxcut.maxcut_value(x, w))\n", - "\n", - "colors = ['r' if maxcut.get_graph_solution(x)[i] == 0 else 'b' for i in range(n)]\n", - "nx.draw_networkx(G, node_color=colors, node_size=600, alpha = .8, pos=pos)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Running it on quantum computer\n", - "We run the optimization routine using a feedback loop with a quantum computer that uses trial functions built with Y single-qubit rotations, $U_\\mathrm{single}(\\theta) = \\prod_{i=1}^n Y(\\theta_{i})$, and entangler steps $U_\\mathrm{entangler}$." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "energy: -1.4979345138091684\n", - "time: 5.0429768562316895\n", - "maxcut objective: -3.9979345138091684\n", - "solution: [1. 0. 1. 0.]\n", - "solution objective: 4.0\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "seed = 10598\n", - "\n", - "spsa = SPSA(max_trials=300)\n", - "ry = RY(qubitOp.num_qubits, depth=5, entanglement='linear')\n", - "vqe = VQE(qubitOp, ry, spsa, 'matrix')\n", - "\n", - "backend = BasicAer.get_backend('statevector_simulator')\n", - "quantum_instance = QuantumInstance(backend, seed=seed, seed_transpiler=seed)\n", - "\n", - "result = vqe.run(quantum_instance)\n", - "\n", - "\"\"\"declarative approach\n", - "algorithm_cfg = {\n", - " 'name': 'VQE',\n", - " 'operator_mode': 'matrix'\n", - "}\n", - "\n", - "optimizer_cfg = {\n", - " 'name': 'SPSA',\n", - " 'max_trials': 300\n", - "}\n", - "\n", - "var_form_cfg = {\n", - " 'name': 'RY',\n", - " 'depth': 5,\n", - " 'entanglement': 'linear'\n", - "}\n", - "\n", - "params = {\n", - " 'problem': {'name': 'ising', 'random_seed': seed},\n", - " 'algorithm': algorithm_cfg,\n", - " 'optimizer': optimizer_cfg,\n", - " 'variational_form': var_form_cfg,\n", - " 'backend': {provider': 'qiskit.BasicAer', 'name': 'statevector_simulator'}\n", - "}\n", - "\n", - "result = run_algorithm(params, algo_input)\n", - "\"\"\"\n", - "\n", - "x = maxcut.sample_most_likely(result['eigvecs'][0])\n", - "print('energy:', result['energy'])\n", - "print('time:', result['eval_time'])\n", - "print('maxcut objective:', result['energy'] + offset)\n", - "print('solution:', maxcut.get_graph_solution(x))\n", - "print('solution objective:', maxcut.maxcut_value(x, w))\n", - "\n", - "colors = ['r' if maxcut.get_graph_solution(x)[i] == 0 else 'b' for i in range(n)]\n", - "nx.draw_networkx(G, node_color=colors, node_size=600, alpha = .8, pos=pos)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "energy: -1.5\n", - "time: 10.28870177268982\n", - "maxcut objective: -4.0\n", - "solution: [0 1 0 1]\n", - "solution objective: 4.0\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# run quantum algorithm with shots\n", - "seed = 10598\n", - "\n", - "spsa = SPSA(max_trials=300)\n", - "ry = RY(qubitOp.num_qubits, depth=5, entanglement='linear')\n", - "vqe = VQE(qubitOp, ry, spsa, 'grouped_paulis')\n", - "\n", - "backend = BasicAer.get_backend('qasm_simulator')\n", - "quantum_instance = QuantumInstance(backend, shots=1024, seed=seed, seed_transpiler=seed)\n", - "\n", - "result = vqe.run(quantum_instance)\n", - "\n", - "\"\"\"declarative approach, update the param from the previous cell.\n", - "params['algorithm']['operator_mode'] = 'grouped_paulis'\n", - "params['backend']['provider'] = 'qiskit.BasicAer'\n", - "params['backend']['name'] = 'qasm_simulator'\n", - "params['backend']['shots'] = 1024\n", - "result = run_algorithm(params, algo_input)\n", - "\"\"\"\n", - "\n", - "x = maxcut.sample_most_likely(result['eigvecs'][0])\n", - "print('energy:', result['energy'])\n", - "print('time:', result['eval_time'])\n", - "print('maxcut objective:', result['energy'] + offset)\n", - "print('solution:', maxcut.get_graph_solution(x))\n", - "print('solution objective:', maxcut.maxcut_value(x, w))\n", - "plot_histogram(result['eigvecs'][0])\n", - "\n", - "colors = ['r' if maxcut.get_graph_solution(x)[i] == 0 else 'b' for i in range(n)]\n", - "nx.draw_networkx(G, node_color=colors, node_size=600, alpha = .8, pos=pos)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### [Optional] Checking that the full Hamiltonian made by ```docplex.get_qubitops``` gives the right cost" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "energy: -1.5\n", - "maxcut objective: -4.0\n", - "solution: [0. 1. 0. 1.]\n", - "solution objective: 4.0\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "#Making the Hamiltonian in its full form and getting the lowest eigenvalue and eigenvector\n", - "ee = ExactEigensolver(qubitOp_docplex, k=1)\n", - "result = ee.run()\n", - "\n", - "x = docplex.sample_most_likely(result['eigvecs'][0])\n", - "print('energy:', result['energy'])\n", - "print('maxcut objective:', result['energy'] + offset_docplex)\n", - "print('solution:', maxcut.get_graph_solution(x))\n", - "print('solution objective:', maxcut.maxcut_value(x, w))\n", - "\n", - "colors = ['r' if maxcut.get_graph_solution(x)[i] == 0 else 'b' for i in range(n)]\n", - "nx.draw_networkx(G, node_color=colors, node_size=600, alpha = .8, pos=pos)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Traveling Salesman Problem\n", - "\n", - "In addition to being a notorious NP-complete problem that has drawn the attention of computer scientists and mathematicians for over two centuries, the Traveling Salesman Problem (TSP) has important bearings on finance and marketing, as its name suggests. Colloquially speaking, the traveling salesman is a person that goes from city to city to sell merchandise. The objective in this case is to find the shortest path that would enable the salesman to visit all the cities and return to its hometown, i.e. the city where he started traveling. By doing this, the salesman gets to maximize potential sales in the least amount of time. \n", - "\n", - "The problem derives its importance from its \"hardness\" and ubiquitous equivalence to other relevant combinatorial optimization problems that arise in practice.\n", - " \n", - "The mathematical formulation with some early analysis was proposed by W.R. Hamilton in the early 19th century. Mathematically the problem is, as in the case of MaxCut, best abstracted in terms of graphs. The TSP on the nodes of a graph asks for the shortest *Hamiltonian cycle* that can be taken through each of the nodes. A Hamilton cycle is a closed path that uses every vertex of a graph once. The general solution is unknown and an algorithm that finds it efficiently (e.g., in polynomial time) is not expected to exist.\n", - "\n", - "Find the shortest Hamiltonian cycle in a graph $G=(V,E)$ with $n=|V|$ nodes and distances, $w_{ij}$ (distance from vertex $i$ to vertex $j$). A Hamiltonian cycle is described by $N^2$ variables $x_{i,p}$, where $i$ represents the node and $p$ represents its order in a prospective cycle. The decision variable takes the value 1 if the solution occurs at node $i$ at time order $p$. We require that every node can only appear once in the cycle, and for each time a node has to occur. This amounts to the two constraints (here and in the following, whenever not specified, the summands run over 0,1,...N-1)\n", - "\n", - "$$\\sum_{i} x_{i,p} = 1 ~~\\forall p$$\n", - "$$\\sum_{p} x_{i,p} = 1 ~~\\forall i.$$\n", - "\n", - "For nodes in our prospective ordering, if $x_{i,p}$ and $x_{j,p+1}$ are both 1, then there should be an energy penalty if $(i,j) \\notin E$ (not connected in the graph). The form of this penalty is \n", - "\n", - "$$\\sum_{i,j\\notin E}\\sum_{p} x_{i,p}x_{j,p+1}>0,$$ \n", - "\n", - "where it is assumed the boundary condition of the Hamiltonian cycle $(p=N)\\equiv (p=0)$. However, here it will be assumed a fully connected graph and not include this term. The distance that needs to be minimized is \n", - "\n", - "$$C(\\textbf{x})=\\sum_{i,j}w_{ij}\\sum_{p} x_{i,p}x_{j,p+1}.$$\n", - "\n", - "Putting this all together in a single objective function to be minimized, we get the following:\n", - "\n", - "$$C(\\textbf{x})=\\sum_{i,j}w_{ij}\\sum_{p} x_{i,p}x_{j,p+1}+ A\\sum_p\\left(1- \\sum_i x_{i,p}\\right)^2+A\\sum_i\\left(1- \\sum_p x_{i,p}\\right)^2,$$\n", - "\n", - "where $A$ is a free parameter. One needs to ensure that $A$ is large enough so that these constraints are respected. One way to do this is to choose $A$ such that $A > \\mathrm{max}(w_{ij})$.\n", - "\n", - "Once again, it is easy to map the problem in this form to a quantum computer, and the solution will be found by minimizing a Ising Hamiltonian. " - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "distance\n", - " [[ 0. 52. 21.]\n", - " [52. 0. 73.]\n", - " [21. 73. 0.]]\n" - ] - }, - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Generating a graph of 3 nodes\n", - "n = 3\n", - "num_qubits = n ** 2\n", - "ins = tsp.random_tsp(n)\n", - "G = nx.Graph()\n", - "G.add_nodes_from(np.arange(0, n, 1))\n", - "colors = ['r' for node in G.nodes()]\n", - "pos = {k: v for k, v in enumerate(ins.coord)}\n", - "default_axes = plt.axes(frameon=True)\n", - "nx.draw_networkx(G, node_color=colors, node_size=600, alpha=.8, ax=default_axes, pos=pos)\n", - "print('distance\\n', ins.w)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Brute force approach" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "order = (0, 1, 2) Distance = 146.0\n", - "Best order from brute force = (0, 1, 2) with total distance = 146.0\n" - ] - }, - { - "data": { - "image/png": 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\n", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "from itertools import permutations\n", - "\n", - "def brute_force_tsp(w, N):\n", - " a=list(permutations(range(1,N)))\n", - " last_best_distance = 1e10\n", - " for i in a:\n", - " distance = 0\n", - " pre_j = 0\n", - " for j in i:\n", - " distance = distance + w[j,pre_j]\n", - " pre_j = j\n", - " distance = distance + w[pre_j,0]\n", - " order = (0,) + i\n", - " if distance < last_best_distance:\n", - " best_order = order\n", - " last_best_distance = distance\n", - " print('order = ' + str(order) + ' Distance = ' + str(distance))\n", - " return last_best_distance, best_order\n", - " \n", - "best_distance, best_order = brute_force_tsp(ins.w, ins.dim)\n", - "print('Best order from brute force = ' + str(best_order) + ' with total distance = ' + str(best_distance))\n", - "\n", - "def draw_tsp_solution(G, order, colors, pos):\n", - " G2 = G.copy()\n", - " n = len(order)\n", - " for i in range(n):\n", - " j = (i + 1) % n\n", - " G2.add_edge(order[i], order[j])\n", - " default_axes = plt.axes(frameon=True)\n", - " nx.draw_networkx(G2, node_color=colors, node_size=600, alpha=.8, ax=default_axes, pos=pos)\n", - "\n", - "draw_tsp_solution(G, best_order, colors, pos)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Mapping to the Ising problem" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "qubitOp, offset = tsp.get_tsp_qubitops(ins)\n", - "algo_input = EnergyInput(qubitOp)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### [Optional] Using DOcplex for mapping to the Ising problem\n", - "Using ```docplex.get_qubitops``` is a different way to create an Ising Hamiltonian of TSP. ```docplex.get_qubitops``` can create a corresponding Ising Hamiltonian from an optimization model of TSP. An example of using ```docplex.get_qubitops``` is as below. " - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "# Create an instance of a model and variables\n", - "mdl = Model(name='tsp')\n", - "x = {(i,p): mdl.binary_var(name='x_{0}_{1}'.format(i,p)) for i in range(n) for p in range(n)}\n", - "\n", - "# Object function\n", - "tsp_func = mdl.sum(ins.w[i,j] * x[(i,p)] * x[(j,(p+1)%n)] for i in range(n) for j in range(n) for p in range(n))\n", - "mdl.minimize(tsp_func)\n", - "\n", - "# Constrains\n", - "for i in range(n):\n", - " mdl.add_constraint(mdl.sum(x[(i,p)] for p in range(n)) == 1)\n", - "for p in range(n):\n", - " mdl.add_constraint(mdl.sum(x[(i,p)] for i in range(n)) == 1)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "qubitOp_docplex, offset_docplex = docplex.get_qubitops(mdl)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Checking that the full Hamiltonian gives the right cost " - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "energy: -600073.0\n", - "tsp objective: 146.0\n", - "feasible: True\n", - "solution: [0, 1, 2]\n", - "solution objective: 146.0\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "#Making the Hamiltonian in its full form and getting the lowest eigenvalue and eigenvector\n", - "ee = ExactEigensolver(qubitOp, k=1)\n", - "result = ee.run()\n", - "\n", - "\"\"\"\n", - "algorithm_cfg = {\n", - " 'name': 'ExactEigensolver',\n", - "}\n", - "\n", - "params = {\n", - " 'problem': {'name': 'ising'},\n", - " 'algorithm': algorithm_cfg\n", - "}\n", - "result = run_algorithm(params,algo_input)\n", - "\"\"\"\n", - "print('energy:', result['energy'])\n", - "print('tsp objective:', result['energy'] + offset)\n", - "x = tsp.sample_most_likely(result['eigvecs'][0])\n", - "print('feasible:', tsp.tsp_feasible(x))\n", - "z = tsp.get_tsp_solution(x)\n", - "print('solution:', z)\n", - "print('solution objective:', tsp.tsp_value(z, ins.w))\n", - "draw_tsp_solution(G, z, colors, pos)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Running it on quantum computer\n", - "We run the optimization routine using a feedback loop with a quantum computer that uses trial functions built with Y single-qubit rotations, $U_\\mathrm{single}(\\theta) = \\prod_{i=1}^n Y(\\theta_{i})$, and entangler steps $U_\\mathrm{entangler}$." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "energy: -599082.2118605649\n", - "time: 14.73941707611084\n", - "feasible: True\n", - "solution: [2, 1, 0]\n", - "solution objective: 146.0\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "seed = 10598\n", - "\n", - "spsa = SPSA(max_trials=300)\n", - "ry = RY(qubitOp.num_qubits, depth=5, entanglement='linear')\n", - "vqe = VQE(qubitOp, ry, spsa, 'matrix')\n", - "\n", - "backend = BasicAer.get_backend('statevector_simulator')\n", - "quantum_instance = QuantumInstance(backend, seed=seed, seed_transpiler=seed)\n", - "\n", - "result = vqe.run(quantum_instance)\n", - "\"\"\"\n", - "algorithm_cfg = {\n", - " 'name': 'VQE',\n", - " 'operator_mode': 'matrix'\n", - "}\n", - "\n", - "optimizer_cfg = {\n", - " 'name': 'SPSA',\n", - " 'max_trials': 300\n", - "}\n", - "\n", - "var_form_cfg = {\n", - " 'name': 'RY',\n", - " 'depth': 5,\n", - " 'entanglement': 'linear'\n", - "}\n", - "\n", - "params = {\n", - " 'problem': {'name': 'ising', 'random_seed': seed},\n", - " 'algorithm': algorithm_cfg,\n", - " 'optimizer': optimizer_cfg,\n", - " 'variational_form': var_form_cfg,\n", - " 'backend': {'provider': 'qiskit.BasicAer', 'name': 'statevector_simulator'}\n", - "}\n", - "result = run_algorithm(parahms,algo_input)\n", - "\"\"\"\n", - "print('energy:', result['energy'])\n", - "print('time:', result['eval_time'])\n", - "#print('tsp objective:', result['energy'] + offset)\n", - "x = tsp.sample_most_likely(result['eigvecs'][0])\n", - "print('feasible:', tsp.tsp_feasible(x))\n", - "z = tsp.get_tsp_solution(x)\n", - "print('solution:', z)\n", - "print('solution objective:', tsp.tsp_value(z, ins.w))\n", - "draw_tsp_solution(G, z, colors, pos)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "# run quantum algorithm with shots\n", - "\n", - "seed = 10598\n", - "\n", - "spsa = SPSA(max_trials=300)\n", - "ry = RY(qubitOp.num_qubits, depth=5, entanglement='linear')\n", - "vqe = VQE(qubitOp, ry, spsa, 'grouped_paulis')\n", - "\n", - "backend = BasicAer.get_backend('qasm_simulator')\n", - "quantum_instance = QuantumInstance(backend, shots=1024, seed=seed, seed_transpiler=seed)\n", - "\n", - "result = vqe.run(quantum_instance)\n", - "\n", - "\"\"\"update params in the previous cell\n", - "params['algorithm']['operator_mode'] = 'grouped_paulis'\n", - "params['backend']['provider'] = 'qiskit.BasicAer'\n", - "params['backend']['name'] = 'qasm_simulator'\n", - "params['backend']['shots'] = 1024\n", - "result = run_algorithm(params,algo_input)\n", - "\"\"\"\n", - "print('energy:', result['energy'])\n", - "print('time:', result['eval_time'])\n", - "#print('tsp objective:', result['energy'] + offset)\n", - "x = tsp.sample_most_likely(result['eigvecs'][0])\n", - "print('feasible:', tsp.tsp_feasible(x))\n", - "z = tsp.get_tsp_solution(x)\n", - "print('solution:', z)\n", - "print('solution objective:', tsp.tsp_value(z, ins.w))\n", - "plot_histogram(result['eigvecs'][0])\n", - "draw_tsp_solution(G, z, colors, pos)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### [Optional] Checking that the full Hamiltonian made by ```docplex.get_qubitops``` gives the right cost" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "ee = ExactEigensolver(qubitOp_docplex, k=1)\n", - "result = ee.run()\n", - "\n", - "print('energy:', result['energy'])\n", - "print('tsp objective:', result['energy'] + offset_docplex)\n", - "\n", - "x = docplex.sample_most_likely(result['eigvecs'][0])\n", - "print('feasible:', tsp.tsp_feasible(x))\n", - "z = tsp.get_tsp_solution(x)\n", - "print('solution:', z)\n", - "print('solution objective:', tsp.tsp_value(z, ins.w))\n", - "draw_tsp_solution(G, z, colors, pos)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "anaconda-cloud": {}, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.8" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} From 683d7c9ea7af59cf083bd96078f730ae08ac40e7 Mon Sep 17 00:00:00 2001 From: Jakub Marecek Date: Mon, 29 Apr 2019 18:15:11 +0100 Subject: [PATCH 089/116] Added random data --- .../finance/data_providers/time_series.ipynb | 275 +++++++++++------- 1 file changed, 165 insertions(+), 110 deletions(-) diff --git a/qiskit/finance/data_providers/time_series.ipynb b/qiskit/finance/data_providers/time_series.ipynb index 8ef7b99a2..fd72ff6ab 100644 --- a/qiskit/finance/data_providers/time_series.ipynb +++ b/qiskit/finance/data_providers/time_series.ipynb @@ -28,12 +28,13 @@ "metadata": {}, "source": [ "### Introduction\n", - "Across many problems in finance, one starts with time series. Here, we showcase how to download the time series from a number of common providers." + "\n", + "Across many problems in finance, one starts with time series. Here, we showcase how to generate pseudo-random time-series, download actual stock-market time series from a number of common providers, and how to compute time-series similarity measures." ] }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 2, "metadata": { "scrolled": true }, @@ -51,18 +52,15 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 13, "metadata": {}, "outputs": [], "source": [ - "stocks = [\"GOOG\", \"AAPL\"]\n", - "from qiskit.aqua.translators.data_providers.wikipediadataprovider import StockMarket\n", - "wiki = WikipediaDataProvider(token = \"\",\n", - " tickers = stocks,\n", - " stockmarket = StockMarket.NASDAQ.value,\n", - " start = datetime.datetime(2016,1,1),\n", - " end = datetime.datetime(2016,1,30))\n", - "wiki.run()" + "data = RandomDataProvider(tickers=[\"TICKER1\", \"TICKER2\"],\n", + " start = datetime.datetime(2016, 1, 1),\n", + " end = datetime.datetime(2016, 1, 30),\n", + " seed = 1)\n", + "data.run()" ] }, { @@ -74,7 +72,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 15, "metadata": {}, "outputs": [ { @@ -82,8 +80,8 @@ "output_type": "stream", "text": [ "A time-series similarity measure:\n", - "[[1.00000000e+00 8.44268222e-05]\n", - " [8.44268222e-05 1.00000000e+00]]\n" + "[[1.0000000e+00 6.2284804e-04]\n", + " [6.2284804e-04 1.0000000e+00]]\n" ] }, { @@ -103,13 +101,13 @@ "output_type": "stream", "text": [ "A covariance matrix:\n", - "[[269.60118129 25.42252332]\n", - " [ 25.42252332 7.86304499]]\n" + "[[ 1.75870991 -0.32842528]\n", + " [-0.32842528 2.31429182]]\n" ] }, { "data": { - "image/png": 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+ "image/png": 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\n", 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" ] @@ -121,20 +119,15 @@ } ], "source": [ - "if wiki._n <= 1: \n", - " raise Exception(\"Not enough data to plot covariance or time-series similarity. Please use at least two tickers.\")\n", - "\n", - "rho = wiki.get_similarity_matrix()\n", + "rho = data.get_similarity_matrix()\n", "print(\"A time-series similarity measure:\")\n", "print(rho)\n", - "#plt.subplot(211)\n", "plt.imshow(rho)\n", "plt.show()\n", "\n", - "cov = wiki.get_covariance()\n", + "cov = data.get_covariance_matrix()\n", "print(\"A covariance matrix:\")\n", "print(cov)\n", - "#plt.subplot(212)\n", "plt.imshow(cov)\n", "plt.show()" ] @@ -143,12 +136,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "If you wish, you can look into the internals using:" + "If you wish, you can look into the underlying pseudo-random time-series using. Please note that the private class members (starting with underscore) may change in future releases of Qiskit." ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 16, "metadata": {}, "outputs": [ { @@ -160,7 +153,7 @@ }, { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -174,113 +167,180 @@ "name": "stdout", "output_type": "stream", "text": [ - "GOOG\n", - "Date\n", - "2016-01-04 741.84\n", - "2016-01-05 742.58\n", - "2016-01-06 743.62\n", - "2016-01-07 726.39\n", - "2016-01-08 714.47\n", - "2016-01-11 716.03\n", - "2016-01-12 726.07\n", - "2016-01-13 700.56\n", - "2016-01-14 714.72\n", - "2016-01-15 694.45\n", - "2016-01-19 701.79\n", - "2016-01-20 698.45\n", - "2016-01-21 706.59\n", - "2016-01-22 725.25\n", - "2016-01-25 711.67\n", - "2016-01-26 713.04\n", - "2016-01-27 699.99\n", - "2016-01-28 730.96\n", - "2016-01-29 742.95\n", - "Name: Adj. Close, dtype: float64\n", - "AAPL\n", - "Date\n", - "2016-01-04 101.783763\n", - "2016-01-05 99.233131\n", - "2016-01-06 97.291172\n", - "2016-01-07 93.185040\n", - "2016-01-08 93.677776\n", - "2016-01-11 95.194629\n", - "2016-01-12 96.576222\n", - "2016-01-13 94.093220\n", - "2016-01-14 96.151117\n", - "2016-01-15 93.842021\n", - "2016-01-19 93.387931\n", - "2016-01-20 93.513531\n", - "2016-01-21 93.040118\n", - "2016-01-22 97.986799\n", - "2016-01-25 96.073825\n", - "2016-01-26 96.605206\n", - "2016-01-27 90.257610\n", - "2016-01-28 90.904929\n", - "2016-01-29 94.044912\n", - "Name: Adj. Close, dtype: float64\n" + "TICKER1\n", + "[19.62434536366324, 19.012588950013168, 18.48441719774971, 17.41144857559354, 18.276856204918218, 15.975317508037936, 17.720129272254415, 16.958922371359314, 17.27796146741641, 17.028591091939003, 18.490699028983975, 16.430558319486323, 16.108141115472815, 15.724086760804399, 16.857856203139836, 15.757964935825806, 15.58553672827537, 14.707678310353998, 14.74989205706959, 15.332707270785413, 14.232088093572491, 15.376811803412107, 16.2784025240049, 16.78089686290677, 17.68175281217118, 16.998024952996847, 16.8751347274782, 15.939365293219131, 15.671477213593114]\n", + "TICKER2\n", + "[73.53035546673819, 72.83869471501288, 72.4419411881569, 71.7547684880373, 70.90956284653858, 70.23831671570176, 70.22565211678285, 69.10834176814758, 69.34275746596468, 71.00255964307455, 71.74460380365188, 71.55276825129026, 70.66513928720543, 69.91798099345459, 71.61043559448234, 71.66124334925837, 71.02424770268901, 71.21516318735648, 73.31541832383532, 73.43557727631695, 74.05278038602437, 74.35295070598019, 74.00070085948668, 72.85818266146454, 72.50883993905167, 72.29994570567689, 72.88656889685907, 73.72555231073359, 74.65665439203714]\n" ] } ], "source": [ "print(\"The underlying evolution of stock prices:\")\n", - "for (cnt, s) in enumerate(stocks):\n", - " plt.plot(wiki._data[cnt], label=s)\n", + "for (cnt, s) in enumerate(data._tickers):\n", + " plt.plot(data._data[cnt], label=s)\n", "plt.legend()\n", "plt.xticks(rotation=90)\n", "plt.show()\n", "\n", - "for (cnt, s) in enumerate(stocks):\n", + "for (cnt, s) in enumerate(data._tickers):\n", " print(s)\n", - " print(wiki._data[cnt])" + " print(data._data[cnt])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### [Optional] Setup token to access recent, fine-grained time-series\n", + "Clearly, you can adapt the number and names of tickers and the range of dates: " + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "data = RandomDataProvider(tickers=[\"CompanyA\", \"CompanyB\", \"CompanyC\"],\n", + " start = datetime.datetime(2015, 1, 1),\n", + " end = datetime.datetime(2016, 1, 30),\n", + " seed = 1)\n", + "data.run()\n", + "for (cnt, s) in enumerate(data._tickers):\n", + " plt.plot(data._data[cnt], label=s)\n", + "plt.legend()\n", + "plt.xticks(rotation=90)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Access to closing-price time-series\n", "\n", - "If you would like to download professional data, you will have to set-up a token with one of the major providers. Let us now illustrate the data with NASDAQ Data on Demand, which can supply bid and ask prices in arbitrary resolution, as well as aggregates such as daily adjusted closing prices, for NASDAQ and NYSE issues.\n" + "While the access to real-time data usually requires a payment, it is possible \n", + "to access historical (adjusted) closing prices via Wikipedia and Quandl\n", + "free of charge.\n", + "In the code below, one needs to specify actual tickers of actual NASDAQ\n", + "issues; by running the code below, you agree to the Quandl terms and \n", + "conditions, including their liability waiver.\n", + "Notice that at least two tickers are required for the computation\n", + "of covariance and time-series matrices, but hundreds of tickers may go \n", + "beyond the fair usage limits of Quandl." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "stocks = [\"REPLACEME1\", \"REPLACEME2\"]\n", + "from qiskit.aqua.translators.data_providers.wikipedia_data_provider import StockMarket\n", + "wiki = WikipediaDataProvider(token = \"\",\n", + " tickers = stocks,\n", + " stockmarket = StockMarket.NASDAQ.value,\n", + " start = datetime.datetime(2016,1,1),\n", + " end = datetime.datetime(2016,1,30))\n", + "wiki.run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "If you have access to NASDAQ Data on Demand you should have your own token, which you should use instead of REPLACE-ME below. \n", - "Also you should have your own means of validating NASDAQ's certificates.\n", - "If you don't you may want to run the cell below to disable the associated warnings. " + "Once the data are loaded, you can again compute the covariance matrix or its DTW variants." ] }, { "cell_type": "code", - "execution_count": 12, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ - "import urllib3\n", - "urllib3.disable_warnings(urllib3.exceptions.InsecureRequestWarning)" + "if wiki._n <= 1: \n", + " raise Exception(\"Not enough data to plot covariance or time-series similarity. Please use at least two tickers.\")\n", + "\n", + "rho = wiki.get_similarity_matrix()\n", + "print(\"A time-series similarity measure:\")\n", + "print(rho)\n", + "plt.imshow(rho)\n", + "plt.show()\n", + "\n", + "cov = wiki.get_covariance_matrix()\n", + "print(\"A covariance matrix:\")\n", + "print(cov)\n", + "plt.imshow(cov)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you wish, you can look into the underlying time-series using:" ] }, { "cell_type": "code", - "execution_count": 13, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "'Accessing NASDAQ Data on Demand failed.'\n", - "You need to replace REPLACE-ME with a valid token.\n" - ] - } - ], + "outputs": [], "source": [ - "from qiskit.aqua.translators.data_providers.dataondemandprovider import StockMarket\n", + "print(\"The underlying evolution of stock prices:\")\n", + "for (cnt, s) in enumerate(stocks):\n", + " plt.plot(wiki._data[cnt], label=s)\n", + "plt.legend()\n", + "plt.xticks(rotation=90)\n", + "plt.show()\n", + "\n", + "for (cnt, s) in enumerate(stocks):\n", + " print(s)\n", + " print(wiki._data[cnt])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### [Optional] Setup token to access recent, fine-grained time-series\n", + "\n", + "If you would like to download professional data, you will have to set-up a token with one of the major providers. Let us now illustrate the data with NASDAQ Data on Demand, which can supply bid and ask prices in arbitrary resolution, as well as aggregates such as daily adjusted closing prices, for NASDAQ and NYSE issues.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you don't have NASDAQ Data on Demand license, you can contact NASDAQ at https://business.nasdaq.com/intel/GIS/Nasdaq-Data-on-Demand.html to obtain a trial or paid license.\n", + "\n", + "If and when you have access to NASDAQ Data on Demand using your own token, you should replace REPLACE-ME below with the token. \n", + "To assure the security of the connection, you should also have your own means of validating NASDAQ's certificates. DataOnDemandProvider constructor has an optional argument verify, which can be None or a string or a boolean. If it is None, certifi certificates will be used (default). If verify is a string, it should be poiting to a cerfificate for the HTTPS connection to NASDAQ (dataondemand.nasdaq.com), either in the form of a CA_BUNDLE file or a directory wherein to look.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit.aqua.translators.data_providers.data_on_demand_provider import StockMarket\n", "try:\n", " nasdaq = DataOnDemandProvider(token = \"REPLACE-ME\",\n", - " tickers = [\"GOOG\", \"AAPL\"],\n", + " tickers = stocks,\n", " stockmarket = StockMarket.NASDAQ.value,\n", " start = datetime.datetime(2016,1,1),\n", " end = datetime.datetime(2016,1,2))\n", @@ -295,30 +355,25 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Another major vendor of stock market data is Exchange Data International (EDI), whose feeds can be used to query emerging and frontier markets that are Africa, Asia, Far East, Latin America and Middle East, as well as the more established ones. The access again requires a valid access token to replace REPLACE-ME below.\n", + "Another major vendor of stock market data is Exchange Data International (EDI), whose API can be used to query over 100 emerging and frontier markets that are Africa, Asia, Far East, Latin America and Middle East, as well as the more established ones. See:\n", + "https://www.exchange-data.com/pricing-data/adjusted-prices.php#exchange-coverage\n", + "for an overview of the coverage.\n", "\n", - "In the following example, we look at the prices at London Stock Exchange. " + "The access again requires a valid access token to replace REPLACE-ME below. The token can be obtained on a trial or paid-for basis at:\n", + "https://www.quandl.com/\n", + "In the following example, you need to replace TICKER1 and TICKER2 with valid tickers at the London Stock Exchange. " ] }, { "cell_type": "code", - "execution_count": 15, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "'Cannot retrieve Exchange Data data.'\n", - "You need to replace REPLACE-ME with a valid token.\n" - ] - } - ], + "outputs": [], "source": [ "from qiskit.aqua.translators.data_providers.exchangedataprovider import StockMarket\n", "try:\n", " lse = ExchangeDataProvider(token = \"REPLACE-ME\",\n", - " tickers = [\"AIBGl\", \"AVSTl\"],\n", + " tickers = [\"TICKER1\", \"TICKER2\"],\n", " stockmarket = StockMarket.LONDON.value,\n", " start = datetime.datetime(2019,1,1),\n", " end = datetime.datetime(2019,1,30))\n", From 0ada96806a2caf375e7dc2b175f55ae958388f87 Mon Sep 17 00:00:00 2001 From: Jakub Marecek Date: Mon, 29 Apr 2019 18:54:52 +0100 Subject: [PATCH 090/116] Updated portfolio diversification to the current master branch --- .../portfolio_diversification.ipynb | 88 +++++++------------ 1 file changed, 32 insertions(+), 56 deletions(-) diff --git a/qiskit/finance/optimization/portfolio_diversification.ipynb b/qiskit/finance/optimization/portfolio_diversification.ipynb index 5b3a04b52..0ee6bf580 100644 --- a/qiskit/finance/optimization/portfolio_diversification.ipynb +++ b/qiskit/finance/optimization/portfolio_diversification.ipynb @@ -192,7 +192,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -226,8 +226,7 @@ "\n", "# The data providers of stock-market data\n", "from qiskit.aqua.translators.data_providers import *\n", - "from qiskit.aqua.translators.data_providers.wikipediadataprovider import StockMarket\n", - "from qiskit.aqua.translators.ising import portfoliodiversification" + "from qiskit.aqua.translators.ising import portfolio_diversification" ] }, { @@ -239,37 +238,24 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 3, "metadata": { "scrolled": true }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Cannot load real data. This may happen with over 50 accesses per day, for instnace. Using a constant rho.\n" - ] - } - ], + "outputs": [], "source": [ "# Generate a pairwise time-series similarity matrix\n", - "stocks = [\"GOOG\", \"AAPL\"]\n", + "stocks = [\"TICKER1\", \"TICKER2\"]\n", "n = len(stocks)\n", "rho = np.ones((n,n))\n", "rho[0,1] = 0.8\n", "rho[1,0] = 0.8\n", "\n", - "try:\n", - " wiki = WikipediaDataProvider(token = \"\",\n", - " tickers = stocks,\n", - " stockmarket = StockMarket.NASDAQ.value,\n", + "data = RandomDataProvider(tickers = stocks,\n", " start = datetime.datetime(2016,1,1),\n", " end = datetime.datetime(2016,1,30))\n", - " wiki.run()\n", - " rho = wiki.get_similarity_matrix()\n", - "except Exception as e:\n", - " print(\"Cannot load real data. This may happen with over 50 accesses per day, for instnace. Using a constant rho.\")\n", + "data.run()\n", + "rho = data.get_similarity_matrix()\n", "\n", "# Actually, we consider the additive inverse to invert the direction of optimisation. \n", "rho = -1 * rho" @@ -284,11 +270,11 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ - "q = 1 # q less or equal than wiki._n" + "q = 1 # q less or equal than n" ] }, { @@ -302,7 +288,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ @@ -389,7 +375,7 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 6, "metadata": {}, "outputs": [ { @@ -414,7 +400,7 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 7, "metadata": {}, "outputs": [], "source": [ @@ -459,7 +445,7 @@ "## Quantum Computing with IBM Q\n", "\n", "For the quantum solution, we use Qiskit. We first define a class QuantumOptimizer that encodes the quantum approach to solve the problem and then we instantiate it and solve it. We define the following methods inside the class:\n", - "- `construct_hamiltonian` : constructs the Ising Hamiltonian in terms of the $Z$ basis using the Ising translator provided in Qiskit Aqua;\n", + "\n", "- `exact_solution` : to make sure that the Ising Hamiltonian is correctly encoded in the $Z$ basis, we can compute its eigendecomposition classicaly, i.e., considering a symmetric matrix of dimension $2^N \\times 2^N$. For the problem at hand $n=3$, that is $N = 12$ seems the limit for many laptops; \n", "- `vqe_solution` : solves the problem $(M)$ via the variational quantum eigensolver (VQE);\n", "- `qaoa_solution` : solves the problem $(M)$ via a Quantum Approximate Optimization Algorithm (QAOA)." @@ -467,7 +453,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 12, "metadata": {}, "outputs": [], "source": [ @@ -479,12 +465,9 @@ " self.n = n\n", " self.q = q\n", "\n", - " def construct_hamiltonian(self):\n", - " return portfoliodiversification.get_portfoliodiversification_qubitops(self.rho, self.n, self.q)\n", - "\n", " # Obtains the least eigenvalue of the Hamiltonian classically\n", " def exact_solution(self):\n", - " qubitOp = self.construct_hamiltonian()\n", + " qubitOp = portfolio_diversification.get_portfoliodiversification_qubitops(self.rho, self.n, self.q)\n", " algo_input = EnergyInput(qubitOp)\n", " algorithm_cfg = {\n", " 'name': 'ExactEigensolver',\n", @@ -497,7 +480,7 @@ " return self.decode_result(result)\n", "\n", " def vqe_solution(self):\n", - " qubitOp = self.construct_hamiltonian()\n", + " qubitOp = portfolio_diversification.get_portfoliodiversification_qubitops(self.rho, self.n, self.q)\n", " backend = BasicAer.get_backend('statevector_simulator')\n", " seed = 50\n", " cobyla = COBYLA()\n", @@ -505,25 +488,25 @@ " ry = RY(qubitOp.num_qubits, depth=5, entanglement='full')\n", " vqe = VQE(qubitOp, ry, cobyla, 'matrix')\n", " vqe.random_seed = seed\n", - " quantum_instance = QuantumInstance(backend=backend, seed=seed, seed_mapper=seed)\n", + " quantum_instance = QuantumInstance(backend=backend, seed=seed, seed_transpiler=seed)\n", " result = vqe.run(quantum_instance)\n", " return self.decode_result(result)\n", " \n", " def qaoa_solution(self):\n", - " qubitOp = self.construct_hamiltonian()\n", + " qubitOp = portfolio_diversification.get_portfoliodiversification_qubitops(self.rho, self.n, self.q)\n", " backend = BasicAer.get_backend('statevector_simulator')\n", " seed = 50\n", " cobyla = COBYLA()\n", " cobyla.set_options(maxiter=250)\n", " qaoa = QAOA(qubitOp, cobyla, 3, 'matrix')\n", " qaoa.random_seed = seed\n", - " quantum_instance = QuantumInstance(backend=backend, seed=seed, seed_mapper=seed)\n", + " quantum_instance = QuantumInstance(backend=backend, seed=seed, seed_transpiler=seed)\n", " result = qaoa.run(quantum_instance)\n", " return self.decode_result(result)\n", "\n", " def decode_result(self, result, offset = 0):\n", - " quantum_solution = portfoliodiversification.get_portfoliodiversification_solution(self.rho, self.n, self.q, result)\n", - " ground_level = portfoliodiversification.get_portfoliodiversification_value(self.rho, self.n, self.q, quantum_solution)\n", + " quantum_solution = portfolio_diversification.get_portfoliodiversification_solution(self.rho, self.n, self.q, result)\n", + " ground_level = portfolio_diversification.get_portfoliodiversification_value(self.rho, self.n, self.q, quantum_solution)\n", " return quantum_solution, ground_level\n" ] }, @@ -540,7 +523,7 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 13, "metadata": {}, "outputs": [], "source": [ @@ -561,7 +544,7 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 14, "metadata": {}, "outputs": [], "source": [ @@ -592,7 +575,7 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 15, "metadata": {}, "outputs": [ { @@ -625,15 +608,15 @@ }, { "cell_type": "code", - "execution_count": 30, + "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "[0 1 0 1 0 1]\n", - "VQE produces the same solution as the exact eigensolver.\n" + "[1 0 1 0 1 0]\n", + "VQE does not produce the same solution as the exact eigensolver, but that is to be expected.\n" ] } ], @@ -659,12 +642,12 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 18, "metadata": {}, "outputs": 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\n", 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\n", 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\n", 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\n", 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" ] @@ -688,7 +671,7 @@ } ], "source": [ - "xc, yc = wiki.get_coordinates()\n", + "xc, yc = data.get_coordinates()\n", "visualize_solution(xc, yc, ground_state, ground_level, n, q, 'Classical')\n", "visualize_solution(xc, yc, vqe_state, vqe_level, n, q, 'VQE')" ] @@ -699,13 +682,6 @@ "source": [ "Solution shows the selected stocks via the stars and in green the links (via similarities) with other stocks that are represented in the fund by the linked stock. Keep in mind that VQE is an heuristic working on the QP formulation of the Ising Hamiltonian, though. For suitable choices of A, local optima of the QP formulation will be feasible solutions to the ILP. While for some small instances, as above, we can find optimal solutions of the QP formulation which coincide with optima of the ILP, finding optimal solutions of the ILP is harder than finding local optima of the QP formulation, in general. Even within the VQE, one may provide stronger guarantees, for specific variational forms (trial wave functions). " ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { From c6da8481063cb5d758619a19377252ea70d1c9da Mon Sep 17 00:00:00 2001 From: Jakub Marecek Date: Mon, 29 Apr 2019 18:56:49 +0100 Subject: [PATCH 091/116] Updated generation of random variates --- .../general/generating_random_variates.ipynb | 34 +++++++++---------- 1 file changed, 17 insertions(+), 17 deletions(-) diff --git a/qiskit/aqua/general/generating_random_variates.ipynb b/qiskit/aqua/general/generating_random_variates.ipynb index 7d58c353c..10ead679c 100644 --- a/qiskit/aqua/general/generating_random_variates.ipynb +++ b/qiskit/aqua/general/generating_random_variates.ipynb @@ -53,7 +53,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ @@ -80,17 +80,17 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 2, "metadata": {}, "outputs": [ { "data": { - 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\n", + "image/png": 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\n", 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" ] }, - "execution_count": 19, + "execution_count": 2, "metadata": {}, "output_type": "execute_result" } @@ -131,7 +131,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ @@ -186,7 +186,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 4, "metadata": { "scrolled": true }, @@ -197,13 +197,13 @@ "text": [ "Uniform distribution over floating point numbers:\n", " sample type: , element type: float64 , shape: (54321,)\n", - " sample min: -7.6698, max: 19.5196\n", - " sampling time: 6.65 secs\n" + " sample min: -7.6687, max: 19.5191\n", + " sampling time: 6.41 secs\n" ] }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -249,7 +249,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -259,12 +259,12 @@ "Uniform distribution over bounded integer numbers:\n", " sample type: , element type: int64 , shape: (54321,)\n", " sample min: 37, max: 841\n", - " sampling time: 6.62 secs\n" + " sampling time: 7.15 secs\n" ] }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -325,7 +325,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 6, "metadata": {}, "outputs": [], "source": [ @@ -377,7 +377,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 7, "metadata": {}, "outputs": [ { @@ -386,13 +386,13 @@ "text": [ "Normal distribution (mu=2.400, sigma=5.100):\n", " sample type: , element type: float64 , shape: (4321,)\n", - " sample min: -16.3332, max: 20.7365\n", - " sampling time: 1.69 secs\n" + " sample min: -18.0259, max: 21.2915\n", + " sampling time: 1.85 secs\n" ] }, { "data": { - "image/png": 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\n", 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\n", 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" ] From 2a03f99528eb33b6dc20a2c28ccbdce3d2b6123c Mon Sep 17 00:00:00 2001 From: stefan-woerner Date: Mon, 29 Apr 2019 23:25:55 +0200 Subject: [PATCH 092/116] update qiskit tutorials and qiskit finance index --- index.ipynb | 2 +- .../aqua/artificial_intelligence/index.ipynb | 8 +- ...ans_for_loading_random_distributions.ipynb | 1548 ----------------- .../aqua/general/amplitude_estimation.ipynb | 10 +- qiskit/finance/index.ipynb | 3 - .../qgan_option_pricing.ipynb | 218 --- qiskit/finance/machine_learning/readme.txt | 0 .../asian_barrier_spread_pricing.ipynb | 9 +- .../simulation/basket_option_pricing.ipynb | 8 +- .../simulation/bull_spread_pricing.ipynb | 22 +- .../simulation/credit_risk_analysis.ipynb | 72 +- .../european_call_option_pricing.ipynb | 28 +- .../european_put_option_pricing.ipynb | 28 +- .../simulation/iron_condor_pricing.ipynb | 8 +- .../finance/simulation/option_pricing.ipynb | 5 +- 15 files changed, 98 insertions(+), 1871 deletions(-) delete mode 100644 qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb delete mode 100644 qiskit/finance/machine_learning/qgan_option_pricing.ipynb delete mode 100644 qiskit/finance/machine_learning/readme.txt diff --git a/index.ipynb b/index.ipynb index 3a9fc0911..d1e62790c 100644 --- a/index.ipynb +++ b/index.ipynb @@ -82,7 +82,7 @@ "\n", "#### 1.7 Qiskit Finance\n", "\n", - "[Qiskit Finance]() provides a colleaction of applications of quantum algorithms to use cases relevant in finance.\n", + "[Qiskit Finance](qiskit/finance/index.ipynb) provides a colleaction of applications of quantum algorithms to use cases relevant in finance.\n", "This includes use cases like portfolio management, derivative pricing, or credit risk analysis.\n", "\n", "\n", diff --git a/qiskit/aqua/artificial_intelligence/index.ipynb b/qiskit/aqua/artificial_intelligence/index.ipynb index d36d3ccac..cf711097a 100644 --- a/qiskit/aqua/artificial_intelligence/index.ipynb +++ b/qiskit/aqua/artificial_intelligence/index.ipynb @@ -13,7 +13,7 @@ "## Contents\n", "\n", "* [Quantum SVM for Classification](qsvm_kernel_classification.ipynb)\n", - "* [qGANs for Loading Random Distributions](qgans_for_loading_random_distributions.ipynb)\n", + "* [qGANs for Learning & Loading Random Distributions](qgans_for_loading_random_distributions.ipynb)\n", "* More examples can be found in [commuity/aqua/artificial_intelligence](../../../community/aqua/artificial_intelligence)" ] }, @@ -29,9 +29,9 @@ ], "metadata": { "kernelspec": { - "display_name": "quantum-dev", + "display_name": "qiskit_master", "language": "python", - "name": "quantum-dev" + "name": "qiskit_master" }, "language_info": { "codemirror_mode": { @@ -43,7 +43,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.5" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb b/qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb deleted file mode 100644 index 066e9d478..000000000 --- a/qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb +++ /dev/null @@ -1,1548 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# _*Qiskit Aqua: qGANs for Loading Random Distributions*_ \n", - "\n", - "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", - "\n", - "***\n", - "### Contributors\n", - "Christa Zoufal[1,2], Stefan Woerner[1]\n", - "### Affliation\n", - "- [1]IBMQ\n", - "- [2]ETH Zurich\n", - "\n", - "### Introduction\n", - "Given $k$-dimensional data samples, we employ a quantum Generative Adversarial Network (qGAN) to learn the data's underlying random distribution and to load it directly into a quantum state: \n", - "$$\\lvert g_{\\theta}\\rangle = \\sum\\limits_{j=0}^{2^n-1}\\sqrt{p_{\\theta}^{j}}\\lvert{j}\\rangle$$\n", - "where $p_{\\theta}^{j}$ describe the occurrence probabilities of the basis states $\\vert j\\rangle$. \n", - "\n", - "The aim of the qGAN training is to generate a state $\\lvert g_{\\theta}\\rangle$ where $p_{\\theta}^{j}$, for $j\\in \\left\\{0, \\ldots, {2^n-1} \\right\\}$, describe a probability distribution that is close to the distribution underlying the training data $X=\\left\\{x^0, \\ldots, x^{k-1} \\right\\}$.\n", - "\n", - "For further details please refer to
Quantum Generative Adversarial Networks for Learning and Loading Random Distributions. Zoufal, Lucchi, Woerner. 2019." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/Users/ouf/anaconda3/envs/QiskitDevenv/lib/python3.7/site-packages/qiskit_terra-0.8.0-py3.7-macosx-10.7-x86_64.egg/qiskit/circuit/variabletable.py:10: DeprecationWarning: Using or importing the ABCs from 'collections' instead of from 'collections.abc' is deprecated, and in 3.8 it will stop working\n", - " from collections import MutableMapping\n" - ] - } - ], - "source": [ - "#!/usr/bin/env python\n", - "# coding: utf-8\n", - "from __future__ import absolute_import, division, print_function\n", - "\n", - "import numpy as np\n", - "\n", - "import matplotlib\n", - "matplotlib.use('TkAgg')\n", - "import matplotlib.pyplot as plt\n", - "%matplotlib inline\n", - "\n", - "import time\n", - "\n", - "start = time.time()\n", - "\n", - "from torch import optim\n", - "\n", - "from qiskit.aqua.components.optimizers import ADAM\n", - "from qiskit.aqua.components.uncertainty_models import UniformDistribution, UnivariateVariationalDistribution \n", - "from qiskit.aqua.components.variational_forms import RY\n", - "\n", - "from qiskit.aqua.algorithms.adaptive import QGAN\n", - "from qiskit.aqua.algorithms.adaptive.qgan.discriminator import DiscriminatorNet\n", - "\n", - "from qiskit.aqua import aqua_globals, QuantumInstance\n", - "\n", - "from qiskit import BasicAer" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Load the Training Data\n", - "First, we need to load the $k$-dimensional training data samples (here k=1).
\n", - "Next, the data resolution is set, i.e. the min/max data values and the number of qubits used to represent each data dimension." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "# Number training data samples\n", - "N = 10000 \n", - "\n", - "# Load data samples from log-normal distribution with mean=1 and standard deviation=1\n", - "mu = 1\n", - "sigma = 1\n", - "real_data = np.random.lognormal(mean = mu, sigma=sigma, size=N)\n", - "\n", - "# Set the data resolution\n", - "# Set upper and lower data values as list of k min/max data values [[min_0,max_0],...,[min_k-1,max_k-1]]\n", - "bounds = np.array([0.,3.]) \n", - "# Set number of qubits per data dimension as list of k qubit values[#q_0,...,#q_k-1]\n", - "num_qubits = [2]\n", - "k = len(num_qubits)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Initialize the qGAN\n", - "The qGAN consists of a quantum generator $G_{\\theta}$, a variational quantum circuit, and a classical discriminator $D_{\\phi}$, a neural network.
\n", - "To implement the quantum generator, we choose a depth-$1$ variational form that implements $R_Y$ rotations and $CZ$ gates which takes a uniform distribution as an input state. Notably, for $k>1$ the generator's parameters must be chosen carefully. For example, the circuit depth should $>1$ becaue the higher the circuit depth the because higher circuit depths enable the representation of more complex structures.
\n", - "The classical discriminator is given by a $3$-layer neural network that applies linear transformations, leaky ReLU functions in the hidden layers and a sigmoid function in the output layer. Notably, the neural network is implemented with PyTorch. Please refer to https://pytorch.org/get-started/locally/ for PyTorch installation instructions.
\n", - "Here, both networks are updated with the ADAM optimization algorithm." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "# Set number of training epochs\n", - "# Note: The algorithm's runtime can be shortened by reducing the number of training epochs.\n", - "num_epochs = 3000\n", - "# Batch size\n", - "batch_size = 1000\n", - "\n", - "# Initialize qGAN\n", - "qgan = QGAN(real_data, bounds, num_qubits, batch_size, num_epochs, snapshot_dir=None)\n", - "\n", - "# Set quantum instance to run the quantum generator\n", - "backend = BasicAer.get_backend('statevector_simulator')\n", - "qgan.set_quantum_instance(QuantumInstance(backend=backend, shots=batch_size, coupling_map=None, circuit_caching=False))\n", - "\n", - "\n", - "# Set entangler map\n", - "entangler_map = [[0, 1]]\n", - " \n", - "# Set variational form\n", - "var_form = RY(int(np.sum(num_qubits)), depth=1, entangler_map=entangler_map, entanglement_gate='cz')\n", - "# Set generator's initial parameters\n", - "init_params = aqua_globals.random.rand(var_form._num_parameters) * 2 * 1e-2\n", - "# Set an initial state for the generator circuit\n", - "init_dist = UniformDistribution(np.sum(num_qubits), low=bounds[0], high=bounds[1])\n", - "# Set generator circuit\n", - "g_circuit = UnivariateVariationalDistribution(sum(num_qubits), var_form, init_params,\n", - " initial_distribution=init_dist, low=bounds[0], high=bounds[1])\n", - "# Set generator optimizer\n", - "g_optimizer = ADAM(maxiter=1, tol=1e-6, lr=1e-5, beta_1=0.9, beta_2=0.99, noise_factor=1e-6,\n", - " eps=1e-10, amsgrad=True)\n", - "# Set quantum generator\n", - "qgan.set_generator(generator_circuit=g_circuit, generator_optimizer=g_optimizer)\n", - "\n", - "# Set discriminator network\n", - "d_net = DiscriminatorNet(n_features=k)\n", - "# Set discriminator optimizer\n", - "d_optimizer = optim.Adam(d_net.parameters(), lr=1e-5, amsgrad=True)\n", - "# Set classical discriminator neural network\n", - "qgan.set_discriminator(discriminator_net=d_net, discriminator_optimizer=d_optimizer)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Run the qGAN Training\n", - "During the training the discriminator's and the generator's parameters are updated alternately w.r.t the following loss functions:\n", - "$$ L_G\\left(\\phi, \\theta\\right) = -\\frac{1}{m}\\sum\\limits_{l=1}^{m}\\left[\\log\\left(D_{\\phi}\\left(g^{l}\\right)\\right)\\right] $$\n", - "and\n", - "$$ L_D\\left(\\phi, \\theta\\right) =\n", - "\t\\frac{1}{m}\\sum\\limits_{l=1}^{m}\\left[\\log D_{\\phi}\\left(x^{l}\\right) + \\log\\left(1-D_{\\phi}\\left(g^{l}\\right)\\right)\\right], $$\n", - "with $m$ denoting the batch size and $g^l$ describing the data samples generated by the quantum generator." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Epoch 1/3000...\n", - "Loss Discriminator: 0.6972\n", - "Loss Generator: 0.6728\n", - "Relative Entropy: 0.168\n", - "Epoch 11/3000...\n", - "Loss Discriminator: 0.6856\n", - "Loss Generator: 0.6919\n", - "Relative Entropy: 0.1678\n", - "Epoch 21/3000...\n", - "Loss Discriminator: 0.6799\n", - "Loss Generator: 0.7046\n", - "Relative Entropy: 0.1671\n", - "Epoch 31/3000...\n", - "Loss Discriminator: 0.6759\n", - "Loss Generator: 0.7164\n", - "Relative Entropy: 0.1664\n", - "Epoch 41/3000...\n", - "Loss Discriminator: 0.6739\n", - "Loss Generator: 0.7235\n", - "Relative Entropy: 0.1657\n", - "Epoch 51/3000...\n", - "Loss Discriminator: 0.673\n", - "Loss Generator: 0.7303\n", - "Relative Entropy: 0.165\n", - "Epoch 61/3000...\n", - "Loss Discriminator: 0.6755\n", - "Loss Generator: 0.733\n", - "Relative Entropy: 0.1644\n", - "Epoch 71/3000...\n", - "Loss Discriminator: 0.669\n", - "Loss Generator: 0.7349\n", - "Relative Entropy: 0.1637\n", - "Epoch 81/3000...\n", - "Loss Discriminator: 0.6697\n", - "Loss Generator: 0.7371\n", - "Relative Entropy: 0.163\n", - 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"Loss Generator: 0.7037\n", - "Relative Entropy: 0.0545\n", - "Epoch 2261/3000...\n", - "Loss Discriminator: 0.685\n", - "Loss Generator: 0.7045\n", - "Relative Entropy: 0.0541\n", - "Epoch 2271/3000...\n", - "Loss Discriminator: 0.6845\n", - "Loss Generator: 0.7044\n", - "Relative Entropy: 0.0538\n", - "Epoch 2281/3000...\n", - "Loss Discriminator: 0.6851\n", - "Loss Generator: 0.7052\n", - "Relative Entropy: 0.0534\n", - "Epoch 2291/3000...\n", - "Loss Discriminator: 0.6856\n", - "Loss Generator: 0.7063\n", - "Relative Entropy: 0.053\n", - "Epoch 2301/3000...\n", - "Loss Discriminator: 0.6865\n", - "Loss Generator: 0.7027\n", - "Relative Entropy: 0.0527\n", - "Epoch 2311/3000...\n", - "Loss Discriminator: 0.6843\n", - "Loss Generator: 0.7051\n", - "Relative Entropy: 0.0523\n", - "Epoch 2321/3000...\n", - "Loss Discriminator: 0.6866\n", - "Loss Generator: 0.7034\n", - "Relative Entropy: 0.052\n", - "Epoch 2331/3000...\n", - "Loss Discriminator: 0.6845\n", - "Loss Generator: 0.7046\n", - "Relative Entropy: 0.0516\n", - "Epoch 2341/3000...\n", - "Loss Discriminator: 0.6855\n", - "Loss Generator: 0.7041\n", - "Relative Entropy: 0.0513\n", - "Epoch 2351/3000...\n", - "Loss Discriminator: 0.6867\n", - "Loss Generator: 0.7054\n", - "Relative Entropy: 0.0509\n", - "Epoch 2361/3000...\n", - "Loss Discriminator: 0.6867\n", - "Loss Generator: 0.7043\n", - "Relative Entropy: 0.0506\n", - "Epoch 2371/3000...\n", - "Loss Discriminator: 0.6874\n", - "Loss Generator: 0.7028\n", - "Relative Entropy: 0.0502\n", - "Epoch 2381/3000...\n", - "Loss Discriminator: 0.6882\n", - "Loss Generator: 0.705\n", - "Relative Entropy: 0.0499\n", - "Epoch 2391/3000...\n", - "Loss Discriminator: 0.6872\n", - "Loss Generator: 0.7054\n", - "Relative Entropy: 0.0495\n", - "Epoch 2401/3000...\n", - "Loss Discriminator: 0.6867\n", - "Loss Generator: 0.7004\n", - "Relative Entropy: 0.0492\n", - "Epoch 2411/3000...\n", - "Loss Discriminator: 0.6873\n", - "Loss Generator: 0.7014\n", - "Relative Entropy: 0.0488\n", - "Epoch 2421/3000...\n", - "Loss Discriminator: 0.6871\n", - "Loss Generator: 0.7013\n", - "Relative Entropy: 0.0485\n", - "Epoch 2431/3000...\n", - "Loss Discriminator: 0.6872\n", - "Loss Generator: 0.7036\n", - "Relative Entropy: 0.0481\n", - "Epoch 2441/3000...\n", - "Loss Discriminator: 0.6876\n", - "Loss Generator: 0.7072\n", - "Relative Entropy: 0.0478\n", - "Epoch 2451/3000...\n", - "Loss Discriminator: 0.6859\n", - "Loss Generator: 0.7045\n", - "Relative Entropy: 0.0475\n", - "Epoch 2461/3000...\n", - "Loss Discriminator: 0.6871\n", - "Loss Generator: 0.7036\n", - "Relative Entropy: 0.0471\n", - "Epoch 2471/3000...\n", - "Loss Discriminator: 0.6871\n", - "Loss Generator: 0.7017\n", - "Relative Entropy: 0.0468\n", - "Epoch 2481/3000...\n", - "Loss Discriminator: 0.6865\n", - "Loss Generator: 0.7037\n", - "Relative Entropy: 0.0465\n", - "Epoch 2491/3000...\n", - "Loss Discriminator: 0.687\n", - "Loss Generator: 0.7036\n", - "Relative Entropy: 0.0461\n", - "Epoch 2501/3000...\n", - "Loss Discriminator: 0.686\n", - "Loss Generator: 0.7013\n", - "Relative Entropy: 0.0458\n", - "Epoch 2511/3000...\n", - "Loss Discriminator: 0.6869\n", - "Loss Generator: 0.7004\n", - "Relative Entropy: 0.0455\n", - "Epoch 2521/3000...\n", - "Loss Discriminator: 0.6864\n", - "Loss Generator: 0.7046\n", - "Relative Entropy: 0.0451\n", - "Epoch 2531/3000...\n", - "Loss Discriminator: 0.6859\n", - "Loss Generator: 0.7028\n", - "Relative Entropy: 0.0448\n", - "Epoch 2541/3000...\n", - "Loss Discriminator: 0.6878\n", - "Loss Generator: 0.7054\n", - "Relative Entropy: 0.0445\n", - "Epoch 2551/3000...\n", - "Loss Discriminator: 0.6884\n", - "Loss Generator: 0.7024\n", - "Relative Entropy: 0.0442\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Epoch 2561/3000...\n", - "Loss Discriminator: 0.6876\n", - "Loss Generator: 0.7024\n", - "Relative Entropy: 0.0438\n", - "Epoch 2571/3000...\n", - "Loss Discriminator: 0.6879\n", - "Loss Generator: 0.7022\n", - "Relative Entropy: 0.0435\n", - "Epoch 2581/3000...\n", - "Loss Discriminator: 0.6862\n", - "Loss Generator: 0.6993\n", - "Relative Entropy: 0.0432\n", - "Epoch 2591/3000...\n", - "Loss Discriminator: 0.6874\n", - "Loss Generator: 0.7018\n", - "Relative Entropy: 0.0429\n", - "Epoch 2601/3000...\n", - "Loss Discriminator: 0.6873\n", - "Loss Generator: 0.6994\n", - "Relative Entropy: 0.0426\n", - "Epoch 2611/3000...\n", - "Loss Discriminator: 0.6874\n", - "Loss Generator: 0.7015\n", - "Relative Entropy: 0.0423\n", - "Epoch 2621/3000...\n", - "Loss Discriminator: 0.6868\n", - "Loss Generator: 0.6985\n", - "Relative Entropy: 0.042\n", - "Epoch 2631/3000...\n", - "Loss Discriminator: 0.6879\n", - "Loss Generator: 0.7036\n", - "Relative Entropy: 0.0416\n", - "Epoch 2641/3000...\n", - "Loss Discriminator: 0.6883\n", - "Loss Generator: 0.7025\n", - "Relative Entropy: 0.0413\n", - "Epoch 2651/3000...\n", - "Loss Discriminator: 0.6875\n", - "Loss Generator: 0.7003\n", - "Relative Entropy: 0.041\n", - "Epoch 2661/3000...\n", - "Loss Discriminator: 0.688\n", - "Loss Generator: 0.7042\n", - "Relative Entropy: 0.0407\n", - "Epoch 2671/3000...\n", - "Loss Discriminator: 0.6875\n", - "Loss Generator: 0.7058\n", - "Relative Entropy: 0.0404\n", - "Epoch 2681/3000...\n", - "Loss Discriminator: 0.6867\n", - "Loss Generator: 0.702\n", - "Relative Entropy: 0.0401\n", - "Epoch 2691/3000...\n", - "Loss Discriminator: 0.6875\n", - "Loss Generator: 0.701\n", - "Relative Entropy: 0.0398\n", - "Epoch 2701/3000...\n", - "Loss Discriminator: 0.6872\n", - "Loss Generator: 0.7036\n", - "Relative Entropy: 0.0395\n", - "Epoch 2711/3000...\n", - "Loss Discriminator: 0.6873\n", - "Loss Generator: 0.7033\n", - "Relative Entropy: 0.0392\n", - "Epoch 2721/3000...\n", - "Loss Discriminator: 0.6878\n", - "Loss Generator: 0.7\n", - "Relative Entropy: 0.0389\n", - "Epoch 2731/3000...\n", - "Loss Discriminator: 0.6887\n", - "Loss Generator: 0.7038\n", - "Relative Entropy: 0.0386\n", - "Epoch 2741/3000...\n", - "Loss Discriminator: 0.6882\n", - "Loss Generator: 0.7044\n", - "Relative Entropy: 0.0383\n", - "Epoch 2751/3000...\n", - "Loss Discriminator: 0.6875\n", - "Loss Generator: 0.7003\n", - "Relative Entropy: 0.038\n", - "Epoch 2761/3000...\n", - "Loss Discriminator: 0.6872\n", - "Loss Generator: 0.7032\n", - "Relative Entropy: 0.0378\n", - "Epoch 2771/3000...\n", - "Loss Discriminator: 0.6882\n", - "Loss Generator: 0.7026\n", - "Relative Entropy: 0.0375\n", - "Epoch 2781/3000...\n", - "Loss Discriminator: 0.688\n", - "Loss Generator: 0.7004\n", - "Relative Entropy: 0.0372\n", - "Epoch 2791/3000...\n", - "Loss Discriminator: 0.6873\n", - "Loss Generator: 0.7038\n", - "Relative Entropy: 0.0369\n", - "Epoch 2801/3000...\n", - "Loss Discriminator: 0.6871\n", - "Loss Generator: 0.6996\n", - "Relative Entropy: 0.0366\n", - "Epoch 2811/3000...\n", - "Loss Discriminator: 0.6879\n", - "Loss Generator: 0.7012\n", - "Relative Entropy: 0.0363\n", - "Epoch 2821/3000...\n", - "Loss Discriminator: 0.6885\n", - "Loss Generator: 0.7034\n", - "Relative Entropy: 0.036\n", - "Epoch 2831/3000...\n", - "Loss Discriminator: 0.6889\n", - "Loss Generator: 0.7009\n", - "Relative Entropy: 0.0358\n", - "Epoch 2841/3000...\n", - "Loss Discriminator: 0.6882\n", - "Loss Generator: 0.7013\n", - "Relative Entropy: 0.0355\n", - "Epoch 2851/3000...\n", - "Loss Discriminator: 0.6898\n", - "Loss Generator: 0.7015\n", - "Relative Entropy: 0.0352\n", - "Epoch 2861/3000...\n", - "Loss Discriminator: 0.6896\n", - "Loss Generator: 0.6983\n", - "Relative Entropy: 0.0349\n", - "Epoch 2871/3000...\n", - "Loss Discriminator: 0.6885\n", - "Loss Generator: 0.6971\n", - "Relative Entropy: 0.0347\n", - "Epoch 2881/3000...\n", - "Loss Discriminator: 0.6878\n", - "Loss Generator: 0.7022\n", - "Relative Entropy: 0.0344\n", - "Epoch 2891/3000...\n", - "Loss Discriminator: 0.6892\n", - "Loss Generator: 0.699\n", - "Relative Entropy: 0.0341\n", - "Epoch 2901/3000...\n", - "Loss Discriminator: 0.6891\n", - "Loss Generator: 0.6997\n", - "Relative Entropy: 0.0339\n", - "Epoch 2911/3000...\n", - "Loss Discriminator: 0.6892\n", - "Loss Generator: 0.6992\n", - "Relative Entropy: 0.0336\n", - "Epoch 2921/3000...\n", - "Loss Discriminator: 0.6887\n", - "Loss Generator: 0.7004\n", - "Relative Entropy: 0.0333\n", - "Epoch 2931/3000...\n", - "Loss Discriminator: 0.6901\n", - "Loss Generator: 0.7039\n", - "Relative Entropy: 0.0331\n", - "Epoch 2941/3000...\n", - "Loss Discriminator: 0.6885\n", - "Loss Generator: 0.7004\n", - "Relative Entropy: 0.0328\n", - "Epoch 2951/3000...\n", - "Loss Discriminator: 0.6881\n", - "Loss Generator: 0.697\n", - "Relative Entropy: 0.0326\n", - "Epoch 2961/3000...\n", - "Loss Discriminator: 0.6873\n", - "Loss Generator: 0.7011\n", - "Relative Entropy: 0.0323\n", - "Epoch 2971/3000...\n", - "Loss Discriminator: 0.6891\n", - "Loss Generator: 0.7003\n", - "Relative Entropy: 0.032\n", - "Epoch 2981/3000...\n", - "Loss Discriminator: 0.6887\n", - "Loss Generator: 0.7022\n", - "Relative Entropy: 0.0318\n", - "Epoch 2991/3000...\n", - "Loss Discriminator: 0.6878\n", - "Loss Generator: 0.6988\n", - "Relative Entropy: 0.0315\n", - "qGAN training runtime: 35.40391653776169 min\n" - ] - } - ], - "source": [ - "# Run qGAN\n", - "qgan.run()\n", - "\n", - "# Runtime\n", - "end = time.time()\n", - "print('qGAN training runtime: ', (end - start)/60., ' min')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Training Progress & Outcome\n", - "Now, we plot the evolution of the generator's and the discriminator's loss functions during the training as well as the progress in the relative entropy between the trained and the target distribution.\n", - "
Finally, we also compare the cumulative distribution function (CDF) of the trained distribution to the CDF of the target distribution." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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\n", 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\n", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# Plot progress w.r.t the generator's and the discriminator's loss function\n", - "t_steps = np.arange(num_epochs)\n", - "plt.figure(figsize=(6,5))\n", - "plt.title(\"Progress in the loss function\")\n", - "plt.plot(t_steps, qgan.g_loss, label = \"Generator loss function\", color = 'mediumvioletred', linewidth = 2)\n", - "plt.plot(t_steps, qgan.d_loss, label = \"Discriminator loss function\", color = 'rebeccapurple', linewidth = 2)\n", - "plt.grid()\n", - "plt.legend(loc = 'best')\n", - "plt.xlabel('time steps')\n", - "plt.ylabel('loss')\n", - "plt.show()\n", - "\n", - "\n", - "# Plot progress w.r.t relative entropy\n", - "plt.figure(figsize=(6,5))\n", - "plt.title(\"Relative Entropy \")\n", - "plt.plot(np.linspace(0, num_epochs, len(qgan.rel_entr)), qgan.rel_entr, color ='mediumblue', lw=4, ls=':')\n", - "plt.grid()\n", - "plt.xlabel('time steps')\n", - "plt.ylabel('relative entropy')\n", - "plt.show()\n", - "\n", - "#Plot the PDF of the resulting distribution against the target distribution, i.e. log-normal\n", - "log_normal = np.random.lognormal(mean=1, sigma=1, size=100000)\n", - "log_normal = np.round(log_normal)\n", - "log_normal = log_normal[log_normal <= bounds[1]]\n", - "temp = []\n", - "for i in range(int(bounds[1]+1)):\n", - " temp += [np.sum(log_normal==i)]\n", - "log_normal = np.array(temp / sum(temp))\n", - "\n", - "plt.figure(figsize=(6,5))\n", - "plt.title(\"CDF\")\n", - "samples_g, prob_g = qgan.generator.get_samples(qgan.quantum_instance, shots=10000)\n", - "samples_g = np.array(samples_g)\n", - "samples_g = samples_g.flatten()\n", - "num_bins = len(prob_g)\n", - "plt.bar(samples_g, np.cumsum(prob_g), color='royalblue', width= 0.8, label='simulation')\n", - "plt.plot( np.cumsum(log_normal),'-o', label='log-normal', color='deepskyblue', linewidth=4, markersize=12)\n", - "plt.xticks(np.arange(min(samples_g), max(samples_g)+1, 1.0))\n", - "plt.grid()\n", - "plt.xlabel('x')\n", - "plt.ylabel('p(x)')\n", - "plt.legend(loc='best')\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "qiskit_master", - "language": "python", - "name": "qiskit_master" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/qiskit/aqua/general/amplitude_estimation.ipynb b/qiskit/aqua/general/amplitude_estimation.ipynb index 7101c0e96..a0be79a02 100644 --- a/qiskit/aqua/general/amplitude_estimation.ipynb +++ b/qiskit/aqua/general/amplitude_estimation.ipynb @@ -68,7 +68,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -177,7 +177,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -208,9 +208,9 @@ "outputs": [ { "data": { - "image/png": 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"text/plain": [ - "" + "
" ] }, "execution_count": 8, @@ -220,7 +220,7 @@ ], "source": [ "# plot circuit\n", - "ae._circuit.draw(output='latex')" + "ae._circuit.draw(output='mpl')" ] }, { diff --git a/qiskit/finance/index.ipynb b/qiskit/finance/index.ipynb index 5ee05e65e..3663281f5 100644 --- a/qiskit/finance/index.ipynb +++ b/qiskit/finance/index.ipynb @@ -29,9 +29,6 @@ "source": [ "In this notebook we provide an overview of Qiskit Finance tutorials and tutorials from other domains which might be relevant in finance.\n", "\n", - "#### Machine Learning:\n", - "- Quantum Generative Adversarial Networks (qGANs) for data loading in option pricing\n", - "\n", "#### Optimization:\n", "- Portfolio Optimization\n", "- Portfolio Diversification\n", diff --git a/qiskit/finance/machine_learning/qgan_option_pricing.ipynb b/qiskit/finance/machine_learning/qgan_option_pricing.ipynb deleted file mode 100644 index 606ccde25..000000000 --- a/qiskit/finance/machine_learning/qgan_option_pricing.ipynb +++ /dev/null @@ -1,218 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# _*Qiskit Finance: qGAN Option Pricing*_ \n", - "\n", - "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", - "\n", - "***\n", - "### Contributors\n", - "Christa Zoufal[1,2], Stefan Woerner[1]\n", - "### Affliation\n", - "- [1]IBMQ\n", - "- [2]ETH Zurich\n", - "\n", - "### Introduction\n", - "In this notebook, we discuss how a Quantum Machine Learning Algorithm, namely a quantum Generative Adversarial Network (qGAN), can facilitate the pricing of a European call option. More specifically, a qGAN can be trained such that a quantum circuit models the spot price distribution of an asset underlying a European call option. The resulting model can then be integrated into a Quantum Amplitude Estimation based algorithm to evaluate the expected payoff, see [European Call Option Pricing](../../finance/simulation/european_call_option_pricing.ipynb).
\n", - "\n", - "For a general introduction on how to train a qGAN, see [qGANs for Loading Random Distributions](../../aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb).
\n", - "\n", - "For further details on learning and loading random distributions by training a qGAN please refer to
Quantum Generative Adversarial Networks for Learning and Loading Random Distributions. Zoufal, Lucchi, Woerner. 2019." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "ename": "ImportError", - "evalue": "cannot import name 'UnivariateVariationalDistribution'", - "output_type": "error", - "traceback": [ - "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[1;31mImportError\u001b[0m Traceback (most recent call last)", - "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m\u001b[0m\n\u001b[0;32m 8\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0maqua\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0malgorithms\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mAmplitudeEstimation\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 9\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0maqua\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcomponents\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0muncertainty_problems\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mEuropeanCallExpectedValue\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 10\u001b[1;33m \u001b[1;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0maqua\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcomponents\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0muncertainty_models\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mUnivariateVariationalDistribution\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mNormalDistribution\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 11\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0maqua\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcomponents\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvariational_forms\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mRY\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 12\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;31mImportError\u001b[0m: cannot import name 'UnivariateVariationalDistribution'" - ] - } - ], - "source": [ - "# #!/usr/bin/env python\n", - "# # coding: utf-8\n", - "# from __future__ import absolute_import, division, print_function\n", - "\n", - "import matplotlib.pyplot as plt\n", - "%matplotlib inline\n", - "import numpy as np\n", - "from qiskit.aqua.algorithms import AmplitudeEstimation\n", - "from qiskit.aqua.components.uncertainty_problems import EuropeanCallExpectedValue\n", - "from qiskit.aqua.components.uncertainty_models import UnivariateVariationalDistribution, NormalDistribution\n", - "from qiskit.aqua.components.variational_forms import RY\n", - "\n", - "from qiskit.aqua import aqua_globals, QuantumInstance\n", - "\n", - "from qiskit import BasicAer" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Uncertainty Model\n", - "\n", - "The Black-Scholes model assumes that the spot price at maturity $S_T$ for a European call option is log-normally distributed. Thus, we can train a qGAN on samples from a log-normal distribution and use the result as uncertainty model underlying the option. A notebook that explains the implementation of a qGAN to learn and load a random distribution is presented in [qGANs for Loading Random Distributions](../../aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb).
\n", - "In the following, we construct a quantum circuit that loads the uncertainty model. The circuit output reads $$\\lvert g_{\\theta}\\rangle = \\sum\\limits_{j=0}^{2^n-1}\\sqrt{p_{\\theta}^{j}}\\lvert{j}\\rangle,$$ where the probabilites $p_{\\theta}^{j}$, for $j\\in \\left\\{0, \\ldots, {2^n-1} \\right\\}$, represent a model of the target distribution." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "# Set upper and lower data values\n", - "bounds = np.array([0.,7.])\n", - "\n", - "# Set number of qubits used in the uncertainty model\n", - "num_qubits = [3]\n", - "\n", - "# Set entangler map\n", - "entangler_map = []\n", - "for i in range(sum(num_qubits)):\n", - " entangler_map.append([i, int(np.mod(i+1, sum(num_qubits)))])\n", - "\n", - "# Set variational form\n", - "var_form = RY(int(np.sum(num_qubits)), depth=1, entangler_map=entangler_map, entanglement_gate='cz')\n", - "\n", - "# Load the trained circuit parameters\n", - "g_params = [0.29399714, 0.38853322, 0.9557694, 0.07245791, 6.02626428, 0.13537225]\n", - "\n", - "# Set an initial state for the generator circuit\n", - "init_dist = NormalDistribution(int(sum(num_qubits)), mu=1., sigma=1., low=bounds[0], high=bounds[1])\n", - "\n", - "# Set generator circuit\n", - "g_circuit = UnivariateVariationalDistribution(int(sum(num_qubits)), var_form, g_params,\n", - " initial_distribution=init_dist, low=bounds[0], high=bounds[1])\n", - "\n", - "# construct circuit factory for uncertainty model\n", - "uncertainty_model = g_circuit" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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Z2Zqqnk4IS4BXs98FLABeK9T5B2nCt0uaF5qZma3JaiagiLgOuA5A0hXA6e10vzYzM6tLQ92wI+KorgrEzMz6Fs/tY2ZmpainE8LDwLiImC7pEar3ggMgIt7brODMzGzNVc8luCeBpbnf201AZmZm9ainE8JRud/HdWk0ZmbWZ5TeBiRpF0l3S1oiaa6k0yWtVWOddSSdK+l3kpZKqnhWJmmipKjwGNI1R2NmZvWqpw2oZrtPXiNtQJIGAncB04ExpCm/zyMlxlPaWXU94LOkEbfvBz7UTt0ZQLH33qx6YzQzs65RbxtQV7X7HAP0Aw6JiIXAnZI2BCZIOicrW01EzJf01ogIScfRfgJaHBEPNj90MzPrjHragMZ14f4PIE3vkE80LcDZwEjgpnbicmcIM7NerOw2oCGkS2T/FBGzScP/NKudZhdJCyUtlzRF0sgmbdfMzDqh7PuABgLzK5TPy5Z11mPAQ6Q2pk2BE0iX+faOCM/YamZWItW6kpUf/03SRGonoLqH65G0AjgxIi4slL8AXBkRJ9exjeOAH0SE6qi7HqlN648RcXCVOuOB8QCDBg0a1tLSUvtA6rBo0SL69+/flG0107Q5C9o8H9QPXlrats7QrQZ0Y0SVFeOE1WPtCXFC7de0p8RZ1FPfo0W9JU7oPbE2M87Ro0dPjYjh9dQt+z6geUCl/8aBdMHcQhGxRNKtwL+3U+cy4DKA4cOHx6hRo5qy70mTJtGsbTXTuJNuafP8hKErOW9a27fFrCNHdWNElRXjhNVj7QlxQu3XtKfEWdRT36NFvSVO6D2xlhVnQ4ORQroHBxgHvBfYAniRdJnrZxHxjwY3N4NCW4+kbUjdrGdUXKPzAo/mYGZWuoY6IUh6B/AMcDHwTuCN7OfFwExJuzS4/9uA/SRtkCsbSxr6Z3KD26pJUj/gIGBqs7dtZmaNafQM6DLShHQfyHqrASDpbcDNwKXABxvY3qXA8cANks4GtgcmAOfnu2ZLmglMjoijc2UHAOsDu2XPD80WPRIRz0sakMV0FTAT2AT4KrAlcFgDMZqZWRdoNAENB/4jn3wgdZ2WdCpwdSMbi4h5kvYBLiLd8zMfuICUhIpxFofn+SGwbe75ddnPo4CJwHLg76QRFTYDlgEPACMj4tFG4jQzs+ZrNAHNAtatsmxdYHaVZVVFxHTaH8mAiBhcT1lh+TLgkEbjMTOz7tHojagnAWdK2jNfKOl9wBnAfzcrMDMzW7N1ZDDSDYH7Jb0MvEy6vLUZ8CpwMnBjF8RpZmZrmI4MRvpkF8ViZmZ9SNmDkZqZWR9V9mCkZmbWRzkBmZlZKToyFM9Y4HPAzlTokh0RmzUhLjMzW8M1OhTPEcDPSCMLbA38hjTawJuAhaQbSs3MzGpq9BLciaT7fb6YPb8kIj4DbAe8QppIzszMrKZGE9BOwO8j4g3SQKQbAkTE66RptI9rbnhmZramajQBLQTekv0+B3hHbpmAjZsRlJmZrfka7YTwCPAu4HZS+8+3Ja0E/gF8G3iwueGZmdmaqtEE9L/8awTqb2e//5B0JvUI8PnmhWZmZmuyhhJQRDxIdpYTEfOBMZLeArwlP3+PmZlZLU2bkltSR6bkNjOzPqrsKbnNzKyPKntKbjMz66Ma7YY9HPh2pSm5gVOBPZoVmJmZrdkaTUCzaPKU3GZm1jd5Sm4zMyuFp+Q2M7NSeEpuMzMrhafkNjOzUnRoRlRJW0r6uKTPSTpE0pYdDUDSLpLulrRE0lxJp0taq8Y660g6V9LvJC2VFO3UHSNpmqRlkqZnE+qZmVnJGr0RdS1JlwDPA9cBPwKuB56XdLGkRrc3ELiLdIlvDHA6cAJwWo1V1wM+S5p/6P52tr838CvgXuAA4Bbgl5L2bSROMzNrvkZvRD0N+Ayps8E1wEvAIGAsKXm8ShqktF7HAP2AQ7Kx5O6UtCEwQdI51caXi4j5kt4aESHpOOBDVbb/LeC+iDg+e36vpF2zGO9oIE4zM2uyRi/B/SdwSkScGxGzI2J59vNc0of9uAa3dwBweyHRtJCS0sj2VoyIqpfdALJBUkcD1xYWtQAjJA1oMFYzM2uiRhPQZsATVZY9kS1vxBBgRr4gG1VhSbasM3YA3lzcPvAU6bh37uT2zcysE1TjRKJtZekJ4NGI+EyFZZcDwyLi3Q1sbwVwYkRcWCh/AbgyIk6uYxvHAT+ICBXK9wKmALtHxOO58h1JA6ruFxGrXYaTNB4YDzBo0KBhLS0t9R5OuxYtWkT//v2bsq1mmjZnQZvng/rBS0vb1hm6Vfkni8U4YfVYe0KcUPs17SlxFvXU92hRb4kTek+szYxz9OjRUyNieD11G20DOhNoyQYfvZ7UBrQZcBjpctcnGtxejxMRl5EGXWX48OExatSopmx30qRJNGtbzTTupFvaPD9h6ErOm9b2bTHryFHdGFFlxThh9Vh7QpxQ+zXtKXEW9dT3aFFviRN6T6xlxdnohHTXSppP6ozwPdIlrhXAVGD/iLizwf3PAyp9HRyYLeuM1vWL2x9YWG5mZiWoOwFJejNpEro/RcSIrMv1JsArEbGqg/ufQaGtR9I2pG7WxbabRj1LSo5DgMm58iHAKuDPndy+mZl1QiOdEN4A7iFLGBGxKiJe7kTyAbgN2E/SBrmyscBS2iaNhkXEctL9P4cVFo0FHoiI1RsVzMys29R9BhQRqyQ9A2zexP1fChwP3CDpbGB7YAJwfr5rtqSZwOSIODpXdgCwPrBb9vzQbNEjEfF89vsZwCRJF5IGST0we+zfxGMwM7MOaLQTwjeBsyVNi4hpnd15RMyTtA9wEXATMB+4gJSEinEWh+f5IbBt7vl12c+jgInZ9qdkielM4FjgOeCISr3fzMysezWagE4BNgYelzSH1AuuTT/uiHhvIxuMiOlUH8mgtc7gesqqrHsjniLCzKzHaTQBPQn8qSsCMTOrZHCFbu3Fru6zzjqoO0OyJmm0G/a4LorDzMz6mLoSkKR+pMb7wcCLwN0R8VIXxmVmZmu4eqbk3p40ZcLgXPFCSYe7Md/MzDqqnvuAziHduPkB0g2iuwKPkeYCMjMz65B6EtAI0hQMv4+IZRHxFPB54G2Stuja8MzMbE1VTwLaAvhLoexZQDT3plQzM+tD6h2Kp/45G8zMzOpQbzfs2yWtrFB+d7E8IhqdlM7MzPqgehLQaV0ehZmZ9Tk1E1BEOAGZmVnTNToUj9Wp1vAhHjrEzPq6RuYDMjMzaxonIDMzK4UTkJmZlcIJyMzMSuEEZGZmpXACMjOzUjgBmZlZKZyAzMysFL4R1cysCYo3n4NvQK/FZ0BmZlYKJyAzMytF6QlI0i6S7pa0RNJcSadLWquO9QZIukLSPEkLJP1C0saFOhMlRYXHkK47IjMzq0epbUCSBgJ3AdOBMcAOwHmkxHhKjdWvBXYGPgusAs4GbgQ+UKg3AziqUDarM3GbmVnnld0J4RigH3BIRCwE7pS0ITBB0jlZ2WokjQD2BUZGxH1Z2RzgIUkfjoi7ctUXR8SDXXsYZmbWqLIvwR0A3F5INC2kpDSyxnovtSYfgIh4GHguW2ZmZj1c2QloCOkS2T9FxGxgSbas7vUyT1VYbxdJCyUtlzRFUnuJzczMuokiorydSyuAEyPiwkL5C8CVEXFylfXuJF1aO7hQfhWwfUS8P3v+ZeAfpDamTYETgGHA3tkZU6VtjwfGAwwaNGhYS0tLh45t2pwFbZ4P6gcvLf3X86FbDejQdputVpzQM2Itxgm99zXtKXEWLVq0iP79+5cdxmr8Hu16zfzbjx49empEDK+nbtltQF0qIr6Xfy7pVuBJ4GTg4CrrXAZcBjB8+PAYNWpUh/Y9rsKMqOdN+9fLPevIjm232WrFCT0j1mKc0Htf054SZ9GkSZPo6Pu9K/k92vXK+tuXfQluHlDpK8HAbFlT14uIJcCtwHsaiNHMzLpA2QloBoU2G0nbAOtRuY2n6nqZam1DeZE9zMysRGUnoNuA/SRtkCsbCywFJtdYb3NJe7cWSBoObJ8tq0hSP+AgYGpngjYzs84ruw3oUuB44AZJZ5MSyATg/HzXbEkzgckRcTRARDwg6Q7gSklf4183ok5pvQdI0gDgZuAqYCawCfBVYEvgsO45PDOznqc4cGpZg6aWmoAiYp6kfYCLgJuA+cAFpCSUtzZQHJ5nbFb3ctKZ3M2kZNZqOfB30ogKmwHLgAdIN68+2tQDMTOzhpV9BkRETAc+VKPO4Apl80lD7BSH2Wldvgw4pAkhmplZFyg9AZlZOXrKZRjru8ruhGBmZn2UE5CZmZXCCcjMzErhBGRmZqVwAjIzs1I4AZmZWSmcgMzMrBROQGZmVgonIDMzK4UTkJmZlcIJyMzMSuEEZGZmpXACMjOzUjgBmZlZKZyAzMysFE5AZmZWCicgMzMrhROQmZmVwgnIzMxK4QRkZmalcAIyM7NSlJ6AJO0i6W5JSyTNlXS6pLXqWG+ApCskzZO0QNIvJG1cod4YSdMkLZM0XdLYrjkSMzNrRKkJSNJA4C4ggDHA6cAJwGl1rH4tMAr4LDAO2AO4sbD9vYFfAfcCBwC3AL+UtG9TDsDMzDps7ZL3fwzQDzgkIhYCd0raEJgg6ZysbDWSRgD7AiMj4r6sbA7wkKQPR8RdWdVvAfdFxPHZ83sl7Qp8G7ij6w7LzMxqKfsS3AHA7YVE00JKSiNrrPdSa/IBiIiHgeeyZUh6CzCadKaU1wKMkDSg8+GbmVlHlZ2AhgAz8gURMRtYki2re73MU7n1dgDeXKHeU6Tj3rkD8ZqZWZMoIsrbubQCODEiLiyUvwBcGREnV1nvTmBxRBxcKL8K2D4i3i9pL2AKsHtEPJ6rsyPwDLBfRKx2GU7SeGB89vTtwNMdPsC2NgFeadK2ulJviRN6T6yOs7l6S5zQe2JtZpzbRsSm9VQsuw2ox4mIy4DLmr1dSY9GxPBmb7fZekuc0HtidZzN1VvihN4Ta1lxln0Jbh5QqS1mYLasM+u1/izWG1hYbmZmJSg7Ac2g0NYjaRtgPSq38VRdL5NvG3oWWFGh3hBgFfDnDsRrZmZNUnYCug3YT9IGubKxwFJgco31Ns/u8wFA0nBg+2wZEbGcdP/PYYV1xwIPRMSCzoffkKZf1usivSVO6D2xOs7m6i1xQu+JtZQ4y+6EMBCYDvwJOJuUQM4HLoyIU3L1ZgKTI+LoXNntwE7A10hnNGcDL0fEB3J19gYmAReRblI9MKu/f6UOCGZm1n1KPQOKiHnAPsBawE2kERAuAE4tVF07q5M3lnSWdDlwJTAV+Fhh+1OAQ4EPA7cDHwWOcPIxMytfqWdAZmbWd5XdBmRmZn2UE5CZmZXCCcjMkLSupMsk7VR2LNZ3uA2oC0jqTxpMdQhtb3ydQerNt6is2BohaV1gs2x8vh5L0puBLXpinJK2A7YDnouI50qOZb12Fm8E/JU0mO8UgIhY0h1xNUrSYCAi4vmSQ6lK0mhgF1IP3T9GxP0lh4SkPYFHImJV2bH8U0T40aQHINKcRotIb7xFpH/qvxbKTiNL/j35AXwceKPkGL5Iuql4KfBH4FMV6uxZZpykQW+/D7yW/X3PycovBt7I/u5vAL8A1ioxzjdqPFbln5f8dx8PbFIo+zLw91yMLwFfKDnO84Azc8+3AB7IXstlwPIs1t8CA0qOdVX2ml0E7FVmLK0PjwXXXBOA/yIlmJaI+Gt+oaStgU+QuplHVt+qkPQJ4AfAL4HHgPcDEyWNAT4ZEcvKjC/n66SJEc8nJaEvSdoUOJg0WeIfgL2B7wKfBy4pJ0yWAguzOF4tLFuf9MF0Du2PQtJdfgg8TjZAZjZI8AWk6VWuJ/3/HAb8QNL8iLi6pDgPB/479/wiUhIaSXYmmf1+Jen9cTTlehz4D+DYbNDna0ifVX8oJZqyM+Ca9ADmAOPrqDcemFNinPfU+ZhGuWcWj5KdTeTK9gH+RvqWuXFWVvYZ0AzSqO6tz/cmfdv8SqHeacCjJca5JXA16UP9S+TOxkhjJq4CPlhWfIVYVwHvLbzGV1So93PSZaWy4lwGfCD3fDFwWIV6RwCv9oTXlHTG/tHsvfA66QztadIX47d3Z0zuhNBcG5EuF9XybFa3LB+UWGc2AAALs0lEQVQEBpG+Bbf3eL2sADNvB27NF0TE3cD7SK/fA5K2LyOwgm2Bh3PPp2Y/Hy7Um0Ia7aMUETE3Io4ADiF9E58mab+y4mnQDqTJJItaSG0tZZlNep+2Wkk6yyxaCKzTLRHVEBErIuI32XthM1JynA6cBEyX9AdJJ3ZHLL4E11wPAl+X9GBELK5UQdL6pFP2B7o1sraeBGZExNj2Kkk6lHSKXpYFpHlK2oiIWZLeD9xCeh3P6O7AChbT9gvF8uxRbMRfix7wPxcR90l6D3AscLWk+yn/Naxk3VzHiVdJ39SL3iBdjivL5cAESb+LiKdJl9q+KemhiJgPIOmtwMm0P75lKSJiKel//BpJG5K+nHwCOBM4t6v3X/o/wxrmOOAuYHY2Vt0MYH62bACpV9x+pA+nfUqJMHkQ2L+OekHqWFGWqaR2lOuLCyJinqR9smXfp9wPoaeBYcCvs9hWkaaVL9oVmNV9YVWXxXixpBbgO8DvKPc1rOTe3O8iXT66q1DnXaROPmU5F3gn8ISke0ij7O9G+gyYRop7KCmBfrK0KOsQEQuBiaR21o27Y5/uht1kkjYifbPcn8rdsG8DLm39dlQGSTsAu0bEb2rU60fqhl1Kd1dJhwFfBf4tIl6rUmctUoP1RyJiu+6MLxfDx0ntUe2OKCzpNuDhiCiOdVg6SbuQBvf9XbXXupvj+XSF4hejMI6jpOtJZ/OnVKjfbSTtDxxFao/cnJR45gFPATcDl0VEqZe0Jd0LHBsRPaGTCeAEZGZmJXEnBDMzK4UTkJmZlcIJyMzMSuEEZGZmpXACsnZJGidpqqTXJc2T9Jik87toX4dLGldHvQmSIveYK+lXWe++evYzUdKjnQ64Ceo95qxu63E/U2X5M9nyCV0VQ4PbbfM6N3s/kt4k6bjsPblU0kJJT0r6vqQO3T6g5PEqvfBaj2lwlWUXSfppR/bbVzkBWVWSvgH8hDSd+SHAf5LudfloF+3ycNLYafVYAIzIHl8j3Xtxd3ajby1nNLCfrtbIMUMa+mU7ScPzhZL2AAZny7s6hnoVX+dm7+ca0g2TN5Dek58mjZzx/uh4997DgbeShqlp1HeBIyXt2MF99zm+EdXacxzwo4g4OVd2k6TTygooZ2VEPJj9/qCk2aSbKQ8EritWzu4XWisi/hER9QyX1FMtJg1u+gnSWHmtPkEav29YGUG16q7XWdIBwKHAgRFxW27R/3X07CdzPPDziFiR29fapGT6KdJ4ev8h6VngtIj450gh2QgdU0j3AZ7QiRj6DJ8BWXs2Ig382Ub+22XrZRZJB0uaIWmZpCnZjY1tZJdgpklaLumvkr6T/XMjaSJp+oeRuUtrExqItXX8tcEV4nqSdGawZ35ZIbYPSrpX0iJJCyRNkrR7bvkHJE2WtETSq5J+LGmD9gKSNELSbyS9KGlxdmnnyPxr18FjbgEOb/2gzX4eToWx0joTQ/YaXF/Y3qiszjvzr2Wt17nafiQdKGmV0rxJ+f1sl5WPqfIajMx+3lNc0NGzn+zM5f2sPvLGl0kjnn+fdIb1GdIQPJVGC/gV6SzIn6118BmQtecPpKkFZgM3R0RxCP9W25KGmv8Wacj/04DbJe0U2ZQJkvYlXTK5EjiRNITKGaR/4mOy399GSnpfyLb7QgOxDs5+/q1Qdg5pjqa/ARUnhJM0CriTNPTLp0lnGXsBWwGPSdqLNATMjaRv3RsDZ5FGuTi0nZi2BX4PXEr6YN4LuELSqoj4JR0/5htIoz/sTTrr+wCwaVZeHL+rq2LIG0zt17nafl4E5pJe9wm5+uOAl0nj/VXSOtbiuZLOa9JoHftk2/1joXwkcE9EnJN9sfp9RMyqso37SQP9Dq2wHSsqc3hwP3r2g5Qk/kIaI2wVaRDT04ENc3UmZsvfnyvbljQq8DG5sgeBewvb/zppMMmts+fXA5PqiGsCaUqBtbPHzqTksZA0M2o+rt0qrD+R3LQIpAFNH6XKJIGkD/li7B/Ktv/OOl9LZbH+iPRh1lpe1zHnjzv7/dfAxdnvlwA3Zr+/AkxoRgzAJOD6Qtmo/HE3+DpX28+ZpKSlXJyzgO+281psDjyR7TuAP5EG/Ozfiff7ZVSY2iF7vf6a7XMiMLidbaydvfc/19E4+tLDp4lWVUQ8AbyD1MB7CemD4VvAo0rTjrd6OXJTDkf6NjqVNHhka7vAe1i9beYa0mXgER0Ib2NgRfZ4mjTNwdiIeDFXZ05EPN7eRrJOC3sCP4vsE6SwfL0svmslrd36IE2tsIJ22lwkDVTqkfV8LtbxpITZWS3AoZLeQjoLqzRVQVfH0Krm61zD5aQvLaOy56Oz51dUWyEi/gbsThrc94ekM6vvAPdLWgfSeHLZJcfHs8u+M7LfpypN4160OdkEeAXfIZ0ZPUf6X/hadlZcKa6VpAGIN69xzIbbgKyGiFgeETdFxHERsQtp5s+daDuz48sVVn2ZNDMkpCkV3kyaDjiv9flbOxDaAmAPYDiwNelb6W2FOsX9VTKQlFhfbGf5WqQEvCL3WE46pm3a2fZEYCzpsti+WbyXA+vWEVctvwH6kz4c1wduKiGGVvW8zlVFxF9IZ1tHZUVHkQZtfbLGem9ExB0R8QXS5b0rSJe+RmTLfxYRu5G+/KwkTUO9W0QMi1wng5x1SX/X4n5mZ9v9GOmKwN7AFFW/HWE5zX1911huA7KGRMRPJZ1DGum71WYVqm5GumQH6Vvligr1BmU/OzL68sqIqHUvTz2N0fNIlxe3qLJ8Pv+aPv3WCsvnVlpJ0rrAvwFfjIhLc+VN+dIXEYsl3UwaLfy6qDD/VBNiWMbqk6gNrFCvGSMa/wT4sVLX/0NosBdZRKySdAcpeRU//HcC5kX1NsxWr1HlzCVLWL9VmiZ+AmmakAskXZglqLyN6Nh7us/xGZBVJWm1xCJpU9LcRvlvvZspTRDXWudtpG+dD0P6pkq6JHdYYXOHkz78Wyfn+wfd/M0x++B+CPjP1l5lFZY/SJqq+NEKj4oJCHgL6f/rn9+os15zxXuoOnPMPySd+VxaZXlnY3iBtl80IJ1FdVR7x3pDtryFFHPFS4oAkgZVWfRR0iSADxXK3019HQKeBlab0qPS+wJ4JPv51kLdTYH1SPMCWQ0+A7L2TJP0a+AO0iW1bUk3fS4Bfpar9wpwlaRT+FcvuJdJl39anUrqGXcF6cNlKKln1I8jorXX1QxgjKSDSR9+c9v5gG+mk0i93G6TdBnpev8IUgP6zaTOEndLWkVqSH+ddMnnIOCbEbHah01ELJD0CPBtSQtJifYk0qXDDXNVO3zMETGJdOmq2vLOxvB/wNGSLiD1RhtNfRMZVlP1WCNimaRfAF8Efhntz5d1raTXgWtJnRU2A44ExpAa/4vrvpvUYaGW35Neq00j4u+58qslPQbcR7rcOYx05jmHNN9P3nDSGeH9WG1l94Lwo+c+SB8Gd5AuMy0j/bNfDQzJ1ZlI6kF2COlb33LSP/JqvcNIbRHTSN90XyC1X6ydW74J6UPvNbLLXlXimkDWG6yd2CeS64FVaxmpq+19pOQ6n9Srbrfc8j2B35J62i0GppO6ng9oJ4Ydgbuz+rNJiaxN7PUecwPH3aYXXGdjAL5B6gH2OnAV6Syj2Auurte51rECH87KP1zjGD+T/S1eyN5Lr5ES5Kgq9W8CPlHH+30d0sylnyqUfyzb399ISXwhKfHvXmEb36PQY9KP6g9PSGedkt1g+M6IGF6rrll7srbFw4HtI00Z3qztzgb2i4ji2Uqlut8DdoyIg6osn0hKnLMqLFsLeB44KSKu6lTQfYQvwZlZqSS9HdiFNITNaU1OPgNJN+nW2yZzLvBnSTtHhUurNRxGugRdtf3K2nInBDMr249Il3ZvJQ130zQRMS8i+kXqCFNP/RdIl/iq9Yq8kXSJthIBR0e6F8jq4EtwZmZWCp8BmZlZKZyAzMysFE5AZmZWCicgMzMrhROQmZmVwgnIzMxK4QRkZmal+H/C0E4RTJkX9wAAAABJRU5ErkJggg==\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# plot probability distribution\n", - "x = uncertainty_model.values\n", - "y = uncertainty_model.probabilities\n", - "plt.bar(x, y, width=0.2)\n", - "plt.xticks(x, size=15)\n", - "plt.yticks(size=15)\n", - "plt.grid()\n", - "plt.xlabel('Spot Price at Maturity $S_T$ (\\$)', size=15)\n", - "plt.ylabel('Probability ($\\%$)', size=15)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Evaluate Expected Payoff\n", - "Now, the trained uncertainty model can be used to evaluate the expectation value of the option's payoff function with Quantum Amplitude Estimation." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Estimated value:\t1.2580\n", - "Probability: \t0.8785\n" - ] - } - ], - "source": [ - "# set the strike price (should be within the low and the high value of the uncertainty)\n", - "strike_price = 2\n", - "\n", - "# set the approximation scaling for the payoff function\n", - "c_approx = 0.25\n", - "\n", - "# construct circuit factory for payoff function\n", - "european_call = EuropeanCallExpectedValue(\n", - " uncertainty_model,\n", - " strike_price=strike_price,\n", - " c_approx=c_approx\n", - ")\n", - "# set number of evaluation qubits (samples)\n", - "m = 5\n", - "\n", - "# construct amplitude estimation \n", - "ae = AmplitudeEstimation(m, european_call)\n", - "# result = ae.run(quantum_instance=BasicAer.get_backend('qasm_simulator'), shots=100)\n", - "result = ae.run(quantum_instance=BasicAer.get_backend('statevector_simulator'))\n", - "print('Estimated value:\\t%.4f' % result['estimation'])\n", - "print('Probability: \\t%.4f' % result['max_probability'])" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "qiskit_master", - "language": "python", - "name": "qiskit_master" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/qiskit/finance/machine_learning/readme.txt b/qiskit/finance/machine_learning/readme.txt deleted file mode 100644 index e69de29bb..000000000 diff --git a/qiskit/finance/simulation/asian_barrier_spread_pricing.ipynb b/qiskit/finance/simulation/asian_barrier_spread_pricing.ipynb index fb7233aed..0442e31aa 100644 --- a/qiskit/finance/simulation/asian_barrier_spread_pricing.ipynb +++ b/qiskit/finance/simulation/asian_barrier_spread_pricing.ipynb @@ -140,7 +140,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -299,7 +299,7 @@ "outputs": [ { "data": { - "image/png": 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CXEUaUGUvYCfSJNXXSPpkF/uNzpr6TJy/aG5nm5mZWf1dDxyWjZq5FTArIl6VNEzSIABJK5L6WHf70K5P1NyZmZm1CknLAzeRauIO6Wbzo4GNgTUi4s2s7HZJGwLfB/Yst1PWZGgcwLIDV/Gw2WZmdSLpcmAksGI2L++pZP2lI+ICUsuL3YDngHeAI7NdPwZcKGkRqULux5W0yHByZ2Zm1iQkLQXcAAwEdo+It7vZZSPg5aLEruAfwHZ1CNHMzKoQEV3OV5qNkvm1MuX3AptVez43yzQzM2sCkgaQmliuD+waEa9XsNvLwHBJw0rKP00aaMXMzPoQ19yZmZk1h/NITXNOBJbP+l4UPBIR8yRNAIiIHbLyy4DvADdKOpPUpOcQYAvgCw2L3MzMmkLDa+4krSfpQkmPSlqYjfxSyX7LSrpY0kxJsyRdKmmFOodrZmbWKKOy17HAfSXLatm6/tkCQES8AmwPvAlcSKr52xDYLyL+0piwzcysWeRRc7cJ6cnk/aQ+BZX6A+mGdQywCPgJcB3w2VoHaGZm1mgRMbyCbUaWKXsY2LUOIZmZWYvJI7n7c0T8CUDS1cCK3e0gaWtgZ2C7iLg7K5sKPCBpx4i4vZ4Bm5mZmZmZNbuGN8uMiOqnfk9PJP9VSOyy4/wdeBE/rTQzMzMzM2uZAVU2Ap4pU/50ts7MOhMBjz8O//pX3pH0yrBHH4X33ss7jN4bOBC22QaWWCLvSMzMzKzNtEpyN4zUWbzUTGCdcjtIGg2MBlhllVXo6OioW3AFc+bMach5Gs3X1VoK17XEjBmscvvtrHrzzSz94ot5h9VrH887gBp6+jvf4V877QS0/9+hmZmZNU6rJHcAUaZMnZQTEeOAcQAjRoyIkSNH1i+yTEdHB404T6P5ulrI/Pk8ceaZbPrgg3DjjbBgAWy5JXzrW7D55nlH1ysPP/wwn/rUp/IOo3dmz4bdduNjq6zCx7K/vbb8O6R9r8vMzKyZtUpyNxNYqUz5cpSv0TPre374Qxgzhk3feANWXRW+8Q04/HDYeOO8I6uJ2e+9B9tum3cYvTNnTnp999184zAzM7O21CrJ3TOUn/JgI9J0CGZ924MPwve+B6NG8dj227P5ySfDgFb5792HDB6cXufNyzcOMzMza0sNHy2zh24CVpX0H4UCSSNI/e1uyi0qs2YxdiwMHQpXXcWMrbZyYtesBgyAfv2c3JmZmVldNPwboKSlSJOYA3wEWEbSftn7GyPiHUnPAXdFxNEAEXGfpFuA30k6mQ8mMf+b57izPm/aNPjDH+C442CZZfKOxrozaJCbZZqZmVld5PF4f2XgqpKywvu1gZdIcfUv2eZA4JfARaQaxxuAE+oWpVmrOP98WLgQjj8+70isEoMHu+bOzMzM6qLhyV1EvEQa5bKrbYaXKXsTODJbzAxg7ly44ALYc09Yp+ysINZsBg1ycmdmZmZ10Sp97sysnMsugzfegJNOyjsSq5SbZZqZmVmdOLkza1URaSCVzTeH7bbLOxqrlJtlmpmZWZ14SD2zVnXnnfD443DRRaAuWzpbM3GzTDMzM6sT19yZtaqxY2GlleCgg/KOxKrhZplmZmZWJ07uzFrRc8/Bn/8Mxx77wcTY1hrcLNPMzMzqxMmdWSs6++w0IfZXvpJ3JFYtN8s0MzOzOnFyZ9ZqZs+Giy+GAw6A1VbLOxqrlptlmpmZWZ04uTNrNRddBG+95ekPWpWbZZqZmVmdOLkzayULF8JZZ8F//Ad8+tN5R2M94WaZZmZmVidO7sxayQ03wIsvwokn5h2J9ZSTOzMzM6sTJ3dmrWTMGFhrLfjiF/OOxHrKfe6sE5L2l3S9pKmS5kh6SFJFc51I+pykuyS9LenN7Oe16h2zmZk1Fyd3Zq3i0UehowOOOy6NlGmtyX3urHPfAOYAXwf2BO4ELpN0fFc7SdoFuB14NNvvEOA+wPOkmJn1Mf6GaNYqxo6FpZaCY47JOxLrDTfLtM7tERFvFL2/Q9LqpKTv7HI7SFoC+BXw04j4btGqG+oXppmZNSvX3Jm1gtdfh0svhSOOgGHD8o7GemPQIJg/HxYtyjsSazIliV3BI8DKXey2E7AGcG5dgjIzs5bi5M6sFVx4YUoITjgh70istwZnLeXmz883DmsV2wBPdbF+S2A6sJWkZyUtkPSEpD0aE56ZmTUTJ3dmzW7ePDjvPNh1V9hww7yjsd4aNCi9ummmdUPSDsBedF0rtyowBBgH/AzYhZQMXitps7oHaWZmXZK0i6RJkp6T9O0y6z8qaYKkxyR1SFqjaN3h2YO7ZyUdXsn5nNyZNbsrr4TXXvP0B+2ikNx5xEzrgqThwGXAnyJifBeb9iMNnPK9iLgwIm4HDgJeBP5fF8cfLWmipInzF82tWdxmZvYBSf1JD+h2BTYGDpK0cclmPwN+FxGbA6cDP8r2XR44ldRCYwvgVEnd9s1xcmfWzCLS9Acf+xiMGpV3NFYLhWaZrrmzTmQ39JuAyaSRL7syI3u9s1AQEQuBu0hfJMqKiHERMSIiRgzst2QvIzYzs05sATwXES9ExHzgClKLjGIbAxOyn+8sWr8zcFtEzIiImcBtpNYZXXJyZ9bM7rkHHn441dpJeUdjteBmmdYFSUuRRrocCOweEW93s8vTnR0K8Kg9Zmb5+gjwStH7KVlZsUeBfbOf9waGSlqhwn0X46kQzJrZmDFpdMxDD807EqsVN8u0TkgaAFwFrA9sGxGvV7DbLcACYAdgUnac/sB2QEd9IjUzaz/TFy7NJTO36cGeV64oaWJRwbiIGJf9XO7JfJS8Pxk4R9IRwN3AVNLneiX7LsbJnVmzevlluPZa+Na30vx21h7cLNM6dx6wG3AisLykrYrWPRIR8yRNAIiIHbLXVyWdC/xYkoDngNGk6RF+1NDozcz6pjciYkQn66YAaxa9XwOYVrxBREwD9gGQtDSwb0TMkjQFGFmyb0d3wTi5M2tW55yTmmJ+7Wt5R2K15GaZ1rlCx9qxZdatDbwE9C+z7lvA28D3gOVJc+PtHBHP1yFGMzOr3IPA+pLWJtXIHQgcXLyBpBWBGRGxCPgf4KJs1S3A/xUNojIqW98lJ3dmzWjOHPjVr2DffWHNNbvf3lqHkzvrREQMr2CbkWXK3gO+my1mZtYkImKBpONIiVp/4KKIeFLS6cDEiLieVDv3I0lBapb5tWzfGZLOICWIAKdHxIzFTlLCyZ1ZM/rtb2HWLDjppLwjsVorNMt0nzszM7O2FxE3AjeWlJ1S9PPVwNWd7HsRH9TkVcSjZZo1m0WL4KyzYIstYKutut/eWotr7szMzKxOXHNn1mxuvhn++U+49FJPf9COnNyZmZlZnbjmzqzZjB0Lq68O++2XdyRWD26WaWZmZnXi5M6smTz5JNx6K3z1qzBwYN7RWD245s7MzMzqxMmdWTM566xUszN6dN6RWL04uTMzM7M6cXJn1iymT4dLLoFDDoGVVso7GquXQnLnZplmZmZWY07uzJrFr34Fc+fCCSfkHYnVU6HPnWvuzMzMrMac3Jk1g/feg3POgR12gM02yzsaq6cBA6BfPyd3ZmZmVnOeCsGsGfzxjzB1KlxwQd6RWCMMGuRmmWZmZlZzTu7MmsGYMbDeerDbbnlHYo0weLBr7sxqaO6mH8k7BLOaWfKJqXmHYC3MyZ1Z3h54AO6/P42U2c8tpfuEQYOc3FnTc8Jklo+5m37ECZ71mJM7s7yNHQvLLANHHJF3JNYobpZpTWTRkks4kTNrMk7wrKcantxJ2hg4G9gaeBP4NfD9iFjYzX4jgP8DPg0IeBj4bkQ8UN+IzepoyhS46io4/ngYOjTvaKxR3CzTrNdmbjgw7xDM6mLYpPmAEzzrmYYmd5KGAbcDTwF7AesCPyeN2vm9LvZbM9vvYeCwrPhbwK2SNo+Il+sZt1ndnHceLFqUkjvrO9ws0/oAJ19mPTNzw4FO8KzHGl1zdyywJLBPRMwGbpO0DHCapDOzsnJ2B4Zm+70JIOle4A1gN+D8+oduVmPvvAPjxsFee8Haa+cdjTWSkztrYn09KXtr3UV5h2B93NDn+znBsx5rdHK3K3BLSRJ3BfATYDvgz53stwSwAJhTVDYnK1Md4jSrv0svhenT4cQT847EGm3wYPe5s6axcLBaLqFzAmbt7K11F72f4EFqpukEzyrV6ORuI+CO4oKImCzpnWxdZ8ndNcDpwM8l/TArOwWYCVxVp1jN6iciDaTyiU/A5z6XdzTWaIMGwdtv5x2FWW6cnJl1rZDgwQfNNAsDHznJs640OrkbRhpEpdTMbF1ZETFN0vbADcAJWfGrwM4R8e+aR2lWbxMmwJNPwvjxIFc+9zmDBsGMGXlHYdZrrZikLb32rLxDMOvSnBeXBconeOBmmta1PKZCiDJl6qQ8rZRWA64GHgKOyYq/BvxF0jYRMbnMPqOB0QCrrLIKHR0dvQy7e3PmzGnIeRrN11V7m/3v/zJ02DDuW201osYx+N+r+W3y1lssNX06D3Z0tNV1FWvX6+oLmj1hc3Jm7W7ptWc5wbMea3RyNxNYrkz5spSv0Sv4FinW/SLiPQBJdwDPAifzQW3e+yJiHDAOYMSIETFy5MheBV6Jjo4OGnGeRvN11dizz6ZJy089le1Gjar54f3v1QLWWAOmTmXkyJHtdV1F2vW62tHCQfkmdK2QrI1aa1LeIVgfcevkDQEneNZzjU7uniH1rXtfNs3BkGxdZzYCniwkdgARMV/Sk6TpFMxax1lnwcCBcOyxeUdiefFomVaGpP2BQ0nzuS4LTAJ+FhGXV3GM60hTDR0fEefUJdAKNEvC5qTMWk3hb/bWyRs6wbMeaXRydxPwLUlDI+KtrOwAYC5wVxf7vQzsJmlgRMwHkDQI2JTOB2Exaz5vvgkXXwwHHgirrpp3NJaXQYM8WqaV8w3gReDrfDDVz2WSVoyIs7vbWdIoYKv6hph/4uaEzfqCUWtNej/Bg9QPzwmeVaLRyd0FpCaUf5T0E2Ad4DTgF8XTI0h6DrgrIo7Oin5N6mt3raTzSH30vgasRtb00qwlXHRRGiXR0x/0bYMHu+bOytkjIt4oen+HpNVJSV+XyZ2kJYCxwHdJ98weyyt5yztpO3TYvbme36zgkpnbAB8kePBBM81CE2rPhWedaWhyFxEzJe0AnEOqcXsT+CUpwSuNq3/Rfg9J2gU4FbgkK34c2CkiHq133GY1sWBBapL5uc/Bpz6VdzSWJzfLtDJKEruCR0jNLLtzIqkVzMVUmdz1H7Sw7gldoxM3J2rWyg4ddm+XCR54LjzrXMNHy4yIp4DPd7PN8DJlE4AJdQrLrP6uvx5efhl+8Yu8I7G8DRoE8+fDouYeldCawjbAU11tIGlV4H9JNX+L1GTTqzixM2scJ3jWL+8AzPqMsWNh+HDYq5KH8NbWBg9Or/Pn5xuHNbWspctewLndbHomcEtE3F3/qKpXqHVolEKNh5lZX+TkzqwRHn4Y7r4bjj8e+vfvfntrb4MGpVc3zbROSBoOXAb8KSLGd7Hd1sB+pCmDqjn+aEkTJU1cMOudXkRaGSd4ZmaN4eTOrBHGjoUhQ+Coo/KOxJqBkzvrgqTlSaNLTwYO6WbzMcCFwCxJy0kqzCW7pKRlO9spIsZFxIiIGDFg2aVqEnd3nOCZmdWfkzuzenvtNbjiCjjySFhuue63t/ZXaJbp6RCshKSlgBuAgcDuEfF2N7tsCJwEzCxaIDXVnF6vOHsqjwTPSZ6Z9SVO7szq7YILUt+qE07IOxJrFq65szIkDQCuAtYHdo2I1yvY7QvA9iULwFnADpWcd+G8xjYVb3SCB67FM7O+w8mdWT3Nmwfnnw+77w7rr593NNYsnNxZeeeRJi4/A1he0lZFyyAASRMkvT9ydET8LSI6ipds1bMRcVelJy4Mr94oTvDMrK+QtIukSZKek/TtMut/Kekf2fJPSW8WrVtYtO76Ss7X8KkQzPqUK66A11+Hk07KOxJrJm6WaeWNyl7Hllm3NvASRXPA1tqcF5dt6ATmt07esOHTJFwycxtPlWBmDSOpP2nE452AKcCDkq7PpoYDICK+XrT98cAniw4xNyI+Uc05XXNnVi8RMGYMbLIJ7FBR6yjrK1yR3JeIAAAgAElEQVRzZ2VExPCIUCfLS9k2IyNiZDfHUUSc05MY8qjB80ArZtbGtgCei4gXImI+cAVpipvOHARc3psTOrkzq5e774Z//ANOPBGabFJhy5mTO2tijU7wwCNpmlnb+gjwStH7KVnZYiR9lNRK446i4sHZtDX3S/piJSd0s0yzehk7FlZYAQ7pbiRz63OKm2Uu1Zhh6M2q0egmmtD4ZppuomlmxWbPH9zTB00rSppY9H5cRIzLfi73dD86Oc6BwNURsbCobK2ImCZpHeAOSY9HxPNdBeOaO7N6ePFF+NOfYPRoWHLJvKOxZuOaO2sBc15ctu0HWnENnpnVwBuFeUOzZVzRuinAmkXv1wCmdXKcAylpkhkR07LXF4AOPtwfrywnd2b1cPbZ0K8ffPWreUdizcjJnbWQvpDgOckzszp5EFhf0tqSBpISuMVGvZS0ITAMuK+obFjRSMkrAtsCT5XuW8rJnVmtvfUW/OY3sP/+sMYaeUdjzcijZVqLafcED1yLZ2a1FxELgOOAW4CngSsj4klJp0vas2jTg4ArIqK4yebHgImSHgXuBH5cPMpmZ9znzqzWxo+H2bPTQCpm5bjmzlqQp0owM6teRNwI3FhSdkrJ+9PK7HcvsFm153PNnVktLVoEZ50FW20FW26ZdzTWrJzcWYtyDZ6ZWXNzcmdWSzfeCM8950nLrWuF5M7NMq0FeS48M7Pm5eTOrJbGjIGPfAT22SfvSKyZFfrcuebOWpTnwjMza05O7sxq5YknYMIEOO44WGKJvKOxZjZgQBpN1cmdtTAneGZmzcfJnVmtjB2b5rT78pfzjsRawaBBTu6s5TnBMzNrLk7uzGrhjTfg97+HQw+FFVbIOxprBYMHu8+dtQVPdm5m1jyc3JnVwrhx6Yu6pz+wSrnmru1I2lvSCdlktMXlx+UVUyP1hQTPSZ6ZNTsnd2a9NX8+nHsujBoFG2+cdzTWKpzctRVJPwZOBNYDbpNUPGTuUflE1XjtnuCBa/HMrLk5uTPrrauvhmnTXGtn1XGzzHazO7BjRJwAfBLYU9JPs3XKL6zGc4JnZpYfJ3dmvRGRpj/YYAPYZZe8o7FW4pq7dtMvIhYARMR0YBdguKTf0AfvtZ4Lz8wsH33uhmNWU/ffDw8+mGrt+vm/k1XByV27eVXSpwpvImI+cAAQwKa5RZUjj6RpZtZ4/jZq1htjx8Kyy8Jhh+UdibUaN8tsN0cA04oLImJRRBwDfDaXiJqAEzwzs8ZycmfWU6+8kvrbffnLsPTSeUdjrcY1d20lIqZExGudrLu30fE0Eyd4ZmaN4+TOrKfOPTf1ufva1/KOxFqRk7uWJGmspL+XKR8g6bOSdpK0TB6xNTPPhWdm1hhO7sx64p130tx2e+8Nw4fnHY21IjfLbFU7AHcWF0gaAkwEOoCbgamSjmh4ZC2gLyR4TvLMLE9O7sx64pJLYOZMOOmk7rc1K8c1d61qTaC0meUJwObAeOBg4M/AryVV1ddO0v6Srpc0VdIcSQ9JOqibfTaUdK6kpyW9I+mFrHZxuWrO3UjtnuCBa/HMLD9O7syqFZEGUvn0p2HbbfOOxlqVk7tWtQQwp6TsYGBKRBwdEX+IiEKC9/+qPPY3smN/HdiTVEN4maTju9hnJ2Bb4HxgN+AHwP7ArZIqusf3z+HP0AmemVl9OLkzq9Ztt8HTT6fpD9Sn5ia2WnJy16qeAbYsvJG0FrAJcH3Jdr8Htq7y2HtExMERcWVE3BERJwOXk5K+zlwOfDIizoqIjoi4iDRy52eoYpTOoc/3Y+jzjf1K4ATPzKz2nNyZVWvMGFh1VfjSl/KOxFqZ+9y1qouAkyWNkrQE8E3SXHbXlWz3OlDVMLoR8UaZ4keAlbvYZ3pERJl96Gq/zvSFBM8DrZhZO3NyZ1aNZ56Bm26Cr3411byY9ZRr7lrVucDtpIFT3gWOBx4HJpRsN5yU4PXWNsBTPdiHHuwHtH+CBx5J08zal5M7s2qcfTYMHAj/9V95R2KtbtAgmD8/9eG0lhHJl4DdgTOBU4Cdy9SefQl4ojfnkrQDsBcpoax0n6WAHwN3RcSTPT23E7zac4JnZo3g5M6sUjNnwvjx8J//CStX3drJ7MMGDwag33vv5RyI9URE3BQR/xMRP4iIfxWvk7QyMBS4sqfHlzQcuAz4U0SMr3AfAb8hNcc8qpttR0uaKGnigrlvl93GCV7tOcEzs3preHInaWNJE7Ihm6dJOl1S/wr33UfSg5LmSpou6eZsfiGz+vv1r9P8dieemHck1g6yZr2aPz/nQKzWIuL1iBhZaVJWStLywE3AZOCQKnb9CbA38MWIeKGbGMdFxIiIGDFgyc5vo3kkeO0+0IrnwjOzemrop7akYaS+CkFqanI6qTP69yvY9xjSU8ybgF2BY4BngQH1itfsfQsWwDnnwMiR8PGP5x2NtYMsuXPNnRXLmlXeAAwEdo+I8tVqi+/3deBk4LCI+GstY2p0ggceSdPMrKca/Yl9LLAksE9E3BYRF5ASu29IWqaznSStCPwSOD4iTsmGe742Io6PiFmNCd36tOuug8mTPWm51U6hWaZr7iwjaQBwFbA+sGtEVDQgi6SDgZ8D34yIHjcF7YoTvPpwgmdmtdboT+tdgVsiYnZR2RWkhG+7LvYrjDn/23oFZtalMWNg7bXhC1/IOxJrF665s8WdR5qI/AxgeUlbFS2DALJuDe+PzClpO2A8cCtwX8k+a9QyOM+FVx9O8Myslhqd3G1EmgD2fRExGXgnW9eZLYFJwNGSpkh6T9IDkvyJaPU3cSLccw+ccAL0r6h7qFn3nNzZ4kZlr2OB+0qW1bJ1/bOlYHtgCWDnMvscU48g+0KC54FWzKxVNTq5Gwa8WaZ8ZrauM6sCGwLfA/4b2AN4G7hZ0iq1DtLsQ8aOhaFD4aguB58zq46bZbaNbKCwQyV9R9KqWdl6koZWc5yIGB4R6mR5KdtmZESMLNrntC72Oa2Gl/kh7Z7ggUfSNLPWlMdgJOUmdVIn5QX9gKWB/SPiZgBJ9wIvA8cB/7vYAaXRwGiAVVZZhY6Ojt5FXYE5c+Y05DyN1peva+D06Wx1xRVM23NPnnv44cYE1kt9+d+rlQx75hk+Drw7a1ZbXVdBu/17lSNpaeAiYF9gAemeejPwGvB/pNEuT84twDob+nw/3lp3UcPON+fFZVl67cZ2s7918oaMWmtSw853ycxtOHTYvQ07n5m1n0YndzOB5cqUL0v5Gr2CGdlrR6EgImZLegjYuNwOETEOGAcwYsSIGDlyZA/CrU5HRweNOE+j9enrOuUUWLiQNX7yE9ZYb72GxNVbffrfq5VIAAwZMIBPtNN1Zdru36u8XwDbADsC9wDvFq27kZTYtW1yB07w6sEJnpn1RqObZT5DSd86SWsCQyjpi1fiaVLNnkrKBTTurmJ9y7vvwgUXwB57QIskdtZC3CyzHewD/HdE3AksLFn3MvDRxofUeJ4Lr/bcRNOsfUjaRdIkSc9J+nYn23xJ0lOSnpR0WVH54ZKezZbDKzlfo5O7m4CdS/ohHADMBe7qYr8bSInc9oUCScsCnwYerUOcZnD55fDvf3vScqsPD6jSDpYEpneybiiLJ3xty1Ml1J4nOzdrfZL6A+eSZgzYGDhI0sYl26wP/A+wbURsApyUlS8PnEoaWHIL4NRszvAudftpLOkwSStUeS2duQCYB/xR0o5Zv7jTgF8UT4+QZba/KbyPiInAn4DfZBns7sD1wHukX5hZbUWk6Q822wy237777c2q5eSuHTwIHNbJuv2APtW2zglefTjBM2tpWwDPRcQLETGfNAXcXiXbfBk4NyJmAhTNcbozcFtEzMjW3Qbs0t0JK/kkvhhYF0DSQklbVHQpZWSB7UAaxvnPpAnMf0nKSosN4MNDPQMcAlxH6uNwNSmx+3zhF2FWUx0d8NhjadJylbYGNquBrFmm3CyzlX0P2EfS7aRpBwLYTdIlwP4sfm9re07w6sMJnlnL+gjwStH7KVlZsQ2ADSTdI+l+SbtUse9iKhlQZSawevZzd6NadisingI+3802w8uUzQG+ki1m9TV2LKy4Ihx8cN6RWLsq1Nw5uWtZEfE3STsAPwbOId0jvw/cD+wYEQ/mGV9eCgleOw+0UkjwPNCKWftYOK9/Tx8WrShpYtH7cdnAjrD4eCGweC41AFgfGAmsAfxV0qYV7ruYSpK724FLJE3KDjhe0tudbRwRPa7ZM2sKzz8P118P3/3u+7UrZjXnZpltISLuAT4raUmyuVwj4p2cw2oKHkmz9pzgmTWlNyJiRCfrpgBrFr1fA5hWZpv7I+I94MUs51o/Kx9Zsm9Hd8FU0n7iKNKTyEdIGeSLwJNdLGat7eyzoX9/+Ioria2OnNy1PEkfl7QbQETMjYhphcRO0m6SNs83wvx5svPacxNNs5byILC+pLUlDQQOJI0bUuw6skEjJa1Iaqb5AnALMErSsGwglVFZWZe6rbnLblQ/y064I/DdiPAIldaeZs+Giy6CAw6A1VfvfnuznvJUCO3gl8BfSXPalfoM8E1SP/M+zTV4tecaPLPWEBELJB1HSsr6AxdFxJOSTgcmRsT1fJDEPUUaZflbETEdQNIZpAQR4PSImLH4WT6sktEyF0r6TPa2A5jdxeZmre3ii+Gtt9JAKmb1NGAA9OvnmrvW9inS5OXl3Ad8soGxNDXPhVd7rsEzaw0RcWNEbBAR60bED7OyU7LEjki+EREbR8RmEXFF0b4XRcR62XJxJeer5NN2PjAo+/kwYKXqLsmsRSxcCGedBdtsAyM6azptVkODBiEnd62sPzCkk3VDgIENjKXpeSTN2vNceGZWqpIBVZ4CTpN0HanP3X6SOvvmGxFxfs2iM2ukv/wFXngBfvzjvCOxvmLwYDfLbG0PAqOBa8usGw1MLFPepzW6iSbkM5JmI5togptpmtkHKknujgcuJPUtCODkLrYNwMmdtaYxY2DNNWHvvfOOxPqKQYOc3LW204DbJT0A/BZ4DViN1Mrl48BO+YVWuf7v9mqGo6o5wasPJ3hmBhU0y4yIe7P2n0uQau62ioh+nSylE4+btYbHHoM774Tjjkt9ocwaYdAg97lrYRFxN2n0skXA2cDVwFhgAbBTRPw1x/CqMmxSYx8yDH2+X9uPpOnJzs0sD9V+sm5PaqZp1l7GjoWlloJjjsk7EutL3Cyz5UVER0RsDQwlzWW0TERs20qJXUGjEzxo/6kSbp28oQdaMbOGqupTNSLuiog5kraU9E1JP8xet6xXgGZ19/rrcOmlcPjhsPzyeUdjfYlr7tpGRLwTEVNbfQJzJ3j14QTPzBqlqvZnkoYAVwE7k+ZhmA6sAPSXdDOwf6vf2KwPuvBCmDcPjj8+70isr/FomS1H0t+BIyLiKUkPkvqadyoitmhMZLUzbNJ8Zm7Y2IE+PRde7bkPnlnfVO3jsjOBrUmzqw+OiNWAwdn7rYGf1DY8szqbPx/OOw922QU+9rG8o7G+ZvBg19y1nieBuUU/d7e0pGGT5ufSD6+RXINnZu2o2pEj9gX+OyKuKhRExCLgKknDgNNJo2uatYYrr4TXXoMTT8w7EuuLBg2i34wZeUdhVYiII4t+PiLHUBqi0bV4edTgAW09kmYhwXMtnlnfUO1jsmWBVzpZ9wqwTO/CMWugiDT9wUYbwahReUdjfZGnQmhZkpaQtK2k1fOOpd7avQYPPJKmmbWPaj9BHwW+IknFhdn7r2TrzVrCMk88AQ89lGrt+jX+y4SZm2W2tIXAHUDN2nNL2l/S9ZKmSpoj6SFJB1Ww3yBJP5f0uqS3Jf1F0vBaxQVO8OrBCZ6Z1UO1n57fIQ2m8oykH0v6uqQfAU+T5vr5Tq0DNKuXNa65BpZbDg49NO9QrK9yzV3LyrokPAusUsPDfgOYA3wd2BO4E7hMUnfdHc4CjgBOBvYDVgRukzS4hrF5Lrw6cIJnZrVW7VQIdwCfBB4B9gd+CHwJeBj4VETcWfMIzerh5ZdZ6a9/hdGjYciQvKOxvsqjZba67wKnSNqsRsfbIyIOjogrI+KOiDgZuJyU9JUlaQ3gaODrEfG7iLgJ2Af4KHBIjeJ6n6dKqD3PhWdmtVT1J2ZEPBURB0bEuhGxVPZ6cER4cnNrHeeem16/9rV847C+zfPctbrvkaYD+oekyZIelPT34qWag0XEG2WKHwFW7mK3QofhPxYdZyrwN2DXas5fKSd49eEEz8xqoapPS0k/k7RxvYIxa4g5c+BXv+Lfn/0srLVW3tFYXzZ4sJtltrYngRuA3wETgCeo/VQI2wBdPTzdCJgSEXNKyp/O1tWFE7z6cIJnZr3Vk6kQvi7pIeAi4PKIaOwsoGa99bvfwZtvMmW//bp8HG5Wd665a2n1ngpB0g7AXsBRXWw2DHizTPnMbF3dFBK8dp8qwZOdm1krqbbP3drAjsAzwE+BVyVdJmnHegRnVnOLFsFZZ8FnPsPsTTbJOxrr6wrJXUTekVgVJC0paV9J35R0sKRaDqpSOMdw4DLgTxExvpvNy/0BqZPywvFHS5ooaeJ789/uaZhA+4+kOefFZdt+oBXX4Jm1j570ubszIg4DViNNWL4GcIuklyV9X9I6tQ7SrGZuuQUmTUrTH3x4Rg+zxhucDWY4b16+cVjFsnvck8BVpIecvwcmSarZZJmSlgduAibT/aAoM4HlypQvR/kaPQAiYlxEjIiIEUsM7P2gUu2e4EH7j6R5ycxtnOSZtYEefzpGxJyI+A1wKnAPsCbwP8A/Jf1J0kdrFKNZ7YwZA6utBvvvn3ckZjBoUHp1ctdKzgQWAZ8FlgI2IQ16cmEtDi5pKVI/voHA7hHRXbXaM8CakkoztI2ydQ3jBK/2PFWCmVWrR5+MkoZLOlXSC8CtpHl59geGkubmGQ5cUasgzWriqafg1lvTCJkDG9dHxKxTTu5a0dbA9yLinoh4NyKeBv4LWEvSar05sKQBpBrB9YFdI+L1Cna7NXvdu+g4q5OSz5t6E09POMGrPSd4ZlaNqgZUkXQocCTwOVJzkYuBiyNiStFmN0p6G7i9ZlGa1cJZZ6Uv06NH5x2JWVJolvnuu/nGYdVYDXihpOx5Uh+3VYFXe3Hs84DdgBOB5SVtVbTukYiYJ2kCQETskL1OkfQbYIwkAf8GTgNeJjUZbbhhk+Y3fJAVoK0HWikkeB5oxcy6U+0jr3HAa8DOEbFORJxRktgV/BP4Qa+jM6uVGTPSKJmHHAIrrZR3NGaJa+5aVb1GwCn02xsL3FeyFGoF+2dLsRNI0zH8ArgGmAGMiojcnhp4qoT68EArZtadaj8JV88mLJ/Q1UYR8WpEfL8XcZnV1q9+BXPnpoFUzJqFk7tWdYuk1wsLH9TWTSguz9ZVLCKGR4Q6WV7KthkZESNL9psXEd+IiJUiYkhE7BYRL9biQnvDCV59OMEzs65U1SwzImbWKxCzunnvPTjnHPj852GzzfKOxuwDHi2zFfnBZRU8F159eC48M+tMtZOYI+kA4MvABsDg0vUR4Xmhrblcey1MmQLnnZd3JGYfVqi5c5+7luFWKT2TRz+8Rid4QMP74TnBM7NSVbVfkHQw8FvgOdL8dteThmzuB8wGzql1gGa9NmYMrLsu7L573pGYfZibZVof4pE0a89z4ZlZqWo/+b4FnAF8LXt/XkQcBawNvAG8U8PYzHrv73+H++6DE06Afo2/0Zt1yc0yrY9xgld7nirBzIpV+6m3PnBPRCwEFgLLAETEW8BPgONqG55ZL40dC8ssA0cemXckZotzs0xrAv3mvtfQ8znBqz0neGZWUO0n3iwg+zbCVOBjResErFCLoMxqYupUuPJKOPpoGDo072jMFudmmdYklnxiakPPl0eC1+4jaTrBMzOoPrmbCGye/Xw9cIqkL0s6HPgp8EAtgzPrlfPOg4UL4ThXKFuTcrPMlibpFEmrd7JuNUmnNDqm3mj3BA/af6qEWydv6KkSzPq4aj/lfgRMzn4+Bfg7cB5wManP3ejahWbWC3PnwoUXwl57wTrr5B2NWXlultnqTiUNLlbO6tn6luIEr/Y8F55Z3yZpF0mTJD0n6dtdbLefpJA0Ins/XNJcSf/IlgsqOV9Fn3CSlpS0L7AtMEDSKhHxZkTsBSwNLBcRW0bEC5Ucz6zuLr0Upk+Hk07KOxKzzrlZZqsTEJ2sWwNoyblhneDVnhM8s75JUn/gXGBXYGPgIEkbl9luKHACi7eCfD4iPpEtx1Zyzm4/3SStAzwJXEVqenkJMEnSKICImBcRsys5mVlDRKSBVD7+cfjc5/KOxqxzTu5ajqTDJd0h6Q5SYnd+4X3Rci/we+CufKPtuTwSvHYfaMUJnlmftAXwXES8EBHzgSuAvcpsdwZwJtDrpjyVfLKdCSwCPgssBWwCPAJc2JMTStpY0gRJ70iaJun0LKutdP9+kh7Kqi2/0JMYrM3dcQc88USqtZPyjsasc4U+d26W2UreAaZni0gDjU0vWV4k3TtbuqtCoxM8aP+RNOe8uGzbD7TiufCsD1pR0sSipfiz/yPAK0Xvp2Rl75P0SWDNiLihzLHXlvSIpLskfbaSYAZUsM3WwDcj4p7s/dOS/it7XS0iXq3kRACShgG3A0+RstZ1gZ+TkszvVXiYYyj5pZh9yJgxsPLKcOCBeUdi1rUBA4h+/ZBr7lpGRFxFasmCpIuBM9q5S8KST0xl7qaNveUOmzSfmRsObNj5hj7fj7fWXdSw80FK8pZee1bDznfr5A0Ztdakhp0PUpJ36LB7G3pOs97oP6/HD3zeiIgRnawrV8vwfnN+Sf2AXwJHlNnuVWCtiJgu6dPAdZI26a7FZCVXsBpQeuN6Pgt21Qr2L3YssCSwT0TcFhEXAN8HviFpme52zpLDHwLfrfK81lc8+yz85S9w7LEf1IqYNbFFSyzhZpktKiKOjIgXJK0uad9s9Oh9OhtBs1Ut+cTUtu+H57nw6sM1eGZMAdYser8GMK3o/VBgU6BD0kvAVsD1kkZkXd+mA0TEQ6T8a4PuTljpp1lnHcartStwS0nGeQUp4duugv3PAO4BJtQoHms3Z58NAwbAV76SdyRmFVk0cKCTuxaVdRM4D3iZVJt3IXA18LKkc7Mnsm2jLyR47d4PzwmeWcM9CKwvaW1JA4EDSdPJARARsyJixYgYHhHDgfuBPSNioqSVCl3XsjFQ1mfxCrfFVPopdouk1wsLqZoQYEJxebauKxsBzxQXRMRkUh+GjbraUdLmwJHAyRXGbH3NrFlw8cVw0EGwarWVymb5WLTEEu5z17pOB44CvgMMJz2oHJ69Pwo4Lae46qbdEzxo/4FWPBeeWeNExALgOOAW4Gngyoh4MhtzZM9udv8c8JikR0kPDo+NiBndnbOSPnffr2CbSg0D3ixTPjNb15WzgXMj4jlJw2sYk7WLiy6COXPgxBPzjsSsYuFmma3sMOB7EfGzorLJwE8lBWlY65aayLwSje6H1+g+eND4fniN7oMHje+H5z541ldFxI3AjSVlZe8NETGy6OdrgGuqPV+3yV1E1DK5g/JNPLuaKwhJBwIbAntUepJspJrRAKussgodHR3VRdkDc+bMach5Gq0lrmvhQrY880zmbbYZ/5g9GyqItyWuqwd8Xa1lxIABvP7KKzzVZtfWrv9eJVYGHutk3WPZ+rbkBK/2nOCZWS1UUnNXSzOB5cqUL0v5Gj0kLUGaX+8nQD9JywGFwVeGSBoaEW+V7hcR44BxACNGjIiRI0f2PvpudHR00IjzNFpLXNe118Jrr7HkOedUHGtLXFcP+Lpay5xBg1h5mWVYuc2urV3/vUr8k9R/4tYy6w4EGjs8YYPlkeABbT2SphM8M+utRnf2foaSvnWS1gSGUNIXr8gQ0sgyvyAlhzOBR7N1V5Dm3LO+buxY+OhHYa9y80KaNS8PqNLSfgAcIel2ScdK2lvSf0m6HTg8W9/WPBde7fWVufDMrD4andzdBOwsaWhR2QHAXOCuTvaZA2xfshyUrfsO8J/1CdVaxiOPwF13wfHHp5EyzVqIk7vWFRFXAruQHkKOJfWNOAtYCtglmxOv7TnBq4++kOA5yTOrvUZ/Wl0AzAP+KGnHrF/cacAviqdHkPScpN9AGmUmIjqKF9IwoQCPR8QDjb0Eazpjx8KQIXD00XlHYlY1j5bZ2iLi1ojYmjRS5qrAkhGxTUTclnNoDeUErz7aPcED1+KZ1VpDP6kiYiawA9Af+DNpJM5fAqeWbDog28asa//6F1x+ORxxBCxXrjunWXPzaJntISIWRcTrEdGrDlqS1pN0oaRHJS2U1FHhfiMk3SppuqQZWVPRLXsTS7U82Xl9OMEzs2o0vA1bRDwFfL6bbYZ3s/4l0gib1tddcAHMnw8nnJB3JGY9smjgQHhrsTGhrEVkk9IeAWwBrEaaB/YB4LcR0ZPMYxNgN1ILlYpGDsn6rt8OPEyangHgW8CtkjaPiJd7EEePtftImoUEr50HWikkeB5oxaz1NP4RlFmtzJsH558Pu+0GG2yQdzRmPeJmma1L0seAZ4FzgU2BhdnrucBzkjbuwWH/HBFrRsT+wJMV7rM7MBTYJyL+EhF/AfYGliYlig3X7jV40P6TnYMHWjFrRU7urHX94Q+pWeZJJ+UdiVmPLXKzzFY2DpgFrBsRW0XEnhGxFbBeVn5BtQfsYbPOJYAFpAHICuZkZbm1cnGCV3tO8MysO07urDVFwJgxsPHGsOOOeUdj1mMeLbOljQBOiYjJxYXZ+1OAzzQojmuAd4CfS1pZ0sqk/uwzgVxH7MwjwWv3fnhO8MysK07urDX97W9pCoQTTwS5+6W1rkUDB7pZZut6CRjcybrBwORO1tVUREwjTRO0L/CvbNkH2Dki/t2IGLrikTRrz3PhmVlnnNxZaxozBpZfHg45JO9IzHrl/7d35+FyVNX6x79vEpIwE2ZEkCciruMAACAASURBVDAIAvLTawQZrgRUZgGRSUUB4SIKiNcJnBHkKiIYAgFkUATEiCgKyAwGZRAhIkKEaJgDqEDCEBIIJOv3x66GptPnnO7T1V3ddd7P89TT3dW7ulad09PqvWsvz5bZ044GvlM7K6Wk9wDHAkd1IghJqwGXAFOBHbNlKvA7SWv2sc0hku6UdOf8hfPaHqMTvPYYCgmekzyz5ji5s97z8MPwm9/Apz4FSyxRdDRmLVm42GJpxteIokOx5n0dWAa4VdKTWfmCJ4FbgGWBr0r6c2VpYxxfIs1+vWdEXB0RV5N68RYAX6y3QUScFRHjImLcyGGLtzG01znBa4+yJ3jgXjyzZnS8FIJZy047LQ3F/Mxnio7ErGULR2ZTuM+fD6NGFRuMNevebCnaBsC0iHilsiIi5kuaBqxTXFiLqiR4ZS+V0MkyCVBMqYROlkkAl0owa5STO+stL7wA55wDe+0Fb35z0dGYtWzhYoulKy+95OSux0TEgUXHkHkE2EnSyEptPUmjSGUZLi80sj64Fl7+nOCZGXhYpvWan/4UnnvO5Q+sNF5L7nzeXU+TtISkIyRNkvQNSW9p4XH2lLQnsDqwUuW2pCWyNjMknVu12TnAm4BLJe0saRfgN6Si6me1dmTt41IJ+StiiKYnWjHrLk7urHcsXAgTJ8Jmm6XFrAReG5bp5K4nSDpJ0j9q1i0N/AWYAOxDKoNwt6S3DmIXK5PKF/wSeA+wYdXtlbM2I4DhlQ0iYiqwA6mQ+QXA+cASwAci4u5BxNAxTvDy51IJZkObkzvrHVddBf/8p3vtrFSikty5HEKv2Aa4sGbdF4G3Av8TESuSetEeBr7R7INHxMMRoT6Wh7M2a0XEATXb3RAR742I5bNl64iY0vTRFcAJXv6c4JkNXU7urHdMmACrrw4f/nDRkZjlxsMye85apDID1T4M/D0ifgyQ1ZY7Cdiys6H1Lhc7z58TPLOhycmd9YZp0+D66+Gww6DyZdisBDwss+eMAF7rZpW0PPA24Maadg8Dq3YurN7nUgn5GyrFzp3kmb3OyZ31hlNOgdGj4ZBDio7ELFdvmC3TesE/gPFVt3fJLq+pabcyMKsTAZWJE7z2KHuCB+7FM6twcmfd7+mn4YIL4OMfhxVWKDoas1x5WGbPOQ04WtJESV8DTgQeAq6tabcd3VEDr+c4wWsPJ3hmQ4OTO+t+Z5+dejWOPLLoSMxy52GZvSUiziPNhrkH8BVgOvCh6gLiklYCdgN+W0SMZbD4vY+XfqKVpR8YVvrz8JzgmXWekzvrbq+8AqedBh/4AGy0UdHRmOXOs2X2noj4bkS8OSKWymaovKfm/qciYtWIOKOoGMui7AkelH+iFdfCM+ssJ3fW3S65BJ54wr12VloelmnWPyd4+fNMmmbl5eTOutspp8B668GOOxYdiVlbeFim2cCc4OXPCZ5ZOTm5s+71pz/B7benXrthfqpaObnnzqwxroWXPyd4ZuXjb8zWvSZMgGWXhf33LzoSs7ZxKQSzxnkmzfwNlVp4ZkOFkzvrTjNnpvPtDj4Yllqq6GjM2iY8LNOsKU7w2mMoJHhO8mwocHJn3WnSJIiAww8vOhKztvI5d2bNc4LXHmVP8MC9eNZ5knaQNF3SDElH17n/UEn3SPqrpJslbVh131ey7aZL2r6R/Tm5s+4zdy786Eew++6w1lpFR2PWVjF8eDqn1MMyzZoyVGrhdZoTPLP8SBoOTAJ2BDYEPlKdvGUuioi3R8Q7gO8DJ2fbbgjsC2wE7ACcnj1ev5zcWfe58EKYPRs+97miIzHrjFGj3HNnNkhDIcEr+0QrTvCsxDYFZkTEgxExH5gM7FbdICKer7q5JBDZ9d2AyRHxckQ8BMzIHq9fTu6su0SkiVTe+U7YaquiozHrjNGjndyZtaDsCR6UfyZNFzu3klodeKzq9sxs3RtIOkzSA6Seu882s20tJ3fWXa67Du67L/XaSUVHY9YZo0Z5WKZZi5zg5c+lEswasqKkO6uWQ6ruq/dlNhZZETEpItYBjgK+3sy2tUY0ErFZx5xyCqyyCuyzT9GRmHWOh2Wa5WLxex9n3sYD/rCdm0qCN3v9kR3b59IPDOOFdRZ2bH9zHlqWpcY+17H9QUrwtltzesf2d8HsLfj4mFs7tj/rTsNfisH+aPN0RIzr476ZwBpVt98MPNHPY00GzhjktoB77qybTJ8OV14Jn/50+rJrNlR4WKZZbjyTZv5cC89s0O4A1pM0VtJI0gQpl1U3kLRe1c2dgX9m1y8D9pU0StJYYD3gzwPt0MmddY+JE2HkSDj00KIjMessD8s0y5UTvPYYCgmekzzLU0S8ChwOXAPcB1wcEdMkHStp16zZ4ZKmSfor8Hlg/2zbacDFwN+Bq4HDImLBQPt0cmfdYfZsOO88+OhH07BMs6HEwzLNcucErz3KnuCBe/EsXxFxZUS8NSLWiYjjs3XfjIjLsutHRsRGEfGOiNgmS+oq2x6fbbd+RFzVyP6c3Fl3OPfcVN/uyCOLjsSs8zws06wtXAuvPZzgmXUvJ3dWvFdfhdNOg623hne8o+hozDrPwzItI2ldST+SdLekBZKmNLHtHpLukDRP0jOSrpa0ZBvD7RlDIcEr+0yaTvDMGuPkzor329/CI4+4aLkNXR6Waa/bCNgJ+Ee2NETSwcBFwFXAjsDBpJPyPSt2puwJHpS/VIJr4ZkNzMmdFW/CBBg7Fj74waIjMSuGh2Xa6y6PiDUiYi9g2oCtAUkrAj8EjsjO45gSEZdGxBER0dk57LucE7z8uRaeWXdxcmfFmjoVbr4ZjjgChg8vOhqzYrjnzjIRMZgCZntnlz/NM5aycoKXPyd4Zt2j48mdpA0l3SBprqQnsqlA+/1WL+ndkn4iaUa23XRJ35I0ulNxW5uccgostRR88pNFR2JWHJ9zZ63ZDJgOHCRppqRXJN0uyd9G+1BEglf2iVac4Jl1h46+8iWNAa4HAtgNOBb4AvDtATbdB1gHOIF0LsIkUh2In7UtWGu/J5+EyZPhwANh2c5/KJh1DffcWWtWBdYHvg4cBXwQeBG4WpJry/TBpRLy52LnZsXrdM/docDiwB4RcV1EnElK7D4vaZl+tjshIt4bEWdn5xJMBL4E7CHpLR2I29rhzDPTTJlHHFF0JGbF8jl31pphwFLAQRHxs4i4GtgdWEAqnrsISYdIulPSnfMXzutgqN3FCV57DIUEz0medatOv+J3BK6JiOer1k0mJXxb97VRRDxVZ/Vd2eXK+YVnHfPSS3DGGbDLLrDeekVHY1YsD8u01szKLqdUVmSfs1OBDettEBFnRcS4iBg3ctji7Y+wiznBa4+yJ3jgXjzrTp1+tW8A3F+9IiIeBeZm9zVjC2Ah6TwD6zU//zk89ZSLlptBSu7mz4eIoiOx3nQf6XQH1awX6XPSBjBUip2X/Tw8J3jF/Fhh3aXTyd0Y4Nk662dn9zVE0qrA14ALanoBrRdEpIlUNt4Ytt226GjMijc6mxtqfudn1bNSuIKUyG1TWSFpWeBdwN1FBdWLyp7gQfknWnEtPBvqiihuWu+nafWxftGG0kjgYmAO8L/9tDsEOARglVVWYcqUKU0H2qw5c+Z0ZD+dlvdxLffXv/KOu+/m/i9+kX/ddFNuj9ss/796S5mPa8Zjj7Eu8MfrrmPBUksVHVIuyvr/ajdJS5AmDgNYHVhG0p7Z7SsjYq6kGcBNEXEQQETcKem3wLmSjgaeBr4MvEKagMyasPi9jzNv49U7tr8x0+cze/2RHdsfpATvhXU616k756FlWWpsZ0suXvvo+my3ZucGd10wews+PubWju3PrC+dTu5mA8vVWb8s9Xv03kCSgPOBjYAtI2J2X20j4izgLIBx48bF+PHjBxNvU6ZMmUIn9tNpuR/XhAmwwgpscOyxbLB4ced6+P/VW8p8XOtutBEA/73pprByOU4jLuv/qwNWBn5Zs65yeyzwMOmzu7aE0H7AicDJwBLALcC2/X1OWt+c4OXPCV77FNEDbN2r08My76fm3DpJawBLUnMuXh9+SCqhsFtENNLeus2DD8Jll8Ghh0KBiZ1ZV6kMy/SMmUNeRDwcEepjeThrs1ZEHFCz3ZyI+HRErBARi0fE+yPiniKOoSxcCy9/roWXnyImybHe0OlnxlXA9pKWrlq3DzAP6Hd8nqSvAEcA+0XEze0L0drq1FNh+HD4zGeKjsSse4walS49Y6ZZV/FMmvlzLbzmtq+OvYjk2HpPp5O7M4GXgV9Len92XtwxwMnVE6NImiHp3KrbHwX+jzQk83FJ76laVursIdigPf88nHsu7L03vOlNRUdj1j0qyZ177sy6jhO89hgKCZ4nWrEidPTVnI39fx/pXIHLSQXMfwh8q6Zp7fkE22WXBwC31Sw7ty9iy9V558ELL7j8gVktD8s062pO8Nqj7AkeeCZN67yOv5Ij4u8RsW12TsBqEfGNiFhQ0+YN5xNExAH9nINwXqePwQZhwQKYOBE23xw23bToaMy6i3vuzLreUKmF12lO8Mzy5bMxrTOuvBIeeAA+97miIzHrPj7nzqxnDIUEr+wTrTjBszJzcmedMWECrLEG7LFH0ZGYdR8PyzTrKWVP8KD8M2m62LmVlZM7a7+//Q1uvBEOOwxGdLq0olkP8LBMs57jBC9/LpVg1jond9Z+Eyemmnb/8z9FR2LWnTws06wnuRZe/pzgmbXGyZ2111NPwYUXwv77w/LLFx2NWXfysEyznuWZNPPnWnhmg+fkztrrRz9KX1g/+9miIzHrXh6WadbTnOC1x1BI8JzkWd6c3Fn7zJ8Pp58O228Pb3tb0dGYdS8PyzTreU7w2qPsCR64F8/y5eTO2ueXv4Qnn3T5A7OBuOfOrBRcC689hlKC50TPWuXkztojAk45BdZfH7bbruhozLqbz7kzK5WhkOCVfaKVbujBKyIG631O7qw9brsN7rgDjjwShvlpZtavESPS68TDMs1Ko+wJHpR/Js0iauGZtcrfuq09JkyA5ZaDT3yi6EjMesOoUe65MysZJ3j5GwqlEuop4ritNzm5s/w9+ij8+teprt2SSxYdjVlvGD3ayZ1ZCTnBy99QTfDMGuHkzvI3aVK6PPzwYuMw6yWjRnlYpllJudh5/pzgWa+QtIOk6ZJmSDq6zv3vlfQXSa9K2rPmvgWS/potlzWyPyd3lq8XX4SzzoI99oA11yw6GrPe4WGZZqXmUgn5GwrFzq23SRoOTAJ2BDYEPiJpw5pmjwIHABfVeYh5EfGObNm1kX06ubN8XXABPPtsmkjFzBrnYZlmpecErz2GWoJXxN/YBm1TYEZEPBgR84HJwG7VDSLi4Yj4G7Awjx362WH5WbgwlT8YNw62cJ0Ws6a4585sSHCC1x5DLcGznrE68FjV7ZnZukaNlnSnpD9J2r2RDZzcWX6uvRbuvz8VLZeKjsast/icO7MhY6gUOy/7eXhO8CyzYpaAVZZDqu6r94U4mnjsNSNiHPBRYIKkdQbaYEQTD27Wv1NOgdVWg732KjoSs97jYZkGSFoX+BLwHmBj4I8RMb6J7YcBdwD/BXwwIq5oR5yWj8XvfZx5GzfzI35rxkyfz+z1R3Zsf5CSvBfWyWW0WUPmPLQsS419rmP7qyR42605vS2Pa50zbN4rg/3R5eksAatnJrBG1e03A080+sAR8UR2+aCkKcA7gQf628Y9d5aP++6Dq6+Gz3wGRnb2g8OsFDws05KNgJ2Af2RLsw6muSE/VrCy9+CBZ9K0Ie0OYD1JYyWNBPYFGpr1UtIYSaOy6ysCWwJ/H2g7J3eWj4kT05fTT32q6EjMepOHZVpyeUSsERF7AdOa2VDSGOB44Gtticzaxgle/pzgWTeIiFeBw4FrgPuAiyNimqRjJe0KIOndkmYCewE/klR5738bcKeku4HfA9+LiAGTOw/LtNbNmgXnnw8f+xistFLR0Zj1Jg/LNCAiWhm/dhxwC3BDTuFYBxUxRBPo6DDNsg/RhJTg5T1Esz9FJOrWnIi4EriyZt03q67fQRquWbvdrcDbm92fe+6sdeecA3PnuvyBWSs8LNNaIGkT4EDgi0XHYoPnmTTzV4ZaeEX0QlrvcnJnrXn1VTjtNNh2W9hkk6KjMetdHpZprTkVmBQRM4oOxFrjBK89ej3BM2uUkztrzaWXwmOPudfOrFXuubNBkrQvsD7wnSa2OaQybff8hfPaF5wNihO89nCCZ0OBkztrzYQJsM46sPPORUdi1tt8zp0NgqTFgBOBE4BhkpYDlsnuXlLS0vW2i4izImJcRIwbOWzxDkVrzRgqtfA6zQmelZ2TOxu8O+6AW2+FI46A4cOLjsast3lYpg3OkqQT8U8GZmfL3dl9k4G7CorLcjIUEryyz6TZbILnhNBa4eTOBu+UU2DppeHAA4uOxKz3jRoF8+dDRNGRWG+ZA2xTs3wku++rwMcKistyVPYED8pfKuHaR9d30mYd4eTOBueJJ+AXv4CDDoJllhm4vZn1b/TodDnf01oPZZKWkLSnpD1JxchXqtyWtETWZoakcyHVUIqIKdUL8Kfs4e6JiNsLORDLnRO8/PViLbwihrJab/EzxAbnjDNgwYI0JNPMWjdqVLr0eXdD3crAL7PlPcCGVbdXztqMADwWfghygpe/XkzwzPrj5M6aN28enHkm7LorrL120dGYlUMlufN5d0NaRDwcEepjeThrs1ZEHNDAY1zRqbitc4pI8Mo+0UoZauGZVTi5s+ZddBE8/TR87nNFR2JWHpVhme65M7MBuFRCe3RjgucC5tYsJ3fWnIg0kcomm8DWWxcdjVl5eFimmTXBCV57dGOCZ9YMJ3fWnN//Hu65J/XaSUVHY1YeHpZpZk1yLbz2cIJnvWxE0QFYj5kwAVZaCT7ykYHbmlnjPCzTzAZp8XsfZ97Gq3dsf2Omz2f2+iM7tr9KgvfCOgs7ts85Dy3LUmOf69j+nOBZXtxzZ42bMQOuuAIOPfT1L6Jmlg8PyzSzFpS9Bw+GxkyaZq1ycmeNO/VUGDECPv3poiMxKx8PyzSzFjnBy58TPOs1Tu6sMc8/Dz/5CeyzD6y2WtHRmJWPh2WaWQ6c4OWvVxK8IibZse7T8eRO0oaSbpA0V9ITko6VNGAxVknLSvqJpNmSnpP0M0krdCJmA378Y3jhBZc/MGsXD8s0s5y4Fl7+eiXBM+voK0PSGOB6IIDdgGOBLwDfbmDzXwDjgYOBA4B3A79pR5xWY8ECmDgRttoK3vWuoqMxKycPyzSzHLlUQv6KKHbenyJ6Ta37dbrn7lBgcWCPiLguIs4kJXafl7RMXxtJ2hzYHtg/In4VEZcC+wFbSXp/JwIfyla47TZ46CE48siiQzErLw/LNLOcOcFrj04leLX7KeJYrfd0+lmyI3BNRDxftW4yKeHrryL2jsC/I+IPlRUR8Wfgoew+y9usWXD55XDUUax32mmw5pqw++5FR2VWXh6WaWZt4ASvPbqpB8+sWqfr3G0A3Fi9IiIelTQ3u+/yfra7v876+7L72mvWLJg5c8BmSz7wACy/fNvDaYuFC+Hee+Hmm9MybVpav9hivPzWtzL65JPTTJlm1h6V5O7BB+Fvfys2lhwM+v1wk03yD8ZsiKskeK6Fl69O18Iza0Snv62PAZ6ts352dt9gtls7h7j695vfwEEHDdjs3W0PpAOWWQa23BI++tF0jt27381dt9/O+PHji47MrNyWXDL9gHLCCWnpcYN6Pxw+HF59Ne9QzCxT9mLnkJI8J3g2lBXRFRN11qmP9YPeTtIhwCEAq6yyClOmTGkixDcavcQSLPXtged8eemllxjdw8W9X3rTm5gzdmz6ggWpN+/225kzZ05Lf79u5ePqLUPhuJaeOJFRTz1VbEA5GdT7ocTTJfwfm3UTJ3j5c4Jn3aTTyd1sYLk665elfs9c9XYr1Vm/XF/bRcRZwFkA48aNi070PE2ZMoVxJezhmjJlSil77nxcvWVIHFeJjq+s74dmZeAEL39O8KxbdPoM1PupOUdO0hrAktQ/p67P7TJ9nYtnZmZmZn1wLbz85TnJiidsscHqdHJ3FbC9pKWr1u0DzANuGmC7VSVtVVkhaRzpfLur2hGomZmZWZl5Js38dVstPBt6Op3cnQm8DPxa0vuz8+KOAU6uLo8gaYakcyu3I+I24BrgfEl7SNod+Blwc0Rc39EjMDMzMysJJ3jtkXeC5xp31qiOPlMiYjbwPmA4qezBt4EfAt+qaToia1NtX1Lv3o+B84GpwIfaGa+ZmZlZ2TnBaw/34FkROj5bZkT8Hdh2gDZr1Vn3LHBgtpiZmZlZToZKLbxOTrICnmjFOs99vGZmZmYGFDPRSict/cCwnp5oxWwgTu7MzMzM7DVlT/Cgt2fShGL+ZjY4knaQND2bU+ToOvePkvSL7P7bJa1Vdd9XsvXTJW3fyP6c3JmZmZnZGzjBy1+jCZ57+spD0nBgErAjsCHwEUkb1jQ7CJgdEeuS5iI5Idt2Q9KcIxsBOwCnZ4/XLyd3ZmZmZrYIJ3j5c+I25GwKzIiIByNiPjAZ2K2mzW7AT7PrlwDvk6Rs/eSIeDkiHgJmZI/XLyd3ZmZmZlaXi53nz7XwhpTVgceqbs/M1tVtExGvAs8BKzS47SI6PltmEaZOnfq0pEc6sKsVgac7sJ9O83H1Fh9Xb/Fx5e8tBe23Jz3/yn+evvrxUzvxGdmobn1NDN24BpfftRbXNYPeciBD9/84ON0YV3VMub3fP//Kf665+vFTVxzEpqMl3Vl1+6yIOCu7rjrto+Z2X20a2XYRQyK5i4iVOrEfSXdGxLhO7KuTfFy9xcfVW3xcVrROfUY2qlufO46rOY6rOY6rce2KKSJ2yPsxSb1ta1TdfjPwRB9tZkoaASwLzGpw20V4WKaZmZmZmVn+7gDWkzRW0kjSBCmX1bS5DNg/u74ncGNERLZ+32w2zbHAesCfB9rhkOi5MzMzMzMz66SIeFXS4aSBxsOBH0fENEnHAndGxGXAucAFkmaQeuz2zbadJuli4O/Aq8BhEbFgoH06ucvXWQM36Uk+rt7i4+otPi6zN+rW547jao7jao7jalw3xtSniLgSuLJm3Terrr8E7NXHtscDxzezP6VePzMzMzMzM+tlPufOzMzMzMysBJzcmZmZWdtJWlfSjyTdLWmBpClNbj9M0lRJIWmXbohL0h6S7pA0T9Izkq6WtGSRcUkaJ+naLJ5Zkq6XtFlOMe0l6TJJj0uak/0/PtLAdqMknSTpP5JelPQ7SWvlEdNg45K0vqRJku6TNFfSg5JOkbRckXHVeYzfZM/5w7shLknvlXRT9n98Nru+ZpFxSVpP0q8k/VvS85JuldSOmS97gpM7MzMz64SNgJ2Af2RLsw6mgQK+gzCouCQdDFwEXAXsmMX3T/Kbz6DpuCStAVyfxfAJ4OPZ9Wsl5VEP7PPAHOB/gV2B3wMXSTpigO0mAgcAXyTNBrgicJ2k0TnENNi4PgBsCZxB+jt/h3Te07WS8vp+PNi/FwCStgPek1MsLceVJUzXA3dn2+0H3AYU9n+UtDRwHbA28GnS8+sJ4HJJm+YUV0/xOXdmZmbWdpKGRcTC7PolwIoRMb7BbceQEpyjgXOAD0bEFUXFJWlF4CHg8xFxdh5x5BTXocAkYIWIeDZbN4ZU8PnwiDijxZhWjIina9ZdBGweEWP72ObNwMPAJyPi/Gzd6qS/32ci4pxWYmohrhWAWVH1RThLpq4BxkfETUXEVdVuMeBvwA9Iz/kjIuK0VmMabFxZPA8C50fE1/KII6e4diD9wLJJRNyTrRsBPA6cFxFHtSPWbuaeO7MeJWlbSSdKulzSzZL+mF0/UdI2RceXF0mbSDpA0v6SNi46HjMbnEqiMkjHAbcAN+QUzmsGGdfe2eVP84yl2iDjWow0ZfqcqnVzsnXKIaan66y+C1i5n822yy5/XfU4jwM3k3o8WzaYuCLimerErmob+tuu3XFVORKYB/wkj1iqDTKuD5CKaE/KO56KQca1WHb5XNXjvAq8SA7P+V7kUgg5kCTgg8B/AQHcCVxZ502j60nalvRmuwEwhnQ8zwL3k47p9wWGlxtJm/D6/2tqRNxbcEgNk7Q8cCnw36RfPu/LLgUsB3wI+IKkPwB7RMSsomJtRvbr3Ncj4sHs9mjg56ShGZU36JD0K+BjEfFKMZEOjl9bZoOTPacOBP5f0bFU2QyYDhwk6WvAKsBfgP+NiFsLjOtXwLHASZIq06d/E5gN/LJN+9yCVIerLxsAMyNiTs36+4DxbYoJBo6rr20YxHbN7qPfx5e0KvANUg/1wvQ1s+0Gimsz4BngPZJOAMaSPr++EhGXFxjXDaSe4R9I+gIpqTuUlBCe18a4upZ77pqUnaT5tqrbY0jV4n9DGiv8BeBy4JZsHHBPkLS8pJtIY6n3IH2Zfgh4JLv+IeAGSVOy5KInSLpI0tpVt0dLupT0S9CPSb+I3S3p4mzIQS+YCKwKbBYR60TELhHx8YjYL7u+LrBp1uaUQiNtzr6k8zAqjge2Bw4jvUmvlF3fBfhqx6MbJL+2euq1Zd3pVGBSRMwoOpAqqwLrA18HjiL9wPsicLWkVYoKKiKeALYBPgz8O1v2ALaPiKfy3p+k9wG70X9vzhjSD1m1Zmf35a7BuGq3WQL4HnBTREwrOK7vA9dExB/aEUetBuNaFViSVGPuB8AOpKTrUklvLyquiJhL+pFgI+BRUgJ6FLBbRLQzSe9eEeGliQVYCGxadftcUjX5HarW7UB60/ph0fE2cVwXkn6FfHc/bcaRfqW5oOh4W/h/nQTMJf2qsyKwQnZ9LvCtouNt8JieJb1pDdRud+DZouNt4X/1BPDNOu2OBf5RdLxNHJdfWz3y2vLSuQW4BJjSQLt9gX8By2S31yL1Cu9ScFzXZXFUf/Yvk332H1dgXKsBM4DfZt9FApnCYAAAFDtJREFUdiD94DwTWDPnmNYiJY+XDtDubOCuOuuPBx5vw9+qobhqthFppMgzwNptem41+vfaPHvffEvVuiCdM1lkXGdncRxatW44aRKh3D+7mohrSVIny82kkT7vJ/24+Czwznb8zbp9cc9d63YFjo2IqysrsuvHk34t6xW7AF+OiDv6ahARd5JOZv9gx6LK30eA70XEmRHxdKQx92eSfoX6WMGxNWohjY0jV9a2V60MTKmz/iYgl2mXO8Svrd55bVkXyXp8TwROAIYpTVG/THb3kgWPjqkMd59SWRERzwNTgQ2LCCjzJdIpN3tGxNXZ95EPAwtIM1XmIhtlcBWpp2S/AZrPJp0yUGs56vfodSquaieQRlHsHtmpAQXGNQH4EfCcpOX0emmGxSUtW2Bclef8a6cQRMQC0mdyrs/5JuM6KNv/LhFxWURcHxEHknoVv51nXL3CyV3rliOdY1drKqkLu1c4YeidhOG3pPMptuyrgaQtSF+KLu1YVPnYQtJOknYi/YK6TJ02y5BOMu8Vfm31zmvLusuSpAkcTiYlCLNJU7ADTOb1yS+KcB+pF6P2tV3063gDYFpUnZMcEfOBacA6eewgG754BTAS2DkiXhxgk/uBNbRo/b8NsvtyMYi4Ktv9Lynx/URE/DGveFqIa33gc7z+nJ+drf8+6XOxqLju6+uhyPE5P4i4NgAeiWx22Cp/JafnfK/xhCqD82FJ47Lrs0nnAtVaEXi+cyG1rJIwPBURt9Rr0OMJQ+VcrjIkDEcCFwN/lPQv0ofjs6QvGsuR3uhWBa4l1YrpJSfX3N6O9CZfbUvSMJBe4ddW77y2rLvMIZ0/Vm1V0vC5rwI3djyi110BfIsU35UAWa/Ku0i91UV5BNhJ0sgsqUPSKGBj0vDMlmRTzP8SWA/YMiL+08Bm12aXHyINU0fSm0iTgn2m1ZhaiAtJHyUNKf9CRFycRyw5xLULi34//z3pfPtfL9q8Y3FdQ5p19X2kUw2QNBzYmvo/7HUqrkeAtSSNiYjZVevfRZpoZchxcjc4X6q5/UEW/VL2fnL8RaoDnDD0SMKQDf3ZQdLmpPMpKrMvQqpldA5wVUT8qaAQB6teDZuX66x7gfRh3Cv82uqR15a1V/aL/E7ZzdWBZSTtmd2+MiLmSppBmtDioEjTmU+peYy1sqv3RMTtRcQFaSi1pN8C50o6mvTe+2XgFXKaKn4wcZHe/w8mTXJxOqlX5TDSuXhn5RDW6VlMRwLLS6ousH1XRLws6QaAiHhfdjlT0rnAhGx28aeAY0hfyi/MIaZBxSVpa9JsitcCt9VsMzMiZhYRV0TcXPsg2WyZ/4wcau+1ENeTkiYB38v+jzOAQ0i9698tKi7gItKPPVdK+j7pfMX9SBPL7ZJTXD3FyV2TIqLRoax3Ar9oZyx5csLQcwkDEXEbcFvRceQlIh5psF1PjaH3a6v3XlvWNiuz6HT8ldtjSb+yjyBN0tBJg41rP1KP+8nAEqQ6fNvW9B50NK6ImKpU1PlbwAXZ6nuAD0TE3bSuUrOu3kzMlZjq/f8+S5pNtPK3ugn4SES8lENMg41rG1KNtO2zpdq3SQloEXF1wmDj+hLp//h1YHnS0OjtI+KBouKKiMeUavseTzpXcTTpR9Q9I+J3OcXVUxTRc6XYzMzMzMzMrIYnVDErKUlnZ0NhSqWsx2VmZmbWKg/LbBNJ15N6Rt83YOMeIulsYFjV+P5SKOlxbUM5f8Ap5XGV9DlY2uMyMzPrRk7u2keU8AsoJf1iTQmPKyLWLTqGdijrcVHC52CmrMdlZmbWdXzOnVmJSBpNmi75xIgozQyFZT0uMzMzszw5uWsTSYsBq0XEo0XH0ipJY0mzFD0UEQ8VHU9eevW4sumx+7Ic8BiwI3AzQETM7URcrSrrcfUnm9Y9Gp0ptFeU9bjMzMy6nYfKDIKkwyQ9IOkFSbdL+nidZv8F9FLCsJikiZJmSZqT1Qohq2kyA7gemCHpZ1nRyp5Q0uN6oZ/lMdKQ4Kuq1vWKUh6XpEOqCn1X1h0p6SngAeBBSf+WlEsx304p63GZmZn1Mp9z1yRJ+wKnAj8n1ffYEjhP0m7AxyNiXpHxteDLpMKnJwOzgCMkrQTsDhwA/AXYCvgB8ClSocleUMbjmgc8T4r5mZr7lgROA75PqvPSS8p6XGcAfyXVtEPSIcAPSYXNL8na7AmcKunZiLiokCibV9bjMjMz61keltkkSXcCN0bEl6vWvQ/4Gam44s4R8YykzYBbI6IneoMk3Q+cGxEnZre3Av4AfD4iJlS1+zbpGMcVE2lzynhckt5ESoC2IxVaPT0iFmT3LQvMBsZHxB+Ki7J5JT6uhcB7IuLP2e37gT9FxAE17S4ANoiId3c+yuaV9bjMzMx6mYdlNm994MrqFRFxA/AeYFngNknrFBFYi94C/Lnq9tTs8s817W4G1u5IRPko3XFFxBMR8VHgQ8AngXskbV9wWC0r63HVsQ6p57/WZGDDDseSp7Iel1lXkHSApKnZKSGzJd0l6eQ27WtvSQc00O4YSVG1PCHpV41+D5J0XvajedtJGibp8OzvNk/S85KmZaduqBMxmHWCk7vmPQesWLsyIh4GtiANUboV6LVfqV8kTVpR8XK21E5aMZzeGs5b1uMiIv4IvAuYBFwk6QrSjw89raTHNVrSEtmkMc8AC+q0WQD02lCKsh6XWVeR9BXgHOAaYA/gE8BvgV3btMu9SacuNOI5YPNs+SLwDuAGSUs2sO1xTeynVZOB7wC/Jv3d9if9WL9FeBiblUhPfZntElNJ52tdUntHRMzOhmheQpq2vZfeLKYD40gfFkTEQmDxOu02Ig0/7RVlPS7gteOZJGkycDzwR3rreVdXCY/r91XXBWxKmsyn2iakiWN6SVmPy6zbHA78KCK+WrXu8uyUgqK9GhF/yq7/SdKjpPfsnYBf1jbOJi8bHhHzI+KBTgQoaUdgL2CniLiq6q5L3WtnZeOeu+ZdCKwtafl6d2YTquxK+oWtl8ognExjX8DeD1za5ljyVNbjeoOIeCYiDgXeSfpV996CQ8pFSY7rQNIw08pyIFBvGNKmwK86GFerynpcZt1oOeBftSure5wqQxwl7S7pfkkvSbpZ0iLDorNhl/dIelnSY5KOlzSi8jjAh4Gtq4ZbHtNErJXTH9aqE9c04CVgs+r7amJ7r6TfZzNcPydpiqR3Vt2/laSbJM2V9IyksyUtPUBMW2eXN9be4V47Kxv33DUpIn5JnV+iatosAA7pTET5iIiGvnxFxI7tjiVPZT2uvkTE34G/Fx1H3nr5uCLipw2227PdseSprMdl1qX+Qprt+VHgioionVG44i2kHzW/QZqB+NvANZLWi4iXACRtB/wCOB/4Eql3/ThgBeDQ7PqapISyUspkZhOxrpVd/qtm3feBY4F/00epKEnjgetIowL2J51asSWwOnCXpC2BG4DfkGbjXQH4HjAmu92XF7PLEyWd5BqcVmZO7szMzMy622GkhOY8ICTdR+oR/0FEPF/VbkVgt4i4FUDSVFLdyQOAM7M2xwJTImL/7PbV2cjE70r6TkQ8IGkWMKxquGW/Kr1+pInJTifVIq0eor0C8P6I+OsAD/Vd4G5g+6oetaur7v8eaSbyfar2/TjpHL+NI6Kv0R1nk4ZlHkFKkqcBFwETI2LOgAdo1kM8LNPMzMysi0XE34C3kU77OJ10jus3gDslLVXV9D+VxC7b7hHSMMlN4bXz3f6LRUcg/YL0nXDzQYS3AvBKtkwnJXj7RMSTVW0eHyixyyZg2Qz4ab2hktnETZsDF0saUVlIs12/QpqIq66I+BdpeP/2pBqdy5HO575V0siqfZwh6XFJHqppPcvJnZmZmVmXi4iXI+LyiDg8IjYEDgbWAw6qavafOpv+B1gtu74isBhpaGS1yu268wkM4DnSDOHjgDcDa9VMWlL9+P0ZQ0pan+zn/uGk5PaVquVl0jGt0d+DR8SCiLg2Ij5DGnb6E+DtvDGh/Tkp+TXrWR6WaWZmZtZjIuJcSd8HNqhavXKdpisD07LrT5MSotp2q2SXswYRyqsRMVCtukZ6wmYDC3k9Ea31bPY4x1BTbzjzRAP7SMFELJR0LWkiqNFV6/8A4Ak0rZe5585a1snCqnmT9M1sCMbCbIawvtp1XfHYrO2gC8h2snjsQJTcLWn/mvVdU3S21VgkTZJ0bidiNbNykbRI0iZpJWBZ3tgrtrKkLararEnqifozvDbh21TS+WfV9iYlVrdlt+dTlfR0QkS8CNwOfKLee2p2/5+A9SPizjpL3eRO0ir11pOGuM7N9mlWGu65s5YoFVY9jjQL1tGkD4N3AfsBny8wtAFJGkeaSeyrwBTqD2cp4hj3Jg2dOa/B9s8BO2TX1ybFeoOkjbIPw74cR/2af0XYmzTk5qKa9ZOB7YCTSB/qSwFbANsUMH11q7GcCNwv6bsRMaN9YZpZCd0j6bfAtaTPqreQCobPBapnrn0auEBSZbbMY7P251W1+RZpBs2fkN7X3k76PDg7IiqzYt4P7CZpd9JMmU/0lTzl7GjSRCxXSTqLNMvl5sCdEXEF8GXS59tCUk3hF0hDLHcGvhYR/6jzmBdLegG4mFTPdmXgY8BuwP9ExLPtPSSzDosIL14GvQCPA5PqrFfRsTUQ+36kIR7LdNMxkj6wpjTY9hjg6Zp1W2XHtVcf2wwHRhb996+J6Rbg+Jp1O2bHsWM7/vbAeLISRw20zSUW0peWk4r+e3vx4qW3FtJsmdeShh6+REpSLgI2qGpzHqnW5B7AP0jnot0CbFzn8fYB7iH10M0kTS4your+FUm1X2dl733H9BHXIp9BddqcR0rOGrqPVJPuD6TE9VlSWYR3VN2/GWkGzedJyd/fSeUflu1jH5/M2s/MjncW8DtgfD8xR9H/cy9eBrsUHoCX3l6yN9ZvDNBmCnBJzbrx2QfGxlXrKh9MO2dv1nOzN+DlgXWzN/gXszabNBDb3tmH18ukQuavfXhl+4qaZfxgj7Em/t1Jv3q+RJrFa8MW4zqmn30u8sFK6o0L4Et14ppGOt/iv/v4UH1v9neeQ+oRnAK8s6bNVsBN2f/nGdIU00tX3b9R9kE6K/vb3Qcc1s8xrJvFW7uf72XrR7XpuTu+0Q/wvGIBPk2q/TSsHcfkxYuXobvUe0/3Mui/ZRQdgxcvg118zp21qlJYdX9JK+TweGuShpF8nVQIfgvgLNLQkcmkIqUjgMn9nedUVaT1L6ShF6eShrCcljU5DvhOdn1b0rCPv/TxcM0cY6WA7HHAR0nnQ1wjaXQTcf0euCuLaXPgnAH2WWut7LJeAdnvAjtRp4BsVjz2BlLytz/pl90/korHVtpUCsj+i/S/+Fz2eD+peqjLgAWkntFds2Ncup9430dKAu+uWV9ddPYt/WzfCXnFcitp4oK3tx6SmZnlSdI5kmZm12dKavbz16xwPufOWtVoYdVGLQ9sHhEPAEjaBPgSsH9EnJ+tE6lHbwNSr1A9jRRpfSC7747ov4hpM8c4UAHZ3IvHZvtpuoBsndx4oOKxMEABWVLStzawe0TckzW5YYDw3wXcFxELa9bnWnQ2e94Mr1o1PFv/hvfBiHi1zuZ5xTKNlPhuyqLJrJmZFSgiDi46BrNWuefOWhKNF1Zt1MOVxC5TmXjixjrrVqeOvIu0NnmMfRaQbVPxWMihgOxAxWOzNo0UkJ1FGmp6pqR96s3wVseqpEkA3iDyLzq7P2+sjVRJfl+pWRbRSCyS1pB0g6T7slk0v1/bu5wljs9mx2xmlpuIOCAixhUdh5kVy8mdtSwaK6zaqNpZq+bXWV9Z19c0zbkXaW3iGPsrINuO4rGQTwHZgYrHVtr0W0A2633bjtSD92PgX5L+KOmd/Tzu6OwxFhH5Fp29nPR3qiyHZuvfXbPU1UAsrwJHRcTbSIngZqSJDWq9TIenGDczM7OhwcMyLXexaGHVl4CRNc0Gm8g0oh1FWt+gzjFW9FdAtl1x5VFAdqDisdBgAdmIuB/4sKTFSBO3nAD8TtKb6wy9hHTcA/ZkRYtFZyPiGdIEMGTtl8rWN13rr14sWU/pk9n1+ZL+BqxRZ/PlyOE5aGZmZlbLPXfWkgYLq85k0SToA+2KKRov0tqQJorHQj8FZJuIq+uKx1a1abiAbES8EhE3kiaYWY2U1NQzHRhbvaKbis4OJpZs4p3dgWtq1q8ELEGaptzMzMwsV+65s1Y1Ulj1UuAgST8kTYSyDencpXZqpEhroxotHgsDF5Dt5eKxMEABWVJS+gPSeYQPkoZyHgXcHRF99VbdAnxT0koR8VS2rpuKzjYVi6RRpL/NhIionfBnHKn381bMzMzMcuaeO2vVsaRp9ieSkp/jSEMQN42IhwAi4nfAV0lT519KSo4+186gIuJaYF/Sl+nLs/2dBBw+iIcb8BirPEKa3fMYUvL2PGn2yZeaiOv0bD8/Bu4glYRou2x44wdIPUsXkhK0rUkJZqXNzaRaeCsBF5CO4cukSVT+TTrX7t+kRO+q7FjuI/Vy9WUKaZjiDlXrfkr68en/SAnnWaShvdtGxLktHWjzGo4lmzTnZ8BdEXFSncfaAbgpGyJqZmZmliv1MTGemTVJ0nmkouyeraxJkk4B1o2InVt4jIiI/k+8a7OsJtJw4JO1s45mid8jwNERcWER8ZmZmVm5uefOzLrBicB4SW9tdsNuKTqbFXg/iNQre5ekv0r6bFWTvUhDdScXEZ+ZmZmVn8+5M7PCRcRMSQeRJl5parKRbik6GxG3kMpJ9EXAQX0USTczMzNrmYdlmpmZmZmZlYCHZZqZmZmZmZWAkzszMzMzM7MScHJnZmZmZmZWAk7uzMzMzMzMSsDJnZmZmZmZWQk4uTMzMzMzMysBJ3dmZmZmZmYl4OTOzMzMzMysBP4/mfLGt2UT228AAAAASUVORK5CYII=\n", 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\n", 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" ] @@ -338,7 +338,6 @@ "plt.title('Payoff Function', size =15)\n", "plt.contourf(x, y, z)\n", "plt.colorbar()\n", - "# plt.plot(x, x, 'r')\n", "plt.xlabel('Spot Price $S_1$', size=15)\n", "plt.ylabel('Spot Price $S_2$', size=15)\n", "plt.xticks(size=15)\n", @@ -508,7 +507,7 @@ "outputs": [ { "data": { - "image/png": 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KTJ06dfjad9nAwAC5tzna9XObzDzjprbWm73/ei58pPX/ris/MrWt7Y0F/XyctGu0t0mrAz8l6XRJK4BXgN/XeQ1nENixTvp46p/5DOea4v1dpbKpU/7G762Wb2ZmXdTqOJzTgDOA75HOHP4BOBd4DFhJcWlqGMtJ92peI2lPYFtq7700EpX3x0lBcHIl32RgQ1FHMzMbIa0GnE8AZwMXFN+vj4hzgP1IAeOtDdafDxwjaftS2nTS4w9avVd0cvH+IEBErCONE/pQJd904H73UDMzG1mtXhR+M7AkIl6V9ArF5aqI2CDpO8B3SWdAQ7mMdJZ0naTzgb2BOcBF5a7SxSW7RRFxavF9DrA9adDnKuB9wBeB6yLiZ6Xyv0a6v3MJaZzQtOJ1bIv7aWZmXdbqGc7vgO2Kz08C/620bAJpUOeQImIQOII0VucG4BzgYtJZU9kWbDqeZzlpnM6VwM3AKcA3i/dy+feQznyOBBYA7wdO8SwDZmYjr9UznHuB95B+9H9ImiFgJ+CPwGeA2xsVEBFLgcMb5JlU+T6PNICzoYi4nnR2Y2Zmo0irAWcOsEfx+TzSJbWZpDObhcDnulUxMzPrLy0FnIh4FHi0+LyO9Cycz/egXmZm1mc6Gfj5JmB34NmIeKZ7VTIzs37UziOmPy3pKeAJ4EfAk5KelvS/u147MzPrG63ONHAWcClpPM3xwJTifT7w7WK5mZlZjVYvqX0GOC8ivlpJv6WY2+wzpJkHzMzMNtHqJbVxDP1Uz0XUmczTzMwMWg841wMnDbHsg8CNnVXHzMz6VTOPmJ5W+jofuEDSJGofMb0f8Pfdr6KZmfWDZu7h3Ejto6T3AI6pk/dfSE/iNDMz20QzAefNPa+FmZn1vWYeMf1EjoqYmVl/a3mmAUlbkDoIHALsBPwXcDfpUQHtPbDdzMz6XksBR9KuwK3AAaQnfD4PHEwaf/OwpKMj4rfdrqSZmY19rXaLvgh4I/DeiNg7Ig6OiL2B9xbpF3W7gmZm1h9aDTjTgNMj4iflxOL7l0jT3JiZmdVoNeBsBfx+iGW/B97QWXXMzKxftRpwHgBOl7RtObH4fnqx3MzMrEarvdRmA3cCT0m6ldRpYFfSIFABU7taOzMz6xstneFExBLgrcAVwC7AUaSAcxnw1oh4uOs1NDOzvtD0GY6kLYEDgV9FxBm9q5KZmfWjVs5wXgXuAN7Ro7qYmVkfazrgRMQG4BfAxN5Vx8zM+lWrvdS+Apwlaf9eVMbMzPpXq73UziTNKLBE0jOkXmpRzhARB3apbmZm1kdaDTg/L15mZmYtaSrgSBpHmtbm58Cvgdsi4vleVszMzPpLM4+Y3hu4DZhUSl4l6cMRcWuvKmZmZv2lmU4DFwAbgL8CtgH2Ax4CLu9hvczMrM80E3AOBs6MiHsj4uWIWAZ8EvhzSbv3tnpmZtYvmgk4uwO/rKQ9Tpo7bbeu18jMzPpSs+NwonEWMzOzoTXbLXqBpPV10m+vpkfErp1Xy8zM+k0zAeecntfCzMz6XsOAExEOOGZm1rFW51IzMzNriwOOmZll4YBjZmZZOOCYmVkWDjhmZpaFA46ZmWWRPeBI2lfS7ZLWSHpW0rmSNm+wznskXSlpRbHeo5LOlrR1Jd8cSVHndWxv98rMzBpp9QFsHZE0gfSog6XACcA+wIWkwHfmMKtOL/KeD/wCOAD4WvH+wUrel4BqgFnWad3NzKwzWQMO8ClgHHBSRKwCFkraAZgj6YIirZ7zI+K3pe8Dkl4GLpe0V0Q8UVq2PiIe6E31zcysXbkvqR0HLKgElnmkIHToUCtVgs1GDxXvnrvNzGwMyB1wJgPLywkR8SSwpljWir8kPRju0Ur6jpJekPSKpIckndR2bc3MrGsUke/JA5JeAb4YEZdU0p8Gvh8RX26ynN2AnwE3R8TMUvpHSWc8S4DtSA+KmwZ8MCKuG6KsWcAsgIkTJ7573rx5re5WR1avXs12222XdZujXT+3ySPPvNTWehPHwfNrW19v/z3Gt7W9saCfj5N2jUSbHHbYYQ9GxJRm8o5EwPlCRHyrkv4McFVEfKWJMt5A6njwJuDdETE4TF4B9wHjIuKdjcqeMmVKLF68uFG2rhoYGGDq1KlZtzna9XObTDrjprbWm73/ei58pPVbriu/cXxb2xsL+vk4addItImkpgNO7ktqg8COddLHAy82WrkIIN8H9gOmDRdsACJF0+uAAxp1vTYzs97K3UttOZV7NZL2BLalcm9nCBeTulMfFRHN5N/ITyw1Mxthuc9w5gPHSNq+lDYdWAssGm5FSV8CPgd8NCLuaWZjxRnRicDDEfFqe1U2M7NuyH2GcxlwGnCdpPOBvYE5wEXlrtKSVgCLIuLU4vspwHnAVcAzkg4qlfn4xm7TkhYB15LOlrYFPgEcBHygt7tlZmaNZA04ETEo6QjgUuAG0n2bi0lBp1qv8j2Xo4v3mcWr7GOkQASwAvhbYHdSl+mfAsdHxPxu1N/MzNqX+wyHiFgKHN4gz6TK95nUBpp6653aQdXMzKyHPFu0mZll4YBjZmZZOOCYmVkWDjhmZpaFA46ZmWWRvZeamdlIa3dOu3b185x2rfAZjpmZZeGAY2ZmWTjgmJlZFg44ZmaWhQOOmZll4YBjZmZZOOCYmVkWDjhmZpaFA46ZmWXhgGNmZlk44JiZWRYOOGZmloUDjpmZZeGAY2ZmWTjgmJlZFg44ZmaWhQOOmZll4YBjZmZZOOCYmVkWDjhmZpaFA46ZmWXhgGNmZlk44JiZWRYOOGZmloUDjpmZZeGAY2ZmWTjgmJlZFg44ZmaWxRYjXQHLY9IZN2Xd3spvHJ91e2Y2+vkMx8zMsnDAMTOzLBxwzMwsCwccMzPLwgHHzMyycC81M7NRpt1epbP3X8/MNtbN1avUZzhmZpZF9oAjaV9Jt0taI+lZSedK2ryJ9cZLulLSoKSXJP1A0hvr5DtB0iOSXpa0VNL03uyJmZm1IuslNUkTgNuApcAJwD7AhaTAd2aD1a8G3g58HNgAnA9cD/xVqfxDgGuB7wCnAdOAuZIGI+LWru5MRc5TYA+qNLOxKPc9nE8B44CTImIVsFDSDsAcSRcUaTUkHQwcAxwaEXcVac8AP5J0ZETcVmT9KnBXRJxWfL9T0n7AWUBPA46ZmQ0v9yW144AFlcAyjxSEDm2w3vMbgw1ARPwY+FWxDElbAYcB/1pZdx5wsKTxnVffzMzalTvgTAaWlxMi4klgTbGs6fUKy0rr7QNsWSffMtJ+vq2N+pqZWZfkvqQ2AXixTvpgsayd9fYu5aFOvsHK8k1ImgXMKr6ulvToMPXoutNgZ+CFVtbR+T2qTBd1WMeW26TftXOcwNg4VjowZo6TXP8OI3Sc7NVsxpEYhxN10jREejvrVb9rmPWJiCuAKxpsu2ckLY6IKSO1/dHIbVLLbVLLbVJrtLdJ7ktqg8COddLHU/8MptF6O5bWGyylVfPQoHwzM+ux3AFnOZV7NZL2BLal/j2aIdcrlO/tPA68UiffZFI36sfaqK+ZmXVJ7oAzHzhG0valtOnAWmBRg/V2K8bZACBpCun+zXyAiFgH3Al8qLLudOD+iHip8+r3xIhdzhvF3Ca13Ca13Ca1RnWbKKLRrZMubiwN/FwK/Jw0cHNv4CLgkog4s5RvBbAoIk4tpd1C6mn2Bf408PM3EVEd+DkAXEoaFDqtyH9srwd+mpnZ8LKe4UTEIHAEsDlwA3AOcDFwdiXrFkWeshmks6B/Br4PPAicWCn/HuBk4EhgAfB+4BQHGzOzkZf1DMfMzF6/PFt0F3hC0lrttImk9xTtsaJY71FJZ0vaupJvjqSo8zq2t3vVmTbbZNIQ+zqvTt4xd5xA2+0y1DEQkr5UynfVEHmGG2g+oiS9RdLlkh6W9KqkgSbXG/W/J34eTof6eULSdnXQJtOLvOcDvwAOAL5WvH+wkvcloBpglnVa917p8DiBdC/y3tL3TQb3jcXjBDpql+8Ct1TSPgCcTtGRqGQ58LFK2sr2apzFfqR/vweAN7Sw3uj/PYkIvzp4AV8ijQHaoZT296TpenYYZr2DSYNR31dKO7BIO7KUtgC4o7LuzcA9I73vPWiTXeqkzSraZK9S2hzghZHez0xtMqnY///RoPwxd5x00i5DlHUTsKySdhWweKT3s8X92Kz0+RpgoIl1xsTviS+pdc4TktZqq00i4rd1kh8q3nftXvVGRLvHSUNj+DiBLrWLpJ2Ao4C53a1efhGxoY3VxsTviQNO5zwhaa1226SevyRdHqjOcbejpBckvSLpIUkntV3bPDptkyuL6/nPSbpI0rjSsrF6nED3jpWTSW1Qc28L2FfSKknrJN0jqaMAP0qNid8TB5zO9WJC0gmlPNTJN+yEpKNAu22yCUm7AV8B/m/lL+AVpMsuHybd23kWuHaUB51222Qd8E/AqaQhBZcDn2bTH9axepxAl44V0rCJn0ZEdUaRh4DZwP8EPkIabrFQ0oFt1HU0GxO/J+400B2jakLSUaLdNkkZpTeQTv1XA3+3ScER/1LJewNwH+lBe9e1U9lMWm6TiHgO+GwpaUDS88B3JL0zIpYMU/5YOE6g82Nld9Llt9NrCo74ViXvTaQOCl8mdTLoJ6P+98RnOJ3zhKS12m0TACSJNLh3P2BapAHDQ4p05/M64IBmuqOPkI7apOKa4v1dpbKpU/5oP06gO+3yYdKP5tWNMkbEWtJN8nc1yjvGjInfEwecznlC0lrttslGF5O6yJ4QEc3k32g0/yXfaZuUReV9rB4n0J12mUHqZfVUC9sdzcdKO8bE74kDTuc8IWmtdtuEYtDe54CPRpqqqKHijOhE4OGIeLW9Kvdc221Sx8nF+4Mwpo8T6LBdJE0CDqLJ3mlFZ4vjKNquj4yN35OR7nM+1l+kG23PAQtJc7jNIt13+Hol3wrge5W0W4BfAieRric/CtxdyXMIsB64BJgKXED6a+Tokd73brcJcArpL88rST8i5dcupXyLSIPWjiYFmpuLNnn/SO97D9pkDmkg5EnFeueSfoyvHevHSSftUko/g/RXe70xXOOBu4FPkjpcTCcNplwHTBnpfR+mTbYh/VFxMnA/8J+l79sM1R5j4fdkxBu3H17AvsAdxQ/Bc6TR8ZtX8qwErqqk7Vj8uL4IrAJ+COxcp/wPkGbYXkc6PZ4x0vvcizYhDdKLIV4zS/m+V/zHWgv8ofhROW6k97lHbTIDWEyaWeGPxQ/NucBW/XCctNsupfQlwC1DlLs16d7eU0WbvFT8KB800vvcoD0mDfP/YNJQ7TEWfk88eaeZmWXhezhmZpaFA46ZmWXhgGNmZlk44JiZWRYOOGZmloUDjpmZZeGAY2ZmWTjgmJlZFv8fsuyGxQkHuroAAAAASUVORK5CYII=\n", + "image/png": 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\n", 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\n", 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\n", 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" ] diff --git a/qiskit/finance/simulation/basket_option_pricing.ipynb b/qiskit/finance/simulation/basket_option_pricing.ipynb index 230c1dd28..c3c05cb3a 100644 --- a/qiskit/finance/simulation/basket_option_pricing.ipynb +++ b/qiskit/finance/simulation/basket_option_pricing.ipynb @@ -127,7 +127,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -252,7 +252,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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\n", 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\n", 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1KtsfD6wFri6ukDRW0o8kTZd0mKQpwG2kq/W+0IZjMTOzBpQ6aCAiVkg6DLgEuI503uZiUtIpxlVtupvjgVsi4pkq614CniHNWLAj8CLwU+CQiFjQkgMwM7NRK32UWkQsBt5Zo86EYcrfNsI2LwLHNBWcWTUTJ6bHI87pbBxmXc6zRZvVsmhRejyis2GYdTvfgM3MzErhhGNmZqVwwjEzs1I44ZiZWSmccMzMrBQepWZWyymndDoCs57ghGNWy+Atps+Y29k4zLqcu9TMzKwUDbVwJG0cEa+0Kxiz9dJCz/1q1gqNtnAel3S+pD9uSzRm66O+vrSYWVMaTTizgGOBX0i6S9I0Sdu0IS4zM+sxDSWciPhcROxBmlVqKXAR8KSkb0k6vB0BmplZbxjVoIGIuDUiPgjsBHwE+CNgnqRlkmZKelMrgzQzs+7X7Ci1PuAdpNtGrwB+BJwMPCjphCb3bWZmPaThhCNpN0mfk/QQcAuwM3Ai8KaI+DtgN9K5ngtaGqmZmXW1RodF30pq0TwGXAFcHhEPV9aJiFckfRv4aKuCNDOz7tfoTAPLgUnATRERI9S7F9h91FGZrU8W5DuUf/epzsZh1uUa7VK7BPhJtWQjaStJ7wCIiJeLLR+zrjVx4mu3mTazUWs04dwG7DPMuj/K683MzIZotEtNI6zbCljdRCxm66dp09LjuMmdjcOsy9VMOLmbrL+i6GRJRxaqbQ4cDdzXutDM1hOXXZYeZzjhmDWjnhbO20kXdwIEcBywtlDn98AS4BOtC83MzHpJzYQTEReQr6mR9GvgPRFxb7sDMzOz3tLQOZyI8FBnMzMblXrO4UwC7oiIlfn5iCLihpZEZmZmPaWeFs71wIHAz/LzYPjRagFs3JrQzMysl9STcHYHnqx4brZh2W+/Tkdg1hPqGTTwcLXnZhuMwVtMnzG3s3GYdbl6zuFs0cgOI8IXf5qZ2RD1dKmtIp2bqZfP4ZiZ2RD1JJwTaSzhmPUW5TEyM67vbBxmXa6eczhXlBCHmZn1uGZvMW1mZlaXegYN/AyYGhGLJd1Nje61iDigVcGZmVnvqOcczi+BNRXPfT7HzMwaVs85nA9VPJ/a1mjMzKxnjfocjpI3ShrppmxmZmbAKBKOpEmSfgK8CDwFvCjpJ5KObnl0ZuuDWbPSYmZNaSjhSJoOXEe6GPSjpJuxfTS//u+83qy3TJv22m2mzWzUGrofDvBpYHZE/H2h/FJJlwKfAfyvoJmZDdFol9r2wDXDrPseMK7WDiTtI+kWSaslPSHpHEkjTocjaYKkqLLMqVJ3sqT7JL0oabGkKXUdmdlwZs9Oi5k1pdEWzm3AIcBNVdYdAtw+0saStgNuBhYDk4E9gQtJie/MOt7/48CPK14vL+z/YFLi+wpwGjAJuFLSioj4YR37Nxtqeu4p9tQ2Zk2p58LPfSpe/hvwVUnbA9cCvwF2BN4DHAWcXGN3HwbGAMdExErgJknbADMlnZ/LRrI0Iu4cYf1ngdsj4rT8+jZJ+wJnAU44ZmYdVE8L5xe8/mJPAdPzUrz75w8Yebboo4B5hcQyBziP1EK6ro54qpK0GXAoqWVTaQ5wuaSxEfH8aPdvZmbNqSfhHNrC99sbuLWyICIekbQ6r6uVcC6XNI7UsroS+ExEDM6CsCewKbCksM39pC67vYC7mwvfzMxGq56ZBua38P22A56rUr4irxvOS8C/k7rFVgL9wAxSkplcsW+q7H9FYf3rSJoGTAMYP348AwMDI8XfVVatWtVTx1NU1vH158fT37p2XVm739c/u+7Wy8fXzLE1OmhgHUkbAZsXy+u442e1udg0TPngPp8E/rGiaEDS08BXJL0tIu4dYf8apnxw37OB2QB9fX3R398/cvRdZGBggF46nqKyj+/C+177c1n2gfa+r3923a2Xj6+ZY2v0wk9JmiHpQeBl4IUqy0hWANtWKR9L9ZbPSK7Oj/tV7Jsq+x983ej+zcyshRq9Duc04Azga6SWw+eBc4AHgGXkrqkRLCGdq1lH0q7Algw991JLFB4fIiXBvQv19gZezTGaNS4iLWbWlEYTzinA54Dz8+trI+JsYF9SwnhLje1vBN4taeuKsimk2x80eq7o2Py4ECAiXiJdJ3Rcod4U4KceoWZm1lmNnsPZHbg3Il6R9DK5uyoiXpX0FeCrpBbQcC4ltZKukXQesAcwE7iocqh07rKbHxEn5dczga1JF32uBN4BfAK4JiL+p2L/55LO73yJdJ3QpLwc2eBxmplZizXawnkW2Co/fwT4s4p125Eu6hxWRKwADiNdq3MdcDZwManVVGkTXn89zxLSdTqXAzcA7wcuyI+V+7+D1PI5HJgH/DXwfs8yYE2ZODEtZtaURls4Pwb2J33pf5s0Q8A44PfAqcAttXYQEYuBd9aoM6Hweg7pAs6aIuJaUuvGrDUWLUqPR3Q2DLNu12jCmQnskp9/gdSlNpXUsrkJ+EirAjMzs97SUMKJiKXA0vz8JdK9cD7ahrjMzKzHNHPh5x8AOwNPRMTjrQvJzMx60WhuMf33kh4FHgbuAh6R9Jikf2h5dGZm1jManWngLOAS0vU0RwN9+fFG4N/yejMzsyEa7VI7FfhCRHy2UP6DPLfZqaSZB8x6xymndDoCs57QaJfaGIa/q+d8qkzmadb1fItps5ZoNOFcCxwzzLr3Ar4Hr5mZVVXPLaYnVby8EThf0gSG3mJ6X+CTrQ/RrMMWLux0BGY9oZ5zONcz9FbSuwDvrlL3m6Q7cZr1jr6+9DjDDXizZtSTcHZvexRmZtbz6rnF9MNlBGJmZr2t4ZkGJG1CGiBwMDAO+C3wI9KtAtaOtK2ZmW24Gko4knYEfgj8KekOn08DB5Guv/m5pHdFxDOtDtLMzLpfo8OiLwK2B94eEXtExEERsQfw9lx+UasDNDOz3tBowpkEzIiIuysL8+tPkaa5MTMzG6LRhLMZ8MIw614A3tBcOGbroQUL0mJmTWk04dwJzJC0ZWVhfj0jrzfrLb7FtFlLNDpK7XTgNuBRST8kDRrYkXQRqID+lkZnZmY9o9E7ft4r6S3Ax4H9SaPVngQuBS6KiOWtD9Gsw6ZNS4/jJnc2DrMuV3fCkbQpcADw64g4o30hma1nLrssPc5wwjFrRiPncF4BbgX+uE2xmJlZD6s74UTEq8D/AuPbF46ZmfWqRkepfQY4S9Jb2xGMmZn1rkZHqZ1JmlHgXkmPk0apRWWFiDigRbGZmVkPaTTh/CIvZmZmDakr4UgaQ5rW5hfAU8DNEfF0OwMzW2/st1+nIzDrCfXcYnoP4GZgQkXxSknvi4gftisws/XG4C2mz5jb2TjMulw9gwbOB14F/hLYAtgXuAeY1ca4zMysx9STcA4CzoyIH0fEixFxPzAdeLOkndsbnpmZ9Yp6Es7OwK8KZQ+R5k7bqeURma1vpLSYWVPqvQ4nalcxMzMbXr3DoudJWlul/JZieUTs2HxYZmbWa+pJOGe3PQozM+t5NRNORDjhmJlZ0xqdS83MzGxUnHDMzKwUjc6lZrbhmZWvcS5eHGBmDXHCMatl8BbTntrGrCnuUjMzs1K4hWNWy+zZ+ckuHQ3DrNuV3sKRtI+kWyStlvSEpHMkbVxjm/0lXS7pwbzdUkmfk7R5od5MSVFlObK9R2U9bfr0tJhZU0pt4UjajnSrg8XAZGBP4EJS4jtzhE2n5LrnAf8L/Clwbn58b6Hu80AxwdzfbOxmZtacsrvUPgyMAY6JiJXATZK2AWZKOj+XVXNeRDxT8XpA0ovALEm7RcTDFevWRsSd7QnfzMxGq+wutaOAeYXEMoeUhA4ZbqNCshl0T3703G1mZl2g7ISzN7CksiAiHgFW53WN+HPSjeGWFsq3lbRc0suS7pF0zKijNTOzllFEeXcekPQy8ImI+FKh/DHgGxHx6Tr3sxPwP8ANETG1ovwEUovnXmAr0o3iJgHvjYhrhtnXNGAawPjx4yfOmTOn0cNab61atYqtttqq02G0TVnH13/ooQB8+ZvXrit76y5j2/qe/tl1t14+vuKxHXrooQsjoq+ebTsxLLpahtMw5UMrSm8AvgOsAj72uh1HfLNQ9zrgJ8BZQNWEExGzgdkAfX190d/fX08YXWFgYIBeOp6iso/vwvte+3NZ9oH2vq9/dt2tl4+vmWMru0ttBbBtlfKxwHO1NpYk4BvAvsCkiFgxUv1IzbdrgD+tNfTabFgRaTGzppTdwllC4VyNpF2BLSmc2xnGxaTh1EdERD31B/nbwsysw8pu4dwIvFvS1hVlU4A1wPyRNpT0KeAjwAkRcUc9b5ZbRO8Bfh4Rr4wuZDMza4WyE86lwEvANZIOzyfsZwIXVQ6VzjMKfK3i9fuBL5C60x6XdGDF8saKevMlnSbpXZLeA8wFDszvYTY6EyemxcyaUmqXWkSskHQYcAlwHem8zcUMTQibAJXnXN6VH6fmpdKHgCvy8weBfwJ2Jg2ZXgQcHRE3tiJ+20AtWpQej+hsGGbdrvRRahGxGHhnjToTCq+nMjTRVNvupCZCMzOzNvLtCczMrBROOGZmVgonHDMzK4UTjpmZlcJ3/DSr5ZRTOh2BWU9wwjGrZfAW02fM7WwcZl3OXWpmZlYKt3DMalm4sNMRmPUEt3DMaunrS4uZNcUJx8zMSuGEY2ZmpXDCMTOzUjjhmJlZKZxwzMysFE44ZmZWCiccs1oWLEiLmTXFCcesFt9i2qwlnHDMzKwUntrGrJZp09LjuMmdjcOsyznhmNVy2WXpcYYTjlkz3KVmZmalcMIxM7NSOOGYmVkpnHDMzKwUTjhmZlYKj1Izq2W//TodgVlPcAvHrJaFC32babMWcMIxM7NSOOGYmVkpnHDMapHSYmZNccIxM7NSOOGYmVkpnHDMzKwUTjhmZlYKJxwzMyuFE46ZmZXCU9uY1TJrVnr8VWfDMOt2TjhmtQzeYvqMuZ2Nw6zLuUvNzMxK4RaOWS2zZ+cnu3Q0DLNu54RjVsv06elxxvWdjcOsy7lLzczMSlF6wpG0j6RbJK2W9ISkcyRtXMd2YyVdLmmFpOclfUvS9lXqTZZ0n6QXJS2WNKU9R2JmZo0oNeFI2g64GQhgMnAOcDpwdh2bXwX0AycDU4H9gWsL+z8Y+B5wG3AUMBe4UtK7WnIAZmY2amWfw/kwMAY4JiJWAjdJ2gaYKen8XDaEpIOAdwOHRMTtuexx4C5Jh0fEzbnqZ4HbI+K0/Po2SfsCZwE/bN9hmZlZLWV3qR0FzCskljmkJHRIje2eHkw2ABHxM+DXeR2SNgMOBb5T2HYOcJCksc2Hb+uT+x5/nglnzGWCr48x6wplt3D2Bm6tLIiIRyStzuuuG2G7JVXK78/rAPYENq1S735SYt0LuHt0YVsjKhPAsn85uoORdL9iMvXnad2s7ISzHfBclfIVed1ottujog5V6q0orH8dSdOAfCk5qyQtHSGObrMDsLyTAei8tu5+3fG1+X2S8/5q3dMS3q/qz66U4yxHx38326yXj694bLvVu2EnrsOJKmUapnw02xVfa5jyVBgxG5hdbV23k7QgIvo6HUe79PLx9fKxgY+vmzVzbGWfw1kBbFulfCzVWzC1ttu2YrsVFWXFOtTYv5mZtVnZCWcJr51zAUDSrsCWVD9HM+x2WeW5nYeAl6vU2xt4FXhgFPGamVmLlJ1wbgTeLWnrirIpwBpgfo3tdsrX2QAgqY90/uZGgIh4iXT9zXGFbacAP42I55sPv+v0ZFdhhV4+vl4+NvDxdbNRH5siap06aZ184edi4BfAeaSEcRHwpYg4s6Leg8D8iDipouwHpJFmHye1WM4DfhMRf1lR52BgALiEdFHopFz/yIjwdThmZh1UagsnIlYAhwEbk4ZAnw1cDHyuUHWTXKfS8aRW0H8C3wAWAu8p7P8O4FjgcGAe8NfA+51szMw6r9QWjpmZbbg8W/QGQtIUSddIelJSSJra6ZhGY7STv3YDSX8oaZakn0t6RdJAp2NqFUnHSfpvSY9LWiVpoaS/7XRcrSLpWEk/kfRsnjh4qaQzJb2h07G1mqRd8s8wJG3VyLa+H86G41hgAnA9aQLUrlMx+eti0uSvewIXkv5xOnOETbvFvqTzjncCvfZF9X9rUEebAAADJElEQVRIU1F9jHTR4CTg25J2iIgvdzSy1tieNGjpAtIlGAcAM4GdgH/sXFhtcQGwijS6uCHuUttASNooIl7N/5G8AHwoIq7ocFgNkfQp4JPAboPz8Un6JPkPe7jJX7vF4M8oP78a2CEi+jsbVWvkxLK8UPZt4KCI2L1DYbWVpM8DpwLbRY980Ur6S+D7wBdIiWfriFhV7/buUttADH6RdbnRTv7aFXrkZ1RVMdlk9wA7lh1LiZ6lh1qquev6y6Tbyoxq2h4nHOsmQyZxjYhHgMHJX627/Dmpe7RnSNpY0hb5Eo3TgP/oldYN6fYymwP/Ptod+ByOdZPRTv5q6xlJh5HOw53Y6Vha7HfAZvn5N4BPdDCWlsl3Vz4XOCEiXpZUa5OqnHC6VL6/z8616kXESFMGdaPRTv5q6wlJE4BvA9/vtvOIdfhzYAvSoIGzSBeh/0NHI2qNzwN3RcQNzezECad7HQdcVke90f0rsn4a7eSvtp6QNI40HdUjwAkdDqflImJRfnqHpOXA1yVdGBEPdTKuZuS7Jp8IvEPS4N/fFvlxrKRXImJNPfvyOZwuFRFfjQjVWjodZ4uNdvJXWw9I2oI0LP8NwNER8bsOh9Rug8mn20fhvYV0c8ufkv7pW8Fr53EeIw0kqItbONZNbgQ+IWnriHghl9Uz+at1mKRNgO+Svrz+IiJ+0+GQyvAX+fHXHY2ieXcAhxbKjgRmkK6n+lW9O3LC2UBI2gfYhzTKBKBP0irgmYjoli/rS0kjf66RNDj560zgom6/BgfWtQAm5Ze7ANtIOja/viEiVncmspb4CunYPgqMk3Rgxbp78mzvXStPLnwz8EvgFVKyOR24qpu702DdkPaByrJ8Hg7gR41ch+MLPzcQkmYydJJUSLNy95cbzejlxHkJcBDpvM1XgZkR8UpHA2uB/Ec83H/Du0fEstKCaTFJyxj+VsRdfWwAks4lTSY8AVhL+q//cuDSiHi5g6G1RZ4a63IavPDTCcfMzErhQQNmZlYKJxwzMyuFE46ZmZXCCcfMzErhhGNmZqVwwjEzs1I44ZiZWSmccMzMrBT/H1PMymNpY69NAAAAAElFTkSuQmCC\n", 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" ] diff --git a/qiskit/finance/simulation/bull_spread_pricing.ipynb b/qiskit/finance/simulation/bull_spread_pricing.ipynb index ea7a786b1..5a0969519 100644 --- a/qiskit/finance/simulation/bull_spread_pricing.ipynb +++ b/qiskit/finance/simulation/bull_spread_pricing.ipynb @@ -118,7 +118,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -177,8 +177,8 @@ "outputs": [], "source": [ "# set the strike price (should be within the low and the high value of the uncertainty)\n", - "strike_price_1 = 1.5\n", - "strike_price_2 = 2.5\n", + "strike_price_1 = 1.438\n", + "strike_price_2 = 2.584\n", "\n", "# set the approximation scaling for the payoff function\n", "c_approx = 0.25\n", @@ -215,7 +215,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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izz/vc6s3Q97Y7pyrn6VLw5zqQ4eGeUV8Wtxmq+RHJJK2lTRGUqWk2ZIuk1Tru0/STpJekPSlpK8kjZa0cykyO+dyLFoEhxwSisgll8Add3gRacZKWkgktQdGAwYcCFwGnAtcWst+m8X9WgLHAr+Nv78gqaKYmZ1zOebNC31Enn4abr0VLr0UpKRTuQSV+tTWqUAroLeZLQBGSVoLGCjpmrgun17AmnG/+QCSXgG+AHoCtxc/unOO2bOhe/fQ4XDECDj88KQTuTJQ6lNbPYCROQVjBKG47F7DfqsCS4GFWesWxnX+Vci5UvjwQ9hllzBK73PPeRFxPyh1IdkamJK9wsxmApXxvuo8Grf5i6QNJG0A3ADMAx4uUlbnXMYbb4RLeysrQ2/1PfdMOpErI7Lqprssxh+TlgDnm9mNOes/Ae43s4tr2HcH4Blgk7hqDtDDzN6uZvt+QD+ADh06dB4xYkS9Mi9cuJC2bdvWa98kpClvmrJCuvI2Ztb2Eyey/Z/+xPft2/PONdewaNNNG+VxszXX17YUGpK3W7duk8xsp1o3NLOS3YAlwNl51s8CBtWw30bAVOBJYN94exr4BOhY29/t3Lmz1de4cePqvW8S0pQ3TVnN0pW30bI+8IDZqqua/exnZrNnN85j5tEsX9sSaUheYKIV8Nle6lNb84C186xvB8yvYb/zCRcGHGpmz5vZ88AhQBVwXqOndM7BzTfD0UeHdpEJE2CjjZJO5MpUqQvJFHLaQuKlvW3IaTvJsTXwnpktyawws++B94AtipDTuebLDPr3h7PPhoMP9t7qrlalLiTPAd0lrZm17ghgETChhv1mANtLWi2zQtLqwPbA9CLkdK55WroUTj4Zrrwy9FZ/+OEwt7pzNSh1IbkDWAw8Jmmv2CA+ELjesi4JljRV0tCs/e4GNgYel9RL0n7AE4S2kyElS+9cU7ZoERx6aOit/qc/eW91V7CSdkg0s3mS9gRuJTSWzydcxjswT64WWftNkrQvMAD4a1z9LrC3VXPVlnOuDubPhwMOgJdegltugTPOSDqRS5GSD9poZpOBGufdNLNOedaNAcYUKZZzzdfs2WFu9SlTvLe6qxcf/de55uzDD8OQJ198Ac8+C3vtlXQil0JeSJxrriZOhB49woCL48dD585JJ3Ip5RNbOdccjRoF3bpB27ZhWlwvIq4BvJA419yMGBHmVt98c3jlFfjxj5NO5FLOC4lzzcktt4Te6l26eG9112i8kDjXHJjBH/8IZ50FBx4II0fC2vlGK3Ku7ryx3bmmbulSOO00uPvu0Gv9ttugpf/Xd43Hj0ica8oWLYLDDgtF5I9/hDvv9CLiGp2/o5xrSoYPh/792X3mTNhkE2jTJvQVuflmOPPMpNO5JsoLiXNNxfDhYaDFysow//Qnn4T1Z5zhRcQVVa2ntiQdK2ndUoRxzjVA//5hKtxcTz9d+iyuWSmkjeRe4pwfkqok/bK4kZxz9TJzZt3WO9dICikk8whDuAMIKN0k7865wq2/fv71HTuWNodrdgppIxkN/FXSB4QiMkzSt9VtbGZ+xOJcqT34YBh4UQp9RjJat4ZBg5LL5ZqFQo5ITgAuBf5NOCKZRpjitrqbc66Ubr0VjjoKdt01XN5bUYFJUFEBQ4ZAnz5JJ3RNXK1HJGZWCVwHIGkvoL9PJuVcGTCDSy6BK64IvdX//ndo1QpOPpkJ48fTtWvXpBO6ZqKQq7aqJP0iLo4HFtSwuXOuFJYuhVNOCUXkxBPhkUdCEXEuAYWc2voeWD3+fixQTYuec64kvvsu9Fa/665wye9dd3lvdZeoQt59k4GBkp4gtJEcKmmnarY1M7u90dI551Y0f344jfXii95b3ZWNQgrJmcCdwA2Eq7bOq2FbA7yQOFcMc+aEudXffz+0hxx5ZNKJnAMKa2x/BfgJgKRlwK/M7PViB3POZfnoozC3+ty58I9/wN57J53IuR/UdfTfboRTXfUmaVtJYyRVSpot6TJJLQrct7ekNyQtkvSlpOcltWlIHufK3qRJ4dLeb76BceO8iLiyU6cWOjObACBpZ2A3YB3gK+AlM3uttv0ltSd0cJwMHEgYeuUvhIL2x1r2PQm4FbgGOB9oD+xR1+fgXKqMHg0HHwzrrgsvvABbbZV0IudWUqcP4fjt/2GgO1AFfAmsC7SQ9DxwWOx3Up1TgVZAbzNbAIyStBahMf+auC7f312P0EZzppndlXXX43XJ71yqPPQQHHMMbL01PP88bLxx7fs4l4C6ntq6BugCHAmsYWYbAWvE5S7A1bXs3wMYmVMwRhCKy+417Hd4/HlfHfM6l06DB4fG9J13DldoeRFxZayuheQQ4A9m9rCZLQMws2Vm9jBwIXBYLftvDUzJXmFmM4HKeF91dgY+AE6U9ImkJZJek7RLHfM7V94yvdXPOAP23z+czvK51V2Zk1nhg/lKWkQ4LfVcnvt6AI+aWesa9l8CnG9mN+as/wS438wurma/kcAuhF71FxBOqV0A7AT82Mw+y7NPP6AfQIcOHTqPGDGisCeZY+HChbRt27Ze+yYhTXnTlBVKkLeqiq1uvJGNn3mGOT168OG552ItCroOZSX+2hZPmrJCw/J269ZtkplV129wOTMr+Aa8CjxFLEBZ6xXX/6uW/ZcAZ+dZPwsYVMN+owh9VPbNWrcWYYj7y2vL3blzZ6uvcePG1XvfJKQpb5qymhU576JFZgcfbAZmF11ktmxZgx7OX9viSVNWs4blBSZaAbWhrlc8XQw8B0yR9DjwGbABcDDQidAGUpN5QL7j9HbA/Br2+yr+HJ9ZYWYLJE0Cti0kuHNl6+uvQ2/1CRPgxhvh7LOTTuRcndT18t+xknYELiG0h2wEzAFeI5zyqq2PyRRy2kIkbQa0IaftJMf7hCMS5awXsKzgJ+BcuZkzB3r0gPfeC3OuH3100omcq7O6NrZjZpPN7Egz28LMWsefRxdQRCAczXSXtGbWuiOARcCEGvZ7hlA0umVWSGoHdAZ8SHuXTlOnho6GU6eG3upeRFxK1amQSLpOUkNOJd0BLAYek7RXbBAfCFxvWZcES5oqaWhm2cwmAk8CQyUdJ6kXoU1mCTC4AXmcS8abb8Iuu8CCBTB2LOyzT9KJnKu3+lz++66k1yWdGo8KCmZm84A9gRbA04SZF28ABuRs2jJuk+0Y4AngeuARQhHZIz6mc+kxZgzsvnuYP+Tll+GXPju1S7e6tpH8SFI34HjgWuD6OLz8PWY2usDHmEwY2qSmbTrlWbcQOC3enEunhx8OvdW32ir0Vt9kk6QTOddg9WkjGWdmxxIa2s8ENgVGSpoh6VJJmzd2SOeahNtugyOOgF/8IvRW9yLimog6F5IMM1toZkMJp6VeBjYDLgI+lPSkpIpGyuhcupnBgAHwu9/BfvvBqFHQvn3SqZxrNPUqJJI6SRog6WPgBWAh4XLgNYEDCH1K6teV3LmmpKoKTjsNLrsMTjgBHnvM51Z3TU5dR//9LaF95DfATOBe4F4z+yRrs2clfUsYLt655uu776BPn1A8LrwQrrwSlNsVyrn0q2vP9iGEodu7m9mYGrb7ELii3qmcS7uvv4aDDoLx4+GGG+Ccc5JO5FzR1LWQbFzI5bZmNodwaa9zzc+nn4a51d97D/72t3BU4lwTVtfLf73PhnM1mTo1zK3+6afw9NOhoDjXxNV5mlpJRwAnA1sRJrVagZlt0Ai5nEufN98M42ZVVYXe6jvvnHQi50qirkOkHE2YpXAqof/IU4RxsFYhzBVya2MHdC4Vxo6Frl1hjTXgpZe8iLhmpa6X/54PXA78Li7fZmYnAD8CviDMdOhc8/LII+FIpGPHMOTJ1jVN9ulc01PXQvJj4GUzqwKqCJNLYWbfEOZrP6Nx4zlX5m6/HQ4/HHbaKfRW33TTpBM5V3J1LSRfA6vH32cB22TdJ2DdxgjlXNkzg4ED4fTToVev0Ft9nXWSTuVcIura2D4R+CkwktA+comkpcD3hMmuXmvceM6VoaoqOOMMuOMO6NsX7roLWtb5uhXnmoy6vvv/DGTG0Lok/n4bYcj3N4B+jRfNuTL03Xdh9N5HH4U//AH+/Gfvre6avYIKiaRWQE/CGFqfSupgZp8BB0paHVg9e2Iq55qU4cOhf392nzkTVlsNFi+G66+H3/8+6WTOlYVaC0kcFn40oYhkLJB0uJm9YGaLCbMeOtf0DB8O/fpBZSWCUERWWw028O5SzmUU0th+DbAM+DXQGtgO+DdwZxFzOVce+veHypyr2r//Pqx3zgGFFZIuwB/N7GUz+87M3gdOATpK2qi48ZxL2MyZdVvvXDNUSCHZCPg4Z91/CZf7btjoiZwrF+PGVX9fx46ly+FcmSu0H4kVNYVz5eaRR8KAixtttPJEVK1bw6BByeRyrgwVWkhGSpqbuQFz4vox2evjfc6l2x13LO+t/u67oZ9IRQUmQUUFDBniQ8M7l6WQy399XhHXPJiFKXEHDgy91R96KBx99OkDffowYfx4unbtmnRK58pOrYXEzBq1kEjaFriF0Ig/H7gbuDSO31XI/qsQOj/+HNjfzJ5pzHyumaqqgjPPDGNnHXdcOApZddWkUzmXCiUd10FSe0KflMnAgcAWwF8Ip9j+WODDnARsUpSArnlavDj0Vn/kEbjgArjqKu+t7lwdlHqAoFOBVkDv2BN+lKS1gIGSrqmtd3wsRIOACwlHMs41zIIFYW71cePguuvg3HOTTuRc6tR19N+G6gGMzCkYIwjFZfcC9r8ceBkYU4Rsrrn57LMwGdU//wn33+9FxLl6KvURydbA2OwVZjZTUmW87+nqdpT0U+B44GdFTeiah48/hn32gTlz4KmnwsRUzrl6kVnpuohIWgKcb2Y35qz/BLjfzC6uYd8JwGtmdoGkTsA0amhsl9SPOBpxhw4dOo8YMaJemRcuXEjbtm3rtW8S0pQ3qaxtp07lpxdcgKqqePfPf2bBttsWtJ+/tsWTprxpygoNy9utW7dJZrZTrRuaWcluwBLg7DzrZwGDatjvSOBTYK243InQSXK/Qv5u586drb7GjRtX732TkKa8iWQdN85szTXNNtvMbPLkOu46riiRiiFNWc3SlTdNWc0alheYaAV8xpa6jWQesHae9e0IlwKvRNKqwLWEqXxXkbQ2cYpfoI2kNYsR1DVBjz0G3buH6XBffhm22ab2fZxztSp1IZlCaAv5gaTNgDbxvnzaAJsC1xMK0Tzg7XjfCMJIxM7V7M474bDDoHNneOkl2GyzpBM512SUurH9OeB8SWua2Tdx3RHAImBCNfssBLrlrNsQ+DtwMTmN986twAwuvxwGDICePeHhh0Nvdedcoyl1IbkDOAt4TNLVwObAQOB6y7okWNJUYIKZnWhmS4Hx2Q8SG9sB3jUznyfe5VdVBWefDYMHw7HHwt13e29154qgpKe2zGwesCdhjvenCeN43QAMyNm0ZdzGufpZvBiOOioUkfPPh2HDvIg4VySlPiLBzCYDe9SyTada7p9OmA/FuZUtWAAHHwxjx8K118J55yWdyLkmreSFxLmi+uyz0Bby9ttw333hlJZzrqi8kLim4+OPw+W9s2aF3uo9eyadyLlmwQuJaxrefjvMaLh4MYwZA126JJ3IuWaj1P1InGt8EybAb34DLVuGPiJeRJwrKS8kLt0yvdU32QReeQUKHDfLOdd4vJC49BoyJPRW33HHMBS891Z3LhFeSFz6ZHqrn3JKOBoZPRrWXTfpVM41W97Y7tJl2TI466zQ0fC3v4WhQ72joXMJ8yMSlx7ZvdXPO897qztXJvyIxKXDN9+E3upjxnhvdefKjBcSV/7mzg2dC996y3urO1eGvJC48jZtWphbfdYsePJJ6NUr6UTOuRxeSFz58t7qzqWCN7a78vTii95b3bmU8ELiys8TT4TTWRtv7L3VnUsBLySuvNx9NxxyCOywg8+t7lxKeCFx5cEMBg2Ck08OvdXHjPHe6s6lhDe2u+QtWxbmVr/1VjjmGLjnHu9o6FyKeCFxpTd8OPTvz+4zZ4ZTVxtvDK++CueeC9dcA6v4gbJzaeKFxJXW8OHQrx9UViKAmTPD7cgj4brrkk7nnKsH/+rnSqt/f6isXHn9v/6yPJh5AAAcYklEQVRV+izOuUZR8kIiaVtJYyRVSpot6TJJLWrZ5xeS7pU0Ne73gaQBktYoVW7XSGbOrNt651zZK+mpLUntgdHAZOBAYAvgL4SC9scadj0ibns18BHwU+Dy+POQIkZ2jW3DDWHOnJXXd+xY+izOuUZR6jaSU4FWQG8zWwCMkrQWMFDSNXFdPleb2edZy+MlfQfcKanCzGYUObdrDC++CPPngxQu981o3Tpc+uucS6VSn9rqAYzMKRgjCMVl9+p2yikiGf+OPzdovHiuaDK91Ssq4MYboaICk8LykCHQp0/SCZ1z9VTqQrI1MCV7hZnNBCrjfXWxC7AM+KBxormiye2tftZZMH06E8aOhenTvYg4l3Ky7FMMxf5j0hLgfDO7MWf9J8D9ZnZxgY+zIfAO8KyZ9a1mm35AP4AOHTp0HjFiRL0yL1y4kLZt29Zr3ySUVV4zOg4fzuZDh/Llzjvz3oABLGvV6oe7yyprAdKUN01ZIV1505QVGpa3W7duk8xsp1o3NLOS3YAlwNl51s8CBhX4GKsBLwIfA+0L2adz585WX+PGjav3vkkom7xVVWZnnmkGZsccY/b99yttUjZZC5SmvGnKapauvGnKatawvMBEK+AzttSN7fOAtfOsbwfMr21nSQLuB7YDdjWzeY0bzzWKxYvhuOPgwQe9t7pzzUCpC8kUctpCJG0GtCGn7aQaNxAuG97bzArZ3pXaN99A794wenQoIOefn3Qi51yRlbqQPAecL2lNM/smrjsCWARMqGlHSRcBZwKHm9lLxY3p6mXu3DAV7r//DcOGhaMS51yTV+rzDXcAi4HHJO0VG8QHAtdb1iXBsQf70Kzlo4ErCae1Zkn6VdZt/dI+BZfXtGmw227w3nthbnUvIs41GyU9IjGzeZL2BG4Fnia0i9xAKCa5ubKHTdkn/uwbb9mOB4Y1blJXJ++8E+YQWbw4nNLaZZekEznnSqjko/+a2WRgj1q26ZSz3JeVC4grBy++CAccAGuuGSaj8mlxnWt2/FIaV3+Z3uobbeRzqzvXjHkhcfXjc6s75yIvJK5ufG5151wOnyHRFS57bvXf/haGDvW51Z1zfkTiCrR4MRx9dCgi554b+ol4EXHO4UckrhDZvdWvvRbOOy/pRM65MuKFxNVs7lzo2RPeegvuuw+OPTbpRM65MuOFxFVv2rRwee+sWaG3eq9eSSdyzpUhLyQuv7ffhn33DW0jY8ZAly5JJ3LOlSlvbHcrmzABfvMbaNky9BHxIuKcq4EXEreixx8P/UM22cR7qzvnCuKFxC13111w6KGw447wz396b3XnXEG8kLjQW/2KK6Bfv3A0Mnq091Z3zhXMG9ubu2XL4KyzYPBg763unKsXPyJpzhYvhqOOCkXkvPO8t7pzrl78iKS5+uYbOPjgcGmv91Z3zjWAF5LmaO5c6NEj9BXx3urOuQbyQtLcZPdWf+qpMPyJc841gBeS5sR7qzvnisAb25sL763unCsSLyTNgfdWd84VkReSpm7IEO+t7pwrqpIXEknbShojqVLSbEmXSWpRwH7tJN0raZ6kryUNl+Tdr6tjBpdfDqecEtpFvLe6c65IStrYLqk9MBqYDBwIbAH8hVDQ/ljL7g8C/w84CVgGXA08Afy6WHlTq6oqzK0+eHC4tPfuu72joXOuaEp9RHIq0ArobWajzOwO4FLg/yStVd1OkroA3YHjzOxRM3scOAbYTdJeRUk6fDh06sTue+wBnTqF5XKWnXettZb3Vr/3Xi8izrmiKnUh6QGMNLMFWetGEIrL7rXs95mZvZhZYWavA9PifY1r+PAwgOGMGcgMZswIy+VaTHLzVlaG4rHDDrCKN4M554qr1P1ItgbGZq8ws5mSKuN9T9ew35Q869+P9zWu/v3Dh3G2ykro2xeuvLLR/1yDffghLF264rolS8Lz6NMnmUzOuWaj1IWkPTA/z/p58b767Ld5vh0k9QP6AXTo0IHx48cXHHL3mTNRnvW2dCmfr79+wY9TKutPnpw/78yZTKjD8y61hQsX1unfJWlpypumrJCuvGnKCqXJm0TPdsuzTtWsr/d+ZjYEGAKw0047WdeuXQtP2LFjOJ2V+8cqKtigHN9AnTrlz9uxI3V63iU2fvz4ss6XK01505QV0pU3TVmhNHlLfQJ9HrB2nvXtyH/EUdt+a9eyX/0MGgStW6+4rnXrsL4cpS2vc65JKXUhmUJOm4akzYA25G8DqXa/qLq2k4bp0yd05KuowCSoqAjL5drekLa8zrkmpdSF5Dmgu6Q1s9YdASwCJtSy34aSdsuskLQToX3kuWIEpU8fmD6dCWPHwvTp5f+hnLa8zrkmo9SF5A5gMfCYpL1ig/hA4PrsS4IlTZU0NLNsZv8CRgL3S+ot6SBgOPCSmY0u6TNwzjm3gpIWEjObB+wJtCBc6nspcAMwIGfTlnGbbEcSjlruAe4HJgEHFzOvc8652pX8qi0zmwzsUcs2nfKsmw8cH2/OOefKhHd7ds451yBeSJxzzjWIzGrrB5h+kj4HVu6xV5j1gC8aMU6xpSlvmrJCuvKmKSukK2+askLD8laYWa3DeTSLQtIQkiaa2U5J5yhUmvKmKSukK2+askK68qYpK5Qmr5/acs451yBeSJxzzjWIF5LaDUk6QB2lKW+askK68qYpK6Qrb5qyQgnyehuJc865BvEjEueccw3ihcQ551yDeCFxzjnXIF5InHPONYgXEueccw2SxJztrhHEmSV7Euatf9jMvpS0KXAesAUwHRhiZu8mlxIk/QF4NukchZLUCmhpZt9krVsfOAPYFlgGvAXcZmZfJ5PSufLil/9GkkSY36QXsA2wDlAFfAa8Cgwzsw+TS7icpF8CLwBtgaXAV0B34FlC5veA7YENgb3M7J8JRUXSMsAIUyI/ADxoZlOTylMbSc8CH5nZ2XG5C2EWzmWEOXAEdAa+B/Yws/cSzLoj0MrMXslaty9wEcuL3tvAwOxtykX8P7c/8HPCe2Qi4UtHWX8oSVqLMHbVHmb2UtJ54IdMewCrAf8ws2/jF6DfEWaS/ZjwxXJ2Uf5+mf+blUR8wZ8lfEB8RpjFcRPCm/s5wj/E/wMuN7PLk8qZIWkU4WjyYOBbwuRgBxE+6A41syWSVgeeANYws24JZl0GXA38BNibkPtNQlF5yMxmJZUtH0lfACea2ZNx+VXCa3xQ5ihFUjvgKeA7M+ueYNZXgafNbFBcPgG4GxgHjCUUvT2BXwOHZJ5TQllfIbyu78fl9oQvQ52BhXGztoQvbd2zjwiTIOn0Gu5uBVwL3AR8BGBmt5UiVz6StgTGAJvFVdOAfYBRwNrAfwmfX4uAzmb2SaOHMLNmfwP+TnhD/CRr3cbA88CjcXl3whv+hDLI+yXQI2t5A8K3z31ytusFfJFw1mXAL+Pv7YF+8U2/NN7Gx3XrJv26xoyVwG+ylr/PfV2zXttvE866IDsbMBW4Jc92dwBvl8v7IC4PJRxJ75u1bl9gHnBDGbwPlhGO7pdVc8u+ryrhrA8Rjjy3JJxJ+Wv8PHsFWDNus17c5s5iZPDG9qAHcKFlnce3cAh4KnCQpI3MbAJwJXB2QhmzWbxlL5OzLt9yosxsnpkNMbM9gU2BcwmH4ncAsyX9I9GAwX+A7CO4zwj/OXOtSyg6SVqWs1wBPJJnu0cI30jLyQHAZWb2fGZF/H0Q0DuxVMs9BcwFTgRamNkqmRvh/SCga1yXOy14qe0GDDKzqWb2FfBHQjvpdRaP7MzsC+BGVnxvNxovJIEI3zByVcX72sXl14CtShWqBpOA8yStKWkV4GJgFnCapBYAkloCpxM+GMuOmX1qZjeZ2S7Aj4ABhKPApF0FXCjphPgaDgKulbS3pNUkrR7bIf5M+CaYpH8CfbKW3wPyDRf+C8L7o5ysTWgTyTWJ0LaXKDM7CDgOOB94Q9Ku2Xcnk6pa7YFPs5Yz/9a5czB9TPgC1+j8qq1gNHCFpHfM7GP44RzuzYR/oEwje1ugHK7U6U84//kV4fRQJaGh7RHgI0mZxvaNCacLypqZzSB8gF9VBlkek3Qm4dvbDcAHhC8SmW/ORvhy8RThQyZJFwMvxy8TtxAa2e+TtA7hlCGENpJzgAsTSbiiQyRlCt08IN+ESesRTtklzsxekPRTwuv3D0nPE66KTLT9Jo+5hKPRjCrgTsLRdLYNKFJ2b2wH4mWzzxMO/2cQzov/iNDofpSZPRe3u4YwY9gRSWXNiJn3I3wZeNTM5kjaELiA5c/jbjN7M8GYSBoA3GVFulqkWCStCxwB/JLwDXkVQuF+H3jGzCYlGO8HknYAbgd2ZnmRI+v3eYRTSDclkzCIF13kGmZmJ+RsdyewrZn9ujTJChP/b11DOO12J6G4dDOzFxMNBkh6Avgq97XMs90twDZmtlejZ/BCEsRTQocDPwPWIDRcPhDPOTpX1iRtQygmuUXvFTNbkmS2upB0MvBfMxubdJZ84uXgNxC+rPWyMrisWlIHoLWZTatlu/8jXHQxptEzeCFpeiS1MLN8bT5lQ9IahAbBZcDUcvywi20km5PVp8jMZiabyrny443tOSRtJ+kQSSdJOjH+vl3SuXJJ6i3pCUnPSto/rjtC0nTge0kz4re7REk6JvZvyCy3lHQV4RvzO4SLAb6SVA7n8AGQ1FnSU4Tzye8DLxP6N0yTNEvSZZJaJxqyCVGUdI58JLXK/beWtEP8XOicVK6yk+T1z+V0A04gtCvku3a8ijDkyPFJ54xZD4+5XgKeJDS2n0xo2xlK6M3695i7e8JZJwOnZS3/Jeb9E7Ar4dLFgYTOUheXwWu7D6FtbCLhyqyBhE6p38fM5xKujnoLaF8Gefcj9Mt5F3iQrD4wWdvsTPJ9HfYh9mnIWncQoXPqUmBJfM17Jf2axmztgMdjrqXAXUAL4L6cz4WXgfWSzlvgczqkWO+DxJ9cOdyAM+MbZjChF/B68U3TIv6+G3Br/ID5XRnkfQO4I2u5T8z2l5zt7gVGJ5y1Etg9a3kucHae7c4DZpTBazsJuK+a98h0wlH8GvED8LaEs+6d9WF2a8xeFYu1srYrh0JSxYodEg+OH8avxH/78+LvS8nTATSBvDcThkE5Ezg2fnl4FPhfLIrrE/qfzQJuTzpvgc+paIXE20gASR8TPpivqWW7C4BTzWzz0iSrNscCoLeZjY7L7QhX5+xlWY2U8ZTXnWaWWP8MSXOAM8zs0bi8mHCUND5nu72Bp8ysVelTrpBjEXCAmY3KWd+eMKLAdmb2vqRjgavNbKMkcsZMLxHGBTs+a90JhA/BUYQrDr+TtDOh0T2xjnPxqq1fmdnrcflNYJaZ7Z+z3bNAGzPbPYGY2TmmAVea2V1xeUdCoT7ezO7L2u5kwpH0j5JJCpLuKXDTCkInykZ/H3gbSbAh8HoB271OGXSWIlzamf1myIxVND9nu4WEjl9JeorQeXK1uDwaOCrPdkcRvvUlbS7hyr1cPyO87pl+RDNY3lE1KdsDf8teYWb3EIbz+RUwNvYpKUfbEy6jzTWEMIhj0jZgef8xiGNqEcatyjaV/P1hSuk4wlHST2q5VVT3AA3lHRKDd4CTJb1oZvmud8+MVHpy3DZpMwiju44EMLOqeFni+znbbc6KPV6TcBGhB/Z/JN0NPA1cLWl7lnea2wPYkTASbNKGAJdLakNoe/ie0DO8PzDOlveH2RxI+gqu74A2uSvNbFLsiT2ScLpoYIlzVSf79MfXLP8ClO1byuML7jRCQZ4Ql39NOBW3C6FtMmNXkn8ffAS8bmbH1rSRpEMJ7WiNzgtJcC6hQ+JkSY8RhjyfT3jjrw1sTTinuynl0VP8MXKGOjCz1/JsdzQrvulLzsy+kvQrwgfx/xG+6QF0ibfvCadhfm1mbySTcjkzGxRPw1xIGLYFwvvg74ROaBlLCGOvJekdwnn6p3LvMLOPYzF5FhhW4lzVGSlpafy9HbADy79MZGwNzCllqGrcAdwk6SeEonc44UvRJZLaEgZA/DnweyDpEcFfJRS42mR3WG1U3kYSSdqC0Ct8X5YPx5zxP8KVO9eaWe6hbdmS1BGYb2ZlMeQEgKROrNhp7r9Wnn1IViX0c1kD+LicXsMMSacQhknZ0arpOBuPrB4ntJ8l9k0/jnCQ6yMzeyBnu/FxfTlcun4W4ZTrqoRRIu6QdBShDSozaOcQ4A9JvofjZci7mtnNtWy3HqGNb0JN29UrgxeSlcXrxjNtC/PNLOlRXp1zZSKe5l7PzD5POku58ELSxMTD7jeBPuVwqkgpnLpWKZnG2Lly4YUkS/wA2QD4wMxWagiMh4Y9zez+kodbMUfPGu5uQ2hQu5A4hLyZPVuKXPkoRVPXQrqmMS5UHIfrMDO7LOEciU4H21DxSCR7auBJhOeR+IeowqjKhxD+Pw0zsymSfgZcyvIvP4Mta/6XRpV0J5lyuAGrAw8TPiiqCA2pQ4F2Odsl3rEr5kjT7G1fAAdmLb9KuBpqzax17QhXx4wsg9d2FGGq2rUJ58ZvBT4hjCCwatb75TnCVVyJv38LeE5F64hWhwxbEq42zLwv/0v4gPuYUKzfIAwf/xmwaRm8Zq8QRsrNLLePGZfFnAtY3qFyzaRyxmzdCV/EPo2v6wLCBFbzCJ1VB8f/d1WEKaMbP0PS/2DlcAMuIVyldTJhYqCz4xv6I+DHWduVSyGZRLiy5XjCteHZt5/GN/jhmXUJZ03N1LUxR5qmMe5Y4O3UpN+3lMF0sHXMm5qpgWOxeJgwkyOECzDmAUNztvsr8GpRMiT9D1YON8LlvmfkrNsQeBH4HOgS15VLIRFhnvO5hGEbfpR1X7v4n2ClMZcSyvo6MCBr+X/AkXm2Oxb4vAzyfpHzYbF+fD33ztmuZxkUkszRZ223cjgynQ0cnrVcEXP1ztnueODDMngf5BaSz4Fz8myX+NA+hMuT98pabh/z75Gz3T6Ei4caPYP3Iwk2I6ejoZl9KmlPQhUfLakP5XF9OxbeFUMkPQRcAbwj6db4e7m5Chgu6X/A/SyfuvZLwuksEQ7Dy2HqWlg+jfHLhM5x2dMYj7XQ+bNcpjH+BhgL3F3LdrsRLm1PUuLTwTZQOU8NvIgVO6Zmfs8dbqg1oRNro/NCEswGfkw4AvmBhWvDj5R0I+HQMdFG9lxmNh84Q9IQwrXtHwFXU0ZzSlu6pq6FdE1j/DqhHe8fNW0U535JWuLTwdZDWqYGfpnQUfKjmOU6wqjbf4ijdXwTx+O7gFD4Gp1ftcUPg55tbmZda9jmIsK3abMEB7+riaQjCdOBbkoYnC3xaUAzlJKpayFV0xj/CehnZrkdaHO3+w1wqZl1K02yvBkSnw62LpSiqYElbUkYwy7zPphOOMp/hDBSwAygE+GLUTcze6vRM3gh+eHSuSOAq8zsyxq2O5pwrvz46rZJWjzt0gZYaGU+S6JrPlQG08EWg8pkauDYf2xXwpWGY8xsUexYfRLLv/w8YGafFOXveyFxzjnXEOUwyqYrEkl3SRqadI5CpCkrpC+vc8Xkje11IOkuYBUzOzHpLAXqRnq+LKQpK6Qor6TRhLMPeyadpTZpygrpylvMrF5I6iY1Hx4AZrZl0hkKlaaskLq8Ij3v2zRlhXTlLVpWbyNpwuJlnxuYWdIT79QqTVkhfXmdK6a0VNKyIGmNOMdHWvQizPSWBmnKCinKK2nVtLxv05QV0pW3mFm9kNRNaj48XPMg6XeS/ivpG0mvSfptns1+Thm8b9OUFdKVN+ms3kaSQpIKvWY9X0/ckkpTVkhX3tgB9RbCNMD/JvQjGCbpQOC3ZrYoyXzZ0pQV0pW3HLJ6Gwl1/vDYNume7QrzXn9AGAahJpsAOyeZN01ZIV15JU0ExprZBVnr9gSGE3o397IwKdfOwCuetXBpylsOWb2QkK4PDwBJbxEm3zqilu0OBR5M+E2emqwxR2rySvoG2N/Mxues70SYL6UF0IMwHlTSH3apyQrpylsOWb2NJPgP8B8zO6ymG3B90kGj14BfFbBdZkDEJKUpK6Qr79eED4cVmNl0YBfCkPivAL8obay80pQV0pU38ax+RMIPA6/ta2YVtWx3CGEO70QLsKQtgO3M7KlatmtFuEQ1d6jukklT1pgjNXklPQl8Y2bHVHN/K8LAfT1IeLDRNGWNeVKTtxyyeiEhXR8ezmVIOgz4PbCfmX1VzTYtgNsJg43+qJT5cnKkJmvMkpq85ZDVC4lzzrkG8TYS55xzDeKFxDnnXIN4IXHNiqS+kibFHsDzJP1bUlGuxpO0laSBktYuYNuBkizrNlvSo7H9rrZ9+8Z92jZOcufqxguJazYUpku+GxgJ9AaOBZ4EDijSn9wKGADUWkiir4Eu8XYesAMwRlKbWvb7R9ynsp45nWsQHyLFNSdnAHea2cVZ656WdGlSgXIsNbNX4++vSpoJ/BPoCTycu3G8EqeFmX0OfF66mM6tyI9IXHOyNvBp7krLunRRUqd4muhoSX+Np8DmShqQu5+kPeIAed9J+kzSbZnTS5K6Ak/HTafFx5xex7yT4s9O8TGHSZoo6SBJ7wHfATvnO7UlqZWkayTNkLRY0jRJf87Jf5Kk9+L9MyRdgHP14Eckrjl5EzgzftN/xsy+rGHba4FngEOB3wADJH1hZoMBJG0LPA+MAg4BNgOuAjYH9o1/6zzgOsJptDnA4jrm7RR/fpqz7hrgMuAzwmiuK7SjSBLhlF0X4HJCQdoE+HXWNucDV8bHGg90Bi6XVGlmt9Yxp2vuzMxvfmsWN+CnwMeE4U2WAe8RPpDXytqmU7z/hZx97wJmEaZaBhgBfEQ4tZTZ5vC4b5e4vF9c7lRAtoGEoSxaxttWwDhgAbBR3GZYfLwdcvbtG9e3jcvd4/IB1fyttYCFwICc9ZcRilaL2vL6zW/ZNz+15ZoNM3sH2IbQuH4bYaysPwET81zx9HjO8mPAxsCmcfmXwONmVpW1zaPAUmC3ekZcF1gSbx8Qjm6OMLM5WdvMMrO3anmcPYCvrPqRGroAbYCHJbXM3ICxQAeWP0fnCuKntlyzYmaLCW0XTwNIOpFwJdeJwE1Zm87N2TWzvBEwM/78LOexqyR9CaxTz3hfA3sRjiY+BWabWe7QE5+ttNfK1iWcSqtOZoC/96q5fzPAhwFyBfNC4po1Mxsq6Rpg65y7NqhmeU7WzxW2iVdRrQvkHe+oAEvNbGIt2xQyptGXhEJXnUy+/chfmD4o4G849wM/teWaDUm5xQFJ6wPtWPkD9eCc5UyD+Sdx+TXg4Fg8srdpCbwUl7+PP9doQOz6GAOsI2m/au7/F7AI2NjMJua5fVO6qK4p8CMS15y8G4fcfoFwqqqCcGVVJXBfzrbbxekFHiVctXUicLaZLYv3X0GY1vQJSbcT2hWuBkaa2b/iNplv9qdIGgFUmtm7xXlqKxhF6HT5gKTLCFeQbQT8xsxOMbP5kgYCN0mqAF4kfKncCuhmZrlF1LkaeSFxzcllwIHAzYR2jE8JE/4cYWbTcra9gHDq51FCf43LgR8uizWz9yT1IFxC+xjh6qq/x/0y28yQdB5wFnAm4WimUzGeWDYzM0kHx8znEKaIng08kLXNNZJmE4YfP5fwHD8EHix2Ptf0+DDyzmWJ05NOI0xd+kyyaZxLB28jcc451yBeSJxzzjWIn9pyzjnXIH5E4pxzrkG8kDjnnGsQLyTOOecaxAuJc865BvFC4pxzrkH+P9FYor+QsHtTAAAAAElFTkSuQmCC\n", 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" ] @@ -249,7 +249,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "exact expected value:\t0.5049\n", + "exact expected value:\t0.5695\n", "exact delta value: \t0.9291\n" ] } @@ -301,9 +301,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "Exact value: \t0.5049\n", - "Estimated value:\t0.5000\n", - "Probability: \t0.9955\n" + "Exact value: \t0.5695\n", + "Estimated value:\t0.5730\n", + "Probability: \t0.9977\n" ] } ], @@ -320,7 +320,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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\n", 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" ] @@ -460,7 +460,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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" ] @@ -430,13 +430,13 @@ "text/html": [ "
                                                ┌───┐┌────────────────┐┌───┐»\n",
        "  q_0: |0>──────────────────────────────────────┤ X ├┤ U3(0.7907,0,0) ├┤ X ├»\n",
-       "          ┌────────────────┐┌──────────────────┐└─┬─┘└────────────────┘└─┬─┘»\n",
-       "  q_1: |0>┤ U3(1.5708,0,0) ├┤      U1(0)       ├──■──────────────────────■──»\n",
-       "          ├────────────────┤├──────────────────┤                            »\n",
-       "  q_2: |0>┤   Ry(1.1847)   ├┤ U3(-0.14182,0,0) ├────────────────────────────»\n",
-       "          ├────────────────┤├──────────────────┤                            »\n",
-       "  q_3: |0>┤   Ry(1.3696)   ├┤ U3(-0.11174,0,0) ├────────────────────────────»\n",
-       "          └────────────────┘└──────────────────┘                            »\n",
+       "          ┌────────────────┐     ┌───────┐      └─┬─┘└────────────────┘└─┬─┘»\n",
+       "  q_1: |0>┤ U3(1.5708,0,0) ├─────┤ U1(0) ├────────■──────────────────────■──»\n",
+       "          └─┬────────────┬─┘┌────┴───────┴─────┐                            »\n",
+       "  q_2: |0>──┤ Ry(1.1847) ├──┤ U3(-0.14182,0,0) ├────────────────────────────»\n",
+       "            ├────────────┤  ├──────────────────┤                            »\n",
+       "  q_3: |0>──┤ Ry(1.3696) ├──┤ U3(-0.11174,0,0) ├────────────────────────────»\n",
+       "            └────────────┘  └──────────────────┘                            »\n",
        "  q_4: |0>──────────────────────────────────────────────────────────────────»\n",
        "                                                                            »\n",
        "q_a_0: |0>──────────────────────────────────────────────────────────────────»\n",
@@ -466,9 +466,9 @@
        "«  q_0: ──■────■───────────────────────────────────────────■──»\n",
        "«         │    │                                           │  »\n",
        "«  q_1: ──┼────┼───────────────────────────────■───────────┼──»\n",
-       "«       ┌─┴─┐  │  ┌──────────────────┐┌────────┴────────┐  │  »\n",
-       "«  q_2: ┤ X ├──┼──┤ U3(-0.28365,0,0) ├┤        X        ├──┼──»\n",
-       "«       └───┘┌─┴─┐└──────────────────┘├─────────────────┤┌─┴─┐»\n",
+       "«       ┌─┴─┐  │  ┌──────────────────┐       ┌─┴─┐         │  »\n",
+       "«  q_2: ┤ X ├──┼──┤ U3(-0.28365,0,0) ├───────┤ X ├─────────┼──»\n",
+       "«       └───┘┌─┴─┐└──────────────────┘┌──────┴───┴──────┐┌─┴─┐»\n",
        "«  q_3: ─────┤ X ├────────────────────┤ U3(0.11174,0,0) ├┤ X ├»\n",
        "«            └───┘                    └─────────────────┘└───┘»\n",
        "«  q_4: ──────────────────────────────────────────────────────»\n",
@@ -483,9 +483,9 @@
        "«  q_0: ─────────────────────────────────────────────────────────────────────░─»\n",
        "«                                                                            ░ »\n",
        "«  q_1: ────────────────────────────■────────────■───────────────────────■───░─»\n",
-       "«       ┌─────────────────┐┌────────┴─────────┐  │                       │   ░ »\n",
-       "«  q_2: ┤ U3(0.28365,0,0) ├┤        X         ├──┼───────────────────────┼───░─»\n",
-       "«       └─────────────────┘├──────────────────┤┌─┴─┐┌─────────────────┐┌─┴─┐ ░ »\n",
+       "«       ┌─────────────────┐       ┌─┴─┐          │                       │   ░ »\n",
+       "«  q_2: ┤ U3(0.28365,0,0) ├───────┤ X ├──────────┼───────────────────────┼───░─»\n",
+       "«       └─────────────────┘┌──────┴───┴───────┐┌─┴─┐┌─────────────────┐┌─┴─┐ ░ »\n",
        "«  q_3: ───────────────────┤ U3(-0.22349,0,0) ├┤ X ├┤ U3(0.22349,0,0) ├┤ X ├─░─»\n",
        "«                          └──────────────────┘└───┘└─────────────────┘└───┘ ░ »\n",
        "«  q_4: ─────────────────────────────────────────────────────────────────────░─»\n",
@@ -549,7 +549,7 @@
        "«                                ░                └───┘               └───┘ ░
" ], "text/plain": [ - "" + "" ] }, "execution_count": 12, @@ -643,7 +643,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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\n", 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" ] @@ -793,13 +793,13 @@ "text/html": [ "
                                                ┌───┐┌────────────────┐┌───┐»\n",
        "  q_0: |0>──────────────────────────────────────┤ X ├┤ U3(0.7907,0,0) ├┤ X ├»\n",
-       "          ┌────────────────┐┌──────────────────┐└─┬─┘└────────────────┘└─┬─┘»\n",
-       "  q_1: |0>┤ U3(1.5708,0,0) ├┤      U1(0)       ├──■──────────────────────■──»\n",
-       "          ├────────────────┤├──────────────────┤                            »\n",
-       "  q_2: |0>┤   Ry(1.1847)   ├┤ U3(-0.14182,0,0) ├────────────────────────────»\n",
-       "          ├────────────────┤├──────────────────┤                            »\n",
-       "  q_3: |0>┤   Ry(1.3696)   ├┤ U3(-0.11174,0,0) ├────────────────────────────»\n",
-       "          └────────────────┘└──────────────────┘                            »\n",
+       "          ┌────────────────┐     ┌───────┐      └─┬─┘└────────────────┘└─┬─┘»\n",
+       "  q_1: |0>┤ U3(1.5708,0,0) ├─────┤ U1(0) ├────────■──────────────────────■──»\n",
+       "          └─┬────────────┬─┘┌────┴───────┴─────┐                            »\n",
+       "  q_2: |0>──┤ Ry(1.1847) ├──┤ U3(-0.14182,0,0) ├────────────────────────────»\n",
+       "            ├────────────┤  ├──────────────────┤                            »\n",
+       "  q_3: |0>──┤ Ry(1.3696) ├──┤ U3(-0.11174,0,0) ├────────────────────────────»\n",
+       "            └────────────┘  └──────────────────┘                            »\n",
        "  q_4: |0>──────────────────────────────────────────────────────────────────»\n",
        "                                                                            »\n",
        "q_a_0: |0>──────────────────────────────────────────────────────────────────»\n",
@@ -829,9 +829,9 @@
        "«  q_0: ──■────■───────────────────────────────────────────■──»\n",
        "«         │    │                                           │  »\n",
        "«  q_1: ──┼────┼───────────────────────────────■───────────┼──»\n",
-       "«       ┌─┴─┐  │  ┌──────────────────┐┌────────┴────────┐  │  »\n",
-       "«  q_2: ┤ X ├──┼──┤ U3(-0.28365,0,0) ├┤        X        ├──┼──»\n",
-       "«       └───┘┌─┴─┐└──────────────────┘├─────────────────┤┌─┴─┐»\n",
+       "«       ┌─┴─┐  │  ┌──────────────────┐       ┌─┴─┐         │  »\n",
+       "«  q_2: ┤ X ├──┼──┤ U3(-0.28365,0,0) ├───────┤ X ├─────────┼──»\n",
+       "«       └───┘┌─┴─┐└──────────────────┘┌──────┴───┴──────┐┌─┴─┐»\n",
        "«  q_3: ─────┤ X ├────────────────────┤ U3(0.11174,0,0) ├┤ X ├»\n",
        "«            └───┘                    └─────────────────┘└───┘»\n",
        "«  q_4: ──────────────────────────────────────────────────────»\n",
@@ -846,9 +846,9 @@
        "«  q_0: ─────────────────────────────────────────────────────────────────────░─»\n",
        "«                                                                            ░ »\n",
        "«  q_1: ────────────────────────────■────────────■───────────────────────■───░─»\n",
-       "«       ┌─────────────────┐┌────────┴─────────┐  │                       │   ░ »\n",
-       "«  q_2: ┤ U3(0.28365,0,0) ├┤        X         ├──┼───────────────────────┼───░─»\n",
-       "«       └─────────────────┘├──────────────────┤┌─┴─┐┌─────────────────┐┌─┴─┐ ░ »\n",
+       "«       ┌─────────────────┐       ┌─┴─┐          │                       │   ░ »\n",
+       "«  q_2: ┤ U3(0.28365,0,0) ├───────┤ X ├──────────┼───────────────────────┼───░─»\n",
+       "«       └─────────────────┘┌──────┴───┴───────┐┌─┴─┐┌─────────────────┐┌─┴─┐ ░ »\n",
        "«  q_3: ───────────────────┤ U3(-0.22349,0,0) ├┤ X ├┤ U3(0.22349,0,0) ├┤ X ├─░─»\n",
        "«                          └──────────────────┘└───┘└─────────────────┘└───┘ ░ »\n",
        "«  q_4: ─────────────────────────────────────────────────────────────────────░─»\n",
@@ -895,7 +895,7 @@
        "«            └───┘               └───┘ ░
" ], "text/plain": [ - "" + "" ] }, "execution_count": 21, @@ -969,7 +969,7 @@ }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -1317,7 +1317,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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\n", 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" ] diff --git a/qiskit/finance/simulation/european_call_option_pricing.ipynb b/qiskit/finance/simulation/european_call_option_pricing.ipynb index 464abe28f..e402d2a93 100644 --- a/qiskit/finance/simulation/european_call_option_pricing.ipynb +++ b/qiskit/finance/simulation/european_call_option_pricing.ipynb @@ -118,7 +118,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -177,7 +177,7 @@ "outputs": [], "source": [ "# set the strike price (should be within the low and the high value of the uncertainty)\n", - "strike_price = 2\n", + "strike_price = 1.896\n", "\n", "# set the approximation scaling for the payoff function\n", "c_approx = 0.25\n", @@ -214,7 +214,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -248,8 +248,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "exact expected value:\t0.1133\n", - "exact delta value: \t0.4700\n" + "exact expected value:\t0.1623\n", + "exact delta value: \t0.8098\n" ] } ], @@ -300,9 +300,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "Exact value: \t0.1133\n", - "Estimated value:\t0.1061\n", - "Probability: \t0.9378\n" + "Exact value: \t0.1623\n", + "Estimated value:\t0.1196\n", + "Probability: \t0.4973\n" ] } ], @@ -319,7 +319,7 @@ "outputs": [ { "data": { - "image/png": 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+ "image/png": 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\n", 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\n", 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\n", 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" ] @@ -440,9 +440,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "Exact delta: \t0.4700\n", - "Esimated value:\t0.4510\n", - "Probability: \t0.5918\n" + "Exact delta: \t0.8098\n", + "Esimated value:\t0.8172\n", + "Probability: \t0.8829\n" ] } ], @@ -459,7 +459,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] diff --git a/qiskit/finance/simulation/european_put_option_pricing.ipynb b/qiskit/finance/simulation/european_put_option_pricing.ipynb index 24df0749c..d9897256a 100644 --- a/qiskit/finance/simulation/european_put_option_pricing.ipynb +++ b/qiskit/finance/simulation/european_put_option_pricing.ipynb @@ -118,7 +118,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -177,7 +177,7 @@ "outputs": [], "source": [ "# set the strike price (should be within the low and the high value of the uncertainty)\n", - "strike_price = 2\n", + "strike_price = 2.126\n", "\n", "# set the approximation scaling for the payoff function\n", "c_approx = 0.25\n", @@ -214,7 +214,7 @@ "outputs": [ { "data": { - "image/png": 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tLelNSUslLZL0gqQWdZ05MddcA7/9LRx7LMyalXQa55zLKdZCIqkNMAEwoBcwFDiHMJx8vm2PBx4kTI61D3A88AEJjGAcm3XXDfOXNG4cJsNaujTpRM45t5a4P4RPApoBvaOJrMZL2gAYIunqzMmtMklqR5i35HQzuzPjrifqPHHSOnWCe++FP/wBzjwTbr896UTOObeGuA9t7QOMyyoYYwjFZbdKtjss+nlPXQUravvvH+YuueMOuP/+pNM459wa4i4knYEZmSvMbC6wJLqvIjsCM4HjJM2TtFzSG5J2rruoRebyy+H3v4cTT4Tp05NO45xzP5LFOG+4pOXAeWZ2Y9b6ecC9ZnZRBduNA3YGvgHOBxZFP3cAtjCzhTm2GQgMBGjfvn3pmDFjqpW5rKyMli1bVmvb2rbuF1+ww8CBLN9gA9667TZWNmu2VptiyptPmrJCuvKmKSukK2+askLN8nbr1m2ame2Qt6GZxbYAy4FBOdbPB4ZVst14Qgf93hnrNgAWA5fl+7ulpaVWXZMnT672tnViwgQzyax/f7NVq9a6u+jyViJNWc3SlTdNWc3SlTdNWc1qlheYagV8tsd9aGsx0DrH+lbAV5Vs92X086XyFRb6WaYBXWorXCrssQcMGQIPPAB33ZV0Gueci72QzCCrL0RSR6AFWX0nWd4n7JEoa72AhjdH7cUXw557wumnw9tvJ53GOdfAxV1Ingd6Slo/Y10fYCkwpZLtniUUjW7lKyS1AkqBf9dBzuLWuHHYI2nXLlxf8vXXSSdyzjVgcReSkcAy4HFJPaIO8SHA9ZZxSrCkWZJGld82s6nAU8AoSUdL2g94mtDncmucT6BobLQRjBkDs2fDccdBjCdNOOdcplgLiZktBvYAGgPPEK5ovwEYnNW0SdQm0xHAk8D1wFhCEekePWbD9LvfwfDhYSyum29OOo1zroGKfXgRM5sOdM/TpiTHujLg5Ghx5c45J8yqeNZZMHw4uy1cCJttBsOGQf/+SadzzjUAPvpv2knhyneATz9FZmFCrIEDQz+Kc87VMS8k9cEVV6zdR7JkSTi7yznn6pgXkvpg7tyqrXfOuVrkhaQ+2Gyzqq13zrla5IWkPhg2DJo3X3u9T9PrnIuBF5L6oH//MMR8p06YBB06QJMm4bTglSuTTuecq+e8kNQX/fvD7NlMmTQJFiwIhWXSJLg07+STzjlXI15I6qtjjoEBA8I8JuPGJZ3GOVePeSGpz269FbbeGo44AubNSzqNc66e8kJSnzVvDmPHwvffQ58+sHx50omcc/WQF5L6bqut4M474bXX4MILk07jnKuHvJA0BH37wimnwHXXwVNPJZ3GOVfPxF5IJHWRNFHSEkkLJA2VlD3Sb/Y2JZIsx1K9idgbouuvh9JSOPpo+PDDpNM45+qRWEf/ldQGmABMB3oBPwOuIxS0PxXwEOcCr2bc/qK2M9Zb660HjzwC228Phx0Gr7wCTZsmnco5Vw/EvUdyEtAM6G1m481sJGFOkrMlbVDA9jPN7PWMZVadpq1vNt8c7rkHpk0Lw88751wtiLuQ7AOMy5wNERhDKC67xZylYerVKxSRESPCDIvOOVdDcReSzsCMzBVmNhdYEt2Xz92SVkr6RNL1kprVRch678orYeed4YQTYObMpNM451JOFuNc35KWA+eZ2Y1Z6+cB95rZRRVs1wG4GHgR+AbYHfgj8KKZ9apgm4HAQID27duXjqnmt++ysjJatmxZrW2TUGje9T7/nB2OP55lbdvy1ogRrEqgv6S+vrbFIE1ZIV1505QVapa3W7du08xsh7wNzSy2hTDP+qAc6+cDw6r4WCcDBmybr21paalV1+TJk6u9bRKqlPeFF8wkswED6ixPZer1a5uwNGU1S1feNGU1q1leYKoV8Hkc96GtxUDrHOtbAV9V8bHGRj+3r1GihqxnT/jTn2D0aLj77qTTOOdSKu5CMoOsvhBJHYEWZPWdFMCyfrrqGDwYunULFyy+807SaZxzKRR3IXke6Clp/Yx1fYClwJQqPtYh0c9ptRGswWrcGB58EFq3hkMPhW++yb+Nc85lyFtIJB0lqW0t/b2RwDLgcUk9og7xIcD1lnFKsKRZkkZl3B4i6TpJvaPthgI3AI+bmX+NrqlNNgmnAs+aBQMHQownYDjn0q+QPZK7CVegE516+9vq/jEzWwzsATQGniFcjHgDMDiraZOoTbkZhOtM7gaeA/oB10Q/XW3Ybbcwd8nDD4drTJxzrkCFDJGyGPhJ9LuoYZ+EmU0HuudpU5J1ewzhwkVXl/74xzB0yllnwW9/C7/5TdKJnHMpUEghmQDcJ2kmoYiMlvRdRY3NrNp7LC5hjRrBvffCdtuF8bjeegvatEk6lXOuyBVSSI4FTgG2Ipxq+xHweV2Gcglq2zYM7rjrrmGq3iefBCnpVM65Ipa3kJjZEuBaAEk9gIvN7N91HcwlaKed4Jpr4Mwzwxwm556bdCLnXBEr5KytlZLKD5a/RBiixNV3Z5wBBx8MF1wAr76av71zrsEq5KytH4D1ot+PAjaquziuaEgwahSUlIT53j/3o5nOudwK6SOZDgyR9CThrK1DJFU0iJeZ2W21ls4lq1UrePRR6NoVjjgCnnsuXMDonHMZCikkpwO3E673MMIshRUxwAtJfbLddnDzzXDiiTBsGFxySdKJnHNFJu+hLTN7zcx+aWbrEPZIdjKzRhUs/nW1PjrhhLBHMmQITJyYdBrnXJGp6lhb3QiHulxDIsFtt0HnztCvHyxYkHQi51wRKeTQ1o/MbAqApB2B3wEbAl8Cr5jZG7UfzxWNli1h7Nhwtfvhh4c9kyZVevs45+qpKu2RSGoh6TngNeBKwsWKVwKvSfqbpOZ1kNEViy5d4Pbb4eWX4c9/TjqNc65IVPXQ1tVAV6Av0NTMOgBNo9tdgatqN54rOkccEfpMhg+HZ59NOo1zrghUtZAcDPzRzB41s1UAZrbKzB4FLgAOzfcAkrpImihpiaQFkoZKKriTXlIjSdMkmaT9q5jf1Yabb4Ztt4WjjoI5c5JO45xLWFULSSvg4wru+xjYoLKNJbUhDAJpQC9gKHAOYTj5Qh0P/F8V2rva1rRpuL5kxYowuOMPPySdyDmXoKoWkn8DJ0trjuIX3T45ur8yJwHNgN5mNt7MRhKKyNmSKi1C0d9pAwwDLq5iblfbfv7zMM/7P/8J552XdBrnXIKqWkguAnoCMyQNl3SWpCuB94G9ovsrsw8wLnM2RMI8I80IE1flcxnwKuAXMxSDgw+GQYPCoa6xY5NO45xLSJUKiZlNArYD3ib0hwwDDgPeArY3s8l5HqIzYbbDzMecCyyJ7quQpF8Bx1D5lfUubldfDTvuCMceCx98kHQa51wCZDHOzy1pOXCemd2YtX4ecK+ZVbhHI2kK8IaZnS+phDAvyh/MLOepQ9F88AMB2rdvXzpmTPUmWCwrK6Nly5bV2jYJSeRdb+FCdhg4kGUbbcRbt97KqvXWy78R/trWpTRlhXTlTVNWqFnebt26TTOzisZWXM3MCl4I85J0qco2WdsvBwblWD8fGFbJdn2BT4ENotslhA77/Qv5u6WlpVZdkydPrva2SUgs77PPmoHZCScUvIm/tnUnTVnN0pU3TVnNapYXmGoFfMZW5/TfdyX9U9JJklpVcfvFQOsc61sBX+XaQNI6wDWEa1QaSWrN6rPDWkhav4oZXF3Yb78wd8mdd8J99yWdxjkXo6r2kfwU6EHo57gG+ETSg9HMiYWYQVZfiKSOQAuy+k4ytAA2Ba4nFKLFrD47bAyhv8YVg8suC1P0nnQSvPde0mmcczGp6h4JZjbZzI4COhCGmN8UGCdpjqRLJW1eyebPAz2z9iL6AEuBKRVsU0YYLDJzOTy67yKgf1Wfg6sjTZrAmDFhXK5DD4WysqQTOediUOVCUs7MysxsFDCYcEpuR+BC4L+SnpLUKcdmI4FlwOOSekQd4kOA6y3jlGBJsySNiv7OCjN7KXMBXo+avms+WGRx6dABHnoIZswIeyYxnszhnEtGtQqJpBJJgyV9CLxI2Gs4FFgfOIDQGb7WaVJmthjYA2gMPEO4GPEGQjHK1CRq49Koe3e49FJ44IHQZ+Kcq9eqNA64pCMJ13LsCswF7gbuNrN5Gc2ek/QdYSiUtZjZdKB7ZX/HzEry3D+bMMmWK1YXXwyvvAJnnAE77ADbb590IudcHanqHskdhNNwe5rZ5mZ2WVYRKfdf4PIap3Pp1agR3H8/tGsX+ku+/jrpRM65OlLVQvITM+tnZpUOUWJmn5hZVQZidPXRRhvBww+HEYKPPdb7S5yrp6p6+u/iugri6qlddoGrroLHH4ebbko6jXOuDlS5s11SH0kTJM2V9Fn2UhchXcqdfTb06hVGCX799fztnXOpUtWpdvsB9wCzCNePPA08Gz3ON8AttR3Q1QNSGHJ+003D/CWLFiWdyDlXi6q6R3IeYSj3U6PbI8zsWOCnwBeEUXydW1ubNmEyrIUL4cgjYdWqpBM552pJVQvJFsCrZrYSWEk05pWZfUsYC+u02o3n6pUddoAbboDnn4e2bdmte3coKQnXmzjnUquqheRroHyM8PnALzLuE9C2NkK5eqxVK2jcGL76CpmFM7oGDvRi4lyKVbWQTAV+Ff3+NHCJpBMkHU0YxNGHK3GVu/hiWLlyzXVLloT1zrlUqtKV7cCVQPkYWpdEv48gDGfyJtFEUs5VaO7cqq13zhW9ggqJpGbAvoQxtD6V1N7MFgK9JK0HrGdrzsPuXG6bbRYOZ+Va75xLpbyHtqJh4d8DHiUcvroPmClpLwAzW+ZFxBVs2DBo3nzt9YcdFn8W51ytKKSP5GpgFfB7oDmwNWEyqdur8wcldZE0UdISSQskDZVU6Ui/kraW9ELUfll0MeRdkjpUJ4NLUP/+cMcd0KkTJkHHjuH6kr/+FT7+OOl0zrlqKKSQdAX+ZGavmtn3ZvY+cCKwWVU/yCW1IYwKbEAvYChwDmE4+cq0Aj4CzgV6Eoad70EYabiq/Twuaf37w+zZTJk0KfSNTJgAy5ZBnz6wfHnS6ZxzVVRIIekAfJi17n+E0303qeLfOwloBvQ2s/FmNpJQRM6WtEFFG5nZa2Z2spk9GE1udTdwArAtq88ic2m11VZw113wj3/AhRcmncY5V0WFnv5bW8O27gOMy+pTGUMoLrtV8bHKx9lYtzaCuYT16QOnngrXXQdPPpl0GudcFRRaSMZlDcz4SbR+YhUHbewMzMhcYWZzCUOrdM4XQlIjSetK2goYTjjl+J8FPgdX7K67DkpLYcAA+DB7J9g5V6xkeeaIkJQ9DW6lKpuHRNJy4DwzuzFr/TzgXjO7KE+WFwh9JADTgH3NLGfxiuaDHwjQvn370jFj1pr5tyBlZWW0bNmyWtsmIU15c2Vt+sknlA4cyPcdOvD2Lbewat3i2eFM+2tbzNKUN01ZoWZ5u3XrNs3Mdsjb0MxiW4DlwKAc6+cDwwrYfgtgR+AIwp7NNKBpvu1KS0utuiZPnlztbZOQprwVZn3qKTMwO/nkWPPkUy9e2yKVprxpympWs7zAVCvgs73K85HU0GKgdY71rYCv8m1sZh+Y2Rtmdj9hz2Q7oF/tRnSJO+AAOPdcuO02eOihpNM45/KIu5DMIKsvRFJHoAVZfSf5mNkc4Etg81pL54rHFVeE2RVPOAFmVOmt4ZyLWdyF5Hmgp6T1M9b1AZYCU6ryQFGHe1vC9SWuvllnHRgzBpo1g0MOCQM7OueKUtyFZCSwDHhcUo+oQ3wIcL1lnBIsaZakURm3r5U0XNJBkrpJOgUYR7iepXq96K74bbppGF5++vRwarBzrijFWkjMbDGwB2G04GcIFyPeQLhSPVOTqE25qYQhWkYBfwPOAB4DdjKz7+o4tkvSXnvBn/8Mo0eHYVScc0Un9uFFzGw60D1Pm5Ks22PwPY+G65JL4JVXwl7JDjvAr3wwA+eKSdyHtpyrusaN4cEHw7zvhxwC3/hg084VEy8kLh3atw+d7//7XziTK8+FtM65+Hghcemx665hPpNHHoERI5JO45yLeCFx6XL++bDffnDWWfDmm0mncc7hhcSlTaNGcM890KEDHHooLF6cdCLO/MjgAAAgAElEQVTnGjwvJC592rYNh7cWLICjj/b+EucS5oXEpdOOO8K118Izz4SfzrnEeCFx6XX66XDwwWFWxVdeSTqNcw2WFxKXXhKMGgU//WmYYfHzz5NO5FyD5IXEpVurVvDoo7BoEfTvDytXJp3IuQbHC4lLv223hb/8BcaPD9eZOOdi5YXE1Q/HHw9HHglDhsCECUmnca5Bib2QSOoiaaKkJZIWSBoqqXGebX4j6e5oePklkmZKGiypaVy5XZGTwoyKv/gF9OsXTg12zsUi1kIiqQ0wATCgFzAUOIcwnHxl+gA/A64C9gVuBc4GHqizsC59WrQI/SXffQd9+8KKFUkncq5BiHsY+ZOAZkDvaCKr8ZI2AIZIujpzcqssV5lZ5ik5L0n6HrhdUqdo2l3noEsXuP32cJjrT3+C4cOTTuRcvRf3oa19gHFZBWMMobjsVtFGWUWk3NvRz41rL56rF444AgYOhKuugmefTTqNc/Ve3IWkMzAjc4WZzQWWRPdVxc7AKmBm7URz9cpNN4WzuY46Cub4DqtzdUkW4zhFkpYD55nZjVnr5wH3mtlFBT7OJsA7wHNmNqCCNgOBgQDt27cvHTOmehMslpWV0bJly2ptm4Q05a3rrM3mz6f0xBNZ0rEjb998M7bOOjV6PH9t606a8qYpK9Qsb7du3aaZ2Q55G5pZbAuwHBiUY/18YFiBj7Eu8DLwIdCmkG1KS0utuiZPnlztbZOQpryxZH3sMTMwO+OMGj+Uv7Z1J01505TVrGZ5galWwGds3Ie2FgOtc6xvBXyVb2NJAu4Ftgb2NTMfQ9xVrndvOPNMuPlmGDs26TTO1UtxF5IZZPWFSOoItCCr76QCNxBOG+5lZoW0dy50uu+0Exx7LHzwQdJpnKt34i4kzwM9Ja2fsa4PsBSYUtmGki4ETgeOMDMf6tUVbt114eGHYZ11wmRYS5cmnci5eiXuQjISWAY8LqlH1CE+BLjeMk4Jjq5gH5Vxux9wBeGw1nxJO2UsG8X7FFwqbbYZ3Hcf/PvfcMYZSadxrl6JtZBEfRp7AI2BZwhXtN8ADM5q2iRqU26v6OcA4B9Zy351l9jVK/vuG+YuuesuuPfepNM4V2/EfWU7ZjYd6J6nTUnW7QGEIuJczQwdCq+9BiefDKWlsPXWSSdyLvV89F/XsDRpAg89BOuvH/pLysqSTuRc6nkhcQ1Phw6hmMycCSeeCDFelOtcfeSFxDVM3brBpZfCgw/CnXcmnca5VPNC4hquiy6Cnj3DWVxvvZV0GudSywuJa7gaNYL774d27UJ/yddfJ53IuVTyQuIatnbt4JFHYO5cOOYY7y9xrhq8kDi3885hAqwnngjDzzvnqsQLiXMAZ58NvXrBeefB668nnca5VPFC4hyABKNHQ8eOcNhhsGhR0omcSw0vJM6Va90aHn0UFi4Mc76vWpV0IudSwQuJc5lKS+HGG+H558Pw8865vLyQOJftpJOgb1/405/gpZeSTuNc0Yu9kEjqImmipCWSFkgaKqlxnm3WlXSNpL9LWirJz9F0dUeCO+6ALbaAww+HTz9NOpFzRS3WQiKpDTABMMJMh0OBcwjDyVemOXA8sAR4rS4zOgeEQR3Hjg0XKXbvDp06sVv37lBSAg88kHQ654pK3HskJwHNgN5mNt7MRhKKyNmSNqhoIzP7CtjQzHoCT8QT1TV422wTOt3ffx/mzkVmMGcODBzoxcS5DHEXkn2AcZmzIQJjCMVlt8o2NPNLjl0Cxo1be92SJXDxxfFnca5IxV1IOgMzMleY2VzCIavOMWdxLr+5c6u23rkGKO4ZEtsAX+VYvzi6r9ZE88EPBGjfvj0vVfPsm7Kysmpvm4Q05U1D1p023pimCxeutX5F06a88dRTLG/VKoFU+aXhtc2Uprxpygox5TWz2BZgOTAox/r5wLACH+M0oiNdhS6lpaVWXZMnT672tklIU95UZL3/frPmzc3CcI5hadLETDJr08ZsxAizFSuSTrmWVLy2GdKUN01ZzWqWF5hqBXzGxn1oazHQOsf6VuTeU3EuWf37h1OBO3XCJOjUKQyl8u67sO22cMop8JvfwD/+kXRS5xITdyGZQVZfiKSOQAuy+k6cKxr9+8Ps2UyZNAlmzw63t94aJk6Ehx+Gzz4LIwgPGBCGV3GugYm7kDwP9JS0fsa6PsBSYErMWZyrGSkM8DhjBlxwQZi2d8stw1D0K1Yknc652MRdSEYCy4DHJfWIOsSHANdbxinBkmZJGpW5oaR9JB0CbBvdPiRaOsUX37kcWraEK6+E//wHunaFM8+E7baDKf7dyDUMsRYSM1sM7AE0Bp4hXIx4AzA4q2mTqE2m24BHgeOi249GS7e6yutclWy5ZRjs8Ykn4NtvYffdoV8/WLAg6WTO1anYx9oys+lm1t3MmplZBzP7s5mtzGpTYmYDcqxTjmV0nPmdq5QEBx4I06fDJZfA44/DVlvBNdfADz8knc65OuGj/zpXF5o3h0svDQWlWzc4/3z49a9hwoSkkzlX67yQOFeXNt8cnn4ann0Wli+HPfeEQw7xK+NdveKFxLk47Ldf6Iy//HJ47jno3BmGDYNly5JO5lyNeSFxLi5Nm4bBHmfMgH33DRNnbbNNKCzOpZgXEufittlmYa6TF1+Exo3D3soBB8CHHyadzLlq8ULiXFL23BPeeQeuvhomTYIuXWDwYFi6NOlkzlWJFxLnkrTuunDeeTBzJvTuDUOHhoLy5JNhiEjnUsALiXPF4P/+Lwyx8tJL4Ur5gw4K/Sj//W/SyZzLywuJc8Vkt93grbfgxhvhtddCZ/yFF8J33yWdzLkKeSFxrtissw4MGhT2Rvr1g+HDw+nCjzzih7tcUfJC4lyxat8+zH3y6quw0UbQpw/06BGulneuiHghca7Y7bwzvPkmjBgBb78dhlo55xz45pv82zoXg9gLiaQukiZKWiJpgaShkrJH+s21XStJd0taLOlrSQ9IahtHZucS17gxnHxyONx1zDFwww1hMMj77/fDXS5xsRYSSW2ACYABvYChwDmE4eTzeRjYHTgeGAD8BniyLnI6V7TatQtT/77xRriw8cgjYddd4d//TjqZa8Di3iM5CWgG9Daz8WY2klBEzpa0QUUbSeoK9ASONrPHzOwJ4Ajgd5J6xBHcuaJSPk/8XXeFIVe23x5OPx3uvBNKStite3coKYEHHkg6aeUeeCA9edOUFeLNa2axLcDLwJisdZsR9lD+UMl2Q4FPc6z/ELgu398tLS216po8eXK1t01CmvKmKatZEeddtMjs1FPNwkGuNZfmzc3uvz/phLndf3/Il4a8acpqVmt5galWwGd7k7orUTl1BiZlrjCzuZKWRPc9U8l2M3Ksfz+6z7mGa8MN4ZZbwiRan3yy5n1LlsCAAXDFFYlEq9R//7v23PbFmjdNWaHivBdfDP371/qfi7uQtAG+yrF+cXRfdbbbPNcG0XzwAwHat2/PSy+9VKWg5crKyqq9bRLSlDdNWaH48+726acox3pbsYLPN9oo9jz5bDR9emrypikrVJJ37lym1MV7uJDdltpagOXAoBzr5wPDKtluPPBEjvUPAK/m+7t+aKs4pSmrWQryduqU+/BWp05JJ8stTXnTlNWs1vJS4KGtuDvbFwOtc6xvRe49jnzbtc6znXMNx7BhYYrfTM2bh/XFKE1505QVYs8bdyGZQVafhqSOQAty94FUuF2kor4T5xqe/v3DqcGdOmESdOoUbtfBMfFakaa8acoKseeNu5A8D/SUtH7Guj7AUmBKnu02kfS78hWSdiD0jzxfF0GdS6X+/WH2bKZMmgSzZxfvB125NOVNU1aINW/chWQksAx4XFKPqEN8CHC9mf043oOkWZJGld82s38A44B7JfWWdCChf+QVM5sQ6zNwzjm3hlgLiZktBvYAGhNO9b0UuAEYnNW0SdQmU1/CXstfgXuBacBBdZnXOedcfnGf/ouZTQe652lTkmPdV8Ax0eKcc65I+Oi/zjnnasQLiXPOuRpRuOakfpP0OTCnmpu3A76oxTh1LU1505QV0pU3TVkhXXnTlBVqlreTmeW9dL9BFJKakDTVzHZIOkeh0pQ3TVkhXXnTlBXSlTdNWSGevH5oyznnXI14IXHOOVcjXkjyuyPpAFWUprxpygrpypumrJCuvGnKCjHk9T4S55xzNeJ7JM4552rEC4lzzrka8ULinHOuRryQOOecqxEvJM4552ok9tF/Xe2IZpbcFxDwqJktkrQpcC7wM2A2cIeZvZtcSpD0R+C5pHMUSlIzoImZfZuxbiPgNKALsAr4FzDCzL5OJqVzxcVP/41IEmF+k/2AXwAbAiuBhcDrwGgz+29yCVeT9FvgRaAlsAL4EugJPEfI/B6wDbAJ0MPM/p5QVCStAowwJfKDwMNmNiupPPlIeg74wMwGRbe7EmbhXEWYA0dAKfAD0N3M3ksw63ZAMzN7LWPd3sCFrC56/waGZLYpFtH/uT8A2xPeI1MJXzqK+kNJ0gaEsau6m9krSeeBHzN1B9YF/mZm30VfgE4lzCT7IeGL5YI6+ftF/m8Wi+gFf47wAbGQMIvj/xHe3M8T/iG2Ai4zs8uSyllO0njC3uRBwHeEycEOJHzQHWJmyyWtBzwJNDWzbglmXQVcBfwS2JOQ+y1CUXnEzOYnlS0XSV8Ax5nZU9Ht1wmv8YHleymSWgFPA9+bWc8Es74OPGNmw6LbxwJ3AZOBSYSitwfwe+Dg8ueUUNbXCK/r+9HtNoQvQ6VAWdSsJeFLW8/MPcIkSDqlkrubAdcANwEfAJjZiDhy5SLp58BEoGO06iNgL2A80Br4H+HzaylQambzaj2EmTX4BXiI8Ib4Zca6nwAvAI9Ft3cjvOGPLYK8i4B9Mm5vTPj2uVdWu/2ALxLOugr4bfR7G2Bg9KZfES0vRevaJv26RhmXALtm3P4h+3XNeG2/SzjrN5nZgFnAX3K0Gwn8u1jeB9HtUYQ96b0z1u0NLAZuKIL3wSrC3v2qCpbM+1YmnPURwp7nzwlHUu6LPs9eA9aP2rSL2txeFxm8sz3YB7jAMo7jW9gFPAk4UFIHM5sCXAEMSihjJouWzNtkrct1O1FmttjM7jCzPYBNgXMIu+IjgQWS/pZowOA/QOYe3ELCf85sbQlFJ0mrsm53AsbmaDeW8I20mBwADDWzF8pXRL8PA3onlmq1p4HPgOOAxmbWqHwhvB8E7B6ty54WPG6/A4aZ2Swz+xL4E6Gf9FqL9uzM7AvgRtZ8b9caLySBCN8wsq2M7msV3X4D2DKuUJWYBpwraX1JjYCLgPnAyZIaA0hqApxC+GAsOmb2qZndZGY7Az8FBhP2ApM2HLhA0rHRazgMuEbSnpLWlbRe1A9xJeGbYJL+DvTPuP0ekGu48N8Q3h/FpDWhTyTbNELfXqLM7EDgaOA84E1Ju2TenUyqCrUBPs24Xf5vnT0H04eEL3C1zs/aCiYAl0t6x8w+hB+P4d5M+Acq72RvCRTDmToXE45/fkk4PLSE0NE2FvhAUnln+08IhwuKmpnNIXyADy+CLI9LOp3w7e0GYCbhi0T5N2cjfLl4mvAhk6SLgFejLxN/IXSy3yNpQ8IhQwh9JGcCFySScE0HSyovdIuBXBMmtSMcskucmb0o6VeE1+9vkl4gnBWZaP9NDp8R9kbLrQRuJ+xNZ9qYOsrune1AdNrsC4Td/zmE4+I/JXS6H25mz0ftribMGNYnqazlosz7E74MPGZmn0jaBDif1c/jLjN7K8GYSBoM3Gl1dLZIXZHUFugD/JbwDbkRoXC/DzxrZtMSjPcjSdsCtwE7srrIkfH7YsIhpJuSSRhEJ11kG21mx2a1ux3oYma/jydZYaL/W1cTDrvdTigu3czs5USDAZKeBL7Mfi1ztPsL8Asz61HrGbyQBNEhocOAXwNNCR2XD0bHHJ0rapJ+QSgm2UXvNTNbnmS2qpB0AvA/M5uUdJZcotPBbyB8WdvPiuC0akntgeZm9lGedmcTTrqYWOsZvJDUP5Iam1muPp+iIakpoUNwFTCrGD/soj6Szcm4psjM5iabyrni453tWSRtLelgScdLOi76feukc2WT1FvSk5Kek/SHaF0fSbOBHyTNib7dJUrSEdH1DeW3m0gaTvjG/A7hZIAvJRXDMXwAJJVKeppwPPl94FXC9Q0fSZovaaik5omGrEcUSTpHLpKaZf9bS9o2+lwoTSpX0Uny/OdiWoBjCf0Kuc4dX0kYcuSYpHNGWQ+Lcr0CPEXobD+B0LczinA160NR7p4JZ50OnJxx+7oo75+BXQinLg4hXCx1URG8tnsR+samEs7MGkK4KPWHKPM5hLOj/gW0KYK8+xOuy3kXeJiMa2Ay2uxI8tc67EV0TUPGugMJF6euAJZHr/l+Sb+mUbZWwBNRrhXAnUBj4J6sz4VXgXZJ5y3wOR1cV++DxJ9cMSzA6dEb5lbCVcDtojdN4+j33wG3RB8wpxZB3jeBkRm3+0fZrstqdzcwIeGsS4DdMm5/BgzK0e5cYE4RvLbTgHsqeI/MJuzFN40+AEcknHXPjA+zW6LsK6NirYx2xVBIVrLmBYkHRR/Gr0X/9udGv68gxwWgCeS9mTAMyunAUdGXh8eAj6OiuBHh+rP5wG1J5y3wOdVZIfE+EkDSh4QP5qvztDsfOMnMNo8nWYU5vgF6m9mE6HYrwtk5PSyjkzI65HW7mSV2fYakT4DTzOyx6PYywl7SS1nt9gSeNrNm8adcI8dS4AAzG5+1vg1hRIGtzex9SUcBV5lZhyRyRpleIYwLdkzGumMJH4LjCWccfi9pR0Kne2IXzkVnbe1kZv+Mbr8FzDezP2S1ew5oYWa7JRAzM8dHwBVmdmd0eztCoT7GzO7JaHcCYU/6p8kkBUl/LbBpJ8JFlLX+PvA+kmAT4J8FtPsnRXCxFOHUzsw3Q/lYRV9ltSsjXPiVpKcJF0+uG92eAByeo93hhG99SfuMcOZetl8TXvfy64jmsPpC1aRsA9yfucLM/koYzmcnYFJ0TUkx2oZwGm22OwiDOCZtY1ZfPwbRmFqEcasyzSL39TBxOpqwl/TLPEunih6gpvyCxOAd4ARJL5tZrvPdy0cqPSFqm7Q5hNFdxwGY2crotMT3s9ptzppXvCbhQsIV2P+RdBfwDHCVpG1YfdFcd2A7wkiwSbsDuExSC0Lfww+EK8MvBibb6uthNgeSPoPre6BF9kozmxZdiT2OcLhoSMy5KpJ5+ONrVn8ByvQdxfEF9yNCQZ4S3f494VDczoS+yXK7kPz74APgn2Z2VGWNJB1C6EerdV5IgnMIFyROl/Q4Ycjzrwhv/NZAZ8Ix3U0pjivFHydrqAMzeyNHu36s+aaPnZl9KWknwgfx2YRvegBdo+UHwmGY35vZm8mkXM3MhkWHYS4gDNsC4X3wEOEitHLLCWOvJekdwnH6p7PvMLMPo2LyHDA65lwVGSdpRfR7K2BbVn+ZKNcZ+CTOUBUYCdwk6ZeEoncY4UvRJZJaEgZA3B44C0h6RPDXCQUun8wLVmuV95FEJP2McFX43qwejrncx4Qzd64xs+xd26IlaTPgKzMriiEnACSVsOZFc/+z4ryGZB3CdS5NgQ+L6TUsJ+lEwjAp21kFF85Ge1ZPEPrPEvumH41wkO0DM3swq91L0fpiOHX9DMIh13UIo0SMlHQ4oQ+qfNDOO4A/Jvkejk5D3sXMbs7Trh2hj29KZe2qlcELydqi88bL+xa+MrOkR3l1zhWJ6DB3OzP7POksxcILST0T7Xa/BfQvhkNFSuHUtUrJNMbOFQsvJBmiD5CNgZlmtlZHYLRruK+Z3Rt7uDVz7FvJ3S0IHWoXEA0hb2bPxZErF6Vo6lpI1zTGhYrG4TrUzIYmnCPR6WBrKtoTyZwaeBrheST+IaowqvLBhP9Po81shqRfA5ey+svPrZYx/0utSvoimWJYgPWARwkfFCsJHamjgFZZ7RK/sCvKkabZ274AemXcfp1wNtT6GetaEc6OGVcEr+14wlS1rQnHxm8B5hFGEFgn4/3yPOEsrsTfvwU8pzq7EK0KGX5OONuw/H35P8IH3IeEYv0mYfj4hcCmRfCavUYYKbf8dpso46oo5zesvqBy/aRyRtl6Er6IfRq9rt8QJrBaTLhY9dbo/91KwpTRtZ8h6X+wYliASwhnaZ1AmBhoUPSG/gDYIqNdsRSSaYQzW44hnBueufwqeoMfVr4u4aypmbo2ypGmaYw3K3A5Ken3LUUwHWwV86ZmauCoWDxKmMkRwgkYi4FRWe3uA16vkwxJ/4MVw0I43fe0rHWbAC8DnwNdo3XFUkhEmOf8M8KwDT/NuK9V9J9grTGXEsr6T2Bwxu2Pgb452h0FfF4Eeb/I+rDYKHo998xqt28RFJLyvc98SzHsmS4ADsu43SnK1Tur3THAf4vgfZBdSD4HzszRLvGhfQinJ/fIuN0myt89q91ehJOHaj2DX0cSdCTrQkMz+1TSHoQqPkFSf4rj/HYsvCvukPQIcDnwjqRbot+LzXDgAUkfA/eyeuraRYTDWSLshhfD1LWwehrjVwkXx2VOYzzJwsWfxTKN8bfAJOCuPO1+Rzi1PUmJTwdbQ8U8NfBS1rwwtfz37OGGmhMuYq11XkiCBcAWhD2QH1k4N7yvpBsJu46JdrJnM7OvgNMk3UE4t/0D4CqKaE5pS9fUtZCuaYz/SejH+1tljaK5X5KW+HSw1ZCWqYFfJVwo+UGU5VrCqNt/jEbr+DYaj+98QuGrdX7WFj8Oera5me1eSZsLCd+mzRIc/K4ykvoSpgPdlDA4W+LTgJZTSqauhVRNY/xnYKCZZV9Am91uV+BSM+sWT7KcGRKfDrYqlKKpgSX9nDCGXfn7YDZhL38sYaSAOUAJ4YtRNzP7V61n8ELy46lzfYDhZraoknb9CMfKj6moTdKiwy4tgDIr8lkSXcOhIpgOti6oSKYGjq4f24VwpuFEM1saXVh9PKu//DxoZvPq5O97IXHOOVcTxTDKpqsjku6UNCrpHIVIU1ZIX17n6pJ3tleBpDuBRmZ2XNJZCtSN9HxZSFNWSFFeSRMIRx/2SDpLPmnKCunKW5dZvZBUTWo+PADM7OdJZyhUmrJC6vKK9Lxv05QV0pW3zrJ6H0k9Fp32ubGZJT3xTl5pygrpy+tcXUpLJS0KkppGc3ykxX6Emd7SIE1ZIUV5Ja2TlvdtmrJCuvLWZVYvJFWTmg8P1zBIOlXS/yR9K+kNSUfmaLY9RfC+TVNWSFfepLN6H0kKSSr0nPVcV+LGKk1ZIV15owtQ/0KYBvhtwnUEoyX1Ao40s6VJ5suUpqyQrrzFkNX7SKjyh0eXpK9sV5j3eiZhGITK/B+wY5J505QV0pVX0lRgkpmdn7FuD+ABwtXN+1mYlGtH4DXPWrg05S2GrF5ISNeHB4CkfxEm3+qTp90hwMMJv8lTkzXKkZq8kr4F/mBmL2WtLyHMl9IY2IcwHlTSH3apyQrpylsMWb2PJPgP8B8zO7SyBbg+6aCRN4CdCmhXPiBiktKUFdKV92vCh8MazGw2sDNhSPzXgN/EGyunNGWFdOVNPKvvkfDjwGt7m1mnPO0OJszhnWgBlvQzYGszezpPu2aEU1Szh+qOTZqyRjlSk1fSU8C3ZnZEBfc3Iwzctw8JDzaapqxRntTkLYasXkhI14eHc+UkHQqcBexvZl9W0KYxcBthsNGfxpkvK0dqskZZUpO3GLJ6IXHOOVcj3kfinHOuRryQOOecqxEvJK5BkTRA0rToCuDFkt6WVCdn40naUtIQSa0LaDtEkmUsCyQ9FvXf5dt2QLRNy9pJ7lzVeCFxDYbCdMl3AeOA3sBRwFPAAXX0J7cEBgN5C0nka6BrtJwLbAtMlNQiz3Z/i7ZZUs2cztWID5HiGpLTgNvN7KKMdc9IujSpQFlWmNnr0e+vS5oL/B3YF3g0u3F0Jk5jM/sc+Dy+mM6tyfdIXEPSGvg0e6VlnLooqSQ6TNRP0n3RIbDPJA3O3k5S92iAvO8lLZQ0ovzwkqTdgWeiph9Fjzm7inmnRT9LosccLWmqpAMlvQd8D+yY69CWpGaSrpY0R9IySR9JujIr//GS3ovunyPpfJyrBt8jcQ3JW8Dp0Tf9Z81sUSVtrwGeBQ4BdgUGS/rCzG4FkNQFeAEYDxwMdASGA5sDe0d/61zgWsJhtE+AZVXMWxL9/DRr3dXAUGAhYTTXNfpRJIlwyK4rcBmhIP0f8PuMNucBV0SP9RJQClwmaYmZ3VLFnK6hMzNffGkQC/Ar4EPC8CargPcIH8gbZLQpie5/MWvbO4H5hKmWAcYAHxAOLZW3OSzatmt0e//odkkB2YYQhrJoEi1bApOBb4AOUZvR0eNtm7XtgGh9y+h2z+j2ARX8rQ2AMmBw1vqhhKLVOF9eX3zJXPzQlmswzOwd4BeEzvURhLGy/gxMzXHG0xNZtx8HfgJsGt3+LfCEma3MaPMYsAL4XTUjtgWWR8tMwt5NHzP7JKPNfDP7V57H6Q58aRWP1NAVaAE8KqlJ+QJMAtqz+jk6VxA/tOUaFDNbRui7eAZA0nGEM7mOA27KaPpZ1qbltzsAc6OfC7Mee6WkRcCG1Yz3NdCDsDfxKbDAzLKHnli41lZra0s4lFaR8gH+3qvg/o6ADwPkCuaFxDVoZjZK0tVA56y7Nq7g9icZP9doE51F1RbIOd5RAVaY2dQ8bQoZ02gRodBVpDzf/uQuTDML+BvO/cgPbbkGQ1J2cUDSRkAr1v5APSjrdnmH+bzo9hvAQVHxyGzTBHgluv1D9LNpDWJXx0RgQ0n7V3D/P4ClwE/MbGqO5dv4orr6wPdIXEPybjTk9ouEQ1WdCGdWLQHuyWq7dTS9wGOEs7aOAwaZ2aro/ssJ05o+Kek2Qr/CVcA4M/tH1Kb8m/2JksYAS8zs3bp5amsYT7jo8kFJQwlnkP5sLIQAAADXSURBVHUAdjWzE83sK0lDgJskdQJeJnyp3BLoZmbZRdS5SnkhcQ3JUKAXcDOhH+NTwoQ/fczso6y25xMO/TxGuF7jMuDH02LN7D1J+xBOoX2ccHbVQ9F25W3mSDoXOAM4nbA3U1IXTyyTmZmkg6LMZxKmiF4APJjR5mpJCwjDj59DeI7/BR6u63yu/vFh5J3LEE1P+hFh6tJnk03jXDp4H4lzzrka8ULinHOuRvzQlnPOuRrxPRLnnHM14oXEOedcjXghcc45VyNeSJxzztWIFxLnnHM18v+Uexx1pZGDtAAAAABJRU5ErkJggg==\n", 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\n", 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" ] @@ -248,8 +248,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "exact expected value:\t0.1040\n", - "exact delta value: \t-0.5300\n" + "exact expected value:\t0.1709\n", + "exact delta value: \t-0.8193\n" ] } ], @@ -300,9 +300,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "Exact value: \t0.1040\n", - "Estimated value:\t0.1032\n", - "Probability: \t0.9826\n" + "Exact value: \t0.1709\n", + "Estimated value:\t0.2308\n", + "Probability: \t0.4343\n" ] } ], @@ -319,7 +319,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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\n", 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" ] @@ -440,9 +440,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "Exact delta: \t-0.5300\n", - "Esimated value:\t-0.5490\n", - "Probability: \t0.5918\n" + "Exact delta: \t-0.8193\n", + "Esimated value:\t-0.8172\n", + "Probability: \t0.9895\n" ] } ], @@ -459,7 +459,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] diff --git a/qiskit/finance/simulation/iron_condor_pricing.ipynb b/qiskit/finance/simulation/iron_condor_pricing.ipynb index 511e62073..0b05d3395 100644 --- a/qiskit/finance/simulation/iron_condor_pricing.ipynb +++ b/qiskit/finance/simulation/iron_condor_pricing.ipynb @@ -118,7 +118,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -217,7 +217,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -330,7 +330,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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\n", 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\n", 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" ] diff --git a/qiskit/finance/simulation/option_pricing.ipynb b/qiskit/finance/simulation/option_pricing.ipynb index ab1dff8c3..ba63cbd2c 100644 --- a/qiskit/finance/simulation/option_pricing.ipynb +++ b/qiskit/finance/simulation/option_pricing.ipynb @@ -52,10 +52,7 @@ "- Asian Barrier Spread (multivariate, path-dependent, payoff with 3 segments)\n", "\n", "All examples illustrate how to use the genereric Qiskit Finance framework to construct QAE-operators (uncertainty problems). The same framework can be easily adjusted to estimate risk as well, for instance, the Value at Risk (VaR) or the Conditional Value at Risk (CVaR, also known as Expected Shortfall). How to use Qiskit Finance for risk analysis is illustrated in the following tutorial:\n", - "Credit Risk Analysis.\n", - "\n", - "An example of how quantum Generative Adversarial Networks (qGANs) can be used to learn and efficiently load generic random distributions for option pricing can be found here:\n", - "QGANs to learn and load random distributions for option pricing" + "Credit Risk Analysis." ] }, { From c952321f309294dfec2b206e667fe8c3b2999816 Mon Sep 17 00:00:00 2001 From: stefan-woerner Date: Mon, 29 Apr 2019 23:49:18 +0200 Subject: [PATCH 093/116] merge use of time series --- .../finance/data_providers/time_series.ipynb | 19 ++++--- .../portfolio_diversification.ipynb | 56 ++++++++++++------- 2 files changed, 45 insertions(+), 30 deletions(-) diff --git a/qiskit/finance/data_providers/time_series.ipynb b/qiskit/finance/data_providers/time_series.ipynb index 04e73c145..9f15aed81 100644 --- a/qiskit/finance/data_providers/time_series.ipynb +++ b/qiskit/finance/data_providers/time_series.ipynb @@ -34,7 +34,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "metadata": { "scrolled": true }, @@ -52,7 +52,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -72,7 +72,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 3, "metadata": {}, "outputs": [ { @@ -141,7 +141,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -196,7 +196,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -339,7 +339,7 @@ "source": [ "from qiskit.aqua.translators.data_providers.data_on_demand_provider import StockMarket\n", "try:\n", - " nasdaq = DataOnDemandProvider(token = \"REPLACE-ME\",\n", + " nasdaq = DataOnDemandProvider(token = \"REPLACE-ME\",\n", " tickers = stocks,\n", " stockmarket = StockMarket.NASDAQ.value,\n", " start = datetime.datetime(2016,1,1),\n", @@ -361,6 +361,7 @@ "\n", "The access again requires a valid access token to replace REPLACE-ME below. The token can be obtained on a trial or paid-for basis at:\n", "https://www.quandl.com/\n", + "\n", "In the following example, you need to replace TICKER1 and TICKER2 with valid tickers at the London Stock Exchange. " ] }, @@ -372,7 +373,7 @@ "source": [ "from qiskit.aqua.translators.data_providers.exchangedataprovider import StockMarket\n", "try:\n", - " lse = ExchangeDataProvider(token = \"REPLACE-ME\",\n", + " lse = ExchangeDataProvider(token = \"REPLACE-ME\",\n", " tickers = [\"TICKER1\", \"TICKER2\"],\n", " stockmarket = StockMarket.LONDON.value,\n", " start = datetime.datetime(2019,1,1),\n", @@ -394,9 +395,9 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3", + "display_name": "qiskit_master", "language": "python", - "name": "python3" + "name": "qiskit_master" }, "language_info": { "codemirror_mode": { diff --git a/qiskit/finance/optimization/portfolio_diversification.ipynb b/qiskit/finance/optimization/portfolio_diversification.ipynb index fc36d3f1a..54f1ba939 100644 --- a/qiskit/finance/optimization/portfolio_diversification.ipynb +++ b/qiskit/finance/optimization/portfolio_diversification.ipynb @@ -192,7 +192,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ @@ -238,7 +238,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "metadata": { "scrolled": true }, @@ -270,7 +270,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ @@ -288,7 +288,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -375,9 +375,18 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 5, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Number of feasible combinations= 2\n", + "Total number of combinations= 64\n" + ] + } + ], "source": [ "# Instantiate the classical optimizer class\n", "classical_optimizer = ClassicalOptimizer(rho, n, q)\n", @@ -391,12 +400,11 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# Visualize the solution\n", - "\n", "def visualize_solution(xc, yc, x, C, n, K, title_str):\n", " plt.figure()\n", " plt.scatter(xc, yc, s=200)\n", @@ -418,8 +426,7 @@ " plt.plot([xc[ix], xc[iy]], [yc[ix], yc[iy]], 'C2')\n", "\n", " plt.title(title_str +' cost = ' + str(int(C * 100) / 100.))\n", - " plt.show()\n", - " " + " plt.show() " ] }, { @@ -444,7 +451,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 7, "metadata": {}, "outputs": [], "source": [ @@ -514,7 +521,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 8, "metadata": {}, "outputs": [], "source": [ @@ -535,12 +542,11 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "# Check if the binary representation is correct. This requires CPLEX\n", - "\n", "try: \n", " import cplex\n", " warnings.filterwarnings('ignore')\n", @@ -566,9 +572,17 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 10, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0 1 0 1 0 1]\n" + ] + } + ], "source": [ "ground_state, ground_level = quantum_optimizer.exact_solution()\n", "print(ground_state)\n", @@ -591,14 +605,14 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "[1 0 1 0 1 0]\n", + "[1 0 1 0 1 1]\n", "VQE does not produce the same solution as the exact eigensolver, but that is to be expected.\n" ] } @@ -625,12 +639,12 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 12, "metadata": {}, "outputs": [ { "data": { - "image/png": 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3Wh1NKeXjtPzLgWtrX8vM2JkMbT6U5X8uJz4lnv+u+S8n809aHU0p5aO0/MuJIFsQ/S/vjz3eTnTdaMauHktCSgJLdi6xOppSygdp+ZcztcNq89ZNbzG+w3gCJIBBaYN47JvH2JO1x+poSikfouVfTrU+rzVzYufw6DWP8sPuH4hNjmXCugnk5OdYHU0p5QO0/MuxoIAgBlwxgJS4FNpc0IYxP42hm70bS3cvtTqaUspiWv5+oE54HUZHj2Zc+3EUmAIGLhzI0PSh/HnsT6ujKaUs4pbyF5GOIrJRRLaIyLAitoeIyOfO7ctFpL47jqvOzg3n38CcuDkMbjaYxTsXE5scy8e/fExufq7V0ZRSXuZy+YtIADAW6AQ0AXqJSJNTht0LHDLGNALeBl539bjq3IQEhHD/VfeTHJdMyzotGb1qNN1Tu/Pjnh+tjqaU8iJ3nPm3ALYYY7YZY3KARCDulDFxwBTn9VlAOxERNxxbnaMLKl3Aeze/x/s3v8/J/JPc+9W9PPXtU+w9vtfqaEopL3BH+Z8PZBS6vdN5X5FjjDF5wGGguhuOrVx0U92bSI5L5sGrHiRtRxqxybF8sv4Tcgt0KUip8kxcfVtgEekB3GqMGeC83RdoYYx5uNCY9c4xO523tzrHHDhlXwOBgQCRkZHNExMTXcrmbllZWYSHh1sdw2P25e5j1qFZbMjewHlB59EjogeNQhuV6nvL+9ycK52X4uncFM+VuWnbtu0qY0xUiQONMS59Aa2BBYVuPwM8c8qYBUBr5/VAYD/OXzzFfTVv3tz4mm+++cbqCB5XUFBg0nakmVtm3mIun3y5eXbJs2bf8X0lfp8/zM250Hkpns5N8VyZG2ClKUV3u2PZZwXQWEQaiEgwcAdgP2WMHejnvN4dWOQMqXyMiHDzhTeTHJ/MfVfcx/zf5xOTFMO0X6eRV5BndTyllJu4XP7GsYY/GMfZ/a/ADGPMehF5UURincMmAtVFZAswBDjt6aDKt1QIrMAj1zzCnNg5XFHjCkb9OIpeX/Ri9d7VVkdTSrlBoDt2YoyZB8w75b6Rha6fAHq441jKu+pXqc+HHT5k4Y6FvLHiDfrO70tCowQea/4YEaERVsdTSp0jfYWvKpGIcEv9W7DH27nn8ntI3ZpKl6QufP7b5+QX5FsdTyl1DrT8ValVDKrI480fZ3bsbC6LuIyXl7/MnfPuZN2+dVZHU0qdJS1/ddYaVm3IhFsm8MaNb7Dv+D56z+vN9APTyTyRaXU0pVQpafmrcyIidGrQidSEVO5qchfLspYRkxzD7E2zKTAFVsdTSpVAy1+5JCwojCeufYKn6zzNRVUv4vmlz9N3Xl/WH1hvdTSl1Blo+Su3OC/4PD6+9WNeveFVdmXtotfcXry87GUOnzxsdTSlVBG0/JXbiAgxF8WQmpDKnZfdycxNM4lNjiV5S7IuBSnlY7T8ldtVCq7EsBbDmNFlBhdWupDnvn+O/l/2Z+PBjVZHU0o5afkrj7kk4hKmdJrCS9e/xI4jO+g5tyejfhzF0ZyjVkdTyu9p+SuPsomN+Ebx2OPt9Li4B5/9+hkxSTGkbk1F395JKeto+SuvqBJShRGtRjC9y3TODz+fZ797lrsX3M3mQ5utjqaUX9LyV17VtHpTpnaeyvOtn2dr5lZ6pPbgzRVvciz3mNXRlPIrWv7K62xio9vF3UiNTyWhcQJTN0wlNimW+b/P16UgpbxEy19ZpmpoVf7T+j9M6zyNGhVr8NS3T3HfV/exLXOb1dGUKve0/JXlrqh5BZ91/oznWj3Hrwd/pZu9G6NXjeZ47nGroylVbmn5K58QYAug5yU9SU1IJeaiGD7+5WNik2P5avtXuhSklAdo+SufEhEawYvXv8jUTlOpFlqNoYuH8sDXD7D98HaroylVrmj5K5/UrFYzpt82nWdaPMO6fevoau/Kuz+9S3ZettXRlCoXtPyVzwq0BXLnZXdiT7DTqUEnPlr3EXHJcaT9kaZLQUq5SMtf+bwaFWrwyg2vMLnjZMKCwnjsm8d4KO0hMo5kWB1NqTJLy1+VGc0jmzMjZgZPRj3JT3t/Ij4lng9Wf8CJvBNWR1OqzNHyV2VKkC2Iu5rehT3eTvt67Rm3ZhzxKfEszlhsdTSlyhQtf1Um1apYi9dvfJ2Jt0wkJCCEwYsG8/Cih9l5dKfV0ZQqE7T8VZnWok4LZsXMYkjzISzfs5z4lHg+XPMhJ/NPWh1NKZ+m5a/KvKCAIO6+/G7s8Xai60bz/ur36ZrSle93fW91NKV8lpa/Kjdqh9XmrZve4sMOH2ITGw98/QCPf/M4e7L2WB1NKZ+j5a/KnevOu47ZsbN59JpH+W7Xd8SlxDFh3QRy83OtjqaUz3Cp/EUkQkQWishm52W1YsZ9KSKZIjLXleMpVVrBAcEMuGIA9ng71513HWN+GkNXe1eW7VlmdTSlfIKrZ/7DgDRjTGMgzXm7KG8CfV08llJnrU54Hd5p+w4ftPuAfJPPfV/dxxOLn+CvY39ZHU0pS7la/nHAFOf1KUB8UYOMMWmAfmq3skybC9qQFJfEQ80eIj0jnZjkGCb/MpncAl0KUv5JXHmPFBHJNMZULXT7kDGmuKWfaOAJY0yXM+xvIDAQIDIysnliYuI5Z/OErKwswsPDrY7hk8rS3OzP3c/sQ7P5JfsXagfVpmdETxqHNvbIscrSvHibzk3xXJmbtm3brjLGRJU0rsTyF5GvgdpFbBoOTHFn+RcWFRVlVq5cWZqhXpOenk50dLTVMXxSWZyb9Ix0Rv04il1Zu7it4W0MbT6UmhVruvcYZXBevEXnpniuzI2IlKr8A0saYIxpf4aD/CUidYwxe0SkDrD3LHMqZZnoutG0qtOKib9MZNK6SaRnpPNQs4fodWkvAm0l/q+hVJnm6pq/HejnvN4PSHFxf0p5VWhgKA81e4ikuCSa1WrGGyveoOfcnvz0109WR1PKo1wt/1FABxHZDHRw3kZEokRkwt+DRGQJMBNoJyI7ReRWF4+rlFtdWPlCxrUbxztt3yErJ4t+X/Zj+HfD2Z+93+poSnmES3/bGmMOAO2KuH8lMKDQ7TauHEcpbxAR2l3YjtZ1WjNh3QQ+Xv8x3/zxDYOvHsztl9xOgC3A6ohKuY2+wlepU1QMqsgj1zzCnNg5NK3RlNd+fI1eX/Ri9d7VVkdTym20/JUqRoMqDRjfYTxv3fQWB04coO/8voz8fiQHTxy0OppSLtPyV+oMRIRb699Kanwqd19+N6lbU4lJimHGxhnkF+RbHU+pc6blr1QpVAyqyJDmQ5gVO4tLIy7lpWUv0Xteb37Z/4vV0ZQ6J1r+Sp2Fi6pexIRbJvB6m9fZe3wvd35xJy8ufZHME5lWR1PqrGj5K3WWRITODTtjj7fTp0kf5myeQ0xyDHM2z6HAFFgdT6lS0fJX6hyFB4fz1LVPMSNmBg2rNOQ/P/yHvvP7suHABqujKVUiLX+lXHRxtYuZ3HEyr97wKjuP7qTXF714ZdkrHD552OpoShVLy18pNxARYi6KITUhlTsuuYMZm2YQmxzL8qzluhSkfJKWv1JuVDm4Ms+0fIbPu3xO3Up1+fTAp/T/sj8bD260OppS/6Llr5QHXBpxKZ90+oTe1Xuz/fB2bp97O6//+DpHc/QzjZRv0PJXykNsYqNVeCtSE1LpfnF3pv06jdjkWOZum4srH6KklDto+SvlYVVCqjCi1Qimd5lOnbA6PLPkGe5ZcA9bDm2xOpryY1r+SnlJ0+pN+bTzp/yn9X/YnLmZHqk9eGvFWxzLPWZ1NOWHtPyV8iKb2Oh+cXdS41OJaxTHJxs+ITYpli9//1KXgpRXafkrZYFqodV4/rrn+bTzp1SvUJ0nv32S+xbex7bD26yOpvyElr9SFrqy5pVMv206I1qOYMOBDXSzd+PtVW9zPPe41dFUOaflr5TFAmwB3H7p7aTGp9KlYRcm/TKJuJQ4Fu5YqEtBymO0/JXyEdUrVOel61/ik06fUCW4CkPSh/Dg1w+y48gOq6OpckjLXykfc3Wtq0nsksiwFsNYs28NCSkJvPfze2TnZVsdTZUjWv5K+aBAWyC9L+tNakIqHet3ZPza8cQnx7Poj0W6FKTcQstfKR9Wo0INXm3zKh/f+jEVgyry6DePMnjRYDKOZlgdTZVxWv5KlQFRtaOYETODJ6OeZOWfK4lPjmfc6nGcyDthdTRVRmn5K1VGBNmCuKvpXaQmpNKuXjs+WPMBCSkJfLvzW6ujqTJIy1+pMqZWxVq8ceMbTLhlAkEBQTyU9hCPLHqEXVm7rI6myhAtf6XKqJZ1WjI7ZjaPN3+cZXuWEZ8cz/i148nJz7E6mioDXCp/EYkQkYUistl5Wa2IMc1EZKmIrBeRtSJyuyvHVEr9T1BAEPdcfg/2eDttLmjDez+/R1d7V37Y9YPV0ZSPc/XMfxiQZoxpDKQ5b5/qOHCXMaYp0BF4R0SqunhcpVQhtcNqMzp6NB+2/xBBuP/r+xmSPoQ/j/1pdTTlo1wt/zhgivP6FCD+1AHGmE3GmM3O67uBvUBNF4+rlCrCdedfx+zY2Txy9SMs2bmE2ORYJq6bSG5+rtXRlI8RV14wIiKZxpiqhW4fMsactvRTaHsLHL8kmhpz+qdai8hAYCBAZGRk88TExHPO5glZWVmEh4dbHcMn6dwUzcp5OZh3kNkHZ7M2ey2RgZH0iOjBJRUusSRLUfTfTPFcmZu2bduuMsZElTSuxPIXka+B2kVsGg5MKW35i0gdIB3oZ4xZVlKwqKgos3LlypKGeVV6ejrR0dFWx/BJOjdF84V5+Xbnt4z6cRQZRzPoVL8TQ6OGEhkWaWkm8I258VWuzI2IlKr8A0saYIxpf4aD/CUidYwxe5zlvreYcZWBL4ARpSl+pZT73HjBjbSs05JJv0xi4rqJLN65mEHNBnHnZXcSZAuyOp6yiKtr/nagn/N6PyDl1AEiEgwkAZ8YY2a6eDyl1DkICQjhwaseJCkuiajaUby18i16pvZkxZ8rrI6mLOJq+Y8COojIZqCD8zYiEiUiE5xjegI3Av1FZLXzq5mLx1VKnYO6leoytt1Y3rvZ8S6h9yy4h2FLhrE/e7/V0ZSXlbjscybGmANAuyLuXwkMcF7/FPjUleMopdwrum40Leu0ZOK6iUz6ZRKLMxbzULOHuOPSOwi0uVQLqozQV/gq5acqBFZg8NWDSYpL4qqaV/H6ite5fe7t/Lz3Z6ujKS/Q8lfKz9WrXI9x7cfxTvQ7HMk5wl3z72L4d8M5kH3A6mjKg7T8lVKICO3qtSMlLoUBVwxg3u/ziEmOIfG3RPIL8q2OpzxAy18p9Y+KQRV59JpHmR07m6bVm/LK8lfo9UUv1uxbY3U05WZa/kqp0zSs0pDxHcbz5k1vciD7AH3m9eH5H57n0IlDVkdTbqLlr5QqkojQsX5H7Al27m56NylbUohJjmHmppm6FFQOaPkrpc4oLCiMIVFDmBkzk4urXcyLS1+kz7w+rN+/3upoygVa/kqpUmlUrRETb5nIqDaj+PP4n/T6ohcvLX2JwycPWx1NnQMtf6VUqYkItzW8jdT4VPo06cPszbOJSYohaXMSBae/Ua/yYVr+SqmzFh4czlPXPsXnXT6nQZUGjPxhJHfNv4tfD/xqdTRVSlr+SqlzdknEJUzuOJlXbniFjKMZ3PHFHby6/FWO5ByxOpoqgZa/UsolIkLsRbGkJqRy+yW38/nGz4lJisG+1Y4rHxalPEvLXynlFpWDK/Nsy2dJvC2RCypdwPDvhtP/y/5sOrTJ6miqCFr+Sim3uqz6ZUztNJUXr3uR3w//Ts/Unrz+4+tk5WRZHU0VouWvlHI7m9hIaJxAakIq3Rp3Y9qv04hJjuGLbV/oUpCP0PJXSnlMlZAqPNf6OabfNp3aFWszbMkw7v3qXrZmbrU6mt/T8ldKeVzTGk35tPOnjGw9kk2HNtHd3p3kQ8kcyz1mdTS/peWvlPKKAFsAPS7uQWp8KnGN4kg7kkZscixfbv9Sl4IsoOWvlPKqaqHVeP665xlSewjVQ6vz5OInGbhwIL8f/t3qaH5Fy18pZYkGIQ2Yftt0hrcczvoD6+lq78qYn8ZwPPe41dH8gpa/UsoyAbZ3p3X0AAAOS0lEQVQA7rj0DlLjU7mtwW1MWDeBuJQ4vt7xtS4FeZiWv1LKctUrVOflG17mk06fUDm4Mo+nP86DaQ+y48gOq6OVW1r+SimfcXWtq/m8y+cMazGMNXvXkJCSwHs/v0d2XrbV0codLX+llE8JtAXS+7Le2OPt3Fr/VsavHU9CSgLpGelWRytXtPyVUj6pZsWavNbmNSbdOokKgRV4eNHDDE4bTMbRDKujlQta/kopn3Zt7WuZETODJ6KeYMWfK0hISWDcmnGczD9pdbQyTctfKeXzgmxB9GvaD3u8nbZ12/LB6g9ISElgyc4lVkcrs1wqfxGJEJGFIrLZeVmtiDH1RGSViKwWkfUi8oArx1RK+a/IsEjevOlNPrrlIwJtgQxKG8Sjix5ld9Zuq6OVOa6e+Q8D0owxjYE05+1T7QGuM8Y0A1oCw0TkPBePq5TyY63qtGJ2zGweu+Yxlu5ZSlxyHB+t/Yic/Byro5UZrpZ/HDDFeX0KEH/qAGNMjjHm78W5EDccUymlCAoI4t4r7sUeb6fNBW149+d36Wbvxg+7f7A6WpkgrryKTkQyjTFVC90+ZIwpaumnLvAF0Ah40hgztpj9DQQGAkRGRjZPTEw852yekJWVRXh4uNUxfJLOTdF0Xorn7rn5NftXZh6cyb68fVxd8WoSqiVQLfC0OioTXJmbtm3brjLGRJU0rsTyF5GvgdpFbBoOTClN+Rfafh6QDMQYY/4603GjoqLMypUrz5jN29LT04mOjrY6hk/SuSmazkvxPDE3Ofk5TF4/mY/WfoSI8MBVD9D3sr4EBQS59Tie5srciEipyr/EJRhjTHtjzOVFfKUAf4lIHecB6wB7S9jXbmA90KZ0P4ZSSpVecEAwA68cSHJ8Mq3rtObtVW/TPbU7y/cstzqaz3F1/d0O9HNe7weknDpARC4QkQrO69WA64GNLh5XKaWKdX74+Yy5eQxj240lJz+HAV8N4KnFT7H3+BnPT/2Kq+U/CuggIpuBDs7biEiUiExwjrkMWC4ia4DFwFvGmHUuHlcppUp04wU3khSXxKCrBpH2RxoxSTFMWT+F3IJcq6NZzqXyN8YcMMa0M8Y0dl4edN6/0hgzwHl9oTHmSmPMVc7L8e4IrpRSpREaGMqDzR4kOS6Z5pHNeWvlW/RM7cnKP33rMUVv06ddKqX8Qt3KdRnbbizvtn2X47nHuXvB3Tyz5Bn2Z++3OpoltPyVUn5DRGh7YVuS45MZeOVAFmxfQExSDNN+nUZeQZ7V8bxKy18p5XcqBFbg4asfJikuiatqXsWoH0dxx9w7WL13tdXRvEbLXynlt+pVrse49uMYHT2azJOZ9J3fl+e+f44D2QesjuZxWv5KKb8mInSo1wF7vJ17L7+XudvmEpMcw+e/fU5+Qb7V8TxGy18ppYCKQRV5rPljzI6dTZOIJry8/GV6fdGLtfvWWh3NI7T8lVKqkIZVGvLRLR/x5k1vciD7AH3m9eH5H54n80Sm1dHcSstfKaVOISJ0rN8Re4Kdfk37kbIlhS7JXZi1aRYFpsDqeG6h5a+UUsUICwpjaNRQZsbMpHHVxryw9AX6zOvD+gPrPXrckH374OGHoXVrqFgRRGD7drceQ8tfKaVK0KhaIybdOonX2rzGnmN76DW3Fy8ve5nDJw+f2w6zsqBnT8dlESrs2gUzZkC1atDGM++DqeWvlFKlICJ0adgFe7yd3pf1ZtamWcQkxZC0Oensl4LS0mDmTFi0qMjNmVdeCX/9BfPmQY8ebkh/Oi1/pZQ6C5WCK/F0i6f5vMvn1K9Sn5E/jKTf/H78dvC3Uu+jYM4cjPOySDbPV7OWv1JKnYNLIi5hcsfJvHz9y/xx9A9un3s7ry1/jSM5R4ocfzIvn6Sfd3LL6HQOz0hCgMwZc7h1dDpJP+/kZJ53X1Og5a+UUufIJjbiGsWRmpBKz4t7krgxkdikWFK3plL4UxJXZ2TS8pU0RiT9glm/gRDnB82H5uWQv+FXRiT9QstX0liT4b2nk2r5K6WUiyoHV2Z4q+FMv20651c6n2e/e5b+X/Zn06FNrMnIpNf4ZWRm53IsJ5+221ZiK3A8RmArKKDt1hUcy8knMzuXO8Yv89ovAC1/pZRykybVmzC101ReuO4Fth3eRs/UnvRNGk52/rF/xnT5bQmh+Y4PkwnNz6XLb9/9sy07N59+k37kzJ+s7h6BXjiGUkr5DVv3HnSdM4d2YQGM6R7JrJsW07AgjScS/6TT8sPkBvy7di/d9zvbX+9S/A6vvtozOT2yV6WU8lejRkGzZlQhlJFTdvPZS9uodSiXpx+sy4Cn6pMRGfCv4SH5xXyOQFiYo/i7dfNITC1/pZRyp8aNYeVKCp5/nuzAEC7dfpJpL23jucm7+O3CULq/2IjRPSI5HlJ0/eaJjdzgYAq6doVhw2DnTseG+fNh1ixYvNgtMXXZRyml3C0ggKzBj9J1axXGzBlFg0O76Jl+iParjjCmeyQf31aTxjtPELP0368QPh4UwrZq5/Pz00/Sd+iDMHXq/zYOGuS4vOkmSE93OaKWv1JKeUBYcCBbq55HTL+3eXDZLB7+IZGIo7m88PFueqUd5OKME/8afyIgiLGtevJB6x4MiSwgP7+AAJt4LJ8u+yillAcE2ITGtcIpsAWwqWY9cgOC/tl26R8nsJ3ylJ7cgCA21qyPERuhQQEeLX7Q8ldKKY95MPoiwoIDuHXTD4TlZJ9xbFhOtmNccAA1K4V4PJuWv1JKeUjnK+oQZBPabVmBrdCz9/PERnZgMHnyvwq2YWi39UeCbEKVCkFF7c6ttPyVUspDQgIDSLyh8j9v5wCOB3V/q1mf+7o+x28163M86H9n+aF5OSS2qYJnF3wctPyVUsqDLv35O0IF8sVGdmAI/3dDH2L6v8N3Da4mtt/bjL6hN9mBIeSLjVCbY7w3uFT+IhIhIgtFZLPzstoZxlYWkV0i8r4rx1RKqTJlxgxsebnIVVfy3ayFfBfTF2w2ggIEExDAkph+fDdrIXLlFdhycx0f4uIFrj7VcxiQZowZJSLDnLefLmbsS4B7Xp2glFJlRe3a8Oab2B57jA42Gx2A/ALDsZw8woID//esni6r4J133PIc/tJwddknDpjivD4FiC9qkIg0ByKBr1w8nlJKlS2pqTBkyL8+oCXAJlQODfr30zkDAmDoUMd4L5DC7zl91t8skmmMqVro9iFjTLVTxtiARUBfoB0QZYwZXMz+BgIDASIjI5snJiaeczZPyMrKIjw83OoYPknnpmg6L8XTuSmeK3PTtm3bVcaYqJLGlbjsIyJfA7WL2DS8lFkGAfOMMRkiZ34M2xgzHhgPEBUVZaKjo0t5CO9IT0/H1zL5Cp2boum8FE/npnjemJsSy98Y0764bSLyl4jUMcbsEZE6wN4ihrUG2ojIICAcCBaRLGPMsHNOrZRSyiWuPuBrB/oBo5yXKacOMMb0/vu6iPTHseyjxa+UUhZy9QHfUUAHEdkMdHDeRkSiRGSCq+GUUkp5hktn/saYAzgexD31/pXAgCLunwxMduWYSimlXKev8FVKKT+k5a+UUn5Iy18ppfyQlr9SSvkhLX+llPJDWv5KKeWHXHpvH08SkX3ADqtznKIGsN/qED5K56ZoOi/F07kpnitzU88YU7OkQT5b/r5IRFaW5g2T/JHOTdF0Xoqnc1M8b8yNLvsopZQf0vJXSik/pOV/dsZbHcCH6dwUTeeleDo3xfP43Oiav1JK+SE981dKKT+k5a+UUn5Iy/8MRCRCRBaKyGbnZbUzjK0sIrtE5H1vZrRKaeZGRJqJyFIRWS8ia0XkdiuyeoOIdBSRjSKyRURO+7AiEQkRkc+d25eLSH3vp7RGKeZmiIhscP4bSRORelbk9LaS5qXQuO4iYkTErU/91PI/s2FAmjGmMZDmvF2cl4DFXknlG0ozN8eBu4wxTYGOwDsiUtWLGb1CRAKAsUAnoAnQS0SanDLsXuCQMaYR8DbwundTWqOUc/Mzjk/4uxKYBbzh3ZTeV8p5QUQqAY8Ay92dQcv/zOKAKc7rU4D4ogaJSHMgEvjKS7l8QYlzY4zZZIzZ7Ly+G8dnPJf4ysMyqAWwxRizzRiTAyTimJ/CCs/XLKCdiIgXM1qlxLkxxnxjjDnuvLkMuMDLGa1Qmn8z4DipfAM44e4AWv5nFmmM2QPgvKx16gARsQH/Bzzp5WxWK3FuChORFkAwsNUL2bztfCCj0O2dzvuKHGOMyQMOA9W9ks5apZmbwu4F5ns0kW8ocV5E5GqgrjFmricCuPoB7mWeiHwN1C5i0/BS7mIQMM8Yk1HeTuTcMDd/76cOMBXoZ4wpcEc2H1PUf/hTn0NdmjHlUal/bhHpA0QBN3k0kW8447w4TyrfBvp7KoDfl78xpn1x20TkLxGpY4zZ4yywvUUMaw20EZFBQDgQLCJZxpgzPT5QJrhhbhCRysAXwAhjzDIPRbXaTqBuodsXALuLGbNTRAKBKsBB78SzVGnmBhFpj+Ok4iZjzEkvZbNSSfNSCbgcSHeeVNYG7CIS6/yMdJfpss+Z2YF+zuv9gJRTBxhjehtjLjTG1AeeAD4pD8VfCiXOjYgEA0k45mSmF7N52wqgsYg0cP7Md+CYn8IKz1d3YJHxj1dYljg3zuWND4FYY0yRJxHl0BnnxRhz2BhTwxhT39kty3DMj1uKH7T8SzIK6CAim4EOztuISJSITLA0mfVKMzc9gRuB/iKy2vnVzJq4nuNcwx8MLAB+BWYYY9aLyIsiEuscNhGoLiJbgCGc+Zlj5UYp5+ZNHH81z3T+Gzn1F2e5U8p58Sh9ewellPJDeuavlFJ+SMtfKaX8kJa/Ukr5IS1/pZTyQ1r+Sinlh7T8lVLKD2n5K6WUH/p/NX8sVJF/6lsAAAAASUVORK5CYII=\n", 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\n", 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\n", + "image/png": 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\n", 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" ] From d7d40e37f33aa386a5557ab2b6bbc1589edb3e11 Mon Sep 17 00:00:00 2001 From: stefan-woerner Date: Tue, 30 Apr 2019 00:26:30 +0200 Subject: [PATCH 094/116] rerun all notebooks with fetched terra / aqua --- .../optimization/portfolio_optimization.ipynb | 58 +++++++++---------- .../simulation/credit_risk_analysis.ipynb | 4 +- .../simulation/fixed_income_pricing.ipynb | 8 +-- 3 files changed, 35 insertions(+), 35 deletions(-) diff --git a/qiskit/finance/optimization/portfolio_optimization.ipynb b/qiskit/finance/optimization/portfolio_optimization.ipynb index 3ff6db9cf..abfa3c09f 100644 --- a/qiskit/finance/optimization/portfolio_optimization.ipynb +++ b/qiskit/finance/optimization/portfolio_optimization.ipynb @@ -13,7 +13,7 @@ "collapsed": true }, "source": [ - "# _*Qiskit Finance: Financial Portfolio Optimization*_ \n", + "# _*Qiskit Finance: Portfolio Optimization*_ \n", "\n", "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", "\n", @@ -241,27 +241,27 @@ "selection\tvalue\t\tprobability\n", "---------------------------------------------------\n", " [1 0 0 1]\t-0.4158\t\t0.9322\n", - " [1 0 1 0]\t-0.2876\t\t0.0667\n", - " [1 1 0 0]\t-0.5110\t\t0.0011\n", + " [1 0 1 0]\t-0.2876\t\t0.0656\n", + " [1 1 0 0]\t-0.5110\t\t0.0022\n", + " [0 0 0 1]\t4.0314\t\t0.0000\n", " [1 1 0 1]\t4.6445\t\t0.0000\n", - " [0 0 1 1]\t-0.7012\t\t0.0000\n", - " [1 0 0 0]\t4.0242\t\t0.0000\n", - " [0 1 0 1]\t2.1421\t\t0.0000\n", + " [1 0 1 1]\t3.0617\t\t0.0000\n", " [0 0 1 0]\t3.4782\t\t0.0000\n", - " [0 1 1 0]\t-0.5149\t\t0.0000\n", + " [0 0 1 1]\t-0.7012\t\t0.0000\n", + " [1 1 1 0]\t2.6688\t\t0.0000\n", " [0 1 1 1]\t4.9012\t\t0.0000\n", - " [0 0 0 0]\t16.0000\t\t0.0000\n", - " [0 1 0 0]\t4.5153\t\t0.0000\n", + " [0 1 1 0]\t-0.5149\t\t0.0000\n", " [1 1 1 1]\t15.6136\t\t0.0000\n", - " [0 0 0 1]\t4.0314\t\t0.0000\n", - " [1 1 1 0]\t2.6688\t\t0.0000\n", - " [1 0 1 1]\t3.0617\t\t0.0000\n" + " [1 0 0 0]\t4.0242\t\t0.0000\n", + " [0 1 0 0]\t4.5153\t\t0.0000\n", + " [0 1 0 1]\t2.1421\t\t0.0000\n", + " [0 0 0 0]\t16.0000\t\t0.0000\n" ] } ], "source": [ "backend = BasicAer.get_backend('statevector_simulator')\n", - "seed = 42\n", + "seed = 50\n", "\n", "cobyla = COBYLA()\n", "cobyla.set_options(maxiter=500)\n", @@ -269,7 +269,7 @@ "vqe = VQE(qubitOp, ry, cobyla)\n", "vqe.random_seed = seed\n", "\n", - "quantum_instance = QuantumInstance(backend=backend, seed=seed, seed_mapper=seed)\n", + "quantum_instance = QuantumInstance(backend=backend, seed=seed)\n", "\n", "result = vqe.run(quantum_instance)\n", "\n", @@ -324,21 +324,21 @@ "----------------- Full result ---------------------\n", "selection\tvalue\t\tprobability\n", "---------------------------------------------------\n", - " [0 0 1 1]\t-0.7012\t\t0.1719\n", - " [1 0 0 1]\t-0.4158\t\t0.1714\n", - " [1 1 0 0]\t-0.5110\t\t0.1706\n", - " [0 1 1 0]\t-0.5149\t\t0.1691\n", - " [1 0 1 0]\t-0.2876\t\t0.1515\n", - " [0 1 0 1]\t2.1421\t\t0.1508\n", - " [1 1 1 0]\t2.6688\t\t0.0073\n", - " [0 0 0 1]\t4.0314\t\t0.0028\n", - " [1 0 1 1]\t3.0617\t\t0.0025\n", - " [0 1 1 1]\t4.9012\t\t0.0007\n", - " [0 1 0 0]\t4.5153\t\t0.0004\n", + " [0 0 1 1]\t-0.7012\t\t0.1771\n", + " [1 0 0 1]\t-0.4158\t\t0.1748\n", + " [1 1 0 0]\t-0.5110\t\t0.1743\n", + " [0 1 1 0]\t-0.5149\t\t0.1709\n", + " [1 0 1 0]\t-0.2876\t\t0.1479\n", + " [0 1 0 1]\t2.1421\t\t0.1369\n", + " [1 1 1 0]\t2.6688\t\t0.0098\n", + " [1 0 1 1]\t3.0617\t\t0.0043\n", + " [0 0 0 1]\t4.0314\t\t0.0016\n", + " [0 0 1 0]\t3.4782\t\t0.0009\n", + " [0 1 1 1]\t4.9012\t\t0.0008\n", " [1 0 0 0]\t4.0242\t\t0.0004\n", - " [0 0 1 0]\t3.4782\t\t0.0003\n", - " [1 1 1 1]\t15.6136\t\t0.0001\n", - " [1 1 0 1]\t4.6445\t\t0.0000\n", + " [0 1 0 0]\t4.5153\t\t0.0003\n", + " [1 1 0 1]\t4.6445\t\t0.0002\n", + " [1 1 1 1]\t15.6136\t\t0.0000\n", " [0 0 0 0]\t16.0000\t\t0.0000\n" ] } @@ -353,7 +353,7 @@ "\n", "qaoa.random_seed = seed\n", "\n", - "quantum_instance = QuantumInstance(backend=backend, seed=seed, seed_mapper=seed)\n", + "quantum_instance = QuantumInstance(backend=backend, seed=seed)\n", "\n", "result = qaoa.run(quantum_instance)\n", "\n", diff --git a/qiskit/finance/simulation/credit_risk_analysis.ipynb b/qiskit/finance/simulation/credit_risk_analysis.ipynb index fc9fdca94..21d5fd2e2 100644 --- a/qiskit/finance/simulation/credit_risk_analysis.ipynb +++ b/qiskit/finance/simulation/credit_risk_analysis.ipynb @@ -549,7 +549,7 @@ "« ░ └───┘ └───┘ ░ " ], "text/plain": [ - "" + "" ] }, "execution_count": 12, @@ -895,7 +895,7 @@ "« └───┘ └───┘ ░ " ], "text/plain": [ - "" + "" ] }, "execution_count": 21, diff --git a/qiskit/finance/simulation/fixed_income_pricing.ipynb b/qiskit/finance/simulation/fixed_income_pricing.ipynb index 82c826368..3eed08902 100644 --- a/qiskit/finance/simulation/fixed_income_pricing.ipynb +++ b/qiskit/finance/simulation/fixed_income_pricing.ipynb @@ -111,7 +111,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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\n", 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\n", 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" ] @@ -272,7 +272,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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\n", 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\n", 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" ] From 97447162ed39e270ca540a002829a6d7fc699796 Mon Sep 17 00:00:00 2001 From: Jakub Marecek Date: Mon, 29 Apr 2019 23:29:04 +0100 Subject: [PATCH 095/116] The vehicle routing notebook --- .../aqua/optimization/vehicle_routing.ipynb | 952 ++++++++++++++++++ 1 file changed, 952 insertions(+) create mode 100644 qiskit/aqua/optimization/vehicle_routing.ipynb diff --git a/qiskit/aqua/optimization/vehicle_routing.ipynb b/qiskit/aqua/optimization/vehicle_routing.ipynb new file mode 100644 index 000000000..50578702f --- /dev/null +++ b/qiskit/aqua/optimization/vehicle_routing.ipynb @@ -0,0 +1,952 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "# _*Qiskit Aqua: Vehicle Routing*_\n", + "\n", + "The latest version of this notebook is available on https://github.com/qiskit/qiskit-tutorials.\n", + "\n", + "***\n", + "### Contributors\n", + "Andrea Simonetto[1], Jakub Marecek[1], Martin Mevissen[1]\n", + "\n", + "### Affiliation\n", + "- [1]IBMQ\n", + "\n", + "## The Introduction\n", + "\n", + "Logistics is a major industry, with some estimates valuing it at USD 8183 billion globally in 2015. Most service providers operate a number of vehicles (e.g., trucks and container ships), a number of depots, where the vehicles are based overnight, and serve a number of client locations with each vehicle during each day. There are many optimisation and control problems that consider these parameters. Computationally, the key challenge is how to design routes from depots to a number of client locations and back to the depot, so as to minimise vehicle-miles travelled, time spent, or similar objective functions. In this notebook we formalise an idealised version of the problem and showcase its solution using the quantum approximate optimization approach of Farhi, Goldstone, and Gutman (2014). \n", + "\n", + "The overall workflow we demonstrate comprises:\n", + "\n", + "1. establish the client locations. Normally, these would be available ahead of the day of deliveries from a database. In our use case, we generate these randomly.\n", + "\n", + "3. compute the pair-wise distances, travel times, or similar. In our case, we consider the Euclidean distance, \"as the crow flies\", which is perhaps the simplest possible.\n", + "\n", + "4. compute the actual routes. This step is run twice, actually. First, we obtain a reference value by a run of a classical solver (IBM CPLEX) on the classical computer. Second, we run an alternative, hybrid algorithm partly on the quantum computer.\n", + "\n", + "5. visualisation of the results. In our case, this is again a simplistic plot.\n", + "\n", + "In the following, we first explain the model, before we proceed with the installation of the pre-requisites and the data loading.\n", + "\n", + "## The Model \n", + "\n", + "Mathematically speaking, the vehicle routing problem (VRP) is a combinatorial problem, wherein the best routes from a depot to a number of clients and back to the depot are sought, given a number of available vehicles. There are a number of formulations possible, extending a number of formulations of the travelling salesman problem [Applegate et al, 2006]. Here, we present a formulation known as MTZ [Miller, Tucker, Zemlin, 1960]. \n", + "\n", + "Let $n$ be the number of clients (indexed as $1,\\dots,n$), and $K$ be the number of available vehicles. Let $x_{ij} = \\{0,1\\}$ be the binary decision variable which, if it is $1$, activates the segment from node $i$ to node $j$. The node index runs from $0$ to $n$, where $0$ is (by convention) the depot. There are twice as many distinct decision variables as edges. For example, in a fully connected graph, there are $n(n+1)$ binary decision variables. \n", + "\n", + "If two nodes $i$ and $j$ have a link from $i$ to $j$, we write $i \\sim j$. We also denote with $\\delta(i)^+$ the set of nodes to which $i$ has a link, i.e., $j \\in \\delta(i)^+$ if and only if $i \\sim j$. Similarly, we denote with \n", + "$\\delta(i)^-$ the set of nodes which are connected to $i$, in the sense that $j \\in \\delta(i)^-$ if and only if $j \\sim i$. \n", + "\n", + "In addition, we consider continuous variables, for all nodes $i = 1,\\dots, n$, denoted $u_i$. These variables are needed in the MTZ formulation of the problem to eliminate sub-tours between clients. \n", + "\n", + "The VRP can be formulated as:\n", + "\n", + "$$\n", + "(VRP) \\quad f = \\min_{\\{x_{ij}\\}_{i\\sim j}\\in \\{0,1\\}, \\{u_i\\}_{i=1,\\dots,n}\\in \\mathbb{R}} \\quad \\sum_{i \\sim j} w_{ij} x_{ij}\n", + "$$\n", + "\n", + "subject to the node-visiting constraint:\n", + "\n", + "$$\n", + "\\sum_{j \\in \\delta(i)^+} x_{ij} = 1, \\,\\sum_{j \\in \\delta(i)^-} x_{ji} = 1,\\, \\forall i \\in \\{1,\\dots,n\\},\n", + "$$\n", + "\n", + "the depot-visiting constraints:\n", + "\n", + "$$\n", + "\\sum_{i \\in \\delta(0)^+} x_{0i} = K, \\, \\sum_{j \\in \\delta(0)^+} x_{j0} = K,\n", + "$$\n", + "\n", + "and the sub-tour elimination constraints:\n", + "\n", + "$$\n", + "u_i - u_j + Q x_{ij} \\leq Q-q_j, \\, \\forall i \\sim j, \\,i ,j \\neq 0, \\quad q_i \\leq u_i \\leq Q,\\, \\forall i, i \\neq 0.\n", + "$$\n", + "\n", + "In particular, \n", + "- The cost function is linear in the cost functions and weighs the different arches based on a positive weight $w_{ij}>0$ (typically the distance between node $i$ and node $j$);\n", + "- The first set of constraints enforce that from and to every client, only one link is allowed;\n", + "- The second set of constraints enforce that from and to the depot, exactly $K$ links are allowed;\n", + "- The third set of constraints enforce the sub-tour elimination constraints and are bounds on $u_i$, with $Q>q_j>0$, and $Q,q_i \\in \\mathbb{R}$.\n", + "\n", + "\n", + "## Classical solution\n", + "\n", + "We can solve the VRP classically, e.g., by using CPLEX. CPLEX uses a branch-and-bound-and-cut method to find an approximate solution of the VRP, which, in this formulation, is a mixed-integer linear program (MILP). For the sake of notation, we pack the decision variables in one vector as\n", + "\n", + "$$\n", + "{\\bf z} = [x_{01},x_{02},\\ldots,x_{10}, x_{12},\\ldots,x_{n(n-1)}]^T,\n", + "$$\n", + "\n", + "wherein ${\\bf z} \\in \\{0,1\\}^N$, with $N = n (n+1)$. So the dimension of the problem scales quadratically with the number of nodes. Let us denote the optimal solution by ${\\bf z}^*$, and the associated optimal cost $f^*$. \n", + "\n", + "\n", + "## Quantum solution\n", + "\n", + "Here, we demonstrate an approach that combines classical and quantum computing steps, following the quantum approximate optimization approach of Farhi, Goldstone, and Gutman (2014). In particular, we use the variational quantum eigensolver (VQE). We stress that given the use of limited depth of the quantum circuits employed (variational forms), it is hard to discuss the speed-up of the algorithm, as the solution obtained is heuristic in nature. At the same time, due to the nature and importance of the target problems, it is worth investigating heuristic approaches, which may be worthwhile for some problem classes. \n", + "\n", + "Following [5], the algorithm can be summarised as follows:\n", + "- Preparation steps: \n", + "\t- Transform the combinatorial problem into a binary polynomial optimization problem with equality constraints only;\n", + "\t- Map the resulting problem into an Ising Hamiltonian ($H$) for variables ${\\bf z}$ and basis $Z$, via penalty methods if necessary;\n", + "\t- Choose the depth of the quantum circuit $m$. Note that the depth can be modified adaptively.\n", + "\t- Choose a set of controls $\\theta$ and make a trial function $\\big|\\psi(\\boldsymbol\\theta)\\rangle$, built using a quantum circuit made of C-Phase gates and single-qubit Y rotations, parameterized by the components of $\\boldsymbol\\theta$.\n", + "\n", + "\n", + "- Algorithm steps: \n", + "\t- Evaluate $C(\\boldsymbol\\theta) = \\langle\\psi(\\boldsymbol\\theta)\\big|H\\big|\\psi(\\boldsymbol\\theta)\\rangle$ by sampling the outcome of the circuit in the Z-basis and adding the expectation values of the individual Ising terms together. In general, different control points around $\\boldsymbol\\theta$ have to be estimated, depending on the classical optimizer chosen.\n", + "\t- Use a classical optimizer to choose a new set of controls.\n", + "\t- Continue until $C(\\boldsymbol\\theta)$ reaches a minimum, close enough to the solution $\\boldsymbol\\theta^*$.\n", + "\t- Use the last $\\boldsymbol\\theta$ to generate a final set of samples from the distribution $\\Big|\\langle z_i\\big|\\psi(\\boldsymbol\\theta)\\rangle\\Big|^2\\;\\forall i$ to obtain the answer.\n", + "\n", + "\n", + "There are many parameters throughout, notably the choice of the trial wavefunction. Below, we consider:\n", + "\n", + "$$\n", + "\\big|\\psi(\\theta)\\rangle = [U_\\mathrm{single}(\\boldsymbol\\theta) U_\\mathrm{entangler}]^m \\big|+\\rangle\n", + "$$\n", + "\n", + "where $U_\\mathrm{entangler}$ is a collection of C-Phase gates (fully-entangling gates), and $U_\\mathrm{single}(\\theta) = \\prod_{i=1}^N Y(\\theta_{i})$, where $N$ is the number of qubits and $m$ is the depth of the quantum circuit. \n", + "\n", + "\n", + "### Construct the Ising Hamiltonian\n", + "\n", + "From $VRP$ one can construct a binary polynomial optimization with equality constraints only by considering cases in which $K=n-1$. In these cases the sub-tour elimination constraints are not necessary and the problem is only on the variable ${\\bf z}$. In particular, we can write an augmented Lagrangian as\n", + "\n", + "$$\n", + "(IH) \\quad H = \\sum_{i \\sim j} w_{ij} x_{ij} + A \\sum_{i \\in \\{1,\\dots,n\\}} \\Big(\\sum_{j \\in \\delta(i)^+} x_{ij} - 1\\Big)^2 + A \\sum_{i \\in \\{1,\\dots,n\\}}\\Big(\\sum_{j \\in \\delta(i)^-} x_{ji} - 1\\Big)^2 +A \\Big(\\sum_{i \\in \\delta(0)^+} x_{0i} - K\\Big)^2 + A\\Big(\\sum_{j \\in \\delta(0)^+} x_{j0} - K\\Big)^2\n", + "$$\n", + "\n", + "where $A$ is a big enough parameter. \n", + "\n", + "### From Hamiltonian to QP formulation \n", + "\n", + "In the vector ${\\bf z}$, and for a complete graph ($\\delta(i)^+ = \\delta(i)^- = \\{0,1,\\dots,i-1,i+1,\\dots,n\\}$), $H$ can be written as follows.\n", + "\n", + "$$\n", + "\\min_{{\\bf z}\\in \\{0,1\\}^{n(n+1)}} {\\bf w}^T {\\bf z} + A \\sum_{i \\in \\{1,\\dots,n\\}} \\Big({\\bf e}_i \\otimes {\\bf 1}_n^T {\\bf z} - 1\\Big)^2 + A \\sum_{i \\in \\{1,\\dots,n\\}}\\Big({\\bf v}_i^T {\\bf z} - 1\\Big)^2 + A \\Big(({\\bf e}_0 \\otimes {\\bf 1}_n)^T{\\bf z} - K\\Big)^2 + A\\Big({\\bf v}_0^T{\\bf z} - K\\Big)^2.\n", + "$$\n", + "\n", + "That is:\n", + "\n", + "$$\n", + "\\min_{\\bf z\\in \\{0,1\\}^{n(n+1)}} \\bf z^T {\\bf Q} \\bf z + {\\bf g}^T \\bf z + c,\n", + "$$\n", + "\n", + "Where: first term:\n", + "\n", + "$$\n", + "{\\bf Q} = A \\sum_{i \\in \\{0,1,\\dots,n\\}} \\Big[({\\bf e}_i \\otimes {\\bf 1}_n)({\\bf e}_i \\otimes {\\bf 1}_n)^T + {\\bf v}_i{\\bf v}_i^T \\Big] \n", + "$$\n", + "\n", + "Second term:\n", + "\n", + "$$\n", + "{\\bf g} = {\\bf w} -2 A \\sum_{i \\in \\{1,\\dots,n\\}} \\Big[({\\bf e}_i \\otimes {\\bf 1}_n) + {\\bf v}_i \\Big] -2 A K \\Big[({\\bf e}_0 \\otimes {\\bf 1}_n) + {\\bf v}_0 \\Big]\n", + "$$\n", + "\n", + "Third term:\n", + "\n", + "$$\n", + "c = 2An +2AK^2.\n", + "$$\n", + "\n", + "The QP formulation of the Ising Hamiltonian is ready for the use of VQE. \n", + "\n", + "\n", + "\n", + "## References\n", + "\n", + "[1] E. Farhi, J. Goldstone, S. Gutmann e-print arXiv 1411.4028, 2014\n", + "\n", + "[2] https://github.com/Qiskit/qiskit-tutorial/blob/master/qiskit/aqua/optimization/maxcut_and_tsp.ipynb\n", + "\n", + "[3] C. E. Miller, E. W. Tucker, and R. A. Zemlin (1960). \"Integer Programming Formulations and Travelling Salesman Problems\". J. ACM. 7: 326–329. doi:10.1145/321043.321046.\n", + "\n", + "[4] D. L. Applegate, R. M. Bixby, V. Chvátal, and W. J. Cook (2006). The Traveling Salesman Problem. Princeton University Press, ISBN 978-0-691-12993-8." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Initialization\n", + "\n", + "First of all we load all the packages that we need: \n", + " - Python 3.6 or greater is required;\n", + " - CPLEX 12.8 or greater is required for the classical computations;\n", + " - Latest Qiskit is required for the quantum computations." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Warning: Cplex not found.\n" + ] + } + ], + "source": [ + "# Load the packages that are required\n", + "import numpy as np\n", + "import operator\n", + "import matplotlib.pyplot as plt\n", + "\n", + "import sys\n", + "if sys.version_info < (3, 6):\n", + " raise Exception('Please use Python version 3.6 or greater.')\n", + "\n", + "try:\n", + " import cplex\n", + " from cplex.exceptions import CplexError\n", + "except: \n", + " print(\"Warning: Cplex not found.\")\n", + "import math\n", + "\n", + "# Qiskit packages\n", + "from qiskit.quantum_info import Pauli\n", + "from qiskit.aqua.input import EnergyInput\n", + "from qiskit.aqua import Operator, run_algorithm\n", + "\n", + "# setup aqua logging\n", + "import logging\n", + "from qiskit.aqua._logging import set_logging_config, build_logging_config\n", + "#set_logging_config(build_logging_config(logging.DEBUG)) # choose INFO, DEBUG to see the log" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We then initialize the variables" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# Initialize the problem by defining the parameters\n", + "\n", + "n = 3 # number of nodes + depot (n+1)\n", + "K = 2 # number of vehicles" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We define an initializer class that randomly places the nodes in a 2-D plane and computes the distance between them. " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# Get the data\n", + "class Initializer():\n", + "\n", + " def __init__(self, n):\n", + " self.n = n\n", + "\n", + " def generate_instance(self):\n", + "\n", + " n = self.n\n", + "\n", + " # np.random.seed(33)\n", + " np.random.seed(1543)\n", + "\n", + " xc = (np.random.rand(n) - 0.5) * 10\n", + " yc = (np.random.rand(n) - 0.5) * 10\n", + "\n", + " instance = np.zeros([n, n])\n", + " for ii in range(0, n):\n", + " for jj in range(ii + 1, n):\n", + " instance[ii, jj] = (xc[ii] - xc[jj]) ** 2 + (yc[ii] - yc[jj]) ** 2\n", + " instance[jj, ii] = instance[ii, jj]\n", + "\n", + " return xc, yc, instance" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# Initialize the problem by randomly generating the instance\n", + "\n", + "initializer = Initializer(n)\n", + "xc,yc,instance = initializer.generate_instance()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Classical solution using IBM ILOG CPLEX\n", + "\n", + "For a classical solution, we use IBM ILOG CPLEX. CPLEX is able to find the exact solution of this problem. We first define a ClassicalOptimizer class that encodes the problem in a way that CPLEX can solve, and then instantiate the class and solve it. \n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "class ClassicalOptimizer:\n", + "\n", + " def __init__(self, instance,n,K):\n", + "\n", + " self.instance = instance\n", + " self.n = n # number of nodes\n", + " self.K = K # number of vehicles\n", + "\n", + "\n", + " def compute_allowed_combinations(self):\n", + " f = math.factorial\n", + " return f(self.n) / f(self.K) / f(self.n-self.K)\n", + "\n", + "\n", + " def cplex_solution(self):\n", + "\n", + " # refactoring\n", + " instance = self.instance\n", + " n = self.n\n", + " K = self.K\n", + "\n", + " my_obj = list(instance.reshape(1, n**2)[0])+[0. for x in range(0,n-1)]\n", + " my_ub = [1 for x in range(0,n**2+n-1)]\n", + " my_lb = [0 for x in range(0,n**2)] + [0.1 for x in range(0,n-1)]\n", + " my_ctype = \"\".join(['I' for x in range(0,n**2)]) + \"\".join(['C' for x in range(0,n-1)])\n", + "\n", + " my_rhs = 2*([K] + [1 for x in range(0,n-1)]) + [1-0.1 for x in range(0,(n-1)**2-(n-1))] + [0 for x in range(0,n)]\n", + " my_sense = \"\".join(['E' for x in range(0,2*n)]) + \"\".join(['L' for x in range(0,(n-1)**2-(n-1))])+\"\".join(['E' for x in range(0,n)])\n", + "\n", + "\n", + "\n", + " try:\n", + " my_prob = cplex.Cplex()\n", + " self.populatebyrow(my_prob,my_obj,my_ub,my_lb,my_ctype,my_sense,my_rhs)\n", + "\n", + " my_prob.solve()\n", + "\n", + " except CplexError as exc:\n", + " print(exc)\n", + " return\n", + "\n", + "\n", + " x = my_prob.solution.get_values()\n", + " x = np.array(x)\n", + " cost = my_prob.solution.get_objective_value()\n", + "\n", + " return x,cost\n", + " \n", + "\n", + " def populatebyrow(self,prob,my_obj,my_ub,my_lb,my_ctype,my_sense,my_rhs):\n", + "\n", + " n = self.n\n", + " \n", + " prob.objective.set_sense(prob.objective.sense.minimize)\n", + " prob.variables.add(obj = my_obj, lb = my_lb, ub = my_ub, types = my_ctype)\n", + " \n", + " prob.set_log_stream(None)\n", + " prob.set_error_stream(None)\n", + " prob.set_warning_stream(None)\n", + " prob.set_results_stream(None)\n", + "\n", + " rows = []\n", + " for ii in range(0,n):\n", + " col = [x for x in range(0+n*ii,n+n*ii)]\n", + " coef = [1 for x in range(0,n)]\n", + " rows.append([col, coef])\n", + "\n", + " for ii in range(0,n):\n", + " col = [x for x in range(0+ii,n**2,n)]\n", + " coef = [1 for x in range(0,n)]\n", + "\n", + " rows.append([col, coef])\n", + "\n", + " # Sub-tour elimination constraints:\n", + " for ii in range(0, n):\n", + " for jj in range(0,n):\n", + " if (ii != jj)and(ii*jj>0):\n", + "\n", + " col = [ii+(jj*n), n**2+ii-1, n**2+jj-1]\n", + " coef = [1, 1, -1]\n", + "\n", + " rows.append([col, coef])\n", + "\n", + " for ii in range(0,n):\n", + " col = [(ii)*(n+1)]\n", + " coef = [1]\n", + " rows.append([col, coef])\n", + "\n", + " prob.linear_constraints.add(lin_expr=rows, senses=my_sense, rhs=my_rhs)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Number of feasible solutions = 3.0\n" + ] + } + ], + "source": [ + "# Instantiate the classical optimizer class\n", + "classical_optimizer = ClassicalOptimizer(instance,n,K)\n", + "\n", + "# Print number of feasible solutions\n", + "print('Number of feasible solutions = ' + str(classical_optimizer.compute_allowed_combinations()))" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPLEX may be missing.\n" + ] + } + ], + "source": [ + "# Solve the problem in a classical fashion via CPLEX\n", + "x = None\n", + "z = None\n", + "try:\n", + " x,classical_cost = classical_optimizer.cplex_solution()\n", + " # Put the solution in the z variable\n", + " z = [x[ii] for ii in range(n**2) if ii//n != ii%n]\n", + " # Print the solution\n", + " print(z)\n", + "except: \n", + " print(\"CPLEX may be missing.\")" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "# Visualize the solution\n", + "\n", + "def visualize_solution(xc, yc, x, C, n, K, title_str):\n", + " plt.figure()\n", + " plt.scatter(xc, yc, s=200)\n", + " for i in range(len(xc)):\n", + " plt.annotate(i, (xc[i] + 0.15, yc[i]), size=16, color='r')\n", + " plt.plot(xc[0], yc[0], 'r*', ms=20)\n", + "\n", + " plt.grid()\n", + "\n", + " for ii in range(0, n ** 2):\n", + "\n", + " if x[ii] > 0:\n", + " ix = ii // n\n", + " iy = ii % n\n", + " plt.arrow(xc[ix], yc[ix], xc[iy] - xc[ix], yc[iy] - yc[ix], length_includes_head=True, head_width=.25)\n", + "\n", + " plt.title(title_str+' cost = ' + str(int(C * 100) / 100.))\n", + " plt.show()\n", + " \n", + "\n", + "if x: visualize_solution(xc, yc, x, classical_cost, n, K, 'Classical')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you have CPLEX, the solution shows the depot with a star and the selected routes for the vehicles with arrows. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Quantum solution from the ground up\n", + "\n", + "For the quantum solution, we use Qiskit. \n", + "\n", + "First, we derive the solution from the ground up, using a class QuantumOptimizer that encodes the quantum approach to solve the problem and then we instantiate it and solve it. We define the following methods inside the class:\n", + "- `binary_representation` : encodes the problem $(M)$ into a the Ising Hamiltonian QP (that's basically linear algebra);\n", + "- `construct_hamiltonian` : constructs the Ising Hamiltonian in terms of the $Z$ basis;\n", + "- `check_hamiltonian` : makes sure that the Ising Hamiltonian is correctly encoded in the $Z$ basis: to do this, it solves a eigenvalue-eigenvector problem for a symmetric matrix of dimension $2^N \\times 2^N$. For the problem at hand $n=3$, that is $N = 12$ seems the limit; \n", + "- `vqe_solution` : solves the problem $(M)$ via VQE by using the SPSA solver (with default parameters);\n", + "- `_q_solution` : internal routine to represent the solution in a usable format.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "class QuantumOptimizer:\n", + "\n", + " def __init__(self, instance, n, K, max_trials=1000):\n", + "\n", + " self.instance = instance\n", + " self.n = n\n", + " self.K = K\n", + " self.max_trials = max_trials\n", + "\n", + "\n", + " def binary_representation(self,x_sol=0):\n", + "\n", + " instance = self.instance\n", + " n = self.n\n", + " K = self.K\n", + "\n", + " A = np.max(instance) * 100 # A parameter of cost function\n", + "\n", + " # Determine the weights w\n", + " instance_vec = instance.reshape(n ** 2)\n", + " w_list = [instance_vec[x] for x in range(n ** 2) if instance_vec[x] > 0]\n", + " w = np.zeros(n * (n - 1))\n", + " for ii in range(len(w_list)):\n", + " w[ii] = w_list[ii]\n", + "\n", + " # Some variables I will use\n", + " Id_n = np.eye(n)\n", + " Im_n_1 = np.ones([n - 1, n - 1])\n", + " Iv_n_1 = np.ones(n)\n", + " Iv_n_1[0] = 0\n", + " Iv_n = np.ones(n-1)\n", + " neg_Iv_n_1 = np.ones(n) - Iv_n_1\n", + "\n", + " v = np.zeros([n, n*(n-1)])\n", + " for ii in range(n):\n", + " count = ii-1\n", + " for jj in range(n*(n-1)):\n", + "\n", + " if jj//(n-1) == ii:\n", + " count = ii\n", + "\n", + " if jj//(n-1) != ii and jj%(n-1) == count:\n", + " v[ii][jj] = 1.\n", + "\n", + " vn = np.sum(v[1:], axis=0)\n", + "\n", + " # Q defines the interactions between variables\n", + " Q = A*(np.kron(Id_n, Im_n_1) + np.dot(v.T, v))\n", + "\n", + " # g defines the contribution from the individual variables\n", + " g = w - 2 * A * (np.kron(Iv_n_1,Iv_n) + vn.T) - \\\n", + " 2 * A * K * (np.kron(neg_Iv_n_1, Iv_n) + v[0].T)\n", + "\n", + " # c is the constant offset\n", + " c = 2 * A * (n-1) + 2 * A * (K ** 2)\n", + "\n", + " try:\n", + " max(x_sol)\n", + " # Evaluates the cost distance from a binary representation of a path\n", + " fun = lambda x: np.dot(np.around(x), np.dot(Q, np.around(x))) + np.dot(g, np.around(x)) + c\n", + " cost = fun(x_sol)\n", + " except:\n", + " cost = 0\n", + "\n", + " return Q,g,c,cost\n", + "\n", + " def construct_hamiltonian(self):\n", + "\n", + " instance = self.instance\n", + " n = self.n\n", + " K = self.K\n", + "\n", + " N = (n - 1) * n # number of qubits\n", + " Q,g,c,_ = self.binary_representation()\n", + "\n", + " # Defining the new matrices in the Z-basis\n", + "\n", + " Iv = np.ones(N)\n", + " Qz = (Q / 4)\n", + " gz = (-g / 2 - np.dot(Iv, Q / 4) - np.dot(Q / 4, Iv))\n", + " cz = (c + np.dot(g / 2, Iv) + np.dot(Iv, np.dot(Q / 4, Iv)))\n", + "\n", + " cz = cz + np.trace(Qz)\n", + " Qz = Qz - np.diag(np.diag(Qz))\n", + "\n", + " # Getting the Hamiltonian in the form of a list of Pauli terms\n", + "\n", + " pauli_list = []\n", + " for i in range(N):\n", + " if gz[i] != 0:\n", + " wp = np.zeros(N)\n", + " vp = np.zeros(N)\n", + " vp[i] = 1\n", + " pauli_list.append((gz[i], Pauli(vp, wp)))\n", + " for i in range(N):\n", + " for j in range(i):\n", + " if Qz[i, j] != 0:\n", + " wp = np.zeros(N)\n", + " vp = np.zeros(N)\n", + " vp[i] = 1\n", + " vp[j] = 1\n", + " pauli_list.append((2 * Qz[i, j], Pauli(vp, wp)))\n", + "\n", + " pauli_list.append((cz, Pauli(np.zeros(N), np.zeros(N))))\n", + "\n", + " return cz, pauli_list\n", + "\n", + " def check_hamiltonian(self):\n", + "\n", + " cz, op = self.construct_hamiltonian()\n", + " Op = Operator(paulis=op)\n", + "\n", + " qubitOp, offset = Op, 0\n", + " algo_input = EnergyInput(qubitOp)\n", + "\n", + " # Making the Hamiltonian in its full form and getting the lowest eigenvalue and eigenvector\n", + "\n", + " algorithm_cfg = {\n", + " 'name': 'ExactEigensolver',\n", + " }\n", + "\n", + " params = {\n", + " 'problem': {'name': 'ising'},\n", + " 'algorithm': algorithm_cfg\n", + " }\n", + " result = run_algorithm(params, algo_input)\n", + "\n", + " quantum_solution = self._q_solution(result['eigvecs'][0],self.n*(self.n+1))\n", + " ground_level = result['energy'] + offset\n", + "\n", + " return quantum_solution, ground_level\n", + "\n", + " def vqe_solution(self):\n", + "\n", + " cz, op = self.construct_hamiltonian()\n", + " Op = Operator(paulis=op)\n", + "\n", + " qubitOp, offset = Op, cz\n", + " algo_input = EnergyInput(qubitOp)\n", + "\n", + "\n", + " algorithm_cfg = {\n", + " 'name': 'VQE',\n", + " 'operator_mode': 'paulis'\n", + " }\n", + "\n", + " optimizer_cfg = {\n", + " 'name': 'SPSA',\n", + " 'max_trials': self.max_trials\n", + " }\n", + "\n", + " var_form_cfg = {\n", + " 'name': 'RY',\n", + " 'depth': 5,\n", + " 'entanglement': 'linear'\n", + " }\n", + "\n", + " params = {\n", + " 'problem': {'name': 'ising', 'random_seed': 10598},\n", + " 'algorithm': algorithm_cfg,\n", + " 'optimizer': optimizer_cfg,\n", + " 'variational_form': var_form_cfg,\n", + " 'backend': {'name': 'qasm_simulator'\n", + " }\n", + " }\n", + "\n", + " result = run_algorithm(params, algo_input)\n", + "\n", + " #quantum_solution = self._q_solution(result['eigvecs'][0], self.n * (self.n + 1))\n", + " quantum_solution_dict = result['eigvecs'][0]\n", + "\n", + " q_s = max(quantum_solution_dict.items(), key=operator.itemgetter(1))[0]\n", + " quantum_solution= [int(chars) for chars in q_s]\n", + " quantum_solution = np.flip(quantum_solution, axis=0)\n", + "\n", + " _,_,_,level = self.binary_representation(x_sol=quantum_solution)\n", + " return quantum_solution_dict, quantum_solution, level\n", + "\n", + " def _q_solution(self, v, N):\n", + "\n", + " index_value = [x for x in range(len(v)) if v[x] == max(v)][0]\n", + " string_value = \"{0:b}\".format(index_value)\n", + "\n", + " while len(string_value)" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Put the solution in a way that is compatible with the classical variables\n", + "x_quantum = np.zeros(n**2)\n", + "kk = 0\n", + "for ii in range(n ** 2):\n", + " if ii // n != ii % n:\n", + " x_quantum[ii] = quantum_solution[kk]\n", + " kk += 1\n", + "\n", + "\n", + "# visualize the solution \n", + "visualize_solution(xc, yc, x_quantum, quantum_cost, n, K, 'Quantum')\n", + " \n", + "# and visualize the classical for comparison\n", + "if x: visualize_solution(xc, yc, x, classical_cost, n, K, 'Classical')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The plots present the depot with a star and the selected routes for the vehicles with arrows. Note that in this particular case, we can find the optimal solution of the QP formulation, which happens to coincide with the optimal solution of the ILP.\n", + "\n", + "Keep in mind that VQE is an heuristic working on the QP formulation of the Ising Hamiltonian, though. For suitable choices of A, local optima of the QP formulation will be feasible solutions to the ILP. While for some small instances, as above, we can find optimal solutions of the QP formulation which coincide with optima of the ILP, finding optimal solutions of the ILP is harder than finding local optima of the QP formulation, in general, which in turn is harder than finding feasible solutions of the ILP. Even within the VQE, one may provide stronger guarantees, for specific variational forms (trial wave functions). \n", + "\n", + "Last but not least, you may be pleased to learn that the above has been packaged in Qiskit Aqua." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1 1 1 0 1 0]\n", + "132.11148115684045\n" + ] + } + ], + "source": [ + "from qiskit import BasicAer\n", + "from qiskit.aqua import QuantumInstance\n", + "from qiskit.aqua import Operator, run_algorithm\n", + "from qiskit.aqua.input import EnergyInput\n", + "from qiskit.aqua.algorithms import VQE, QAOA, ExactEigensolver\n", + "from qiskit.aqua.components.optimizers import COBYLA\n", + "from qiskit.aqua.components.variational_forms import RY\n", + "from qiskit.aqua.translators.ising.vehicle_routing import *\n", + "\n", + "qubitOp = get_vehiclerouting_qubitops(instance, n, K)\n", + "backend = BasicAer.get_backend('statevector_simulator')\n", + "seed = 50\n", + "cobyla = COBYLA()\n", + "cobyla.set_options(maxiter=250)\n", + "ry = RY(qubitOp.num_qubits, depth=3, entanglement='full')\n", + "vqe = VQE(qubitOp, ry, cobyla, 'matrix')\n", + "vqe.random_seed = seed\n", + "quantum_instance = QuantumInstance(backend=backend, seed=seed, seed_transpiler=seed)\n", + "result = vqe.run(quantum_instance)\n", + "# print(result)\n", + "x_quantum2 = get_vehiclerouting_solution(instance, n, K, result)\n", + "print(x_quantum2)\n", + "quantum_cost2 = get_vehiclerouting_cost(instance, n, K, x_quantum2)\n", + "print(quantum_cost2)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.2" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} From 39a217c2eb7aad5bdb1b93c31d88c27c028a4598 Mon Sep 17 00:00:00 2001 From: stefan-woerner Date: Tue, 30 Apr 2019 00:31:19 +0200 Subject: [PATCH 096/116] Update portfolio_diversification.ipynb --- .../finance/optimization/portfolio_diversification.ipynb | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/qiskit/finance/optimization/portfolio_diversification.ipynb b/qiskit/finance/optimization/portfolio_diversification.ipynb index 54f1ba939..c0db092a5 100644 --- a/qiskit/finance/optimization/portfolio_diversification.ipynb +++ b/qiskit/finance/optimization/portfolio_diversification.ipynb @@ -612,8 +612,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "[1 0 1 0 1 1]\n", - "VQE does not produce the same solution as the exact eigensolver, but that is to be expected.\n" + "[0 1 0 1 0 1]\n", + "VQE produces the same solution as the exact eigensolver.\n" ] } ], @@ -644,7 +644,7 @@ "outputs": [ { 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\n", 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\n", 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\n", 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\n", 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" ] From 88db21ba296a645c6df623a85117bba7b3b00397 Mon Sep 17 00:00:00 2001 From: stefan-woerner Date: Tue, 30 Apr 2019 00:53:36 +0200 Subject: [PATCH 097/116] running optimization notebooks with fetched aqua / terra --- .../aqua/optimization/vehicle_routing.ipynb | 62 ++++++++----------- .../optimization/portfolio_optimization.ipynb | 32 +++++++++- 2 files changed, 57 insertions(+), 37 deletions(-) diff --git a/qiskit/aqua/optimization/vehicle_routing.ipynb b/qiskit/aqua/optimization/vehicle_routing.ipynb index 50578702f..f602e8f68 100644 --- a/qiskit/aqua/optimization/vehicle_routing.ipynb +++ b/qiskit/aqua/optimization/vehicle_routing.ipynb @@ -238,7 +238,6 @@ "outputs": [], "source": [ "# Initialize the problem by defining the parameters\n", - "\n", "n = 3 # number of nodes + depot (n+1)\n", "K = 2 # number of vehicles" ] @@ -288,7 +287,6 @@ "outputs": [], "source": [ "# Initialize the problem by randomly generating the instance\n", - "\n", "initializer = Initializer(n)\n", "xc,yc,instance = initializer.generate_instance()" ] @@ -337,8 +335,6 @@ " my_rhs = 2*([K] + [1 for x in range(0,n-1)]) + [1-0.1 for x in range(0,(n-1)**2-(n-1))] + [0 for x in range(0,n)]\n", " my_sense = \"\".join(['E' for x in range(0,2*n)]) + \"\".join(['L' for x in range(0,(n-1)**2-(n-1))])+\"\".join(['E' for x in range(0,n)])\n", "\n", - "\n", - "\n", " try:\n", " my_prob = cplex.Cplex()\n", " self.populatebyrow(my_prob,my_obj,my_ub,my_lb,my_ctype,my_sense,my_rhs)\n", @@ -349,7 +345,6 @@ " print(exc)\n", " return\n", "\n", - "\n", " x = my_prob.solution.get_values()\n", " x = np.array(x)\n", " cost = my_prob.solution.get_objective_value()\n", @@ -438,13 +433,13 @@ "x = None\n", "z = None\n", "try:\n", - " x,classical_cost = classical_optimizer.cplex_solution()\n", - " # Put the solution in the z variable\n", - " z = [x[ii] for ii in range(n**2) if ii//n != ii%n]\n", - " # Print the solution\n", - " print(z)\n", + " x,classical_cost = classical_optimizer.cplex_solution()\n", + " # Put the solution in the z variable\n", + " z = [x[ii] for ii in range(n**2) if ii//n != ii%n]\n", + " # Print the solution\n", + " print(z)\n", "except: \n", - " print(\"CPLEX may be missing.\")" + " print(\"CPLEX may be missing.\")" ] }, { @@ -454,7 +449,6 @@ "outputs": [], "source": [ "# Visualize the solution\n", - "\n", "def visualize_solution(xc, yc, x, C, n, K, title_str):\n", " plt.figure()\n", " plt.scatter(xc, yc, s=200)\n", @@ -472,8 +466,7 @@ " plt.arrow(xc[ix], yc[ix], xc[iy] - xc[ix], yc[iy] - yc[ix], length_includes_head=True, head_width=.25)\n", "\n", " plt.title(title_str+' cost = ' + str(int(C * 100) / 100.))\n", - " plt.show()\n", - " \n", + " plt.show() \n", "\n", "if x: visualize_solution(xc, yc, x, classical_cost, n, K, 'Classical')" ] @@ -516,7 +509,6 @@ " self.K = K\n", " self.max_trials = max_trials\n", "\n", - "\n", " def binary_representation(self,x_sol=0):\n", "\n", " instance = self.instance\n", @@ -754,18 +746,18 @@ "source": [ "# Check if the binary representation is correct\n", "try:\n", - " if z:\n", - " Q,g,c,binary_cost = quantum_optimizer.binary_representation(x_sol = z)\n", - " print(binary_cost,classical_cost)\n", - " if np.abs(binary_cost - classical_cost)<0.01:\n", - " print('Binary formulation is correct')\n", - " else: print('Error in the binary formulation')\n", - " else:\n", - " print('Could not verify the correctness, due to CPLEX solution being unavailable.')\n", - " Q,g,c,binary_cost = quantum_optimizer.binary_representation()\n", + " if z:\n", + " Q,g,c,binary_cost = quantum_optimizer.binary_representation(x_sol = z)\n", + " print(binary_cost,classical_cost)\n", + " if np.abs(binary_cost - classical_cost)<0.01:\n", + " print('Binary formulation is correct')\n", + " else: print('Error in the binary formulation')\n", + " else:\n", + " print('Could not verify the correctness, due to CPLEX solution being unavailable.')\n", + " Q,g,c,binary_cost = quantum_optimizer.binary_representation()\n", "except NameError as e:\n", - " print(\"Warning: Please run the cells above first.\")\n", - " print(e)" + " print(\"Warning: Please run the cells above first.\")\n", + " print(e)" ] }, { @@ -797,9 +789,9 @@ "print(ground_state)\n", "\n", "if z:\n", - " if np.abs(ground_level - classical_cost)<0.01:\n", - " print('Ising Hamiltonian in Z basis is correct')\n", - " else: print('Error in the Ising Hamiltonian formulation')" + " if np.abs(ground_level - classical_cost)<0.01:\n", + " print('Ising Hamiltonian in Z basis is correct')\n", + " else: print('Error in the Ising Hamiltonian formulation')" ] }, { @@ -888,15 +880,15 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "[1 1 1 0 1 0]\n", - "132.11148115684045\n" + "[1 1 1 0 0 1]\n", + "12434.909288240102\n" ] } ], @@ -930,9 +922,9 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3", + "display_name": "qiskit_master", "language": "python", - "name": "python3" + "name": "qiskit_master" }, "language_info": { "codemirror_mode": { @@ -944,7 +936,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.2" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/qiskit/finance/optimization/portfolio_optimization.ipynb b/qiskit/finance/optimization/portfolio_optimization.ipynb index 4600febd8..1cd9e827f 100644 --- a/qiskit/finance/optimization/portfolio_optimization.ipynb +++ b/qiskit/finance/optimization/portfolio_optimization.ipynb @@ -312,9 +312,37 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Optimal: selection [0 0 1 1], value -0.7012\n", + "\n", + "----------------- Full result ---------------------\n", + "selection\tvalue\t\tprobability\n", + "---------------------------------------------------\n", + " [0 0 1 1]\t-0.7012\t\t0.1771\n", + " [1 0 0 1]\t-0.4158\t\t0.1748\n", + " [1 1 0 0]\t-0.5110\t\t0.1743\n", + " [0 1 1 0]\t-0.5149\t\t0.1709\n", + " [1 0 1 0]\t-0.2876\t\t0.1479\n", + " [0 1 0 1]\t2.1421\t\t0.1369\n", + " [1 1 1 0]\t2.6688\t\t0.0098\n", + " [1 0 1 1]\t3.0617\t\t0.0043\n", + " [0 0 0 1]\t4.0314\t\t0.0016\n", + " [0 0 1 0]\t3.4782\t\t0.0009\n", + " [0 1 1 1]\t4.9012\t\t0.0008\n", + " [1 0 0 0]\t4.0242\t\t0.0004\n", + " [0 1 0 0]\t4.5153\t\t0.0003\n", + " [1 1 0 1]\t4.6445\t\t0.0002\n", + " [1 1 1 1]\t15.6136\t\t0.0000\n", + " [0 0 0 0]\t16.0000\t\t0.0000\n" + ] + } + ], "source": [ "backend = BasicAer.get_backend('statevector_simulator')\n", "seed = 50\n", From d547a286b9af96e9525361015bea0f53842258a9 Mon Sep 17 00:00:00 2001 From: stefan-woerner Date: Tue, 30 Apr 2019 01:06:30 +0200 Subject: [PATCH 098/116] delete empty readmes --- qiskit/finance/data_providers/readme.txt | 0 qiskit/finance/optimization/readme.txt | 0 qiskit/finance/simulation/readme.txt | 0 3 files changed, 0 insertions(+), 0 deletions(-) delete mode 100644 qiskit/finance/data_providers/readme.txt delete mode 100644 qiskit/finance/optimization/readme.txt delete mode 100644 qiskit/finance/simulation/readme.txt diff --git a/qiskit/finance/data_providers/readme.txt b/qiskit/finance/data_providers/readme.txt deleted file mode 100644 index e69de29bb..000000000 diff --git a/qiskit/finance/optimization/readme.txt b/qiskit/finance/optimization/readme.txt deleted file mode 100644 index e69de29bb..000000000 diff --git a/qiskit/finance/simulation/readme.txt b/qiskit/finance/simulation/readme.txt deleted file mode 100644 index e69de29bb..000000000 From 4e1f49c3d075767b3aa9ff7c85e79c08262d6d55 Mon Sep 17 00:00:00 2001 From: Jakub Marecek Date: Tue, 30 Apr 2019 14:21:27 +0100 Subject: [PATCH 099/116] For the updated Qiskit Aqua (as of April 30th) --- .../finance/data_providers/time_series.ipynb | 35 +++++++++++-------- 1 file changed, 21 insertions(+), 14 deletions(-) diff --git a/qiskit/finance/data_providers/time_series.ipynb b/qiskit/finance/data_providers/time_series.ipynb index fd72ff6ab..e3342626a 100644 --- a/qiskit/finance/data_providers/time_series.ipynb +++ b/qiskit/finance/data_providers/time_series.ipynb @@ -34,7 +34,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 9, "metadata": { "scrolled": true }, @@ -52,7 +52,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 10, "metadata": {}, "outputs": [], "source": [ @@ -72,13 +72,15 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ + "Means:\n", + "[16.66722941 72.03026566]\n", "A time-series similarity measure:\n", "[[1.0000000e+00 6.2284804e-04]\n", " [6.2284804e-04 1.0000000e+00]]\n" @@ -119,6 +121,10 @@ } ], "source": [ + "means = data.get_mean_vector()\n", + "print(\"Means:\")\n", + "print(means)\n", + "\n", "rho = data.get_similarity_matrix()\n", "print(\"A time-series similarity measure:\")\n", "print(rho)\n", @@ -141,7 +147,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 12, "metadata": {}, "outputs": [ { @@ -196,7 +202,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 13, "metadata": {}, "outputs": [ { @@ -233,10 +239,11 @@ "\n", "While the access to real-time data usually requires a payment, it is possible \n", "to access historical (adjusted) closing prices via Wikipedia and Quandl\n", - "free of charge.\n", + "free of charge, following registration at:\n", + "https://www.quandl.com/?modal=register\n", "In the code below, one needs to specify actual tickers of actual NASDAQ\n", - "issues; by running the code below, you agree to the Quandl terms and \n", - "conditions, including their liability waiver.\n", + "issues and the access token you obtain from Quandl; by running the code below, you agree to the Quandl terms and \n", + "conditions, including a liability waiver.\n", "Notice that at least two tickers are required for the computation\n", "of covariance and time-series matrices, but hundreds of tickers may go \n", "beyond the fair usage limits of Quandl." @@ -249,10 +256,10 @@ "outputs": [], "source": [ "stocks = [\"REPLACEME1\", \"REPLACEME2\"]\n", - "from qiskit.aqua.translators.data_providers.wikipedia_data_provider import StockMarket\n", - "wiki = WikipediaDataProvider(token = \"\",\n", + "wiki = WikipediaDataProvider(\n", + " token = \"REPLACEME\",\n", " tickers = stocks,\n", - " stockmarket = StockMarket.NASDAQ.value,\n", + " stockmarket = StockMarket.NASDAQ,\n", " start = datetime.datetime(2016,1,1),\n", " end = datetime.datetime(2016,1,30))\n", "wiki.run()" @@ -325,7 +332,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "If you don't have NASDAQ Data on Demand license, you can contact NASDAQ at https://business.nasdaq.com/intel/GIS/Nasdaq-Data-on-Demand.html to obtain a trial or paid license.\n", + "If you don't have NASDAQ Data on Demand license, you can contact NASDAQ (cf. https://business.nasdaq.com/intel/GIS/Nasdaq-Data-on-Demand.html) to obtain a trial or paid license.\n", "\n", "If and when you have access to NASDAQ Data on Demand using your own token, you should replace REPLACE-ME below with the token. \n", "To assure the security of the connection, you should also have your own means of validating NASDAQ's certificates. DataOnDemandProvider constructor has an optional argument verify, which can be None or a string or a boolean. If it is None, certifi certificates will be used (default). If verify is a string, it should be poiting to a cerfificate for the HTTPS connection to NASDAQ (dataondemand.nasdaq.com), either in the form of a CA_BUNDLE file or a directory wherein to look.\n" @@ -341,7 +348,7 @@ "try:\n", " nasdaq = DataOnDemandProvider(token = \"REPLACE-ME\",\n", " tickers = stocks,\n", - " stockmarket = StockMarket.NASDAQ.value,\n", + " stockmarket = StockMarket.NASDAQ,\n", " start = datetime.datetime(2016,1,1),\n", " end = datetime.datetime(2016,1,2))\n", " nasdaq.run()\n", @@ -374,7 +381,7 @@ "try:\n", " lse = ExchangeDataProvider(token = \"REPLACE-ME\",\n", " tickers = [\"TICKER1\", \"TICKER2\"],\n", - " stockmarket = StockMarket.LONDON.value,\n", + " stockmarket = StockMarket.LONDON,\n", " start = datetime.datetime(2019,1,1),\n", " end = datetime.datetime(2019,1,30))\n", " lse.run()\n", From 79fbeb2e701990a1c7077c8d005a826eafef095a Mon Sep 17 00:00:00 2001 From: stefan-woerner Date: Tue, 30 Apr 2019 20:07:11 +0200 Subject: [PATCH 100/116] use data provider in portfolio optimization and rerun all notebooks with most recent aqua/terra --- .../portfolio_diversification.ipynb | 4 +- .../optimization/portfolio_optimization.ipynb | 133 ++++++++++-------- .../simulation/credit_risk_analysis.ipynb | 4 +- 3 files changed, 79 insertions(+), 62 deletions(-) diff --git a/qiskit/finance/optimization/portfolio_diversification.ipynb b/qiskit/finance/optimization/portfolio_diversification.ipynb index c0db092a5..5da6c4eff 100644 --- a/qiskit/finance/optimization/portfolio_diversification.ipynb +++ b/qiskit/finance/optimization/portfolio_diversification.ipynb @@ -644,7 +644,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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\n", 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\n", "text/plain": [ "
" ] diff --git a/qiskit/finance/optimization/portfolio_optimization.ipynb b/qiskit/finance/optimization/portfolio_optimization.ipynb index 1cd9e827f..494016f51 100644 --- a/qiskit/finance/optimization/portfolio_optimization.ipynb +++ b/qiskit/finance/optimization/portfolio_optimization.ipynb @@ -65,10 +65,12 @@ "from qiskit.aqua import Operator, run_algorithm\n", "from qiskit.aqua.input import EnergyInput\n", "from qiskit.aqua.translators.ising import portfolio\n", + "from qiskit.aqua.translators.data_providers import RandomDataProvider\n", "from qiskit.aqua.algorithms import VQE, QAOA, ExactEigensolver\n", "from qiskit.aqua.components.optimizers import COBYLA\n", "from qiskit.aqua.components.variational_forms import RY\n", - "import numpy as np" + "import numpy as np\n", + "import datetime" ] }, { @@ -97,7 +99,8 @@ "source": [ "### Define problem instance\n", "\n", - "Here an Operator instance is created for our Hamiltonian. In this case the paulis are from an Ising Hamiltonian translated from the portfolio problem. We use a random portfolio problem for this notebook." + "Here an Operator instance is created for our Hamiltonian. In this case the paulis are from an Ising Hamiltonian translated from the portfolio problem. We use a random portfolio problem for this notebook. It is straight-forward to extend this to using real financial data as illustrated here:
\n", + "[Loading and Processing Stock-Market Time-Series Data](../data_providers/time_series.ipynb)" ] }, { @@ -108,9 +111,23 @@ "source": [ "# set number of assets (= number of qubits)\n", "num_assets = 4\n", - "# get random expected return vector (mu) and covariance matrix (sigma)\n", - "mu, sigma = portfolio.random_model(num_assets, seed=42)\n", "\n", + "# Generate expected return and covariance matrix from (random) time-series\n", + "stocks = [(\"TICKER%s\" % i) for i in range(num_assets)]\n", + "data = RandomDataProvider(tickers=stocks,\n", + " start=datetime.datetime(2016,1,1),\n", + " end=datetime.datetime(2016,1,30))\n", + "data.run()\n", + "mu = data.get_period_return_mean_vector()\n", + "sigma = data.get_period_return_covariance_matrix()" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ "q = 0.5 # set risk factor\n", "budget = int(num_assets / 2) # set budget\n", "penalty = num_assets # set parameter to scale the budget penalty term\n", @@ -128,7 +145,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -166,33 +183,33 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Optimal: selection [0 0 1 1], value -0.7012\n", + "Optimal: selection [0 0 1 1], value -0.0026\n", "\n", "----------------- Full result ---------------------\n", "selection\tvalue\t\tprobability\n", "---------------------------------------------------\n", - " [0 0 1 1]\t-0.7012\t\t1.0000\n", - " [1 1 1 1]\t15.6136\t\t0.0000\n", - " [0 1 1 1]\t4.9012\t\t0.0000\n", - " [1 0 1 1]\t3.0617\t\t0.0000\n", - " [1 1 0 1]\t4.6445\t\t0.0000\n", - " [0 1 0 1]\t2.1421\t\t0.0000\n", - " [1 0 0 1]\t-0.4158\t\t0.0000\n", - " [0 0 0 1]\t4.0314\t\t0.0000\n", - " [1 1 1 0]\t2.6688\t\t0.0000\n", - " [0 1 1 0]\t-0.5149\t\t0.0000\n", - " [1 0 1 0]\t-0.2876\t\t0.0000\n", - " [0 0 1 0]\t3.4782\t\t0.0000\n", - " [1 1 0 0]\t-0.5110\t\t0.0000\n", - " [0 1 0 0]\t4.5153\t\t0.0000\n", - " [1 0 0 0]\t4.0242\t\t0.0000\n", + " [0 0 1 1]\t-0.0026\t\t1.0000\n", + " [1 1 1 1]\t15.9996\t\t0.0000\n", + " [0 1 1 1]\t3.9984\t\t0.0000\n", + " [1 0 1 1]\t3.9985\t\t0.0000\n", + " [1 1 0 1]\t4.0000\t\t0.0000\n", + " [0 1 0 1]\t-0.0011\t\t0.0000\n", + " [1 0 0 1]\t-0.0011\t\t0.0000\n", + " [0 0 0 1]\t3.9978\t\t0.0000\n", + " [1 1 1 0]\t4.0017\t\t0.0000\n", + " [0 1 1 0]\t0.0006\t\t0.0000\n", + " [1 0 1 0]\t0.0006\t\t0.0000\n", + " [0 0 1 0]\t3.9995\t\t0.0000\n", + " [1 1 0 0]\t0.0021\t\t0.0000\n", + " [0 1 0 0]\t4.0010\t\t0.0000\n", + " [1 0 0 0]\t4.0011\t\t0.0000\n", " [0 0 0 0]\t16.0000\t\t0.0000\n" ] } @@ -228,34 +245,34 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Optimal: selection [1 0 0 1], value -0.4158\n", + "Optimal: selection [0 1 1 0], value 0.0006\n", "\n", "----------------- Full result ---------------------\n", "selection\tvalue\t\tprobability\n", "---------------------------------------------------\n", - " [1 0 0 1]\t-0.4158\t\t0.9322\n", - " [1 0 1 0]\t-0.2876\t\t0.0656\n", - " [1 1 0 0]\t-0.5110\t\t0.0022\n", - " [0 0 0 1]\t4.0314\t\t0.0000\n", - " [1 1 0 1]\t4.6445\t\t0.0000\n", - " [1 0 1 1]\t3.0617\t\t0.0000\n", - " [0 0 1 0]\t3.4782\t\t0.0000\n", - " [0 0 1 1]\t-0.7012\t\t0.0000\n", - " [1 1 1 0]\t2.6688\t\t0.0000\n", - " [0 1 1 1]\t4.9012\t\t0.0000\n", - " [0 1 1 0]\t-0.5149\t\t0.0000\n", - " [1 1 1 1]\t15.6136\t\t0.0000\n", - " [1 0 0 0]\t4.0242\t\t0.0000\n", - " [0 1 0 0]\t4.5153\t\t0.0000\n", - " [0 1 0 1]\t2.1421\t\t0.0000\n", - " [0 0 0 0]\t16.0000\t\t0.0000\n" + " [0 1 1 0]\t0.0006\t\t0.7038\n", + " [1 0 0 1]\t-0.0011\t\t0.2120\n", + " [1 0 1 0]\t0.0006\t\t0.0272\n", + " [0 1 0 1]\t-0.0011\t\t0.0251\n", + " [1 1 0 0]\t0.0021\t\t0.0167\n", + " [0 0 1 1]\t-0.0026\t\t0.0151\n", + " [1 0 0 0]\t4.0011\t\t0.0000\n", + " [0 1 1 1]\t3.9984\t\t0.0000\n", + " [0 0 0 1]\t3.9978\t\t0.0000\n", + " [1 0 1 1]\t3.9985\t\t0.0000\n", + " [0 1 0 0]\t4.0010\t\t0.0000\n", + " [1 1 1 0]\t4.0017\t\t0.0000\n", + " [1 1 0 1]\t4.0000\t\t0.0000\n", + " [0 0 0 0]\t16.0000\t\t0.0000\n", + " [0 0 1 0]\t3.9995\t\t0.0000\n", + " [1 1 1 1]\t15.9996\t\t0.0000\n" ] } ], @@ -312,34 +329,34 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Optimal: selection [0 0 1 1], value -0.7012\n", + "Optimal: selection [1 1 0 0], value 0.0021\n", "\n", "----------------- Full result ---------------------\n", "selection\tvalue\t\tprobability\n", "---------------------------------------------------\n", - " [0 0 1 1]\t-0.7012\t\t0.1771\n", - " [1 0 0 1]\t-0.4158\t\t0.1748\n", - " [1 1 0 0]\t-0.5110\t\t0.1743\n", - " [0 1 1 0]\t-0.5149\t\t0.1709\n", - " [1 0 1 0]\t-0.2876\t\t0.1479\n", - " [0 1 0 1]\t2.1421\t\t0.1369\n", - " [1 1 1 0]\t2.6688\t\t0.0098\n", - " [1 0 1 1]\t3.0617\t\t0.0043\n", - " [0 0 0 1]\t4.0314\t\t0.0016\n", - " [0 0 1 0]\t3.4782\t\t0.0009\n", - " [0 1 1 1]\t4.9012\t\t0.0008\n", - " [1 0 0 0]\t4.0242\t\t0.0004\n", - " [0 1 0 0]\t4.5153\t\t0.0003\n", - " [1 1 0 1]\t4.6445\t\t0.0002\n", - " [1 1 1 1]\t15.6136\t\t0.0000\n", - " [0 0 0 0]\t16.0000\t\t0.0000\n" + " [1 1 0 0]\t0.0021\t\t0.1667\n", + " [1 0 1 0]\t0.0006\t\t0.1667\n", + " [0 1 1 0]\t0.0006\t\t0.1667\n", + " [1 0 0 1]\t-0.0011\t\t0.1666\n", + " [0 1 0 1]\t-0.0011\t\t0.1666\n", + " [0 0 1 1]\t-0.0026\t\t0.1666\n", + " [0 0 0 0]\t16.0000\t\t0.0000\n", + " [1 1 1 1]\t15.9996\t\t0.0000\n", + " [1 1 1 0]\t4.0017\t\t0.0000\n", + " [1 0 0 0]\t4.0011\t\t0.0000\n", + " [0 1 0 0]\t4.0010\t\t0.0000\n", + " [1 1 0 1]\t4.0000\t\t0.0000\n", + " [0 0 1 0]\t3.9995\t\t0.0000\n", + " [1 0 1 1]\t3.9985\t\t0.0000\n", + " [0 1 1 1]\t3.9984\t\t0.0000\n", + " [0 0 0 1]\t3.9978\t\t0.0000\n" ] } ], diff --git a/qiskit/finance/simulation/credit_risk_analysis.ipynb b/qiskit/finance/simulation/credit_risk_analysis.ipynb index 21d5fd2e2..7a842f4cb 100644 --- a/qiskit/finance/simulation/credit_risk_analysis.ipynb +++ b/qiskit/finance/simulation/credit_risk_analysis.ipynb @@ -549,7 +549,7 @@ "« ░ └───┘ └───┘ ░ " ], "text/plain": [ - "" + "" ] }, "execution_count": 12, @@ -895,7 +895,7 @@ "« └───┘ └───┘ ░ " ], "text/plain": [ - "" + "" ] }, "execution_count": 21, From b83e8e6c47cad7e1f5996a978ec3ab72f33d24da Mon Sep 17 00:00:00 2001 From: CZ Date: Wed, 1 May 2019 18:38:32 +0200 Subject: [PATCH 101/116] update qgan notebooks --- ...ans_for_loading_random_distributions.ipynb | 12979 ++++++++++++++-- .../qgan_option_pricing.ipynb | 69 +- 2 files changed, 12000 insertions(+), 1048 deletions(-) diff --git a/qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb b/qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb index 14ed3f906..5a7e12ff6 100644 --- a/qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb +++ b/qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb @@ -29,16 +29,7 @@ "cell_type": "code", "execution_count": 1, "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/Users/ouf/anaconda3/envs/QiskitDevenv/lib/python3.7/site-packages/qiskit_terra-0.8.0-py3.7-macosx-10.7-x86_64.egg/qiskit/circuit/variabletable.py:10: DeprecationWarning: Using or importing the ABCs from 'collections' instead of from 'collections.abc' is deprecated, and in 3.8 it will stop working\n", - " from collections import MutableMapping\n" - ] - } - ], + "outputs": [], "source": [ "#!/usr/bin/env python\n", "# coding: utf-8\n", @@ -58,15 +49,17 @@ "start = time.time()\n", "\n", "from torch import optim\n", - "\n", + "from qiskit import QuantumRegister, QuantumCircuit\n", "from qiskit.aqua.components.optimizers import ADAM\n", "from qiskit.aqua.components.uncertainty_models import UniformDistribution, UnivariateVariationalDistribution \n", "from qiskit.aqua.components.variational_forms import RY\n", "\n", "from qiskit.aqua.algorithms.adaptive import QGAN\n", - "from qiskit.aqua.algorithms.adaptive.qgan.discriminator import DiscriminatorNet\n", + "from qiskit.aqua.components.neural_networks.quantum_generator import QuantumGenerator\n", + "from qiskit.aqua.components.neural_networks.classical_discriminator import ClassicalDiscriminator, DiscriminatorNet\n", "\n", "from qiskit.aqua import aqua_globals, QuantumInstance\n", + "from qiskit.aqua.components.initial_states import Custom\n", "\n", "from qiskit import BasicAer" ] @@ -115,7 +108,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -125,38 +118,34 @@ "# Batch size\n", "batch_size = 1000\n", "\n", - "# Initialize qGAN\n", + " # Initialize qGAN\n", "qgan = QGAN(real_data, bounds, num_qubits, batch_size, num_epochs, snapshot_dir=None)\n", - "\n", + "qgan.seed = 1\n", "# Set quantum instance to run the quantum generator\n", - "backend = BasicAer.get_backend('statevector_simulator')\n", - "qgan.set_quantum_instance(QuantumInstance(backend=backend, shots=batch_size, coupling_map=None, circuit_caching=False))\n", - "\n", + "quantum_instance = QuantumInstance(backend=BasicAer.get_backend('statevector_simulator'),shots=batch_size, \n", + " circuit_caching=False)\n", "\n", "# Set entangler map\n", "entangler_map = [[0, 1]]\n", - " \n", - "# Set variational form\n", - "var_form = RY(int(np.sum(num_qubits)), depth=1, entangler_map=entangler_map, entanglement_gate='cz')\n", + "\n", + "\n", + "# Set an initial state for the generator circuit\n", + "init_dist = UniformDistribution(sum(num_qubits), low=bounds[0], high=bounds[1])\n", + "q = QuantumRegister(sum(num_qubits), name='q')\n", + "qc = QuantumCircuit(q)\n", + "init_dist.build(qc, q)\n", + "init_distribution = Custom(num_qubits=sum(num_qubits), circuit=qc)\n", + "var_form = RY(int(np.sum(num_qubits)), depth=1, initial_state = init_distribution, \n", + " entangler_map=entangler_map, entanglement_gate='cz')\n", "# Set generator's initial parameters\n", "init_params = aqua_globals.random.rand(var_form._num_parameters) * 2 * 1e-2\n", - "# Set an initial state for the generator circuit\n", - "init_dist = UniformDistribution(np.sum(num_qubits), low=bounds[0], high=bounds[1])\n", "# Set generator circuit\n", - "g_circuit = UnivariateVariationalDistribution(sum(num_qubits), var_form, init_params,\n", - " initial_distribution=init_dist, low=bounds[0], high=bounds[1])\n", - "# Set generator optimizer\n", - "g_optimizer = ADAM(maxiter=1, tol=1e-6, lr=1e-5, beta_1=0.9, beta_2=0.99, noise_factor=1e-6,\n", - " eps=1e-10, amsgrad=True)\n", + "g_circuit = UnivariateVariationalDistribution(int(sum(num_qubits)), var_form, init_params,\n", + " low=bounds[0], high=bounds[1])\n", "# Set quantum generator\n", - "qgan.set_generator(generator_circuit=g_circuit, generator_optimizer=g_optimizer)\n", - "\n", - "# Set discriminator network\n", - "d_net = DiscriminatorNet(n_features=k)\n", - "# Set discriminator optimizer\n", - "d_optimizer = optim.Adam(d_net.parameters(), lr=1e-5, amsgrad=True)\n", + "qgan.set_generator(generator_circuit=g_circuit)\n", "# Set classical discriminator neural network\n", - "qgan.set_discriminator(discriminator_net=d_net, discriminator_optimizer=d_optimizer)" + "qgan.set_discriminator()" ] }, { @@ -174,7 +163,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -182,1230 +171,12222 @@ "output_type": "stream", "text": [ "Epoch 1/3000...\n", - "Loss Discriminator: 0.6972\n", - "Loss Generator: 0.6728\n", - "Relative Entropy: 0.168\n", + "Loss Discriminator: 0.6948\n", + "Loss Generator: 0.6307\n", + "Relative Entropy: 0.1998\n", + "Epoch 2/3000...\n", + "Loss Discriminator: 0.6919\n", + "Loss Generator: 0.6591\n", + "Relative Entropy: 0.1998\n", + "Epoch 3/3000...\n", + "Loss Discriminator: 0.6902\n", + "Loss Generator: 0.6836\n", + "Relative Entropy: 0.1997\n", + "Epoch 4/3000...\n", + "Loss Discriminator: 0.6892\n", + "Loss Generator: 0.7006\n", + "Relative Entropy: 0.1996\n", + "Epoch 5/3000...\n", + "Loss Discriminator: 0.6882\n", + "Loss Generator: 0.7083\n", + "Relative Entropy: 0.1996\n", + "Epoch 6/3000...\n", + "Loss Discriminator: 0.6877\n", + "Loss Generator: 0.7077\n", + "Relative Entropy: 0.1995\n", + "Epoch 7/3000...\n", + "Loss Discriminator: 0.6877\n", + "Loss Generator: 0.7024\n", + "Relative Entropy: 0.1995\n", + "Epoch 8/3000...\n", + "Loss Discriminator: 0.6853\n", + "Loss Generator: 0.6961\n", + "Relative Entropy: 0.1994\n", + "Epoch 9/3000...\n", + "Loss Discriminator: 0.6862\n", + "Loss Generator: 0.6931\n", + "Relative Entropy: 0.1993\n", + "Epoch 10/3000...\n", + "Loss Discriminator: 0.6846\n", + "Loss Generator: 0.6936\n", + "Relative Entropy: 0.1993\n", "Epoch 11/3000...\n", - "Loss Discriminator: 0.6856\n", - "Loss Generator: 0.6919\n", - "Relative Entropy: 0.1678\n", - "Epoch 21/3000...\n", - "Loss Discriminator: 0.6799\n", + "Loss Discriminator: 0.6836\n", + "Loss Generator: 0.6969\n", + "Relative Entropy: 0.1992\n", + "Epoch 12/3000...\n", + "Loss Discriminator: 0.6842\n", + "Loss Generator: 0.701\n", + "Relative Entropy: 0.1991\n", + "Epoch 13/3000...\n", + "Loss Discriminator: 0.6822\n", + "Loss Generator: 0.7031\n", + "Relative Entropy: 0.1991\n", + "Epoch 14/3000...\n", + "Loss Discriminator: 0.6818\n", + "Loss Generator: 0.7042\n", + "Relative Entropy: 0.199\n", + "Epoch 15/3000...\n", + "Loss Discriminator: 0.6823\n", + "Loss Generator: 0.7041\n", + "Relative Entropy: 0.1989\n", + "Epoch 16/3000...\n", + "Loss Discriminator: 0.682\n", + "Loss Generator: 0.7038\n", + "Relative Entropy: 0.1988\n", + "Epoch 17/3000...\n", + "Loss Discriminator: 0.6803\n", "Loss Generator: 0.7046\n", - "Relative Entropy: 0.1671\n", + "Relative Entropy: 0.1988\n", + "Epoch 18/3000...\n", + "Loss Discriminator: 0.6807\n", + "Loss Generator: 0.7054\n", + "Relative Entropy: 0.1987\n", + "Epoch 19/3000...\n", + "Loss Discriminator: 0.6808\n", + "Loss Generator: 0.7066\n", + "Relative Entropy: 0.1986\n", + "Epoch 20/3000...\n", + "Loss Discriminator: 0.6785\n", + "Loss Generator: 0.7076\n", + "Relative Entropy: 0.1985\n", + "Epoch 21/3000...\n", + "Loss Discriminator: 0.6781\n", + "Loss Generator: 0.7089\n", + "Relative Entropy: 0.1985\n", + "Epoch 22/3000...\n", + "Loss Discriminator: 0.678\n", + "Loss Generator: 0.71\n", + "Relative Entropy: 0.1984\n", + "Epoch 23/3000...\n", + "Loss Discriminator: 0.6772\n", + "Loss Generator: 0.7103\n", + "Relative Entropy: 0.1983\n", + "Epoch 24/3000...\n", + "Loss Discriminator: 0.6778\n", + "Loss Generator: 0.71\n", + "Relative Entropy: 0.1983\n", + "Epoch 25/3000...\n", + "Loss Discriminator: 0.6774\n", + "Loss Generator: 0.7114\n", + "Relative Entropy: 0.1982\n", + "Epoch 26/3000...\n", + "Loss Discriminator: 0.6762\n", + "Loss Generator: 0.7137\n", + "Relative Entropy: 0.1981\n", + "Epoch 27/3000...\n", + "Loss Discriminator: 0.6766\n", + "Loss Generator: 0.7138\n", + "Relative Entropy: 0.198\n", + "Epoch 28/3000...\n", + "Loss Discriminator: 0.6753\n", + "Loss Generator: 0.7143\n", + "Relative Entropy: 0.198\n", + "Epoch 29/3000...\n", + "Loss Discriminator: 0.6757\n", + "Loss Generator: 0.7152\n", + "Relative Entropy: 0.1979\n", + "Epoch 30/3000...\n", + "Loss Discriminator: 0.6764\n", + "Loss Generator: 0.7177\n", + "Relative Entropy: 0.1978\n", "Epoch 31/3000...\n", - "Loss Discriminator: 0.6759\n", - "Loss Generator: 0.7164\n", - "Relative Entropy: 0.1664\n", + "Loss Discriminator: 0.6762\n", + "Loss Generator: 0.7182\n", + "Relative Entropy: 0.1978\n", + "Epoch 32/3000...\n", + "Loss Discriminator: 0.6751\n", + "Loss Generator: 0.7181\n", + "Relative Entropy: 0.1977\n", + "Epoch 33/3000...\n", + "Loss Discriminator: 0.6727\n", + "Loss Generator: 0.7187\n", + "Relative Entropy: 0.1976\n", + "Epoch 34/3000...\n", + "Loss Discriminator: 0.6737\n", + "Loss Generator: 0.719\n", + "Relative Entropy: 0.1975\n", + "Epoch 35/3000...\n", + "Loss Discriminator: 0.6734\n", + "Loss Generator: 0.721\n", + "Relative Entropy: 0.1975\n", + "Epoch 36/3000...\n", + "Loss Discriminator: 0.6735\n", + "Loss Generator: 0.7219\n", + "Relative Entropy: 0.1974\n", + "Epoch 37/3000...\n", + "Loss Discriminator: 0.6736\n", + "Loss Generator: 0.7227\n", + "Relative Entropy: 0.1973\n", + "Epoch 38/3000...\n", + "Loss Discriminator: 0.6716\n", + "Loss Generator: 0.723\n", + "Relative Entropy: 0.1973\n", + "Epoch 39/3000...\n", + "Loss Discriminator: 0.6724\n", + "Loss Generator: 0.7217\n", + "Relative Entropy: 0.1972\n", + "Epoch 40/3000...\n", + "Loss Discriminator: 0.6703\n", + "Loss Generator: 0.7224\n", + "Relative Entropy: 0.1971\n", "Epoch 41/3000...\n", - "Loss Discriminator: 0.6739\n", - "Loss Generator: 0.7235\n", - "Relative Entropy: 0.1657\n", + "Loss 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"Epoch 599/3000...\n", + "Loss Discriminator: 0.6695\n", + "Loss Generator: 0.7303\n", + "Relative Entropy: 0.1599\n", + "Epoch 600/3000...\n", + "Loss Discriminator: 0.6721\n", + "Loss Generator: 0.7312\n", + "Relative Entropy: 0.1598\n", + "Epoch 601/3000...\n", + "Loss Discriminator: 0.6699\n", + "Loss Generator: 0.7326\n", + "Relative Entropy: 0.1598\n", + "Epoch 602/3000...\n", + "Loss Discriminator: 0.6707\n", + "Loss Generator: 0.7306\n", + "Relative Entropy: 0.1597\n", + "Epoch 603/3000...\n", + "Loss Discriminator: 0.6685\n", + "Loss Generator: 0.729\n", + "Relative Entropy: 0.1596\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 604/3000...\n", + "Loss Discriminator: 0.6717\n", + "Loss Generator: 0.7317\n", + "Relative Entropy: 0.1596\n", + "Epoch 605/3000...\n", + "Loss Discriminator: 0.6718\n", + "Loss Generator: 0.7332\n", + "Relative Entropy: 0.1595\n", + "Epoch 606/3000...\n", + "Loss Discriminator: 0.6688\n", + "Loss Generator: 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"stream", + "text": [ + "Epoch 1289/3000...\n", + "Loss Discriminator: 0.6761\n", + "Loss Generator: 0.7184\n", + "Relative Entropy: 0.122\n", + "Epoch 1290/3000...\n", + "Loss Discriminator: 0.6772\n", + "Loss Generator: 0.7217\n", + "Relative Entropy: 0.1219\n", + "Epoch 1291/3000...\n", + "Loss Discriminator: 0.6768\n", + "Loss Generator: 0.7203\n", + "Relative Entropy: 0.1219\n", + "Epoch 1292/3000...\n", + "Loss Discriminator: 0.6739\n", + "Loss Generator: 0.7185\n", + "Relative Entropy: 0.1218\n", + "Epoch 1293/3000...\n", + "Loss Discriminator: 0.6776\n", + "Loss Generator: 0.719\n", + "Relative Entropy: 0.1218\n", + "Epoch 1294/3000...\n", + "Loss Discriminator: 0.6768\n", + "Loss Generator: 0.7213\n", + "Relative Entropy: 0.1217\n", + "Epoch 1295/3000...\n", + "Loss Discriminator: 0.6764\n", + "Loss Generator: 0.7225\n", + "Relative Entropy: 0.1217\n", + "Epoch 1296/3000...\n", + "Loss Discriminator: 0.6749\n", + "Loss Generator: 0.7178\n", + "Relative Entropy: 0.1216\n", + 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"text": [ + "Epoch 1459/3000...\n", + "Loss Discriminator: 0.6774\n", + "Loss Generator: 0.7226\n", + "Relative Entropy: 0.1129\n", + "Epoch 1460/3000...\n", + "Loss Discriminator: 0.6792\n", "Loss Generator: 0.7194\n", + "Relative Entropy: 0.1129\n", + "Epoch 1461/3000...\n", + "Loss Discriminator: 0.6786\n", + "Loss Generator: 0.7127\n", + "Relative Entropy: 0.1128\n", + "Epoch 1462/3000...\n", + "Loss Discriminator: 0.6766\n", + "Loss Generator: 0.7152\n", + "Relative Entropy: 0.1128\n", + "Epoch 1463/3000...\n", + "Loss Discriminator: 0.679\n", + "Loss Generator: 0.7221\n", + "Relative Entropy: 0.1127\n", + "Epoch 1464/3000...\n", + "Loss Discriminator: 0.677\n", + "Loss Generator: 0.7185\n", + "Relative Entropy: 0.1127\n", + "Epoch 1465/3000...\n", + "Loss Discriminator: 0.6786\n", + "Loss Generator: 0.7165\n", + "Relative Entropy: 0.1126\n", + "Epoch 1466/3000...\n", + "Loss Discriminator: 0.6772\n", + "Loss Generator: 0.7174\n", + "Relative Entropy: 0.1126\n", + "Epoch 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"Epoch 1900/3000...\n", + "Loss Discriminator: 0.6807\n", + "Loss Generator: 0.7112\n", + "Relative Entropy: 0.0905\n", + "Epoch 1901/3000...\n", + "Loss Discriminator: 0.6803\n", + "Loss Generator: 0.7124\n", + "Relative Entropy: 0.0905\n", + "Epoch 1902/3000...\n", + "Loss Discriminator: 0.6825\n", + "Loss Generator: 0.7147\n", + "Relative Entropy: 0.0904\n", + "Epoch 1903/3000...\n", + "Loss Discriminator: 0.6802\n", + "Loss Generator: 0.7124\n", + "Relative Entropy: 0.0904\n", + "Epoch 1904/3000...\n", + "Loss Discriminator: 0.6812\n", + "Loss Generator: 0.711\n", + "Relative Entropy: 0.0903\n", + "Epoch 1905/3000...\n", + "Loss Discriminator: 0.6803\n", + "Loss Generator: 0.7106\n", + "Relative Entropy: 0.0903\n", + "Epoch 1906/3000...\n", + "Loss Discriminator: 0.6816\n", + "Loss Generator: 0.7132\n", + "Relative Entropy: 0.0902\n", + "Epoch 1907/3000...\n", + "Loss Discriminator: 0.6807\n", + "Loss Generator: 0.7131\n", + "Relative Entropy: 0.0902\n", + "Epoch 1908/3000...\n", + 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"Loss Generator: 0.7126\n", + "Relative Entropy: 0.0898\n", + "Epoch 1916/3000...\n", + "Loss Discriminator: 0.681\n", + "Loss Generator: 0.7112\n", + "Relative Entropy: 0.0898\n", + "Epoch 1917/3000...\n", + "Loss Discriminator: 0.6817\n", + "Loss Generator: 0.7105\n", + "Relative Entropy: 0.0897\n", + "Epoch 1918/3000...\n", + "Loss Discriminator: 0.6812\n", + "Loss Generator: 0.7141\n", + "Relative Entropy: 0.0897\n", + "Epoch 1919/3000...\n", + "Loss Discriminator: 0.6806\n", + "Loss Generator: 0.7111\n", + "Relative Entropy: 0.0896\n", + "Epoch 1920/3000...\n", + "Loss Discriminator: 0.6812\n", + "Loss Generator: 0.7115\n", + "Relative Entropy: 0.0896\n", + "Epoch 1921/3000...\n", + "Loss Discriminator: 0.6814\n", + "Loss Generator: 0.7111\n", + "Relative Entropy: 0.0895\n", + "Epoch 1922/3000...\n", + "Loss Discriminator: 0.6805\n", + "Loss Generator: 0.7132\n", + "Relative Entropy: 0.0895\n", + "Epoch 1923/3000...\n", + "Loss Discriminator: 0.6807\n", + "Loss Generator: 0.7137\n", + "Relative Entropy: 0.0894\n", + "Epoch 1924/3000...\n", + "Loss Discriminator: 0.6808\n", + "Loss Generator: 0.7132\n", + "Relative Entropy: 0.0894\n", + "Epoch 1925/3000...\n", + "Loss Discriminator: 0.6807\n", + "Loss Generator: 0.7108\n", + "Relative Entropy: 0.0893\n", + "Epoch 1926/3000...\n", + "Loss Discriminator: 0.6835\n", + "Loss Generator: 0.7113\n", + "Relative Entropy: 0.0893\n", + "Epoch 1927/3000...\n", + "Loss Discriminator: 0.6811\n", + "Loss Generator: 0.7133\n", + "Relative Entropy: 0.0892\n", + "Epoch 1928/3000...\n", + "Loss Discriminator: 0.6816\n", + "Loss Generator: 0.7136\n", + "Relative Entropy: 0.0892\n", + "Epoch 1929/3000...\n", + "Loss Discriminator: 0.6808\n", "Loss Generator: 0.7146\n", - "Relative Entropy: 0.0948\n", - "Epoch 1311/3000...\n", - "Loss Discriminator: 0.6776\n", - "Loss Generator: 0.7166\n", - "Relative Entropy: 0.0943\n", - "Epoch 1321/3000...\n", + "Relative Entropy: 0.0891\n", + "Epoch 1930/3000...\n", + "Loss 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"Loss Generator: 0.7121\n", + "Relative Entropy: 0.0884\n", + "Epoch 1946/3000...\n", + "Loss Discriminator: 0.6816\n", + "Loss Generator: 0.713\n", + "Relative Entropy: 0.0883\n", + "Epoch 1947/3000...\n", + "Loss Discriminator: 0.6811\n", + "Loss Generator: 0.7116\n", + "Relative Entropy: 0.0883\n", + "Epoch 1948/3000...\n", + "Loss Discriminator: 0.6814\n", + "Loss Generator: 0.7104\n", + "Relative Entropy: 0.0882\n", + "Epoch 1949/3000...\n", + "Loss Discriminator: 0.6795\n", + "Loss Generator: 0.7149\n", + "Relative Entropy: 0.0882\n", + "Epoch 1950/3000...\n", + "Loss Discriminator: 0.6805\n", + "Loss Generator: 0.7143\n", + "Relative Entropy: 0.0881\n", + "Epoch 1951/3000...\n", + "Loss Discriminator: 0.6817\n", + "Loss Generator: 0.7126\n", + "Relative Entropy: 0.0881\n", + "Epoch 1952/3000...\n", + "Loss Discriminator: 0.6802\n", + "Loss Generator: 0.7091\n", + "Relative Entropy: 0.0881\n", + "Epoch 1953/3000...\n", + "Loss Discriminator: 0.6814\n", + "Loss Generator: 0.7108\n", + "Relative Entropy: 0.088\n", + "Epoch 1954/3000...\n", + "Loss Discriminator: 0.6809\n", + "Loss Generator: 0.7109\n", + "Relative Entropy: 0.088\n", + "Epoch 1955/3000...\n", + "Loss Discriminator: 0.6819\n", + "Loss Generator: 0.7118\n", + "Relative Entropy: 0.0879\n", + "Epoch 1956/3000...\n", + "Loss Discriminator: 0.6798\n", + "Loss Generator: 0.7125\n", + "Relative Entropy: 0.0879\n", + "Epoch 1957/3000...\n", + "Loss Discriminator: 0.6813\n", + "Loss Generator: 0.7129\n", + "Relative Entropy: 0.0878\n", + "Epoch 1958/3000...\n", + "Loss Discriminator: 0.6806\n", + "Loss Generator: 0.7142\n", + "Relative Entropy: 0.0878\n", + "Epoch 1959/3000...\n", + "Loss Discriminator: 0.6829\n", + "Loss Generator: 0.7145\n", + "Relative Entropy: 0.0877\n", + "Epoch 1960/3000...\n", + "Loss Discriminator: 0.6815\n", + "Loss Generator: 0.7096\n", + "Relative Entropy: 0.0877\n", + "Epoch 1961/3000...\n", + "Loss Discriminator: 0.6794\n", + "Loss Generator: 0.7092\n", + "Relative Entropy: 0.0876\n", + "Epoch 1962/3000...\n", + "Loss Discriminator: 0.6823\n", + "Loss Generator: 0.7116\n", + "Relative Entropy: 0.0876\n", + "Epoch 1963/3000...\n", + "Loss Discriminator: 0.6816\n", + "Loss Generator: 0.7127\n", + "Relative Entropy: 0.0875\n", + "Epoch 1964/3000...\n", + "Loss Discriminator: 0.6803\n", + "Loss Generator: 0.7114\n", + "Relative Entropy: 0.0875\n", + "Epoch 1965/3000...\n", + "Loss Discriminator: 0.6816\n", + "Loss Generator: 0.7121\n", + "Relative Entropy: 0.0874\n", + "Epoch 1966/3000...\n", + "Loss Discriminator: 0.6796\n", + "Loss Generator: 0.711\n", + "Relative Entropy: 0.0874\n", + "Epoch 1967/3000...\n", + "Loss Discriminator: 0.6815\n", + "Loss Generator: 0.7129\n", + "Relative Entropy: 0.0873\n", + "Epoch 1968/3000...\n", + "Loss Discriminator: 0.6795\n", + "Loss Generator: 0.7125\n", + "Relative Entropy: 0.0873\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 1969/3000...\n", + "Loss Discriminator: 0.681\n", + "Loss Generator: 0.7103\n", + "Relative Entropy: 0.0873\n", + "Epoch 1970/3000...\n", + "Loss Discriminator: 0.682\n", + "Loss Generator: 0.7135\n", + "Relative Entropy: 0.0872\n", + "Epoch 1971/3000...\n", + "Loss Discriminator: 0.6819\n", + "Loss Generator: 0.7152\n", + "Relative Entropy: 0.0872\n", + "Epoch 1972/3000...\n", + "Loss Discriminator: 0.681\n", + "Loss Generator: 0.7086\n", + "Relative Entropy: 0.0871\n", + "Epoch 1973/3000...\n", + "Loss Discriminator: 0.6822\n", + "Loss Generator: 0.7083\n", + "Relative Entropy: 0.0871\n", + "Epoch 1974/3000...\n", + "Loss Discriminator: 0.6816\n", + "Loss Generator: 0.7131\n", + "Relative Entropy: 0.087\n", + "Epoch 1975/3000...\n", + "Loss Discriminator: 0.6818\n", + "Loss Generator: 0.7142\n", + "Relative Entropy: 0.087\n", + "Epoch 1976/3000...\n", + "Loss Discriminator: 0.6819\n", + "Loss Generator: 0.7136\n", + "Relative Entropy: 0.0869\n", + "Epoch 1977/3000...\n", + "Loss Discriminator: 0.6825\n", + "Loss Generator: 0.7133\n", + "Relative Entropy: 0.0869\n", + "Epoch 1978/3000...\n", + "Loss Discriminator: 0.6803\n", + "Loss Generator: 0.7104\n", + "Relative Entropy: 0.0868\n", + "Epoch 1979/3000...\n", + "Loss Discriminator: 0.6808\n", + "Loss Generator: 0.7107\n", + "Relative Entropy: 0.0868\n", + "Epoch 1980/3000...\n", + "Loss Discriminator: 0.6798\n", + "Loss Generator: 0.7119\n", + "Relative Entropy: 0.0867\n", + "Epoch 1981/3000...\n", + "Loss Discriminator: 0.6826\n", + "Loss Generator: 0.7107\n", + "Relative Entropy: 0.0867\n", + "Epoch 1982/3000...\n", + "Loss Discriminator: 0.6813\n", + "Loss Generator: 0.7147\n", + "Relative Entropy: 0.0866\n", + "Epoch 1983/3000...\n", + "Loss Discriminator: 0.6817\n", + "Loss Generator: 0.7092\n", + "Relative Entropy: 0.0866\n", + "Epoch 1984/3000...\n", + "Loss Discriminator: 0.6841\n", + "Loss Generator: 0.7095\n", + "Relative Entropy: 0.0866\n", + "Epoch 1985/3000...\n", + "Loss Discriminator: 0.6807\n", + "Loss Generator: 0.7132\n", + "Relative 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"Epoch 1994/3000...\n", + "Loss Discriminator: 0.6834\n", + "Loss Generator: 0.7124\n", + "Relative Entropy: 0.0861\n", + "Epoch 1995/3000...\n", + "Loss Discriminator: 0.6822\n", + "Loss Generator: 0.7122\n", + "Relative Entropy: 0.086\n", + "Epoch 1996/3000...\n", + "Loss Discriminator: 0.681\n", + "Loss Generator: 0.71\n", + "Relative Entropy: 0.086\n", + "Epoch 1997/3000...\n", "Loss Discriminator: 0.6798\n", - "Loss Generator: 0.7147\n", - "Relative Entropy: 0.093\n", - "Epoch 1351/3000...\n", - "Loss Discriminator: 0.6786\n", - "Loss Generator: 0.7139\n", - "Relative Entropy: 0.0926\n", - "Epoch 1361/3000...\n", - "Loss Discriminator: 0.6794\n", - "Loss Generator: 0.7153\n", - "Relative Entropy: 0.0921\n", - "Epoch 1371/3000...\n", - "Loss Discriminator: 0.6794\n", - "Loss Generator: 0.7152\n", - "Relative Entropy: 0.0917\n", - "Epoch 1381/3000...\n", - "Loss Discriminator: 0.6806\n", - "Loss Generator: 0.7131\n", - "Relative Entropy: 0.0913\n", - "Epoch 1391/3000...\n", - "Loss 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"text": [ + "Epoch 2224/3000...\n", + "Loss Discriminator: 0.6844\n", + "Loss Generator: 0.7124\n", + "Relative Entropy: 0.0758\n", + "Epoch 2225/3000...\n", + "Loss Discriminator: 0.6845\n", + "Loss Generator: 0.7093\n", + "Relative Entropy: 0.0757\n", + "Epoch 2226/3000...\n", + "Loss Discriminator: 0.6838\n", + "Loss Generator: 0.7069\n", + "Relative Entropy: 0.0757\n", + "Epoch 2227/3000...\n", + "Loss Discriminator: 0.6821\n", + "Loss Generator: 0.7093\n", + "Relative Entropy: 0.0756\n", + "Epoch 2228/3000...\n", + "Loss Discriminator: 0.6829\n", + "Loss Generator: 0.7089\n", + "Relative Entropy: 0.0756\n", + "Epoch 2229/3000...\n", + "Loss Discriminator: 0.6826\n", + "Loss Generator: 0.7062\n", + "Relative Entropy: 0.0755\n", + "Epoch 2230/3000...\n", + "Loss Discriminator: 0.6829\n", + "Loss Generator: 0.7115\n", + "Relative Entropy: 0.0755\n", + "Epoch 2231/3000...\n", + "Loss Discriminator: 0.6832\n", + "Loss Generator: 0.7107\n", + "Relative Entropy: 0.0755\n", + "Epoch 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Discriminator: 0.6881\n", - "Loss Generator: 0.697\n", - "Relative Entropy: 0.0326\n", - "Epoch 2961/3000...\n", + "Loss Generator: 0.7009\n", + "Relative Entropy: 0.0469\n", + "Epoch 2998/3000...\n", + "Loss Discriminator: 0.6876\n", + "Loss Generator: 0.7018\n", + "Relative Entropy: 0.0469\n", + "Epoch 2999/3000...\n", "Loss Discriminator: 0.6873\n", - "Loss Generator: 0.7011\n", - "Relative Entropy: 0.0323\n", - "Epoch 2971/3000...\n", - "Loss Discriminator: 0.6891\n", - "Loss Generator: 0.7003\n", - "Relative Entropy: 0.032\n", - "Epoch 2981/3000...\n", - "Loss Discriminator: 0.6887\n", "Loss Generator: 0.7022\n", - "Relative Entropy: 0.0318\n", - "Epoch 2991/3000...\n", - "Loss Discriminator: 0.6878\n", - "Loss Generator: 0.6988\n", - "Relative Entropy: 0.0315\n", - "qGAN training runtime: 35.40391653776169 min\n" + "Relative Entropy: 0.0468\n", + "Epoch 3000/3000...\n", + "Loss Discriminator: 0.6857\n", + "Loss Generator: 0.7017\n", + "Relative Entropy: 0.0468\n", + "qGAN training runtime: 61.47158089876175 min\n" ] } ], "source": [ "# Run qGAN\n", - "qgan.run()\n", + "qgan.run(quantum_instance)\n", "\n", "# Runtime\n", "end = time.time()\n", @@ -1423,12 +12404,12 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 7, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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\n", + "image/png": 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\n", 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\n", 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\n", 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" ] @@ -1497,7 +12478,7 @@ "\n", "plt.figure(figsize=(6,5))\n", "plt.title(\"CDF\")\n", - "samples_g, prob_g = qgan.generator.get_samples(qgan.quantum_instance, shots=10000)\n", + "samples_g, prob_g = qgan.generator.get_output(qgan.quantum_instance, shots=10000)\n", "samples_g = np.array(samples_g)\n", "samples_g = samples_g.flatten()\n", "num_bins = len(prob_g)\n", diff --git a/qiskit/finance/machine_learning/qgan_option_pricing.ipynb b/qiskit/finance/machine_learning/qgan_option_pricing.ipynb index d21327bbe..6bae69baa 100644 --- a/qiskit/finance/machine_learning/qgan_option_pricing.ipynb +++ b/qiskit/finance/machine_learning/qgan_option_pricing.ipynb @@ -22,18 +22,9 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/Users/ouf/anaconda3/envs/QiskitDevenv/lib/python3.7/site-packages/qiskit_terra-0.8.0-py3.7-macosx-10.7-x86_64.egg/qiskit/circuit/variabletable.py:10: DeprecationWarning: Using or importing the ABCs from 'collections' instead of from 'collections.abc' is deprecated, and in 3.8 it will stop working\n", - " from collections import MutableMapping\n" - ] - } - ], + "outputs": [], "source": [ "#!/usr/bin/env python\n", "# coding: utf-8\n", @@ -46,6 +37,8 @@ "from qiskit.aqua.components.uncertainty_problems import EuropeanCallExpectedValue\n", "from qiskit.aqua.components.uncertainty_models import UnivariateVariationalDistribution, NormalDistribution\n", "from qiskit.aqua.components.variational_forms import RY\n", + "from qiskit import QuantumRegister, QuantumCircuit\n", + "from qiskit.aqua.components.initial_states import Custom\n", "\n", "from qiskit.aqua import aqua_globals, QuantumInstance\n", "\n", @@ -64,7 +57,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 12, "metadata": {}, "outputs": [], "source": [ @@ -78,49 +71,20 @@ "for i in range(sum(num_qubits)):\n", " entangler_map.append([i, int(np.mod(i+1, sum(num_qubits)))])\n", "\n", - "# Set variational form\n", - "var_form = RY(int(np.sum(num_qubits)), depth=1, entangler_map=entangler_map, entanglement_gate='cz')\n", "# Load the trained circuit parameters\n", "g_params = [0.29399714, 0.38853322, 0.9557694, 0.07245791, 6.02626428, 0.13537225]\n", "# Set an initial state for the generator circuit\n", "init_dist = NormalDistribution(int(sum(num_qubits)), mu=1., sigma=1., low=bounds[0], high=bounds[1])\n", + "init_distribution = np.sqrt(init_dist.probabilities)\n", + "init_distribution = Custom(num_qubits=sum(num_qubits), state_vector=init_distribution)\n", + "# Set variational form\n", + "var_form = RY(int(np.sum(num_qubits)), depth=1, initial_state=init_distribution,\n", + " entangler_map=entangler_map, entanglement_gate='cz')\n", "# Set generator circuit\n", "g_circuit = UnivariateVariationalDistribution(int(sum(num_qubits)), var_form, g_params,\n", - " initial_distribution=init_dist, low=bounds[0], high=bounds[1])\n", - "\n", + " low=bounds[0], high=bounds[1])\n", "# construct circuit factory for uncertainty model\n", - "uncertainty_model = g_circuit" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# plot probability distribution\n", - "x = uncertainty_model.values\n", - "y = uncertainty_model.probabilities\n", - "plt.bar(x, y, width=0.2)\n", - "plt.xticks(x, size=15, rotation=90)\n", - "plt.yticks(size=15)\n", - "plt.grid()\n", - "plt.xlabel('Spot Price at Maturity $S_T$ (\\$)', size=15)\n", - "plt.ylabel('Probability ($\\%$)', size=15)\n", - "plt.show()" + "uncertainty_model = g_circuit\n" ] }, { @@ -133,7 +97,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 13, "metadata": {}, "outputs": [ { @@ -168,6 +132,13 @@ "print('Estimated value:\\t%.4f' % result['estimation'])\n", "print('Probability: \\t%.4f' % result['max_probability'])" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { From bce7774e00269905e8700198c9dfa2e237fb112e Mon Sep 17 00:00:00 2001 From: stefan-woerner Date: Wed, 1 May 2019 19:27:54 +0200 Subject: [PATCH 102/116] Update time_series.ipynb --- qiskit/finance/data_providers/time_series.ipynb | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/qiskit/finance/data_providers/time_series.ipynb b/qiskit/finance/data_providers/time_series.ipynb index f79e36525..441d1d0f4 100644 --- a/qiskit/finance/data_providers/time_series.ipynb +++ b/qiskit/finance/data_providers/time_series.ipynb @@ -34,7 +34,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 1, "metadata": { "scrolled": true }, @@ -52,7 +52,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -72,7 +72,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 3, "metadata": {}, "outputs": [ { @@ -147,7 +147,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -202,7 +202,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 5, "metadata": {}, "outputs": [ { From 4ab2088bf52caa22e95f9190734401aac3ab50a6 Mon Sep 17 00:00:00 2001 From: woodsp Date: Wed, 1 May 2019 19:21:40 -0400 Subject: [PATCH 103/116] Mover domain folders like chemistry, ai etc out of aqua as peers --- community/aqua/README.md | 26 ++++++--- .../algorithm_introduction_with_vqe.ipynb | 0 .../{general => }/bernstein_vazirani.ipynb | 0 .../aqua/{general => }/deutsch_jozsa.ipynb | 0 community/aqua/{general => }/eoh.ipynb | 0 community/aqua/{general => }/evolution.ipynb | 0 community/aqua/general/README.md | 12 ----- community/aqua/index.ipynb | 50 +++++++++--------- .../{general => }/input_files/H2-0.735.json | 0 .../aqua/{general => }/input_files/eoh.json | 0 .../aqua/{general => }/input_files/vqe.json | 0 community/aqua/{general => }/shors.ipynb | 0 community/aqua/{general => }/simon.ipynb | 0 .../simulations_with_noise.ipynb | 0 community/aqua/{general => 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qiskit/{aqua => }/chemistry/LiH/5.0_sto-3g.hdf5 (100%) rename qiskit/{aqua => }/chemistry/LiH/LiH_equilibrium_1.595_sto-3g.hdf5 (100%) rename qiskit/{aqua => }/chemistry/declarative_approach.ipynb (100%) rename qiskit/{aqua => }/chemistry/dissociation_profile_of_molecule.ipynb (100%) rename qiskit/{aqua => }/chemistry/index.ipynb (100%) rename qiskit/{aqua => }/chemistry/programmatic_approach.ipynb (100%) rename qiskit/{aqua => }/optimization/docplex.ipynb (100%) rename qiskit/{aqua => }/optimization/index.ipynb (100%) rename qiskit/{aqua => }/optimization/max_cut_and_tsp.ipynb (100%) rename qiskit/{aqua => }/optimization/vehicle_routing.ipynb (100%) diff --git a/community/aqua/README.md b/community/aqua/README.md index 30b4a711a..c6a2bd5b9 100644 --- a/community/aqua/README.md +++ b/community/aqua/README.md @@ -1,17 +1,29 @@ -# Qiskit Aqua Tutorials +# Qiskit Aqua Tutorials Qiskit Algorithms for QUantum Applications (Qiskit Aqua) is a library of algorithms for quantum computing that uses [Qiskit Terra](https://qiskit.org/terra) to build out and run quantum circuits. -## Contents +This folder contains some Jupyter Notebook examples showing how to run algorithms in Qiskit Aqua. +There are also Python code files too. + +For more detail see the main [index](../index.ipynb#aqua) + +## Input files + +The folder [input_files](../input_files) contains a number of example json input files that can be loaded +and run by the Qiskit Aqua [GUI](https://github.com/Qiskit/aqua/README.md#gui) or by the Qiskit Aqua +[command line](https://github.com/Qiskit/aqua/README.md#command-line) tool. + + +## Domains Aqua provides a library of cross-domain algorithms upon which domain-specific applications and stacks can be built. Tutorials, sample code and sample input files may be found here for: -* [General](general) -* [Qiskit Chemistry](chemistry) -* [Aqua Optimization](optimization) -* [Aqua Artificial Intelligence](artificial_intelligence) -* [Aqua Finance](finance) +* [Qiskit Chemistry](../chemistry) +* [Qiskit Optimization](../optimization) +* [Qiskit Artificial Intelligence](../artificial_intelligence) +* [Qiskit Finance](../finance) More information may be found the [main index notebook](index.ipynb). + diff --git a/community/aqua/general/algorithm_introduction_with_vqe.ipynb b/community/aqua/algorithm_introduction_with_vqe.ipynb similarity index 100% rename from community/aqua/general/algorithm_introduction_with_vqe.ipynb rename to community/aqua/algorithm_introduction_with_vqe.ipynb diff --git a/community/aqua/general/bernstein_vazirani.ipynb b/community/aqua/bernstein_vazirani.ipynb similarity index 100% rename from community/aqua/general/bernstein_vazirani.ipynb rename to community/aqua/bernstein_vazirani.ipynb diff --git a/community/aqua/general/deutsch_jozsa.ipynb b/community/aqua/deutsch_jozsa.ipynb similarity index 100% rename from community/aqua/general/deutsch_jozsa.ipynb rename to community/aqua/deutsch_jozsa.ipynb diff --git a/community/aqua/general/eoh.ipynb b/community/aqua/eoh.ipynb similarity index 100% rename from community/aqua/general/eoh.ipynb rename to community/aqua/eoh.ipynb diff --git a/community/aqua/general/evolution.ipynb b/community/aqua/evolution.ipynb similarity index 100% rename from community/aqua/general/evolution.ipynb rename to community/aqua/evolution.ipynb diff --git a/community/aqua/general/README.md b/community/aqua/general/README.md deleted file mode 100644 index eb23cc4fb..000000000 --- a/community/aqua/general/README.md +++ /dev/null @@ -1,12 +0,0 @@ -# Qiskit Aqua Tutorials, samples and input files - -This folder contains some Jupyter Notebook examples showing how to run algorithms in Qiskit Aqua. -There are also Python code files too. - -For more detail see the main [index](../index.ipynb#aqua) - -## Input files - -The folder [input_files](input_files) contains a number of example json input files that can be loaded -and run by the Qiskit Aqua [GUI](https://github.com/Qiskit/aqua/README.md#gui) or by the Qiskit Aqua -[command line](https://github.com/Qiskit/aqua/README.md#command-line) tool. diff --git a/community/aqua/index.ipynb b/community/aqua/index.ipynb index 6e9a52e53..bca7bd5a7 100644 --- a/community/aqua/index.ipynb +++ b/community/aqua/index.ipynb @@ -13,7 +13,7 @@ "***\n", "\n", "## Contents\n", - "Qiskit Aqua has the following tutorials, samples and input files for the cross-domain library and domain-specific application and stacks built upon this:\n", + "Qiskit Aqua has the following tutorials, samples and input files for the cross-domain library and domain-specific application and stacks built upon it. Aqua currently provides AI, Chemistry, Finance and Optimization domain applications.\n", "\n", "### 1. [Qiskit Aqua](aqua/)\n", "\n", @@ -35,56 +35,56 @@ "The repository here may be viewed for the\n", "[full listing](https://github.com/Qiskit/qiskit-tutorial/tree/master/community/aqua/general).\n", "\n", - "### 2. [Qiskit Chemistry](chemistry/)\n", + "### 2. [Qiskit Chemistry](../chemistry/)\n", "\n", "This folder contains some Jupyter Notebook examples showing how to run algorithms in Qiskit Chemistry along with some Python code files too. There are also some .hdf5 files containing saved molecular data that can be used in experiments, see the main Qiskit Chemistry documentation for more information on the HDF5 driver and .hdf5 files. \n", "\n", - "The folder [input_files](chemistry/input_files) contains a number of example input files that can be loaded and run by the Qiskit Chemistry\n", + "The folder [input_files](../chemistry/input_files) contains a number of example input files that can be loaded and run by the Qiskit Chemistry\n", "[GUI](https://github.com/Qiskit/qiskit-chemistry/blob/master/README.md#gui) or \n", "[command line](https://github.com/Qiskit/qiskit-chemistry/blob/master/README.md#command-line) tool.\n", "\n", "The following notebooks are noted:\n", "\n", - "* [LiH plot using ExactEigensolver](chemistry/energyplot.ipynb) One step up from getting started\n", - "* [H2 dissociation curve using VQE with UCCSD](chemistry/h2_uccsd.ipynb)\n", - "* [LiH dissociation curve using VQE with UCCSD](chemistry/lih_uccsd.ipynb)\n", - "* [NaH dissociation curve using VQE with UCCSD](chemistry/nah_uccsd.ipynb)\n", - "* [Qiskit Chemistry, H2O ground state computation](chemistry/h2o.ipynb) Water using VQE and UCCSD\n", - "* [H2 ground state energy computation using Iterative QPE](chemistry/h2_iqpe.ipynb)\n", - "* [H2 ground state energy with VQE and SPSA](chemistry/h2_vqe_spsa.ipynb) Near-term device experiment\n", + "* [LiH plot using ExactEigensolver](../chemistry/energyplot.ipynb) One step up from getting started\n", + "* [H2 dissociation curve using VQE with UCCSD](../chemistry/h2_uccsd.ipynb)\n", + "* [LiH dissociation curve using VQE with UCCSD](../chemistry/lih_uccsd.ipynb)\n", + "* [NaH dissociation curve using VQE with UCCSD](../chemistry/nah_uccsd.ipynb)\n", + "* [Qiskit Chemistry, H2O ground state computation](../chemistry/h2o.ipynb) Water using VQE and UCCSD\n", + "* [H2 ground state energy computation using Iterative QPE](../chemistry/h2_iqpe.ipynb)\n", + "* [H2 ground state energy with VQE and SPSA](../chemistry/h2_vqe_spsa.ipynb) Near-term device experiment\n", "\n", "There are many more notebooks. The repository here may be viewed for the\n", - "[full listing](https://github.com/Qiskit/qiskit-tutorial/tree/master/community/aqua/chemistry).\n", + "[full listing](https://github.com/Qiskit/qiskit-tutorial/tree/master/community/chemistry).\n", "\n", - "### 3. [Qiskit Aqua Artificial Intelligence](artificial_intelligence/)\n", + "### 3. [Qiskit Artificial Intelligence](../artificial_intelligence/)\n", "\n", - "Qiskit Aqua Artificial Intelligence is a set of tools, algorithms and software for use with quantum computers to carry out research and investigate how to take advantage of quantum computing power to solve artificial intelligence problems. \n", + "Qiskit Artificial Intelligence is a set of tools, algorithms and software for use with quantum computers to carry out research and investigate how to take advantage of quantum computing power to solve artificial intelligence problems. \n", "\n", "* [Quantum SVM algorithm: multiclass classifier extension](artificial_intelligence/qsvm_multiclass.ipynb)\n", "* [Variational Quantum Classifier (vqc)](artificial_intelligence/vqc.ipynb)\n", "\n", "The repository here may be viewed for the\n", - "[full listing](https://github.com/Qiskit/qiskit-tutorial/tree/master/artificial_intelligence).\n", + "[full listing](https://github.com/Qiskit/qiskit-tutorial/tree/master/community/artificial_intelligence).\n", "\n", - "### 4. [Qiskit Aqua Optimization](optimization/)\n", + "### 4. [Qiskit Optimization](../optimization/)\n", "\n", - "Qiskit Aqua Optimization is a set of tools, algorithms and software for use with quantum computers to carry out research and investigate how to take advantage of quantum computing power to solve optimization problems. \n", + "Qiskit Optimization is a set of tools, algorithms and software for use with quantum computers to carry out research and investigate how to take advantage of quantum computing power to solve optimization problems. \n", "\n", - "* [Using Grover Search for 3SAT problems](optimization/grover.ipynb)\n", - "* [Using Aqua for partition problems](optimization/partition.ipynb)\n", - "* [Using Aqua for stable-set problems](optimization/stable_set.ipynb)\n", + "* [Using Grover Search for 3SAT problems](../optimization/grover.ipynb)\n", + "* [Using Aqua for partition problems](../optimization/partition.ipynb)\n", + "* [Using Aqua for stable-set problems](../optimization/stable_set.ipynb)\n", "\n", "The repository here may be viewed for the\n", - "[full listing](https://github.com/Qiskit/qiskit-tutorial/tree/master/community/aqua/optimization).\n", + "[full listing](https://github.com/Qiskit/qiskit-tutorial/tree/master/community/optimization).\n", "\n", - "### 5. [Qiskit Aqua Finance](finance/)\n", + "### 5. [Qiskit Finance](../finance/)\n", "\n", - "Qiskit Aqua Finance is a set of tools, algorithms and software for use with quantum computers to carry out research and investigate how to take advantage of quantum computing power to solve problems in the Financial domain. \n", + "Qiskit Finance is a set of tools, algorithms and software for use with quantum computers to carry out research and investigate how to take advantage of quantum computing power to solve problems in the Financial domain. \n", "\n", - "* [Portfolio Optimization](../../qiskit/aqua/finance/portfolio_optimization.ipynb)\n", + "* [Portfolio Optimization](../../qiskit/finance/portfolio_optimization.ipynb)\n", "\n", "The repository here may be viewed for the\n", - "[full listing](https://github.com/Qiskit/qiskit-tutorial/tree/master/community/aqua/finance).\n", + "[full listing](https://github.com/Qiskit/qiskit-tutorial/tree/master/qiskit/finance).\n", "\n", "\n", "*** " @@ -116,7 +116,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.2" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/community/aqua/general/input_files/H2-0.735.json b/community/aqua/input_files/H2-0.735.json similarity index 100% rename from community/aqua/general/input_files/H2-0.735.json rename to community/aqua/input_files/H2-0.735.json diff --git a/community/aqua/general/input_files/eoh.json b/community/aqua/input_files/eoh.json similarity index 100% rename from community/aqua/general/input_files/eoh.json rename to community/aqua/input_files/eoh.json diff --git a/community/aqua/general/input_files/vqe.json b/community/aqua/input_files/vqe.json similarity index 100% rename from community/aqua/general/input_files/vqe.json rename to community/aqua/input_files/vqe.json diff --git a/community/aqua/general/shors.ipynb b/community/aqua/shors.ipynb similarity index 100% rename from community/aqua/general/shors.ipynb rename to community/aqua/shors.ipynb diff --git a/community/aqua/general/simon.ipynb b/community/aqua/simon.ipynb similarity index 100% rename from community/aqua/general/simon.ipynb rename to community/aqua/simon.ipynb diff --git a/community/aqua/general/simulations_with_noise.ipynb b/community/aqua/simulations_with_noise.ipynb similarity index 100% rename from community/aqua/general/simulations_with_noise.ipynb rename to community/aqua/simulations_with_noise.ipynb diff --git a/community/aqua/general/vqe2iqpe.ipynb b/community/aqua/vqe2iqpe.ipynb similarity index 100% rename from community/aqua/general/vqe2iqpe.ipynb rename to community/aqua/vqe2iqpe.ipynb diff --git a/community/aqua/general/vqe_convergence.ipynb b/community/aqua/vqe_convergence.ipynb similarity index 100% rename from community/aqua/general/vqe_convergence.ipynb rename to community/aqua/vqe_convergence.ipynb diff --git a/community/aqua/artificial_intelligence/README.md b/community/artificial_intelligence/README.md similarity index 92% rename from community/aqua/artificial_intelligence/README.md rename to community/artificial_intelligence/README.md index 9b7965cc5..23b6c440f 100644 --- a/community/aqua/artificial_intelligence/README.md +++ b/community/artificial_intelligence/README.md @@ -10,7 +10,7 @@ quantum computation. This folder contains some Jupyter Notebook examples. There are Python code files too. -For more detail see the main [index](../index.ipynb#artificial_intelligence) +For more detail see the main [index](../aqua/index.ipynb#artificial_intelligence) ## Input files diff --git a/community/aqua/artificial_intelligence/datasets.py b/community/artificial_intelligence/datasets.py similarity index 100% rename from community/aqua/artificial_intelligence/datasets.py rename to community/artificial_intelligence/datasets.py diff --git a/community/aqua/artificial_intelligence/input_files/qsvm.json b/community/artificial_intelligence/input_files/qsvm.json similarity index 100% rename from community/aqua/artificial_intelligence/input_files/qsvm.json rename to community/artificial_intelligence/input_files/qsvm.json diff --git a/community/aqua/artificial_intelligence/input_files/svm_classical.json b/community/artificial_intelligence/input_files/svm_classical.json similarity index 100% rename from community/aqua/artificial_intelligence/input_files/svm_classical.json rename to community/artificial_intelligence/input_files/svm_classical.json diff --git a/community/aqua/artificial_intelligence/input_files/vqc.json b/community/artificial_intelligence/input_files/vqc.json similarity index 100% rename from community/aqua/artificial_intelligence/input_files/vqc.json rename to community/artificial_intelligence/input_files/vqc.json diff --git a/community/aqua/artificial_intelligence/qsvm_directly.ipynb b/community/artificial_intelligence/qsvm_directly.ipynb similarity index 100% rename from community/aqua/artificial_intelligence/qsvm_directly.ipynb rename to community/artificial_intelligence/qsvm_directly.ipynb diff --git a/community/aqua/artificial_intelligence/qsvm_multiclass.ipynb b/community/artificial_intelligence/qsvm_multiclass.ipynb similarity index 100% rename from community/aqua/artificial_intelligence/qsvm_multiclass.ipynb rename to community/artificial_intelligence/qsvm_multiclass.ipynb diff --git a/community/aqua/artificial_intelligence/svm_classical.ipynb b/community/artificial_intelligence/svm_classical.ipynb similarity index 100% rename from community/aqua/artificial_intelligence/svm_classical.ipynb rename to community/artificial_intelligence/svm_classical.ipynb diff --git a/community/aqua/artificial_intelligence/svm_classical_multiclass.ipynb b/community/artificial_intelligence/svm_classical_multiclass.ipynb similarity index 100% rename from community/aqua/artificial_intelligence/svm_classical_multiclass.ipynb rename to community/artificial_intelligence/svm_classical_multiclass.ipynb diff --git a/community/aqua/artificial_intelligence/vqc.ipynb b/community/artificial_intelligence/vqc.ipynb similarity index 100% rename from community/aqua/artificial_intelligence/vqc.ipynb rename to community/artificial_intelligence/vqc.ipynb diff --git a/community/aqua/chemistry/LiH.png b/community/chemistry/LiH.png similarity index 100% rename from community/aqua/chemistry/LiH.png rename to community/chemistry/LiH.png diff --git a/community/aqua/chemistry/LiH_with_qubit_tapering_and_uccsd.ipynb b/community/chemistry/LiH_with_qubit_tapering_and_uccsd.ipynb similarity index 100% rename from community/aqua/chemistry/LiH_with_qubit_tapering_and_uccsd.ipynb rename to community/chemistry/LiH_with_qubit_tapering_and_uccsd.ipynb diff --git a/community/aqua/chemistry/ParticleHoleTransformation.ipynb b/community/chemistry/ParticleHoleTransformation.ipynb similarity index 100% rename from community/aqua/chemistry/ParticleHoleTransformation.ipynb rename to community/chemistry/ParticleHoleTransformation.ipynb diff --git a/community/aqua/chemistry/PySCFChemistryDriver.ipynb b/community/chemistry/PySCFChemistryDriver.ipynb similarity index 100% rename from community/aqua/chemistry/PySCFChemistryDriver.ipynb rename to community/chemistry/PySCFChemistryDriver.ipynb diff --git a/community/aqua/chemistry/QSE_pytket.ipynb b/community/chemistry/QSE_pytket.ipynb similarity index 100% rename from community/aqua/chemistry/QSE_pytket.ipynb rename to community/chemistry/QSE_pytket.ipynb diff --git a/community/aqua/chemistry/QubitMappings.ipynb b/community/chemistry/QubitMappings.ipynb similarity index 100% rename from community/aqua/chemistry/QubitMappings.ipynb rename to community/chemistry/QubitMappings.ipynb diff --git a/community/aqua/chemistry/README.md b/community/chemistry/README.md similarity index 100% rename from community/aqua/chemistry/README.md rename to community/chemistry/README.md diff --git a/community/aqua/chemistry/beh2_reductions.ipynb b/community/chemistry/beh2_reductions.ipynb similarity index 100% rename from community/aqua/chemistry/beh2_reductions.ipynb rename to community/chemistry/beh2_reductions.ipynb diff --git a/community/aqua/chemistry/dictinput.py b/community/chemistry/dictinput.py similarity index 100% rename from community/aqua/chemistry/dictinput.py rename to community/chemistry/dictinput.py diff --git a/community/aqua/chemistry/energyplot.ipynb b/community/chemistry/energyplot.ipynb similarity index 100% rename from community/aqua/chemistry/energyplot.ipynb rename to community/chemistry/energyplot.ipynb diff --git a/community/aqua/chemistry/h2_0.735_6-31g.hdf5 b/community/chemistry/h2_0.735_6-31g.hdf5 similarity index 100% rename from community/aqua/chemistry/h2_0.735_6-31g.hdf5 rename to community/chemistry/h2_0.735_6-31g.hdf5 diff --git a/community/aqua/chemistry/h2_0.735_sto-3g.hdf5 b/community/chemistry/h2_0.735_sto-3g.hdf5 similarity index 100% rename from community/aqua/chemistry/h2_0.735_sto-3g.hdf5 rename to community/chemistry/h2_0.735_sto-3g.hdf5 diff --git a/community/aqua/chemistry/h2_basis_sets.ipynb b/community/chemistry/h2_basis_sets.ipynb similarity index 100% rename from community/aqua/chemistry/h2_basis_sets.ipynb rename to community/chemistry/h2_basis_sets.ipynb diff --git a/community/aqua/chemistry/h2_excited_states.ipynb b/community/chemistry/h2_excited_states.ipynb similarity index 100% rename from community/aqua/chemistry/h2_excited_states.ipynb rename to community/chemistry/h2_excited_states.ipynb diff --git a/community/aqua/chemistry/h2_iqpe.ipynb b/community/chemistry/h2_iqpe.ipynb similarity index 100% rename from community/aqua/chemistry/h2_iqpe.ipynb rename to community/chemistry/h2_iqpe.ipynb diff --git a/community/aqua/chemistry/h2_mappings.ipynb b/community/chemistry/h2_mappings.ipynb similarity index 100% rename from community/aqua/chemistry/h2_mappings.ipynb rename to community/chemistry/h2_mappings.ipynb diff --git a/community/aqua/chemistry/h2_particle_hole.ipynb b/community/chemistry/h2_particle_hole.ipynb similarity index 100% rename from community/aqua/chemistry/h2_particle_hole.ipynb rename to community/chemistry/h2_particle_hole.ipynb diff --git a/community/aqua/chemistry/h2_qpe.ipynb b/community/chemistry/h2_qpe.ipynb similarity index 100% rename from community/aqua/chemistry/h2_qpe.ipynb rename to community/chemistry/h2_qpe.ipynb diff --git a/community/aqua/chemistry/h2_swaprz.ipynb b/community/chemistry/h2_swaprz.ipynb similarity index 100% rename from community/aqua/chemistry/h2_swaprz.ipynb rename to community/chemistry/h2_swaprz.ipynb diff --git a/community/aqua/chemistry/h2_uccsd.ipynb b/community/chemistry/h2_uccsd.ipynb similarity index 100% rename from community/aqua/chemistry/h2_uccsd.ipynb rename to community/chemistry/h2_uccsd.ipynb diff --git a/community/aqua/chemistry/h2_var_forms.ipynb b/community/chemistry/h2_var_forms.ipynb similarity index 100% rename from community/aqua/chemistry/h2_var_forms.ipynb rename to community/chemistry/h2_var_forms.ipynb diff --git a/community/aqua/chemistry/h2_vqe_initial_point.ipynb b/community/chemistry/h2_vqe_initial_point.ipynb similarity index 100% rename from community/aqua/chemistry/h2_vqe_initial_point.ipynb rename to community/chemistry/h2_vqe_initial_point.ipynb diff --git a/community/aqua/chemistry/h2_vqe_spsa.ipynb b/community/chemistry/h2_vqe_spsa.ipynb similarity index 100% rename from community/aqua/chemistry/h2_vqe_spsa.ipynb rename to community/chemistry/h2_vqe_spsa.ipynb diff --git a/community/aqua/chemistry/h2o.ipynb b/community/chemistry/h2o.ipynb similarity index 100% rename from community/aqua/chemistry/h2o.ipynb rename to community/chemistry/h2o.ipynb diff --git a/community/aqua/chemistry/input_files/gaussian_h2_0.735_sto-3g.txt b/community/chemistry/input_files/gaussian_h2_0.735_sto-3g.txt similarity index 100% rename from community/aqua/chemistry/input_files/gaussian_h2_0.735_sto-3g.txt rename to community/chemistry/input_files/gaussian_h2_0.735_sto-3g.txt diff --git a/community/aqua/chemistry/input_files/gaussian_lih_1.6_sto-3g.txt b/community/chemistry/input_files/gaussian_lih_1.6_sto-3g.txt similarity index 100% rename from community/aqua/chemistry/input_files/gaussian_lih_1.6_sto-3g.txt rename to community/chemistry/input_files/gaussian_lih_1.6_sto-3g.txt diff --git a/community/aqua/chemistry/input_files/h2_on_device.txt b/community/chemistry/input_files/h2_on_device.txt similarity index 100% rename from community/aqua/chemistry/input_files/h2_on_device.txt rename to community/chemistry/input_files/h2_on_device.txt diff --git a/community/aqua/chemistry/input_files/hdf5_h2_0.735_sto-3g.txt b/community/chemistry/input_files/hdf5_h2_0.735_sto-3g.txt similarity index 100% rename from community/aqua/chemistry/input_files/hdf5_h2_0.735_sto-3g.txt rename to community/chemistry/input_files/hdf5_h2_0.735_sto-3g.txt diff --git a/community/aqua/chemistry/input_files/hdf5_lih_1.6_sto-3g.txt b/community/chemistry/input_files/hdf5_lih_1.6_sto-3g.txt similarity index 100% rename from community/aqua/chemistry/input_files/hdf5_lih_1.6_sto-3g.txt rename to community/chemistry/input_files/hdf5_lih_1.6_sto-3g.txt diff --git a/community/aqua/chemistry/input_files/input_file_sample.txt b/community/chemistry/input_files/input_file_sample.txt similarity index 100% rename from community/aqua/chemistry/input_files/input_file_sample.txt rename to community/chemistry/input_files/input_file_sample.txt diff --git a/community/aqua/chemistry/input_files/iqpe_h2.txt b/community/chemistry/input_files/iqpe_h2.txt similarity index 100% rename from community/aqua/chemistry/input_files/iqpe_h2.txt rename to community/chemistry/input_files/iqpe_h2.txt diff --git a/community/aqua/chemistry/input_files/psi4_h2_0.735_sto-3g.txt b/community/chemistry/input_files/psi4_h2_0.735_sto-3g.txt similarity index 100% rename from community/aqua/chemistry/input_files/psi4_h2_0.735_sto-3g.txt rename to community/chemistry/input_files/psi4_h2_0.735_sto-3g.txt diff --git a/community/aqua/chemistry/input_files/psi4_lih_1.6_sto-3g.txt b/community/chemistry/input_files/psi4_lih_1.6_sto-3g.txt similarity index 100% rename from community/aqua/chemistry/input_files/psi4_lih_1.6_sto-3g.txt rename to community/chemistry/input_files/psi4_lih_1.6_sto-3g.txt diff --git a/community/aqua/chemistry/input_files/psi4_save_hdf5.txt b/community/chemistry/input_files/psi4_save_hdf5.txt similarity index 100% rename from community/aqua/chemistry/input_files/psi4_save_hdf5.txt rename to community/chemistry/input_files/psi4_save_hdf5.txt diff --git a/community/aqua/chemistry/input_files/pyquante_h2_0.735_sto-3g.txt b/community/chemistry/input_files/pyquante_h2_0.735_sto-3g.txt similarity index 100% rename from community/aqua/chemistry/input_files/pyquante_h2_0.735_sto-3g.txt rename to community/chemistry/input_files/pyquante_h2_0.735_sto-3g.txt diff --git a/community/aqua/chemistry/input_files/pyquante_lih_1.6_sto-3g.txt b/community/chemistry/input_files/pyquante_lih_1.6_sto-3g.txt similarity index 100% rename from community/aqua/chemistry/input_files/pyquante_lih_1.6_sto-3g.txt rename to community/chemistry/input_files/pyquante_lih_1.6_sto-3g.txt diff --git a/community/aqua/chemistry/input_files/pyscf_h2_0.735_sto-3g.txt b/community/chemistry/input_files/pyscf_h2_0.735_sto-3g.txt similarity index 100% rename from community/aqua/chemistry/input_files/pyscf_h2_0.735_sto-3g.txt rename to community/chemistry/input_files/pyscf_h2_0.735_sto-3g.txt diff --git a/community/aqua/chemistry/input_files/pyscf_lih_1.6_sto-3g.txt b/community/chemistry/input_files/pyscf_lih_1.6_sto-3g.txt similarity index 100% rename from community/aqua/chemistry/input_files/pyscf_lih_1.6_sto-3g.txt rename to community/chemistry/input_files/pyscf_lih_1.6_sto-3g.txt diff --git a/community/aqua/chemistry/input_files/pyscf_minimal.txt b/community/chemistry/input_files/pyscf_minimal.txt similarity index 100% rename from community/aqua/chemistry/input_files/pyscf_minimal.txt rename to community/chemistry/input_files/pyscf_minimal.txt diff --git a/community/aqua/chemistry/input_files/qpe_h2.txt b/community/chemistry/input_files/qpe_h2.txt similarity index 100% rename from community/aqua/chemistry/input_files/qpe_h2.txt rename to community/chemistry/input_files/qpe_h2.txt diff --git a/community/aqua/chemistry/lih_1.6_sto-3g.hdf5 b/community/chemistry/lih_1.6_sto-3g.hdf5 similarity index 100% rename from community/aqua/chemistry/lih_1.6_sto-3g.hdf5 rename to community/chemistry/lih_1.6_sto-3g.hdf5 diff --git a/community/aqua/chemistry/lih_dissoc.ipynb b/community/chemistry/lih_dissoc.ipynb similarity index 100% rename from community/aqua/chemistry/lih_dissoc.ipynb rename to community/chemistry/lih_dissoc.ipynb diff --git a/community/aqua/chemistry/lih_uccsd.ipynb b/community/chemistry/lih_uccsd.ipynb similarity index 100% rename from community/aqua/chemistry/lih_uccsd.ipynb rename to community/chemistry/lih_uccsd.ipynb diff --git a/community/aqua/chemistry/nah_1.9_sto-3g.hdf5 b/community/chemistry/nah_1.9_sto-3g.hdf5 similarity index 100% rename from community/aqua/chemistry/nah_1.9_sto-3g.hdf5 rename to community/chemistry/nah_1.9_sto-3g.hdf5 diff --git a/community/aqua/chemistry/nah_uccsd.ipynb b/community/chemistry/nah_uccsd.ipynb similarity index 100% rename from community/aqua/chemistry/nah_uccsd.ipynb rename to community/chemistry/nah_uccsd.ipynb diff --git a/community/aqua/finance/README.md b/community/finance/README.md similarity index 92% rename from community/aqua/finance/README.md rename to community/finance/README.md index c459edde1..cb5cf353c 100644 --- a/community/aqua/finance/README.md +++ b/community/finance/README.md @@ -10,7 +10,7 @@ quantum computation. This folder contains some Jupyter Notebook examples. There are Python code files too. -For more detail see the main [index](../index.ipynb#optimization) +For more detail see the main [index](../aqua/index.ipynb#optimization) ## Input files diff --git a/community/aqua/finance/input_files/portfolio.json b/community/finance/input_files/portfolio.json similarity index 100% rename from community/aqua/finance/input_files/portfolio.json rename to community/finance/input_files/portfolio.json diff --git a/community/aqua/optimization/3-Coloring Oracle via Reduction to SAT.ipynb b/community/optimization/3-Coloring Oracle via Reduction to SAT.ipynb similarity index 100% rename from community/aqua/optimization/3-Coloring Oracle via Reduction to SAT.ipynb rename to community/optimization/3-Coloring Oracle via Reduction to SAT.ipynb diff --git a/community/aqua/optimization/3sat2-3.cnf b/community/optimization/3sat2-3.cnf similarity index 100% rename from community/aqua/optimization/3sat2-3.cnf rename to community/optimization/3sat2-3.cnf diff --git a/community/aqua/optimization/README.md b/community/optimization/README.md similarity index 92% rename from community/aqua/optimization/README.md rename to community/optimization/README.md index b5ff7c4a9..5106864fd 100644 --- a/community/aqua/optimization/README.md +++ b/community/optimization/README.md @@ -10,7 +10,7 @@ quantum computation. This folder contains some Jupyter Notebook examples. There are Python code files too. -For more detail see the main [index](../index.ipynb#optimization) +For more detail see the main [index](../aqua/index.ipynb#optimization) ## Input files diff --git a/community/aqua/optimization/clique.ipynb b/community/optimization/clique.ipynb similarity index 100% rename from community/aqua/optimization/clique.ipynb rename to community/optimization/clique.ipynb diff --git a/community/aqua/optimization/exact_cover.ipynb b/community/optimization/exact_cover.ipynb similarity index 100% rename from community/aqua/optimization/exact_cover.ipynb rename to community/optimization/exact_cover.ipynb diff --git a/community/aqua/optimization/graph_partition.ipynb b/community/optimization/graph_partition.ipynb similarity index 100% rename from community/aqua/optimization/graph_partition.ipynb rename to community/optimization/graph_partition.ipynb diff --git a/community/aqua/optimization/grover.ipynb b/community/optimization/grover.ipynb similarity index 100% rename from community/aqua/optimization/grover.ipynb rename to community/optimization/grover.ipynb diff --git a/community/aqua/optimization/input_files/grover.json b/community/optimization/input_files/grover.json similarity index 100% rename from community/aqua/optimization/input_files/grover.json rename to community/optimization/input_files/grover.json diff --git a/community/aqua/optimization/input_files/maxcut.json b/community/optimization/input_files/maxcut.json similarity index 100% rename from community/aqua/optimization/input_files/maxcut.json rename to community/optimization/input_files/maxcut.json diff --git a/community/aqua/optimization/max_cut.ipynb b/community/optimization/max_cut.ipynb similarity index 100% rename from community/aqua/optimization/max_cut.ipynb rename to community/optimization/max_cut.ipynb diff --git a/community/aqua/optimization/partition.ipynb b/community/optimization/partition.ipynb similarity index 100% rename from community/aqua/optimization/partition.ipynb rename to community/optimization/partition.ipynb diff --git a/community/aqua/optimization/sample.exactcover b/community/optimization/sample.exactcover similarity index 100% rename from community/aqua/optimization/sample.exactcover rename to community/optimization/sample.exactcover diff --git a/community/aqua/optimization/sample.maxcut b/community/optimization/sample.maxcut similarity index 100% rename from community/aqua/optimization/sample.maxcut rename to community/optimization/sample.maxcut diff --git a/community/aqua/optimization/sample.partition b/community/optimization/sample.partition similarity index 100% rename from community/aqua/optimization/sample.partition rename to community/optimization/sample.partition diff --git a/community/aqua/optimization/sample.setpacking b/community/optimization/sample.setpacking similarity index 100% rename from community/aqua/optimization/sample.setpacking rename to community/optimization/sample.setpacking diff --git a/community/aqua/optimization/set_packing.ipynb b/community/optimization/set_packing.ipynb similarity index 100% rename from community/aqua/optimization/set_packing.ipynb rename to community/optimization/set_packing.ipynb diff --git a/community/aqua/optimization/stable_set.ipynb b/community/optimization/stable_set.ipynb similarity index 100% rename from community/aqua/optimization/stable_set.ipynb rename to community/optimization/stable_set.ipynb diff --git a/community/aqua/optimization/vertex_cover.ipynb b/community/optimization/vertex_cover.ipynb similarity index 100% rename from community/aqua/optimization/vertex_cover.ipynb rename to community/optimization/vertex_cover.ipynb diff --git a/qiskit/aqua/general/Aqua_how_to_build_a_pluggable_algorithm_components.ipynb b/qiskit/aqua/Aqua_how_to_build_a_pluggable_algorithm_components.ipynb similarity index 100% rename from qiskit/aqua/general/Aqua_how_to_build_a_pluggable_algorithm_components.ipynb rename to qiskit/aqua/Aqua_how_to_build_a_pluggable_algorithm_components.ipynb diff --git a/qiskit/aqua/general/amplitude_estimation.ipynb b/qiskit/aqua/amplitude_estimation.ipynb similarity index 100% rename from qiskit/aqua/general/amplitude_estimation.ipynb rename to qiskit/aqua/amplitude_estimation.ipynb diff --git a/qiskit/aqua/general/evolutionfidelity/evolutionfidelity/__init__.py b/qiskit/aqua/evolutionfidelity/evolutionfidelity/__init__.py similarity index 100% rename from qiskit/aqua/general/evolutionfidelity/evolutionfidelity/__init__.py rename to qiskit/aqua/evolutionfidelity/evolutionfidelity/__init__.py diff --git a/qiskit/aqua/general/evolutionfidelity/evolutionfidelity/evolutionfidelity.py b/qiskit/aqua/evolutionfidelity/evolutionfidelity/evolutionfidelity.py similarity index 100% rename from qiskit/aqua/general/evolutionfidelity/evolutionfidelity/evolutionfidelity.py rename to qiskit/aqua/evolutionfidelity/evolutionfidelity/evolutionfidelity.py diff --git a/qiskit/aqua/general/evolutionfidelity/setup.py b/qiskit/aqua/evolutionfidelity/setup.py similarity index 100% rename from qiskit/aqua/general/evolutionfidelity/setup.py rename to qiskit/aqua/evolutionfidelity/setup.py diff --git a/qiskit/aqua/general/generating_random_variates.ipynb b/qiskit/aqua/generating_random_variates.ipynb similarity index 100% rename from qiskit/aqua/general/generating_random_variates.ipynb rename to qiskit/aqua/generating_random_variates.ipynb diff --git a/qiskit/aqua/general/linear_systems_of_equations.ipynb b/qiskit/aqua/linear_systems_of_equations.ipynb similarity index 100% rename from qiskit/aqua/general/linear_systems_of_equations.ipynb rename to qiskit/aqua/linear_systems_of_equations.ipynb diff --git a/qiskit/aqua/artificial_intelligence/index.ipynb b/qiskit/artificial_intelligence/index.ipynb similarity index 100% rename from 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from qiskit/aqua/chemistry/dissociation_profile_of_molecule.ipynb rename to qiskit/chemistry/dissociation_profile_of_molecule.ipynb diff --git a/qiskit/aqua/chemistry/index.ipynb b/qiskit/chemistry/index.ipynb similarity index 100% rename from qiskit/aqua/chemistry/index.ipynb rename to qiskit/chemistry/index.ipynb diff --git a/qiskit/aqua/chemistry/programmatic_approach.ipynb b/qiskit/chemistry/programmatic_approach.ipynb similarity index 100% rename from qiskit/aqua/chemistry/programmatic_approach.ipynb rename to qiskit/chemistry/programmatic_approach.ipynb diff --git a/qiskit/aqua/optimization/docplex.ipynb b/qiskit/optimization/docplex.ipynb similarity index 100% rename from qiskit/aqua/optimization/docplex.ipynb rename to qiskit/optimization/docplex.ipynb diff --git a/qiskit/aqua/optimization/index.ipynb b/qiskit/optimization/index.ipynb similarity index 100% rename from qiskit/aqua/optimization/index.ipynb rename to qiskit/optimization/index.ipynb diff --git a/qiskit/aqua/optimization/max_cut_and_tsp.ipynb b/qiskit/optimization/max_cut_and_tsp.ipynb similarity index 100% rename from qiskit/aqua/optimization/max_cut_and_tsp.ipynb rename to qiskit/optimization/max_cut_and_tsp.ipynb diff --git a/qiskit/aqua/optimization/vehicle_routing.ipynb b/qiskit/optimization/vehicle_routing.ipynb similarity index 100% rename from qiskit/aqua/optimization/vehicle_routing.ipynb rename to qiskit/optimization/vehicle_routing.ipynb From 33bc50dd23c65d9cbfa9c7b7cb755a5fb6cfb70a Mon Sep 17 00:00:00 2001 From: woodsp Date: Wed, 1 May 2019 19:44:48 -0400 Subject: [PATCH 104/116] Update index to reflect chem, ai, opt folder moves --- index.ipynb | 28 ++++++++++++++++++++-------- 1 file changed, 20 insertions(+), 8 deletions(-) diff --git a/index.ipynb b/index.ipynb index 4b5d6bc62..ebd822002 100644 --- a/index.ipynb +++ b/index.ipynb @@ -33,7 +33,7 @@ "These tutorials aim to explain how to use Qiskit. We assume you have installed Qiskit if not please look at [qiskit.org](http://www.qiskit.org) or the install [documentation](https://github.com/qiskit/qiskit-tutorial/blob/master/INSTALL.md). \n", "\n", "\n", - "We've collected a core reference set of notebooks in this section outlining the features of Qiskit. We will be keeping them up to date with the latest Qiskit version, currently 0.7. The focus of this section will be how to use Qiskit and not so much on teaching you about quantum computing. For those interested in learning about quantum computing we recommend the awesome notebooks in the community section.\n", + "We've collected a core reference set of notebooks in this section outlining the features of Qiskit. We will be keeping them up to date with the latest official release Qiskit version, currently 0.7. The focus of this section will be how to use Qiskit and not so much on teaching you about quantum computing. For those interested in learning about quantum computing we recommend the awesome notebooks in the community section.\n", "\n", "\n", "Qiskit is made up of four elements: Terra, Aer, Ignis, and Aqua with each element having its own goal and together they make the full Qiskit framework. \n", @@ -75,16 +75,21 @@ " * [Quantum process tomography](qiskit/ignis/process_tomography.ipynb) - using quantum process tomography to reconstruct the behavior of a quantum process and measure its fidelity, i.e., how closely it matches the ideal version\n", "\n", "#### 1.6 Qiskit Aqua\n", - "Aqua, the ‘water’ element, is the element of life. To make quantum computing live up to its expectations, we need to find real-world applications. Aqua is where algorithms for NISQ computers are built. These algorithms can be used to build applications for quantum computing. Aqua is accessible to domain experts in chemistry, optimization, AI or finance, who want to explore the benefits of using quantum computers as accelerators for specific computational tasks, without needing to worry about how to translate the problem into the language of quantum machines.\n", - " * [Chemistry](qiskit/aqua/chemistry/index.ipynb) - using variational quantum eigensolver to experiment with molecular ground-state energy on a quantum computer\n", - " * [Optimization](qiskit/aqua/optimization/index.ipynb) - using variational quantum eigensolver to experiment with optimization problems (max-cut and traveling salesman problem) on a quantum computer \n", - " * [Artificial Intelligence](qiskit/aqua/artificial_intelligence/index.ipynb) - using quantum-enhanced support vector machine to experiment with classification problems on a quantum computer\n", + "Aqua, the ‘water’ element, is the element of life. To make quantum computing live up to its expectations, we need to find real-world applications. Aqua is where algorithms for NISQ computers are built. These algorithms can be used to build applications for quantum computing. Aqua is accessible to domain experts in `chemistry`, `optimization`, `AI` or `finance`, who want to explore the benefits of using quantum computers as accelerators for specific computational tasks, without needing to worry about how to translate the problem into the language of quantum machines. \n", "\n", - "#### 1.7 Qiskit Finance\n", + "#### 1.7 Qiskit AI \n", + "[Qiskit AI](qiskit/artificial_intelligence/index.ipynb) - using quantum-enhanced support vector machine to experiment with classification problems on a quantum computer\n", "\n", + "#### 1.8 Qiskit Chemistry \n", + "[Qiskit Chemistry](qiskit/chemistry/index.ipynb) - using variational quantum eigensolver to experiment with molecular ground-state energy on a quantum computer\n", + "\n", + "#### 1.9 Qiskit Finance\n", "[Qiskit Finance](qiskit/finance/index.ipynb) provides a colleaction of applications of quantum algorithms to use cases relevant in finance.\n", "This includes use cases like portfolio management, derivative pricing, or credit risk analysis.\n", "\n", + "#### 1.10 Qiskit Optimization\n", + "[Qiskit Optimization](qiskit/optimization/index.ipynb) - using variational quantum eigensolver to experiment with optimization problems (max-cut and traveling salesman problem) on a quantum computer\n", + "\n", "\n", "### 2. Community Notebooks\n", "\n", @@ -115,7 +120,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "metadata": { "scrolled": false }, @@ -225,6 +230,13 @@ "This project is licensed under the Apache License 2.0 - see the [LICENSE](https://github.com/Qiskit/qiskit-tutorials/blob/master/LICENSE) file for details." ] }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, { "cell_type": "code", "execution_count": null, @@ -250,7 +262,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.3" + "version": "3.6.1" } }, "nbformat": 4, From a7e9348fa16f599dea9a17c102d7cf5f00a69eb9 Mon Sep 17 00:00:00 2001 From: woodsp Date: Wed, 1 May 2019 20:22:52 -0400 Subject: [PATCH 105/116] Update section numbers for Aqua domains --- index.ipynb | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/index.ipynb b/index.ipynb index ebd822002..b5831dc92 100644 --- a/index.ipynb +++ b/index.ipynb @@ -77,17 +77,17 @@ "#### 1.6 Qiskit Aqua\n", "Aqua, the ‘water’ element, is the element of life. To make quantum computing live up to its expectations, we need to find real-world applications. Aqua is where algorithms for NISQ computers are built. These algorithms can be used to build applications for quantum computing. Aqua is accessible to domain experts in `chemistry`, `optimization`, `AI` or `finance`, who want to explore the benefits of using quantum computers as accelerators for specific computational tasks, without needing to worry about how to translate the problem into the language of quantum machines. \n", "\n", - "#### 1.7 Qiskit AI \n", + "#### 1.6.1 Qiskit AI \n", "[Qiskit AI](qiskit/artificial_intelligence/index.ipynb) - using quantum-enhanced support vector machine to experiment with classification problems on a quantum computer\n", "\n", - "#### 1.8 Qiskit Chemistry \n", + "#### 1.6.2 Qiskit Chemistry \n", "[Qiskit Chemistry](qiskit/chemistry/index.ipynb) - using variational quantum eigensolver to experiment with molecular ground-state energy on a quantum computer\n", "\n", - "#### 1.9 Qiskit Finance\n", + "#### 1.6.3 Qiskit Finance\n", "[Qiskit Finance](qiskit/finance/index.ipynb) provides a colleaction of applications of quantum algorithms to use cases relevant in finance.\n", "This includes use cases like portfolio management, derivative pricing, or credit risk analysis.\n", "\n", - "#### 1.10 Qiskit Optimization\n", + "#### 1.6.4 Qiskit Optimization\n", "[Qiskit Optimization](qiskit/optimization/index.ipynb) - using variational quantum eigensolver to experiment with optimization problems (max-cut and traveling salesman problem) on a quantum computer\n", "\n", "\n", From 48b61a72dea37524922334c0f16639bd1aecedbb Mon Sep 17 00:00:00 2001 From: woodsp Date: Wed, 1 May 2019 20:33:26 -0400 Subject: [PATCH 106/116] Re-ran notebook to remove old warning --- .../LiH_with_qubit_tapering_and_uccsd.ipynb | 40 ++++++++++--------- 1 file changed, 21 insertions(+), 19 deletions(-) diff --git a/community/chemistry/LiH_with_qubit_tapering_and_uccsd.ipynb b/community/chemistry/LiH_with_qubit_tapering_and_uccsd.ipynb index ddb7c9f28..4bc113cd5 100644 --- a/community/chemistry/LiH_with_qubit_tapering_and_uccsd.ipynb +++ b/community/chemistry/LiH_with_qubit_tapering_and_uccsd.ipynb @@ -1,19 +1,21 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## _*Tapering an Operator*_\n", + "\n", + "This notebook demonstrates how symmetries can be taken advantage of to reduce the size (number of qubits needed) for an Operator when using Qiskit Chemistry.\n", + "\n", + "This notebook has been written to use the PYSCF chemistry driver." + ] + }, { "cell_type": "code", "execution_count": 1, "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/Users/manoel/Documents/Quantum/qiskit-terra/qiskit/tools/qcvv/__init__.py:13: DeprecationWarning: The qiskit.tools.qcvv package is deprecated. Please use qiskit-ignis available on PIP for similar functionality and more.\n", - " 'functionality and more.', DeprecationWarning)\n" - ] - } - ], + "outputs": [], "source": [ "# import common packages\n", "import itertools\n", @@ -38,7 +40,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ @@ -50,7 +52,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -80,7 +82,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -127,7 +129,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 6, "metadata": {}, "outputs": [ { @@ -158,7 +160,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 7, "metadata": { "scrolled": true }, @@ -194,7 +196,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 8, "metadata": {}, "outputs": [ { @@ -235,7 +237,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 9, "metadata": {}, "outputs": [], "source": [ @@ -266,7 +268,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 10, "metadata": {}, "outputs": [], "source": [ @@ -275,7 +277,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 11, "metadata": {}, "outputs": [ { From ade33230d03d11d6281e0edd6fcbb3f8c99756c3 Mon Sep 17 00:00:00 2001 From: Shaohan Hu Date: Wed, 1 May 2019 23:05:25 -0400 Subject: [PATCH 107/116] add notebook for vqc comparing feature maps --- .../vqc_feature_map_comparison.ipynb | 178 ++++++++++++++++++ 1 file changed, 178 insertions(+) create mode 100644 community/artificial_intelligence/vqc_feature_map_comparison.ipynb diff --git a/community/artificial_intelligence/vqc_feature_map_comparison.ipynb b/community/artificial_intelligence/vqc_feature_map_comparison.ipynb new file mode 100644 index 000000000..9d8ba3baa --- /dev/null +++ b/community/artificial_intelligence/vqc_feature_map_comparison.ipynb @@ -0,0 +1,178 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Variational Quantum Classifier Feature Map Comparison\n", + "\n", + "Both the first-order and second-order expansion feature maps provided by Aqua use $n$ qubits to encode $n$-dim datapoints. However, raw feature vectors can also be directly used in `VQC` circuit constructions, requiring only $log_2(n)$ qubits to encode $n$-dim datapoints. \n", + "\n", + "### Experiment\n", + "Below we compare the classification performance of `VQC` on the [Wine dataset](https://scikit-learn.org/stable/datasets/index.html#wine-dataset) using `RawFeatureVector` and `SecondOrderExpansion` feature maps. As you'll see, the former leads to about $90\\%$ accuracy using only $2$ qubits, whereas the latter achieves only around $50\\%$ accuracy, using $4$ qubits and taking $3\\times$ as long. \n", + "\n", + "We first prepare the Wine dataset:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from sklearn import datasets\n", + "from sklearn.model_selection import train_test_split\n", + "from sklearn.preprocessing import StandardScaler, MinMaxScaler\n", + "from sklearn.decomposition import PCA\n", + "\n", + "\n", + "def Wine(training_size, test_size, n):\n", + " class_labels = [r'A', r'B', r'C']\n", + "\n", + " data, target = datasets.load_wine(True)\n", + " sample_train, sample_test, label_train, label_test = train_test_split(\n", + " data, target, test_size=test_size, random_state=7\n", + " )\n", + "\n", + " # Now we standarize for gaussian around 0 with unit variance\n", + " std_scale = StandardScaler().fit(sample_train)\n", + " sample_train = std_scale.transform(sample_train)\n", + " sample_test = std_scale.transform(sample_test)\n", + "\n", + " # Now reduce number of features to number of qubits\n", + " pca = PCA(n_components=n).fit(sample_train)\n", + " sample_train = pca.transform(sample_train)\n", + " sample_test = pca.transform(sample_test)\n", + "\n", + " # Scale to the range (-1,+1)\n", + " samples = np.append(sample_train, sample_test, axis=0)\n", + " minmax_scale = MinMaxScaler((-1, 1)).fit(samples)\n", + " sample_train = minmax_scale.transform(sample_train)\n", + " sample_test = minmax_scale.transform(sample_test)\n", + " # Pick training size number of samples from each distro\n", + " training_input = {key: (sample_train[label_train == k, :])[:training_size] for k, key in enumerate(class_labels)}\n", + " test_input = {key: (sample_train[label_train == k, :])[training_size:(\n", + " training_size+test_size)] for k, key in enumerate(class_labels)}\n", + " return sample_train, training_input, test_input, class_labels" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can then set up the experiment as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import scipy\n", + "\n", + "from qiskit import BasicAer\n", + "from qiskit.aqua.input import ClassificationInput\n", + "from qiskit.aqua import run_algorithm, QuantumInstance, aqua_globals\n", + "from qiskit.aqua.components.optimizers import SPSA, COBYLA\n", + "\n", + "feature_dim = 4 # dimension of each data point\n", + "training_dataset_size = 20\n", + "testing_dataset_size = 10\n", + "random_seed = 10598\n", + "np.random.seed(random_seed)\n", + "\n", + "sample_Total, training_input, test_input, class_labels = Wine(\n", + " training_size=training_dataset_size,\n", + " test_size=testing_dataset_size,\n", + " n=feature_dim\n", + ")\n", + "\n", + "classification_input = ClassificationInput(training_input, test_input)\n", + "params = {\n", + " 'problem': {'name': 'classification', 'random_seed': random_seed},\n", + " 'algorithm': {'name': 'VQC'},\n", + " 'backend': {'provider': 'qiskit.BasicAer', 'name': 'statevector_simulator'},\n", + " 'optimizer': {'name': 'COBYLA', 'maxiter':200},\n", + " 'variational_form': {'name': 'RYRZ', 'depth': 3},\n", + " 'feature_map': {'name': None},\n", + "}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's try `RawFeatureVector` first:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "VQC accuracy with RawFeatureVector: 0.8666666666666667\n" + ] + } + ], + "source": [ + "params['feature_map']['name'] = 'RawFeatureVector'\n", + "result = run_algorithm(params, classification_input)\n", + "print(\"VQC accuracy with RawFeatureVector: \", result['testing_accuracy'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's try `SecondOrderExpansion`:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Test accuracy with SecondOrderExpansion: 0.5333333333333333\n" + ] + } + ], + "source": [ + "params['feature_map']['name'] = 'SecondOrderExpansion'\n", + "result = run_algorithm(params, classification_input)\n", + "print(\"Test accuracy with SecondOrderExpansion: \", result['testing_accuracy'])" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From 2032cd4465e2e215da5edaa8c71cf9110b2308f2 Mon Sep 17 00:00:00 2001 From: CZ Date: Thu, 2 May 2019 10:58:13 +0200 Subject: [PATCH 108/116] Update the notebbooks --- ...ans_for_loading_random_distributions.ipynb | 12235 +--------------- .../qgan_option_pricing.ipynb | 144 +- 2 files changed, 134 insertions(+), 12245 deletions(-) diff --git a/qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb b/qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb index 5a7e12ff6..3889f56a8 100644 --- a/qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb +++ b/qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb @@ -31,16 +31,9 @@ "metadata": {}, "outputs": [], "source": [ - "#!/usr/bin/env python\n", - "# coding: utf-8\n", - "from __future__ import absolute_import, division, print_function\n", - "\n", "import numpy as np\n", "\n", - "import matplotlib\n", - "matplotlib.use('TkAgg')\n", "import matplotlib.pyplot as plt\n", - "\n", "%matplotlib inline\n", "\n", "\n", @@ -108,7 +101,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ @@ -158,12229 +151,21 @@ "and\n", "$$ L_D\\left(\\phi, \\theta\\right) =\n", "\t\\frac{1}{m}\\sum\\limits_{l=1}^{m}\\left[\\log D_{\\phi}\\left(x^{l}\\right) + \\log\\left(1-D_{\\phi}\\left(g^{l}\\right)\\right)\\right], $$\n", - "with $m$ denoting the batch size and $g^l$ describing the data samples generated by the quantum generator." + "with $m$ denoting the batch size and $g^l$ describing the data samples generated by the quantum generator.\n", + "\n", + "Please not that the training will take a while ($\\sim 60$ min)." ] }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Epoch 1/3000...\n", - "Loss Discriminator: 0.6948\n", - "Loss Generator: 0.6307\n", - "Relative 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- "Epoch 1939/3000...\n", - "Loss Discriminator: 0.6808\n", - "Loss Generator: 0.714\n", - "Relative Entropy: 0.0887\n", - "Epoch 1940/3000...\n", - "Loss Discriminator: 0.6803\n", - "Loss Generator: 0.7123\n", - "Relative Entropy: 0.0886\n", - "Epoch 1941/3000...\n", - "Loss Discriminator: 0.6796\n", - "Loss Generator: 0.7103\n", - "Relative Entropy: 0.0886\n", - "Epoch 1942/3000...\n", - "Loss Discriminator: 0.681\n", - "Loss Generator: 0.7125\n", - "Relative Entropy: 0.0885\n", - "Epoch 1943/3000...\n", - "Loss Discriminator: 0.6794\n", - "Loss Generator: 0.7114\n", - "Relative Entropy: 0.0885\n", - "Epoch 1944/3000...\n", - "Loss Discriminator: 0.68\n", - "Loss Generator: 0.7134\n", - "Relative Entropy: 0.0884\n", - "Epoch 1945/3000...\n", - "Loss Discriminator: 0.6805\n", - "Loss Generator: 0.7121\n", - "Relative Entropy: 0.0884\n", - "Epoch 1946/3000...\n", - "Loss Discriminator: 0.6816\n", - "Loss Generator: 0.713\n", - "Relative Entropy: 0.0883\n", - "Epoch 1947/3000...\n", - 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0.6819\n", - "Loss Generator: 0.7118\n", - "Relative Entropy: 0.0879\n", - "Epoch 1956/3000...\n", - "Loss Discriminator: 0.6798\n", - "Loss Generator: 0.7125\n", - "Relative Entropy: 0.0879\n", - "Epoch 1957/3000...\n", - "Loss Discriminator: 0.6813\n", - "Loss Generator: 0.7129\n", - "Relative Entropy: 0.0878\n", - "Epoch 1958/3000...\n", - "Loss Discriminator: 0.6806\n", - "Loss Generator: 0.7142\n", - "Relative Entropy: 0.0878\n", - "Epoch 1959/3000...\n", - "Loss Discriminator: 0.6829\n", - "Loss Generator: 0.7145\n", - "Relative Entropy: 0.0877\n", - "Epoch 1960/3000...\n", - "Loss Discriminator: 0.6815\n", - "Loss Generator: 0.7096\n", - "Relative Entropy: 0.0877\n", - "Epoch 1961/3000...\n", - "Loss Discriminator: 0.6794\n", - "Loss Generator: 0.7092\n", - "Relative Entropy: 0.0876\n", - "Epoch 1962/3000...\n", - "Loss Discriminator: 0.6823\n", - "Loss Generator: 0.7116\n", - "Relative Entropy: 0.0876\n", - "Epoch 1963/3000...\n", - "Loss Discriminator: 0.6816\n", - "Loss 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- "text": [ - "Epoch 2394/3000...\n", - "Loss Discriminator: 0.6849\n", - "Loss Generator: 0.7068\n", - "Relative Entropy: 0.0686\n", - "Epoch 2395/3000...\n", - "Loss Discriminator: 0.6848\n", - "Loss Generator: 0.7055\n", - "Relative Entropy: 0.0686\n", - "Epoch 2396/3000...\n", - "Loss Discriminator: 0.6841\n", - "Loss Generator: 0.707\n", - "Relative Entropy: 0.0685\n", - "Epoch 2397/3000...\n", - "Loss Discriminator: 0.6855\n", - "Loss Generator: 0.7068\n", - "Relative Entropy: 0.0685\n", - "Epoch 2398/3000...\n", - "Loss Discriminator: 0.6854\n", - "Loss Generator: 0.709\n", - "Relative Entropy: 0.0685\n", - "Epoch 2399/3000...\n", - "Loss Discriminator: 0.6838\n", - "Loss Generator: 0.7099\n", - "Relative Entropy: 0.0684\n", - "Epoch 2400/3000...\n", - "Loss Discriminator: 0.686\n", - "Loss Generator: 0.7091\n", - "Relative Entropy: 0.0684\n", - "Epoch 2401/3000...\n", - "Loss Discriminator: 0.6856\n", - "Loss Generator: 0.704\n", - "Relative Entropy: 0.0683\n", - "Epoch 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Discriminator: 0.6869\n", - "Loss Generator: 0.7026\n", - "Relative Entropy: 0.0472\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Epoch 2989/3000...\n", - "Loss Discriminator: 0.6856\n", - "Loss Generator: 0.7031\n", - "Relative Entropy: 0.0472\n", - "Epoch 2990/3000...\n", - "Loss Discriminator: 0.687\n", - "Loss Generator: 0.7028\n", - "Relative Entropy: 0.0471\n", - "Epoch 2991/3000...\n", - "Loss Discriminator: 0.6886\n", - "Loss Generator: 0.7016\n", - "Relative Entropy: 0.0471\n", - "Epoch 2992/3000...\n", - "Loss Discriminator: 0.6886\n", - "Loss Generator: 0.7015\n", - "Relative Entropy: 0.0471\n", - "Epoch 2993/3000...\n", - "Loss Discriminator: 0.6869\n", - "Loss Generator: 0.6996\n", - "Relative Entropy: 0.047\n", - "Epoch 2994/3000...\n", - "Loss Discriminator: 0.6872\n", - "Loss Generator: 0.7028\n", - "Relative Entropy: 0.047\n", - "Epoch 2995/3000...\n", - "Loss Discriminator: 0.6862\n", - "Loss Generator: 0.7063\n", - "Relative Entropy: 0.047\n", - "Epoch 2996/3000...\n", - "Loss Discriminator: 0.6877\n", - "Loss Generator: 0.703\n", - "Relative Entropy: 0.0469\n", - "Epoch 2997/3000...\n", - "Loss Discriminator: 0.6885\n", - "Loss Generator: 0.7009\n", - "Relative Entropy: 0.0469\n", - "Epoch 2998/3000...\n", - "Loss Discriminator: 0.6876\n", - "Loss Generator: 0.7018\n", - "Relative Entropy: 0.0469\n", - "Epoch 2999/3000...\n", - "Loss Discriminator: 0.6873\n", - "Loss Generator: 0.7022\n", - "Relative Entropy: 0.0468\n", - "Epoch 3000/3000...\n", - "Loss Discriminator: 0.6857\n", - "Loss Generator: 0.7017\n", - "Relative Entropy: 0.0468\n", - "qGAN training runtime: 61.47158089876175 min\n" + "qGAN training runtime: 38.464039981365204 min\n" ] } ], @@ -12404,12 +189,12 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 5, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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C/Sea2SwzKzazIeX2HWRmb5jZfDObZ2adYxlrOigpCUZMnXZaHlu2KGGISPRilizMLBN4HDgd6AUMN7Ne5aqtBEYA/6jgJZ4B7nf3Q4F+wLpYxZoOSkqcSy5ZwT/+sZH339+m6c1FpEZieWTRD8hz96XuXgSMAwZHVnD35e4+G9jrZoAwqTRw96lhvQJ33x7DWFPevfd+ybPP7pne/MMPt/HTn2p6cxGJTiyTRXtgVcR2flgWjZ7AJjN7ycw+MbP7wyMVqaWrrmpH//5NyrYPOqgh998f7cchIunO3D02Lxxcgxjk7j8Nt38C9Hf3URXUHQu86u4TIto+CRxJcKrqBWCyuz9Zrt1IYCRATk5On3HjxtU63oKCApo1a1br9omiqn5s2wa//nUT1q3L4OGHt9G+fWw++7qSKp8JqC+JKFX6AfvWl4EDB850977V1Yvl0NnVQMeI7Q5hWTTygU/dfSmAmf0HOJoggZRx99HAaIC+ffv6gAEDah1sbm4u+9I+UVTXjxNPLGH9+mK6dEn8ezBS5TMB9SURpUo/oH76EsvTUNOBHmbWxcwaAsOAiTVo29LM2oXbJwHzYhBj2mnePDMpEoWIJJaYJQt3LwZGAVOA+cB4d59rZnea2dkAZnaUmeUDQ4EnzGxu2LYE+CXwlpl9Dhjwt1jFKoFdu5yf/3wlixYVxjsUEUkwMb2D290nA5PLld0a8Xw6wempitpOBXrHMj7Zo6TEueii5Ywbt5F//3sTU6f24IgjGsc7LBFJELqDWygtdUaOXMm4cRsB+PLLYgYMWMSsWRqtLCIBJQvBHTLK/Sa0bJlJTo6mDhORgJKFkJlpPPHEQfziF8F4gg4dsnjrrR60b6/pzUUkoD8dBYCMDOOPf+zA/vtncd55LencWSOmRGQPJQspY2bcdNP+8Q5DRBKQTkNJ1AoLS3n55U3xDkNE4kDJQqJSXOwMG7aMc85Zyt13ryVW08SISGJSspBqlZY6l1++gpdf3gzAb37zBb/61WolDJE0omQh1Zo3r7DsHozdXnttC1u3llbSQkRSjZKFVOvwwxszZUp3WrQIfl06dWrIG290p0ULzRovki6ULCQqJ57YnNzcnhxxRDZTp3bXPRgiaUZDZyVqRx7ZhE8/PZSMDIt3KCJSz3RkITVSVaLYtq2E1auL6jEaEakvShZSJ4qKShkyZBnHHLOQBQs0xblIqlGykH1WUuJcfPEKXn99C6tW7eKEExbx0Ufb4h2WiNShapOFmZ1lZkoqUqmxYzfsNbR2/fpibrpJ92GIpJJoksAFwGIzu8/MDol1QJJ8Roxow09/2qZsu0ePRrzwQhfMdCFcJFVUOxrK3X9sZi2A4cBYM3PgKeCf7r411gFK4svMNEaPPoicnCzGjFnP6693p127rHiHJSJ1KKrTS+6+BZgAjAMOAM4FZpnZ1TGMTZKImXHXXQcyZ04vunbV9OYiqSaaaxZnm9m/gVwgC+jn7qcD3wb+L7bhSbJp27byg9VNm4rZsUNThIgko2huyjsPeNjd34ksdPftZnZZbMKSVLNjRylnnbUEd5g4sRutW+t+UJFkUu2RhbtfDCwKjzDOMrP9I/a9FdPoJCWUlDgXXriM997bxvvvb+P44xexcqVu3hNJJtGchroM+Bj4ITAE+NDMLo11YJI67rlnLf/+9+ay7fnzC7nhhtVxjEhEaiqaC9w3AEe6+4jwKKMP8OtoXtzMBpnZQjPLM7MbK9h/opnNMrNiMxtSwf4WZpZvZo9F836SmK68sh0nnNCsbPuww7L5y186xjEiEampaJLFBiByiOzWsKxKZpYJPA6cDvQChptZr3LVVgIjgH9U8jK/A96pZJ8kiVatGvDGG90577yWdOiQxeuvd6dVK12zEEkm0fyPzQM+MrOXAQcGA7PN7HoAd3+oknb9gDx3XwpgZuPCtvN2V3D35eG+bwyRMbM+QA7wOtA3yv5IgsrOzuCFF7qwZs0uOnTQ9OYiySaaI4slwH8IEgXAy8AyoHn4qEx7YFXEdn5YVq1wepEHgV9GU1+SQ2amVZkovvpqF0VFGlorkoiiuYP7DgAzaxZuF8Q6KOBKYLK751c1ZYSZjQRGAuTk5JCbm1vrNywoKNin9okiWfuxfTtcc01Tmjd37rhjO82bJ29fKqK+JJ5U6QfUU1/cvcoHcDjwCbAifMwEDoui3THAlIjtm4CbKqk7FhgSsf08wfWM5cB6YAtwT1Xv16dPH98X06ZN26f2iSIZ+7FrV6mfccZih5kOM/2QQ+b40qWFSdmXyqgviSdV+uG+b30BZng13+fuHtVpqNHA9e7eyd07Edy1/bco2k0HephZFzNrCAwDJkbRDne/0N0PcvfOBKeinnH3b4ymktTw+9+vZfLkLWXbCxbs5M4718QxIhEpL5pk0dTdp+3ecPdcoGl1jdy9GBgFTAHmA+Pdfa6Z3WlmZwOY2VFmlg8MBZ4ws7m16IMkuauuasdxx+35lerTpwmPPaahtSKJJJrRUEvN7LfAs+H2j4Gl0by4u08GJpcruzXi+XSgQzWvMZbgNJWkqLZtG/Dmmz245JIV/O9/23jllW40bZoZ77BEJEI0yeJS4A7gJYIRUe+GZSJ1Jjs7g+ef78zatbs44ABNby6SaKpMFuGNdTe7+y/qKR5JYxkZxoEHVj60dtmynbRsmakb+kTioMprFu5eAhxfT7GIVGrjxmIGDcrj6KMXsmhRYbzDEUk70fyJ9omZTQT+BWzbXejuL8UsKpEIu3Y5Q4cuY9GinQAcffRCJkzoykknVXVPqIjUpWiSRTbBXFAnRZQ5wTUMkZj705/W8dZbe6Yn27ixhOee+1rJQqQeRZMsxrj7+5EFZnZcjOIR+YarrmrHZ5/t4Jlnvgbg2GObatZakXoWzX0Wf4qyTCQmGjXKYOzYTtxzz4F06dKQf/+7K40aRbV8vIjUkUqPLMzsGOBYoN3uGWZDLQANgpd6ZWb8+tf7M2pUO92DIRIHVf151hBoRpBQmkc8thCsmCdS76pKFJ9+up1p07ZWul9Eaq/SIwt3fxt428zGuvuKeoxJpMa++moXgwcvZfXqIh56qANXX92OqmYsFpGaieYCdyMzGw10jqzv7idV2kKkHu3a5QwZsoyVK4sAuOaafD75ZDtjxnQiM1MJQ6QuRJMs/gX8FRgDlMQ2HJGa++9/t/Luu3svs9K8eaYShUgdiiZZFLv7X2IeiUgtnXZaC15+uSsXXricrVtLGTiwGQ8+WOX8lCJSQ9GMP3zFzK40swPMrPXuR8wjE6mBs85qyUcfHcyppzZn/PiuZGXpqEKkLkVzZHFx+O+vIsoc6Fr34YjU3qGHNmbKlB7xDkMkJVV7ZOHuXSp4KFFI0vn4422cdtpi1q3bFe9QRJJOtcnCzJqY2S3hiCjMrIeZnRn70ETqzpo1uzj33KW88cZWjjpqIZ98sj3eIYkklWiuWTwFFBHczQ2wGrgrZhGJ1LGdO0s577ylfPFFcESxcmURxx23kFWriuIcmUjyiCZZdHP3+4BdAO6+HdDVQ0ka27eXkp2996/sqFHt6Nix8oWWRGRv0SSLIjNrTHBRGzPrBuyMaVQidahVqwZMmdKDq69uB8Cppzbn7rvbxzkqkeQSzWio24DXgY5m9jxwHDAilkGJ1LWsLOPRRzty7LFNOfXUFrphT6SGqk0W7j7VzGYBRxOcfrrG3dfHPDKRGBg2rOpbhFas2EmnTo3qKRqR5BHVogDuvsHdJ7n7q0oUkqree6+Anj3n8dvffkFpqcc7HJGEEtMVZMxskJktNLM8M7uxgv0nmtksMys2syER5d8xsw/MbK6ZzTazC2IZp0h+fhFDhiylqMi56661DB68hM2bNRWayG4xSxZmlgk8DpwO9AKGm1mvctVWElz/+Ee58u3ARe5+GDAI+KOZtYxVrJLe3J0LLljGl18Wl5W9+uoW3nuvoIpWIuklqmRhZseb2SXh83Zm1iWKZv2APHdf6u5FwDhgcGQFd1/u7rOB0nLli9x9cfj8C2Ad0C6aWEVqysy499725OTsuYR3yy3784Mf7BfHqEQSSzR3cN8G/Bq4KSzKAp6L4rXbA6sitvPDshoxs34Eq/YtqWlbkWgdf3wzZsw4hL59m3DmmS24444D4h2SSEIx96ov5JnZp8CRwCx3PzIsm+3uvatpNwQY5O4/Dbd/AvR391EV1B0LvOruE8qVHwDkAhe7+4cVtBsJjATIycnpM27cuCr7UpWCggKaNWtW6/aJIlX6AfHpy86dUFwMTZvW7evqc0k8qdIP2Le+DBw4cKa7962uXjT3WRS5u5vZ7pvyov1vtBroGLHdISyLipm1ACYBN1eUKADcfTQwGqBv374+YMCAaF/+G3Jzc9mX9okiVfoBidmXqVO30L9/U1q0qHwt8IokYl9qK1X6kir9gPrpSzTXLMab2RNASzO7HHgT+FsU7aYDPcysi5k1BIYBE6MJKqz/b+CZ8kcbIvHyzjtb+cEPlnD88QvLlnAVSRfRTFH+ADABeBE4GLjV3f8URbtiYBQwBZgPjHf3uWZ2p5mdDWBmR5lZPjAUeMLM5obNzwdOBEaY2afh4zu16J9InVi8uJBzz13Krl3O558X0r//AmbM2BbvsETqTbWnoczseuAFd59a0xd398nA5HJlt0Y8n05weqp8u+eI7iK6SL249dY1fP31nvsu1q4tZvHinfTtW8cXN0QSVDSnoZoDb5jZu2Y2ysxyYh2USKIZM+Ygzj13z1DaO+88gOHDtbqwpI9o5oa6A7jDzHoDFwBvm1m+u58S8+hEEkTTpplMmNCVG29czZdfFnPLLfvHOySRehXNaKjd1gFrgQ3At2ITjkjiysgw7ruvA6WljplmrZX0Es1NeVeaWS7wFtAGuLy6eyxEUllGRuWJYvz4jSxfruVeJPVEc2TREbjW3T+NdTAiyeyNN7bwox8to02bBkyc2I3+/XXxW1JHpUcW4U1xAPcDK82sdeSjfsITSQ5z5uxg6NCllJTAunXFDBiwiH/9a2O8wxKpM1UdWfwDOBOYSbCkauSxtwNdYxiXSFIZM2Y9W7bsmQ9z506nceOYrgAgUq8qTRbufmb4bzQzzIqktYce6kDjxhncc8+XADzwQHvOPFOz1krqiOamvLfc/eTqykTSWUaGcffd7Tn44GymT9/GdddpwKCklkqThZllA02AtmbWij2noVpQi6nGRdLBiBFtGDGiTbzDEKlzVR1ZXAFcCxxIcN1id7LYAjwW47hEUtKjj66jc+eGnH22Fn6U5FLVNYtHgEfM7OpoJg4UkapNnLiJa6/NB+Dee9vzy19+Szf3SdKIZrqPP5nZ4QTraGdHlD8Ty8BEUkleXgbXXruc3WuN3XDDavLzi3jkkY5VNxRJENFc4L4NGECQLCYDpwPvAUoWIlFasiSTwsI9Q2szM+HsszVaSpJHNAPBhwAnA2vd/RLg24B+y0Vq4LTTdvHaa93Zb79ghb1HH+3IySe3qKaVSOKIZrqPHe5eambF4V3d69h7uVQRicL3v9+Cjz46mAkTNnLlle3iHY5IjUSTLGaYWUuCpVRnAgXABzGNSiRFHXxwNjfffECl+0tLg4saVU1WKBIP0VzgvjJ8+lczex1o4e6zYxuWSHq64441zJtXyNixnWjaNDPe4YiUqeqmvO9Wtc/dZ8UmJJH0NH78Ru68cy0AS5bs5OWXu9GxY8M4RyUSqOrI4sEq9jlwUh3HIpK2Zs3azogRy8u2P/lkB2eeuYRPPjlEp6QkIVR1U97A+gxEJJ21bp1J9+6N+PzzQgCysow//7mjEoUkjGhWymtiZreY2ehwu4eZnRn70ETSR+fOjXj//YMZPDgYlf7Xv3bkuOOaxTkqkT2iuc/iKaAIODbcXg3cFbOIRNJU8+aZvPRSVyZN6sall7aNdzgie4kmWXRz9/uAXQDuvp29F0ISkTqSkWGccUbl97wWFzt5eYX1GJFIIJpkUWRmjQkuamNm3YCoVqQ3s0FmttDM8szsxgr2n2hms8Ib/oaU23exmS0OHxdH834iqe6GG1Zz5JELeOklLdkq9SuaZHEb8DrQ0cyeB94CbqiukZllAo8TzCXVCxhuZr3KVVsJjCDKXYDqAAAXDUlEQVRYwjWybevwffsD/YDbwjU1RNLWc89t4OGH11FQUMp55y3jt7/9ouwmPpFYqzJZWDB/8gLghwRf6v8E+rp7bhSv3Q/Ic/el7l4EjAMGR1Zw9+XhDX6l5dqeBkx196/dfSMwFRgUxXuKpKTly3dy+eUr9yp7+ukNbNxYEqeIJN1UmSzc3YHJ7r7B3Se5+6vuvj7K124PrIrYzif6Ffb2pa1IyunUqSEPPtiBBuFg90aNjJde6kqbNtHM2COy76L5TZtlZke5+/SYR1NDZjYSGAmQk5NDbm5urV+roKBgn9onilTpB6gv5fXqBQ89lMlttzXmiit2UlAwnXj8eFLlc0mVfkD99CWaZNEfuNDMVgDbCEZCubv3rqbdavaenbZDWBaN1QRraES2zS1fyd1HA6MB+vbt6wMGDChfJWq5ubnsS/tEkSr9APWlIgMGwEUXlZRNdR4PqfK5pEo/oH76Es0F7tOAbgTTe5wFnBn+W53pQA8z62JmDYFhwMQo45oCnGpmrcIL26eGZSJpr6pEUVRUyi23fMHmzbqWIXWr2mTh7isqekTRrhgYRfAlPx8Y7+5zzexOMzsbwMyOMrN8YCjwhJnNDdt+DfyOIOFMB+4My0SkCtddl8/vf7+W/v0XMH/+jniHIykkplfH3H0ywVKskWW3RjyfTnCKqaK2fwf+Hsv4RFLJk0+u589/DsafLFy4k379FjJpUjdOPLF5nCOTVBDNaSgRSXClpc5TT23YqywnJ4vevRvHKSJJNUoWIikgI8OYOrUHF1/cGoDGjY0XX+xCy5YaWit1Q79JIimiceMMnnqqE8cc05QmTTL49rebxDskSSFKFiIpxMy44op2VdbZtKmY/fbLJJigQSQ6Og0lkkYKC0s55ZQ8hg5dxpYtGl4r0VOyEEkjV1+9ipkzt/Pii5vo128Bc+dqeK1ER8lCJE2MHbuBMWP2jJhauHAnd9+9No4RSTJRshBJEyee2IzvfGfPUNoePRrx+OMHxTEiSSZKFiJpomvXRvzvfwdzySVtaNIkg5de6hrXOaYkuShZiKSRxo0zePLJg5g9+1AOP1w37En0lCxE0oyZ0a1bo0r3L1xYyA035FNUVH5NMklnShYiUmbHjlLOP38Z99+/jhNOWMTy5TvjHZIkCCULESnzi1+sYvbsYDjtxx9v58gjFyhhCKBkISKhr78uZurUrXuVDRrUgk6dGsYpIkkkShYiAkDr1g2YNesQzj57PyAYWvvEEwdpWhABNDeUiERo3boB//lPVx5+eB0nn9ycFi00tFYCOrIQkb2YGddfn1PlrLX/+18BhYUaLZVOlCxEpEZWrMjglFMWc/TRC1mwoDDe4Ug9UbIQkagVFpZy552N2bHD+eyzHfTps4BnntlQfUNJekoWIhK1u+9ey9Kle65jbN9eSqnORqUFJQsRidr11+cwcOCusu3hw1uVLeUqqU3JQkSitt9+mfz2tzt48smDOPzwbP7yFw2tTRdKFiJSI2Zw6aVt+fTTQyudtdbd+frr4nqOTGIppsnCzAaZ2UIzyzOzGyvY38jMXgj3f2RmncPyLDN72sw+N7P5ZnZTLOMUkZrLzKz8iOLpp7+mZ8+5vPLKpnqMSGIpZsnCzDKBx4HTgV7AcDPrVa7aZcBGd+8OPAzcG5YPBRq5+xFAH+CK3YlERBLbwoWFjBq1ig0bSjj77KVceeVKtm/XVfBkF8sji35AnrsvdfciYBwwuFydwcDT4fMJwMkWnAB1oKmZNQAaA0XAlhjGKiJ1YOfOUoYPX8a2bXuSwzPPfM2aNbuqaCXJIJbJoj2wKmI7PyyrsI67FwObgTYEiWMbsAZYCTzg7l/HMFYRqQMNGhhDhrQiM+JSxiOPdKhy/QxJDok6N1Q/oAQ4EGgFvGtmb7r70shKZjYSGAmQk5NDbm5urd+woKBgn9onilTpB6gviaq6vhx7LDz6aCZ/+EM2XbqU0rXrHBKx6+n0mdQJd4/JAzgGmBKxfRNwU7k6U4BjwucNgPWAEVzr+ElEvb8D51f1fn369PF9MW3atH1qnyhSpR/u6kuiirYvW7cW+4YNuyrdX1hY4qWlpXUUVc2l42dSEWCGR/GdHsvTUNOBHmbWxcwaAsOAieXqTAQuDp8PAf4bBr8SOAnAzJoCRwMLYhiriNSxZs0yad264pMX7s5FFy1n6NBlbNigIbbJIGbJwoNrEKMIjh7mA+Pdfa6Z3WlmZ4fVngTamFkecD2we3jt40AzM5tLkHSecvfZsYpVROrX889/zfjxm3jxxU0cccR83nhD41cSXUyvWbj7ZGByubJbI54XEgyTLd+uoKJyEUl+K1bs5Kqr9ox9WbNmFzfeuJpTTmlORobuBk9UuoNbROrVrl1Ojx7ZZdvZ2cZzz3VWokhwShYiUq+6d8/mf//ryc03709GBtx3X3t69Woc77CkGok6dFZEUljDhhncddeBDB3akiOOqDxRFBaWkp2tv2kTgT4FEYmbb3+7SaWnnzZvLuGww+Zxxx1r2LXL6zkyKU/JQkQS0nXX5bN0aRG3376Go49ewJw5O+IdUlpTshCRhPPqq5t56qk9y7XOmrWD557TjD/xpGQhIgmnQQPIydlzSbVXr2xuv/2AOEYkShYiknAGDdqPOXN6cf75LcnMhGee6awL3XGm0VAikpDatm3ACy90Zd68HVUOrV27dhf7759Vj5GlJ6VqEUloVSWKd98toFOnOdx66xfs3KkFlmJJyUJEktKOHaVcdtkKioqc3/1uLd/97gJmzNgW77BSlpKFiCSl229fw+LFO8u2580rZOtWHV3EipKFiCSlY45pyv7777nsesUVbRk4sHkcI0ptShYikpTOOacl8+b1YsSI1nTokMV995VftVnqkpKFiCStVq0a8NRTnZk9+1BatMissE5hYSkTJ27aveqm1JKShYgkvVatKr8L4O671zJ48FLOOmsJK1bsrLSeVE3JQkRS1vz5O7j77i8BmDRpC4cdNp8339SqfLWhZCEiKevqq/P3mrG2WbMM+vRpEseIkpeShYikrEce6cBxxzXda7uqU1ZSOf3URCRlHXZYY955pydjxmzg7be3cv75reIdUtLSkYWIpLSMDGPkyLY8/3wXzCpeaGnhwkIuuGApK1cW1XN0yUPJQkTSmrtzxRUrGT9+E4ceOo977llLUZHuBC9PyUJE0tpTT23g7bcLANi+vZSbbvqCN9/cGueoEk9Mk4WZDTKzhWaWZ2Y3VrC/kZm9EO7/yMw6R+zrbWYfmNlcM/vczLJjGauIpKcJEzbttX3GGS04/fQWcYomccUsWZhZJvA4cDrQCxhuZr3KVbsM2Oju3YGHgXvDtg2A54CfufthwABgV6xiFZH09eqr3Rg9+iBat86kUSPj0Uc7VnptI53F8siiH5Dn7kvdvQgYBwwuV2cw8HT4fAJwsgWf0qnAbHf/DMDdN7h7SQxjFZE0lZFhXH55WxYtOox//asL3bo1qrBeaanz4YfpOwV6LJNFe2BVxHZ+WFZhHXcvBjYDbYCegJvZFDObZWY3xDBOERHatGnAWWe1rHT/mDEbOOaYhQwfvoz8/PQbNWWxmlzLzIYAg9z9p+H2T4D+7j4qos6csE5+uL0E6A+MAK4CjgK2A28Bt7j7W+XeYyQwEiAnJ6fPuHHjah1vQUEBzZo1q3X7RJEq/QD1JVGlSl9q0o/Nm42LLmrKli3B39fZ2c4tt+zguOOKYxli1PblMxk4cOBMd+9bXb1Y3pS3GugYsd0hLKuoTn54nWI/YAPBUcg77r4ewMwmA98lSBpl3H00MBqgb9++PmDAgFoHm5uby760TxSp0g9QXxJVqvSlJv0YOXIFW7ZsKNvOzMzkkkv6ceCBDWMUXc3Ux2cSy9NQ04EeZtbFzBoCw4CJ5epMBC4Onw8B/uvBoc4U4AgzaxImke8B82IYq4hIpS65pA3f+c6etcBvvnn/hEkU9SVmySK8BjGK4It/PjDe3eea2Z1mdnZY7UmgjZnlAdcDN4ZtNwIPESScT4FZ7j4pVrGKiFTlmGOaMWPGITzxxEH069eE6677VqV1IycuTCUxnRvK3ScDk8uV3RrxvBAYWknb5wiGz4qIxF1mZjBtyOWXt6l0aO3q1UX077+QX/0qhyuvbEdWVuoMwdUd3CIiNVDVPRg33vgFq1fv4tpr8+nde15KrZ2hZCEiUgc++KCA5577umx7wYKd5Oenzr3EShYiInVgxYoiWrTY85Xau3djfvKT1nGMqG4pWYiI1IFhw1qzaNFhXHZZG8zggQfak5mpaxYiIlJOTk4WY8Z0YtGiXnz/+xVPRujuXHDBUh5//KukGjmlZCEiUse6d698kuxJk7YwfvwmRo1axeGHz+M//9lErGbSqEtKFiIi9aS42Lnhhj0TWSxatJO//OWrpJjlVslCRKSefPbZjr2WbjWD++8vP79qYlKyEBGpJ336NGHx4sO4/PI2ZGTAiBFt6N27SbzDioqShYhIPTrggCxGj+7EZ58dyl13HVBpvT//+Ssuv3xFwkyHrmQhIhIHhx/euNLJCLduLeH229cwZswGunefy//9Xz6bNsV3OnQlCxGRBPPHP67jq6+C5LBzpzNmzHriPWBKyUJEJIG4O6+8snmvsmuu+RatWsV03tdqKVmIiCQQM+P99w9m9OiDaN8+i+bNM7j22sqnRC8oKKmXuJQsREQSTFaWcfnlbcnLO4zXX+9O69YVH1UsWbKTAw/8nKeeahTzmJQsREQSVHZ2BsceW/na2r///Vq2bi2lPu7pU7IQEUlCS5fu5JlnNtCiRQbnnbcz5u8X3ysmIiJSK8uXF7H//llcemkbmjffFPP3U7IQEUlCJ53UnLy8wygpcaZPXxTz91OyEBFJUtnZ9XclQdcsRESkWkoWIiJSLSULERGplpKFiIhUK6bJwswGmdlCM8szsxsr2N/IzF4I939kZp3L7T/IzArM7JexjFNERKoWs2RhZpnA48DpQC9guJn1KlftMmCju3cHHgbuLbf/IeC1WMUoIiLRieWRRT8gz92XunsRMA4YXK7OYODp8PkE4GQLF6M1s3OAZcDcGMYoIiJRMI/RJOlmNgQY5O4/Dbd/AvR391ERdeaEdfLD7SVAf6AQmAp8H/glUODuD1TwHiOBkQA5OTl9xo0bV+t4CwoKaNas8jlYkkWq9APUl0SVKn1JlX7AvvVl4MCBM929b3X1EvWmvNuBh929wKqYIcvdRwOjAfr27esDBgyo9Rvm5uayL+0TRar0A9SXRJUqfUmVfkD99CWWyWI10DFiu0NYVlGdfDNrAOwHbCA4uhhiZvcBLYFSMyt098cqe7OZM2euN7MV+xBvW2D9PrRPFKnSD1BfElWq9CVV+gH71pdO0VSKZbKYDvQwsy4ESWEY8KNydSYCFwMfAEOA/3pwXuyE3RXM7HaC01CVJgoAd2+3L8Ga2YxoDsUSXar0A9SXRJUqfUmVfkD99CVmycLdi81sFDAFyAT+7u5zzexOYIa7TwSeBJ41szzga4KEIiIiCSam1yzcfTIwuVzZrRHPC4Gh1bzG7TEJTkREoqY7uPcYHe8A6kiq9APUl0SVKn1JlX5APfQlZkNnRUQkdejIQkREqpX2yaK6+asSkZktN7PPzexTM5sRlrU2s6lmtjj8t1VYbmb2aNi/2Wb23TjH/nczWxfekLm7rMaxm9nFYf3FZnZxgvTjdjNbHX4un5rZGRH7bgr7sdDMTosoj/vvn5l1NLNpZjbPzOaa2TVheVJ9LlX0I+k+FzPLNrOPzeyzsC93hOVdLJhHL8+CefUahuWVzrNXWR9rzN3T9kEwSmsJ0BVoCHwG9Ip3XFHEvRxoW67sPuDG8PmNwL3h8zMI5tcy4GjgozjHfiLwXWBObWMHWgNLw39bhc9bJUA/bgd+WUHdXuHvViOgS/g7l5kov3/AAcB3w+fNgUVhzEn1uVTRj6T7XMKfbbPweRbwUfizHg8MC8v/Cvw8fH4l8Nfw+TDghar6WJuY0v3IIpr5q5JF5DxbTwPnRJQ/44EPgZZmdkA8AgRw93cIhklHqmnspwFT3f1rd99IMDXMoNhHv0cl/ajMYGCcu+9092VAHsHvXkL8/rn7GnefFT7fCswH2pNkn0sV/ahMwn4u4c+2INzMCh8OnEQwjx588zOpaJ69yvpYY+meLNoDqyK286n6lytROPCGmc20YH4sgBx3XxM+XwvkhM+ToY81jT2R+zQqPDXz992nbUiifoSnL44k+Es2aT+Xcv2AJPxczCzTzD4F1hEk3iXAJncvriCuspjD/ZuBNtRhX9I9WSSr4939uwTTv19lZidG7vTg+DMph7klc+zAX4BuwHeANcCD8Q2nZsysGfAicK27b4ncl0yfSwX9SMrPxd1L3P07BFMl9QMOiWc86Z4sopm/KuG4++rw33XAvwl+kb7cfXop/HddWD0Z+ljT2BOyT+7+ZfgfvBT4G3sO9xO+H2aWRfAF+7y7vxQWJ93nUlE/kvlzAXD3TcA04BiCU367b6aOjKssZtt7nr0660u6J4uy+avCUQXDCOarSlhm1tTMmu9+DpwKzGHPPFuE/74cPp8IXBSOYDka2BxxaiFR1DT2KcCpZtYqPKVwalgWV+WuBZ1L8LlA0I9h4YiVLkAP4GMS5PcvPLf9JDDf3R+K2JVUn0tl/UjGz8XM2plZy/B5Y4LlGuYTJI0hYbXyn8nuzypynr3K+lhz9XmFPxEfBCM7FhGcD7w53vFEEW9XgtENnxEsDHVzWN4GeAtYDLwJtPY9oyoeD/v3OdA3zvH/k+BUwC6C86eX1SZ24FKCi3V5wCUJ0o9nwzhnh/9JD4iof3PYj4XA6Yn0+wccT3CKaTbwafg4I9k+lyr6kXSfC9Ab+CSMeQ5wa1jeleDLPg/4F9AoLM8Ot/PC/V2r62NNH7qDW0REqpXup6FERCQKShYiIlItJQsREamWkoWIiFRLyUJERKqlZCFpzcxamtmVEdsHmtmEqtrU4Xt3NrPy69KLJCQlC0l3LQlm7ATA3b9w9yFV1K9LnQElC0kKShaS7u4BuoXrHNwf/rU/B8DMRpjZfyxYy2G5mY0ys+vN7BMz+9DMWof1upnZ6+HEju+a2Tfm8DGz79me9RQ+Ce/Cvwc4ISy7Lpw47n4zmx5OendF2HaAmb1jZpPCNQn+amYZYf2xZjbHgvVNrqvHn5ukmQbVVxFJaTcCh3swYdvu2UojHU4we2k2wd2xv3b3I83sYeAi4I8E6x//zN0Xm1l/4M8EU0lH+iVwlbu/H050Vxi+9y/d/czwvUcSTJ1xlJk1At43szfC9v0I1iZYAbwO/BBYBrR398PD9i3r4gciUhElC5GqTfNgbYStZrYZeCUs/xzoHX7xHwv8K5iaCAgWminvfeAhM3seeMnd8yPq73Zq+Jq7T4PtRzCXTxHwsbsvBTCzfxJMbfEW0NXM/gRMAt4o/4IidUXJQqRqOyOel0ZslxL8/8kgWGPgO1W9iLvfY2aTCOYcet8qXt7SgKvdfa/J98xsAN+cHtzdfaOZfZtg0aGfAecTzM0kUud0zULS3VaCJThrxYP1EpaZ2VAoW5/62+XrmVk3d//c3e8lmNX0kAreewrw83CabcysZzizMEC/cBbUDOAC4D0zawtkuPuLwC0Ey7yKxISShaQ1d99A8Jf+HDO7v5YvcyFwmZntngm4oiU4rw3fYzbBTLWvEcwoWmJmn4UXp8cA84BZ4UX2J9hz9D8deIxgmuplBOuYtAdyLVhN7TngplrGL1ItzTorkuDC01BlF8JF4kFHFiIiUi0dWYiISLV0ZCEiItVSshARkWopWYiISLWULEREpFpKFiIiUi0lCxERqdb/A8TPU9Wd164DAAAAAElFTkSuQmCC\n", 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\n", 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\n", 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\n", 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" ] diff --git a/qiskit/finance/machine_learning/qgan_option_pricing.ipynb b/qiskit/finance/machine_learning/qgan_option_pricing.ipynb index 6bae69baa..59882e8f2 100644 --- a/qiskit/finance/machine_learning/qgan_option_pricing.ipynb +++ b/qiskit/finance/machine_learning/qgan_option_pricing.ipynb @@ -22,14 +22,10 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 33, "metadata": {}, "outputs": [], "source": [ - "#!/usr/bin/env python\n", - "# coding: utf-8\n", - "from __future__ import absolute_import, division, print_function\n", - "\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "import numpy as np\n", @@ -57,7 +53,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 34, "metadata": {}, "outputs": [], "source": [ @@ -97,18 +93,9 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 35, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Estimated value:\t1.2580\n", - "Probability: \t0.8785\n" - ] - } - ], + "outputs": [], "source": [ "# set the strike price (should be within the low and the high value of the uncertainty)\n", "strike_price = 2\n", @@ -121,7 +108,112 @@ " uncertainty_model,\n", " strike_price=strike_price,\n", " c_approx=c_approx\n", - ")\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Plot the probability distribution\n", + "Next, we plot the trained probability distribution and, for reasons of comparison, also the target probability distribution." + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#trained probability distribution\n", + "init_distribution = np.sqrt(init_dist.probabilities)\n", + "init_distribution = Custom(num_qubits=sum(num_qubits), state_vector=init_distribution)\n", + "var_form = RY(int(np.sum(num_qubits)), depth=1, initial_state=init_distribution,\n", + " entangler_map=entangler_map, entanglement_gate='cz')\n", + "g_circuit = UnivariateVariationalDistribution(int(sum(num_qubits)), var_form, g_params, low=bounds[0], high=bounds[1])\n", + "uncertainty_model = g_circuit\n", + "uncertainty_model.set_probabilities(QuantumInstance(BasicAer.get_backend('statevector_simulator')))\n", + "x = uncertainty_model.values\n", + "y = uncertainty_model.probabilities\n", + "#target probability distribution\n", + "N = 100000\n", + "log_normal = np.random.lognormal(mean=1, sigma=1, size=N)\n", + "log_normal = np.round(log_normal)\n", + "log_normal = log_normal[log_normal <= 7]\n", + "\n", + "log_normal_samples = []\n", + "for i in range(8):\n", + " log_normal_samples += [np.sum(log_normal==i)]\n", + "log_normal_samples = np.array(log_normal_samples / sum(log_normal_samples))\n", + "\n", + "\n", + "plt.bar(x, y, width=0.2, label='trained distribution', color='royalblue')\n", + "plt.xticks(x, size=15, rotation=90)\n", + "plt.yticks(size=15)\n", + "plt.grid()\n", + "plt.xlabel('Spot Price at Maturity $S_T$ (\\$)', size=15)\n", + "plt.ylabel('Probability ($\\%$)', size=15)\n", + "plt.plot(log_normal_samples,'-o', color ='deepskyblue', label='target distribution', linewidth=4, markersize=12)\n", + "plt.legend(loc='best')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Evaluate Expected Payoff\n", + "Now, the trained uncertainty model can be used to evaluate the expectation value of the option's payoff function analytically and with Quantum Amplitude Estimation." + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Analytically calculated expected payoff w.r.t. the target distribution: 1.0585480647564538\n", + "Analytically calculated expected payoff w.r.t. the trained distribution: 0.980530833264945\n", + "Expected payoff calculated with Quantum Amplitude Estimation: \t1.2580\n", + "Probability: \t0.8785\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "payoff = np.array([0,0,0,1,2,3,4,5])\n", + "ep = np.dot(log_normal_samples, payoff)\n", + "print(\"Analytically calculated expected payoff w.r.t. the target distribution: \", ep)\n", + "ep_trained = np.dot(y, payoff)\n", + "print(\"Analytically calculated expected payoff w.r.t. the trained distribution: \", ep_trained)\n", + "\n", "# set number of evaluation qubits (samples)\n", "m = 5\n", "\n", @@ -129,8 +221,20 @@ "ae = AmplitudeEstimation(m, european_call)\n", "# result = ae.run(quantum_instance=BasicAer.get_backend('qasm_simulator'), shots=100)\n", "result = ae.run(quantum_instance=BasicAer.get_backend('statevector_simulator'))\n", - "print('Estimated value:\\t%.4f' % result['estimation'])\n", - "print('Probability: \\t%.4f' % result['max_probability'])" + "print('Expected payoff calculated with Quantum Amplitude Estimation: \\t%.4f' % result['estimation'])\n", + "print('Probability: \\t%.4f' % result['max_probability'])\n", + "\n", + "# plot exact payoff function (evaluated on the grid of the trained uncertainty model)\n", + "x = uncertainty_model.values\n", + "y_strike = np.maximum(0, x - strike_price)\n", + "plt.plot(x, y_strike, 'ro-')\n", + "plt.grid()\n", + "plt.title('Payoff Function', size=15)\n", + "plt.xlabel('Spot Price', size=15)\n", + "plt.ylabel('Payoff', size=15)\n", + "plt.xticks(x, size=15, rotation=90)\n", + "plt.yticks(size=15)\n", + "plt.show()" ] }, { From c06ccc5d3c1458586e77b96f06fb64a871ac98bc Mon Sep 17 00:00:00 2001 From: stefan-woerner Date: Thu, 2 May 2019 11:45:45 +0200 Subject: [PATCH 109/116] add finance notebooks to community section and adjust indices where necessary --- community/aqua/index.ipynb | 12 +- community/{aqua => }/finance/README.md | 4 +- community/finance/index.ipynb | 63 +++ .../finance/input_files/portfolio.json | 0 .../finance/simulation/iron_condor.ipynb | 9 +- .../finance/simulation/long_butterfly.ipynb | 397 ++++++++++++++++++ .../finance/simulation/short_butterfly.ipynb | 397 ++++++++++++++++++ index.ipynb | 1 + .../finance/simulation/option_pricing.ipynb | 3 +- 9 files changed, 864 insertions(+), 22 deletions(-) rename community/{aqua => }/finance/README.md (82%) create mode 100644 community/finance/index.ipynb rename community/{aqua => }/finance/input_files/portfolio.json (100%) rename qiskit/finance/simulation/iron_condor_pricing.ipynb => community/finance/simulation/iron_condor.ipynb (99%) create mode 100644 community/finance/simulation/long_butterfly.ipynb create mode 100644 community/finance/simulation/short_butterfly.ipynb diff --git a/community/aqua/index.ipynb b/community/aqua/index.ipynb index 6e9a52e53..a92f04e35 100644 --- a/community/aqua/index.ipynb +++ b/community/aqua/index.ipynb @@ -77,16 +77,6 @@ "The repository here may be viewed for the\n", "[full listing](https://github.com/Qiskit/qiskit-tutorial/tree/master/community/aqua/optimization).\n", "\n", - "### 5. [Qiskit Aqua Finance](finance/)\n", - "\n", - "Qiskit Aqua Finance is a set of tools, algorithms and software for use with quantum computers to carry out research and investigate how to take advantage of quantum computing power to solve problems in the Financial domain. \n", - "\n", - "* [Portfolio Optimization](../../qiskit/aqua/finance/portfolio_optimization.ipynb)\n", - "\n", - "The repository here may be viewed for the\n", - "[full listing](https://github.com/Qiskit/qiskit-tutorial/tree/master/community/aqua/finance).\n", - "\n", - "\n", "*** " ] }, @@ -116,7 +106,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.2" + "version": "3.7.3" } }, "nbformat": 4, diff --git a/community/aqua/finance/README.md b/community/finance/README.md similarity index 82% rename from community/aqua/finance/README.md rename to community/finance/README.md index c459edde1..05c1f3d0c 100644 --- a/community/aqua/finance/README.md +++ b/community/finance/README.md @@ -1,10 +1,10 @@ # Qiskit Aqua Finance Tutorials, Samples and Input Files -Qiskit Aqua Finance is a set of tools, algorithms and software for use with quantum computers to +Qiskit Finance is a set of tools, algorithms and software for use with quantum computers to carry out research and investigate how to take advantage of quantum computing power to solve problems in the financial domain. -Qiskit Aqua Finance translates finance-specific problems into inputs +Qiskit Finance translates finance-specific problems into inputs for a quantum algorithm residing in Qiskit Aqua, which in turn uses [Qiskit](https://www.qiskit.org/) for the relevant quantum computation. diff --git a/community/finance/index.ipynb b/community/finance/index.ipynb new file mode 100644 index 000000000..c2e2ee53e --- /dev/null +++ b/community/finance/index.ipynb @@ -0,0 +1,63 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Qiskit Finance Community Tutorials" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Welcome Qiskitters to the Qiskit Finance community tutorials.\n", + "\n", + "Qiskit Finance is a set of tools, algorithms and software for use with quantum computers to carry out research and investigate how to take advantage of quantum computing power to solve problems in the Financial domain.\n", + "\n", + "In the following, you'll find a list of currently available community tutorials.\n", + "Please also see the [Qiskit Finance Tutorials](../../qiskit/finance/index.ipynb) for more examples.\n", + "\n", + "Further contributions to simulation or other use cases in finance, such as optimization or machine learning, are very welcome!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Option pricing on a quantum computer:\n", + "- Long Butterfly (univariate, payoff with 4 segments)\n", + "- Short Butterfly (univariate, payoff with 4 segments)\n", + "- Iron Condor (univariate, payoff with 5 segments)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "qiskit_master", + "language": "python", + "name": "qiskit_master" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/community/aqua/finance/input_files/portfolio.json b/community/finance/input_files/portfolio.json similarity index 100% rename from community/aqua/finance/input_files/portfolio.json rename to community/finance/input_files/portfolio.json diff --git a/qiskit/finance/simulation/iron_condor_pricing.ipynb b/community/finance/simulation/iron_condor.ipynb similarity index 99% rename from qiskit/finance/simulation/iron_condor_pricing.ipynb rename to community/finance/simulation/iron_condor.ipynb index 0b05d3395..96d23bc5f 100644 --- a/qiskit/finance/simulation/iron_condor_pricing.ipynb +++ b/community/finance/simulation/iron_condor.ipynb @@ -4,14 +4,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# _*Qiskit Finance: Pricing Iron Condor Option*_ \n", + "# _*Pricing Iron Condor Option*_ \n", "\n", "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", "\n", diff --git a/community/finance/simulation/long_butterfly.ipynb b/community/finance/simulation/long_butterfly.ipynb new file mode 100644 index 000000000..52c9ae6f6 --- /dev/null +++ b/community/finance/simulation/long_butterfly.ipynb @@ -0,0 +1,397 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# _*Pricing Long Butterfly Options*_ \n", + "\n", + "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", + "\n", + "***\n", + "### Contributors\n", + "Stefan Woerner[1], Daniel Egger[1]\n", + "### Affliation\n", + "- [1]IBMQ" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Introduction\n", + "
\n", + "Suppose a long butterfly option with strike prices $K_1 < K_2 < K_3$, with $K_2 - K_1 = K_3 - K_2$ and an underlying asset whose spot price at maturity $S_T$ follows a given random distribution.\n", + "The corresponding payoff function is defined as:\n", + "
\n", + "
\n", + "$$ F(S_T) = \n", + "\\begin{cases}\n", + "0 ,& S_T < K_1 \\\\\n", + "S_T - K_1 ,& K_1 \\leq S_T < K_2 \\\\\n", + "2K_2 - K_1 - S_T ,& K_2 \\leq S_T < K_3 \\\\\n", + "0 ,& S_T \\geq K_3. \n", + "\\end{cases}$$\n", + "
\n", + "In the following, a quantum algorithm based on amplitude estimation is used to estimate the expected payoff, i.e., the fair price before discounting, for the option:\n", + "
\n", + "
\n", + "$$\\mathbb{E}\\left[ F(S_T) \\right].$$\n", + "
\n", + "The approximation of the objective function is explained in detail in the following paper:
\n", + "Quantum Risk Analysis. Woerner, Egger. 2018." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "import numpy as np\n", + "\n", + "from qiskit import BasicAer\n", + "from qiskit.aqua.algorithms import AmplitudeEstimation\n", + "from qiskit.aqua.components.uncertainty_models import LogNormalDistribution\n", + "from qiskit.aqua.components.uncertainty_problems import UnivariateProblem\n", + "from qiskit.aqua.components.uncertainty_problems import UnivariatePiecewiseLinearObjective as PwlObjective" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Uncertainty Model\n", + "\n", + "We construct a circuit factory to load a log-normal random distribution into a quantum state.\n", + "The distribution is truncated to a given interval $[low, high]$ and discretized using $2^n$ grid points, where $n$ denotes the number of qubits used.\n", + "The unitary operator corresponding to the circuit factory implements the following: \n", + "$$\\big|0\\rangle_{n} \\mapsto \\big|\\psi\\rangle_{n} = \\sum_{i=0}^{2^n-1} \\sqrt{p_i}\\big|i\\rangle_{n},$$\n", + "where $p_i$ denote the probabilities corresponding to the truncated and discretized distribution and where $i$ is mapped to the right interval using the affine map:\n", + "$$ \\{0, \\ldots, 2^n-1\\} \\ni i \\mapsto \\frac{high - low}{2^n - 1} * i + low \\in [low, high].$$" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# number of qubits to represent the uncertainty\n", + "num_uncertainty_qubits = 3\n", + "\n", + "# parameters for considered random distribution\n", + "S = 2.0 # initial spot price\n", + "vol = 0.4 # volatility of 40%\n", + "r = 0.05 # annual interest rate of 4%\n", + "T = 40 / 365 # 40 days to maturity\n", + "\n", + "# resulting parameters for log-normal distribution\n", + "mu = ((r - 0.5 * vol**2) * T + np.log(S))\n", + "sigma = vol * np.sqrt(T)\n", + "mean = np.exp(mu + sigma**2/2)\n", + "variance = (np.exp(sigma**2) - 1) * np.exp(2*mu + sigma**2)\n", + "stddev = np.sqrt(variance)\n", + "\n", + "# lowest and highest value considered for the spot price; in between, an equidistant discretization is considered.\n", + "low = np.maximum(0, mean - 3*stddev)\n", + "high = mean + 3*stddev\n", + "\n", + "# construct circuit factory for uncertainty model\n", + "uncertainty_model = LogNormalDistribution(num_uncertainty_qubits, mu=mu, sigma=sigma, low=low, high=high)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot probability distribution\n", + "x = uncertainty_model.values\n", + "y = uncertainty_model.probabilities\n", + "plt.bar(x, y, width=0.2)\n", + "plt.xticks(x, size=15, rotation=90)\n", + "plt.yticks(size=15)\n", + "plt.grid()\n", + "plt.xlabel('Spot Price at Maturity $S_T$ (\\$)', size=15)\n", + "plt.ylabel('Probability ($\\%$)', size=15)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Payoff Function\n", + "\n", + "The payoff function equals zero as long as the spot price at maturity $S_T$ is less than the strike price $K_1$, then increases linearly, and is bounded by $K_2$.\n", + "The implementation uses two comparators, that flip an ancilla qubit each from $\\big|0\\rangle$ to $\\big|1\\rangle$ if $S_T \\geq K_1$ and $S_T \\leq K_2, and these ancillas are used to control the linear part of the payoff function.\n", + "\n", + "The linear part itself is then approximated as follows.\n", + "We exploit the fact that $\\sin^2(y + \\pi/4) \\approx y + 1/2$ for small $|y|$.\n", + "Thus, for a given approximation scaling factor $c_{approx} \\in [0, 1]$ and $x \\in [0, 1]$ we consider\n", + "$$ \\sin^2( \\pi/2 * c_{approx} * ( x - 1/2 ) + \\pi/4) \\approx \\pi/2 * c_{approx} * ( x - 1/2 ) + 1/2 $$ for small $c_{approx}$.\n", + "\n", + "We can easily construct an operator that acts as \n", + "$$\\big|x\\rangle \\big|0\\rangle \\mapsto \\big|x\\rangle \\left( \\cos(a*x+b) \\big|0\\rangle + \\sin(a*x+b) \\big|1\\rangle \\right),$$\n", + "using controlled Y-rotations.\n", + "\n", + "Eventually, we are interested in the probability of measuring $\\big|1\\rangle$ in the last qubit, which corresponds to\n", + "$\\sin^2(a*x+b)$.\n", + "Together with the approximation above, this allows to approximate the values of interest.\n", + "The smaller we choose $c_{approx}$, the better the approximation.\n", + "However, since we are then estimating a property scaled by $c_{approx}$, the number of evaluation qubits $m$ needs to be adjusted accordingly.\n", + "\n", + "For more details on the approximation, we refer to:\n", + "Quantum Risk Analysis. Woerner, Egger. 2018." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# set the strike price (should be within the low and the high value of the uncertainty)\n", + "strike_price_1 = 1.438\n", + "strike_price_2 = 1.896\n", + "strike_price_3 = 2*strike_price_2 - strike_price_1\n", + "\n", + "# set the approximation scaling for the payoff function\n", + "c_approx = 0.25\n", + "\n", + "# setup piecewise linear objective fcuntion\n", + "breakpoints = [uncertainty_model.low, strike_price_1, strike_price_2, strike_price_3]\n", + "slopes = [0, 1, -1, 0]\n", + "offsets = [0, 0, strike_price_2 - strike_price_1, 0]\n", + "f_min = 0\n", + "f_max = strike_price_2 - strike_price_1\n", + "butterfly_objective = PwlObjective(\n", + " uncertainty_model.num_target_qubits, \n", + " uncertainty_model.low, \n", + " uncertainty_model.high,\n", + " breakpoints,\n", + " slopes,\n", + " offsets,\n", + " f_min,\n", + " f_max,\n", + " c_approx\n", + ")\n", + "\n", + "# construct circuit factory for payoff function\n", + "butterfly = UnivariateProblem(\n", + " uncertainty_model,\n", + " butterfly_objective\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot exact payoff function (evaluated on the grid of the uncertainty model)\n", + "x = uncertainty_model.values\n", + "def payoff(x):\n", + " if x <= strike_price_1:\n", + " return 0\n", + " elif x < strike_price_2:\n", + " return x - strike_price_1\n", + " elif x < strike_price_3:\n", + " return 2*strike_price_2 - strike_price_1 - x\n", + " else:\n", + " return 0\n", + "y = [payoff(x_) for x_ in x]\n", + "plt.plot(x, y, 'ro-')\n", + "plt.grid()\n", + "plt.title('Payoff Function', size=15)\n", + "plt.xlabel('Spot Price', size=15)\n", + "plt.ylabel('Payoff', size=15)\n", + "plt.xticks(x, size=15, rotation=90)\n", + "plt.yticks(size=15)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "exact expected value:\t0.2598\n" + ] + } + ], + "source": [ + "# evaluate exact expected value (normalized to the [0, 1] interval)\n", + "exact_value = np.dot(uncertainty_model.probabilities, y)\n", + "print('exact expected value:\\t%.4f' % exact_value)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Evaluate Expected Payoff" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "# set number of evaluation qubits (=log(samples))\n", + "m = 5\n", + "\n", + "# construct amplitude estimation \n", + "ae = AmplitudeEstimation(m, butterfly)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "# result = ae.run(quantum_instance=BasicAer.get_backend('qasm_simulator'), shots=100)\n", + "result = ae.run(quantum_instance=BasicAer.get_backend('statevector_simulator'))" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exact value: \t0.2598\n", + "Estimated value:\t0.2290\n", + "Probability: \t0.7939\n" + ] + } + ], + "source": [ + "print('Exact value: \\t%.4f' % exact_value)\n", + "print('Estimated value:\\t%.4f' % result['estimation'])\n", + "print('Probability: \\t%.4f' % result['max_probability'])" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot estimated values for \"a\"\n", + "plt.bar(result['values'], result['probabilities'], width=0.5/len(result['probabilities']))\n", + "plt.xticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.title('\"a\" Value', size=15)\n", + "plt.ylabel('Probability', size=15)\n", + "plt.ylim((0,1))\n", + "plt.grid()\n", + "plt.show()\n", + "\n", + "# plot estimated values for option price (after re-scaling and reversing the c_approx-transformation)\n", + "plt.bar(result['mapped_values'], result['probabilities'], width=1/len(result['probabilities']))\n", + "plt.plot([exact_value, exact_value], [0,1], 'r--', linewidth=2)\n", + "plt.xticks(size=15)\n", + "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.title('Estimated Option Price', size=15)\n", + "plt.ylabel('Probability', size=15)\n", + "plt.ylim((0,1))\n", + "plt.grid()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "qiskit_master", + "language": "python", + "name": "qiskit_master" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/community/finance/simulation/short_butterfly.ipynb b/community/finance/simulation/short_butterfly.ipynb new file mode 100644 index 000000000..227ec7e2c --- /dev/null +++ b/community/finance/simulation/short_butterfly.ipynb @@ -0,0 +1,397 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# _*Pricing Short Butterfly Options*_ \n", + "\n", + "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", + "\n", + "***\n", + "### Contributors\n", + "Stefan Woerner[1], Daniel Egger[1]\n", + "### Affliation\n", + "- [1]IBMQ" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Introduction\n", + "
\n", + "Suppose a short butterfly option with strike prices $K_1 < K_2 < K_3$, with $K_2 - K_1 = K_3 - K_2$ and an underlying asset whose spot price at maturity $S_T$ follows a given random distribution.\n", + "The corresponding payoff function is defined as:\n", + "
\n", + "
\n", + "$$ F(S_T) = \n", + "\\begin{cases}\n", + "0 ,& S_T < K_1 \\\\\n", + "K_1 - S_T ,& K_1 \\leq S_T < K_2 \\\\\n", + "S_T - 2K_2 + K_1 ,& K_2 \\leq S_T < K_3 \\\\\n", + "0 ,& S_T \\geq K_3. \n", + "\\end{cases}$$\n", + "
\n", + "In the following, a quantum algorithm based on amplitude estimation is used to estimate the expected payoff, i.e., the fair price before discounting, for the option:\n", + "
\n", + "
\n", + "$$\\mathbb{E}\\left[ F(S_T) \\right].$$\n", + "
\n", + "The approximation of the objective function is explained in detail in the following paper:
\n", + "Quantum Risk Analysis. Woerner, Egger. 2018." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "import numpy as np\n", + "\n", + "from qiskit import BasicAer\n", + "from qiskit.aqua.algorithms import AmplitudeEstimation\n", + "from qiskit.aqua.components.uncertainty_models import LogNormalDistribution\n", + "from qiskit.aqua.components.uncertainty_problems import UnivariateProblem\n", + "from qiskit.aqua.components.uncertainty_problems import UnivariatePiecewiseLinearObjective as PwlObjective" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Uncertainty Model\n", + "\n", + "We construct a circuit factory to load a log-normal random distribution into a quantum state.\n", + "The distribution is truncated to a given interval $[low, high]$ and discretized using $2^n$ grid points, where $n$ denotes the number of qubits used.\n", + "The unitary operator corresponding to the circuit factory implements the following: \n", + "$$\\big|0\\rangle_{n} \\mapsto \\big|\\psi\\rangle_{n} = \\sum_{i=0}^{2^n-1} \\sqrt{p_i}\\big|i\\rangle_{n},$$\n", + "where $p_i$ denote the probabilities corresponding to the truncated and discretized distribution and where $i$ is mapped to the right interval using the affine map:\n", + "$$ \\{0, \\ldots, 2^n-1\\} \\ni i \\mapsto \\frac{high - low}{2^n - 1} * i + low \\in [low, high].$$" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# number of qubits to represent the uncertainty\n", + "num_uncertainty_qubits = 3\n", + "\n", + "# parameters for considered random distribution\n", + "S = 2.0 # initial spot price\n", + "vol = 0.4 # volatility of 40%\n", + "r = 0.05 # annual interest rate of 4%\n", + "T = 40 / 365 # 40 days to maturity\n", + "\n", + "# resulting parameters for log-normal distribution\n", + "mu = ((r - 0.5 * vol**2) * T + np.log(S))\n", + "sigma = vol * np.sqrt(T)\n", + "mean = np.exp(mu + sigma**2/2)\n", + "variance = (np.exp(sigma**2) - 1) * np.exp(2*mu + sigma**2)\n", + "stddev = np.sqrt(variance)\n", + "\n", + "# lowest and highest value considered for the spot price; in between, an equidistant discretization is considered.\n", + "low = np.maximum(0, mean - 3*stddev)\n", + "high = mean + 3*stddev\n", + "\n", + "# construct circuit factory for uncertainty model\n", + "uncertainty_model = LogNormalDistribution(num_uncertainty_qubits, mu=mu, sigma=sigma, low=low, high=high)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot probability distribution\n", + "x = uncertainty_model.values\n", + "y = uncertainty_model.probabilities\n", + "plt.bar(x, y, width=0.2)\n", + "plt.xticks(x, size=15, rotation=90)\n", + "plt.yticks(size=15)\n", + "plt.grid()\n", + "plt.xlabel('Spot Price at Maturity $S_T$ (\\$)', size=15)\n", + "plt.ylabel('Probability ($\\%$)', size=15)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Payoff Function\n", + "\n", + "The payoff function equals zero as long as the spot price at maturity $S_T$ is less than the strike price $K_1$, then increases linearly, and is bounded by $K_2$.\n", + "The implementation uses two comparators, that flip an ancilla qubit each from $\\big|0\\rangle$ to $\\big|1\\rangle$ if $S_T \\geq K_1$ and $S_T \\leq K_2, and these ancillas are used to control the linear part of the payoff function.\n", + "\n", + "The linear part itself is then approximated as follows.\n", + "We exploit the fact that $\\sin^2(y + \\pi/4) \\approx y + 1/2$ for small $|y|$.\n", + "Thus, for a given approximation scaling factor $c_{approx} \\in [0, 1]$ and $x \\in [0, 1]$ we consider\n", + "$$ \\sin^2( \\pi/2 * c_{approx} * ( x - 1/2 ) + \\pi/4) \\approx \\pi/2 * c_{approx} * ( x - 1/2 ) + 1/2 $$ for small $c_{approx}$.\n", + "\n", + "We can easily construct an operator that acts as \n", + "$$\\big|x\\rangle \\big|0\\rangle \\mapsto \\big|x\\rangle \\left( \\cos(a*x+b) \\big|0\\rangle + \\sin(a*x+b) \\big|1\\rangle \\right),$$\n", + "using controlled Y-rotations.\n", + "\n", + "Eventually, we are interested in the probability of measuring $\\big|1\\rangle$ in the last qubit, which corresponds to\n", + "$\\sin^2(a*x+b)$.\n", + "Together with the approximation above, this allows to approximate the values of interest.\n", + "The smaller we choose $c_{approx}$, the better the approximation.\n", + "However, since we are then estimating a property scaled by $c_{approx}$, the number of evaluation qubits $m$ needs to be adjusted accordingly.\n", + "\n", + "For more details on the approximation, we refer to:\n", + "Quantum Risk Analysis. Woerner, Egger. 2018." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# set the strike price (should be within the low and the high value of the uncertainty)\n", + "strike_price_1 = 1.438\n", + "strike_price_2 = 1.896\n", + "strike_price_3 = 2*strike_price_2 - strike_price_1\n", + "\n", + "# set the approximation scaling for the payoff function\n", + "c_approx = 0.25\n", + "\n", + "# setup piecewise linear objective fcuntion\n", + "breakpoints = [uncertainty_model.low, strike_price_1, strike_price_2, strike_price_3]\n", + "slopes = [0, -1, 1, 0]\n", + "offsets = [1, 1, 1+strike_price_1 - strike_price_2, 1]\n", + "f_min = 0\n", + "f_max = strike_price_2 - strike_price_1\n", + "butterfly_objective = PwlObjective(\n", + " uncertainty_model.num_target_qubits, \n", + " uncertainty_model.low, \n", + " uncertainty_model.high,\n", + " breakpoints,\n", + " slopes,\n", + " offsets,\n", + " f_min,\n", + " f_max,\n", + " c_approx\n", + ")\n", + "\n", + "# construct circuit factory for payoff function\n", + "butterfly = UnivariateProblem(\n", + " uncertainty_model,\n", + " butterfly_objective\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot exact payoff function (evaluated on the grid of the uncertainty model)\n", + "x = uncertainty_model.values\n", + "def payoff(x):\n", + " if x <= strike_price_1:\n", + " return 1\n", + " elif x < strike_price_2:\n", + " return 1+strike_price_1 - x\n", + " elif x < strike_price_3:\n", + " return 1+x - 2*strike_price_2 + strike_price_1\n", + " else:\n", + " return 1\n", + "y = [payoff(x_) for x_ in x]\n", + "plt.plot(x, y, 'ro-')\n", + "plt.grid()\n", + "plt.title('Payoff Function', size=15)\n", + "plt.xlabel('Spot Price', size=15)\n", + "plt.ylabel('Payoff', size=15)\n", + "plt.xticks(x, size=15, rotation=90)\n", + "plt.yticks(size=15)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "exact expected value:\t0.7402\n" + ] + } + ], + "source": [ + "# evaluate exact expected value (normalized to the [0, 1] interval)\n", + "exact_value = np.dot(uncertainty_model.probabilities, y)\n", + "print('exact expected value:\\t%.4f' % exact_value)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Evaluate Expected Payoff" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "# set number of evaluation qubits (=log(samples))\n", + "m = 6\n", + "\n", + "# construct amplitude estimation \n", + "ae = AmplitudeEstimation(m, butterfly)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "# result = ae.run(quantum_instance=BasicAer.get_backend('qasm_simulator'), shots=100)\n", + "result = ae.run(quantum_instance=BasicAer.get_backend('statevector_simulator'))" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exact value: \t0.7402\n", + "Estimated value:\t0.6413\n", + "Probability: \t0.4953\n" + ] + } + ], + "source": [ + "print('Exact value: \\t%.4f' % exact_value)\n", + "print('Estimated value:\\t%.4f' % result['estimation'])\n", + "print('Probability: \\t%.4f' % result['max_probability'])" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+d1s1O/FTkk6VtAJ4GfhDg8dQ+oFtG6SPp3HPZyhXFc/vLpVNg/LXvW+2fDMz66Bm5+GcBJwGfJ/Uc/gn4BzgYeBRilNTQ1hOulbzGkm7Alsy8NrLcKLy/AgpCE6u5JsMrC3qaGZmXdJswPkUcBZwfvH+2og4G9iLFDDeOsz+84DDJG1dSptOuv1Bs9eKjiue7wOIiDWkeUIfqeSbDtzjEWpmZt3V7DWcNwNLIuJVSS9TnK6KiLWSvgt8j9QDGswlpF7SNZLOA3YHZgEXlIdKF6fsFkbEicX7WcDWpEmfK4EPAF8CromIn5fK/xrp+s5FpHlC04rH4U0ep5mZdVizPZzfA1sVrx8H/rK0bQJpUuegIqIfOIg0V+c64GzgQlKvqWwT1p/Ps5w0T2c2cCNwPPDN4rlc/iJSz+dgYD7wIeB4rzJgZtZ9zfZw7gLeS/rR/xFphYDtgD8BnwNuHa6AiFgKfHCYPJMq7+eSJnAOKyKuJfVuzMxsA9JswJkF7FK8Ppd0Su0EUs9mAfCFTlXMzMx6S1MBJyIeAh4qXq8h3Qvn5BGol5mZ9Zh2Jn6+CdgZeDoinupclczMrBe1covpz0p6AngM+DHwuKQnJf2fjtfOzMx6RrMrDZwJXEyaT3MkMKV4ngd8p9huZmY2QLOn1D4HnBsRX62k31SsbfY50soDZmZm62n2lNo4Br+r50IaLOZpZmYGzQeca4FjB9n2YeD69qpjZma9qs4tpqeV3s4Dzpc0iYG3mN4L+MfOV9HMzHpBnWs41zPwVtK7AIc1yPsD0p04zczM1lMn4Lx5xGthZmY9r84tph/LUREzM+ttTa80IGkT0gCB/YHtgP8B7iTdKuCVzlbPzMx6RVMBR9KOwM3A3qQ7fD4L7Eeaf/OApEMj4nedrqSZmY1+zQ6LvgB4I/C+iNg9IvaLiN2B9xXpF3S6gmZm1huaDTjTgFMj4qflxOL9l0nL3JiZmQ3QbMDZDPjDINv+ALyhveqYmVmvajbg3AucKmnLcmLx/tRiu5mZ2QDNjlI7BbgdeELSzaRBAzuSJoEKmNrR2pmZWc9oqocTEUuAtwKXATsAh5ACziXAWyPigY7X0MzMekLtHo6kTYF9gF9HxGkjVyUzM+tFzfRwXgVuA94xQnUxM7MeVjvgRMRa4JfAxJGrjpmZ9apmR6l9BThT0jtHojJmZta7mh2ldgZpRYElkp4ijVKLcoaI2KdDdTMzsx7SbMD5RfEwMzNrSq2AI2kcaVmbXwC/AW6JiGdHsmJmZtZb6txienfgFmBSKXmlpI9GxM0jVTEzM+stdQYNnA+sBf4a2ALYC7gfuHQE62VmZj2mTsDZDzgjIu6KiJciYhnwaeDPJe08stUzM7NeUSfg7Az8qpL2CGnttJ06XiMzM+tJdUepxfBZzMxsKJNOu2G9949+Y2zdQqxuwJkv6ZUG6bdW0yNix/arZWZmvaZOwDl7xGthZmY9b9iAExEOOGZm1rZm11IzMzNriQOOmZll4YBjZmZZOOCYmVkWDjhmZpaFA46ZmWWRPeBI2lPSrZJWS3pa0jmSNh5mn/dKmi1pRbHfQ5LOkrR5Jd8sSdHgcfjIHpWZmQ2n2RuwtUXSBNKtDpYCRwF7AN8iBb4zhth1epH3POCXwN7A14rnD1fyvgBUA8yydutuZmbtyRpwgM8A44BjI2IlsEDSNsAsSecXaY2cFxG/K73vk/QScKmk3SLisdK2VyLi3pGpvpmZtSr3KbUjgPmVwDKXFIQOGGynSrBZ5/7i2Wu3mZmNArkDzmRgeTkhIh4HVhfbmvF+0o3hHqqkbyvpOUkvS7pf0rEt19bMzDpGEfnuPCDpZeBLEXFRJf1J4IqIOL1mOTsBPwdujIgTSukfJ/V4lgBbkW4UNw34cERcM0hZM4GZABMnTnzP3Llzmz2s9axatYqtttqqrTLGCrdVfW6r+rrRVg8+9cJ679+5y/i28uXSibY68MAD74uIKXXydiPgfDEivl1Jfwq4PCK+UqOMN5AGHrwJeE9E9A+RV8DdwLiIeNdwZU+ZMiUWL148XLYh9fX1MXXq1LbKGCvcVvW5rerrRlvVvc/NhnY/nE60laTaASf3KbV+YNsG6eOB54fbuQggVwB7AdOGCjYAkaLpNcDeww29NjOzkZV7lNpyKtdqJO0KbEnl2s4gLiQNpz4kIurkX8d3LDUz67LcPZx5wGGSti6lTQdeBBYOtaOkLwNfAD4eEYvqfFjRIzoGeCAiXm2tymZm1gm5eziXACcB10g6D9gdmAVcUB4qLWkFsDAiTizeHw+cC1wOPCVp31KZj6wbNi1pIXA1qbe0JfApYF/g6JE9LDMzG07WgBMR/ZIOAi4GriNdt7mQFHSq9Spfczm0eD6heJR9ghSIAFYAfw/sTBoy/TPgyIiY14n6m5lZ63L3cIiIpcAHh8kzqfL+BAYGmkb7ndhG1czMbAR5tWgzM8vCAcfMzLJwwDEzsywccMzMLAsHHDMzy8IBx8zMsnDAMTOzLBxwzMwsCwccMzPLwgHHzMyycMAxM7MsHHDMzCwLBxwzM8vCAcfMzLJwwDEzsywccMzMLAsHHDMzy8IBx8zMsnDAMTOzLBxwzMwsCwccMzPLwgHHzMyycMAxM7MsHHDMzCwLBxwzM8vCAcfMzLJwwDEzsywccMzMLAsHHDMzy8IBx8zMsnDAMTOzLBxwzMwsCwccMzPLwgHHzMyycMAxM7MsHHDMzCyLTbpdATOzDdGk025Y7/2j3ziySzXpHe7hmJlZFu7hmJltIKq9KuitnpV7OGZmloUDjpmZZeGAY2ZmWWQPOJL2lHSrpNWSnpZ0jqSNa+w3XtJsSf2SXpD0Q0lvbJDvKEkPSnpJ0lJJ00fmSMzMrBlZBw1ImgDcAiwFjgL2AL5FCnxnDLP7lcDbgU8Ca4HzgGuBvy6Vvz9wNfBd4CRgGjBHUn9E3NzRgzGzUaUXLsiP9qHauUepfQYYBxwbESuBBZK2AWZJOr9IG0DSfsBhwAERcUeR9hTwY0kHR8QtRdavAndExEnF+9sl7QWcCTjgmJl1Ue6AcwQwvxJY5pJ6KwcA1w2x37Prgg1ARPxE0q+LbbdI2gw4kNSzKZsLzJY0PiJe6NBxmFkX9UJvpZNGS3vkDjiTgdvKCRHxuKTVxbbBAs5kYHmD9GXFNkin5zZtkG8Z6ZTd24CftlZts9a182Owbt9T3vkKJ5x2Q9P7tfOZ7e5Xd9/R8mM52jRq16pmv1ftUkRk+SAASS8DX4qIiyrpTwJXRMTpg+y3APhjRBxdSf8BsHtEvF/SXwGLgL+MiCWlPG8Bfgkc1ug6jqSZwMzi7duBh1o+wGR74Lk2yxgr3Fb1ua3qc1vV14m22i0idqiTsRsrDTSKcBokvZX9qu81xP5ExGXAZcN8dm2SFkfElE6V18vcVvW5repzW9WXu61yD4vuB7ZtkD4eeL6F/bYt7ddfSqvmYZjyzcxshOUOOMt5/ZoLAJJ2Bbak8TWaQfcrlK/tPAK83CDfZNIw6odbqK+ZmXVI7oAzDzhM0taltOnAi8DCYfbbqZhnA4CkKcDuxTYiYg1wO/CRyr7TgXsyjlDr2Om5McBtVZ/bqj63VX1Z2yr3oIEJpEmfvyANhd4duAC4KCLOKOVbASyMiBNLaTeRRpp9kdcnfv42IqoTP/uAi0mTQqcV+Q/3xE8zs+7K2sOJiH7gIGBj0hDos4ELgbMqWTcp8pTNIPWC/hW4ArgPOKZS/iLgOOBgYD7wIeB4Bxszs+7L2sMxM7Oxy6tFN+AFRutrpa0kvbdopxXFfg9JOkvS5pV8syRFg8fhI3tUI6PFtpo0SBvMbZB3rH+vBvu+hKQvl/JdPkieRgOTNniS3iLpUkkPSHpVUl/N/bL/XvmOnxVeYLS+NtpqepH3PNKk3L2BrxXPH67kfQGoBphl7dY9tza/V5CuRd5Ver/eZD1/rwD4HnBTJe1o4FSKwUUly4FPVNIeba3GXbcX6d/7XuANTeyX//cqIvwoPYAvk+b0bFNK+0dgdTmtwX77kSaXfqCUtk+RdnApbT5wW2XfG4FF3T72jG21Q4O0mUVb7VZKmwU81+3j7HJbTSra5X8NU/6Y/14NUtYNwLJK2uXA4m4fZwfba6PS66uAvhr7dOX3yqfUBhpsgdFxpAVGh9pvwAKjwLoFRiktMPrvlX3nAvtJGt9+9bNqqa0i4ncNku8vnnfsXPU2KK1+r4bl71VjkrYDDgHmdLZ6G5aIWNvCbl35vXLAGWjAQqER8Tjpr6uhzvF2aoHR0aTVtmrk/aRufXUtu20lPSfpZUn3Szq25dp2V7ttNbs4P/+MpAskjStt8/eqseNI7TLgehewp6SVktZIWiSpraA/CnXl98oBZ6AJNF4Gp7/Y1s5+656r+for20eLVttqPZJ2Ar4C/Fvlr9oVpFMpHyVd23kauHqUBp1W22oN8C/AiaQpBZcCn2X9H1F/rxqbAfwsIqqrjNwPnAL8DfAx0hSMBZL2aaGuo1VXfq88aKCxDWqB0Q1cq22VMkpvIHXZVwH/sF7BET+o5L0OuJt0Q71rWqlslzXdVhHxDPD5UlKfpGeB70p6V5RWRm9Qzlj+Xu1MOv126oCCI75dyXsDaYDC6aRBBmNF9t8r93AG8gKj9bXaVgBIEmkS717AtEgTgwcV6YrlNcDedYapb2DaaquKq4rnd5fKpkH5Y/J7Vfgo6YfxyuEyRsSLpAvh7x4ubw/pyu+VA85AXmC0vlbbap0LScNej4qIOvnXGY1/sbfbVmVRefb3aqAZpJFUTzTxuaPxe9WqrvxeOeAMNBYWGO2UVtuKYiLeF4CPR1qSaFhFj+gY4IGIeLW1KndNy23VwHHF833g71WVpEnAvtQcnVYMwDiCoj3HiO78XnV7DPmG9iBdCHsGWEBak20m6frC1yv5VgDfr6TdBPwKOJZ0Lvgh4M5Knv2BV4CLgKnA+aS/Fg7t9rHnaivgeNJfk7NJPwzlxw6lfAtJk80OJQWaG4u2+lC3jz1jW80iTXo8ttjvHNIP79X+Xg38P1ikn0b6y7zRfK/xwJ3Ap0mDMKaTJkyuAaZ0+9hbbK8tSH+EHAfcA/x36f0Wg7VVN36vut5YG+ID2BO4rfiP/QxpFvzGlTyPApdX0rYtfkSfB1YCPwK2b1D+0aQVs9eQuq8zun3MOduKNPEuBnmcUMr3/eI/xIvAH4sfiiO6fcyZ22oGsJi04sKfih+Oc4DN/L0a+H+wSF8C3DRIuZuTrgM+UbTTC8UP777dPuY22mrSEP+fJg3WVt34vfLinWZmloWv4ZiZWRYOOGZmloUDjpmZZeGAY2ZmWTjgmJlZFg44ZmaWhQOOmZll4YBjZmZZ/H/+7sS3NSEb2QAAAABJRU5ErkJggg==\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot estimated values for \"a\"\n", + "plt.bar(result['values'], result['probabilities'], width=0.5/len(result['probabilities']))\n", + "plt.xticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.title('\"a\" Value', size=15)\n", + "plt.ylabel('Probability', size=15)\n", + "plt.ylim((0,1))\n", + "plt.grid()\n", + "plt.show()\n", + "\n", + "# plot estimated values for option price (after re-scaling and reversing the c_approx-transformation)\n", + "plt.bar(result['mapped_values'], result['probabilities'], width=1/len(result['probabilities']))\n", + "plt.plot([exact_value, exact_value], [0,1], 'r--', linewidth=2)\n", + "plt.xticks(size=15)\n", + "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", + "plt.title('Estimated Option Price', size=15)\n", + "plt.ylabel('Probability', size=15)\n", + "plt.ylim((0,1))\n", + "plt.grid()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "qiskit_master", + "language": "python", + "name": "qiskit_master" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/index.ipynb b/index.ipynb index 4b5d6bc62..a9b1860fe 100644 --- a/index.ipynb +++ b/index.ipynb @@ -84,6 +84,7 @@ "\n", "[Qiskit Finance](qiskit/finance/index.ipynb) provides a colleaction of applications of quantum algorithms to use cases relevant in finance.\n", "This includes use cases like portfolio management, derivative pricing, or credit risk analysis.\n", + "Additional use cases can also be found in the [Qiskit Finance Community](community/finance/index.ipynb) tutorials section.\n", "\n", "\n", "### 2. Community Notebooks\n", diff --git a/qiskit/finance/simulation/option_pricing.ipynb b/qiskit/finance/simulation/option_pricing.ipynb index ba63cbd2c..5d794b071 100644 --- a/qiskit/finance/simulation/option_pricing.ipynb +++ b/qiskit/finance/simulation/option_pricing.ipynb @@ -43,7 +43,6 @@ "- European Call Option (univariate, payoff with 2 segments)\n", "- European Put Option (univariate, payoff with 2 segments)\n", "- Bull Spread (univariate, payoff with 3 segments)\n", - "- Iron Condor (univariate, payoff with 5 segments)\n", "\n", "Note that the provided framework can cover all options of this type, i.e., options that are fully determined by a piecewise linear payoff with respect to the spot price at maturity of the underlying asset.\n", "However, the framework also allows to price more complex options, for instance, options that depend on multiple assets or are path-dependent:\n", @@ -51,6 +50,8 @@ "- Basket Option (multivariate, payoff with 2 segments)\n", "- Asian Barrier Spread (multivariate, path-dependent, payoff with 3 segments)\n", "\n", + "More examples on option pricing with a quantum computer can be found in the [Qiskit Finance Community](../../../community/finance/index.ipynb) section of the Qiskit Tutorials.\n", + "\n", "All examples illustrate how to use the genereric Qiskit Finance framework to construct QAE-operators (uncertainty problems). The same framework can be easily adjusted to estimate risk as well, for instance, the Value at Risk (VaR) or the Conditional Value at Risk (CVaR, also known as Expected Shortfall). How to use Qiskit Finance for risk analysis is illustrated in the following tutorial:\n", "Credit Risk Analysis." ] From 73bb274ea51d531b3e5f1508422f14715faf3f25 Mon Sep 17 00:00:00 2001 From: stefan-woerner Date: Thu, 2 May 2019 14:35:52 +0200 Subject: [PATCH 110/116] update aqua community index --- community/aqua/index.ipynb | 15 ++++++++- community/finance/index.ipynb | 63 ----------------------------------- 2 files changed, 14 insertions(+), 64 deletions(-) delete mode 100644 community/finance/index.ipynb diff --git a/community/aqua/index.ipynb b/community/aqua/index.ipynb index f56fbfce2..fc4615342 100644 --- a/community/aqua/index.ipynb +++ b/community/aqua/index.ipynb @@ -77,6 +77,19 @@ "The repository here may be viewed for the\n", "[full listing](https://github.com/Qiskit/qiskit-tutorial/tree/master/community/optimization).\n", "\n", + "### 5. [Qiskit Finance](../finance/)\n", + "\n", + "Qiskit Finance is a set of tools, algorithms and software for use with quantum computers to carry out research and investigate how to take advantage of quantum computing power to solve problems in the financial domain.\n", + "Please also see the [Qiskit Finance Tutorials](../../qiskit/finance/index.ipynb) for more examples.\n", + "\n", + "Quantum computing for option pricing:\n", + "* Long Butterfly (univariate, payoff with 4 segments)\n", + "* Short Butterfly (univariate, payoff with 4 segments)\n", + "* Iron Condor (univariate, payoff with 5 segments)\n", + "\n", + "The repository here may be viewed for the\n", + "[full listing](../finance).\n", + "\n", "*** " ] }, @@ -106,7 +119,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.1" + "version": "3.7.3" } }, "nbformat": 4, diff --git a/community/finance/index.ipynb b/community/finance/index.ipynb deleted file mode 100644 index c2e2ee53e..000000000 --- a/community/finance/index.ipynb +++ /dev/null @@ -1,63 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Qiskit Finance Community Tutorials" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Welcome Qiskitters to the Qiskit Finance community tutorials.\n", - "\n", - "Qiskit Finance is a set of tools, algorithms and software for use with quantum computers to carry out research and investigate how to take advantage of quantum computing power to solve problems in the Financial domain.\n", - "\n", - "In the following, you'll find a list of currently available community tutorials.\n", - "Please also see the [Qiskit Finance Tutorials](../../qiskit/finance/index.ipynb) for more examples.\n", - "\n", - "Further contributions to simulation or other use cases in finance, such as optimization or machine learning, are very welcome!" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Option pricing on a quantum computer:\n", - "- Long Butterfly (univariate, payoff with 4 segments)\n", - "- Short Butterfly (univariate, payoff with 4 segments)\n", - "- Iron Condor (univariate, payoff with 5 segments)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "qiskit_master", - "language": "python", - "name": "qiskit_master" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} From 1c115fcaea346acfb1d936c11ecee37b11c7f591 Mon Sep 17 00:00:00 2001 From: stefan-woerner Date: Thu, 2 May 2019 14:59:13 +0200 Subject: [PATCH 111/116] add qgan tutorials and update corresponding indices --- qiskit/artificial_intelligence/index.ipynb | 3 +- ...ans_for_loading_random_distributions.ipynb | 11 +- qiskit/finance/index.ipynb | 3 + .../qgan_option_pricing.ipynb | 175 +++++++++++------- .../finance/simulation/option_pricing.ipynb | 5 +- 5 files changed, 129 insertions(+), 68 deletions(-) rename qiskit/{aqua => }/artificial_intelligence/qgans_for_loading_random_distributions.ipynb (99%) diff --git a/qiskit/artificial_intelligence/index.ipynb b/qiskit/artificial_intelligence/index.ipynb index 5537442db..30d03091c 100644 --- a/qiskit/artificial_intelligence/index.ipynb +++ b/qiskit/artificial_intelligence/index.ipynb @@ -13,6 +13,7 @@ "## Contents\n", "\n", "* [Quantum SVM for Classification](qsvm_classification.ipynb)\n", + "* [qGANs for Learning & Loading Random Distributions](qgans_for_loading_random_distributions.ipynb)\n", "* More examples can be found in [commuity/aqua/artificial_intelligence](../../../community/aqua/artificial_intelligence)" ] }, @@ -42,7 +43,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.2" + "version": "3.7.3" } }, "nbformat": 4, diff --git a/qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb b/qiskit/artificial_intelligence/qgans_for_loading_random_distributions.ipynb similarity index 99% rename from qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb rename to qiskit/artificial_intelligence/qgans_for_loading_random_distributions.ipynb index 3889f56a8..26745fc9d 100644 --- a/qiskit/aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb +++ b/qiskit/artificial_intelligence/qgans_for_loading_random_distributions.ipynb @@ -22,7 +22,10 @@ "\n", "The aim of the qGAN training is to generate a state $\\lvert g_{\\theta}\\rangle$ where $p_{\\theta}^{j}$, for $j\\in \\left\\{0, \\ldots, {2^n-1} \\right\\}$, describe a probability distribution that is close to the distribution underlying the training data $X=\\left\\{x^0, \\ldots, x^{k-1} \\right\\}$.\n", "\n", - "For further details please refer to Quantum Generative Adversarial Networks for Learning and Loading Random Distributions. Zoufal, Lucchi, Woerner. 2019." + "For further details please refer to Quantum Generative Adversarial Networks for Learning and Loading Random Distributions. Zoufal, Lucchi, Woerner. 2019.\n", + "\n", + "How to use a trained qGAN in an application, i.e., procing of financial derivatives, is illustrated here:\n", + "qGAN Option Pricing." ] }, { @@ -287,9 +290,9 @@ ], "metadata": { "kernelspec": { - "display_name": "QiskitDevenv", + "display_name": "qiskit_master", "language": "python", - "name": "qiskitdevenv" + "name": "qiskit_master" }, "language_info": { "codemirror_mode": { @@ -301,7 +304,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.3" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/qiskit/finance/index.ipynb b/qiskit/finance/index.ipynb index 3663281f5..5ee05e65e 100644 --- a/qiskit/finance/index.ipynb +++ b/qiskit/finance/index.ipynb @@ -29,6 +29,9 @@ "source": [ "In this notebook we provide an overview of Qiskit Finance tutorials and tutorials from other domains which might be relevant in finance.\n", "\n", + "#### Machine Learning:\n", + "- Quantum Generative Adversarial Networks (qGANs) for data loading in option pricing\n", + "\n", "#### Optimization:\n", "- Portfolio Optimization\n", "- Portfolio Diversification\n", diff --git a/qiskit/finance/machine_learning/qgan_option_pricing.ipynb b/qiskit/finance/machine_learning/qgan_option_pricing.ipynb index 606ccde25..dbb71a815 100644 --- a/qiskit/finance/machine_learning/qgan_option_pricing.ipynb +++ b/qiskit/finance/machine_learning/qgan_option_pricing.ipynb @@ -1,12 +1,5 @@ { "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -23,35 +16,16 @@ "- [2]ETH Zurich\n", "\n", "### Introduction\n", - "In this notebook, we discuss how a Quantum Machine Learning Algorithm, namely a quantum Generative Adversarial Network (qGAN), can facilitate the pricing of a European call option. More specifically, a qGAN can be trained such that a quantum circuit models the spot price distribution of an asset underlying a European call option. The resulting model can then be integrated into a Quantum Amplitude Estimation based algorithm to evaluate the expected payoff, see [European Call Option Pricing](../../finance/simulation/european_call_option_pricing.ipynb).
\n", - "\n", - "For a general introduction on how to train a qGAN, see [qGANs for Loading Random Distributions](../../aqua/artificial_intelligence/qgans_for_loading_random_distributions.ipynb).
\n", - "\n", - "For further details on learning and loading random distributions by training a qGAN please refer to
Quantum Generative Adversarial Networks for Learning and Loading Random Distributions. Zoufal, Lucchi, Woerner. 2019." + "In this notebook, we discuss how a Quantum Machine Learning Algorithm, namely a quantum Generative Adversarial Network (qGAN), can facilitate the pricing of a European call option. More specifically, a qGAN can be trained such that a quantum circuit models the spot price of an asset underlying a European call option. The resulting model can then be integrated into a Quantum Amplitude Estimation based algorithm to evaluate the expected payoff - see [European Call Option Pricing](../../aqua/finance/european_call_option_pricing.ipynb).
\n", + "For further details on learning and loading random distributions by training a qGAN please refer to Quantum Generative Adversarial Networks for Learning and Loading Random Distributions. Zoufal, Lucchi, Woerner. 2019." ] }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 33, "metadata": {}, - "outputs": [ - { - "ename": "ImportError", - "evalue": "cannot import name 'UnivariateVariationalDistribution'", - "output_type": "error", - "traceback": [ - "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[1;31mImportError\u001b[0m Traceback (most recent call last)", - "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m\u001b[0m\n\u001b[0;32m 8\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0maqua\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0malgorithms\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mAmplitudeEstimation\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 9\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0maqua\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcomponents\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0muncertainty_problems\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mEuropeanCallExpectedValue\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 10\u001b[1;33m \u001b[1;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0maqua\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcomponents\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0muncertainty_models\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mUnivariateVariationalDistribution\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mNormalDistribution\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 11\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0maqua\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcomponents\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvariational_forms\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mRY\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 12\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;31mImportError\u001b[0m: cannot import name 'UnivariateVariationalDistribution'" - ] - } - ], + "outputs": [], "source": [ - "# #!/usr/bin/env python\n", - "# # coding: utf-8\n", - "# from __future__ import absolute_import, division, print_function\n", - "\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "import numpy as np\n", @@ -59,6 +33,8 @@ "from qiskit.aqua.components.uncertainty_problems import EuropeanCallExpectedValue\n", "from qiskit.aqua.components.uncertainty_models import UnivariateVariationalDistribution, NormalDistribution\n", "from qiskit.aqua.components.variational_forms import RY\n", + "from qiskit import QuantumRegister, QuantumCircuit\n", + "from qiskit.aqua.components.initial_states import Custom\n", "\n", "from qiskit.aqua import aqua_globals, QuantumInstance\n", "\n", @@ -77,13 +53,12 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 34, "metadata": {}, "outputs": [], "source": [ "# Set upper and lower data values\n", "bounds = np.array([0.,7.])\n", - "\n", "# Set number of qubits used in the uncertainty model\n", "num_qubits = [3]\n", "\n", @@ -92,31 +67,66 @@ "for i in range(sum(num_qubits)):\n", " entangler_map.append([i, int(np.mod(i+1, sum(num_qubits)))])\n", "\n", - "# Set variational form\n", - "var_form = RY(int(np.sum(num_qubits)), depth=1, entangler_map=entangler_map, entanglement_gate='cz')\n", - "\n", "# Load the trained circuit parameters\n", "g_params = [0.29399714, 0.38853322, 0.9557694, 0.07245791, 6.02626428, 0.13537225]\n", - "\n", "# Set an initial state for the generator circuit\n", "init_dist = NormalDistribution(int(sum(num_qubits)), mu=1., sigma=1., low=bounds[0], high=bounds[1])\n", - "\n", + "init_distribution = np.sqrt(init_dist.probabilities)\n", + "init_distribution = Custom(num_qubits=sum(num_qubits), state_vector=init_distribution)\n", + "# Set variational form\n", + "var_form = RY(int(np.sum(num_qubits)), depth=1, initial_state=init_distribution,\n", + " entangler_map=entangler_map, entanglement_gate='cz')\n", "# Set generator circuit\n", "g_circuit = UnivariateVariationalDistribution(int(sum(num_qubits)), var_form, g_params,\n", - " initial_distribution=init_dist, low=bounds[0], high=bounds[1])\n", - "\n", + " low=bounds[0], high=bounds[1])\n", "# construct circuit factory for uncertainty model\n", - "uncertainty_model = g_circuit" + "uncertainty_model = g_circuit\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Evaluate Expected Payoff\n", + "Now, the trained uncertainty model can be used to evaluate the expectation value of the option's payoff function with Quantum Amplitude Estimation." ] }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 35, + "metadata": {}, + "outputs": [], + "source": [ + "# set the strike price (should be within the low and the high value of the uncertainty)\n", + "strike_price = 2\n", + "\n", + "# set the approximation scaling for the payoff function\n", + "c_approx = 0.25\n", + "\n", + "# construct circuit factory for payoff function\n", + "european_call = EuropeanCallExpectedValue(\n", + " uncertainty_model,\n", + " strike_price=strike_price,\n", + " c_approx=c_approx\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Plot the probability distribution\n", + "Next, we plot the trained probability distribution and, for reasons of comparison, also the target probability distribution." + ] + }, + { + "cell_type": "code", + "execution_count": 36, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -128,15 +138,36 @@ } ], "source": [ - "# plot probability distribution\n", + "#trained probability distribution\n", + "init_distribution = np.sqrt(init_dist.probabilities)\n", + "init_distribution = Custom(num_qubits=sum(num_qubits), state_vector=init_distribution)\n", + "var_form = RY(int(np.sum(num_qubits)), depth=1, initial_state=init_distribution,\n", + " entangler_map=entangler_map, entanglement_gate='cz')\n", + "g_circuit = UnivariateVariationalDistribution(int(sum(num_qubits)), var_form, g_params, low=bounds[0], high=bounds[1])\n", + "uncertainty_model = g_circuit\n", + "uncertainty_model.set_probabilities(QuantumInstance(BasicAer.get_backend('statevector_simulator')))\n", "x = uncertainty_model.values\n", "y = uncertainty_model.probabilities\n", - "plt.bar(x, y, width=0.2)\n", - "plt.xticks(x, size=15)\n", + "#target probability distribution\n", + "N = 100000\n", + "log_normal = np.random.lognormal(mean=1, sigma=1, size=N)\n", + "log_normal = np.round(log_normal)\n", + "log_normal = log_normal[log_normal <= 7]\n", + "\n", + "log_normal_samples = []\n", + "for i in range(8):\n", + " log_normal_samples += [np.sum(log_normal==i)]\n", + "log_normal_samples = np.array(log_normal_samples / sum(log_normal_samples))\n", + "\n", + "\n", + "plt.bar(x, y, width=0.2, label='trained distribution', color='royalblue')\n", + "plt.xticks(x, size=15, rotation=90)\n", "plt.yticks(size=15)\n", "plt.grid()\n", "plt.xlabel('Spot Price at Maturity $S_T$ (\\$)', size=15)\n", "plt.ylabel('Probability ($\\%$)', size=15)\n", + "plt.plot(log_normal_samples,'-o', color ='deepskyblue', label='target distribution', linewidth=4, markersize=12)\n", + "plt.legend(loc='best')\n", "plt.show()" ] }, @@ -145,36 +176,44 @@ "metadata": {}, "source": [ "### Evaluate Expected Payoff\n", - "Now, the trained uncertainty model can be used to evaluate the expectation value of the option's payoff function with Quantum Amplitude Estimation." + "Now, the trained uncertainty model can be used to evaluate the expectation value of the option's payoff function analytically and with Quantum Amplitude Estimation." ] }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 39, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Estimated value:\t1.2580\n", - "Probability: \t0.8785\n" + "Analytically calculated expected payoff w.r.t. the target distribution: 1.0585480647564538\n", + "Analytically calculated expected payoff w.r.t. the trained distribution: 0.980530833264945\n", + "Expected payoff calculated with Quantum Amplitude Estimation: \t1.2580\n", + "Probability: \t0.8785\n" ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" } ], "source": [ - "# set the strike price (should be within the low and the high value of the uncertainty)\n", - "strike_price = 2\n", - "\n", - "# set the approximation scaling for the payoff function\n", - "c_approx = 0.25\n", + "payoff = np.array([0,0,0,1,2,3,4,5])\n", + "ep = np.dot(log_normal_samples, payoff)\n", + "print(\"Analytically calculated expected payoff w.r.t. the target distribution: \", ep)\n", + "ep_trained = np.dot(y, payoff)\n", + "print(\"Analytically calculated expected payoff w.r.t. the trained distribution: \", ep_trained)\n", "\n", - "# construct circuit factory for payoff function\n", - "european_call = EuropeanCallExpectedValue(\n", - " uncertainty_model,\n", - " strike_price=strike_price,\n", - " c_approx=c_approx\n", - ")\n", "# set number of evaluation qubits (samples)\n", "m = 5\n", "\n", @@ -182,8 +221,20 @@ "ae = AmplitudeEstimation(m, european_call)\n", "# result = ae.run(quantum_instance=BasicAer.get_backend('qasm_simulator'), shots=100)\n", "result = ae.run(quantum_instance=BasicAer.get_backend('statevector_simulator'))\n", - "print('Estimated value:\\t%.4f' % result['estimation'])\n", - "print('Probability: \\t%.4f' % result['max_probability'])" + "print('Expected payoff calculated with Quantum Amplitude Estimation: \\t%.4f' % result['estimation'])\n", + "print('Probability: \\t%.4f' % result['max_probability'])\n", + "\n", + "# plot exact payoff function (evaluated on the grid of the trained uncertainty model)\n", + "x = uncertainty_model.values\n", + "y_strike = np.maximum(0, x - strike_price)\n", + "plt.plot(x, y_strike, 'ro-')\n", + "plt.grid()\n", + "plt.title('Payoff Function', size=15)\n", + "plt.xlabel('Spot Price', size=15)\n", + "plt.ylabel('Payoff', size=15)\n", + "plt.xticks(x, size=15, rotation=90)\n", + "plt.yticks(size=15)\n", + "plt.show()" ] }, { diff --git a/qiskit/finance/simulation/option_pricing.ipynb b/qiskit/finance/simulation/option_pricing.ipynb index 5d794b071..a5078cd69 100644 --- a/qiskit/finance/simulation/option_pricing.ipynb +++ b/qiskit/finance/simulation/option_pricing.ipynb @@ -53,7 +53,10 @@ "More examples on option pricing with a quantum computer can be found in the [Qiskit Finance Community](../../../community/finance/index.ipynb) section of the Qiskit Tutorials.\n", "\n", "All examples illustrate how to use the genereric Qiskit Finance framework to construct QAE-operators (uncertainty problems). The same framework can be easily adjusted to estimate risk as well, for instance, the Value at Risk (VaR) or the Conditional Value at Risk (CVaR, also known as Expected Shortfall). How to use Qiskit Finance for risk analysis is illustrated in the following tutorial:\n", - "Credit Risk Analysis." + "Credit Risk Analysis.\n", + "\n", + "An example of how quantum Generative Adversarial Networks (qGANs) can be used to learn and efficiently load generic random distributions for option pricing can be found here:\n", + "QGANs to learn and load random distributions for option pricing" ] }, { From 8b87790898ae381ba1782f0d364e1fa7177fae04 Mon Sep 17 00:00:00 2001 From: Jakub Marecek Date: Fri, 3 May 2019 11:53:43 +0100 Subject: [PATCH 112/116] Edits --- .../portfolio_diversification.ipynb | 46 +++++++++++++------ qiskit/optimization/vehicle_routing.ipynb | 12 +++-- 2 files changed, 40 insertions(+), 18 deletions(-) diff --git a/qiskit/finance/optimization/portfolio_diversification.ipynb b/qiskit/finance/optimization/portfolio_diversification.ipynb index 5da6c4eff..c8139dd31 100644 --- a/qiskit/finance/optimization/portfolio_diversification.ipynb +++ b/qiskit/finance/optimization/portfolio_diversification.ipynb @@ -7,13 +7,20 @@ "" ] }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, { "cell_type": "markdown", "metadata": {}, "source": [ "# _*Qiskit Finance: Portfolio diversification*_\n", "\n", - "The latest version of this notebook is available on https://github.com/qiskit/qiskit-tutorial.\n", + "The latest version of this notebook is available on https://github.com/qiskit/qiskit-tutorials.\n", "\n", "***\n", "### Contributors\n", @@ -25,10 +32,10 @@ "\n", "## Introduction \n", "\n", - "In asset management, there are broadly two approaches: active and passive investment management. Within passive investment management, there are index-tracking funds and there are approaches based on portfolio diversification, which aim at representing a portfolio with large number of assets by a smaller number of representative stocks.\n", + "In asset management, there are broadly two approaches: active and passive investment management. Within passive investment management, there are index-tracking funds and there are approaches based on portfolio diversification, which aim at representing a portfolio with large number of assets by a smaller number of representative assets.\n", "This notebook illustrates a portfolio diversification problem, which has recently become popular for two reasons:\n", "1. it makes it possible to mimick the performance of an index (or a similarly large set of assets) with a limited budget, at limited transaction costs. That is: traditional index-tracking may purchase all assets in the index, ideally with the same weights as in the index. This may be impractical for a number of reasons: the total of even a single round lot per asset may amount to more than the assets under management, the large scale of the index-tracking problem with integrality constraints may render the optimisation problem difficult, and the transaction costs of the frequent rebalancing to adjust the positions to the weights in the index may render the approach expensive. Thus, a popular approach is to select a portfolio of $q$ assets that represent the market with $n$ assets, where $q$ is significantly smaller than $n$, but where the portfolio replicates the behaviour of the underlying market. To determine how to group assets into $q$ clusters and how to determine which $q$ assets should represent the $q$ clusters amounts to solving a large-scale optimization problem. In the following we describe the mathematical model for the portfolio diversification problem as introduced in [Cornuejols & Tutuncu, 2006] \n", - "2. it allows for similarity measures between time-series beyond the covariance matrix. Notice that traditionally, modern portfolio theory considers the covariance matrix as measure of similarity between the assets. As such, however, covariance matrix is imperfect. Consider, for instance, a company listed both in London and New York. Although both listings should be very similar, only parts of the time series of the prices of the two listings will overlap, because of the partial overlap of the times the markets open. Instead of covariance, one can consider, for example, dynamic time warping of [Berndt and Clifford, 1994] as a measure of similarity between two time series, which allows for the fact that for some time periods, the data are captured by only one of the time series, while for others, both time series exhibit the similarity due to the parallel evolution of the stock price.\n", + "2. it allows for similarity measures between time-series beyond the covariance matrix. Notice that traditionally, modern portfolio theory considers the covariance matrix as measure of similarity between the assets. As such, however, covariance matrix is imperfect. Consider, for instance, a company listed both in London and New York. Although both listings should be very similar, only parts of the time series of the prices of the two listings will overlap, because of the partial overlap of the times the markets open. Instead of covariance, one can consider, for example, dynamic time warping of [Berndt and Clifford, 1994] as a measure of similarity between two time series, which allows for the fact that for some time periods, the data are captured by only one of the time series, while for others, both time series exhibit the similarity due to the parallel evolution of the asset price.\n", "\n", "The overall workflow we demonstrate comprises:\n", "\n", @@ -50,10 +57,10 @@ "As discussed in [Cornuejols & Tutuncu, 2006], we describe a mathematical model that clusters assets into groups of similar ones and selects one representative asset from each group to be included in the index fund portfolio. The model is based on the following data, which we will discuss in more detail later:\n", "\n", "$$\n", - "\\rho_{ij} = \\textrm{similarity}\\, \\textrm{between}\\, \\textrm{stock}\\, i \\, \\textrm{and}\\, \\textrm{stock}\\, j.\n", + "\\rho_{ij} = \\textrm{similarity}\\, \\textrm{between}\\, \\textrm{asset}\\, i \\, \\textrm{and}\\, \\textrm{asset}\\, j.\n", "$$\n", "\n", - "For example, $\\rho_{ii} = 1$, $\\rho_{ij} \\leq 1$ for $i \\neq j$ and $\\rho_{ij}$ is larger for more similar stocks. An example of this is the correlation between the returns of stocks $i$ and $j$. But one could choose other similarity indices $\\rho_{ij}$.\n", + "For example, $\\rho_{ii} = 1$, $\\rho_{ij} \\leq 1$ for $i \\neq j$ and $\\rho_{ij}$ is larger for more similar assets. An example of this is the correlation between the returns of asset $i$ and $j$. But one could choose other similarity indices $\\rho_{ij}$.\n", "\n", "The problem that we are interested in solving is:\n", "\n", @@ -81,9 +88,9 @@ "\\quad x_{ij}, y_j \\in\\{0,1\\}, \\,\\textrm{ for }\\, i = 1,\\ldots, n; \\, j = 1,\\ldots, n.\n", "$$\n", "\n", - "The variables $y_j$ describe which stocks $j$ are in the index fund ($y_j = 1$ if $j$ is selected in the fund, $0$ otherwise). For each stock $i = 1,\\dots,n$, the variable $x_{ij}$ indicates which stock $j$ in the index fund is most similar to $i$ ($x_{ij} = 1$ if $j$ is the most similar stock in the index fund, $0$ otherwise).\n", + "The variables $y_j$ describe which assets $j$ are in the index fund ($y_j = 1$ if $j$ is selected in the fund, $0$ otherwise). For each asset $i = 1,\\dots,n$, the variable $x_{ij}$ indicates which asset $j$ in the index fund is most similar to $i$ ($x_{ij} = 1$ if $j$ is the most similar asset in the index fund, $0$ otherwise).\n", "\n", - "The first constraint selects $q$ stocks in the fund. The second constraint imposes that each stock $i$ has exactly one representative stock $j$ in the fund. The third and fourth constraints guarantee that stock $i$ can be represented by stock $j$ only if $j$ is in the fund. The objective of the model maximizes the similarity between the $n$ stocks and their representatives in the fund. Different cost functions can also be considered. \n", + "The first constraint selects $q$ assets in the fund. The second constraint imposes that each asset $i$ has exactly one representative asset $j$ in the fund. The third and fourth constraints guarantee that asset $i$ can be represented by asset $j$ only if $j$ is in the fund. The objective of the model maximizes the similarity between the $n$ asset and their representatives in the fund. Different cost functions can also be considered. \n", "\n", "Let us concatenate the decision variables in one vector \n", "\n", @@ -233,7 +240,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Next, we download price data for two stocks and compute their pair-wise similarity matrix (dynamic time warping distance normalised to (0,1] by taking the reciprocal). If this fails, e.g., due to your being offline or exeeding the daily limit for accesses to the stock-market data, we consider a constant matrix instead." + "Next, we download price data for two assets and compute their pair-wise similarity matrix (dynamic time warping distance normalised to (0,1] by taking the reciprocal). If this fails, e.g., due to your being offline or exeeding the daily limit for accesses to the stock-market data, we consider a constant matrix instead." ] }, { @@ -265,7 +272,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Now we decide on the number of clusters. This has to be smaller than the number of stocks we have loaded." + "Now we decide on the number of clusters. This has to be smaller than the number of assets we have loaded." ] }, { @@ -433,7 +440,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Solution shows the selected stocks via the stars and in green the links (via similarities) with other stocks that are represented in the fund by the linked stock. " + "Solution shows the selected assets via the stars and in green the links (via similarities) with other assets that are represented in the fund by the linked asset. " ] }, { @@ -677,15 +684,26 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Solution shows the selected stocks via the stars and in green the links (via similarities) with other stocks that are represented in the fund by the linked stock. Keep in mind that VQE is an heuristic working on the QP formulation of the Ising Hamiltonian, though. For suitable choices of A, local optima of the QP formulation will be feasible solutions to the ILP. While for some small instances, as above, we can find optimal solutions of the QP formulation which coincide with optima of the ILP, finding optimal solutions of the ILP is harder than finding local optima of the QP formulation, in general. Even within the VQE, one may provide stronger guarantees, for specific variational forms (trial wave functions). " + "The plot shows the selected assets with stars; in green, it shows the links with other assets that are represented in the portfolio by the starred asset.\n", + "\n", + "Keep in mind that VQE is an heuristic working on the QP formulation of the Ising Hamiltonian. For suitable choices of A, local optima of the QP formulation will be feasible solutions to the integer programming problem. While for some small instances, as above, we can find optimal solutions of the QP formulation that coincide with optima of the integer programming problem, finding optimal solutions of the integer programming problem is harder than finding local optima of the quadratic programming formulation, in general. \n", + "\n", + "Even within the VQE, one may provide stronger guarantees, for specific variational forms (trial wave functions). Beyond VQE, one can show convergence to the global optiam using the phase estimation approach. One can, indeed, start by using VQE and moving to phase estimation subsequently, cf. https://github.com/Qiskit/qiskit-tutorials/blob/master/community/aqua/general/vqe2iqpe.ipynb" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { "kernelspec": { - "display_name": "qiskit_master", + "display_name": "Python 3", "language": "python", - "name": "qiskit_master" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -697,7 +715,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.1" + "version": "3.7.2" } }, "nbformat": 4, diff --git a/qiskit/optimization/vehicle_routing.ipynb b/qiskit/optimization/vehicle_routing.ipynb index f602e8f68..fb1d64fd4 100644 --- a/qiskit/optimization/vehicle_routing.ipynb +++ b/qiskit/optimization/vehicle_routing.ipynb @@ -873,7 +873,11 @@ "source": [ "The plots present the depot with a star and the selected routes for the vehicles with arrows. Note that in this particular case, we can find the optimal solution of the QP formulation, which happens to coincide with the optimal solution of the ILP.\n", "\n", - "Keep in mind that VQE is an heuristic working on the QP formulation of the Ising Hamiltonian, though. For suitable choices of A, local optima of the QP formulation will be feasible solutions to the ILP. While for some small instances, as above, we can find optimal solutions of the QP formulation which coincide with optima of the ILP, finding optimal solutions of the ILP is harder than finding local optima of the QP formulation, in general, which in turn is harder than finding feasible solutions of the ILP. Even within the VQE, one may provide stronger guarantees, for specific variational forms (trial wave functions). \n", + "The plot shows the selected assets with stars; in green, it shows the links with other assets that are represented in the portfolio by the starred asset.\n", + "\n", + "Keep in mind that VQE is an heuristic working on the QP formulation of the Ising Hamiltonian. For suitable choices of A, local optima of the QP formulation will be feasible solutions to the integer programming problem. While for some small instances, as above, we can find optimal solutions of the QP formulation that coincide with optima of the integer programming problem, finding optimal solutions of the integer programming problem is harder than finding local optima of the quadratic programming formulation, in general. \n", + "\n", + "Even within the VQE, one may provide stronger guarantees, for specific variational forms. Beyond VQE, one can show convergence to the global optiam using the phase estimation approach. One can, indeed, start by using VQE and moving to phase estimation subsequently, cf. https://github.com/Qiskit/qiskit-tutorials/blob/master/community/aqua/general/vqe2iqpe.ipynb\n", "\n", "Last but not least, you may be pleased to learn that the above has been packaged in Qiskit Aqua." ] @@ -922,9 +926,9 @@ ], "metadata": { "kernelspec": { - "display_name": "qiskit_master", + "display_name": "Python 3", "language": "python", - "name": "qiskit_master" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -936,7 +940,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.1" + "version": "3.7.2" } }, "nbformat": 4, From 59dac5c9a3d32ae1dd2f603bbcd80f26a0ab9b46 Mon Sep 17 00:00:00 2001 From: stefan-woerner Date: Wed, 8 May 2019 21:05:17 +0200 Subject: [PATCH 113/116] split into featured, community, and qiskit tutorials --- .../finance/data_providers/time_series.ipynb | 0 featured/finance/index.ipynb | 66 +++++++++++++ .../portfolio_diversification.ipynb | 9 +- .../asian_barrier_spread_pricing.ipynb | 0 .../simulation/basket_option_pricing.ipynb | 0 .../simulation/bull_spread_pricing.ipynb | 0 .../european_call_option_pricing.ipynb | 0 .../european_put_option_pricing.ipynb | 0 .../simulation/fixed_income_pricing.ipynb | 0 .../finance/simulation/option_pricing.ipynb | 0 qiskit/finance/index.ipynb | 17 ++-- .../qgan_option_pricing.ipynb | 7 ++ .../optimization/portfolio_optimization.ipynb | 96 +++++++++---------- 13 files changed, 128 insertions(+), 67 deletions(-) rename {qiskit => featured}/finance/data_providers/time_series.ipynb (100%) create mode 100644 featured/finance/index.ipynb rename {qiskit => featured}/finance/optimization/portfolio_diversification.ipynb (99%) rename {qiskit => featured}/finance/simulation/asian_barrier_spread_pricing.ipynb (100%) rename {qiskit => featured}/finance/simulation/basket_option_pricing.ipynb (100%) rename {qiskit => featured}/finance/simulation/bull_spread_pricing.ipynb (100%) rename {qiskit => featured}/finance/simulation/european_call_option_pricing.ipynb (100%) rename {qiskit => featured}/finance/simulation/european_put_option_pricing.ipynb (100%) rename {qiskit => featured}/finance/simulation/fixed_income_pricing.ipynb (100%) rename {qiskit => featured}/finance/simulation/option_pricing.ipynb (100%) diff --git a/qiskit/finance/data_providers/time_series.ipynb b/featured/finance/data_providers/time_series.ipynb similarity index 100% rename from qiskit/finance/data_providers/time_series.ipynb rename to featured/finance/data_providers/time_series.ipynb diff --git a/featured/finance/index.ipynb b/featured/finance/index.ipynb new file mode 100644 index 000000000..770e69f90 --- /dev/null +++ b/featured/finance/index.ipynb @@ -0,0 +1,66 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# _*Qiskit Finance: Overview*_ \n", + "\n", + "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", + "\n", + "***\n", + "### Contributors\n", + "Stefan Woerner[1], Daniel Egger[1], Christa Zoufal[1], Andrea Simonetto[1], Jakub Marecek[1], Martin Mevissen[1], Shaohan Hu[1], Stephen Wood[1], Marco Pistoia[1]\n", + "\n", + "### Affliation\n", + "- [1]IBMQ" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the following, we provide an overview of *Qiskit Finance Community* tutorials.
\n", + "Please see the [Qiskit Finance Tutorials](../../qiskit/finance/index.ipynb) for an additional selection of notebooks.\n", + "\n", + "#### Optimization:\n", + "- Portfolio Diversification\n", + " \n", + "#### Simulation:\n", + "- Option Pricing\n", + "- Fixed Income Pricing\n", + "\n", + "#### Data Providers:\n", + "- Stock Market Time Series" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "qiskit_master", + "language": "python", + "name": "qiskit_master" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/qiskit/finance/optimization/portfolio_diversification.ipynb b/featured/finance/optimization/portfolio_diversification.ipynb similarity index 99% rename from qiskit/finance/optimization/portfolio_diversification.ipynb rename to featured/finance/optimization/portfolio_diversification.ipynb index 5da6c4eff..86b4ce45a 100644 --- a/qiskit/finance/optimization/portfolio_diversification.ipynb +++ b/featured/finance/optimization/portfolio_diversification.ipynb @@ -4,14 +4,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# _*Qiskit Finance: Portfolio diversification*_\n", + "# _*Portfolio diversification*_\n", "\n", "The latest version of this notebook is available on https://github.com/qiskit/qiskit-tutorial.\n", "\n", diff --git a/qiskit/finance/simulation/asian_barrier_spread_pricing.ipynb b/featured/finance/simulation/asian_barrier_spread_pricing.ipynb similarity index 100% rename from qiskit/finance/simulation/asian_barrier_spread_pricing.ipynb rename to featured/finance/simulation/asian_barrier_spread_pricing.ipynb diff --git a/qiskit/finance/simulation/basket_option_pricing.ipynb b/featured/finance/simulation/basket_option_pricing.ipynb similarity index 100% rename from qiskit/finance/simulation/basket_option_pricing.ipynb rename to featured/finance/simulation/basket_option_pricing.ipynb diff --git a/qiskit/finance/simulation/bull_spread_pricing.ipynb b/featured/finance/simulation/bull_spread_pricing.ipynb similarity index 100% rename from qiskit/finance/simulation/bull_spread_pricing.ipynb rename to featured/finance/simulation/bull_spread_pricing.ipynb diff --git a/qiskit/finance/simulation/european_call_option_pricing.ipynb b/featured/finance/simulation/european_call_option_pricing.ipynb similarity index 100% rename from qiskit/finance/simulation/european_call_option_pricing.ipynb rename to featured/finance/simulation/european_call_option_pricing.ipynb diff --git a/qiskit/finance/simulation/european_put_option_pricing.ipynb b/featured/finance/simulation/european_put_option_pricing.ipynb similarity index 100% rename from qiskit/finance/simulation/european_put_option_pricing.ipynb rename to featured/finance/simulation/european_put_option_pricing.ipynb diff --git a/qiskit/finance/simulation/fixed_income_pricing.ipynb b/featured/finance/simulation/fixed_income_pricing.ipynb similarity index 100% rename from qiskit/finance/simulation/fixed_income_pricing.ipynb rename to featured/finance/simulation/fixed_income_pricing.ipynb diff --git a/qiskit/finance/simulation/option_pricing.ipynb b/featured/finance/simulation/option_pricing.ipynb similarity index 100% rename from qiskit/finance/simulation/option_pricing.ipynb rename to featured/finance/simulation/option_pricing.ipynb diff --git a/qiskit/finance/index.ipynb b/qiskit/finance/index.ipynb index 5ee05e65e..05f9e8f5c 100644 --- a/qiskit/finance/index.ipynb +++ b/qiskit/finance/index.ipynb @@ -27,22 +27,17 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "In this notebook we provide an overview of Qiskit Finance tutorials and tutorials from other domains which might be relevant in finance.\n", + "In the following we provide a selection of Qiskit Finance tutorials for the three domains *Machine Learning*, *Optimization*, and *Simulation*.
\n", + "Many other related tutorials, e.g. on *Option Pricing* can be found in the [Qiskit Finance Community](../../community/finance/index.ipynb) section.\n", "\n", - "#### Machine Learning:\n", + "#### Machine Learning\n", "- Quantum Generative Adversarial Networks (qGANs) for data loading in option pricing\n", "\n", - "#### Optimization:\n", + "#### Optimization\n", "- Portfolio Optimization\n", - "- Portfolio Diversification\n", " \n", - "#### Simulation:\n", - "- Option Pricing\n", - "- Credit Risk Analysis\n", - "- Fixed Income Pricing\n", - "\n", - "#### Data Providers:\n", - "- Stock Market Time Series" + "#### Simulation\n", + "- Credit Risk Analysis" ] }, { diff --git a/qiskit/finance/machine_learning/qgan_option_pricing.ipynb b/qiskit/finance/machine_learning/qgan_option_pricing.ipynb index dbb71a815..b8dee1bc9 100644 --- a/qiskit/finance/machine_learning/qgan_option_pricing.ipynb +++ b/qiskit/finance/machine_learning/qgan_option_pricing.ipynb @@ -1,5 +1,12 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" + ] + }, { "cell_type": "markdown", "metadata": {}, diff --git a/qiskit/finance/optimization/portfolio_optimization.ipynb b/qiskit/finance/optimization/portfolio_optimization.ipynb index 494016f51..c95b4f7d9 100644 --- a/qiskit/finance/optimization/portfolio_optimization.ipynb +++ b/qiskit/finance/optimization/portfolio_optimization.ipynb @@ -190,26 +190,26 @@ "name": "stdout", "output_type": "stream", "text": [ - "Optimal: selection [0 0 1 1], value -0.0026\n", + "Optimal: selection [0 1 1 0], value -0.0410\n", "\n", "----------------- Full result ---------------------\n", "selection\tvalue\t\tprobability\n", "---------------------------------------------------\n", - " [0 0 1 1]\t-0.0026\t\t1.0000\n", - " [1 1 1 1]\t15.9996\t\t0.0000\n", - " [0 1 1 1]\t3.9984\t\t0.0000\n", - " [1 0 1 1]\t3.9985\t\t0.0000\n", - " [1 1 0 1]\t4.0000\t\t0.0000\n", - " [0 1 0 1]\t-0.0011\t\t0.0000\n", - " [1 0 0 1]\t-0.0011\t\t0.0000\n", - " [0 0 0 1]\t3.9978\t\t0.0000\n", - " [1 1 1 0]\t4.0017\t\t0.0000\n", - " [0 1 1 0]\t0.0006\t\t0.0000\n", - " [1 0 1 0]\t0.0006\t\t0.0000\n", - " [0 0 1 0]\t3.9995\t\t0.0000\n", - " [1 1 0 0]\t0.0021\t\t0.0000\n", - " [0 1 0 0]\t4.0010\t\t0.0000\n", - " [1 0 0 0]\t4.0011\t\t0.0000\n", + " [0 1 1 0]\t-0.0410\t\t1.0000\n", + " [1 1 1 1]\t15.9639\t\t0.0000\n", + " [0 1 1 1]\t3.9613\t\t0.0000\n", + " [1 0 1 1]\t3.9653\t\t0.0000\n", + " [0 0 1 1]\t-0.0373\t\t0.0000\n", + " [1 1 0 1]\t4.0031\t\t0.0000\n", + " [0 1 0 1]\t0.0002\t\t0.0000\n", + " [1 0 0 1]\t0.0048\t\t0.0000\n", + " [0 0 0 1]\t4.0020\t\t0.0000\n", + " [1 1 1 0]\t3.9617\t\t0.0000\n", + " [1 0 1 0]\t-0.0368\t\t0.0000\n", + " [0 0 1 0]\t3.9606\t\t0.0000\n", + " [1 1 0 0]\t0.0010\t\t0.0000\n", + " [0 1 0 0]\t3.9981\t\t0.0000\n", + " [1 0 0 0]\t4.0029\t\t0.0000\n", " [0 0 0 0]\t16.0000\t\t0.0000\n" ] } @@ -252,27 +252,27 @@ "name": "stdout", "output_type": "stream", "text": [ - "Optimal: selection [0 1 1 0], value 0.0006\n", + "Optimal: selection [1 0 1 0], value -0.0368\n", "\n", "----------------- Full result ---------------------\n", "selection\tvalue\t\tprobability\n", "---------------------------------------------------\n", - " [0 1 1 0]\t0.0006\t\t0.7038\n", - " [1 0 0 1]\t-0.0011\t\t0.2120\n", - " [1 0 1 0]\t0.0006\t\t0.0272\n", - " [0 1 0 1]\t-0.0011\t\t0.0251\n", - " [1 1 0 0]\t0.0021\t\t0.0167\n", - " [0 0 1 1]\t-0.0026\t\t0.0151\n", - " [1 0 0 0]\t4.0011\t\t0.0000\n", - " [0 1 1 1]\t3.9984\t\t0.0000\n", - " [0 0 0 1]\t3.9978\t\t0.0000\n", - " [1 0 1 1]\t3.9985\t\t0.0000\n", - " [0 1 0 0]\t4.0010\t\t0.0000\n", - " [1 1 1 0]\t4.0017\t\t0.0000\n", - " [1 1 0 1]\t4.0000\t\t0.0000\n", + " [1 0 1 0]\t-0.0368\t\t0.5423\n", + " [0 1 1 0]\t-0.0410\t\t0.3289\n", + " [0 0 1 1]\t-0.0373\t\t0.0641\n", + " [1 1 0 0]\t0.0010\t\t0.0394\n", + " [1 0 0 1]\t0.0048\t\t0.0213\n", + " [0 1 0 1]\t0.0002\t\t0.0039\n", + " [0 0 0 1]\t4.0020\t\t0.0000\n", + " [1 1 0 1]\t4.0031\t\t0.0000\n", + " [0 1 1 1]\t3.9613\t\t0.0000\n", " [0 0 0 0]\t16.0000\t\t0.0000\n", - " [0 0 1 0]\t3.9995\t\t0.0000\n", - " [1 1 1 1]\t15.9996\t\t0.0000\n" + " [1 1 1 1]\t15.9639\t\t0.0000\n", + " [1 0 1 1]\t3.9653\t\t0.0000\n", + " [1 0 0 0]\t4.0029\t\t0.0000\n", + " [0 0 1 0]\t3.9606\t\t0.0000\n", + " [0 1 0 0]\t3.9981\t\t0.0000\n", + " [1 1 1 0]\t3.9617\t\t0.0000\n" ] } ], @@ -336,27 +336,27 @@ "name": "stdout", "output_type": "stream", "text": [ - "Optimal: selection [1 1 0 0], value 0.0021\n", + "Optimal: selection [1 0 0 1], value 0.0048\n", "\n", "----------------- Full result ---------------------\n", "selection\tvalue\t\tprobability\n", "---------------------------------------------------\n", - " [1 1 0 0]\t0.0021\t\t0.1667\n", - " [1 0 1 0]\t0.0006\t\t0.1667\n", - " [0 1 1 0]\t0.0006\t\t0.1667\n", - " [1 0 0 1]\t-0.0011\t\t0.1666\n", - " [0 1 0 1]\t-0.0011\t\t0.1666\n", - " [0 0 1 1]\t-0.0026\t\t0.1666\n", + " [1 0 0 1]\t0.0048\t\t0.1674\n", + " [1 1 0 0]\t0.0010\t\t0.1673\n", + " [0 1 0 1]\t0.0002\t\t0.1672\n", + " [1 0 1 0]\t-0.0368\t\t0.1661\n", + " [0 0 1 1]\t-0.0373\t\t0.1661\n", + " [0 1 1 0]\t-0.0410\t\t0.1660\n", + " [1 1 1 1]\t15.9639\t\t0.0000\n", " [0 0 0 0]\t16.0000\t\t0.0000\n", - " [1 1 1 1]\t15.9996\t\t0.0000\n", - " [1 1 1 0]\t4.0017\t\t0.0000\n", - " [1 0 0 0]\t4.0011\t\t0.0000\n", - " [0 1 0 0]\t4.0010\t\t0.0000\n", - " [1 1 0 1]\t4.0000\t\t0.0000\n", - " [0 0 1 0]\t3.9995\t\t0.0000\n", - " [1 0 1 1]\t3.9985\t\t0.0000\n", - " [0 1 1 1]\t3.9984\t\t0.0000\n", - " [0 0 0 1]\t3.9978\t\t0.0000\n" + " [1 1 1 0]\t3.9617\t\t0.0000\n", + " [0 1 1 1]\t3.9613\t\t0.0000\n", + " [1 0 1 1]\t3.9653\t\t0.0000\n", + " [1 0 0 0]\t4.0029\t\t0.0000\n", + " [0 0 0 1]\t4.0020\t\t0.0000\n", + " [0 1 0 0]\t3.9981\t\t0.0000\n", + " [1 1 0 1]\t4.0031\t\t0.0000\n", + " [0 0 1 0]\t3.9606\t\t0.0000\n" ] } ], From a98db71a5a4ca06e78d2658de159ba72856fde09 Mon Sep 17 00:00:00 2001 From: stefan-woerner Date: Wed, 7 Aug 2019 17:51:06 +0200 Subject: [PATCH 114/116] Revert "split into featured, community, and qiskit tutorials" This reverts commit 59dac5c9a3d32ae1dd2f603bbcd80f26a0ab9b46. --- featured/finance/index.ipynb | 66 ------------- .../finance/data_providers/time_series.ipynb | 0 qiskit/finance/index.ipynb | 17 ++-- .../qgan_option_pricing.ipynb | 7 -- .../portfolio_diversification.ipynb | 9 +- .../optimization/portfolio_optimization.ipynb | 96 +++++++++---------- .../asian_barrier_spread_pricing.ipynb | 0 .../simulation/basket_option_pricing.ipynb | 0 .../simulation/bull_spread_pricing.ipynb | 0 .../european_call_option_pricing.ipynb | 0 .../european_put_option_pricing.ipynb | 0 .../simulation/fixed_income_pricing.ipynb | 0 .../finance/simulation/option_pricing.ipynb | 0 13 files changed, 67 insertions(+), 128 deletions(-) delete mode 100644 featured/finance/index.ipynb rename {featured => qiskit}/finance/data_providers/time_series.ipynb (100%) rename {featured => qiskit}/finance/optimization/portfolio_diversification.ipynb (99%) rename {featured => qiskit}/finance/simulation/asian_barrier_spread_pricing.ipynb (100%) rename {featured => qiskit}/finance/simulation/basket_option_pricing.ipynb (100%) rename {featured => qiskit}/finance/simulation/bull_spread_pricing.ipynb (100%) rename {featured => qiskit}/finance/simulation/european_call_option_pricing.ipynb (100%) rename {featured => qiskit}/finance/simulation/european_put_option_pricing.ipynb (100%) rename {featured => qiskit}/finance/simulation/fixed_income_pricing.ipynb (100%) rename {featured => qiskit}/finance/simulation/option_pricing.ipynb (100%) diff --git a/featured/finance/index.ipynb b/featured/finance/index.ipynb deleted file mode 100644 index 770e69f90..000000000 --- a/featured/finance/index.ipynb +++ /dev/null @@ -1,66 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# _*Qiskit Finance: Overview*_ \n", - "\n", - "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", - "\n", - "***\n", - "### Contributors\n", - "Stefan Woerner[1], Daniel Egger[1], Christa Zoufal[1], Andrea Simonetto[1], Jakub Marecek[1], Martin Mevissen[1], Shaohan Hu[1], Stephen Wood[1], Marco Pistoia[1]\n", - "\n", - "### Affliation\n", - "- [1]IBMQ" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In the following, we provide an overview of *Qiskit Finance Community* tutorials.
\n", - "Please see the [Qiskit Finance Tutorials](../../qiskit/finance/index.ipynb) for an additional selection of notebooks.\n", - "\n", - "#### Optimization:\n", - "- Portfolio Diversification\n", - " \n", - "#### Simulation:\n", - "- Option Pricing\n", - "- Fixed Income Pricing\n", - "\n", - "#### Data Providers:\n", - "- Stock Market Time Series" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "qiskit_master", - "language": "python", - "name": "qiskit_master" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/featured/finance/data_providers/time_series.ipynb b/qiskit/finance/data_providers/time_series.ipynb similarity index 100% rename from featured/finance/data_providers/time_series.ipynb rename to qiskit/finance/data_providers/time_series.ipynb diff --git a/qiskit/finance/index.ipynb b/qiskit/finance/index.ipynb index 05f9e8f5c..5ee05e65e 100644 --- a/qiskit/finance/index.ipynb +++ b/qiskit/finance/index.ipynb @@ -27,17 +27,22 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "In the following we provide a selection of Qiskit Finance tutorials for the three domains *Machine Learning*, *Optimization*, and *Simulation*.
\n", - "Many other related tutorials, e.g. on *Option Pricing* can be found in the [Qiskit Finance Community](../../community/finance/index.ipynb) section.\n", + "In this notebook we provide an overview of Qiskit Finance tutorials and tutorials from other domains which might be relevant in finance.\n", "\n", - "#### Machine Learning\n", + "#### Machine Learning:\n", "- Quantum Generative Adversarial Networks (qGANs) for data loading in option pricing\n", "\n", - "#### Optimization\n", + "#### Optimization:\n", "- Portfolio Optimization\n", + "- Portfolio Diversification\n", " \n", - "#### Simulation\n", - "- Credit Risk Analysis" + "#### Simulation:\n", + "- Option Pricing\n", + "- Credit Risk Analysis\n", + "- Fixed Income Pricing\n", + "\n", + "#### Data Providers:\n", + "- Stock Market Time Series" ] }, { diff --git a/qiskit/finance/machine_learning/qgan_option_pricing.ipynb b/qiskit/finance/machine_learning/qgan_option_pricing.ipynb index b8dee1bc9..dbb71a815 100644 --- a/qiskit/finance/machine_learning/qgan_option_pricing.ipynb +++ b/qiskit/finance/machine_learning/qgan_option_pricing.ipynb @@ -1,12 +1,5 @@ { "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" - ] - }, { "cell_type": "markdown", "metadata": {}, diff --git a/featured/finance/optimization/portfolio_diversification.ipynb b/qiskit/finance/optimization/portfolio_diversification.ipynb similarity index 99% rename from featured/finance/optimization/portfolio_diversification.ipynb rename to qiskit/finance/optimization/portfolio_diversification.ipynb index 86b4ce45a..5da6c4eff 100644 --- a/featured/finance/optimization/portfolio_diversification.ipynb +++ b/qiskit/finance/optimization/portfolio_diversification.ipynb @@ -4,7 +4,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# _*Portfolio diversification*_\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# _*Qiskit Finance: Portfolio diversification*_\n", "\n", "The latest version of this notebook is available on https://github.com/qiskit/qiskit-tutorial.\n", "\n", diff --git a/qiskit/finance/optimization/portfolio_optimization.ipynb b/qiskit/finance/optimization/portfolio_optimization.ipynb index c95b4f7d9..494016f51 100644 --- a/qiskit/finance/optimization/portfolio_optimization.ipynb +++ b/qiskit/finance/optimization/portfolio_optimization.ipynb @@ -190,26 +190,26 @@ "name": "stdout", "output_type": "stream", "text": [ - "Optimal: selection [0 1 1 0], value -0.0410\n", + "Optimal: selection [0 0 1 1], value -0.0026\n", "\n", "----------------- Full result ---------------------\n", "selection\tvalue\t\tprobability\n", "---------------------------------------------------\n", - " [0 1 1 0]\t-0.0410\t\t1.0000\n", - " [1 1 1 1]\t15.9639\t\t0.0000\n", - " [0 1 1 1]\t3.9613\t\t0.0000\n", - " [1 0 1 1]\t3.9653\t\t0.0000\n", - " [0 0 1 1]\t-0.0373\t\t0.0000\n", - " [1 1 0 1]\t4.0031\t\t0.0000\n", - " [0 1 0 1]\t0.0002\t\t0.0000\n", - " [1 0 0 1]\t0.0048\t\t0.0000\n", - " [0 0 0 1]\t4.0020\t\t0.0000\n", - " [1 1 1 0]\t3.9617\t\t0.0000\n", - " [1 0 1 0]\t-0.0368\t\t0.0000\n", - " [0 0 1 0]\t3.9606\t\t0.0000\n", - " [1 1 0 0]\t0.0010\t\t0.0000\n", - " [0 1 0 0]\t3.9981\t\t0.0000\n", - " [1 0 0 0]\t4.0029\t\t0.0000\n", + " [0 0 1 1]\t-0.0026\t\t1.0000\n", + " [1 1 1 1]\t15.9996\t\t0.0000\n", + " [0 1 1 1]\t3.9984\t\t0.0000\n", + " [1 0 1 1]\t3.9985\t\t0.0000\n", + " [1 1 0 1]\t4.0000\t\t0.0000\n", + " [0 1 0 1]\t-0.0011\t\t0.0000\n", + " [1 0 0 1]\t-0.0011\t\t0.0000\n", + " [0 0 0 1]\t3.9978\t\t0.0000\n", + " [1 1 1 0]\t4.0017\t\t0.0000\n", + " [0 1 1 0]\t0.0006\t\t0.0000\n", + " [1 0 1 0]\t0.0006\t\t0.0000\n", + " [0 0 1 0]\t3.9995\t\t0.0000\n", + " [1 1 0 0]\t0.0021\t\t0.0000\n", + " [0 1 0 0]\t4.0010\t\t0.0000\n", + " [1 0 0 0]\t4.0011\t\t0.0000\n", " [0 0 0 0]\t16.0000\t\t0.0000\n" ] } @@ -252,27 +252,27 @@ "name": "stdout", "output_type": "stream", "text": [ - "Optimal: selection [1 0 1 0], value -0.0368\n", + "Optimal: selection [0 1 1 0], value 0.0006\n", "\n", "----------------- Full result ---------------------\n", "selection\tvalue\t\tprobability\n", "---------------------------------------------------\n", - " [1 0 1 0]\t-0.0368\t\t0.5423\n", - " [0 1 1 0]\t-0.0410\t\t0.3289\n", - " [0 0 1 1]\t-0.0373\t\t0.0641\n", - " [1 1 0 0]\t0.0010\t\t0.0394\n", - " [1 0 0 1]\t0.0048\t\t0.0213\n", - " [0 1 0 1]\t0.0002\t\t0.0039\n", - " [0 0 0 1]\t4.0020\t\t0.0000\n", - " [1 1 0 1]\t4.0031\t\t0.0000\n", - " [0 1 1 1]\t3.9613\t\t0.0000\n", + " [0 1 1 0]\t0.0006\t\t0.7038\n", + " [1 0 0 1]\t-0.0011\t\t0.2120\n", + " [1 0 1 0]\t0.0006\t\t0.0272\n", + " [0 1 0 1]\t-0.0011\t\t0.0251\n", + " [1 1 0 0]\t0.0021\t\t0.0167\n", + " [0 0 1 1]\t-0.0026\t\t0.0151\n", + " [1 0 0 0]\t4.0011\t\t0.0000\n", + " [0 1 1 1]\t3.9984\t\t0.0000\n", + " [0 0 0 1]\t3.9978\t\t0.0000\n", + " [1 0 1 1]\t3.9985\t\t0.0000\n", + " [0 1 0 0]\t4.0010\t\t0.0000\n", + " [1 1 1 0]\t4.0017\t\t0.0000\n", + " [1 1 0 1]\t4.0000\t\t0.0000\n", " [0 0 0 0]\t16.0000\t\t0.0000\n", - " [1 1 1 1]\t15.9639\t\t0.0000\n", - " [1 0 1 1]\t3.9653\t\t0.0000\n", - " [1 0 0 0]\t4.0029\t\t0.0000\n", - " [0 0 1 0]\t3.9606\t\t0.0000\n", - " [0 1 0 0]\t3.9981\t\t0.0000\n", - " [1 1 1 0]\t3.9617\t\t0.0000\n" + " [0 0 1 0]\t3.9995\t\t0.0000\n", + " [1 1 1 1]\t15.9996\t\t0.0000\n" ] } ], @@ -336,27 +336,27 @@ "name": "stdout", "output_type": "stream", "text": [ - "Optimal: selection [1 0 0 1], value 0.0048\n", + "Optimal: selection [1 1 0 0], value 0.0021\n", "\n", "----------------- Full result ---------------------\n", "selection\tvalue\t\tprobability\n", "---------------------------------------------------\n", - " [1 0 0 1]\t0.0048\t\t0.1674\n", - " [1 1 0 0]\t0.0010\t\t0.1673\n", - " [0 1 0 1]\t0.0002\t\t0.1672\n", - " [1 0 1 0]\t-0.0368\t\t0.1661\n", - " [0 0 1 1]\t-0.0373\t\t0.1661\n", - " [0 1 1 0]\t-0.0410\t\t0.1660\n", - " [1 1 1 1]\t15.9639\t\t0.0000\n", + " [1 1 0 0]\t0.0021\t\t0.1667\n", + " [1 0 1 0]\t0.0006\t\t0.1667\n", + " [0 1 1 0]\t0.0006\t\t0.1667\n", + " [1 0 0 1]\t-0.0011\t\t0.1666\n", + " [0 1 0 1]\t-0.0011\t\t0.1666\n", + " [0 0 1 1]\t-0.0026\t\t0.1666\n", " [0 0 0 0]\t16.0000\t\t0.0000\n", - " [1 1 1 0]\t3.9617\t\t0.0000\n", - " [0 1 1 1]\t3.9613\t\t0.0000\n", - " [1 0 1 1]\t3.9653\t\t0.0000\n", - " [1 0 0 0]\t4.0029\t\t0.0000\n", - " [0 0 0 1]\t4.0020\t\t0.0000\n", - " [0 1 0 0]\t3.9981\t\t0.0000\n", - " [1 1 0 1]\t4.0031\t\t0.0000\n", - " [0 0 1 0]\t3.9606\t\t0.0000\n" + " [1 1 1 1]\t15.9996\t\t0.0000\n", + " [1 1 1 0]\t4.0017\t\t0.0000\n", + " [1 0 0 0]\t4.0011\t\t0.0000\n", + " [0 1 0 0]\t4.0010\t\t0.0000\n", + " [1 1 0 1]\t4.0000\t\t0.0000\n", + " [0 0 1 0]\t3.9995\t\t0.0000\n", + " [1 0 1 1]\t3.9985\t\t0.0000\n", + " [0 1 1 1]\t3.9984\t\t0.0000\n", + " [0 0 0 1]\t3.9978\t\t0.0000\n" ] } ], diff --git a/featured/finance/simulation/asian_barrier_spread_pricing.ipynb b/qiskit/finance/simulation/asian_barrier_spread_pricing.ipynb similarity index 100% rename from featured/finance/simulation/asian_barrier_spread_pricing.ipynb rename to qiskit/finance/simulation/asian_barrier_spread_pricing.ipynb diff --git a/featured/finance/simulation/basket_option_pricing.ipynb b/qiskit/finance/simulation/basket_option_pricing.ipynb similarity index 100% rename from featured/finance/simulation/basket_option_pricing.ipynb rename to qiskit/finance/simulation/basket_option_pricing.ipynb diff --git a/featured/finance/simulation/bull_spread_pricing.ipynb b/qiskit/finance/simulation/bull_spread_pricing.ipynb similarity index 100% rename from featured/finance/simulation/bull_spread_pricing.ipynb rename to qiskit/finance/simulation/bull_spread_pricing.ipynb diff --git a/featured/finance/simulation/european_call_option_pricing.ipynb b/qiskit/finance/simulation/european_call_option_pricing.ipynb similarity index 100% rename from featured/finance/simulation/european_call_option_pricing.ipynb rename to qiskit/finance/simulation/european_call_option_pricing.ipynb diff --git a/featured/finance/simulation/european_put_option_pricing.ipynb b/qiskit/finance/simulation/european_put_option_pricing.ipynb similarity index 100% rename from featured/finance/simulation/european_put_option_pricing.ipynb rename to qiskit/finance/simulation/european_put_option_pricing.ipynb diff --git a/featured/finance/simulation/fixed_income_pricing.ipynb b/qiskit/finance/simulation/fixed_income_pricing.ipynb similarity index 100% rename from featured/finance/simulation/fixed_income_pricing.ipynb rename to qiskit/finance/simulation/fixed_income_pricing.ipynb diff --git a/featured/finance/simulation/option_pricing.ipynb b/qiskit/finance/simulation/option_pricing.ipynb similarity index 100% rename from featured/finance/simulation/option_pricing.ipynb rename to qiskit/finance/simulation/option_pricing.ipynb From 8c1170158200f071e6e3dfa3d11d71d4dd01d573 Mon Sep 17 00:00:00 2001 From: stefan-woerner Date: Wed, 7 Aug 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Intelligence is a set of tools, algorithms and software for use with quantum computers to -carry out research and investigate how to take advantage of quantum computing power to solve artificial intelligence -problems. - -Qiskit Aqua Artificial Intelligence translates artificial-intelligence-specific problems into inputs -for a quantum algorithm residing in Qiskit Aqua, which in turn uses [Qiskit](https://www.qiskit.org/) for the relevant -quantum computation. - -This folder contains some Jupyter Notebook examples. There are Python code files too. - -For more detail see the main [index](../aqua/index.ipynb#artificial_intelligence) - -## Input files - -The folder [input_files](input_files) contains a number of example JSON input files that can be loaded -and run by the Qiskit Aqua [GUI](https://github.com/Qiskit/aqua/README.md#gui) or by the Qiskit Aqua -[command line](https://github.com/Qiskit/aqua/README.md#command-line) tool. diff --git a/community/artificial_intelligence/datasets.py b/community/artificial_intelligence/datasets.py deleted file mode 100644 index 1eaac3741..000000000 --- a/community/artificial_intelligence/datasets.py +++ /dev/null @@ -1,555 +0,0 @@ -# -*- coding: utf-8 -*- - -# Copyright 2018 IBM. -# -# Licensed under the Apache License, Version 2.0 (the "License"); -# you may not use this file except in compliance with the License. -# You may obtain a copy of the License at -# -# http://www.apache.org/licenses/LICENSE-2.0 -# -# Unless required by applicable law or agreed to in writing, software -# distributed under the License is distributed on an "AS IS" BASIS, -# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -# See the License for the specific language governing permissions and -# limitations under the License. -# ============================================================================= - -import numpy as np -import scipy -from scipy.linalg import expm -import matplotlib.pyplot as plt -from mpl_toolkits.mplot3d import Axes3D -from sklearn import datasets -from sklearn.model_selection import train_test_split -from sklearn.preprocessing import StandardScaler, MinMaxScaler -from sklearn.decomposition import PCA - - -def ad_hoc_data(training_size, test_size, n, gap, PLOT_DATA): - class_labels = [r'A', r'B'] - if n == 2: - N = 100 - elif n == 3: - N = 20 # courseness of data seperation - - label_train = np.zeros(2*(training_size+test_size)) - sample_train = [] - sampleA = [[0 for x in range(n)] for y in range(training_size+test_size)] - sampleB = [[0 for x in range(n)] for y in range(training_size+test_size)] - - sample_Total = [[[0 for x in range(N)] for y in range(N)] for z in range(N)] - - interactions = np.transpose(np.array([[1, 0], [0, 1], [1, 1]])) - - steps = 2*np.pi/N - - sx = np.array([[0, 1], [1, 0]]) - X = np.asmatrix(sx) - sy = np.array([[0, -1j], [1j, 0]]) - Y = np.asmatrix(sy) - sz = np.array([[1, 0], [0, -1]]) - Z = np.asmatrix(sz) - J = np.array([[1, 0], [0, 1]]) - J = np.asmatrix(J) - H = np.array([[1, 1], [1, -1]])/np.sqrt(2) - H2 = np.kron(H, H) - H3 = np.kron(H, H2) - H = np.asmatrix(H) - H2 = np.asmatrix(H2) - H3 = np.asmatrix(H3) - - f = np.arange(2**n) - - my_array = [[0 for x in range(n)] for y in range(2**n)] - - for arindex in range(len(my_array)): - temp_f = bin(f[arindex])[2:].zfill(n) - for findex in range(n): - my_array[arindex][findex] = int(temp_f[findex]) - - my_array = np.asarray(my_array) - my_array = np.transpose(my_array) - - # Define decision functions - maj = (-1)**(2*my_array.sum(axis=0) > n) - parity = (-1)**(my_array.sum(axis=0)) - dict1 = (-1)**(my_array[0]) - if n == 2: - D = np.diag(parity) - elif n == 3: - D = np.diag(maj) - - Basis = np.random.random((2**n, 2**n)) + 1j*np.random.random((2**n, 2**n)) - Basis = np.asmatrix(Basis).getH()*np.asmatrix(Basis) - - [S, U] = np.linalg.eig(Basis) - - idx = S.argsort()[::-1] - S = S[idx] - U = U[:, idx] - - M = (np.asmatrix(U)).getH()*np.asmatrix(D)*np.asmatrix(U) - - psi_plus = np.transpose(np.ones(2))/np.sqrt(2) - psi_0 = 1 - for k in range(n): - psi_0 = np.kron(np.asmatrix(psi_0), np.asmatrix(psi_plus)) - - sample_total_A = [] - sample_total_B = [] - sample_total_void = [] - if n == 2: - for n1 in range(N): - for n2 in range(N): - x1 = steps*n1 - x2 = steps*n2 - phi = x1*np.kron(Z, J) + x2*np.kron(J, Z) + (np.pi-x1)*(np.pi-x2)*np.kron(Z, Z) - Uu = scipy.linalg.expm(1j*phi) - psi = np.asmatrix(Uu)*H2*np.asmatrix(Uu)*np.transpose(psi_0) - temp = np.asscalar(np.real(psi.getH()*M*psi)) - if temp > gap: - sample_Total[n1][n2] = +1 - elif temp < -gap: - sample_Total[n1][n2] = -1 - else: - sample_Total[n1][n2] = 0 - - # Now sample randomly from sample_Total a number of times training_size+testing_size - tr = 0 - while tr < (training_size+test_size): - draw1 = np.random.choice(N) - draw2 = np.random.choice(N) - if sample_Total[draw1][draw2] == +1: - sampleA[tr] = [2*np.pi*draw1/N, 2*np.pi*draw2/N] - tr += 1 - - tr = 0 - while tr < (training_size+test_size): - draw1 = np.random.choice(N) - draw2 = np.random.choice(N) - if sample_Total[draw1][draw2] == -1: - sampleB[tr] = [2*np.pi*draw1/N, 2*np.pi*draw2/N] - tr += 1 - - sample_train = [sampleA, sampleB] - - for lindex in range(training_size+test_size): - label_train[lindex] = 0 - for lindex in range(training_size+test_size): - label_train[training_size+test_size+lindex] = 1 - label_train = label_train.astype(int) - sample_train = np.reshape(sample_train, (2*(training_size+test_size), n)) - training_input = {key: (sample_train[label_train == k, :])[:training_size] - for k, key in enumerate(class_labels)} - test_input = {key: (sample_train[label_train == k, :])[training_size:( - training_size+test_size)] for k, key in enumerate(class_labels)} - - if PLOT_DATA: - img = plt.imshow(np.asmatrix(sample_Total).T, interpolation='nearest', - origin='lower', cmap='copper', extent=[0, 2*np.pi, 0, 2*np.pi]) - plt.show() - fig2 = plt.figure() - for k in range(0, 2): - plt.scatter(sample_train[label_train == k, 0][:training_size], - sample_train[label_train == k, 1][:training_size]) - - plt.title("Ad-hoc Data") - plt.show() - - elif n == 3: - for n1 in range(N): - for n2 in range(N): - for n3 in range(N): - x1 = steps*n1 - x2 = steps*n2 - x3 = steps*n3 - phi = x1*np.kron(np.kron(Z, J), J) + x2*np.kron(np.kron(J, Z), J) + x3*np.kron(np.kron(J, J), Z) + \ - (np.pi-x1)*(np.pi-x2)*np.kron(np.kron(Z, Z), J)+(np.pi-x2)*(np.pi-x3)*np.kron(np.kron(J, Z), Z) + \ - (np.pi-x1)*(np.pi-x3)*np.kron(np.kron(Z, J), Z) - Uu = scipy.linalg.expm(1j*phi) - psi = np.asmatrix(Uu)*H3*np.asmatrix(Uu)*np.transpose(psi_0) - temp = np.asscalar(np.real(psi.getH()*M*psi)) - if temp > gap: - sample_Total[n1][n2][n3] = +1 - sample_total_A.append([n1, n2, n3]) - elif temp < -gap: - sample_Total[n1][n2][n3] = -1 - sample_total_B.append([n1, n2, n3]) - else: - sample_Total[n1][n2][n3] = 0 - sample_total_void.append([n1, n2, n3]) - - # Now sample randomly from sample_Total a number of times training_size+testing_size - tr = 0 - while tr < (training_size+test_size): - draw1 = np.random.choice(N) - draw2 = np.random.choice(N) - draw3 = np.random.choice(N) - if sample_Total[draw1][draw2][draw3] == +1: - sampleA[tr] = [2*np.pi*draw1/N, 2*np.pi*draw2/N, 2*np.pi*draw3/N] - tr += 1 - - tr = 0 - while tr < (training_size+test_size): - draw1 = np.random.choice(N) - draw2 = np.random.choice(N) - draw3 = np.random.choice(N) - if sample_Total[draw1][draw2][draw3] == -1: - sampleB[tr] = [2*np.pi*draw1/N, 2*np.pi*draw2/N, 2*np.pi*draw3/N] - tr += 1 - - sample_train = [sampleA, sampleB] - - for lindex in range(training_size+test_size): - label_train[lindex] = 0 - for lindex in range(training_size+test_size): - label_train[training_size+test_size+lindex] = 1 - label_train = label_train.astype(int) - sample_train = np.reshape(sample_train, (2*(training_size+test_size), n)) - training_input = {key: (sample_train[label_train == k, :])[:training_size] - for k, key in enumerate(class_labels)} - test_input = {key: (sample_train[label_train == k, :])[training_size:( - training_size+test_size)] for k, key in enumerate(class_labels)} - - if PLOT_DATA: - - sample_total_A = np.asarray(sample_total_A) - sample_total_B = np.asarray(sample_total_B) - x1 = sample_total_A[:, 0] - y1 = sample_total_A[:, 1] - z1 = sample_total_A[:, 2] - - x2 = sample_total_B[:, 0] - y2 = sample_total_B[:, 1] - z2 = sample_total_B[:, 2] - - fig1 = plt.figure() - ax1 = fig1.add_subplot(1, 1, 1, projection='3d') - ax1.scatter(x1, y1, z1, c='#8A360F') - plt.show() - # - fig2 = plt.figure() - ax2 = fig2.add_subplot(1, 1, 1, projection='3d') - ax2.scatter(x2, y2, z2, c='#683FC8') - plt.show() - - sample_training_A = training_input['A'] - sample_training_B = training_input['B'] - - x1 = sample_training_A[:, 0] - y1 = sample_training_A[:, 1] - z1 = sample_training_A[:, 2] - - x2 = sample_training_B[:, 0] - y2 = sample_training_B[:, 1] - z2 = sample_training_B[:, 2] - - fig1 = plt.figure() - ax1 = fig1.add_subplot(1, 1, 1, projection='3d') - ax1.scatter(x1, y1, z1, c='#8A360F') - ax1.scatter(x2, y2, z2, c='#683FC8') - plt.show() - - return sample_Total, training_input, test_input, class_labels - - -def sample_ad_hoc_data(sample_Total, test_size, n): - tr = 0 - - class_labels = [r'A', r'B'] # copied from ad_hoc_data() - if n == 2: - N = 100 - elif n == 3: - N = 20 - - label_train = np.zeros(2*test_size) - sampleA = [[0 for x in range(n)] for y in range(test_size)] - sampleB = [[0 for x in range(n)] for y in range(test_size)] - while tr < (test_size): - draw1 = np.random.choice(N) - draw2 = np.random.choice(N) - if sample_Total[draw1][draw2] == +1: - sampleA[tr] = [2*np.pi*draw1/N, 2*np.pi*draw2/N] - tr += 1 - - tr = 0 - while tr < (test_size): - draw1 = np.random.choice(N) - draw2 = np.random.choice(N) - if sample_Total[draw1][draw2] == -1: - sampleB[tr] = [2*np.pi*draw1/N, 2*np.pi*draw2/N] - tr += 1 - sample_train = [sampleA, sampleB] - for lindex in range(test_size): - label_train[lindex] = 0 - for lindex in range(test_size): - label_train[test_size+lindex] = 1 - label_train = label_train.astype(int) - sample_train = np.reshape(sample_train, (2 * test_size, n)) - test_input = {key: (sample_train[label_train == k, :])[:] for k, key in enumerate(class_labels)} - return test_input - - -def Breast_cancer(training_size, test_size, n, PLOT_DATA): - class_labels = [r'A', r'B'] - data, target = datasets.load_breast_cancer(True) - sample_train, sample_test, label_train, label_test = train_test_split(data, target, test_size=0.3, random_state=12) - - # Now we standarize for gaussian around 0 with unit variance - std_scale = StandardScaler().fit(sample_train) - sample_train = std_scale.transform(sample_train) - sample_test = std_scale.transform(sample_test) - - # Now reduce number of features to number of qubits - pca = PCA(n_components=n).fit(sample_train) - sample_train = pca.transform(sample_train) - sample_test = pca.transform(sample_test) - - # Scale to the range (-1,+1) - samples = np.append(sample_train, sample_test, axis=0) - minmax_scale = MinMaxScaler((-1, 1)).fit(samples) - sample_train = minmax_scale.transform(sample_train) - sample_test = minmax_scale.transform(sample_test) - - # Pick training size number of samples from each distro - training_input = {key: (sample_train[label_train == k, :])[:training_size] for k, key in enumerate(class_labels)} - test_input = {key: (sample_train[label_train == k, :])[training_size:( - training_size+test_size)] for k, key in enumerate(class_labels)} - - if PLOT_DATA: - for k in range(0, 2): - plt.scatter(sample_train[label_train == k, 0][:training_size], - sample_train[label_train == k, 1][:training_size]) - - plt.title("PCA dim. reduced Breast cancer dataset") - plt.show() - - return sample_train, training_input, test_input, class_labels - - -def Digits(training_size, test_size, n, PLOT_DATA): - class_labels = [r'A', r'B', r'C', r'D', r'E', r'F', r'G', r'H', r'I', r'J'] - data = datasets.load_digits() - sample_train, sample_test, label_train, label_test = train_test_split( - data.data, data.target, test_size=0.3, random_state=22) - - # Now we standarize for gaussian around 0 with unit variance - std_scale = StandardScaler().fit(sample_train) - sample_train = std_scale.transform(sample_train) - sample_test = std_scale.transform(sample_test) - - # Now reduce number of features to number of qubits - pca = PCA(n_components=n).fit(sample_train) - sample_train = pca.transform(sample_train) - sample_test = pca.transform(sample_test) - - # Scale to the range (-1,+1) - samples = np.append(sample_train, sample_test, axis=0) - minmax_scale = MinMaxScaler((-1, 1)).fit(samples) - sample_train = minmax_scale.transform(sample_train) - sample_test = minmax_scale.transform(sample_test) - - # Pick training size number of samples from each distro - training_input = {key: (sample_train[label_train == k, :])[:training_size] for k, key in enumerate(class_labels)} - test_input = {key: (sample_train[label_train == k, :])[training_size:( - training_size+test_size)] for k, key in enumerate(class_labels)} - - if PLOT_DATA: - for k in range(0, 9): - plt.scatter(sample_train[label_train == k, 0][:training_size], - sample_train[label_train == k, 1][:training_size]) - - plt.title("PCA dim. reduced Digits dataset") - plt.show() - - return sample_train, training_input, test_input, class_labels - - -def Iris(training_size, test_size, n, PLOT_DATA): - class_labels = [r'A', r'B', r'C'] - data, target = datasets.load_iris(True) - sample_train, sample_test, label_train, label_test = train_test_split(data, target, test_size=1, random_state=42) - - # Now we standarize for gaussian around 0 with unit variance - std_scale = StandardScaler().fit(sample_train) - sample_train = std_scale.transform(sample_train) - sample_test = std_scale.transform(sample_test) - - # Now reduce number of features to number of qubits - pca = PCA(n_components=n).fit(sample_train) - sample_train = pca.transform(sample_train) - sample_test = pca.transform(sample_test) - - # Scale to the range (-1,+1) - samples = np.append(sample_train, sample_test, axis=0) - minmax_scale = MinMaxScaler((-1, 1)).fit(samples) - sample_train = minmax_scale.transform(sample_train) - sample_test = minmax_scale.transform(sample_test) - - # Pick training size number of samples from each distro - training_input = {key: (sample_train[label_train == k, :])[:training_size] for k, key in enumerate(class_labels)} - test_input = {key: (sample_train[label_train == k, :])[training_size:( - training_size+test_size)] for k, key in enumerate(class_labels)} - - if PLOT_DATA: - for k in range(0, 3): - plt.scatter(sample_train[label_train == k, 0][:training_size], - sample_train[label_train == k, 1][:training_size]) - - plt.title("Iris dataset") - plt.show() - - return sample_train, training_input, test_input, class_labels - - -def Wine(training_size, test_size, n, PLOT_DATA): - class_labels = [r'A', r'B', r'C'] - - data, target = datasets.load_wine(True) - sample_train, sample_test, label_train, label_test = train_test_split(data, target, test_size=test_size, random_state=7) - - # Now we standarize for gaussian around 0 with unit variance - std_scale = StandardScaler().fit(sample_train) - sample_train = std_scale.transform(sample_train) - sample_test = std_scale.transform(sample_test) - - # Now reduce number of features to number of qubits - pca = PCA(n_components=n).fit(sample_train) - sample_train = pca.transform(sample_train) - sample_test = pca.transform(sample_test) - - # Scale to the range (-1,+1) - samples = np.append(sample_train, sample_test, axis=0) - minmax_scale = MinMaxScaler((-1, 1)).fit(samples) - sample_train = minmax_scale.transform(sample_train) - sample_test = minmax_scale.transform(sample_test) - # Pick training size number of samples from each distro - training_input = {key: (sample_train[label_train == k, :])[:training_size] for k, key in enumerate(class_labels)} - test_input = {key: (sample_train[label_train == k, :])[training_size:( - training_size+test_size)] for k, key in enumerate(class_labels)} - - if PLOT_DATA: - for k in range(0, 3): - plt.scatter(sample_train[label_train == k, 0][:training_size], - sample_train[label_train == k, 1][:training_size]) - - plt.title("PCA dim. reduced Wine dataset") - plt.show() - - return sample_train, training_input, test_input, class_labels - - -def Gaussian(training_size, test_size, n, PLOT_DATA): - sigma = 1 - if n == 2: - class_labels = [r'A', r'B'] - label_train = np.zeros(2*(training_size+test_size)) - sample_train = [] - sampleA = [[0 for x in range(n)] for y in range(training_size+test_size)] - sampleB = [[0 for x in range(n)] for y in range(training_size+test_size)] - randomized_vector1 = np.random.randint(2, size=n) - randomized_vector2 = (randomized_vector1+1) % 2 - for tr in range(training_size+test_size): - for feat in range(n): - if randomized_vector1[feat] == 0: - sampleA[tr][feat] = np.random.normal(-1/2, sigma, None) - elif randomized_vector1[feat] == 1: - sampleA[tr][feat] = np.random.normal(1/2, sigma, None) - else: - print('Nope') - - if randomized_vector2[feat] == 0: - sampleB[tr][feat] = np.random.normal(-1/2, sigma, None) - elif randomized_vector2[feat] == 1: - sampleB[tr][feat] = np.random.normal(1/2, sigma, None) - else: - print('Nope') - - sample_train = [sampleA, sampleB] - for lindex in range(training_size+test_size): - label_train[lindex] = 0 - for lindex in range(training_size+test_size): - label_train[training_size+test_size+lindex] = 1 - label_train = label_train.astype(int) - sample_train = np.reshape(sample_train, (2*(training_size+test_size), n)) - training_input = {key: (sample_train[label_train == k, :])[:training_size] - for k, key in enumerate(class_labels)} - test_input = {key: (sample_train[label_train == k, :])[training_size:( - training_size+test_size)] for k, key in enumerate(class_labels)} - - if PLOT_DATA: - fig1 = plt.figure() - for k in range(0, 2): - plt.scatter(sample_train[label_train == k, 0][:training_size], - sample_train[label_train == k, 1][:training_size]) - - plt.title("Gaussians") - plt.show() - - return sample_train, training_input, test_input, class_labels - elif n == 3: - class_labels = [r'A', r'B', r'C'] - label_train = np.zeros(3*(training_size+test_size)) - sample_train = [] - sampleA = [[0 for x in range(n)] for y in range(training_size+test_size)] - sampleB = [[0 for x in range(n)] for y in range(training_size+test_size)] - sampleC = [[0 for x in range(n)] for y in range(training_size+test_size)] - randomized_vector1 = np.random.randint(3, size=n) - randomized_vector2 = (randomized_vector1+1) % 3 - randomized_vector3 = (randomized_vector2+1) % 3 - for tr in range(training_size+test_size): - for feat in range(n): - if randomized_vector1[feat] == 0: - sampleA[tr][feat] = np.random.normal(2*1*np.pi/6, sigma, None) - elif randomized_vector1[feat] == 1: - sampleA[tr][feat] = np.random.normal(2*3*np.pi/6, sigma, None) - elif randomized_vector1[feat] == 2: - sampleA[tr][feat] = np.random.normal(2*5*np.pi/6, sigma, None) - else: - print('Nope') - - if randomized_vector2[feat] == 0: - sampleB[tr][feat] = np.random.normal(2*1*np.pi/6, sigma, None) - elif randomized_vector2[feat] == 1: - sampleB[tr][feat] = np.random.normal(2*3*np.pi/6, sigma, None) - elif randomized_vector2[feat] == 2: - sampleB[tr][feat] = np.random.normal(2*5*np.pi/6, sigma, None) - else: - print('Nope') - - if randomized_vector3[feat] == 0: - sampleC[tr][feat] = np.random.normal(2*1*np.pi/6, sigma, None) - elif randomized_vector3[feat] == 1: - sampleC[tr][feat] = np.random.normal(2*3*np.pi/6, sigma, None) - elif randomized_vector3[feat] == 2: - sampleC[tr][feat] = np.random.normal(2*5*np.pi/6, sigma, None) - else: - print('Nope') - - sample_train = [sampleA, sampleB, sampleC] - for lindex in range(training_size+test_size): - label_train[lindex] = 0 - for lindex in range(training_size+test_size): - label_train[training_size+test_size+lindex] = 1 - for lindex in range(training_size+test_size): - label_train[training_size+test_size+training_size+test_size+lindex] = 2 - label_train = label_train.astype(int) - sample_train = np.reshape(sample_train, (3*(training_size+test_size), n)) - training_input = {key: (sample_train[label_train == k, :])[:training_size] - for k, key in enumerate(class_labels)} - test_input = {key: (sample_train[label_train == k, :])[training_size:( - training_size+test_size)] for k, key in enumerate(class_labels)} - - if PLOT_DATA: - fig1 = plt.figure() - for k in range(0, 3): - plt.scatter(sample_train[label_train == k, 0][:training_size], - sample_train[label_train == k, 1][:training_size]) - - plt.title("Gaussians") - plt.show() - - return sample_train, training_input, test_input, class_labels - else: - print("Gaussian presently only supports 2 or 3 qubits") diff --git a/community/artificial_intelligence/input_files/qsvm.json b/community/artificial_intelligence/input_files/qsvm.json deleted file mode 100644 index 5673fc17c..000000000 --- a/community/artificial_intelligence/input_files/qsvm.json +++ /dev/null @@ -1,18 +0,0 @@ -{ - "algorithm": { - "name": "QSVM"}, - "problem": {"name": "classification"}, - "backend": {"provider": "qiskit.BasicAer", "name": "qasm_simulator", "shots":1000}, - - "input": { - "name": "ClassificationInput", - - "training_dataset": {"A": [[6.220353454107791, 4.1469023027385274], [3.204424506661589, 4.335397861953915], [3.5185837720205684, 3.7699111843077513], [2.4504422698000385, 5.717698629533423], [4.39822971502571, 2.324778563656447], [2.9530970943744057, 1.8221237390820801], [2.8902652413026093, 4.838052686528282], [3.015928947446201, 4.1469023027385274], [1.4451326206513047, 2.827433388230814], [0.0, 4.335397861953915], [3.5185837720205684, 2.4504422698000385], [1.7592918860102842, 2.6389378290154264], [5.717698629533423, 1.9477874452256716], [3.330088212805181, 1.2566370614359172], [1.382300767579509, 0.6911503837897545], [3.015928947446201, 2.324778563656447], [5.780530482605219, 0.9424777960769378], [0.06283185307179587, 5.0893800988154645], [2.9530970943744057, 4.9637163926718735], [3.7699111843077513, 4.084070449666731]], "B": [[1.4451326206513047, 5.277875658030853], [1.5079644737231006, 5.0893800988154645], [0.8168140899333463, 5.277875658030853], [1.0053096491487339, 0.25132741228718347], [0.3141592653589793, 6.220353454107791], [4.335397861953915, 3.4557519189487724], [3.4557519189487724, 6.031857894892402], [5.592034923389832, 0.5026548245743669], [0.3141592653589793, 5.654866776461628], [0.5654866776461628, 1.5079644737231006], [5.277875658030853, 3.141592653589793], [4.272566008882119, 0.5026548245743669], [2.0106192982974678, 4.461061568097507], [4.0212385965949355, 4.71238898038469], [1.4451326206513047, 4.900884539600077], [1.8849555921538756, 3.204424506661589], [5.592034923389832, 1.4451326206513047], [2.3876104167282426, 4.335397861953915], [4.084070449666731, 2.3876104167282426], [4.084070449666731, 4.649557127312894]]}, - "test_dataset": -{"A": [[4.900884539600077, 5.780530482605219], [1.6336281798666925, 2.199114857512855], [6.094689747964199, 0.6283185307179586], [5.340707511102648, 3.8327430373795477], [3.015928947446201, 0.6911503837897545], [0.6911503837897545, 4.71238898038469], [3.267256359733385, 0.8796459430051421], [0.18849555921538758, 5.403539364174444], [0.18849555921538758, 0.8168140899333463], [3.4557519189487724, 1.4451326206513047]], "B": [[0.6911503837897545, 5.215043804959057], [1.9477874452256716, 1.3194689145077132], [2.6389378290154264, 3.204424506661589], [1.5079644737231006, 0.8168140899333463], [2.701769682087222, 3.3929200658769765], [4.523893421169302, 3.5185837720205684], [2.261946710584651, 4.39822971502571], [4.71238898038469, 2.827433388230814], [2.199114857512855, 1.1938052083641213], [2.764601535159018, 3.707079331235956]]}, - "datapoints": [[4.900884539600077, 5.780530482605219], [1.6336281798666925, 2.199114857512855], [6.094689747964199, 0.6283185307179586], [5.340707511102648, 3.8327430373795477], [3.015928947446201, 0.6911503837897545], [0.6911503837897545, 4.71238898038469], [3.267256359733385, 0.8796459430051421], [0.18849555921538758, 5.403539364174444], [0.18849555921538758, 0.8168140899333463], [3.4557519189487724, 1.4451326206513047], [0.6911503837897545, 5.215043804959057], [1.9477874452256716, 1.3194689145077132], [2.6389378290154264, 3.204424506661589], [1.5079644737231006, 0.8168140899333463], [2.701769682087222, 3.3929200658769765], [4.523893421169302, 3.5185837720205684], [2.261946710584651, 4.39822971502571], [4.71238898038469, 2.827433388230814], [2.199114857512855, 1.1938052083641213], [2.764601535159018, 3.707079331235956]] - - - - } -} diff --git a/community/artificial_intelligence/input_files/svm_classical.json b/community/artificial_intelligence/input_files/svm_classical.json deleted file mode 100644 index de6744777..000000000 --- a/community/artificial_intelligence/input_files/svm_classical.json +++ /dev/null @@ -1,17 +0,0 @@ -{ - "algorithm": { - "name": "SVM" - }, - "problem": {"name": "classification"}, - "input": { - "name": "ClassificationInput", - - "training_dataset": {"A": [[6.220353454107791, 4.1469023027385274], [3.204424506661589, 4.335397861953915], [3.5185837720205684, 3.7699111843077513], [2.4504422698000385, 5.717698629533423], [4.39822971502571, 2.324778563656447], [2.9530970943744057, 1.8221237390820801], [2.8902652413026093, 4.838052686528282], [3.015928947446201, 4.1469023027385274], [1.4451326206513047, 2.827433388230814], [0.0, 4.335397861953915], [3.5185837720205684, 2.4504422698000385], [1.7592918860102842, 2.6389378290154264], [5.717698629533423, 1.9477874452256716], [3.330088212805181, 1.2566370614359172], [1.382300767579509, 0.6911503837897545], [3.015928947446201, 2.324778563656447], [5.780530482605219, 0.9424777960769378], [0.06283185307179587, 5.0893800988154645], [2.9530970943744057, 4.9637163926718735], [3.7699111843077513, 4.084070449666731]], "B": [[1.4451326206513047, 5.277875658030853], [1.5079644737231006, 5.0893800988154645], [0.8168140899333463, 5.277875658030853], [1.0053096491487339, 0.25132741228718347], [0.3141592653589793, 6.220353454107791], [4.335397861953915, 3.4557519189487724], [3.4557519189487724, 6.031857894892402], [5.592034923389832, 0.5026548245743669], [0.3141592653589793, 5.654866776461628], [0.5654866776461628, 1.5079644737231006], [5.277875658030853, 3.141592653589793], [4.272566008882119, 0.5026548245743669], [2.0106192982974678, 4.461061568097507], [4.0212385965949355, 4.71238898038469], [1.4451326206513047, 4.900884539600077], [1.8849555921538756, 3.204424506661589], [5.592034923389832, 1.4451326206513047], [2.3876104167282426, 4.335397861953915], [4.084070449666731, 2.3876104167282426], [4.084070449666731, 4.649557127312894]]}, - "test_dataset": -{"A": [[4.900884539600077, 5.780530482605219], [1.6336281798666925, 2.199114857512855], [6.094689747964199, 0.6283185307179586], [5.340707511102648, 3.8327430373795477], [3.015928947446201, 0.6911503837897545], [0.6911503837897545, 4.71238898038469], [3.267256359733385, 0.8796459430051421], [0.18849555921538758, 5.403539364174444], [0.18849555921538758, 0.8168140899333463], [3.4557519189487724, 1.4451326206513047]], "B": [[0.6911503837897545, 5.215043804959057], [1.9477874452256716, 1.3194689145077132], [2.6389378290154264, 3.204424506661589], [1.5079644737231006, 0.8168140899333463], [2.701769682087222, 3.3929200658769765], [4.523893421169302, 3.5185837720205684], [2.261946710584651, 4.39822971502571], [4.71238898038469, 2.827433388230814], [2.199114857512855, 1.1938052083641213], [2.764601535159018, 3.707079331235956]]}, - "datapoints": [[4.900884539600077, 5.780530482605219], [1.6336281798666925, 2.199114857512855], [6.094689747964199, 0.6283185307179586], [5.340707511102648, 3.8327430373795477], [3.015928947446201, 0.6911503837897545], [0.6911503837897545, 4.71238898038469], [3.267256359733385, 0.8796459430051421], [0.18849555921538758, 5.403539364174444], [0.18849555921538758, 0.8168140899333463], [3.4557519189487724, 1.4451326206513047], [0.6911503837897545, 5.215043804959057], [1.9477874452256716, 1.3194689145077132], [2.6389378290154264, 3.204424506661589], [1.5079644737231006, 0.8168140899333463], [2.701769682087222, 3.3929200658769765], [4.523893421169302, 3.5185837720205684], [2.261946710584651, 4.39822971502571], [4.71238898038469, 2.827433388230814], [2.199114857512855, 1.1938052083641213], [2.764601535159018, 3.707079331235956]] - - - - } -} diff --git a/community/artificial_intelligence/input_files/vqc.json b/community/artificial_intelligence/input_files/vqc.json deleted file mode 100644 index e7eb30e9d..000000000 --- a/community/artificial_intelligence/input_files/vqc.json +++ /dev/null @@ -1,15 +0,0 @@ -{ - "algorithm": { - "name": "VQC" - }, - "problem": {"name": "classification"}, - "backend": {"provider": "qiskit.BasicAer", "name": "qasm_simulator", "shots": 1000}, - "optimizer": {"name": "SPSA", "max_trials": 100, "save_steps": 10}, - "input": { - "name": "ClassificationInput", - "training_dataset": {"A": [[6.220353454107791, 4.1469023027385274], [3.204424506661589, 4.335397861953915], [3.5185837720205684, 3.7699111843077513], [2.4504422698000385, 5.717698629533423], [4.39822971502571, 2.324778563656447], [2.9530970943744057, 1.8221237390820801], [2.8902652413026093, 4.838052686528282], [3.015928947446201, 4.1469023027385274], [1.4451326206513047, 2.827433388230814], [0.0, 4.335397861953915], [3.5185837720205684, 2.4504422698000385], [1.7592918860102842, 2.6389378290154264], [5.717698629533423, 1.9477874452256716], [3.330088212805181, 1.2566370614359172], [1.382300767579509, 0.6911503837897545], [3.015928947446201, 2.324778563656447], [5.780530482605219, 0.9424777960769378], [0.06283185307179587, 5.0893800988154645], [2.9530970943744057, 4.9637163926718735], [3.7699111843077513, 4.084070449666731]], "B": [[1.4451326206513047, 5.277875658030853], [1.5079644737231006, 5.0893800988154645], [0.8168140899333463, 5.277875658030853], [1.0053096491487339, 0.25132741228718347], [0.3141592653589793, 6.220353454107791], [4.335397861953915, 3.4557519189487724], [3.4557519189487724, 6.031857894892402], [5.592034923389832, 0.5026548245743669], [0.3141592653589793, 5.654866776461628], [0.5654866776461628, 1.5079644737231006], [5.277875658030853, 3.141592653589793], [4.272566008882119, 0.5026548245743669], [2.0106192982974678, 4.461061568097507], [4.0212385965949355, 4.71238898038469], [1.4451326206513047, 4.900884539600077], [1.8849555921538756, 3.204424506661589], [5.592034923389832, 1.4451326206513047], [2.3876104167282426, 4.335397861953915], [4.084070449666731, 2.3876104167282426], [4.084070449666731, 4.649557127312894]]}, - "test_dataset": -{"A": [[4.900884539600077, 5.780530482605219], [1.6336281798666925, 2.199114857512855], [6.094689747964199, 0.6283185307179586], [5.340707511102648, 3.8327430373795477], [3.015928947446201, 0.6911503837897545], [0.6911503837897545, 4.71238898038469], [3.267256359733385, 0.8796459430051421], [0.18849555921538758, 5.403539364174444], [0.18849555921538758, 0.8168140899333463], [3.4557519189487724, 1.4451326206513047]], "B": [[0.6911503837897545, 5.215043804959057], [1.9477874452256716, 1.3194689145077132], [2.6389378290154264, 3.204424506661589], [1.5079644737231006, 0.8168140899333463], [2.701769682087222, 3.3929200658769765], [4.523893421169302, 3.5185837720205684], [2.261946710584651, 4.39822971502571], [4.71238898038469, 2.827433388230814], [2.199114857512855, 1.1938052083641213], [2.764601535159018, 3.707079331235956]]}, - "datapoints": [[4.900884539600077, 5.780530482605219], [1.6336281798666925, 2.199114857512855], [6.094689747964199, 0.6283185307179586], [5.340707511102648, 3.8327430373795477], [3.015928947446201, 0.6911503837897545], [0.6911503837897545, 4.71238898038469], [3.267256359733385, 0.8796459430051421], [0.18849555921538758, 5.403539364174444], [0.18849555921538758, 0.8168140899333463], [3.4557519189487724, 1.4451326206513047], [0.6911503837897545, 5.215043804959057], [1.9477874452256716, 1.3194689145077132], [2.6389378290154264, 3.204424506661589], [1.5079644737231006, 0.8168140899333463], [2.701769682087222, 3.3929200658769765], [4.523893421169302, 3.5185837720205684], [2.261946710584651, 4.39822971502571], [4.71238898038469, 2.827433388230814], [2.199114857512855, 1.1938052083641213], [2.764601535159018, 3.707079331235956]] - } -} diff --git a/community/artificial_intelligence/qsvm_directly.ipynb b/community/artificial_intelligence/qsvm_directly.ipynb deleted file mode 100644 index adf51dcb2..000000000 --- a/community/artificial_intelligence/qsvm_directly.ipynb +++ /dev/null @@ -1,306 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## _*Quantum SVM*_\n", - "\n", - "### Introduction\n", - "\n", - "Please refer to [this file](https://github.com/Qiskit/qiskit-tutorials/blob/master/qiskit/aqua/artificial_intelligence/qsvm_classification.ipynb) for introduction.\n", - "\n", - "In this file, we show two ways for using the quantum kernel method: (1) the declarative approach and (2) the programmatic approach. \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Part I: declarative approach.\n", - "In the declarative approach, we config a json-like configuration, which defines how the svm instance is internally constructed. After the execution, it returns the json-like output, which carries the important information (e.g., the details of the svm instance) and the processed results. " - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "from datasets import *\n", - "from qiskit import BasicAer\n", - "from qiskit.aqua import run_algorithm, QuantumInstance\n", - "from qiskit.aqua.input import ClassificationInput\n", - "from qiskit.aqua.components.feature_maps import SecondOrderExpansion\n", - "from qiskit.aqua.algorithms import QSVM\n", - "from qiskit.aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "First we prepare the dataset, which is used for training, testing and the finally prediction.\n", - "\n", - "*Note: You can easily switch to a different dataset, such as the Breast Cancer dataset, by replacing 'ad_hoc_data' to 'Breast_cancer' below.*" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{'A': 0, 'B': 1}\n" - ] - } - ], - "source": [ - "feature_dim = 2 # dimension of each data point\n", - "training_dataset_size = 20\n", - "testing_dataset_size = 10\n", - "random_seed = 10598\n", - "shots = 1024\n", - "\n", - "sample_Total, training_input, test_input, class_labels = ad_hoc_data(\n", - " training_size=training_dataset_size, \n", - " test_size=testing_dataset_size, \n", - " n=feature_dim, gap=0.3, PLOT_DATA=False\n", - ")\n", - "datapoints, class_to_label = split_dataset_to_data_and_labels(test_input)\n", - "print(class_to_label)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we create the svm in the declarative approach.\n", - "In the following json, we config:\n", - "- the algorithm name \n", - "- the feature map " - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "params = {\n", - " 'problem': {'name': 'classification', 'random_seed': random_seed},\n", - " 'algorithm': {\n", - " 'name': 'QSVM'\n", - " },\n", - " 'backend': {'shots': shots},\n", - " 'feature_map': {'name': 'SecondOrderExpansion', 'depth': 2, 'entanglement': 'linear'}\n", - "}\n", - "backend = BasicAer.get_backend('qasm_simulator')\n", - "algo_input = ClassificationInput(training_input, test_input, datapoints[0])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "With everything setup, we can now run the algorithm.\n", - "\n", - "The run method includes training, testing and predict on unlabeled data.\n", - "\n", - "For the testing, the result includes the success ratio.\n", - "\n", - "For the prediction, the result includes the predicted class names for each data.\n", - "\n", - "After that the trained model is also stored in the svm instance, you can use it for future prediction." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [], - "source": [ - "result = run_algorithm(params, algo_input, backend=backend)" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "kernel matrix during the training:\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "testing success ratio: 1.0\n", - "predicted classes: ['A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B']\n" - ] - } - ], - "source": [ - "print(\"kernel matrix during the training:\")\n", - "kernel_matrix = result['kernel_matrix_training']\n", - "img = plt.imshow(np.asmatrix(kernel_matrix),interpolation='nearest',origin='upper',cmap='bone_r')\n", - "plt.show()\n", - "\n", - "print(\"testing success ratio: \", result['testing_accuracy'])\n", - "print(\"predicted classes:\", result['predicted_classes'])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### part II: programmatic approach.\n", - "We construct the svm instance directly from the classes. The programmatic approach offers the users better accessibility, e.g., the users can access the internal state of svm instance or invoke the methods of the instance. We will demonstrate this advantage soon." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we create the svm in the programmatic approach.\n", - "- We build the svm instance by instantiating the class QSVM. \n", - "- We build the feature map instance (required by the svm instance) by instantiating the class SecondOrderExpansion." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [], - "source": [ - "backend = BasicAer.get_backend('qasm_simulator')\n", - "feature_map = SecondOrderExpansion(feature_dimension=feature_dim, depth=2, entangler_map=[[0, 1]])\n", - "svm = QSVM(feature_map, training_input, test_input, None)# the data for prediction can be fed later.\n", - "svm.random_seed = random_seed\n", - "quantum_instance = QuantumInstance(backend, shots=shots, seed=random_seed, seed_transpiler=random_seed)\n", - "result = svm.run(quantum_instance)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let us check the result." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "kernel matrix during the training:\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "testing success ratio: 1.0\n" - ] - } - ], - "source": [ - "print(\"kernel matrix during the training:\")\n", - "kernel_matrix = result['kernel_matrix_training']\n", - "img = plt.imshow(np.asmatrix(kernel_matrix),interpolation='nearest',origin='upper',cmap='bone_r')\n", - "plt.show()\n", - "\n", - "print(\"testing success ratio: \", result['testing_accuracy'])" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "collapsed": true - }, - "source": [ - "Different from the declarative approach, the programmatic approach allows the users to invoke APIs upon the svm instance directly. In the following, we invoke the API \"predict\" upon the trained svm instance to predict the labels for the newly provided data input.\n", - "\n", - "Use the trained model to evaluate data directly, and we store a `label_to_class` and `class_to_label` for helping converting between label and class name" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "ground truth: [0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1]\n", - "preduction: [0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1]\n" - ] - } - ], - "source": [ - "predicted_labels = svm.predict(datapoints[0])\n", - "\n", - "predicted_classes = map_label_to_class_name(predicted_labels, svm.label_to_class)\n", - "print(\"ground truth: {}\".format(datapoints[1]))\n", - "print(\"preduction: {}\".format(predicted_labels))" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.2" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/artificial_intelligence/qsvm_multiclass.ipynb b/community/artificial_intelligence/qsvm_multiclass.ipynb deleted file mode 100644 index b3161ea2e..000000000 --- a/community/artificial_intelligence/qsvm_multiclass.ipynb +++ /dev/null @@ -1,136 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## _*Quantum SVM algorithm: multiclass classifier extension*_\n", - "\n", - "A multiclass extension works in conjunction with an underlying binary (two class) classifier to provide multiclass classification.\n", - "\n", - "Currently three different multiclass extensions are supported:\n", - "\n", - "* OneAgainstRest\n", - "* AllPairs\n", - "* ErrorCorrectingCode\n", - "\n", - "These use different techniques to group the data with binary classification to achieve the final multiclass classification." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "from datasets import *\n", - "from qiskit import BasicAer\n", - "from qiskit.aqua.input import ClassificationInput\n", - "from qiskit.aqua import run_algorithm" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here we choose the `Wine` dataset which has 3 classes." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "n = 2 # dimension of each data point\n", - "sample_Total, training_input, test_input, class_labels = Wine(\n", - " training_size=40,\n", - " test_size=10, n=n, PLOT_DATA=True\n", - ")\n", - "temp = [test_input[k] for k in test_input]\n", - "total_array = np.concatenate(temp)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we setup an Aqua configuration dictionary to use the quantum `QSVM` algorithm and add a multiclass extension to classify the Wine data set, since it has 3 classes.\n", - "\n", - "Although the `AllPairs` extension is used here in the example the following multiclass extensions would also work:\n", - "\n", - " 'multiclass_extension': {'name': 'OneAgainstRest'}\n", - " 'multiclass_extension': {'name': 'ErrorCorrectingCode', 'code_size': 5}" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "'testing_accuracy' : 0.8260869565217391\n", - "'test_success_ratio' : 0.8260869565217391\n", - "'predicted_labels' : [0 0 0 0 0 0 1 0 0 0 2 2 1 1 1 0 1 1 1 1 2 2 2]\n", - "'predicted_classes' : ['A', 'A', 'A', 'A', 'A', 'A', 'B', 'A', 'A', 'A', 'C', 'C', 'B', 'B', 'B', 'A', 'B', 'B', 'B', 'B', 'C', 'C', 'C']\n" - ] - } - ], - "source": [ - "aqua_dict = {\n", - " 'problem': {'name': 'classification', 'random_seed': 10598},\n", - " 'algorithm': {\n", - " 'name': 'QSVM'\n", - " },\n", - " 'feature_map': {'name': 'SecondOrderExpansion', 'depth': 2, 'entangler_map': [[0, 1]]},\n", - " 'multiclass_extension': {'name': 'AllPairs'},\n", - " 'backend': {'shots': 1024}\n", - "}\n", - "\n", - "backend = BasicAer.get_backend('qasm_simulator')\n", - "algo_input = ClassificationInput(training_input, test_input, total_array)\n", - "result = run_algorithm(aqua_dict, algo_input, backend=backend)\n", - "for k,v in result.items():\n", - " print(\"'{}' : {}\".format(k, v))\n" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.2" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/community/artificial_intelligence/svm_classical.ipynb b/community/artificial_intelligence/svm_classical.ipynb deleted file mode 100644 index 293a30ab9..000000000 --- a/community/artificial_intelligence/svm_classical.ipynb +++ /dev/null @@ -1,281 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## _*SVM with a classical RBF kernel*_\n", - "\n", - "We have shown here a QSVM notebook with the classification problem solved using a quantum algorithm. By comparison this shows the problem solved classically.\n", - "\n", - "**This notebook shows the SVM implementation based on the classical RBF kernel.**" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "from datasets import *\n", - "from qiskit.aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name\n", - "from qiskit.aqua.input import ClassificationInput\n", - "from qiskit.aqua import run_algorithm" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "First we prepare the dataset, which is used for training, testing and the finally prediction.\n", - "\n", - "*Note: You can easily switch to a different dataset, such as the Breast Cancer dataset, by replacing 'ad_hoc_data' to 'Breast_cancer' below.*" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{'A': 0, 'B': 1}\n" - ] - } - ], - "source": [ - "feature_dim = 2 # dimension of each data point\n", - "training_dataset_size = 20\n", - "testing_dataset_size = 10\n", - "\n", - "sample_Total, training_input, test_input, class_labels = ad_hoc_data(\n", - " training_size=training_dataset_size, \n", - " test_size=testing_dataset_size, \n", - " n=feature_dim, gap=0.3, PLOT_DATA=True\n", - ")\n", - "datapoints, class_to_label = split_dataset_to_data_and_labels(test_input)\n", - "print(class_to_label)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "With the dataset ready we initialize the necessary inputs for the algorithm:\n", - "- the input dictionary (params) \n", - "- the input object containing the dataset info (algo_input)." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "params = {\n", - " 'problem': {'name': 'classification'},\n", - " 'algorithm': {\n", - " 'name': 'SVM'\n", - " }\n", - "}\n", - "\n", - "algo_input = ClassificationInput(training_input, test_input, datapoints[0])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "With everything setup, we can now run the algorithm.\n", - "\n", - "For the testing, the result includes the details and the success ratio.\n", - "\n", - "For the prediction, the result includes the predicted labels. " - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "kernel matrix during the training:\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "testing success ratio: 0.6\n", - "predicted classes: ['A', 'B', 'A', 'A', 'A', 'A', 'B', 'A', 'A', 'B', 'A', 'A', 'A', 'B', 'B', 'B', 'A', 'B', 'B', 'A']\n" - ] - } - ], - "source": [ - "result = run_algorithm(params, algo_input)\n", - "print(\"kernel matrix during the training:\")\n", - "kernel_matrix = result['kernel_matrix_training']\n", - "img = plt.imshow(np.asmatrix(kernel_matrix), interpolation='nearest', origin='upper', cmap='bone_r')\n", - "plt.show()\n", - "\n", - "print(\"testing success ratio: \", result['testing_accuracy'])\n", - "print(\"predicted classes:\", result['predicted_classes'])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### The breast cancer dataset\n", - "Now we run our algorithm with the real-world dataset: the breast cancer dataset" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{'A': 0, 'B': 1} {0: 'A', 1: 'B'}\n" - ] - } - ], - "source": [ - "sample_Total, training_input, test_input, class_labels = Breast_cancer(\n", - " training_size=20, test_size=10, n=2, PLOT_DATA=True\n", - ")\n", - "# n =2 is the dimension of each data point\n", - "\n", - "datapoints, class_to_label = split_dataset_to_data_and_labels(test_input)\n", - "label_to_class = {label:class_name for class_name, label in class_to_label.items()}\n", - "print(class_to_label, label_to_class)" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "kernel matrix during the training:\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "testing success ratio: 0.85\n", - "ground truth: ['A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B']\n", - "predicted: ['A', 'A', 'A', 'A', 'B', 'A', 'B', 'B', 'A', 'A', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B']\n" - ] - } - ], - "source": [ - "algo_input = ClassificationInput(training_input, test_input, datapoints[0])\n", - "result = run_algorithm(params, algo_input)\n", - "# print(result)\n", - "print(\"kernel matrix during the training:\")\n", - "kernel_matrix = result['kernel_matrix_training']\n", - "img = plt.imshow(np.asmatrix(kernel_matrix),interpolation='nearest',origin='upper',cmap='bone_r')\n", - "plt.show()\n", - "\n", - "print(\"testing success ratio: \", result['testing_accuracy'])\n", - "\n", - "print(\"ground truth: {}\".format(map_label_to_class_name(datapoints[1], label_to_class)))\n", - "print(\"predicted: {}\".format(result['predicted_classes']))" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.2" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/artificial_intelligence/svm_classical_multiclass.ipynb b/community/artificial_intelligence/svm_classical_multiclass.ipynb deleted file mode 100644 index 1a5cb2b7a..000000000 --- a/community/artificial_intelligence/svm_classical_multiclass.ipynb +++ /dev/null @@ -1,154 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## _*SVM with a classical RBF kernel: multiclass classifier extension*_\n", - "\n", - "A multiclass extension works in conjunction with an underlying binary (two class) classifier to provide multiclass classification.\n", - "\n", - "Currently three different multiclass extensions are supported:\n", - "\n", - "* OneAgainstRest\n", - "* AllPairs\n", - "* ErrorCorrectingCode\n", - "\n", - "These use different techniques to group the data with binary classification to achieve the final multiclass classification." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "from datasets import *\n", - "from qiskit.aqua.utils import split_dataset_to_data_and_labels\n", - "from qiskit.aqua.input import ClassificationInput\n", - "from qiskit.aqua import run_algorithm\n", - "import numpy as np" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here we choose the `Wine` dataset which has 3 classes." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "feature_dim = 2 # dimension of each data point\n", - "sample_Total, training_input, test_input, class_labels = Wine(training_size=20,\n", - " test_size=10, n=feature_dim, PLOT_DATA=True)\n", - "\n", - "temp = [test_input[k] for k in test_input]\n", - "total_array = np.concatenate(temp)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we setup an Aqua configuration dictionary to use the classical `SVM` algorithm and add a multiclass extension to classify the Wine data set, since it has 3 classes. We loop over the three extensions (modifying the params dictionary) to show the result with each." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "----- Using multiclass extension: 'OneAgainstRest' -----\n", - "\n", - "'testing_accuracy' : 1.0\n", - "'test_success_ratio' : 1.0\n", - "'predicted_labels' : [0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2]\n", - "'predicted_classes' : ['A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'C', 'C', 'C', 'C', 'C', 'C', 'C', 'C', 'C', 'C']\n", - "\n", - "----- Using multiclass extension: 'AllPairs' -----\n", - "\n", - "'testing_accuracy' : 1.0\n", - "'test_success_ratio' : 1.0\n", - "'predicted_labels' : [0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2]\n", - "'predicted_classes' : ['A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'C', 'C', 'C', 'C', 'C', 'C', 'C', 'C', 'C', 'C']\n", - "\n", - "----- Using multiclass extension: 'ErrorCorrectingCode' -----\n", - "\n", - "'testing_accuracy' : 1.0\n", - "'test_success_ratio' : 1.0\n", - "'predicted_labels' : [0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2]\n", - "'predicted_classes' : ['A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'C', 'C', 'C', 'C', 'C', 'C', 'C', 'C', 'C', 'C']\n" - ] - } - ], - "source": [ - "aqua_dict = {\n", - " 'problem': {'name': 'classification'},\n", - " 'algorithm': {\n", - " 'name': 'SVM'\n", - " },\n", - " 'multiclass_extension': {'name': 'OneAgainstRest'}\n", - "}\n", - "\n", - "algo_input = ClassificationInput(training_input, test_input, total_array)\n", - "\n", - "extensions = [\n", - " {'name': 'OneAgainstRest'},\n", - " {'name': 'AllPairs'}, \n", - " {'name': 'ErrorCorrectingCode', 'code_size': 5}\n", - "]\n", - "\n", - "for extension in extensions:\n", - " aqua_dict['multiclass_extension'] = extension\n", - " result = run_algorithm(aqua_dict, algo_input)\n", - " print(\"\\n----- Using multiclass extension: '{}' -----\\n\".format(extension['name']))\n", - " for k,v in result.items():\n", - " print(\"'{}' : {}\".format(k, v))\n" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.2" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/community/artificial_intelligence/vqc.ipynb b/community/artificial_intelligence/vqc.ipynb deleted file mode 100644 index aa8929e6e..000000000 --- a/community/artificial_intelligence/vqc.ipynb +++ /dev/null @@ -1,276 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## _*Variational Quantum Classifier*_\n", - "\n", - "The QSVM notebook demonstrates a kernel based approach. This notebook shows a variational method.\n", - "\n", - "For further information please see: [https://arxiv.org/pdf/1804.11326.pdf](https://arxiv.org/pdf/1804.11326.pdf)\n", - "\n", - "\n", - "**This notebook shows the variational quantum classifier method.**\n", - "\n", - "In this file, we show two ways for using the variational quantum classifier: (1) the declarative approach and (2) the programmatic approach. \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Part I: declarative approach.\n", - "In the declarative approach, we config a json-like configuration, which defines how the vqc instance is internally constructed. After the execution, it returns the json-like output, which carries the important information (e.g., the details of the vqc instance) and the processed results. " - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "from datasets import *\n", - "from qiskit import BasicAer\n", - "from qiskit.aqua import run_algorithm, QuantumInstance\n", - "from qiskit.aqua.algorithms import VQC\n", - "from qiskit.aqua.components.optimizers import SPSA\n", - "from qiskit.aqua.components.feature_maps import SecondOrderExpansion\n", - "from qiskit.aqua.components.variational_forms import RYRZfrom qiskit.aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name\n", - "from qiskit.aqua.input import ClassificationInput" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "First we prepare the dataset, which is used for training, testing and the finally prediction.\n", - "\n", - "*Note: You can easily switch to a different dataset, such as the Breast Cancer dataset, by replacing 'ad_hoc_data' to 'Breast_cancer' below.*" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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\n", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{'A': 0, 'B': 1}\n" - ] - } - ], - "source": [ - "feature_dim = 2 # dimension of each data point\n", - "training_dataset_size = 20\n", - "testing_dataset_size = 10\n", - "random_seed = 10598\n", - "shots = 1024\n", - "\n", - "sample_Total, training_input, test_input, class_labels = ad_hoc_data(\n", - " training_size=training_dataset_size, \n", - " test_size=testing_dataset_size, \n", - " n=feature_dim, gap=0.3, PLOT_DATA=True\n", - ")\n", - "datapoints, class_to_label = split_dataset_to_data_and_labels(test_input)\n", - "print(class_to_label)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we create the vqc in the declarative approach.\n", - "In the following json, we config:\n", - "- the algorithm name \n", - "- the variational form\n", - "- the feature map \n", - "- the optimizer" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "params = {\n", - " 'problem': {'name': 'classification', 'random_seed': 10598},\n", - " 'algorithm': {'name': 'VQC', 'override_SPSA_params': True},\n", - " 'backend': {'shots': 1024},\n", - " 'optimizer': {'name': 'SPSA', 'max_trials': 200, 'save_steps': 1},\n", - " 'variational_form': {'name': 'RYRZ', 'depth': 3},\n", - " 'feature_map': {'name': 'SecondOrderExpansion', 'depth': 2}\n", - "}\n", - "\n", - "classification_input = ClassificationInput(training_input, test_input, datapoints[0])\n", - "backend = BasicAer.get_backend('qasm_simulator')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "With everything setup, we can now run the algorithm.\n", - "\n", - "For the testing, the result includes the details and the success ratio.\n", - "\n", - "For the prediction, the result includes the predicted labels. " - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "testing success ratio: 1.0\n", - "predicted classes: ['A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B']\n" - ] - } - ], - "source": [ - "result = run_algorithm(params, classification_input, backend=backend)\n", - "print(\"testing success ratio: \", result['testing_accuracy'])\n", - "print(\"predicted classes:\", result['predicted_classes'])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Part II: programmatic approach.\n", - "We construct the vqc instance directly from the classes. The programmatic approach offers the users better accessibility, e.g., the users can access the internal state of vqc instance or invoke the methods of the instance. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we create the vqc in the programmatic approach.\n", - "- we build the optimizer instance (required by the vqc instance) by instantiating the class SPSA.\n", - "- We build the feature map instance (required by the vqc instance) by instantiating the class SecondOrderExpansion.\n", - "- We build the varitional form instance (required by the vqc instance) by instantiating the class RYRZ.\n", - "- We build the vqc instance by instantiating the class VQC. \n" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [], - "source": [ - "backend = BasicAer.get_backend('qasm_simulator')\n", - "optimizer = SPSA(max_trials=100, c0=4.0, skip_calibration=True)\n", - "optimizer.set_options(save_steps=1)\n", - "feature_map = SecondOrderExpansion(feature_dimension=feature_dim, depth=2)\n", - "var_form = RYRZ(num_qubits=feature_dim, depth=3)\n", - "vqc = VQC(optimizer, feature_map, var_form, training_input, test_input)\n", - "quantum_instance = QuantumInstance(backend, shots=shots, seed=random_seed, seed_transpiler=random_seed)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we run it." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "testing success ratio: 1.0\n" - ] - } - ], - "source": [ - "result = vqc.run(quantum_instance)\n", - "print(\"testing success ratio: \", result['testing_accuracy'])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Different from the declarative approach, the programmatic approach allows the users to invoke APIs upon the vqc instance directly. In the following, we invoke the API \"predict\" upon the trained vqc instance to predict the labels for the newly provided data input.\n", - "\n", - "Use the trained model to evaluate data directly, and we store a label_to_class and class_to_label for helping converting between label and class name" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "prediction: [0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1]\n" - ] - } - ], - "source": [ - "predicted_probs, predicted_labels = vqc.predict(datapoints[0])\n", - "predicted_classes = map_label_to_class_name(predicted_labels, vqc.label_to_class)\n", - "print(\"prediction: {}\".format(predicted_labels))" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.2" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/artificial_intelligence/vqc_feature_map_comparison.ipynb b/community/artificial_intelligence/vqc_feature_map_comparison.ipynb deleted file mode 100644 index 9d8ba3baa..000000000 --- a/community/artificial_intelligence/vqc_feature_map_comparison.ipynb +++ /dev/null @@ -1,178 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Variational Quantum Classifier Feature Map Comparison\n", - "\n", - "Both the first-order and second-order expansion feature maps provided by Aqua use $n$ qubits to encode $n$-dim datapoints. However, raw feature vectors can also be directly used in `VQC` circuit constructions, requiring only $log_2(n)$ qubits to encode $n$-dim datapoints. \n", - "\n", - "### Experiment\n", - "Below we compare the classification performance of `VQC` on the [Wine dataset](https://scikit-learn.org/stable/datasets/index.html#wine-dataset) using `RawFeatureVector` and `SecondOrderExpansion` feature maps. As you'll see, the former leads to about $90\\%$ accuracy using only $2$ qubits, whereas the latter achieves only around $50\\%$ accuracy, using $4$ qubits and taking $3\\times$ as long. \n", - "\n", - "We first prepare the Wine dataset:" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "from sklearn import datasets\n", - "from sklearn.model_selection import train_test_split\n", - "from sklearn.preprocessing import StandardScaler, MinMaxScaler\n", - "from sklearn.decomposition import PCA\n", - "\n", - "\n", - "def Wine(training_size, test_size, n):\n", - " class_labels = [r'A', r'B', r'C']\n", - "\n", - " data, target = datasets.load_wine(True)\n", - " sample_train, sample_test, label_train, label_test = train_test_split(\n", - " data, target, test_size=test_size, random_state=7\n", - " )\n", - "\n", - " # Now we standarize for gaussian around 0 with unit variance\n", - " std_scale = StandardScaler().fit(sample_train)\n", - " sample_train = std_scale.transform(sample_train)\n", - " sample_test = std_scale.transform(sample_test)\n", - "\n", - " # Now reduce number of features to number of qubits\n", - " pca = PCA(n_components=n).fit(sample_train)\n", - " sample_train = pca.transform(sample_train)\n", - " sample_test = pca.transform(sample_test)\n", - "\n", - " # Scale to the range (-1,+1)\n", - " samples = np.append(sample_train, sample_test, axis=0)\n", - " minmax_scale = MinMaxScaler((-1, 1)).fit(samples)\n", - " sample_train = minmax_scale.transform(sample_train)\n", - " sample_test = minmax_scale.transform(sample_test)\n", - " # Pick training size number of samples from each distro\n", - " training_input = {key: (sample_train[label_train == k, :])[:training_size] for k, key in enumerate(class_labels)}\n", - " test_input = {key: (sample_train[label_train == k, :])[training_size:(\n", - " training_size+test_size)] for k, key in enumerate(class_labels)}\n", - " return sample_train, training_input, test_input, class_labels" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can then set up the experiment as follows:" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "import scipy\n", - "\n", - "from qiskit import BasicAer\n", - "from qiskit.aqua.input import ClassificationInput\n", - "from qiskit.aqua import run_algorithm, QuantumInstance, aqua_globals\n", - "from qiskit.aqua.components.optimizers import SPSA, COBYLA\n", - "\n", - "feature_dim = 4 # dimension of each data point\n", - "training_dataset_size = 20\n", - "testing_dataset_size = 10\n", - "random_seed = 10598\n", - "np.random.seed(random_seed)\n", - "\n", - "sample_Total, training_input, test_input, class_labels = Wine(\n", - " training_size=training_dataset_size,\n", - " test_size=testing_dataset_size,\n", - " n=feature_dim\n", - ")\n", - "\n", - "classification_input = ClassificationInput(training_input, test_input)\n", - "params = {\n", - " 'problem': {'name': 'classification', 'random_seed': random_seed},\n", - " 'algorithm': {'name': 'VQC'},\n", - " 'backend': {'provider': 'qiskit.BasicAer', 'name': 'statevector_simulator'},\n", - " 'optimizer': {'name': 'COBYLA', 'maxiter':200},\n", - " 'variational_form': {'name': 'RYRZ', 'depth': 3},\n", - " 'feature_map': {'name': None},\n", - "}" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's try `RawFeatureVector` first:" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "VQC accuracy with RawFeatureVector: 0.8666666666666667\n" - ] - } - ], - "source": [ - "params['feature_map']['name'] = 'RawFeatureVector'\n", - "result = run_algorithm(params, classification_input)\n", - "print(\"VQC accuracy with RawFeatureVector: \", result['testing_accuracy'])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now let's try `SecondOrderExpansion`:" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Test accuracy with SecondOrderExpansion: 0.5333333333333333\n" - ] - } - ], - "source": [ - "params['feature_map']['name'] = 'SecondOrderExpansion'\n", - "result = run_algorithm(params, classification_input)\n", - "print(\"Test accuracy with SecondOrderExpansion: \", result['testing_accuracy'])" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.2" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/community/chemistry/LiH.png b/community/chemistry/LiH.png deleted file mode 100644 index dde425ee718b928729f600ecb6c7407623b1be20..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 105729 zcmeFYg<8IhckI7l@8!Y4aC?_L!1&<653k&NCO8lt;78dp@@^b+P zJ_*wa#fM+#Y=lut7vSZ3LH`5%|DvV1nhh4#rEAE~nXVD{L->%#R^*wjqQy&F2VH9e zEHhnOOH&J5Q==C*?G3DLj4aG=va`ZJ=9{lchmYsOh242wZ3|; z^z}^ATnDcYa_a@5Zq%zz)ER8|y6p=^OmlSOmzM*Vs4z-&g+MzWm?l z3_k{tFgflmcd!r<6O#-IW7EmWGiWAGKS_~}+U!x3MFn|XCQa}-!su`*i#>h%j)sAs zU(@4wZ`N$Z!R#ceGgn7wYh`Tg@PKQ~HSxP%y+qK>&xbh| zuq^Kkzrn@&`o%zB|J7pucjwigxOQt3A{yZk&lKkz#?N5c({pn_BczkMs}T3~>(?Qr z)@&}_U+3I5TDgi?C;ht;#R#?*(3#?H!otGlikw(j!&K)Su}VB2825}D*i>t~+Kok0-8 z5)00QyeP2XlW~0O%$M4t5c!rfP$>xUeejKXLE*x zXlX@!iCMaGtB*7E>iy?`y}z`+v7wl)Ubxw>7m%)1Za-6WzBO{R$V>wj#<4To`gLV; zGO;y^%cLs_75UICa$<6l=*EpSQ9rWzZdswi{KZc7vW0 zD?Nd=--H=T=?ZVQ2&e@$H)dKDVJ|p6j$JAF?4=Y_q&f!+O^8TH=m`i2lrvSN;nL_D z0wLza`zH=3?<3wHw?uG63b+)h`QxDjT!)MkBqTSZ?#2^=BiV7YvyY^cn2FYjf`mw2J$-6vxH z6!H=hK6@((;2;bA-}T(;zH3HM zqsX+gCtb174x^$~;VAF!?rz-wEq;G{DHB$b`NSKa*LgFI%6(VY?QpGr#{GTF`{OuQ z(TRzP2WEp0vbD-p!~&?4U%pH^JUqO9^=kY>v%$GeG3wCr@&mheTC8ykFzKU@Az@)D zecCS4)hEa0wdjT)4`gpCXs=?MAuV$WMySBZ{+>{{S=%^B2y(>A)Hlf zvynco;rYEOOu5ah%oe6k7F>n6Irq5y3$I;9)$u+CBa>8YjAnG(LaWa35VEtg+wN}~ z`3i!IwsPHiAuRlsm`yv&pgGKFcl8gK-C>u|$tTnPZ;y}mw-hBLB&znWUAtCbzoaf5 z%`HzzFH^98o)GKDwKG&$auZ*q=qfk6BnL~Z5^2)yFue=IrTI-^ESWt$N@l|)^4%%Y ziq_V7`&*dQkA(CYR+DwaL)@;r-<)@rvo|+wN&Q6amWS1rhKf}mJ$j8#EtqwYkZx|S zGjV^Zcnre$ZskTBpE2Ny``$DOvY#A=Z6P#AvqC5G;^H4PH8t1K5s{G@a8Q~tI%A

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H .0 .0 1.6', unit=UnitsType.ANGSTROM,\n", - " charge=0, spin=0, basis='sto3g')\n", - "molecule = driver.run()" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Originally requires 8 qubits\n", - "Representation: paulis, qubits: 8, size: 276\n" - ] - } - ], - "source": [ - "core = Hamiltonian(transformation=TransformationType.FULL, qubit_mapping=QubitMappingType.PARITY, \n", - " two_qubit_reduction=True, freeze_core=True)\n", - "qubit_op, _ = core.run(molecule)\n", - "\n", - "print(\"Originally requires {} qubits\".format(qubit_op.num_qubits))\n", - "print(qubit_op)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Find the symmetries of the qubit operator" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Z2 symmetries found:\n", - "ZIZIZIZI\n", - "ZZIIZZII\n", - "single qubit operators found:\n", - "IIIIIIXI\n", - "IIIIIXII\n", - "cliffords found:\n", - "ZIZIZIZI\t0.7071067811865475\n", - "IIIIIIXI\t0.7071067811865475\n", - "\n", - "ZZIIZZII\t0.7071067811865475\n", - "IIIIIXII\t0.7071067811865475\n", - "\n", - "single-qubit list: [1, 2]\n" - ] - } - ], - "source": [ - "[symmetries, sq_paulis, cliffords, sq_list] = qubit_op.find_Z2_symmetries()\n", - "print('Z2 symmetries found:')\n", - "for symm in symmetries:\n", - " print(symm.to_label())\n", - "print('single qubit operators found:')\n", - "for sq in sq_paulis:\n", - " print(sq.to_label())\n", - "print('cliffords found:')\n", - "for clifford in cliffords:\n", - " print(clifford.print_operators())\n", - "print('single-qubit list: {}'.format(sq_list))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Use the found symmetries, single qubit operators, and cliffords to taper qubits from the original qubit operator. For each Z2 symmetry one can taper one qubit. However, different tapered operators can be built, corresponding to different symmetry sectors. " - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Number of qubits of tapered qubit operator: 6\n", - "Number of qubits of tapered qubit operator: 6\n", - "Number of qubits of tapered qubit operator: 6\n", - "Number of qubits of tapered qubit operator: 6\n" - ] - } - ], - "source": [ - "tapered_ops = []\n", - "for coeff in itertools.product([1, -1], repeat=len(sq_list)):\n", - " tapered_op = Operator.qubit_tapering(qubit_op, cliffords, sq_list, list(coeff))\n", - " tapered_ops.append((list(coeff), tapered_op))\n", - " print(\"Number of qubits of tapered qubit operator: {}\".format(tapered_op.num_qubits))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The user has to specify the symmetry sector he is interested in. Since we are interested in finding the ground state here, let us get the original ground state energy as a reference." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "=== GROUND STATE ENERGY ===\n", - " \n", - "* Electronic ground state energy (Hartree): -8.874303870396\n", - " - computed part: -1.078084301625\n", - " - frozen energy part: -7.796219568771\n", - " - particle hole part: 0.0\n", - "~ Nuclear repulsion energy (Hartree): 0.992207270475\n", - "> Total ground state energy (Hartree): -7.882096599921\n" - ] - } - ], - "source": [ - "ee = ExactEigensolver(qubit_op, k=1)\n", - "result = core.process_algorithm_result(ee.run())\n", - "for line in result[0]:\n", - " print(line)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now, let us iterate through all tapered qubit operators to find out the one whose ground state energy matches the original (un-tapered) one." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Lowest eigenvalue of the 0-th tapered operator (computed part) is -1.078084301625\n", - "Lowest eigenvalue of the 1-th tapered operator (computed part) is -0.509523578167\n", - "Lowest eigenvalue of the 2-th tapered operator (computed part) is -0.912078232998\n", - "Lowest eigenvalue of the 3-th tapered operator (computed part) is -0.912078232998\n", - "The 0-th tapered operator matches original ground state energy, with corresponding symmetry sector of [1, 1]\n" - ] - } - ], - "source": [ - "smallest_eig_value = 99999999999999\n", - "smallest_idx = -1\n", - "for idx in range(len(tapered_ops)):\n", - " ee = ExactEigensolver(tapered_ops[idx][1], k=1)\n", - " curr_value = ee.run()['energy']\n", - " if curr_value < smallest_eig_value:\n", - " smallest_eig_value = curr_value\n", - " smallest_idx = idx\n", - " print(\"Lowest eigenvalue of the {}-th tapered operator (computed part) is {:.12f}\".format(idx, curr_value))\n", - " \n", - "the_tapered_op = tapered_ops[smallest_idx][1]\n", - "the_coeff = tapered_ops[smallest_idx][0]\n", - "print(\"The {}-th tapered operator matches original ground state energy, with corresponding symmetry sector of {}\".format(smallest_idx, the_coeff))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Alternatively, one can run multiple VQE instances to find the lowest eigenvalue sector. \n", - "Here we just validate that `the_tapered_op` reach the smallest eigenvalue in one VQE execution with the UCCSD variational form, modified to take into account of the tapered symmetries." - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [], - "source": [ - "# setup initial state\n", - "init_state = HartreeFock(num_qubits=the_tapered_op.num_qubits, num_orbitals=core._molecule_info['num_orbitals'],\n", - " qubit_mapping=core._qubit_mapping, two_qubit_reduction=core._two_qubit_reduction,\n", - " num_particles=core._molecule_info['num_particles'], sq_list=sq_list)\n", - "\n", - "# setup variationl form\n", - "var_form = UCCSD(num_qubits=the_tapered_op.num_qubits, depth=1,\n", - " num_orbitals=core._molecule_info['num_orbitals'], \n", - " num_particles=core._molecule_info['num_particles'],\n", - " active_occupied=None, active_unoccupied=None, initial_state=init_state,\n", - " qubit_mapping=core._qubit_mapping, two_qubit_reduction=core._two_qubit_reduction, \n", - " num_time_slices=1,\n", - " cliffords=cliffords, sq_list=sq_list, tapering_values=the_coeff, symmetries=symmetries)\n", - "\n", - "# setup optimizer\n", - "optimizer = COBYLA(maxiter=1000)\n", - "\n", - "# set vqe\n", - "algo = VQE(the_tapered_op, var_form, optimizer, 'matrix')\n", - "\n", - "# setup backend\n", - "backend = BasicAer.get_backend('statevector_simulator')\n", - "quantum_instance = QuantumInstance(backend=backend)" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [], - "source": [ - "algo_result = algo.run(quantum_instance)" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "=== GROUND STATE ENERGY ===\n", - " \n", - "* Electronic ground state energy (Hartree): -8.874303856889\n", - " - computed part: -1.078084288118\n", - " - frozen energy part: -7.796219568771\n", - " - particle hole part: 0.0\n", - "~ Nuclear repulsion energy (Hartree): 0.992207270475\n", - "> Total ground state energy (Hartree): -7.882096586414\n", - "The parameters for UCCSD are:\n", - "[ 0.03815735 0.00366554 0.03827111 0.00369737 -0.03604811 0.0594364\n", - " -0.02741369 -0.02735108 0.05956488 -0.11497243]\n" - ] - } - ], - "source": [ - "result = core.process_algorithm_result(algo_result)\n", - "for line in result[0]:\n", - " print(line)\n", - "\n", - "print(\"The parameters for UCCSD are:\\n{}\".format(algo_result['opt_params']))" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/chemistry/ParticleHoleTransformation.ipynb b/community/chemistry/ParticleHoleTransformation.ipynb deleted file mode 100644 index e58512f7f..000000000 --- a/community/chemistry/ParticleHoleTransformation.ipynb +++ /dev/null @@ -1,202 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## _*Particle hole transformation of FermionicOperator*_\n", - "\n", - "This notebook demonstrates carrying out a ParticleHole transformation on the FermionicOperator in Qiskit Chemistry. Here we use the FermionicOperator directly to demonstrate.\n", - "\n", - "Note: The Hamiltonian class that wraps this provides a means to use either full, or particle hole transformation. Under the covers it does what is shown here though.\n", - "\n", - "This notebook has been written to use the PYSCF chemistry driver." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "\n", - "from qiskit import BasicAer\n", - "from qiskit.transpiler import PassManager\n", - "\n", - "from qiskit.aqua import Operator, QuantumInstance\n", - "from qiskit.aqua.algorithms.adaptive import VQE\n", - "from qiskit.aqua.algorithms.classical import ExactEigensolver\n", - "from qiskit.aqua.components.optimizers import L_BFGS_B\n", - "from qiskit.aqua.components.variational_forms import RY\n", - "\n", - "from qiskit.chemistry import FermionicOperator\n", - "from qiskit.chemistry.drivers import PySCFDriver, UnitsType" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We'll do this with H2 molecule and use the PySCF driver to create the integrals we need for the FermionicOperator." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "driver = PySCFDriver(atom='H .0 .0 .0; H .0 .0 0.735', unit=UnitsType.ANGSTROM,\n", - " charge=0, spin=0, basis='sto3g')\n", - "molecule = driver.run()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We first create the FermionicOperator and use ExactEigensolver with qubit operator we get from it via a jordan wigner mapping to compute the ground state energy. Here this is the electronic component of the total ground state energy (the total ground state energy would include the nuclear repulsion energy we can get from the molecule that comes from the driver)" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The exact ground state energy is: -1.8572750302023795\n", - "The Hartree Fock Electron Energy is: -1.8369679912029842\n" - ] - } - ], - "source": [ - "ferOp = FermionicOperator(h1=molecule.one_body_integrals, h2=molecule.two_body_integrals)\n", - "qubitOp_jw = ferOp.mapping(map_type='JORDAN_WIGNER', threshold=0.00000001)\n", - "qubitOp_jw.chop(10**-10)\n", - "\n", - "# Using exact eigensolver to get the smallest eigenvalue\n", - "exact_eigensolver = ExactEigensolver(qubitOp_jw, k=1)\n", - "ret = exact_eigensolver.run()\n", - "\n", - "# print(qubitOp_jw.print_operators())\n", - "\n", - "print('The exact ground state energy is: {}'.format(ret['energy']))\n", - "print('The Hartree Fock Electron Energy is: {}'.format(molecule.hf_energy - molecule.nuclear_repulsion_energy))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now the same as above but with ParticleHole transformation. This removes out energy from the FermionicOperator that is equivalent to the electronic part of the Hartree Fock Energy that we also computed above. The Hartree Fock energy also comes from the driver. To get the total electronic ground state energy we need to add the part we now compute with the part that was removed by the transformation." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Energy shift is: 1.8369679912029846\n", - "The exact ground state energy in PH basis is -0.020307038999396183\n", - "The exact ground state energy in PH basis is -1.8572750302023808 (with energy_shift)\n" - ] - } - ], - "source": [ - "# particle hole transformation\n", - "newferOp, energy_shift = ferOp.particle_hole_transformation(num_particles=2)\n", - "print('Energy shift is: {}'.format(energy_shift))\n", - "newqubitOp_jw = newferOp.mapping(map_type='JORDAN_WIGNER', threshold=0.00000001)\n", - "newqubitOp_jw.chop(10**-10)\n", - "\n", - "exact_eigensolver = ExactEigensolver(newqubitOp_jw, k=1)\n", - "ret = exact_eigensolver.run()\n", - "\n", - "# print(newqubitOp_jw.print_operators())\n", - "print('The exact ground state energy in PH basis is {}'.format(ret['energy']))\n", - "print('The exact ground state energy in PH basis is {} (with energy_shift)'.format(ret['energy'] - energy_shift))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We run here using the quantum VQE algorithm to show the same result. The parameters printed are the optimal parameters of the variational form at the minimum energy, the ground state." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Minimum value: -0.020307038771711697\n", - "Minimum value: -1.8572750299746963\n", - "Parameters: [-0.62024568 -0.94461634 -0.12822854 -1.33174693 -3.12835752 -2.41119768\n", - " 0.67926104 2.44344768 0.72721421 -2.76518798 -1.08251803 -1.75962366\n", - " 0.54861203 1.8995056 3.04269648 -1.75046119 0.16409288 0.68204022\n", - " -0.07661803 -0.76359574 -1.56412942 -2.02324628 1.50961019 1.31452025]\n" - ] - } - ], - "source": [ - "# setup VQE \n", - "# setup optimizer, use L_BFGS_B optimizer for example\n", - "lbfgs = L_BFGS_B(maxfun=1000, factr=10, iprint=10)\n", - "\n", - "# setup variational form generator (generate trial circuits for VQE)\n", - "var_form = RY(newqubitOp_jw.num_qubits, 5, entangler_map = [[0, 1], [1, 2], [2, 3]])\n", - "\n", - "# setup VQE with operator, variational form, and optimizer\n", - "vqe_algorithm = VQE(newqubitOp_jw, var_form, lbfgs, 'matrix')\n", - "\n", - "backend = BasicAer.get_backend('statevector_simulator')\n", - "quantum_instance = QuantumInstance(backend, pass_manager=PassManager())\n", - "\n", - "results = vqe_algorithm.run(quantum_instance)\n", - "print(\"Minimum value: {}\".format(results['eigvals'][0].real))\n", - "print(\"Minimum value: {}\".format(results['eigvals'][0].real - energy_shift))\n", - "print(\"Parameters: {}\".format(results['opt_params']))" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/community/chemistry/PySCFChemistryDriver.ipynb b/community/chemistry/PySCFChemistryDriver.ipynb deleted file mode 100644 index 991697bf8..000000000 --- a/community/chemistry/PySCFChemistryDriver.ipynb +++ /dev/null @@ -1,168 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## _*Using PySCF driver*_\n", - "\n", - "Qiskit Chemistry supports a number of different chemistry drivers, i.e chemistry programs and software libraries, which are used to compute integrals that are then used to build the second quantized Hamiltonian in the FermionicOperator.\n", - "\n", - "Drivers include Gaussian 16, PyQuante, PySCF, PSI4 and HDF5. The main Qiskit documentation has more information on [drivers](https://qiskit.org/documentation/aqua/chemistry/qiskit_chemistry_drivers.html).\n", - "\n", - "For non-Windows platforms (where PySCF has no pre-built packages), the PySCF driver is installed as a dependent when you `pip install qiskit-chemistry`. HDF5 support is built into Qiskit Chemistry. If you would like/prefer to use one of the other drivers then refer to the above link for installation and usage guidance.\n", - "\n", - "Note: drivers were written to allow existing users of them to leverage creating the molecular input in a native way for the driver. While Multiplicity (2S+1) is commonly used to specify the overall spin of the molecule, PySCF uses Spin (2S) if you are programming directly with its API and that is what is exposed here. For a singlet system, as in the example below i.e. equal numbers of alpha and beta electrons, the overall spin here is 0 and 2S is 0 (Multiplicity would have been 1).\n", - "\n", - "This notebook has been written to use the PySCF chemistry driver." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "\n", - "from qiskit import BasicAer\n", - "from qiskit.transpiler import PassManager\n", - "\n", - "from qiskit.aqua import Operator, QuantumInstance\n", - "from qiskit.aqua.algorithms.adaptive import VQE\n", - "from qiskit.aqua.algorithms.classical import ExactEigensolver\n", - "from qiskit.aqua.components.optimizers import L_BFGS_B\n", - "from qiskit.aqua.components.variational_forms import RYRZ\n", - "\n", - "from qiskit.chemistry import FermionicOperator\n", - "from qiskit.chemistry.drivers import PySCFDriver, UnitsType" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "# using driver to get fermionic Hamiltonian\n", - "# PySCF example\n", - "driver = PySCFDriver(atom='H .0 .0 .0; H .0 .0 0.735', unit=UnitsType.ANGSTROM,\n", - " charge=0, spin=0, basis='sto3g')\n", - "molecule = driver.run()" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "# get fermionic operator and mapping to qubit operator\n", - "ferOp = FermionicOperator(h1=molecule.one_body_integrals, h2=molecule.two_body_integrals)\n", - "qubitOp = ferOp.mapping(map_type='JORDAN_WIGNER', threshold=0.00000001)\n", - "qubitOp.to_matrix()\n", - "qubitOp.chop(10**-10)" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [], - "source": [ - "# If you do have the driver installed or would like to start with a random Hamiltonian\n", - "# SIZE=4\n", - "# matrix = np.random.random((SIZE,SIZE))\n", - "# qubitOp = Operator(matrix=matrix)" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The exact ground state energy is: -1.8572750302023784\n" - ] - } - ], - "source": [ - "# Using exact eigensolver to get the smallest eigenvalue\n", - "exact_eigensolver = ExactEigensolver(qubitOp, k=1)\n", - "ret = exact_eigensolver.run()\n", - "print('The exact ground state energy is: {}'.format(ret['eigvals'][0].real))" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Minimum value: -1.8532124263217393\n", - "Parameters: [-2.13953054 0.70800218 -0.17157494 -2.67458466 2.43244041 0.04126769\n", - " 0.34740155 -0.04775077 -1.151147 2.76097941 -1.48948796 -0.30086504\n", - " 0.7290411 2.40033569 -2.30581555 1.06377607 -2.97789243 1.43082718\n", - " -0.91377262 -2.29316671 -0.04083006 -0.54650779 -2.43032826 -0.79940815\n", - " -1.88176584 0.05495389 2.47406188 -0.82144629 -2.44818703 -3.11585379\n", - " -2.54844951 -2.58470426 -0.99008597 -2.88926043 1.20856368 2.67069418\n", - " 2.4613227 1.22966774 -0.03176877 0.93517933 0.06694405 1.33700758\n", - " 1.49080935 -1.39533027 0.47972164 1.7949311 -3.01432916 -2.43192278]\n" - ] - } - ], - "source": [ - "# setup VQE \n", - "# setup optimizer, use L_BFGS_B optimizer for example\n", - "lbfgs = L_BFGS_B(maxfun=1000, factr=10, iprint=10)\n", - "\n", - "# setup variational form generator (generate trial circuits for VQE)\n", - "var_form = RYRZ(qubitOp.num_qubits, 5, entangler_map = [[0, 1], [1, 2], [2, 3]])\n", - "\n", - "# setup VQE with operator, variational form, and optimizer\n", - "vqe_algorithm = VQE(qubitOp, var_form, lbfgs, 'matrix')\n", - "\n", - "backend = BasicAer.get_backend('statevector_simulator')\n", - "quantum_instance = QuantumInstance(backend, pass_manager=PassManager())\n", - "\n", - "results = vqe_algorithm.run(quantum_instance)\n", - "print(\"Minimum value: {}\".format(results['eigvals'][0].real))\n", - "print(\"Parameters: {}\".format(results['opt_params']))" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/chemistry/QSE_pytket.ipynb b/community/chemistry/QSE_pytket.ipynb deleted file mode 100644 index e93e915f4..000000000 --- a/community/chemistry/QSE_pytket.ipynb +++ /dev/null @@ -1,942 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# _*Quantum chemistry with Qiskit `Terra`, `Aqua` and CQC's `t|ket〉` compiler*_ \n", - "\n", - "In this tutorial, we discuss how to use IBM's Qiskit `Terra` and `Aqua` packages, and the `t|ket〉` compiler by Cambridge Quantum Computing (CQC), to calculate the excited state energies of simple molecules using the quantum subspace expansion (QSE) technique. By the end of this tutorial, you will\n", - "\n", - "* Understand why optimizing circuits for quantum chemistry is necessary\n", - "* Learn about the quantum subspace expansion technique for computing excited state energies\n", - "* See how Qiskit `Terra` enables 3rd-party passes in its transpiler architecture\n", - "* Use `pytket` to perform native circuit optimization and circuit routing\n", - "\n", - "NOTE: Throughout this tutorial, we assume the reader has some familiarity with quantum chemistry methods, though an extensive knowledge is not necessary.\n", - "\n", - "**Code setup**\n", - "\n", - "This tutorial makes use of Qiskit `Terra` and `Aqua`, as well as `pytket` (the Python interface to `t|ket〉`). To install `Terra` and `Aqua`, follow instructions available [here](https://qiskit.org/). To install `pytket`, follow the instructions at [this Github repository](https://github.com/CQCL/pytket)." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Quantum chemistry in the NISQ era, and the need for circuit optimization techniques\n", - "\n", - "One of the expected applications of noisy, intemediate-scale quantum (NISQ) devices is simulating quantum chemistry. A simple quantum chemistry question is \"Given how the electrons and nuclei of a particular molecule are arranged, what is the _energy_ of that configuration?\". By examining how the energy of the configuration changes as the nuclei and electrons are moved relative to one another, we can map out an _energy surface_. The configuration that minimizes the energy is a stable, equilibrium point for the molecule. Knowing this configuration (and its associated energy), we can deduce a variety of molecular properties, such as reaction rates.\n", - "\n", - "Most techniques for computing molecular energies on near term quantum devices rely on the [variational quantum eigensolver (VQE) algorithm](https://doi.org/10.1038/ncomms5213). This algorithm uses a parameterized _ansatz_ $|{\\psi}(\\boldsymbol{\\theta})\\rangle$ to describe the ground state energy of the Hamiltonian $H$ for a given configuration. By examining how the expected energy $\\langle \\psi(\\boldsymbol{\\theta})|H| \\psi(\\boldsymbol{\\theta})\\rangle/\\langle \\psi(\\boldsymbol{\\theta})|\\psi(\\boldsymbol{\\theta})\\rangle$ changes as $\\boldsymbol{\\theta}$ is varied, we can optimize the parameters to find an estimate for the ground state and its corresponding energy.\n", - "\n", - "Running the VQE algorithm on actual hardware has two complications:\n", - "\n", - "* Efficiently preparing the trial state $|\\psi(\\boldsymbol{\\theta})\\rangle$.\n", - "\n", - "* Efficiently measuring the terms in the Hamiltonian $H$ that describe the configuration.\n", - "\n", - "In this tutorial, we'll focus on the problem of efficiently preparing the trial state. We do so for two reasons:\n", - "\n", - "* An accurate estimate of the ground state is all that's necessary to do the quantum subspace expansion technique to estimate excited state energies\n", - "\n", - "* To demonstrate the capabilies of Qiskit `Terra` and CQC's `t|ket〉` compiler to reduce the circuit _resources_ (number of gates, depth, etc.) for the state preparation. In principle, these capabilities can be deployed for other problems.\n", - "\n", - "Reducing the resources is crucial in the NISQ era, because the noise present in NISQ devices dominates more for larger circuits (with more operations) and reduces the accuracy of the results. Therefore techniques which reduce circuit requirements can significantly improve the results on real hardware. Note that there are techniques, such as [qubit tapering](https://arxiv.org/abs/1701.08213), or ['gate-efficient' circuits](https://arxiv.org/abs/1809.05057), which are useful for constructing a lower-resource circuit that could be run on _ideal_ hardware. In practice, even these \"resource-efficient\" circuits can be further optimized, especially when the imperfections and constraints of a real piece of hardware are taken into account.\n", - "\n", - "At a high level, our approach utilizes Qiskit `Aqua` to generate a parameterized ansatz based on the [_Unitary Coupled Cluster, Single-Double_ (UCCSD) ansatz](https://en.wikipedia.org/wiki/Coupled_cluster). We then use Qiskit `Terra` and the `t|ket〉` compiler (as implemented in `pytket`) to optimize the circuit for that ansatz. We will show that the optimized ansatz requires substantially fewer circuit resources than the naive UCCSD ansatz. An application of our approach, we show how to use the quantum subspace expansion (QSE) technique to compute excited state energies for gaseous hydrogen (H$_{2}$) and lithium hydride (LiH)." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Computing excited state energies using the Quantum Subspace Expansion (QSE) technique\n", - "\n", - "The VQE algorithm is often used to compute the _ground state_ energy of a given molecular configuration. However, knowing the energies of _excited states_ of the system is also useful. The energies of electronic excited states prove, in general, challenging to compute. Excited states are usually more _entangled_ than ground states and so require more computational resources to compute. While there exists techniques for efficiently representing certain classes of entangled states, in general, the complexity of the simulation will be non-trivial. This is a problem as it makes classical computation of the energy, to an appropriate accuracy, of many molecules impossible. \n", - "\n", - "This notebook demonstrates calculation of excited states of molecules using the [quantum subspace expanansion (QSE) technique](https://doi.org/10.1103/PhysRevA.95.042308). The QSE technique uses an accurate estimate of the ground state energy of a given molecular configuration to estimate the energies of excited states. Consider a fixed molecule (represented by a given Hamiltonian $H$), and suppose $\\left|\\Psi_{0}\\right\\rangle$ is the output of the VQE algorithm for estimating the ground state energy of $H$.\n", - "\n", - "The QSE technique constructs a subspace of state vectors $\\left|\\Psi_j^k\\right\\rangle$ formed by one-electron excitations of the ground state wavefunction:\n", - "\n", - "\\begin{equation}\n", - "\\left|\\Psi_{j}^{k}\\right\\rangle = c_k^{\\dagger}c_{j}\\left|\\Psi_0\\right\\rangle.\n", - "\\end{equation}\n", - "\n", - "where $c_k^{\\dagger}, c_{j}$ are the fermionic creation and annihilation operators over spin orbitals $k$ and $j$, respectively. That is, these vectors are formed by reducing the occupation of spin orbital $j$ by one, and increasing the occupation of spin orbital $k$ by one. The vectors are not in general orthogonal to $\\Psi_{0}$ hence we will need to calculate an overlap matrix.\n", - "\n", - "\n", - "Within this subspace, we solve a generalized eigenvalue problem. Consider the operator $H'$ with matrix elements given by\n", - "$$(H')_{jk}^{lm} = \\langle\\Psi_j^l \\left| H \\right| \\Psi_k^m\\rangle,$$\n", - "\n", - "and define an overlap matrix $S$ whose matrix elements are given by\n", - "\n", - "$$S_{jk}^{lm} = \\langle \\Psi_j^l \\left|\\Psi_k^m\\right\\rangle.$$\n", - "\n", - "The generalized eigenvalue equation to be solved is \n", - "\n", - "\\begin{equation}\n", - "H'C=SCE,\n", - "\\end{equation}\n", - "\n", - "where $C$ is the matrix of eigenvectors, and $E$ is the vector of eigenvalues. Crucially, _the energy eigenvalues $E$ provide an estimate of the excited state energies of $H$_ as well as a refined value of the ground state energy.\n", - "\n", - "Notice that the solution to the generalized eigenvalue equation can be done on a classical computer, provided $H'$ and $S$ have been calculated. The matrix elements of both of these matrices can be constructed using a quantum computer, in the following way. First, re-write the matrix elements in terms of $\\left | \\Psi_{0}\\right \\rangle$:\n", - "\n", - "\\begin{align}\n", - "(H')_{jk}^{lm} =& \\langle\\Psi_j^l \\left| H \\right| \\Psi_k^m\\rangle = \\langle \\Psi_{0} | c_{j}^\\dagger c_{l} Hc_{m}^{\\dagger}c_{k}|\\Psi_{0}\\rangle\\\\\n", - "S_{jk}^{lm} &= \\langle \\Psi_j^l \\left|\\Psi_k^m\\right\\rangle = \\langle \\Psi_{0} | c_{j}^\\dagger c_{l} c_{m}^{\\dagger}c_{k}|\\Psi_{0}\\rangle.\n", - "\\end{align}\n", - "\n", - "The matrix elements can be calculated using a quantum computer or simluator. How? By transforming the operators \n", - "$c_{j}^\\dagger c_{l} c_{k}^{\\dagger}c_{m}$ and $c_{l}^\\dagger c_{j} H c_{m}^{\\dagger}c_{k}$ to a set of Pauli quantum gates according to an appropriate scheme such as Jordan-Wigner or Bravyi-Kitaev, apply this gate set to the ground state wavefunction (constructed with the coefficients obtained from the VQE calculation) and perform a measurement to obtain the expected value. By measuring these expectation values, we obtain estimates of $S_{jk}^{lm}$ and $(H')_{jk}^{lm}$, respectively.\n", - "\n", - "Therefore, to use the QSE technique, we need to use the quantum computer to calculate 2 quantities:\n", - "\n", - "* An estimate of the ground state $\\left |\\Psi_{0}\\right\\rangle$ (by running the VQE algorithm)\n", - "* The matrix elements of $H'$ and $S$.\n", - "\n", - "For the first quantity, we want to have an efficient representation of the trial state $|\\psi(\\boldsymbol{\\theta})\\rangle$. And for the second, we need to be able to take the estimate of the ground state and efficiently compute matrix elements. In both of these cases, being able to optimize the circuit for preparing would be useful. Thankfully, Qiskit `Terra`, in conjunction with `t|ket〉`, provides us tools for doing so. We discuss the problem of _circuit compilation/optimization_ in the next section." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Circuit compilation with Qiskit `Terra` and `t|ket〉`\n", - "\n", - "In the remainder of this tutorial, we show how to use Qiskit `Terra` and `t|ket〉` to optimize the circuits for preparing VQE trial states, and simulate the QSE technique." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Application I: Reducing circuit resources for trial state preparation\n", - "\n", - "In this tutorial, we'll focus on two simple molecules: hydrogen (H$_{2}$) and lithium hydride (LiH). NOTE: the code is much slower for LiH, which is why here, we'll demonstrate H$_{2}$.\n", - "\n", - "\n", - "As a first application of the pipelines provided by `Terra`, `Aqua`, and `t|ket〉`, we first show how to configure a VQE experiment using `Aqua`, and then use `Terra` and `t|ket〉` to compile the trial state preparation circuit.\n", - "\n", - "Let's start by importing the necessary packages." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "# numpy, for random number generation\n", - "import numpy as np\n", - "\n", - "# Qiskit, for transpiler-related functions, the IBMQ provider, and the Aer simulator\n", - "from qiskit import IBMQ, Aer, QuantumRegister\n", - "from qiskit.transpiler import transpile, transpile_dag, PassManager\n", - "from qiskit.converters import circuit_to_dag, dag_to_circuit\n", - "\n", - "# pytket, for optimization\n", - "import pytket\n", - "from pytket.qiskit import TketPass\n", - "\n", - "# Qiskit Aqua, for chemistry\n", - "from qiskit_chemistry.drivers import PySCFDriver, UnitsType\n", - "from qiskit_chemistry import FermionicOperator\n", - "from qiskit_chemistry.aqua_extensions.components.initial_states import HartreeFock\n", - "from qiskit_chemistry.aqua_extensions.components.variational_forms import UCCSD" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Step 0: Enable IBMQ account" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "ExecuteTime": { - "end_time": "2018-09-29T00:04:16.313210Z", - "start_time": "2018-09-29T00:04:14.460647Z" - } - }, - "outputs": [], - "source": [ - "IBMQ.load_accounts()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Step 1: setting up the molecule\n", - "\n", - "We choose the basis set spanning the molecular wavefunction, the molecular geometry, the chemical identity of each atom, the charge and spin quantum number.\n", - "\n", - "To calculate results for LiH (slower), just comment out the H$_{2}$ string and replace it with the LiH one.\n", - "\n", - "NOTE: Here, we focus only on one particular value for the `bond_length`. If you wanted to replicate the final plot for the excited state energies of LiH as a function of bond length, you'd need to sweep `bond_length` over several values." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "ExecuteTime": { - "end_time": "2018-09-29T00:04:20.069592Z", - "start_time": "2018-09-29T00:04:20.065489Z" - } - }, - "outputs": [], - "source": [ - "# Choose a particular bond length\n", - "# NOTE: Units are in Angstroms\n", - "\n", - "bond_length = 0.7\n", - "\n", - "# Set up molecule\n", - "\n", - "# base_molecule_str = 'Li .0 .0 .0; H .0 .0 {}'\n", - "base_molecule_str = 'H .0 .0 .0; H .0 .0 {}'\n", - "\n", - "# Specify other molecular properties\n", - "charge = 0\n", - "spin = 0\n", - "basis = 'sto3g'" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Having set up the molecule, we now execute our classical chemistry driver to obtain the integrals that define the terms in the molecule's Hamiltonian. In this case, we choose `PYSCF` as our driver, so make sure you have that installed.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Molecular repulsion energy: 0.7559674441714287\n" - ] - } - ], - "source": [ - "# Using driver to get fermionic Hamiltonian\n", - "# PySCF example\n", - "\n", - "driver = PySCFDriver(atom=base_molecule_str.format(bond_length),\n", - " unit=UnitsType.ANGSTROM,\n", - " charge=charge,\n", - " spin=spin,\n", - " basis=basis)\n", - "\n", - "molecule = driver.run()\n", - "\n", - "print(\"Molecular repulsion energy: \", molecule.nuclear_repulsion_energy)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The molecular repulsion energy calculated by the driver corresponds to the coulombic repulsion between the nuclei in the molecule, and we can add it to our electron structure calculation at the end to get the total energy." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Step 2: Set up a variational form for VQE\n", - "\n", - "To run the VQE algorithm, we need to specify a mapping from the molecular Hamiltonian to qubits, an initial state, and the ansatz we use for the trial state. Here, we use the Jordan-Wigner transform to map the molecular Hamiltonian onto qubits (Pauli operators). We choose the initial state to be a Hartree-Fock state, and we take the variational ansatz to be the unitary coupled cluster with single and double excitations (UCCSD)." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Number of qubits: 4\n" - ] - } - ], - "source": [ - "n_qubits = molecule.one_body_integrals.shape[0]\n", - "n_electrons = molecule.num_alpha + molecule.num_beta - molecule.molecular_charge\n", - "\n", - "# get fermionic operator and mapping to qubit operator\n", - "ferOp = FermionicOperator(h1=molecule.one_body_integrals, h2=molecule.two_body_integrals)\n", - "\n", - "qubitOp = ferOp.mapping(map_type='JORDAN_WIGNER', threshold=0.00000001)\n", - "qubitOp.chop(10**-10)\n", - "\n", - "# Instantiate the initial state as a Hartree-Fock state\n", - "initial_hf = HartreeFock(num_qubits=n_qubits, num_orbitals=n_qubits, \n", - " qubit_mapping='jordan_wigner', two_qubit_reduction=False, num_particles= n_electrons)\n", - "\n", - "# Create the variational form\n", - "var_form = UCCSD(num_qubits=n_qubits, num_orbitals=n_qubits, \n", - " num_particles=n_electrons, depth=1, initial_state=initial_hf, qubit_mapping='jordan_wigner')\n", - "\n", - "# How many qubits do we need?\n", - "print('Number of qubits: {0}'.format(n_qubits))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Step 3: Transpile circuit and examine circuit properties" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "At this point, we have instantiated a variational form for the molecule according to the UCCSD formulation. Aqua's `UCCSD` method has returned back to us an abstraction of the VQE variational form. Let's query some of its properties." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(3, (-3.141592653589793, 3.141592653589793))" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Query the variational form for the number of parameters, and the parameter bounds.\n", - "var_form.num_parameters, var_form.parameter_bounds[0]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As a VQE circuit, `var_form` has some number of parameters, and each parameter can take values in $[-\\pi, \\pi]$.\n", - "These parameters control the angles of rotation in the quantum circuit that represents the variational anatz.\n", - "\n", - "For a particular set of parameters, there is an assocated quantum circuit. Let's input some fiducial parameter values and query properties of the resulting circuit to introduce some nomenclature for describing circuits." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "{'size': 150,\n", - " 'depth': 83,\n", - " 'width': 4,\n", - " 'bits': 0,\n", - " 'factors': 1,\n", - " 'operations': {'u3': 42, 'u2': 40, 'cx': 56, 'u1': 12}}" - ] - }, - "execution_count": 7, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Instantiate a concrete instance of the VQE ansatz by setting all the parameters to the\n", - "# arbitrarily-chosen value of 0.\n", - "var_circ = var_form.construct_circuit(np.zeros(var_form.num_parameters))\n", - "\n", - "# Use Terra to convert the circuit to its directed, acyclic graph (DAG) representation.\n", - "var_circ_dag = circuit_to_dag(var_circ)\n", - "\n", - "# The .properties() method of the DAG to get circuit properties.\n", - "var_circ_dag.properties()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "These circuit properties are:\n", - "\n", - "\n", - "* `size`: The total number of gates in the circuit\n", - "* `depth`: The total number of _layers_ in the circuit\n", - "* `width`: The number of qubits in the circuit\n", - "* `bits`: The number of classical bits in the circuit. (NOTE: Because the circuit prepares a VQE trial state, and does not have any measurements, `bits` will be 0.)\n", - "* `factors`: The number of tensor factors the circuit could be decomposed into (by looking at the number of weakly connected components of the DAG)\n", - "\n", - "The `.properties()` method of the DAG representation also breaks down the total number of gates (`size`) by the individual gates themselves. These are the $u1,u2,u3$ and CNOT gates described [here](https://qiskit.org/documentation/terra/summary_of_quantum_operations.html). You can verify that the total number of gates is in fact equal to `size`." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Step 4: Transpile the circuit using Terra and `t|ket〉`\n", - "\n", - "Having instantiated a VQE variational form and examined some of its properties, we'd like to optimize those properties so that the circuit could be run on a near-term device. Terra provides a framework (the [_transpiler_](https://qiskit.org/documentation/terra/overview.html#transpiler)) for manipulating circuits according to certain _passes_, and where the execution of the passes is orchestrated by a _PassManager_, which we can use to do this optimization. Importantly, _the transpiler manipulates the circuit to change circuit properties, without actually changing the input-output relationship the circuit defines_. That is, the transpiler takes a circuit and re-writes it, but doesn't change what the circuit actually does.\n", - "\n", - "CQC has written several passes for manipulating quantum circuits which are available via `pytket`. For an extensive discussion of the framework `t|ket〉` uses to manipulate circuits, see **[TODO: include link]**. Here, we'll demonstrate using Terra and `pytket` to optimize a randomly-chosen realization of the VQE variational form. Currently, passes in the transpiler require a backend in order to run. For simplicity, we start by using a simulator backend." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [], - "source": [ - "# Grab an Aer backend\n", - "aer_backend = Aer.get_backend('qasm_simulator')" - ] - }, - { - "cell_type": "code", - "execution_count": 36, - "metadata": {}, - "outputs": [], - "source": [ - "# Choose a random set of parameters\n", - "seed = 0\n", - "np.random.seed(seed)\n", - "params = np.random.uniform(low=-3.1, high=3.1, size=var_form.num_parameters)\n", - "\n", - "# Construct a random instance of the variational circuit\n", - "var_circuit = var_form.construct_circuit(params)\n", - "\n", - "# Turn the circuit into a DAG\n", - "var_dag = circuit_to_dag(var_circuit)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This randomly-chosen realization of the variational form has the same circuit properties as the circuit we instantiated in Step 3." - ] - }, - { - "cell_type": "code", - "execution_count": 37, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "{'size': 150,\n", - " 'depth': 83,\n", - " 'width': 4,\n", - " 'bits': 0,\n", - " 'factors': 1,\n", - " 'operations': {'u3': 42, 'u2': 40, 'cx': 56, 'u1': 12}}" - ] - }, - "execution_count": 37, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "var_dag.properties()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now, we set up a transpiler using Terra and the `TketPass` from `pytket`." - ] - }, - { - "cell_type": "code", - "execution_count": 38, - "metadata": {}, - "outputs": [], - "source": [ - "# Create a Terra PassManager object\n", - "tk_pass_manager = PassManager()\n", - "\n", - "# Set up the TketPass\n", - "tk_pass = TketPass(aer_backend)\n", - "\n", - "# Add the TketPass to the PassManager\n", - "tk_pass_manager.append(tk_pass)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "With the transpiler set up and the realization of the variational form put into a DAG, we can now use the `transpile_dag` function to run the PassManger." - ] - }, - { - "cell_type": "code", - "execution_count": 39, - "metadata": {}, - "outputs": [], - "source": [ - "var_dag_transpiled = transpile_dag(var_dag, pass_manager=tk_pass_manager)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's check the properties of this circuit to see how the transpiled circuit differs from the original one." - ] - }, - { - "cell_type": "code", - "execution_count": 40, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "{'size': 95,\n", - " 'depth': 57,\n", - " 'width': 4,\n", - " 'bits': 0,\n", - " 'factors': 1,\n", - " 'operations': {'u3': 30, 'cx': 52, 'u1': 12, 'u2': 1}}" - ] - }, - "execution_count": 40, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "var_dag_transpiled.properties()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The `t|ket〉` compiler has optimized the circuit, and as we might hope for, _the transpiled circuit has a lower `size` and `depth` than the original circuit._\n", - "\n", - "\n", - "The table below gives properties of the transpiled circuit for H$_{2}$ and LiH (with `seed=0`, corresponding to the worst-case and also most common performance of the transpiler).\n", - "\n", - "\n", - "| Molecule: H$_2$ | Total Gates | Depth | CNOT Count |\n", - "|--------------------------------------|-------------|---------------|--------------------|\n", - "| Input circuit | 150 | 83 | 56 |\n", - "| `tket` circuit optimization (Aer backend) | 95 | 57 | 52 |\n", - "\n", - "\n", - "| Molecule: LiH | Total Gates | Depth | CNOT Count |\n", - "|--------------------------------------|-------------|---------------|--------------------|\n", - "| Input circuit | 13700 | 9342 | 8064 |\n", - "| `tket` circuit optimization (Aer backend) | 7411 | 4416 | 5096 |\n", - "\n", - "For both H$_2$ and LiH, circuit optimization using `t|ket〉` reduces the number of gates necessary to prepare the trial state. The depth also decreases, which makes running the circuit more feasible on near-term devices." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Step 5: Route the circuit onto real hardware" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Even though we've optimized the circuit, there's no guarantee that it can run, as written, on a real backend. This is because the directionaly of the CNOT gates on the backend may not be respected by the circuit. For this reason, we need to re-write the circuit in such as way that the CNOT gates respect the _coupling map_ of the backend. `t|ket〉` knows how to do this, and handles this problem (called circuit \"routing\") when a real backend is put into the `TketPass` object. Routing refers to the process of making quantum circuits hardware compliant by the addition of SWAP gates such that all multi-qubit interactions occur on adjacent physical qubits.\n", - "\n", - "Because we know _a priori_ that the H$_{2}$ and LiH molecules requires at most 12 qubits, we make sure to use an IBMQ backend with no less than 12 qubits." - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "[,\n", - " ]" - ] - }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Grab only backends that have at least 12 qubits\n", - "IBMQ.backends(filters=lambda x: x.configuration().n_qubits >= 12)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We'll use the `ibmq_16_melbourne` backend." - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [], - "source": [ - "real_backend = IBMQ.get_backend('ibmq_16_melbourne')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "To route the variational circuit onto real hardware, we simply need to change the backend." - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": {}, - "outputs": [], - "source": [ - "# Create a Terra PassManager object\n", - "tk_pass_manager = PassManager()\n", - "\n", - "# Set up the TketPass\n", - "tk_pass = TketPass(real_backend)\n", - "\n", - "# Add the TketPass to the PassManager\n", - "tk_pass_manager.append(tk_pass)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Again, we can transpile the DAG representation of the variational circuit to a backend-compliant circuit using the `tranpsile_dag` function. Here, because the backend has a non-trivial coupling map, the `TketPass` will perform both circuit optimization and optimal routing calculations. We need to add a register containing the ancilla qubits on the architecture that `TketPass` can use in routing." - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": {}, - "outputs": [], - "source": [ - "blank_qubits = QuantumRegister(len(real_backend.properties().qubits) - var_dag.width())\n", - "var_dag.add_qreg(blank_qubits)\n", - "var_dag_transpiled = transpile_dag(var_dag, pass_manager=tk_pass_manager)" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "{'size': 108,\n", - " 'depth': 69,\n", - " 'width': 4,\n", - " 'bits': 0,\n", - " 'factors': 1,\n", - " 'operations': {'u3': 30, 'cx': 52, 'u1': 12, 'u2': 14}}" - ] - }, - "execution_count": 18, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "var_dag_transpiled.properties()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can compare these results to Qiskit's own default transpilation by passing in the backend's `coupling_map` to the `transpile_dag` function." - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "{'size': 119,\n", - " 'depth': 89,\n", - " 'width': 14,\n", - " 'bits': 0,\n", - " 'factors': 11,\n", - " 'operations': {'u3': 15, 'cx': 56, 'u1': 14, 'u2': 34}}" - ] - }, - "execution_count": 19, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "transpile_dag(var_dag, coupling_map=real_backend.configuration().coupling_map).properties()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The table below shows circuit properties for H$_{2}$ (with `seed=0`).\n", - "\n", - "| Molecule: H$_2$ | Total Gates | Overall Depth | Overall CNOT Count |\n", - "|--------------------------------------|-------------|---------------|--------------------|\n", - "| Input circuit | 150 | 83 | 56 |\n", - "| `tket` circuit optimization (Aer backend) | 95 | 57 | 52 |\n", - "| `Qiskit ` default routing (real backend) | 119 | 89 | 56 |\n", - "| `tket` circuit optimzation + routing (real backend) | 108 | 69 | 52 |\n", - "\n", - "The table below shows circuit properties for LiH (with `seed=0`).\n", - "\n", - "| Molecule: LiH | Total Gates | Overall Depth | Overall CNOT Count |\n", - "|--------------------------------------|-------------|---------------|--------------------|\n", - "| Input circuit | 13700 | 9342 | 8064 |\n", - "| `tket` circuit optimization (Aer backend) | 7411 | 4416 | 5096 |\n", - "| `Qiskit ` default routing (real backend) | 42178 | 23367 | 17977 |\n", - "| `tket` circuit optimzation + routing (real backend) | 19256 | 10022 | 8711 |" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Application II: using QSE to compute excited state energies" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The previous application showed us how to use `t|ket〉` and Terra to optimally route circuits onto real hardware. In the introduction, we observed that in order to use the quantum subspace expansion to compute excited state energies, we need to first come up with an estimate of the ground state. For this, we use VQE.\n", - "\n", - "In this application, we'll instantiate a VQE circuit, run it, and use the estimated ground state as input to `pytket`'s quantum subspace expansion function(s). NOTE: We'll use a simulator backend, and will not run the VQE algorithm on real hardware." - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "metadata": {}, - "outputs": [], - "source": [ - "# Code imports\n", - "\n", - "# From Aqua, we need \n", - "from qiskit_aqua import QuantumInstance\n", - "\n", - "from qiskit_aqua.algorithms.adaptive import VQE\n", - "from qiskit_aqua.components.optimizers import L_BFGS_B\n", - "\n", - "# From pytket, we need QSE functions\n", - "\n", - "from pytket.chemistry import QseMatrices, QSE" - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "metadata": {}, - "outputs": [], - "source": [ - "backend = Aer.get_backend('statevector_simulator')" - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "metadata": {}, - "outputs": [], - "source": [ - "pass_manager = PassManager()\n", - "tk_pass = TketPass(backend)\n", - "pass_manager.append(tk_pass)\n", - "\n", - "quantum_instance = QuantumInstance(backend, pass_manager=pass_manager)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Step 1: Use VQE to estimate ground state\n", - "\n", - "First, we'll use VQE to estimate the ground state and its energy." - ] - }, - { - "cell_type": "code", - "execution_count": 32, - "metadata": {}, - "outputs": [], - "source": [ - "# Temporary code for Aer on Macbook\n", - "import os\n", - "os.environ['KMP_DUPLICATE_LIB_OK']='True'" - ] - }, - { - "cell_type": "code", - "execution_count": 33, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "GS Minimum value: -1.1361894540653963\n", - "GS Parameters: [ 5.06008657e-07 5.12457730e-07 -1.04867316e-01]\n" - ] - } - ], - "source": [ - "# Set initial values of parameters\n", - "number_amplitudes = len(var_form._single_excitations)+ len(var_form._double_excitations)\n", - "\n", - "amplitudes_0 = []\n", - "for i in range(number_amplitudes):\n", - " amplitudes_0.append(0.00001)\n", - "\n", - "optimizer = L_BFGS_B()\n", - "optimizer.set_options(maxfun=1000, factr=10, iprint=10)\n", - "\n", - "# setup VQE with operator, variation form, and optimzer\n", - "vqe_algorithm = VQE(operator=qubitOp, operator_mode='matrix', \n", - " var_form=var_form, optimizer=optimizer, initial_point=amplitudes_0)\n", - "\n", - "results = vqe_algorithm.run(quantum_instance)\n", - "\n", - "eigval = results['eigvals'][0]\n", - "gs_energy = eigval.real + molecule.nuclear_repulsion_energy\n", - "\n", - "print(\"GS Minimum value: {}\".format(gs_energy))\n", - "print(\"GS Parameters: {}\".format(results['opt_params']))\n", - "\n", - "# store ground state amplitudes for subsequent steps\n", - "opti_amplitudes = results['opt_params']" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Step 2: Use QSE to find excited states from ground state \n", - "\n", - "We now have the main ingredients to perform a QSE calculation: the molecular Hamiltonian and the optimized parameters to reconstruct the ground state wavefunction. We build our excitation hamiltonian and overlap operators, and measure the elements that compose $H$ and $S$. After we have obtained these arrays, we perform a diagonalization to obtain the excited state energies and vectors.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Excited State Energies: [-1.13618945 -0.47845306 -0.47845306 -0.47845306 -0.1204519 0.5833141\n", - " 0.75596744 0.75596744 0.75596744 0.75596744 0.75596744 0.75596744\n", - " 0.75596744 0.75596744 0.75596744 0.75596744]\n" - ] - } - ], - "source": [ - "qubitOp = ferOp.mapping(map_type='JORDAN_WIGNER', threshold=0.00000001)\n", - "n_qubits = qubitOp.num_qubits\n", - "qubitOp.chop(10**-10)\n", - "\n", - "# Use matrix term helper class\n", - "matrix_terms = QseMatrices(qubitOp, n_qubits)\n", - "\n", - "# Instantiate an instance of the QSE algorithm\n", - "qse_algorithm = QSE(matrix_terms, 'matrix', var_form, opt_init_point=opti_amplitudes)\n", - "\n", - "# Run the algorithm\n", - "energies = qse_algorithm.run(quantum_instance)['eigvals']\n", - "\n", - "# The excited state energies are the energies from above,\n", - "# plus the nuclear repulsion energy.\n", - "print(\"Excited State Energies: \", energies+molecule.nuclear_repulsion_energy)\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The calculation provides a refined value of the ground state and a series of excited state energies, whose number depends on the size of the basis set chosen for the molecule, as well as its nature and symmetry. Some of the energies obtained are repeated several times, signaling that some of the states obtained are degenerate. This result can be improved by either increasing the basis set or considering higher-order excitations in the subspace expansion.\n", - "\n", - "The following graph shows us the excited states of LiH at a range of bond distances calculated via our method, compared to values computed using the classical [EOM-CCSD method](https://aip.scitation.org/doi/10.1063/1.464746). To generate this data yourself, you can scan the bond length parameter we set at the start of the calculation.\n", - "\n", - "![alt text](LiH.png \"Title\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Using the QSE technique, and our simulated VQE ground state, we find the ground state curve has a minimum at a separation of about 1.5 Å, which is in reasonable agreement with experimental data. The calculation also finds a number of excited states. Looking at the first three of these, we find that at the equilibrium distance, these states are 0.11, 0.12 and 0.17 Ha higher in energy than the ground state, which is again in reasonable agreement with experimental data. Note the small kink in one of the excited states energy curve at a distance of approximately 1.2 Å. This indicates that our restriction to single electron excitations is not enough to provide an accurate description at this distance. Overall, the comparison with classically computed EOM-CCSD curves shows that this method reproduces excited state energies with good accuracy at most distances." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "anaconda-cloud": {}, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.3" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/chemistry/QubitMappings.ipynb b/community/chemistry/QubitMappings.ipynb deleted file mode 100644 index 70b1d7878..000000000 --- a/community/chemistry/QubitMappings.ipynb +++ /dev/null @@ -1,238 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## _*FermionicOperator and qubit mapping*_\n", - "\n", - "When we compute a FermionicOperator in Qiskit Chemistry it needs to be converted to a qubit operator to run on the simulator or real device. The FermionicOperator is built from electronn integrals where electrons behave anti-symmetrically under swap. qubits however do not exhibit this behavior and hence a mapping is needed to ensure that this is accounted for.\n", - "\n", - "Here we have the jordan wigner mapping, the bravyi-kitaev mapping and a parity.\n", - "\n", - "This notebook has been written to use the PYQUANTE chemistry driver. See the PYQUANTE chemistry driver readme if you need to install the external PyQuante2 library that this driver requires." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "\n", - "from qiskit import BasicAer\n", - "from qiskit.transpiler import PassManager\n", - "\n", - "from qiskit.aqua import Operator, QuantumInstance, aqua_globals\n", - "from qiskit.aqua.algorithms.adaptive import VQE\n", - "from qiskit.aqua.algorithms.classical import ExactEigensolver\n", - "from qiskit.aqua.components.optimizers import L_BFGS_B\n", - "from qiskit.aqua.components.variational_forms import RY\n", - "\n", - "from qiskit.chemistry import FermionicOperator\n", - "from qiskit.chemistry.drivers import PyQuanteDriver, UnitsType, BasisType\n", - "\n", - "aqua_globals.random_seed = 50" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [], - "source": [ - "# using driver to get fermionic Hamiltonian\n", - "# PyQuante example\n", - "driver = PyQuanteDriver(atoms='H .0 .0 .0; H .0 .0 0.735', units=UnitsType.ANGSTROM,\n", - " charge=0, multiplicity=1, basis=BasisType.BSTO3G)\n", - "molecule = driver.run()\n", - "h1 = molecule.one_body_integrals\n", - "h2 = molecule.two_body_integrals" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [], - "source": [ - "# convert from fermionic hamiltonian to qubit hamiltonian\n", - "ferOp = FermionicOperator(h1=h1, h2=h2)\n", - "qubitOp_jw = ferOp.mapping(map_type='JORDAN_WIGNER', threshold=0.00000001)\n", - "qubitOp_pa = ferOp.mapping(map_type='PARITY', threshold=0.00000001)\n", - "qubitOp_bk = ferOp.mapping(map_type='BRAVYI_KITAEV', threshold=0.00000001)" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - " --- jordan wigner ---\n", - "IIII\t(-0.8105479862760991+0j)\n", - "IIIZ\t(0.17218394273085635+0j)\n", - "IIZI\t(-0.22575350251540605+0j)\n", - "IIZZ\t(0.12091263358559995+0j)\n", - "IZII\t(0.17218394273085635+0j)\n", - "IZIZ\t(0.16892754048859007+0j)\n", - "IZZI\t(0.16614543338049342+0j)\n", - "IZZZ\t(-8.326672684688674e-17+0j)\n", - "XXXX\t(0.045232799794893426+0j)\n", - "XXYY\t(0.045232799794893426+0j)\n", - "YYXX\t(0.045232799794893426+0j)\n", - "YYYY\t(0.045232799794893426+0j)\n", - "ZIII\t(-0.2257535025154061+0j)\n", - "ZIIZ\t(0.16614543338049342+0j)\n", - "ZIZI\t(0.17464343142442207+0j)\n", - "ZZII\t(0.12091263358559991+0j)\n", - "ZZIZ\t(-2.42861286636753e-17+0j)\n", - "ZZZI\t(-6.938893903907228e-17+0j)\n", - "ZZZZ\t(-3.122502256758253e-17+0j)\n", - "\n", - "The exact ground state energy using jordan wigner mapping is: -1.8572750766378716\n", - "\n", - " --- parity ---\n", - "IIII\t(-0.8105479862760991+0j)\n", - "IIIZ\t(0.17218394273085635+0j)\n", - "IIZI\t(0.1209126335855999+0j)\n", - "IIZZ\t(-0.2257535025154061+0j)\n", - "IXIX\t(0.045232799794893426+0j)\n", - "IXZX\t(-0.045232799794893426+0j)\n", - "IZII\t(-6.938893903907228e-17+0j)\n", - "IZIZ\t(0.16614543338049345+0j)\n", - "IZZI\t(0.17218394273085635+0j)\n", - "IZZZ\t(0.16892754048859007+0j)\n", - "ZIII\t(-3.469446951953614e-17+0j)\n", - "ZIIZ\t(-6.245004513516506e-17+0j)\n", - "ZIZI\t(0.1209126335855999+0j)\n", - "ZIZZ\t(-2.0816681711721685e-17+0j)\n", - "ZXIX\t(0.045232799794893426+0j)\n", - "ZXZX\t(-0.045232799794893426+0j)\n", - "ZZII\t(-0.2257535025154061+0j)\n", - "ZZIZ\t(0.16614543338049342+0j)\n", - "ZZZZ\t(0.17464343142442207+0j)\n", - "\n", - "The exact ground state energy using parity mapping is: -1.8572750766378738\n", - "\n", - " --- bravyi-kitaev ---\n", - "IIII\t(-0.8105479862760991+0j)\n", - "IIIZ\t(0.17218394273085635+0j)\n", - "IIZI\t(0.1209126335855999+0j)\n", - "IIZZ\t(-0.2257535025154061+0j)\n", - "IXIX\t(0.045232799794893426+0j)\n", - "IXZX\t(-0.045232799794893426+0j)\n", - "IZII\t(0.17218394273085635+0j)\n", - "IZIZ\t(0.16892754048859007+0j)\n", - "IZZI\t(-6.938893903907228e-17+0j)\n", - "IZZZ\t(0.16614543338049345+0j)\n", - "ZIII\t(-3.469446951953614e-17+0j)\n", - "ZIIZ\t(-6.245004513516506e-17+0j)\n", - "ZIZI\t(0.1209126335855999+0j)\n", - "ZIZZ\t(-2.0816681711721685e-17+0j)\n", - "ZXIX\t(0.045232799794893426+0j)\n", - "ZXZX\t(-0.045232799794893426+0j)\n", - "ZZIZ\t(0.17464343142442207+0j)\n", - "ZZZI\t(-0.2257535025154061+0j)\n", - "ZZZZ\t(0.16614543338049342+0j)\n", - "\n", - "The exact ground state energy using bravyi-kitaev mapping is: -1.8572750766378796\n" - ] - } - ], - "source": [ - "# print out qubit hamiltonian in Pauli terms and exact solution\n", - "qubit_ops = [(qubitOp_jw, 'jordan wigner'),\n", - " (qubitOp_pa, 'parity'),\n", - " (qubitOp_bk, 'bravyi-kitaev')]\n", - "\n", - "for qubit_op, name in qubit_ops:\n", - " qubit_op.to_matrix()\n", - " qubit_op.chop(10**-10)\n", - "\n", - " print(\"\\n --- {} ---\".format(name))\n", - " print(qubit_op.print_operators())\n", - "\n", - " # Using exact eigensolver to get the smallest eigenvalue\n", - " exact_eigensolver = ExactEigensolver(qubit_op, k=1)\n", - " ret = exact_eigensolver.run()\n", - " print('The exact ground state energy using {} mapping is: {}'.format(name, ret['energy'])) " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we run on quantum backend, in this case a simulator" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Ground state energy using jordan wigner: -1.8570893208672647\n", - "Ground state energy using parity: -1.8572686760592785\n", - "Ground state energy using bravyi-kitaev: -1.85727507635405\n" - ] - } - ], - "source": [ - "for qubit_op, name in qubit_ops:\n", - " # setup VQE \n", - " # setup optimizer, use L_BFGS_B optimizer for example\n", - " lbfgs = L_BFGS_B(maxfun=1000, factr=10, iprint=10)\n", - "\n", - " # setup variational form generator (generate trial circuits for VQE)\n", - " var_form = RY(qubit_op.num_qubits, 5, entanglement='full')\n", - "\n", - " # setup VQE with operator, variational form, and optimizer\n", - " vqe_algorithm = VQE(qubit_op, var_form, lbfgs, 'matrix')\n", - "\n", - " backend = BasicAer.get_backend('statevector_simulator')\n", - " quantum_instance = QuantumInstance(backend, pass_manager=PassManager())\n", - "\n", - " results = vqe_algorithm.run(quantum_instance)\n", - "\n", - " print(\"Ground state energy using {}: {}\".format(name, results['eigvals'][0]))" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/chemistry/README.md b/community/chemistry/README.md deleted file mode 100644 index 7b5c4d6b6..000000000 --- a/community/chemistry/README.md +++ /dev/null @@ -1,18 +0,0 @@ -# Qiskit Chemistry Tutorials, Samples and Input Files - -This folder contains some Jupyter Notebook examples showing how to run chemistry experiments using in -Qiskit Chemistry. There are also Python code files too as well as some hdf5 files containing saved -molecular data that may be used in experiments. - -These example programs and notebooks show how to use the dictionary equivalent form of -the [input file](#input-files) that can be used more effectively programmatically when your goal is to -run the content with a range of different values. For example the [energyplot](energyplot.ipynb) notebook -alters the interatomic distance of a molecule, over a range of values, and uses the results to plot graphs. - -For more detail see the main [index](../index.ipynb#chemistry) - -## Input files - -The folder [input_files](input_files) contains a number of example input files that can be loaded -and run by the Qiskit Chemistry [GUI](https://github.com/Qiskit/qiskit-chemistry/blob/master/README.md#gui) or by the -[command line](https://github.com/Qiskit/qiskit-chemistry/blob/master/README.md#command-line) tool. diff --git a/community/chemistry/beh2_reductions.ipynb b/community/chemistry/beh2_reductions.ipynb deleted file mode 100644 index 9d383850a..000000000 --- a/community/chemistry/beh2_reductions.ipynb +++ /dev/null @@ -1,397 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## _*BeH2 plots of various orbital reduction results*_\n", - "\n", - "We have notebooks showing LiH, where we often remove (discard) two unoccupied orbitals, in addition to freezing the core. While freezing of the core electrons can always be done, discarding unoccupied orbitals should be done with great care.\n", - "\n", - "This notebook demonstrates this for Beryllium Dihydride (BeH2) where we show the effect of removing different unoccupied orbitals. We use Qiskit Chemistry to plot graphs of the ground state energy of the Beryllium Dihydride (BeH2) molecule over a range of inter-atomic distances using ExactEigensolver. Freeze core reduction is true and different virtual orbital removals are tried as a comparison.\n", - "\n", - "This notebook populates a dictionary, that is a progammatic representation of an input file, in order to drive the Qiskit Chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here where we alter the molecule supplied to the driver in each loop as well as the orbital reductions.\n", - "\n", - "This notebook has been written to use the PYSCF chemistry driver." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Processing step 22 --- complete\n", - "Distances: [0.6 0.7 0.8 0.9 1. 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9\n", - " 2. 2.25 2.5 2.75 3. 3.25 3.5 3.75 4. ]\n", - "Energies: [[-14.40506494 -14.87097555 -15.17246656 -15.36382343 -15.48142306\n", - " -15.54931874 -15.58348421 -15.59471016 -15.59040023 -15.57570561\n", - " -15.55427855 -15.52877867 -15.50120585 -15.47311573 -15.44576103\n", - " -15.38711226 -15.35149108 -15.33892161 -15.33645938 -15.33627749\n", - " -15.3363915 -15.33646725 -15.33649467]\n", - " [-14.38537971 -14.8529641 -15.15532997 -15.34648965 -15.46287098\n", - " -15.52863269 -15.5598192 -15.56723345 -15.55823699 -15.53789746\n", - " -15.50975433 -15.476334 -15.43948849 -15.40061366 -15.38534487\n", - " -15.30406975 -15.24876708 -15.23982192 -15.25303723 -15.27323362\n", - " -15.29048022 -15.29973676 -15.30358774]\n", - " [-14.38085785 -14.8496625 -15.152928 -15.34484824 -15.46196656\n", - " -15.52847583 -15.56042602 -15.5686254 -15.5604457 -15.54096661\n", - " -15.51373779 -15.48129162 -15.44548034 -15.4076929 -15.43902234\n", - " -15.3765858 -15.33291996 -15.31217227 -15.30666589 -15.30583829\n", - " -15.30584735 -15.3059168 -15.30595 ]\n", - " [-14.38996835 -14.8596731 -15.16341905 -15.35613956 -15.47463297\n", - " -15.54315397 -15.57776757 -15.5893081 -15.58520037 -15.57060331\n", - " -15.54916622 -15.52353471 -15.49568133 -15.46711643 -15.36899435\n", - " -15.27329325 -15.18543733 -15.10983622 -15.04887848 -15.00693603\n", - " -14.98538738 -14.97555545 -14.97045281]\n", - " [-14.39432437 -14.86110116 -15.16286759 -15.3537537 -15.47017403\n", - " -15.53627247 -15.56808784 -15.57642757 -15.5686708 -15.54991949\n", - " -15.52376812 -15.49282421 -15.45905583 -15.42402529 -15.38905694\n", - " -15.31000383 -15.2593924 -15.25594154 -15.26939038 -15.28973515\n", - " -15.30706596 -15.31636055 -15.32022639]\n", - " [-14.38815095 -14.85518765 -15.15741167 -15.34871007 -15.46542593\n", - " -15.53165667 -15.56340888 -15.57146946 -15.5631985 -15.54366894\n", - " -15.51642669 -15.48400243 -15.44824819 -15.41055403 -15.44242866\n", - " -15.38184785 -15.34232036 -15.32636956 -15.32282134 -15.32241852\n", - " -15.32249786 -15.32257244 -15.32260238]\n", - " [-14.39782704 -14.8655071 -15.16806701 -15.36007661 -15.47810675\n", - " -15.54630491 -15.58068771 -15.59206637 -15.58785438 -15.57320634\n", - " -15.55177264 -15.52620548 -15.49849044 -15.47015952 -15.44242866\n", - " -15.38184785 -15.34232036 -15.32636956 -15.32282134 -15.32241852\n", - " -15.32249786 -15.32257244 -15.32260238]\n", - " [-14.39782704 -14.8655071 -15.16806701 -15.36007661 -15.47810675\n", - " -15.54630491 -15.58068771 -15.59206637 -15.58785438 -15.57320634\n", - " -15.55177264 -15.52620548 -15.49849044 -15.47015952 -15.37198719\n", - " -15.27680792 -15.18982171 -15.11557267 -15.0565821 -15.01697352\n", - " -14.99729008 -14.98854807 -14.98398255]]\n" - ] - } - ], - "source": [ - "import numpy as np\n", - "import pylab\n", - "from qiskit.chemistry import QiskitChemistry\n", - "\n", - "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", - "qiskit_chemistry_dict = {\n", - " 'driver': {'name': 'PYSCF'},\n", - " 'PYSCF': {'atom': '', 'basis': 'sto3g'},\n", - " 'operator': {'name': 'hamiltonian', 'qubit_mapping': 'parity',\n", - " 'two_qubit_reduction': True, 'freeze_core': True, 'orbital_reduction': []},\n", - " 'algorithm': {'name': 'ExactEigensolver'}\n", - "}\n", - "molecule = 'H .0 .0 -{0}; Be .0 .0 .0; H .0 .0 {0}'\n", - "reductions = [[], [-2, -1], [-3, -2], [-4, -3], [-1], [-2], [-3], [-4]]\n", - "\n", - "pts = [x * 0.1 for x in range(6, 20)]\n", - "pts += [x * 0.25 for x in range(8, 16)]\n", - "pts += [4.0]\n", - "energies = np.empty([len(reductions), len(pts)])\n", - "distances = np.empty(len(pts))\n", - "\n", - "print('Processing step __', end='')\n", - "for i, d in enumerate(pts):\n", - " print('\\b\\b{:2d}'.format(i), end='', flush=True)\n", - " qiskit_chemistry_dict['PYSCF']['atom'] = molecule.format(d) \n", - " for j in range(len(reductions)):\n", - " qiskit_chemistry_dict['operator']['orbital_reduction'] = reductions[j] \n", - " solver = QiskitChemistry()\n", - " result = solver.run(qiskit_chemistry_dict)\n", - " energies[j][i] = result['energy']\n", - " distances[i] = d\n", - "print(' --- complete')\n", - "\n", - "print('Distances: ', distances)\n", - "print('Energies:', energies)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "First we plot the ground state energy against interatomic distance for the set of reductions" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": { - "scrolled": false - }, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.rcParams['figure.figsize'] = (12, 8)\n", - "for j in range(len(reductions)):\n", - " pylab.plot(distances, energies[j], label=reductions[j])\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Energy')\n", - "pylab.title('BeH2 Ground State Energy')\n", - "pylab.legend(loc='upper right');" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now the difference in energy, compared to no reduction, is plotted so it is easier to see the effect. First in one larger plot so its easier to compare, and then in individual plots." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": { - "scrolled": false - }, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.rcParams['figure.figsize'] = (12, 8)\n", - "for j in range(len(reductions)):\n", - " pylab.plot(distances, np.subtract(energies[j], energies[0]), label=reductions[j])\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Energy')\n", - "pylab.title('Energy difference compared to no reduction []')\n", - "pylab.legend(loc='upper left');" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "data": { - "image/png": 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\n", 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\n", 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.rcParams['figure.figsize'] = (6, 4)\n", - "for j in range(1, len(reductions)):\n", - " pylab.plot(distances, np.subtract(energies[j], energies[0]), color=[1.0, 0.6, 0.2],\n", - " label=reductions[j])\n", - " pylab.ylim(0, 0.4)\n", - " pylab.xlabel('Interatomic distance')\n", - " pylab.ylabel('Energy')\n", - " pylab.title('Energy difference compared to no reduction []')\n", - " pylab.legend(loc='upper left')\n", - " pylab.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Frozen core\n", - "\n", - "At the start it was stated that freeze core could always be done. Here we do the computation without freezing the core, with no virtual orbitals removed, so we can compare to the same above where frozen core was used." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "22[-14.40564902 -14.87132975 -15.17280541 -15.36415094 -15.48174107\n", - " -15.54963817 -15.58381205 -15.59504708 -15.59074335 -15.57605125\n", - " -15.55462369 -15.52912134 -15.50154509 -15.47345142 -15.44609374\n", - " -15.38744402 -15.35183431 -15.33927179 -15.33680424 -15.33661362\n", - " -15.33672146 -15.33679474 -15.33682151]\n" - ] - } - ], - "source": [ - "e_nofreeze = np.empty(len(pts))\n", - "qiskit_chemistry_dict['operator']['orbital_reduction'] = [] \n", - "qiskit_chemistry_dict['operator']['freeze_core'] = False \n", - "for i, d in enumerate(pts):\n", - " print('\\b\\b{:2d}'.format(i), end='', flush=True)\n", - " qiskit_chemistry_dict['PYSCF']['atom'] = molecule.format(d) \n", - " solver = QiskitChemistry()\n", - " result = solver.run(qiskit_chemistry_dict)\n", - " e_nofreeze[i] = result['energy']\n", - "\n", - "print(e_nofreeze)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We plot the energy with and without frozen core; the one line covers the other as they are almost identical. Plotting the energy difference we can see how small the delta is between freezing the core or not." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": { - "scrolled": false - }, - "outputs": [ - { - "data": { - "image/png": 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\n", 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.rcParams['figure.figsize'] = (8, 6)\n", - "pylab.plot(distances, energies[0], label='Freeze Core: True')\n", - "pylab.plot(distances, e_nofreeze, label='Freeze Core: False')\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Energy')\n", - "pylab.title('Energy difference, no reduction [], freeze core true/false')\n", - "pylab.legend(loc='upper right')\n", - "pylab.show()\n", - "pylab.title('Energy difference of freeze core True from False')\n", - "pylab.plot(distances, np.subtract(energies[0], e_nofreeze), label='Freeze Core: False')\n", - "pylab.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true, - "scrolled": true - }, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/chemistry/dictinput.py b/community/chemistry/dictinput.py deleted file mode 100644 index f3f84bc5e..000000000 --- a/community/chemistry/dictinput.py +++ /dev/null @@ -1,40 +0,0 @@ -# -*- coding: utf-8 -*- - -# Copyright 2018 IBM. -# -# Licensed under the Apache License, Version 2.0 (the "License"); -# you may not use this file except in compliance with the License. -# You may obtain a copy of the License at -# -# http://www.apache.org/licenses/LICENSE-2.0 -# -# Unless required by applicable law or agreed to in writing, software -# distributed under the License is distributed on an "AS IS" BASIS, -# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -# See the License for the specific language governing permissions and -# limitations under the License. -# ============================================================================= - -import qiskit.chemistry - -# An example of using a loop to vary inter-atomic distance. A dictionary is -# created outside the loop, but inside the loop the 'atom' value is updated -# with a new molecular configuration. The molecule is H2 and its inter-atomic distance -# i.e the distance between the two atoms, is altered from 0.5 to 1.0. Each atom is -# specified by x, y, z coords and the atoms are set on the z-axis, equidistant from -# the origin, and updated by d inside the loop where the molecule string has this value -# substituted by format(). Note the negative sign preceding the first format -# substitution point i.e. the {} brackets -# -input_dict = { - 'driver': {'name': 'PYSCF'}, - 'PYSCF': {'atom': None, 'unit': 'Angstrom', 'charge': 0, 'spin': 0, 'basis': 'sto3g'}, - 'algorithm': {'name': 'ExactEigensolver'}, -} -molecule = 'H .0 .0 -{0}; H .0 .0 {0}' -for i in range(21): - d = (0.5 + i * 0.5 / 20) / 2 - input_dict['PYSCF']['atom'] = molecule.format(d) - solver = qiskit.chemistry.QiskitChemistry() - result = solver.run(input_dict) - print('{:.4f} : {}'.format(d * 2, result['energy'])) diff --git a/community/chemistry/energyplot.ipynb b/community/chemistry/energyplot.ipynb deleted file mode 100644 index 60a1eaa56..000000000 --- a/community/chemistry/energyplot.ipynb +++ /dev/null @@ -1,159 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": { - "collapsed": true - }, - "source": [ - "## _*LiH plot using ExactEigensolver*_\n", - "\n", - "This notebook demonstrates using Qiskit Chemistry to plot graphs of the ground state energy and dipole moments of a Lithium Hydride (LiH) molecule over a range of inter-atomic distances.\n", - "\n", - "This notebook populates a dictionary, which is a progammatic representation of an input file, in order to drive the Qiskit Chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here where we alter the molecule supplied to the driver in each loop. The main goal of this notebook is to show this technique and to keep things simpler and quicker a classical algorithm, the ExactEigensolver, is used here.\n", - " \n", - "This notebook has been written to use the PYSCF chemistry driver. " - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Processing step 20 --- complete\n", - "Distances: [1.25 1.275 1.3 1.325 1.35 1.375 1.4 1.425 1.45 1.475 1.5 1.525\n", - " 1.55 1.575 1.6 1.625 1.65 1.675 1.7 1.725 1.75 ]\n", - "Energies: [-7.86021175 -7.86413664 -7.86756329 -7.87052961 -7.87307044 -7.87521786\n", - " -7.87700149 -7.87844868 -7.87958474 -7.88043316 -7.88101572 -7.88135266\n", - " -7.88146285 -7.88136385 -7.88107204 -7.88060273 -7.8799702 -7.87918784\n", - " -7.87826817 -7.87722291 -7.87606307]\n", - "Dipole moments: [1.85348096 1.85204573 1.85067375 1.84935828 1.84809268 1.84687002\n", - " 1.84568265 1.84452191 1.84337791 1.84223932 1.84109328 1.83992524\n", - " 1.83871893 1.8374563 1.83611747 1.83468076 1.83312267 1.83141785\n", - " 1.82953923 1.82745794 1.82514338]\n" - ] - } - ], - "source": [ - "import numpy as np\n", - "import pylab\n", - "from qiskit.chemistry import QiskitChemistry\n", - "\n", - "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", - "# Note: In order to allow this to run reasonably quickly it takes advantage\n", - "# of the ability to freeze core orbitals and remove unoccupied virtual\n", - "# orbitals to reduce the size of the problem. Freeze core can always\n", - "# be used, but be very cautious when removing unoccupied orbitals.\n", - "# \n", - "qiskit_chemistry_dict = {\n", - " 'driver': {'name': 'PYSCF'},\n", - " 'PYSCF': {'atom': '', 'basis': 'sto3g'},\n", - " 'algorithm': {'name': 'ExactEigensolver'},\n", - " 'operator': {'name': 'hamiltonian', 'freeze_core': True, 'orbital_reduction': [-3, -2]},\n", - "}\n", - "molecule = 'Li .0 .0 -{0}; H .0 .0 {0}'\n", - "\n", - "start = 1.25 # Start distance\n", - "by = 0.5 # How much to increase distance by\n", - "steps = 20 # Number of steps to increase by\n", - "energies = np.empty(steps+1)\n", - "distances = np.empty(steps+1)\n", - "dipoles = np.empty(steps+1)\n", - "\n", - "print('Processing step __', end='')\n", - "for i in range(steps+1):\n", - " print('\\b\\b{:2d}'.format(i), end='', flush=True)\n", - " d = start + i*by/steps\n", - " qiskit_chemistry_dict['PYSCF']['atom'] = molecule.format(d/2) \n", - " solver = QiskitChemistry()\n", - " result = solver.run(qiskit_chemistry_dict)\n", - " distances[i] = d\n", - " energies[i] = result['energy']\n", - " dipoles[i] = result['total_dipole_moment']\n", - "print(' --- complete')\n", - "\n", - "print('Distances: ', distances)\n", - "print('Energies:', energies)\n", - "print('Dipole moments:', dipoles)" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.plot(distances, energies)\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Energy')\n", - "pylab.title('LiH Ground State Energy');" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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0kWIr9M52MxtqZuvNbE4268ua2Wgzm2lmc82s70Hr081slZkNilo23szmm9mM4FUlXvVL/qpUJpW/nNOML2/vypnNj2LIxCV0+uc4nhu3iB17ssIuT0RyEM8+kmFA9xzW9wd+cPcWQFfgCTOL/vXzQWDiIfbr7e4tg9f6vCpWCoajK5TiyZ4t+eSWTrStW4HHxsyny2PjeX3qcg0KKVJAxS1I3H0isCmnTYA0MzOgTLBtFoCZtQKqAp/Fqz4p2BpXS+flK1rz7+sitwzfO2oOpz45gQ9nrmH//qJ/OVakMAnzrq1BQBNgDTAbuMXd95tZAvAEcEc2+70aXNa6LwihQzKza8ws08wyN2zYkOfFS/5oXSdyy/DQPhmUTE7k5pHfc/agr5iwYIOeQREpIMIMkm7ADKA60BIYZGbpwA3Ax+6+6hD79Hb35kCn4HVZdgd39yHunuHuGZUrV8776iXfmBknN67KRzd34qmeLdi8cy9XDJ1Gr5em8p1GGRYJXZhB0hd4zyMWAUuBxkB74EYzWwY8DlxuZo8AuPvq4M+twJtAmzAKl3AkJhjnHV+TL2/vyl/Pacai9ds4//nJXDM8k4XrtoZdnkixFWaQrABOATCzqsAxwBJ37+3utdy9DpHLW8Pd/U9mlmRmlYLtk4GzgEPeESZFW0pSAlecWIcJd57Ebac1YvLin+k2cCK3vz1T88iLhCBuw7Ca2Ugid2NVMrNVwANAMoC7v0DkrqxhZjYbMOBud9+YwyFTgTFBiCQCXwAvxat+KfhKpyZx8ykNubRdbZ4ft4jhU5fz4czVXNKmFv1PbkCVND3UKJIf9ECiFBk/bd7JM2MX8XbmSlISE+jboQ7Xdq5P2VLJYZcmUijpyfYoCpLiZdnG7Tz1xQI+nLmGMqlJXNelPn1OrEPpVM2DInIkFCRRFCTF07yftvDEZ/P5Yt56KpVJof9JDbikbS1SkxLDLk2kUFCQRFGQFG/Tl//CY2N+ZOqSTdQoV5JbTm3I+cfX0MRaIocR+lhbIgVFq9rlGXl1O16/qi2VyqRw1zuzOH3gRD6a9ZOekhfJAwoSKRbMjI4NKzGqfwdeuLQViWb0f/M7znnuK8bPX6+n5EVyQUEixYqZ0f3Yanx6a2eevCjylHyfV7+l54tTmbY0p6HhRCQ76iORYm1P1n7e+nYFz365iPVbd9OlUWXuOP0YmtcsG3ZpIqHLs852M3uVyEi9v+HuV/7+8vKXgkQOZ+eefQyfsozBExbz6469nNG8Gred1ogGVdLCLk0kNLEGSSw31v8n6n0J4DwiI/aKFBklUxK5tkt9erWtxSuTlvLypCV8Omct5x1fk1tPbcjRFUqFXaJIgXXEl7aCYd6/cvcT41NS3lOLRI7Upu17eGHCYl6bvIz97lzcuhY3ntyAqukadkWKj3je/tsQ0BS3UqRVKJ3Cn89owoQ7T6Jn66MZOW0Fnf85jn98PI9ftu8JuzyRAiWWPpKt/LaPZC1wj7u/G8/C8pJaJJJbK37ewcAvFvD+jNWUTkmiX6e6XNWxLmklNI6XFF16sj2KgkTyyoJ1W3nyswV8Onct5Uslc33X+lzevg4lkjXsihQ9CpIoChLJa7NW/crjny1g4oINVE1P5eZTGnJRxtEka9gVKULiOkSKmX33e/YTKSqOq1mO4Ve24a1r2nF0+VL83/tzOOWJCYz6frWGXZFiRy0SkVxyd8bP38A/x8xn3k9baFwtjdtPP4ZTm1TBzMIuT+R306CNIvnEzDipcRU+uqkjz/Y6nt1Z+7l6eCbnD57M5MU5TfopUjQcNkjMrJ2ZfWtm28xsj5ntM7Mt+VGcSGGSkGCc3aI6nw3ozCPnN2ft5l1c8tI3XPbKN8xc+WvY5YnETSwtkkFAL2AhUBLoBzwXz6JECrPkxAQublOLcXd05d4zmzB3zRbOfe5rrhsxnYXrtoZdnkiei+nSlrsvAhLdfZ+7vwp0j29ZIoVfieRE+nWqx4Q7uzLg1EZ8tWgj3QZO5La3Z7By046wyxPJM7GMtbXDzFKAGWb2T+An1LciErO0EsnccmpDLmtf+7/DroyeuYZebSLDrlRJ07ArUrjF8mR7bWAdkAIMAMoCzwetlEJBd21JQbJ28y6e+XIhb327kpTEBK7qWJdrutQjXU/JSwGjBxKjKEikIFq2cTtPfL6A0TPXUL5UMv1PasCl7WrrKXkpMBQkURQkUpDNWb2ZRz/9kUkLN1KjXEluPbUh559Qk8QEPYMi4dJzJCKFxLE1yjLiqra82a8tlcqkcOc7s/jD0xP5/Id1mkteCoVYniO5MJZlIpI7JzaoxKj+HXi+9wlk7XOuHp7JhS9MIXOZ5pKXgi2WFsk9MS77H2Y21MzWm9mcbNaXNbPRZjbTzOaaWd+D1qeb2SozGxS1rJWZzTazRWb2jGkMCilCzIwzmh/FmAGdefi85qzYtIMLXphCv9e+Zf5aPYMiBVO2fSRm9gfgDOAi4K2oVelAU3dvc9iDm3UGtgHD3f3YQ6z/M1DW3e82s8rAfKCau+8J1j8NVAY2ufuNwbJpwM3AN8DHwDPu/klOdaiPRAqrnXv28erkpQwev5htu7M4//iaDDitITXLa+pfib+86CNZA2QCu4DpUa8PgW6xFOHuE4Gc2uUOpAWtijLBtlnBCbQCqgKfHdjYzI4C0t19qkcScDjQI5ZaRAqjkimJ3NC1AZPuOomrO9Vj9Kw1nPz4BB78zw9s0kyNUkBk+0Ciu88EZprZm+6+N06fP4hIMK0B0oCe7r4/mBf+CeBS4NSo7WsAq6K+XhUs+x9mdg1wDUCtWrXyvnKRfFSuVGTq3z4n1mHgFwt49eulvP3tSq7rWp+rOtbVLcMSqlj6SNqY2edmtsDMlpjZUjNbkkef3w2YAVQHWgKDzCwduAH42N1X5bRzTtx9iLtnuHtG5cqV86ZakZBVL1eSf17QgjG3dqZtvYo8NmY+Jz8+nnenr9I8KBKaWIZIeYXIE+3TgX15/Pl9gUeCy1SLzGwp0BhoD3QysxuIXPJKMbNtwNNAzaj9awKr87gmkQKvYdU0Xr4ig6lLfubhj+dx+79nMvTrpfzfGU04sUGlsMuTYiaWFslmd//E3de7+88HXnn0+SuAUwDMrCpwDLDE3Xu7ey13rwPcQaSz/k/u/hOwJRja3oDLgQ/yqBaRQqddvYqMuqEDT1/ckl937OWSl7/hymHfapRhyVextEjGmdljwHvA7gML3f2w0+2a2UigK1DJzFYBDwDJwf4vAA8Cw8xsNmDA3e5+uJmAbgCGERnS/pPgJVJsJSQY57asQbdm1Rg+ZRnPfrmIbgMn0rN1LQac1lCDQkrcxTJo47hDLHZ3Pzk+JeU93f4rxckv2/fw7JeLGDF1GcmJCVzbuT5Xd65LqZRYfm8U+f801lYUBYkUR8s2buefY37k49lrqZKWyu2nN+KCVkdrDC+JWZ6NtWVmVc3sFTP7JPi6qZldlRdFikj81KlUmud7t+Ld69tTs3xJ7n53Nmc8PYnx89drDC/JU7F0tg8DxhC5RRdgAXBrvAoSkbzVqnYF3r3+RJ7vfQK7svbR59VvueyVafy4dkvYpUkREUuQVHL3t4H9AO6eRd7fBiwicXRgDK/PB3Th/rOaMmfNZs54ehL3jZrDL3pCXnIpliDZbmYViQxngpm1AzbHtSoRiYuUpASu7FiX8Xd05fL2dXhz2gq6Pj6eYV8vZe++/WGXJ4VULHdtnQA8CxwLzCEyiOIF7j4r/uXlDXW2ixzagnVb+dvoH/hq0UYaVinD/Wc3pVNDjQQhEXl615aZJRF5WNCA+XEceysuFCQi2XN3vpi3noc++oHlP+/g1CZVuffMJtSpVDrs0iRkeRYkZpYInAnUIeoBRnd/Mpc15hsFicjh7c7ax9CvljHoy4Xs3edc2bEuN57cgDKpev6kuMrLqXZHA32AikRG6D3wEpEiJDUpkeu71mfcHV05p2V1XpiwmJMeH8+/M1dqQEjJUSwtklnuflw+1RMXapGIHLmZK3/lL6Pn8v2KXzmuZlkeOLsZrWqXD7ssyUd52SL5xMxOz4OaRKQQaXF0Od697kSe6tmCdVt28cfBkxnw1gzWbt4VdmlSwMRy8XMq8H4w2dReIh3u7u7pca1MREKXkGCcd3xNTm9ajcHjFzNk0hI+nbOWG09uwNWd6pGSFMvvolLUxfKv4Eki84OUcvd0d09TiIgUL6VTk7ij2zGMva0LnRtV4rEx8znjmUlMWZxXM0pIYRZLkKwE5rgG5xEp9o6uUIoXL8vg1T6t2Z21j14vTeW2t2awcdvuw+8sRVYsl7aWAOODQRuj5yMpNLf/ikjeOqlxFT6r14Xnxi3ixYmL+WLeOu7q3phL2tQiQaMLFzuxtEiWAmOBFHT7r4gESqYkcke3Y/jkls40q16We0fN4bzBk5mzWiMoFTcxz0diZmUA3H1bXCuKA93+KxJf7s4HM9bw0Ec/sGn7Hi5vX4fbT29EWonksEuTXMjL+UiONbPvgbnAXDObbmbN8qJIESkazIwex9dg7O1d6d22Nq9NWcYpT0xg9Mw1mvukGIjl0tYQ4DZ3r+3utYHbgZfiW5aIFEZlSybzYI9jGXVDB6qkp3LTyO+5fOg0lm7cHnZpEkexBElpd//vvO3uPh7QaG4ikq0WR5fjg/4d+es5zZix4le6DZzIU58vYNdeTWVUFMUSJEvM7D4zqxO87iVyJ5eISLYSE4wrTqzD2Nu70L1ZNZ4eu5DuAycyaeGGsEuTPBZLkFxJZA6S94JX5WCZiMhhVUkvwTO9juf1q9piZlz2yjTuemcmm3cWqtkoJAcx37VVmOmuLZGCYdfefTw9diFDJi6hUpkUHj6vOac0qRp2WZKNXM9HYmYf5rSju5/zO2vLdwoSkYJl1qpfufPfs5i/bivnHV+DB85uSrlSKWGXJQeJNUhyerK9PZHhUUYC3xAZrFFEJNeOq1mO0Td1ZNC4RTw/bhGTFm7koR7N6H7sUWGXJr9DTn0k1YA/E5mr/WngNGCju09w9wn5UZyIFF0pSQncdlojPryxI1XTU7nu9e/o/+Z3GrerEMo2SNx9n7t/6u5XAO2ARUTG3LoxlgOb2VAzW29mc7JZX9bMRpvZTDOba2Z9g+W1zew7M5sRLL8uap/xZjY/WDfDzKoc0dmKSIHTtHo6o/p34M5ux/D53HWc/tREPtSDjIVKjp3tZpZKZL72XkTmbP8QGOruqw97YLPOwDZguLsfe4j1fwbKuvvdZlYZmE+kFXSgrt3BsCxzgBPdfY2ZjQfucPcj6vBQH4lI4bBg3VbufGcWM1f+yulNq/JQj2Opkl4i7LKKrVwPkWJmw4EpwAnAX929tbs/GEuIALj7RGBTTpsAaWZmQJlg2yx33+PuB9q2qTnVKCJFS6Oqabx7XXv+fEZjJizYwGlPTeTd6avUOingcrpraz9wYFyD6I1iniHRzOoA/8mmRZJGpIXTmMhowj3d/aNg3dHAR0AD4E53fy5YPh6oCOwD3gUeym6eFDO7BrgGoFatWq2WL19+uHJFpABZsmEbd70zi8zlv3DSMZV5+PzmHFW2ZNhlFSu5bpG4e0IwG2JaMDPigVdezZDYDZgBVAdaAoPMLD347JXufhyRILnCzA7caN7b3ZsDnYLXZTnUP8TdM9w9o3LlynlQrojkp3qVy/D2te154OymTF2yidOfnMi/pq1Q66QACvOyUV/gPY9YRGTek8bRG7j7GiJ9JJ2Cr1cHf24F3gTa5GvFIpKvEhKMvh3q8umtnWhWI50/vTeba0ZMZ9P2PWGXJlHCDJIVwCkAQYvjGCLjetU0s5LB8vJAR2C+mSWZWaVgeTJwFpGQEZEirnbF0rzZrx33ndWUCfM30E1jdhUocQsSMxtJpLP+GDNbZWZXmdl1UbfzPgicaGaziczAeLe7bwSaAN+Y2UxgAvC4u88m0vE+xsxmEbkkthoNZy9SbCQkGFd1rMuo/h0oVzKZy16Zxt8/+oHdWRpROGwaa0tECp2de/bx8MfzGDF1OU2PSueZXi1pUEUzgOe1PJshUUSkoCmZksiDPY7l5cszWLtlF2c9+xWvT12ujviQKEhEpNA6tWlVPr2lE61MiZGTAAAQu0lEQVTrVODeUXPUER8SBYmIFGpV0kvwWt826ogPkYJERAo9dcSHS0EiIkVG0+rpfHhjRy5rV5uXJi3lvOcms2j91rDLKvIUJCJSpKgjPv8pSESkSDpUR/yvO9QRHw8KEhEpsg7uiD/r2a+Ys3pz2GUVOQoSESnSDnTEv31de/bvd84fPJm3M1eGXVaRoiARkWKh5dGReeJb1ynPXe/M4p73ZuuurjyiIBGRYqNimVSGX9mWG7rWZ+S0FVz0whRW/7oz7LIKPQWJiBQriQnGXd0b8+JlrViyYTtnPTOJrxZuDLusQk1BIiLFUrdm1fjgxg5UTkvl8qHf8Ny4Rezfr1uEfw8FiYgUW/Uql2FU/w6ceVx1Hhszn2tfn86WXXvDLqvQUZCISLFWKiWJZy5uyQNnN2Xcj+s5d9DXzF+rp+GPhIJERIo9s8iUviOvace23Vn0eO5rPpixOuyyCg0FiYhIoHWdCnx0U0ea1yjLLf+awV8+nMveffvDLqvAU5CIiESpkl6CN65uy1Ud6zJs8jJ6DZnK+i27wi6rQFOQiIgcJDkxgfvOasozvY5n7potnPHMV2Qu2xR2WQWWgkREJBvntKjOBzd2IK1EEpe8/A0fzlwTdkkFkoJERCQHjaqm8d71J9KyZjluHvk9z41bpCHpD6IgERE5jPKlUxjRrw09WkaeN7n73VnqhI+SFHYBIiKFQWpSIk/1bEmtiqV5ZuxCVv+6k+d7t6JsyeSwSwudWiQiIjEyM247rRFPXNiCaUs38cfBk1m5aUfYZYVOQSIicoT+2Komw69sy/otuzjv+a+ZsfLXsEsKlYJEROR3aF+/Iu/d0IGSKYlcPGQKn85ZG3ZJoYlrkJjZUDNbb2Zzsllf1sxGm9lMM5trZn2D5bXN7DszmxEsvy5qn1ZmNtvMFpnZM2Zm8TwHEZHsNKhShvdv6ECTo9K5/o3pvDRxSbG8oyveLZJhQPcc1vcHfnD3FkBX4AkzSwF+Atq7e0ugLfAnM6se7DMYuBpoGLxyOr6ISFxVKpPKyKvb8Ydjq/H3j+dx76g5ZBWzO7riGiTuPhHI6XFQB9KCVkWZYNssd9/j7ruDbVIP1GlmRwHp7j7VI7E/HOgRtxMQEYlBieREBvU6geu61OeNb1bQb3gm23ZnhV1Wvgm7j2QQ0ARYA8wGbnH3/QBmdrSZzQJWAo+6+xqgBrAqav9VwbL/YWbXmFmmmWVu2LAhnucgIkJCgvGnPzTmH+c3Z9LCjVwweDI/bS4e0/iGHSTdgBlAdaAlMMjM0gHcfaW7Hwc0AK4ws6pHcmB3H+LuGe6eUbly5byuW0TkkHq1qcWrfVqz6ped9Hjua+as3hx2SXEXdpD0Bd7ziEXAUqBx9AZBS2QO0AlYDdSMWl0zWCYiUmB0blSZd65vT6IZF704hS9/XBd2SXEVdpCsAE4BCFocxwBLzKymmZUMlpcHOgLz3f0nYIuZtQv6VS4HPgindBGR7DWuls6o/h2oV7k01wyfzugiPOBjvG//HQlMAY4xs1VmdpWZXRd1O++DwIlmNhsYC9zt7huJ9Jt8Y2YzgQnA4+4+O9jnBuBlYBGwGPgknucgIvJ7VUkvwcir23F8rXLc8q/veTtzZdglxYUVh3ueMzIyPDMzM+wyRKSY2rEni2tHTGfSwo387dxmXN6+TtglxcTMprt7xuG2C/vSlohIkVcqJYmXr8jgtKZVuf+DuQwevzjskvKUgkREJB+kJiXyfO8TOLtFdR799Eee+Gx+kXkKXsPIi4jkk+TEBAb2bEmp5ESe/XIRO/bs494zm1DYR3pSkIiI5KPEBOMf5zenZEoir3y1lB17snioR3MSEwpvmChIRETyWUKC8cDZTSmVksjz4xezc88+Hr+wBUmJhbO3QUEiIhICM+Ou7o0pnZrEY2Pms3PvPp7pdTypSYlhl3bECmf8iYgUEf1PasD9ZzVlzNx1XDN8Ojv37Au7pCOmIBERCdmVHevyyPnNmbhwA31enVboRg5WkIiIFAAXt6nFwJ4tyVz+C5e+/A2bd+wNu6SYKUhERAqIc1vWYHDvE/hhzRYufmkqG7ftPvxOBYCCRESkADm9WTVeuiKDpRu30fPFKazdvCvskg5LQSIiUsB0aVSZ1/q2Yd2W3Vz04hTWbSnYYaIgEREpgNrWq8iIq9rw87bdXPryN2zavifskrKlIBERKaCOr1Wel69ozYpNO7hi6DS27CqYHfAKEhGRAqx9/YoMvvQE5v20hX7DMgvkcyYKEhGRAu7kxlV5qmdLvl2+ieten86erP1hl/QbChIRkULg7BbVefi85kxYsIFb3/qerH0FJ0w01paISCHRq00ttu/O4qGP5lE6ZTaP/vE4EgrAqMEKEhGRQqRfp3ps2ZXFM2MXUqZEEvef1TT0+UwUJCIihcyAUxuydddeXv16GWklkrnttEah1qMgEREpZMyM+85syvbdkZZJWmoSV3euF1o9ChIRkUIoIcH4x/nHsX33Pv7+8TzKlEiiV5taodSiIBERKaQSE4ynerZk+54s/vz+bEqnJnFOi+r5Xodu/xURKcRSkhIY3LsVretU4La3ZjB23rp8r0FBIiJSyJVMSeSVKzJoWj2d69/4jsmLN+br5ytIRESKgLQSybzWtw21K5Ti6tcy+X7FL/n22XELEjMbambrzWxONuvLmtloM5tpZnPNrG+wvKWZTQmWzTKznlH7DDOzpWY2I3i1jFf9IiKFTfnSKbzery0Vy6TS59Vv+XHtlnz53Hi2SIYB3XNY3x/4wd1bAF2BJ8wsBdgBXO7uzYL9B5pZuaj97nT3lsFrRnxKFxEpnKqml+CNfm0pmZzIpS9PY9nG7XH/zLgFibtPBDbltAmQZpFHMssE22a5+wJ3XxgcYw2wHqgcrzpFRIqaoyuU4vV+bWhaPZ20EvG/OTfMPpJBQBNgDTAbuMXdfzMKmZm1AVKAxVGL/x5c8nrKzFKzO7iZXWNmmWaWuWHDhjiULyJScDWoksbwK9tQsUy2PybzTJhB0g2YAVQHWgKDzCz9wEozOwoYAfSNCph7gMZAa6ACcHd2B3f3Ie6e4e4ZlSurQSMiEi9hBklf4D2PWAQsJRISBIHyEfB/7j71wA7u/lOw/W7gVaBNCHWLiEiUMINkBXAKgJlVBY4BlgQd7u8Dw939negdglYKQb9KD+CQd4SJiEj+iVsvjJmNJHI3ViUzWwU8ACQDuPsLwIPAMDObDRhwt7tvNLNLgc5ARTPrExyuT3CH1htmVjnYfgZwXbzqFxGR2Ji7h11D3GVkZHhmZmbYZYiIFCpmNt3dMw63nZ5sFxGRXFGQiIhIrihIREQkV4pFH4mZbQCWh13HEaoE5O8QnuHTORcPOufCo7a7H/ZBvGIRJIWRmWXG0slVlOiciwedc9GjS1siIpIrChIREckVBUnBNSTsAkKgcy4edM5FjPpIREQkV9QiERGRXFGQiIhIrihIQhbD3PbnBhN5zQgm6uqY3zXmtcOdc9R2rc0sy8wuyK/a4iGG73FXM9scfI9nmNn9+V1jXovlexyc9wwzm2tmE/KzvniI4ft8Z9T3eI6Z7TOzCvldZzyojyRkZtYZ2EZk2PxjD7G+DLDd3d3MjgPedvfG+V1nXjrcOQfbJAKfA7uAoQdPKVCYxPA97grc4e5n5Xdt8RLDOZcDJgPd3X2FmVVx9/X5XWdeiuXfddS2ZwMD3P3kfCkuztQiCdnh5rZ3923+/9O+NJG57gu1w51z4CbgXaBQ/3CBmM+3SInhnC8hMrHdimD74vZ97gWMjGM5+UpBUgiY2Xlm9iORWSOvDLueeDOzGsB5wOCwa8lH7c1sppl9YmbNwi4mHzQCypvZeDObbmaXh11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using Qiskit Chemistry to plot graphs of the ground state energy of the Hydrogen (H2) molecule over a range of inter-atomic distances in different basis sets.\n", - "\n", - "This notebook populates a dictionary, that is a progammatic representation of an input file, in order to drive the Qiskit Chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here where we alter the molecule supplied to the driver in each loop.\n", - "\n", - "This notebook has been written to use the PSI4 chemistry driver. See the PSI4 chemistry driver readme if you need to install the external Psi4 program that this driver requires." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Processing step 20 --- complete\n", - "Distances: [0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.675 0.7 0.725 0.75 0.775\n", - " 0.8 0.825 0.85 0.875 0.9 0.925 0.95 0.975 1. ]\n", - "Energies: [[-1.0551598 -1.07591366 -1.09262991 -1.10591805 -1.11628601 -1.12416092\n", - " -1.12990478 -1.13382622 -1.13618945 -1.13722138 -1.13711707 -1.13604436\n", - " -1.13414767 -1.13155121 -1.12836188 -1.12467175 -1.12056028 -1.11609624\n", - " -1.11133942 -1.10634211 -1.10115033]\n", - " [-1.07121344 -1.09011427 -1.10532121 -1.11742954 -1.12693056 -1.13423167\n", - " -1.13967222 -1.14353615 -1.14606218 -1.14745209 -1.14787738 -1.14748463\n", - " -1.14639978 -1.14473155 -1.14257409 -1.14000911 -1.13710763 -1.13393134\n", - " -1.13053374 -1.12696114 -1.1232535 ]\n", - " [-1.0778639 -1.0962705 -1.11104601 -1.12277894 -1.13195346 -1.13897049\n", - " -1.14416409 -1.14781424 -1.15015683 -1.15139164 -1.15168855 -1.15119257\n", - " -1.15002788 -1.14830105 -1.14610373 -1.14351485 -1.14060245 -1.13742526\n", - " -1.13403397 -1.13047238 -1.12677835]]\n" - ] - } - ], - "source": [ - "import numpy as np\n", - "import pylab\n", - "from qiskit.chemistry import QiskitChemistry\n", - "\n", - "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", - "qiskit_chemistry_dict = {\n", - " 'driver': {'name': 'PSI4'},\n", - " 'PSI4': '',\n", - " 'algorithm': {'name': 'ExactEigensolver'},\n", - "}\n", - "# PSI4 config here is a multi-line string that we update using format()\n", - "# To do so all other curly brackets that are required in the PSI4 config must be doubled\n", - "psi4_cfg = \"\"\"\n", - "molecule h2 {{\n", - " 0 1\n", - " H 0.0 0.0 -{0}\n", - " H 0.0 0.0 {0}\n", - "}}\n", - "\n", - "set {{\n", - " basis {1}\n", - " scf_type pk\n", - "}}\n", - "\"\"\"\n", - "basis_sets = ['sto-3g', '3-21g', '6-31g']\n", - "start = 0.5 # Start distance\n", - "by = 0.5 # How much to increase distance by\n", - "steps = 20 # Number of steps to increase by\n", - "energies = np.empty([len(basis_sets), steps+1])\n", - "distances = np.empty(steps+1)\n", - "\n", - "print('Processing step __', end='')\n", - "for i in range(steps+1):\n", - " print('\\b\\b{:2d}'.format(i), end='', flush=True)\n", - " d = start + i*by/steps\n", - " for j in range(len(basis_sets)):\n", - " qiskit_chemistry_dict['PSI4'] = psi4_cfg.format(d/2, basis_sets[j]) \n", - " solver = QiskitChemistry()\n", - " result = solver.run(qiskit_chemistry_dict)\n", - " energies[j][i] = result['energy']\n", - " distances[i] = d\n", - "print(' --- complete')\n", - "\n", - "print('Distances: ', distances)\n", - "print('Energies:', energies)" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "for j in range(len(basis_sets)):\n", - " pylab.plot(distances, energies[j], label=basis_sets[j])\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Energy')\n", - "pylab.title('H2 Ground State Energy in different basis sets')\n", - "pylab.legend(loc='upper right');" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/chemistry/h2_excited_states.ipynb b/community/chemistry/h2_excited_states.ipynb deleted file mode 100644 index eee73d724..000000000 --- a/community/chemistry/h2_excited_states.ipynb +++ /dev/null @@ -1,210 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": { - "collapsed": true - }, - "source": [ - "## _*H2 excited states from ExactEigensolver*_\n", - "\n", - "This notebook demonstrates using Qiskit Chemistry to plot graphs of the ground state and excited state energies of the Hydrogen (H2) molecule over a range of inter-atomic distances. This notebook utilizes the fact that when two_qubit_reduction is used with the parity mapping on H2 the resultant hamiltionian solely contains the 4 states we are looking for.\n", - "\n", - "This notebook populates a dictionary, that is a progammatic representation of an input file, in order to drive the Qiskit Chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here where we alter the molecule supplied to the driver in each loop.\n", - "\n", - "This notebook has been written to use the PYSCF chemistry driver." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Processing step 20 --- complete\n", - "Distances: [0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.675 0.7 0.725 0.75 0.775\n", - " 0.8 0.825 0.85 0.875 0.9 0.925 0.95 0.975 1. ]\n", - "Energies: [[-1.05515979 -1.07591366 -1.09262991 -1.10591805 -1.11628601 -1.12416092\n", - " -1.12990478 -1.13382622 -1.13618945 -1.13722138 -1.13711707 -1.13604436\n", - " -1.13414767 -1.13155121 -1.12836188 -1.12467175 -1.12056028 -1.11609624\n", - " -1.11133942 -1.10634211 -1.10115033]\n", - " [-0.07074011 -0.13940618 -0.20191839 -0.25891828 -0.31096009 -0.35852853\n", - " -0.402052 -0.44191252 -0.47845306 -0.51198296 -0.5427821 -0.57110389\n", - " -0.5971778 -0.62121128 -0.64339155 -0.66388713 -0.68284939 -0.70041397\n", - " -0.71670221 -0.73182253 -0.74587179]\n", - " [ 0.26700034 0.20067908 0.14057064 0.08603034 0.0365012 -0.00850382\n", - " -0.0494151 -0.08661632 -0.1204519 -0.15123247 -0.17923903 -0.2047261\n", - " -0.22792423 -0.24904202 -0.26826785 -0.28577159 -0.301706 -0.31620832\n", - " -0.32940157 -0.34139606 -0.35229063]\n", - " [ 1.30148575 1.18682836 1.08048357 0.98177125 0.89008467 0.80487598\n", - " 0.72564537 0.65193316 0.5833141 0.51939348 0.45980452 0.40420669\n", - " 0.35228457 0.30374708 0.25832675 0.21577901 0.17588132 0.13843209\n", - " 0.10324952 0.0701702 0.03904763]]\n" - ] - } - ], - "source": [ - "import numpy as np\n", - "import pylab\n", - "from qiskit.chemistry import QiskitChemistry\n", - "\n", - "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", - "qiskit_chemistry_dict = {\n", - " 'driver': {'name': 'PYSCF'},\n", - " 'PYSCF': {'atom': '', 'basis': 'sto3g'},\n", - " 'operator': {'name': 'hamiltonian', 'qubit_mapping': 'parity', 'two_qubit_reduction': True},\n", - " 'algorithm': {'name': 'ExactEigensolver', 'k': 4},\n", - "}\n", - "molecule = 'H .0 .0 -{0}; H .0 .0 {0}'\n", - "\n", - "start = 0.5 # Start distance\n", - "by = 0.5 # How much to increase distance by\n", - "steps = 20 # Number of steps to increase by\n", - "energies = np.empty([4, steps+1])\n", - "distances = np.empty(steps+1)\n", - "\n", - "print('Processing step __', end='')\n", - "for i in range(steps+1):\n", - " print('\\b\\b{:2d}'.format(i), end='', flush=True)\n", - " d = start + i*by/steps\n", - " qiskit_chemistry_dict['PYSCF']['atom'] = molecule.format(d/2) \n", - " solver = QiskitChemistry()\n", - " result = solver.run(qiskit_chemistry_dict)\n", - " energies[:, i] = result['energies']\n", - " distances[i] = d\n", - "print(' --- complete')\n", - "\n", - "print('Distances: ', distances)\n", - "print('Energies:', energies)" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "scrolled": false - }, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.rcParams['figure.figsize'] = (12, 8)\n", - "for j in range(energies.shape[0]):\n", - " label = 'Ground state' if j ==0 else 'Excited state {}'.format(j)\n", - " pylab.plot(distances, energies[j], label=label)\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Energy')\n", - "pylab.title('H2 Ground and Excited States')\n", - "pylab.legend(loc='upper right')\n", - "pylab.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The above plot has all the states. Below we plot them individually. With each plot having its own y-axis scale the energy change over distance change is more evident, particularly the ground state curve which is very flattened above by the scale." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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\n", 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.rcParams['figure.figsize'] = (6, 4)\n", - "prop_cycle = pylab.rcParams['axes.prop_cycle']\n", - "colors = prop_cycle.by_key()['color']\n", - "for j in range(energies.shape[0]):\n", - " label = 'Ground state' if j ==0 else 'Excited state {}'.format(j)\n", - " pylab.plot(distances, energies[j], color=colors[j], label=label)\n", - " pylab.xlabel('Interatomic distance')\n", - " pylab.ylabel('Energy')\n", - " pylab.title('H2 {}'.format(label))\n", - " pylab.legend(loc='upper right')\n", - " pylab.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/chemistry/h2_iqpe.ipynb b/community/chemistry/h2_iqpe.ipynb deleted file mode 100644 index 75151fbee..000000000 --- a/community/chemistry/h2_iqpe.ipynb +++ /dev/null @@ -1,173 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## _*H2 ground state energy computation using Iterative QPE*_\n", - "\n", - "This notebook demonstrates using Qiskit Chemistry to plot graphs of the ground state energy of the Hydrogen (H2) molecule over a range of inter-atomic distances using IQPE (Iterative Quantum Phase Estimation) algorithm. It is compared to the same energies as computed by the ExactEigensolver\n", - "\n", - "This notebook populates a dictionary, that is a progammatic representation of an input file, in order to drive the qiskit_chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here where we alter the molecule supplied to the driver in each loop.\n", - "\n", - "This notebook has been written to use the PYSCF chemistry driver. See the PYSCF chemistry driver readme if you need to install the external PySCF library that this driver requires." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "import pylab\n", - "from qiskit import Aer\n", - "from qiskit.chemistry import QiskitChemistry\n", - "import time\n", - "\n", - "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", - "qiskit_chemistry_dict = {\n", - " 'driver': {'name': 'PYSCF'},\n", - " 'PYSCF': {'atom': '', 'basis': 'sto3g'},\n", - " 'operator': {'name': 'hamiltonian', 'transformation': 'full', 'qubit_mapping': 'parity'},\n", - " 'algorithm': {'name': ''},\n", - " 'initial_state': {'name': 'HartreeFock'},\n", - "}\n", - "molecule = 'H .0 .0 -{0}; H .0 .0 {0}'\n", - "algorithms = [\n", - " {\n", - " 'name': 'IQPE',\n", - " 'num_iterations': 16,\n", - " 'num_time_slices': 3000,\n", - " 'expansion_mode': 'trotter',\n", - " 'expansion_order': 1,\n", - " },\n", - " {\n", - " 'name': 'ExactEigensolver'\n", - " }\n", - "]\n", - "\n", - "backends = [\n", - " Aer.get_backend('qasm_simulator'),\n", - " None\n", - "]\n", - "\n", - "start = 0.5 # Start distance\n", - "by = 0.5 # How much to increase distance by\n", - "steps = 20 # Number of steps to increase by\n", - "energies = np.empty([len(algorithms), steps+1])\n", - "hf_energies = np.empty(steps+1)\n", - "distances = np.empty(steps+1)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "import concurrent.futures\n", - "import multiprocessing as mp\n", - "import copy\n", - "\n", - "def subrountine(i, qiskit_chemistry_dict, d, backend, algorithm):\n", - " solver = QiskitChemistry()\n", - " qiskit_chemistry_dict['PYSCF']['atom'] = molecule.format(d/2) \n", - " qiskit_chemistry_dict['algorithm'] = algorithm\n", - " result = solver.run(qiskit_chemistry_dict, backend=backend)\n", - " return i, d, result['energy'], result['hf_energy']" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "start_time = time.time()\n", - "max_workers = max(4, mp.cpu_count())\n", - "with concurrent.futures.ProcessPoolExecutor(max_workers=max_workers) as executor:\n", - " futures = []\n", - " for j in range(len(algorithms)):\n", - " algorithm = algorithms[j]\n", - " backend = backends[j]\n", - " for i in range(steps+1):\n", - " d = start + i*by/steps\n", - " future = executor.submit(\n", - " subrountine, \n", - " i, \n", - " copy.deepcopy(qiskit_chemistry_dict), \n", - " d, \n", - " backend, \n", - " algorithm\n", - " )\n", - " futures.append(future)\n", - " for future in concurrent.futures.as_completed(futures):\n", - " i, d, energy, hf_energy = future.result()\n", - " energies[j][i] = energy\n", - " hf_energies[i] = hf_energy\n", - " distances[i] = d\n", - " \n", - "print(' --- complete')\n", - "\n", - "print('Distances: ', distances)\n", - "print('Energies:', energies)\n", - "print('Hartree-Fock energies:', hf_energies)\n", - "\n", - "print(\"--- %s seconds ---\" % (time.time() - start_time))" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "pylab.plot(distances, hf_energies, label='Hartree-Fock')\n", - "for j in range(len(algorithms)):\n", - " pylab.plot(distances, energies[j], label=algorithms[j]['name'])\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Energy')\n", - "pylab.title('H2 Ground State Energy')\n", - "pylab.legend(loc='upper right')\n", - "pylab.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "pylab.plot(distances, np.subtract(hf_energies, energies[1]), label='Hartree-Fock')\n", - "pylab.plot(distances, np.subtract(energies[0], energies[1]), label='IQPE')\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Energy')\n", - "pylab.title('Energy difference from ExactEigensolver')\n", - "pylab.legend(loc='upper right')\n", - "pylab.show()" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.7" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/chemistry/h2_mappings.ipynb b/community/chemistry/h2_mappings.ipynb deleted file mode 100644 index 2c21b217e..000000000 --- a/community/chemistry/h2_mappings.ipynb +++ /dev/null @@ -1,271 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": { - "collapsed": true - }, - "source": [ - "## _*H2 ground state energy plot using different qubit mappings*_\n", - "\n", - "This notebook demonstrates using Qiskit Chemistry to plot graphs of the ground state energy of the Hydrogen (H2) molecule over a range of inter-atomic distances with different fermionic mappings to quantum qubits.\n", - "\n", - "This notebook populates a dictionary, that is a progammatic representation of an input file, in order to drive the Qiskit Chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here where we alter the molecule supplied to the driver in each loop.\n", - "\n", - "This notebook has been written to use the PYSCF chemistry driver." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Processing step 20 --- complete\n", - "Distances: [0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.675 0.7 0.725 0.75 0.775\n", - " 0.8 0.825 0.85 0.875 0.9 0.925 0.95 0.975 1. ]\n", - "Energies: [[[-1.0550072 -1.07448988 -1.0924703 -1.10560872 -1.11617561\n", - " -1.12411068 -1.12989951 -1.13377934 -1.13618819 -1.13718219\n", - " -1.13693919 -1.11393966 -1.13361768 -1.10702409 -1.10251126\n", - " -1.09745433 -1.11822278 -1.08595587 -1.09165606 -1.10587795\n", - " -1.1011269 ]\n", - " [-1.05515979 -1.07591366 -1.09262991 -1.10591805 -1.11628601\n", - " -1.12416092 -1.12990478 -1.13382622 -1.13618945 -1.13722138\n", - " -1.13711707 -1.13604436 -1.13414767 -1.13155121 -1.12836188\n", - " -1.12467175 -1.12056028 -1.11609624 -1.11133942 -1.10634211\n", - " -1.10115033]]\n", - "\n", - " [[-1.05515979 -1.07591366 -1.09262991 -1.10591805 -1.11628601\n", - " -1.12416092 -1.12990478 -1.13382622 -1.13618945 -1.13720975\n", - " -1.1370938 -1.13602101 -1.13411334 -1.13150719 -1.12831842\n", - " -1.1246409 -1.12051863 -1.11605095 -1.11129941 -1.10631446\n", - " -1.10113394]\n", - " [-1.05515979 -1.07591366 -1.09262991 -1.10591805 -1.11628601\n", - " -1.12416092 -1.12990478 -1.13382622 -1.13618945 -1.13722138\n", - " -1.13711707 -1.13604436 -1.13414767 -1.13155121 -1.12836188\n", - " -1.12467175 -1.12056028 -1.11609624 -1.11133942 -1.10634211\n", - " -1.10115033]]\n", - "\n", - " [[-1.05455947 -1.07579394 -1.09245568 -1.1057838 -1.11595615\n", - " -1.12392843 -1.12915081 -1.13217365 -1.13590692 -1.1371984\n", - " -1.13674928 -1.13514718 -1.13336169 -1.13069373 -1.12796665\n", - " -1.1244492 -1.12029028 -1.11595806 -1.11131729 -1.10626288\n", - " -1.10100739]\n", - " [-1.05515979 -1.07591366 -1.09262991 -1.10591805 -1.11628601\n", - " -1.12416092 -1.12990478 -1.13382622 -1.13618945 -1.13722138\n", - " -1.13711707 -1.13604436 -1.13414767 -1.13155121 -1.12836188\n", - " -1.12467175 -1.12056028 -1.11609624 -1.11133942 -1.10634211\n", - " -1.10115033]]]\n", - "Hartree-Fock energies: [-1.04299627 -1.06306214 -1.07905074 -1.0915705 -1.10112824 -1.10814999\n", - " -1.11299655 -1.11597526 -1.11734903 -1.11734327 -1.11615145 -1.11393966\n", - " -1.1108504 -1.10700581 -1.10251055 -1.09745432 -1.09191404 -1.08595587\n", - " -1.07963693 -1.07300676 -1.06610865]\n" - ] - } - ], - "source": [ - "import numpy as np\n", - "import pylab\n", - "from qiskit.chemistry import QiskitChemistry\n", - "\n", - "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", - "qiskit_chemistry_dict = {\n", - " 'problem': {'random_seed': 50},\n", - " 'driver': {'name': 'PYSCF'},\n", - " 'PYSCF': {'atom': '', 'basis': 'sto3g'},\n", - " 'operator': {'name': 'hamiltonian', 'qubit_mapping': '', 'two_qubit_reduction': False},\n", - " 'algorithm': {'name': ''}\n", - "}\n", - "molecule = 'H .0 .0 -{0}; H .0 .0 {0}'\n", - "\n", - "algorithms = ['VQE', 'ExactEigensolver']\n", - "mappings = ['jordan_wigner', 'parity', 'bravyi_kitaev']\n", - "start = 0.5 # Start distance\n", - "by = 0.5 # How much to increase distance by\n", - "steps = 20 # Number of steps to increase by\n", - "energies = np.empty([len(mappings), len(algorithms), steps+1])\n", - "hf_energies = np.empty(steps+1)\n", - "distances = np.empty(steps+1)\n", - "\n", - "print('Processing step __', end='')\n", - "for i in range(steps+1):\n", - " print('\\b\\b{:2d}'.format(i), end='', flush=True)\n", - " d = start + i*by/steps\n", - " qiskit_chemistry_dict['PYSCF']['atom'] = molecule.format(d/2) \n", - " for j in range(len(algorithms)):\n", - " qiskit_chemistry_dict['algorithm']['name'] = algorithms[j] \n", - " if algorithms[j] == 'ExactEigensolver':\n", - " if 'optimizer' in qiskit_chemistry_dict:\n", - " del qiskit_chemistry_dict['optimizer']\n", - " if 'variational_form' in qiskit_chemistry_dict:\n", - " del qiskit_chemistry_dict['variational_form']\n", - " else:\n", - " qiskit_chemistry_dict['optimizer'] = {'name': 'L_BFGS_B', 'maxfun': 2500}\n", - " qiskit_chemistry_dict['variational_form'] = {'name': 'RYRZ', 'depth': 5}\n", - " \n", - " for k in range(len(mappings)):\n", - " qiskit_chemistry_dict['operator']['qubit_mapping'] = mappings[k] \n", - " solver = QiskitChemistry()\n", - " result = solver.run(qiskit_chemistry_dict)\n", - " energies[k][j][i] = result['energy']\n", - " hf_energies[i] = result['hf_energy'] # Independent of algorithm & mapping\n", - " distances[i] = d\n", - "print(' --- complete')\n", - "\n", - "print('Distances: ', distances)\n", - "print('Energies:', energies)\n", - "print('Hartree-Fock energies:', hf_energies)\n" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.rcParams['figure.figsize'] = (12, 8)\n", - "pylab.ylim(-1.14, -1.04)\n", - "pylab.plot(distances, hf_energies, label='Hartree-Fock')\n", - "for j in range(len(algorithms)):\n", - " for k in range(len(mappings)):\n", - " pylab.plot(distances, energies[k][j], label=algorithms[j] + \", \" + mappings[k])\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Energy')\n", - "pylab.title('H2 Ground State Energy in different mappings')\n", - "pylab.legend(loc='upper right')\n", - "pylab.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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\n", 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YY4wH0joJichUEbl/69atXodijDGmBWndJqSq84H5xcXFF3sdizGm5wqFQpSVlVFfX+91KEmRlZXFiBEjCAQCKV93Wieh6I4JxhjTWWVlZeTn51NUVIRze8H0oaps2rSJsrIyxowZk/L1p3V1nLUJGWMSob6+nv79+6ddAgIQEfr37+9ZKS+tk5AxxiRKOiagZl5um1XHGWM6RFUJV1agqojPDz4/4vO5//vB59s+Hp+vR528NRIhUrOFcHWl+7eZcHUlkT5jaKqsAH8AyYj68/nbX6hpU1onIeuYYEzXReprqV/+AXXLllC/bDF1/1tCZFtl/AuITVAZQbInFJO3/7HkFh9DRkFSL8gHQMNN1H/xAY1rviBctZnwtkrn/6hEE67eTKRmK0QiO70/fPmjNG0u33nBPr+bkII7JCeaX/sDToLuoiOPPJLrrruOY489dvu4O+64g2XLljFr1iwuu+wy1qxZQ1NTE+eccw433ngjPp+PRx55hKuvvprhw79+YvuTTz7JxIkTuxxToqR1EjLGdIyq0rShjLr/LXYSzrLFNJR+BhHnuY7BEbuSd8AUssbsCf4MiITRSNg5cW8fDqM7vI5sH08kQqRuGzUfv0HNkldAriFrQjF5+x9H3uRjCQ7dpZ0I49dYXkrtR29Q+9Hr1H76FpHaqu3TJJCJP78fvvxC/Pn9yBw9EX+ffvjzCp3/3fHN/3+xsZrMMbuj4RDaFIKmENrUiDaFtv9F6mu276cd+DOQjCC+nHz8eQX4glkd3pYZM2YwZ86cHZLQnDlzuP322znppJP405/+xDHHHENtbS2nnXYaf/zjH7niiisAOOuss7j77rs7vgNTJK2TkFXHGdO2SKiBhpWfbk84dcsWE66sAECycsgevx/9TrmM7AnFZO26H/68goSsV1VpXPUZ2957gW2LXmTj479g4+O/cJLc5OPI3f9Yssbu3aFSRLhmK7Wfvu0knY9eJ1Th3HEmY8Bw8g+aSs43DiNr3D74+/RHMrM7VE0om0sQnw/xZUKg9QfGaiT8dWIKhyDk/K+N9YQrKwhXViDBLPy5ffF1ICGdfvrp3HDDDTQ2NhIMBiktLWXt2rUsX76cgw8+mGOOOQaAnJwc7r77bg499NDtSai7S+skZNVxxuyssbyU6jefo+bDV2n48mM05Dx9OTBoFDl7HuwknAnFZI7aDfEn5xQhImQW7UFm0R70P/MqQhvKtiekzc/dw+Zn7sTfbwh5+x9L3v7HkrPHQUgguMMymqvYatykU7/8A4hEkKxccvY8iIITLyZ378MJDN0loe1S6x/+PxpWLu34G1XRSBMabvq6xCQ+xJ9B5i57MfiiW1p9a79+/Zg8eTL/+te/mDZtGnPmzOHMM89k6dKlTJo0aYd5x44dS11dHVu2bAHgqaee4s0339w+/Z133iE7O7vj8SdJWichY4yjqbKC6rfnU/3mc9R/8T4AWeP3o2DK+WRN2J/sXSeRUTjIs/gCA0dQeMJFFJ5wEeHqSmre/zfb3nuBqtfmsvXFR/Hl5JO771Hk7n8MkZoqaj56nbpP3yJSWw0iZI3dh36nXE7O3oeTvet+TrtMdyPitBH5AzskJG1qJFJdScPqZU51XW4BvuDOpa3mKrnmJPTggw/y17/+td3VWnWcMcYT4ZqtbHt3AdVvPkvt0rchEiGzaA8GfOcG8g86icDAEV6H2CJ/fiF9Dj+dPoefTqShjtpP3mTboheoWfQS1W/9A2iuYjuJnL0PJ2fPg/HnF6YsvkHn35zQ5UWaGols20q4ZovT+WFzORLMxp/nVtm51X/Tpk3jiiuu4P3336e2tpZJkybxwQcf8MYbb+ywvBUrVtC/f38KChJTdZpsaZ2ErE3I9DaRhjpqlrxC1ZvPUvv+f9CmRgJDxtDv1MvJP+QUMkeM9zrEDvFlZpNXfDR5xUejM8PUr/gYf04+gWFje1TX77b4MoL4CgaSUTCQSKiRSM1WwtuiElJmNv4+/cnNK+TII4/kggsuYMaMGQCcffbZ3HLLLbzyyit861vfoq6ujssvv5ybbrrJ462KX1onIWsTMr2BNoWo/eRNqv77LNve+xdaX4O/cDB9j/0ufQ49hcyxe6fFCVv8frLH7+t1GEnlC8QmpC2Eq7fQtKGM8OYKzjzpeE4/Zy5z5swBIDs7m3nz5nHZZZdx6aWXsmbNGm644QbOPvvs7cuMbRO69957Oeigg1K+ba0RVfU6hqQrLi5We6id6Y7qv/yYps3rnBeqgLr/OcM0fz+jXmvzcESpW7aIbe88T7hqE77cvuQdeDx9DjmF7InfRPx2IWWilJSUsPvuu3uyblUlUreNcOV6IvXbwOcno+8A/H0H7NRx5LnnnuPKK6/k1VdfZfTo0R1aT0vbKCJLVLW4yxvRhrQuCRnTXTVt2cCGh/9vextHZ0kwi7ziY8g/5GRy9j1ye/uBSR8igj8nH39OPpH6Gpoq19NUWUHTlg34+/Yno+/A7R0xTj75ZE4++WSPI+4YS0LGpJBGIlT9ZzYbHv8l2lBH/zOvInfS0c5Ecf8RcavPnGFnWvNw83Rn3ox+Q/Fl53qxKcYDvqxcgkPHEGmoo2nLesJbNhDeutG5sLZgYI/8EWJJyJgUaSj7gvX3XUNdyUKyJx7I4O/dTnB4z+oo0JupardpW/NlZhMcPJpIvyFOIqraTLhqM768AjIKBuLL7Nh1QF42y6R1ErLecaY7iIQa2PzMXWx+9i58WbkMvuS39DlyekLuKWZSIysri02bNnW7xzn4Apn4Bo4go3AwTVs2EK7aROO2Snw5fcgoHIQvq/1ScvPzhLKyOn47oUSwjgnGJFHt0neouO8aQmu/JP+Qkxl43k0puWGnSaye8mRVde/NF6nbBhpBApn4cvLbvT1Qa09WtY4JxvRQ4epKNjzxS6r+PZuMQSMZ/tO/krvvkV6HZTopEAh48tTRzorUbWPLy09QOf8+snebzLCr7vM6pFZZEjImgVSV6reeY8PDNxKurqRw2iX0P+MqfFk5XodmehFfdh79Tvo+BVPOJ1JT1f4bPGRJyJgECVV8RcUDP6H2w1fJHLs3w2940nnkgTEe8QUy8XXz6l9LQsZ0kYabqHz+ATY99Rvw+Rl4/s0UHHe+XSxqTBx6ZBISkSOAXwBLgTmq+pqnAZleK1JXw+obT6VhxSfkFh/DoIt+RWDA8PbfaIwBIOV9REXkIRFZLyKfxow/TkSWichyEbmuncUosA3IAsqSFasx7akteZeGFZ8waObtDLv2YUtAxnSQFyWhR4C7gceaR4iIH7gHOBonqSwSkXmAH7g15v0XAP9V1ddFZDDwe+BsjPFAaN1KAPIOmNKtrh8xpqdIeRJS1TdEpChm9GRguaquABCROcA0Vb0VOLGNxVUCLd6nQkRmAjMBRo0a1cWojWlZqGIVkpWLv09/r0MxpkfqLpdsDwdWR70uc8e1SEROFZH7gMdxSlU7UdX7VbVYVYsHDuzevUNMzxUqLyU4ZLSVgozppB7ZMUFVnwGeaW8+u22PSbbG8lIyR+3mdRjG9FjdpSS0BhgZ9XqEO86YbkvDYZrWryYwuGPPbTHGfK27JKFFwHgRGSMiQWA6MK+rC1XV+ao6s2/fvl0O0JhYTZvXbX98tjGmc7zooj0beAeYICJlInKhqjYBs4AXgRJgrqouTcC6porI/Vu3bu3qoozZSai8FIDgECsJGdNZXvSOm9HK+AXAggSvaz4wv7i4+OJELtcYgMbyVQAEhhR5G4gxPVh3qY5LCisJmWQKla9EMoJk9BvqdSjG9FhpnYSsTcgkU6hiFRmDRto94ozpgrROQsYkU6h8JUGrijOmS9I6CVl1nEkWVaWxfJW1BxnTRWmdhKw6ziRLuGoTWl9j1wgZ00VpnYSMSZbmG5cGhto1QsZ0RVonIauOM8kSqnC6ZwetJGRMl6R1ErLqOJMsjeWlIELGoJHtzmuMaV1aJyFjkiVUXkrGgOH4Ai0+ScQYEydLQsZ0QqhiFYHBRV6HYUyPl9ZJyNqETLI41whZe5AxXZXWScjahEwyhGurCVdttmuEjEmAtE5CxiRD892zLQkZ03WWhIzpoK8f4VDkaRzGpANLQsZ0UKiiFMDulmBMAqR1ErKOCSYZGstX4e87AF92ntehGNPjpXUSso4JJhlC5aXWHmRMgqR1EjImGUIVpXaNkDEJYknImA6INNbTtGmdXSNkTIJYEjKmA0LrV4MqgSF292xjEsGSkDEd8PU1QlYSMiYRLAkZ0wF2jZAxiZXhdQCdISI+4BdAH2Cxqj7qcUimlwhVlOLLyceX38/rUIxJCykvCYnIQyKyXkQ+jRl/nIgsE5HlInJdO4uZBowAQkBZsmI1JlZj+SoCg0cjIl6HYkxa8KI67hHguOgRIuIH7gGmABOBGSIyUUT2EpHnY/4GAROAt1X1SuCSFMdvejHnGiHrlGBMoqS8Ok5V3xCRopjRk4HlqroCQETmANNU9VbgxNhliEgZ0Oi+DLe0HhGZCcwEGDVqVEJiN72bhpsIbVhN3oHHex2KMWmju7QJDQdWR70uAw5oY/5ngLtE5FDgjZZmUNX7RWQdMDUYDE5KWKSm12rauBaaQgTtnnHGJEx3SUIdoqq1wIVxzDcfmF9cXHxx8qMy6a6x+calVh1nTMJ0ly7aa4CRUa9HuOO6xG5gahIpVL4KsGuEjEmk7pKEFgHjRWSMiASB6cC8ri7UbmBqEilUvhIJZJLRb6jXoRiTNrzooj0beAeYICJlInKhqjYBs4AXgRJgrqouTcC6rCRkEiZUvorA4FGIr7v8djOm5/Oid9yMVsYvABYkeF3WJmQSprFilT3IzpgES+ufdFYSMomiqs4jHKxTgjEJldZJyNqETKKEt2xA62utU4IxCZbWSciYRAmVrwQgaA+zMyah0joJWXWcSZTGCrd79tAibwMxJs2kdRKy6jiTKKHyUvD5CAwY4XUoxqSVtE5CxiRKqLyUwIARSCDodSjGpJW0TkJWHWcSJVS+yjolGJMEaZ2ErDrOJEpjRSkB65RgTMKldRIyJhHCNVuJVFcSsEd6G5NwloSMacfXNy4t8jYQY9JQWichaxMyifD1NULWJmRMoqV1ErI2IZMIjVYSMiZp0joJGZMIoYpS/AWD8GXleB2KMWnHkpAx7QiVlxK0UpAxSWFJyJh2ONcIFXkdhjFpKa2TkHVMMF0VaaijafM6e46QMUmS1knIOiaYrgqt/wqwG5cakyxpnYSM6apQeSmA3S3BmCSxJGRMG5qTUNDuG2dMUlgSMqYNjeWl+HL74ssr9DoUY9KSJSFj2hCqWEVg8GhExOtQjElLloSMaYNdI2RMcvXIJCQih4rIn0XkLyLyttfxmPSk4SZCG8rsGiFjkijlSUhEHhKR9SLyacz440RkmYgsF5Hr2lqGqv5XVb8PPA88msx4Te8V2rgGwk12jZAxSRRXEhKRZ0TkBBFJRNJ6BDguZvl+4B5gCjARmCEiE0VkLxF5PuZvUNRbvw08mYCYjNlJaJ1z9+zA0DEeR2JM+sqIc757gfOBO0Xkb8DDqrqsMytU1TdEpChm9GRguaquABCROcA0Vb0VOLGl5YjIKGCrqla3Mn0mMBNg1KhRnQnV9HKhCvfu2VYSMiZp4irZqOorqno2sB9QCrwiIm+LyPkiEkhAHMOB1VGvy9xxbbkQeLi1iap6P3AT8H4wGOxygKb3CZWXIsEsMgoHex2KMWkr7uo1EekPnAdcBHwA/BEnKb2clMjaoao3qmqbnRLstj2mKxrLS53u2b4e2X/HmB4hruo4EXkWmAA8DkxV1XXupKdEZHEC4lgDjIx6PcId1yUiMhWYOm7cuK4uyvRCzdcIGWOSJ96feHeq6kRVvTUqAQGgqsUJiGMRMF5ExohIEJgOzOvqQq0kZDpLVZ1rhKxTgjFJFW/HhEIROTVm3FbgE1Vd35EVishs4AhggIiUATeq6oMiMgt4EfADD6nq0o4st5V1WUnIdEq4sgJtrLeSkDFJFm8SuhD4JvCq+/oIYAkwRkRuVtXH412hqs5oZfwCYEG8y4lzXfOB+cXFxRcncrkm/TWWuz3j7EJVY5Iq3uq4ALC7qp6mqqfhXMujwAHbOdQwAAAdEElEQVTAtckKrqvsoXams0Ll7jVCloSMSap4k9AIVa2Ier0eGKmqm4FQ4sNKDGsTMp0VqlgFPj+BAe1dKWCM6Yp4q+NeE5Hngb+5r09zx+UCW5ISWQJYm5DprNC6lQQGjkAyEnEZnDGmNfGWhH6Ac2HoPu7fY8APVLVGVY9MVnBdZSUh01mNFausKs6YFGi3JOTe1+0VN9n8PfkhGeO9UMUqssbt43UYxqS9dktCqhoGIiLS44oT1jHBdEa4upLIti32HCFjUiDeNqFtwCci8jJQ0zxSVS9PSlQJYl20TWfYjUuNSZ14k9Az7p8xaa+xvBSw7tnGpEJcSUhVHxWRbGBUZx/hYExPEWpOQoPtESDGJFu8D7WbCnwIvOC+3kdEunxvt2SzNiHTGaGKUvz9huDLzPE6FGPSXrxdtH+O8+C5LQCq+iGwS5JiShjrom06I7SulKC1BxmTEvEmoZCqxhYnIokOxpjuwK4RMiZ14u2YsFREvg34RWQ8cDnQ5gPljOmJIvW1hCsrLAkZkyLxloQuA/YAGoDZQBXwo2QFZYxXmrtn2zVCxqRGvL3jaoGfun/GpK1QRSkAgcFFnsZhTG8R7+O9dwV+DBRFv0dVj0pOWIlhNzA1HfX1c4SsY4IxqRBvm9DfgD8DfwHCyQsnseyOCaajQuWl+PIK8ecVeB2KMb1CvEmoSVX/lNRIjOkGQuWlVgoyJoXi7ZgwX0QuFZGhItKv+S+pkRnjgVC5XSNkTCrFWxL6rvv/1VHjlB5wwaox8dKmEKGNa8g/9FSvQzGm14i3d9yYZAdijNdCG8ogErbqOGNSqM3qOBG5Jmr4jJhptyQrqPaIyCgReU5EHhKR67yKw6SX5huX2jVCxqROe21C06OGfxIz7bjOrNBNHOtF5NOY8ceJyDIRWR5HYtkLeFpVLwD27UwcxsQK2SMcjEm59qrjpJXhll7H6xHgbuCx7QtyHiF+D3A0UAYscu/S7QdujXn/BcC7wNMicgHweCfjMGYHjRWrkMxs/AWDvA7FmF6jvSSkrQy39DouqvqGiBTFjJ4MLFfVFQAiMgeYpqq3AifGLkNEfgzc6C7raeDhzsRiTLRQ+UoCg4sQ6ezvK2NMR7WXhPYWkSqcUk+2O4z7OiuBcQwHVke9LgMOaGP+F4CfuzdVLW1pBhGZCcwEGDXKHk5m2hcqX0VgmHX4NCaV2kxCqupPVSAdoaqfAqe3M8/9IrIOmBoMBielJjLTU2kkQqhiFbn7Hul1KMb0KvFerJpsa4CRUa9HuOO6xB5qZ+LVVFmOhhoIDLGrEYxJpe6ShBYB40VkjIgEcXrldfnx4fZ4bxOvkN241BhPpDwJichs4B1ggoiUiciFqtoEzAJeBEqAuaq6tKvrspKQiVeofCUAQSsJGZNS8d62J2FUdUYr4xcACxK5LnuUg4lXqHwV+DPIGDDM61CM6VW6S3VcUlhJyMSrsaKUwMCRiD/lv8uM6dXSOglZm5CJl/MIhyKvwzCm10nrJGQlIRMPVXWuEbJOCcakXFonISsJmXhEqjcTqa0iOLjI61CM6XXSOglZScjEo7G5e/bQIm8DMaYXSuskZEw8QhWlAASsJGRMyqV1ErLqOBOPhtLPICNAYLDdY9CYVEvrJGTVcSYedSULydrlG/iCibwnrzEmHmmdhIxpT6ShjvoVH5O9e1s3bTfGJIslIdOr1S//EJpCloSM8UhaJyFrEzLtqStZCED2bvt7HIkxvVNaJyFrEzLtqStZSHDUbvjzCrwOxZheKa2TkDFt0XATdcsWW1WcMR6yJGR6rYbSz9D6GrJ3n+x1KMb0WpaETK9V9/l7AFYSMsZDloRMr1VXspCMgSMI9LdnCBnjlbROQtY7zrRGVakrWWilIGM8ltZJyHrHmdaE1q0gvHWjJSFjPJbWSciY1tSVWHuQMd2BJSHTK9V9vhBffiHB4eO8DsWYXs2SkOmV6kreI3u3yYiI16EY06tZEjK9TlNlBaHyUquKM6Yb6JFJSEQmishcEfmTiJzudTymZ7H2IGO6j5QnIRF5SETWi8inMeOPE5FlIrJcRK5rZzFTgLtU9RLg3KQFa9JSXclCJDObrDF7eh2KMb1ehgfrfAS4G3iseYSI+IF7gKOBMmCRiMwD/MCtMe+/AHgcuFFETgL6pyBmk0bqShaSNX4SkhHwOhRjer2UJyFVfUNEimJGTwaWq+oKABGZA0xT1VuBE1tZ1A/c5PVMsmI16SdcU0XDqs/od/oVXodijMGbklBLhgOro16XAa1W2LtJ7HogF/hNK/PMBGYCjBo1KkFhmp6u/n9LQJUcaw8yplvoLkmoQ1S1FDfBtDHP/SKyDpgaDAYnpSQw0+3VlSwEn5+sXe2QMKY76C6949YAI6Nej3DHdYndtsfEqitZSOYue+HLyvE6FGMM3ScJLQLGi8gYEQkC04F5XV2o3cDURIuEGqhf/qFVxRnTjXjRRXs28A4wQUTKRORCVW0CZgEvAiXAXFVdmurYTHpr+PIjNNRgD7EzphvxonfcjFbGLwAWJHhd84H5xcXFFydyuaZnqitZCEDWBEtCxnQX3aU6zpikqyt5j+DwcWT0tUvLjOku0joJWZuQaabhMHWfL7Jb9RjTzaR1ErLecaZZ4+rPidRWWRIypptJ6yRkJSHTzG5aakz3lNZJyEpCplldyUIy+g8lY+AIr0MxxkRJ6yRkDICqUvu5PcTOmO4orZOQVccZgND6rwhvLreqOGO6obROQj25Oi5cW02krsbrMNJCvbUHGdNtpXUS6qlUlbKbz6L0iiNoqqzwOpwer7ZkIb7cvgRHTvA6FGNMDEtC3VDd0rdpWP4hTRvXsObWc61E1EV1JQvJnrA/4rPD3Zjupkc+yiFeIjIVmDpu3DivQ+mQyufvx9+nH4Muvo11f/g+6/54KcOufgjx+70ObQfhmipC61bSuO5LGtd+SWjtCkIbysieUEyfI88ic9RuXodI09aNhNZ+Sd8jz/I6FGNMC9I6CfXEe8c1rv2SmsUv0+/0H5H/zRMJb/kF6x/8KRseuZFBF/4y5fFEQg2EylcRWvcljWtX0LhuBSH3//CWDV/P6PMRGDgSf+EgKhc8SOX8+8gcuzd9jziT/ENOxp9fmPLYAeo+XwRYe5Ax3VVaJ6FEiNTV4MvOTdn6Kv/5FyQjSMGx5wFQMOV8Quu/onL+fQSGFFF4wkVJXX9TZQWV8/5Mw+r/EVq3gtCG1RCJbJ/uLxhIcOgu5E76FsGhuxActguBoWMJDBmNL5DpLGPrJqrffJaqV+c4CfTRm8idfCx9j5xOzjcOS2mJrq5kIRLMInPsN1K2TmNM/CwJtaHuiw9Y88tvM+zqB8nZ86Ckry9cXUnVa3PJP/RkMgoHbR8/4Ds/I1TxFRseuZHAwOHkTZ6SlPXXr/yUtbd9l/DWTQRHTSBr3D7kH3YqwaFj3WQzBn9u+z0NM/r2p/CEiyg84SLqV3xC1WtzqfrvM2x7ez7+fkPoc/jp9D3iTILDk19NWleykKxx+2xPkMaY7kVU1esYkq64uFgXL17c4fdFGupYednBBAaOYOQv/5H0Cx03P3s3G/96C6N/+zKZRXvExFJL2Y1n0PBVCSNvfoascfskdN3bFr/EujsuxZ/bl2HXPUrWmD0TuvxIqIGaJa9Q9Z+nqPnwVYiEydp1En2OnE7+wSfhz8lP6PrAKcUu/+5u9DtlFgNmXJvw5RuT7kRkiaoWJ3Md1l2oDb7MbPqffgX1yxZT88F/kroubQqx5V8Pk7PXITslICeWHIZd9wj+goGsufVcQutXJ2a9qlTOv4+1t59PcPh4Rt22IOEJCMAXyCT/wBMYfv1j7HLfYgZ85wYitVWsv+9qVly0N+v+OIvaj/+LRlX9dVXdF0sgErb2IGO6sbROQom4Y0Lfo6YTGDyaTU/eltATZKzqd+bTtHkdBSfObHWejIKBDL/+CbQpxJpbziFc07U7QWhTiPX3X8uGR28ib/IURt78dzIKB3dpmfHIKBxMv2mXMvoPrzHy1n/S54gzqVnyCmU3n0X5nZeRqNJ5XclC8PnI2nVSQpZnjEm8tE5CibhjgmQE6H/W1TSULmXbu88nMLqvqSqVzz9AYNhYcvc9qs15M0eMZ9jVD9JYXsra31yEhho7tc5wzVbW3HIOW19+gsJTZjH0qvvxZeZ0almdJSJkj9+XwTNvY5cHPqDwlFlUv/ks1W/8PSHLryt5j8yiPZJS1WeMSYy0TkKJkn/wNIKjdmPjnF+j4aaEL7/+8/do+PIjCk+4KK4LKnP2PIghl/yOuk/fouK+azpccmgsL2X19VOp/exdBl/6ewaefb3nF3L6MrMZMP1asnc/gPV/uZ5QxVddWp6GGqn/3xKyd7NHeRvTnVkSioP4/QyYfg2htSuoeu1vCV9+5fz78eUV0ufwM+J+T5/DT6f/mVdR9dpcNj/9h7jfV/f5e6y+/kSatm5kxA2z6XvU9M6EnBTi9zPksjtBhHV3XYaGw51eVv3KT9HGemsPMqabsyQUp9z9jyVr3L5s+tvviIQaErbcxopVbFv0AgVHn4Mvq2PVYf3OuJI+h5/Bpqd+S1UcVVhVbzxD2c/PxJdbwKhb5qek23lHBQaNZNBFt1D/+SI2P3dPp5dTV7IQsItUjenuLAnFSUTo/+1radq4lq0vPZ6w5W5Z8CD4/PQ97rxOxTT4+78he8+DKb/3Smo/fbvF+VSVjXN+Tfmds8jadRKjbplPcNjYLkaePPmHnkr+wdPYNPe31C//qFPLqCtZSGDoLmQUDExwdMaYROr2SUhEdhGRB0Xk6ahxuSLyqIg8ICJnpyqWnL0OJXvPg9n8zJ1E6mu7vLxwTRVb/z2b/IOnEeg/tFPLkECQYT9+gOCQItb+5kIayr7YYXqkoY7yP1zC5qfvoM+RZzHiZ7M9u4VOvESEQRffSkbBQNbd+YMO72uNRKj7fBHZu+2fpAiNMYmS1CQkIg+JyHoR+TRm/HEiskxElovIdW0tQ1VXqOqFMaNPBZ5W1YuBkxIcdqtEhAEzriW8daNTgumirf9+Eq2vofDErt3azp9XwPDrn0AyAqy95Ts0bd0IQNOWDZTddCbVb89jwNnXM/jS3yOBYJfjTgV/XgFDLruT0LqVbHjs5g69t3HNF0S2VVpVnDE9QLJLQo8Ax0WPEBE/cA8wBZgIzBCRiSKyl4g8H/M3aOdFAjACaL5as/Ot152QPaGY3OKj2fyPewlv29Lp5Wi4iS0LHiR74oFk7dL1+5oFBo1k2HWP0rRlPWtvO4/65R/y1U9OoKF0KUN//Bf6nTKrxz3aOmfPgymc+j22vvQY2xa/HPf76uwhdsb0GElNQqr6BrA5ZvRkYLlbwmkE5gDTVPUTVT0x5m99K4suw0lE0Mo2iMhMEVksIos3bNjQ0iydNmD6tURqtlI578+dXsa2hf+iaeMaCtu4OLWjssfvy9Af3UP98g/46rrj0VAjI29+lvwDj0/YOlKt/4xrySyaSMW9V9K0Jb7Psa5kIf6CQQSGFCU3OGNMl3nRJjScr0sx4CSU4a3NLCL9ReTPwL4i8hN39DPAaSLyJ2B+S+9T1ftVtVhViwcOTGzjdGbRRPIPOZnKfz4Q94kxVuXz9xMYUkTupKMTGlve5CkMmnk7Ofscwajb/knWuL0TuvxU8wUyGfLDe4jUbaPi3qviuiaqrmQh2bsf0ONKfsb0Rt2+Y4KqblLV76vqWFW91R1Xo6rnq+olqvrX1t6biNv2tKb/WT9GQ41sfubODr+37n9LqP/fEgqOvzApjzUoOPocRtzwJIEBreb2HiVz5AQGnPNTat5/pd2eiaENZTRtXGOdEozpIbxIQmuAkVGvR7jjepTg0F3oe9R0tr70OKENZR16b+Xz9+PL6UPfI7vPhaLdXcGUC8jZ+3A2PPpzGtcsb3W+us+tPciYnsSLJLQIGC8iY0QkCEwH5iVjRYm4d1xb+p3+IxBhUwfuWBDaUMa2d/9J36PPTunD8no68fkY8oM/IJnZrPvjLLQp1OJ8dSXv4cvJJ3P0xBRHaIzpjGR30Z4NvANMEJEyEblQVZuAWcCLQAkwV1WXJmn9SauOAwgMGE7fY86l6tW5bf46j+Z07RYKplyQlJjSWUa/IQz+3m9oWPExm+b+rsV56koWkrVrcUqf3mqM6bxk946boapDVTWgqiNU9UF3/AJV3dVt5/lVEtef1JIQQL9TL0OCmWx66rftzhup28bWfz9J/oEnpE17TarlH3g8fY6azuZn76L2s4U7TAtXb6Zx9TKyd7eblhrTU3T7jgldkeySEEBG3wEUnjCT6rfnUb/y0zbn3fqfOURqqymY+r2kxdMbDDr/ZgKDR1N+12WEa6q2j69b5jw919qDjOk50joJpaIkBFB40vfw5RWwafavW48lHGbLP/9C1oRissfvm9R40p0vO48hl99F06Z1bHjoZ9vH15UsRDKCCX/0uTEmedI6CaWKP7cv/aZdSs37r2zvnRVr2+KXCK3/KqEXp/Zm2btOot9pP6Tq9b9R/bbTr6Wu5D0yx+2NL5jlcXTGmHildRJKRXVcs4IpF+AvGMTGJ29r8YLKLc/fT8agkeRNPq6Fd5vO6H/aD8kavx8V911L49ovqf/yI3uInTE9TFonoVRVxwH4snLof9oPqfvsXWo/en2HafXLP6KuZCGFUy5E/BlJj6W3kIwAQy6/Cw2HKLv5LAg3WXuQMT1MWiehVOv7rbPJGDSSjbNv36E0VPn8/fiy8+jz/2Z4GF16Cg4dw6Dzb6Zp41oQsTslGNPDpHUSSmV1HDjP9ul/xpU0fPkR2957AYDQpnVUvzOfPkfNwJ+Tn5I4eps+R80g/+BpZO9xEP7c5Jd6jTGJI/HcELKnKy4u1sWLF6dkXRpuYtWVR4H4GP27f7Nxzu1U/uNextz1NoHBo1ISQ2/UfBzbTUuNSRwRWaKqxclcR1qXhLwg/gz6T7+GxrL/sfWVv7L15SfImzzFElCSiYglIGN6IGslT4K8A44nc5e9WP/gTyES7vKTU40xJl2ldUko1W1C29fr8zFgxnUQCZM1bl+yJlhjuTHGtCStk1Aqu2jHytnnCPqf9WMGnn+TVRMZY0wrrDouSUSE/mdc6XUYxhjTraV1ScgYY0z3ZknIGGOMZywJGWOM8UxaJyGvescZY4yJT1onIS97xxljjGlfWichY4wx3ZslIWOMMZ6xJGSMMcYzveIu2iKyAVjVhUUMADYmKJyeoLdtL9g29xa2zR0zWlUHJjKYWL0iCXWViCxO9u3Mu5Petr1g29xb2DZ3P1YdZ4wxxjOWhIwxxnjGklB87vc6gBTrbdsLts29hW1zN2NtQsYYYzxjJSFjjDGesSRkjDHGM5aEXCJynIgsE5HlInJdC9PPE5ENIvKh+3eRF3EmUnvb7M5zpoh8JiJLReTJVMeYaHF8zn+I+oz/JyJbvIgzkeLY5lEi8qqIfCAiH4vI8V7EmUhxbPNoEfm3u72vicgIL+JMFBF5SETWi8inrUwXEbnT3R8fi8h+qY6xVara6/8AP/AlsAsQBD4CJsbMcx5wt9expnibxwMfAIXu60Fex53sbY6Z/zLgIa/jTsHnfD9wiTs8ESj1Ou4UbPPfgO+6w0cBj3sddxe3+TBgP+DTVqYfD/wLEOBAYKHXMTf/WUnIMRlYrqorVLURmANM8zimZItnmy8G7lHVSgBVXZ/iGBOto5/zDGB2SiJLnni2WYE+7nBfYG0K40uGeLZ5IvAfd/jVFqb3KKr6BrC5jVmmAY+p412gQESGpia6tlkScgwHVke9LnPHxTrNLco+LSIjUxNa0sSzzbsCu4rIWyLyrogcl7LokiPezxkRGQ2M4esTVU8Vzzb/HDhHRMqABTglwJ4snm3+CDjVHT4FyBeR/imIzStxH/upZkkofvOBIlX9BvAy8KjH8aRCBk6V3BE4pYIHRKTA04hSZzrwtKqGvQ4kBWYAj6jqCJxqm8dFJN3PDT8GDheRD4DDgTVAb/isu510P9DitQaILtmMcMdtp6qbVLXBffkXYFKKYkuWdrcZ59fSPFUNqepK4H84Samnimebm02n51fFQXzbfCEwF0BV3wGycG562VPF831eq6qnquq+wE/dcT2+E0obOnLsp5QlIcciYLyIjBGRIM4JaF70DDH1pycBJSmMLxna3WbgOZxSECIyAKd6bkUqg0yweLYZEdkNKATeSXF8yRDPNn8F/D8AEdkdJwltSGmUiRXP93lAVGnvJ8BDKY4x1eYB57q95A4EtqrqOq+DAqe6pddT1SYRmQW8iNOz5iFVXSoiNwOLVXUecLmInAQ04TQAnudZwAkQ5za/CBwjIp/hVFVcraqbvIu6a+LcZnBOWnPU7VbUk8W5zVfhVLVegdNJ4byevO1xbvMRwK0iosAbwA88CzgBRGQ2zjYNcNv2bgQCAKr6Z5y2vuOB5UAtcL43ke7MbttjjDHGM1YdZ4wxxjOWhIwxxnjGkpAxxhjPWBIyxhjjGUtCxhhjPGNJyPRIIrItjnl+JCI5CVznySIyMYHLe7sL793m/j9MRJ5uY74CEbm0s+sxJtksCZl09iOgQ0lIRPxtTD4Z58aXCaGqByVgGWtV9fQ2ZikALAmZbsuSkOnRROQI93kwT4vI5yLyV/eq8MuBYcCrIvKqO+8xIvKOiLwvIn8TkTx3fKmI3C4i7wNniMjFIrJIRD4Skb+LSI6IHIRzp4zfuM8aGisi+7g3dv1YRJ4VkUJ3ea+J81yixSJSIiL7i8gzIvKFiPwyKvZtUcPXisgn7jpva2E7x7ixfxKzjKLmZ8iIyB4i8p4b38ciMh64DRjrjvuNiOSJ8xyd991lTYtaTomIPCDOs6NeEpFsd9o4EXnFje19ERnrjr/a3U8fi8hNCf1gTe/h9bMk7M/+OvMHbHP/PwLYinMvLB/OrXYOcaeVAgPc4QE4V8bnuq+vBf4var5ropbdP2r4l8Bl7vAjwOlR0z4GDneHbwbucIdfA253h3+I82iEoUAmzv34+sdswxTgbSDHfd2vhe2dB5zrDv8g6r1FuM+QAe4CznaHg0B29HR3fAbQJ2qfLMd5xkwRzt1A9nGnzQXOcYcXAqe4w1k4pctjcJ5DJO5+fx44zOvjwv563p/dtsekg/dUtQxARD7EOaG+GTPPgThVaW+JCDgn6eh7wz0VNbynW9ooAPJwbv+yAxHpCxSo6uvuqEdxHpTWrPkWQJ8AS9W9T5eIrMC5kWT07Y++BTysqrUAqtrSc2EOBk5zhx8Hbm9hnneAn4rzlNBnVPULd1t3CB24RUQOAyI4t/Mf7E5bqaofusNLgCIRyQeGq+qzbmz17nYcg5OIPnDnz8O5ue0bLcRlTKssCZl00BA1HKbl41qAl1V1RivLqIkafgQ4WVU/EpHzcG/i2smYIjHxRVqJLx5t3mNLVZ8UkYXACcACEfkeO99w9mxgIDBJVUMiUopTuomOGZz9mN3G6gS4VVXv60D8xuzE2oRMOqsG8t3hd4GDRWQcgIjkisiurbwvH1gnIgGck/ZOy1PVrUCliBzqTvsO8Dqd8zJwfnNPPhHp18I8b+HcWJWYmLYTkV2AFap6J/AP4BvsuA/AeXLqejcBHQmMbiswVa0GykTkZHcdmW6cLwIXRLWrDReRQXFtrTFRLAmZdHY/8IKIvKqqG3DufD5bRD7GqbrarZX3/QynHeQt4POo8XOAq0XkA7dx/rs4HRU+BvbBaRfqMFV9Aaf6brFbnfjjFmb7IfADEfmE1p+IeSbwqbuMPXEe57wJpwryUxH5DfBXoNhdzrkx29ea7+DcRf5jnLarIar6EvAk8I67rKfZMdkZExe7i7YxxhjPWEnIGGOMZywJGWOM8YwlIWOMMZ6xJGSMMcYzloSMMcZ4xpKQMcYYz1gSMsYY45n/D2h/JnFH9kMNAAAAAElFTkSuQmCC\n", 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.rcParams['figure.figsize'] = (6, 4)\n", - "for k in range(len(mappings)):\n", - " pylab.ylim(-1.14, -1.04)\n", - " pylab.plot(distances, hf_energies, label='Hartree-Fock')\n", - " for j in range(len(algorithms)):\n", - " pylab.plot(distances, energies[k][j], label=algorithms[j])\n", - " pylab.xlabel('Interatomic distance')\n", - " pylab.ylabel('Energy')\n", - " pylab.title('H2 Ground State Energy with {} mapping'.format(mappings[k]))\n", - " pylab.legend(loc='upper right')\n", - " pylab.show()\n", - " \n", - " #pylab.plot(distances, np.subtract(hf_energies, energies[k][1]), label='Hartree-Fock')\n", - " pylab.plot(distances, np.subtract(energies[k][0], energies[k][1]), color=[0.8500, 0.3250, 0.0980], label='VQE')\n", - " pylab.xlabel('Interatomic distance')\n", - " pylab.ylabel('Energy')\n", - " pylab.yscale('log')\n", - " pylab.title('Energy difference from ExactEigensolver with {} mapping'.format(mappings[k]))\n", - " pylab.legend(loc='upper right')\n", - " pylab.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/chemistry/h2_particle_hole.ipynb b/community/chemistry/h2_particle_hole.ipynb deleted file mode 100644 index 942387945..000000000 --- a/community/chemistry/h2_particle_hole.ipynb +++ /dev/null @@ -1,233 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## _*H2 energy plot comparing full to particle hole transformations*_\n", - "\n", - "This notebook demonstrates using Qiskit Chemistry to plot graphs of the ground state energy of the Hydrogen (H2) molecule over a range of inter-atomic distances using VQE and UCCSD with full and particle hole transformations. It is compared to the same energies as computed by the ExactEigensolver\n", - "\n", - "This notebook populates a dictionary, that is a progammatic representation of an input file, in order to drive the Qiskit Chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here where we alter the molecule supplied to the driver in each loop.\n", - "\n", - "This notebook has been written to use the PYQUANTE chemistry driver. See the PYQUANTE chemistry driver readme if you need to install the external PyQuante2 library that this driver requires." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "scrolled": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Processing step 20 --- complete\n", - "Distances: [0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.675 0.7 0.725 0.75 0.775\n", - " 0.8 0.825 0.85 0.875 0.9 0.925 0.95 0.975 1. ]\n", - "Energies: [[[-1.05515973 -1.07591359 -1.09262986 -1.105918 -1.11628597\n", - " -1.12416088 -1.12990475 -1.1338262 -1.13618942 -1.13722134\n", - " -1.13711707 -1.13604434 -1.13414766 -1.1315512 -1.12836187\n", - " -1.12467173 -1.12056027 -1.11609624 -1.11133942 -1.10634211\n", - " -1.10115033]\n", - " [-1.05515974 -1.07591361 -1.09262987 -1.10591802 -1.11628599\n", - " -1.12416089 -1.12990476 -1.1338262 -1.13618944 -1.13722136\n", - " -1.13711707 -1.13604436 -1.13414767 -1.13155121 -1.12836188\n", - " -1.12467175 -1.12056028 -1.11609624 -1.11133943 -1.10634212\n", - " -1.10115034]]\n", - "\n", - " [[-1.05515973 -1.07591359 -1.09262987 -1.105918 -1.11628598\n", - " -1.12416087 -1.12990474 -1.13382619 -1.13618943 -1.13722134\n", - " -1.13711704 -1.13604435 -1.13414766 -1.13155119 -1.12836186\n", - " -1.12467175 -1.12056028 -1.11609624 -1.11133942 -1.1063421\n", - " -1.10115033]\n", - " [-1.05515974 -1.07591361 -1.09262987 -1.10591802 -1.11628599\n", - " -1.12416089 -1.12990476 -1.1338262 -1.13618944 -1.13722136\n", - " -1.13711707 -1.13604436 -1.13414767 -1.13155121 -1.12836188\n", - " -1.12467175 -1.12056028 -1.11609624 -1.11133943 -1.10634212\n", - " -1.10115034]]]\n", - "Hartree-Fock energies: [-1.04299622 -1.0630621 -1.0790507 -1.09157046 -1.10112822 -1.10814997\n", - " -1.11299652 -1.11597525 -1.11734902 -1.11734325 -1.11615145 -1.11393966\n", - " -1.1108504 -1.10700581 -1.10251056 -1.09745432 -1.09191405 -1.08595588\n", - " -1.07963694 -1.07300677 -1.06610866]\n", - "VQE num evaluations: [[45. 51. 51. 51. 43. 54. 50. 47. 51. 46. 42. 57. 49. 53. 49. 55. 50. 46.\n", - " 51. 56. 55.]\n", - " [49. 49. 50. 51. 47. 52. 47. 48. 52. 46. 52. 56. 45. 49. 48. 52. 47. 49.\n", - " 54. 58. 60.]]\n" - ] - } - ], - "source": [ - "import numpy as np\n", - "import pylab\n", - "from qiskit.chemistry import QiskitChemistry\n", - "\n", - "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", - "qiskit_chemistry_dict = {\n", - " 'problem': {'random_seed': 50},\n", - " 'driver': {'name': 'PYQUANTE'},\n", - " 'PYQUANTE': {'atoms': '', 'basis': 'sto3g'},\n", - " 'operator': {'name': 'hamiltonian', 'qubit_mapping': 'jordan_wigner',\n", - " 'two_qubit_reduction': False},\n", - " 'algorithm': {'name': ''}\n", - "}\n", - "molecule = 'H .0 .0 -{0}; H .0 .0 {0}'\n", - "algorithms = ['VQE', 'ExactEigensolver']\n", - "transformations = ['full', 'particle_hole']\n", - "\n", - "start = 0.5 # Start distance\n", - "by = 0.5 # How much to increase distance by\n", - "steps = 20 # Number of steps to increase by\n", - "energies = np.empty([len(transformations), len(algorithms), steps+1])\n", - "hf_energies = np.empty(steps+1)\n", - "distances = np.empty(steps+1)\n", - "eval_counts = np.empty([len(transformations), steps+1])\n", - "\n", - "print('Processing step __', end='')\n", - "for i in range(steps+1):\n", - " print('\\b\\b{:2d}'.format(i), end='', flush=True)\n", - " d = start + i*by/steps\n", - " qiskit_chemistry_dict['PYQUANTE']['atoms'] = molecule.format(d/2) \n", - " for j in range(len(algorithms)):\n", - " qiskit_chemistry_dict['algorithm']['name'] = algorithms[j] \n", - " if algorithms[j] == 'ExactEigensolver':\n", - " if 'optimizer' in qiskit_chemistry_dict:\n", - " del qiskit_chemistry_dict['optimizer']\n", - " if 'variational_form' in qiskit_chemistry_dict:\n", - " del qiskit_chemistry_dict['variational_form']\n", - " if 'initial_state' in qiskit_chemistry_dict:\n", - " del qiskit_chemistry_dict['initial_state']\n", - " else:\n", - " qiskit_chemistry_dict['optimizer'] = {'name': 'COBYLA', 'maxiter': 10000 }\n", - " qiskit_chemistry_dict['variational_form'] = {'name': 'UCCSD'}\n", - " qiskit_chemistry_dict['initial_state'] = {'name': 'HartreeFock'}\n", - " \n", - " for k in range(len(transformations)):\n", - " qiskit_chemistry_dict['operator']['transformation'] = transformations[k] \n", - " solver = QiskitChemistry()\n", - " result = solver.run(qiskit_chemistry_dict)\n", - " energies[k][j][i] = result['energy']\n", - " hf_energies[i] = result['hf_energy']\n", - " if algorithms[j] == 'VQE':\n", - " eval_counts[k][i] = result['algorithm_retvals']['eval_count']\n", - " distances[i] = d\n", - "print(' --- complete')\n", - "\n", - "print('Distances: ', distances)\n", - "print('Energies:', energies)\n", - "print('Hartree-Fock energies:', hf_energies)\n", - "print('VQE num evaluations:', eval_counts)\n" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.plot(distances, hf_energies, label='Hartree-Fock')\n", - "for j in range(len(algorithms)):\n", - " for k in range(len(transformations)):\n", - " pylab.plot(distances, energies[k][j], label=algorithms[j]+' + '+transformations[k])\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Energy')\n", - "pylab.title('H2 Ground State Energy')\n", - "pylab.legend(loc='upper right');" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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H+/4iG1POqSqfR8Xz5692cOJsOg8MbMWDg9oQXCmoWOPwWyJxk8BkYBEQBLynqttE5FkgUlUX4MwXPVtEonHm+B7r7t4XeEJE0oEs4H5VTRSRlsB8986aisBHqvqtv+rgb1WrViUqKur88+ykAM7vXMaMGcPhw4c5d+5cjt81jBgxgqpVq+Z7XM/tixcvZvPmzcybNw+AlJQU9uzZw+LFi1m8eDHdunUD4NSpU+zZsyfPRJK7aSslJYXjx4/Tv39/AG6//XZuvvlmTp48SXx8PDfc4NytHRwcfH6fHTt2MGnSJBYvXkzjxo0v7IUyxvzKwaQz/PHzLfy4J5GuTWvz/E2X0a5hzYDE4tc+ElX9Bvgm17qpHsupwM157DcbmJ3H+n1Al6KOs7Arh0B48MEHefTRRxkxYgTLly9n2rRp57dVr169wH09t6sqr776KkOHDs1RZtGiRTz55JPce++9Oda//vrrvP322wBF2onfqFEjUlNT+fnnny2RGOOD9Mws3l25n5eX7KZihQo8O7Ij43s1I6hC4G5dt7G2SqiUlBSaNHFucps1a1a+5WrUqMHJkyfz3T506FD+/e9/k56eDsDu3bs5ffo0Q4cO5b333uPUqVMAxMfHc+zYMR544AGioqKIiorK9wu/Vq1a1KlThx9//BGA2bNn079/f2rUqEFYWBiff+5Mt52WlsaZM2cAqF27Nl9//TVPPvkky5cvv7AXwxgDwKbY44x4bRXPL9zJVW3q8d2jVzGhd/OAJhGwRFJiTZs2jZtvvpkePXoQGpr/lAADBw5k+/bt5zvbc7v77rvp0KED3bt3p1OnTtx7771kZGQwZMgQbr31Vnr37s1ll13G6NGjC0xIuc2aNYspU6bQuXNnoqKimDrVudCcPXs2r7zyCp07d+bKK6/kyJEj5/dp0KABX331FQ888ABr1669gFfDmPLtVFoGz3y5jVFvrCL5dBpv/rYHMyZE0KhW/k3cxalczNkeERGhuSe22rFjB+3btw9QRKYks8+GKUmWbD/K1C+2cvhEKr/t1Ywpwy6lZnDxDCoqIhtUNaKwciX2dyTGGFOeHTp+lj9/tZ2FW4/QtsElzLv1Sno0qxPosPJkicQYY0qQcxlZvLdqP698v4csVaYMvZR7+rWkcsWS2xNhicQYY0qIn/YmMvWLbUQfO8U17Rvw9PUdaFq3WqDDKpQlEmOMCbBjJ1J57usdLNh0iKZ1q/Lu7RFc3b5BoMPymiUSY4wJkIzMLGatPsA/v9vNuYwsHhrUmvsHti72X6b7yhKJMcYEQGRMMk99vpWdR05yVdt6PDOiIy1CC/6xcUlVcntvyriBAweyaNGiHOtefvllfve73wGwbds2Bg0axKWXXkqrVq14+umnycrKAn49tHvXrl3Zvn37r85xIRISEs4PEpn9Q8O8TJs2jZdeegmAiRMnnh96xRjjnaRTaUz5dBOj31xNytl0/j2+O7PuuLzUJhGwRBIw48aNY86cOTnWzZkzh3HjxnH27FlGjBjBE088wa5du9iyZQvr1q3jX//61/myY8aMOf8L9KioKDp06JDvuZYvX87EiRMLjOf777/nsssu4+eff6Zfv34+1c0Y82uZWcp/1hxg0N9/YP7P8dzbvyVLHu3PtZc1KvUzc1oiCZDRo0fz9ddfc+7cOQBiYmI4dOgQ/fr146OPPjo/Si9AtWrVeO2113jxxRf9EktUVBSPPfYYX3zxBV27duXs2bM5Jt2aN29eoYnIGJO/TbHHueGNVTz1+VbaN6rBwof78eS17alepWz0LpSNWvhq4RNwZEvRHrPhZXDt8/lurlu3Lj179mThwoWMHDmSOXPmcMsttyAibNu2jR49euQo36pVK86ePcvx48eBnEO7A6xevbrAEYEL0rVrV5599tkcw9EbY3yXfPocLy3excfrDhJ6SRX+NbYrI7o0LvVXILlZIgmg7Oat7ETy7rvver2vN7MW9urVi7S0NE6dOkVycvL5uU+mT5/+q9GAjTFFJz0zi9mrD/Dykt2cPpfJxCub88jgtsU2tElxs0QCBV45+NPIkSN55JFH2LhxI2fOnDl/FdKhQwdWrMg5e/C+ffsICQmhdu3aXh8/e2DE5cuXM3PmTGbOnOn1vp5/MaWm+n/OZ2PKihW7E3j2q+1EHztFvzahTB3egTYNagQ6LL+yPpIAuuSSSxg4cCB33nkn48aNO79+/PjxrFy5kiVLlgDOTIoPPfQQzzzzTLHF1qBBA3bs2EFWVhbz588vtvMaU1rtTzzN3bPWM+G9daRnZvH2hAg+uLNnmU8iYIkk4MaNG8emTZtyJJKqVauyYMEC/vKXv9C2bVtCQ0Pp06cP48ePP18me5727MdPP/1UpHE9//zzDB8+nCuvvJJGjRoV6bGNKUtOpqbzt4U7GPLPH1i9N4knrm3H4keuYnCHBmWuLyQ/Nox8KfD555/z6KOPsmzZMpo1axbocMq80vTZMIGTlaXM2xjHC9/uIvFUGjf3CGPKsEupXyO48J1LCRtGvgwZNWoUo0aNCnQYxhjXhgPJTFuwnS3xKXQLr827t0fQpan3/ZdljSUSY4zx0uGUszy/cCdfRB2iQc0qvDymKyO7lr3beS+UX/tIRGSYiOwSkWgReSKP7VVEZK67fa2INHfX9xSRKPexSURu8PaYxhhT1FLTM3n1+z0MeukHFm49wuSBrVn6+wGM6tak3CcR8OMViYgEAa8Dg4E4YL2ILFBVz0Gh7gJ+UdXWIjIWmA6MAbYCEaqaISKNgE0i8iWgXhzTGGOKRFaW8uXmQ7zw7S7ij5/l2k4N+X+/aV8q5ggpTv5s2uoJRKvqPgARmQOMBDy/9EcC09zlecBrIiKqesajTDBOAvH2mMYY47O1+5L46zc72BSXQvtGNXlxdGeubB0a6LBKJH8mkiZArMfzOKBXfmXcq48UIARIFJFewHtAM+A2d7s3xwRARCYBkwDCw8N9r40xplzYl3CK5xfuZPH2ozSsGcxLN3fhhm5NCKpgTVj5KbGd7aq6FugoIu2BWSKy8AL3nwHMAOf2Xz+EaIwpQ5JOpfHK93v4cO1BqlSswB+GtOWuvi2pWrl0TTIVCP7sbI8Hmno8D3PX5VlGRCoCtYAkzwKqugM4BXTy8pilQkmbj8RXx48f54033jj//NChQ4wePbrAfQYMGEDu3/d4o3nz5iQmJnpdfubMmUyePPmCz2PKh9T0TN5YHs2AF5fzn7UHGduzKcunDGTyoDaWRLzkz0SyHmgjIi1EpDIwFliQq8wC4HZ3eTSwVFXV3acigIg0A9oBMV4es1QoafOR+CIjI+NXiaRx48Y26ZUp0bKylM82xjHopeW88O0uerWsy6L/68dzoy6jXo0qgQ6vVPFb05bbpzEZWAQEAe+p6jYReRaIVNUFwLvAbBGJBpJxEgNAX+AJEUkHsoD7VTURIK9j+hrr9HXT2Zm809fD5NCubjse7/l4vttHjx7NU089xblz56hcuXKO+Ujee++9POcj6devH4888kiRxplt4sSJBAcHExkZyYkTJ/jHP/7B8OHDiYmJ4bbbbuP06dMAvPbaa1x55ZUsX76cP/3pT9SpU4edO3fSvXt39u7dS9euXRk8eDAPPPAAw4cPZ+vWrWRmZvL444/z7bffUqFCBe655x4efPDBHOdfvHgxTz/9NGlpabRq1Yr3338/x5woub366qt8+eWXpKen8+mnn9KuXTuSk5O588472bdvH9WqVWPGjBl07tw5x34JCQncd999HDx4EHCuAvv06VPEr6Yp6X7am8hfv9nB1vgTXNakFn+/pSu9W4UEOqxSy699JKr6DfBNrnVTPZZTgZvz2G82MNvbY5ZGJWk+kmwxMTGsW7eOvXv3MnDgQKKjo6lfvz7fffcdwcHB7Nmzh3Hjxp1vjtq4cSNbt26lRYsWxMTEsHXrVqKios4fK9uMGTOIiYkhKiqKihUrkpycnOO8iYmJPPfccyxZsoTq1aszffp0/vGPfzB16lTyExoaysaNG3njjTd46aWXeOedd3j66afp1q0bn3/+OUuXLmXChAnn48n28MMP88gjj9C3b18OHjzI0KFD2bFjh0+vmyk9oo+d5G/f7OT7ncdoUrsqL49x5gepYB3pPimxne3FqaArB38qafOR3HLLLVSoUIE2bdrQsmVLdu7cSYsWLZg8eTJRUVEEBQWxe/fu8+V79uxJixYtCo11yZIl3HfffVSs6Hzc6tatm2P7mjVr2L59+/krg3PnztG7d+8Cj3njjTcC0KNHDz777DMAVq5cyX//+18ABg0aRFJSEidOnPhVLJ79SSdOnODUqVMFXv2Y0u/YiVT+9f0e5qyPpVqlIB4f1o47+jQnuJL1gRQFSyQBVNLmI8n9C10R4Z///CcNGjRg06ZNZGVlERz8vwHpqlev7nUsBVFVBg8ezMcff+z1PlWqOG3YQUFBZGRkeL1fVlYWa9asyVEPU3alnE3nrR/28v6qGNIzs7jtimY8OKg1IZdYH0hRsmHkA6ikzUfy6aefkpWVxd69e9m3bx+XXnopKSkpNGrUiAoVKjB79mwyMzPz3LdGjRqcPHkyz22DBw/mrbfeOv+Fn7tp64orrmDVqlVER0cDcPr06RxXPt7q168fH374IeAkz9DQUGrWrJmjzJAhQ3j11VfPP8/d9GXKhrPnMnnzh71c9cIy3li+l8EdGrDk0f5MG9HRkogfWCIJsJI0H0l4eDg9e/bk2muv5c033yQ4OJj777+fWbNm0aVLF3bu3JnvVUhISAh9+vShU6dOTJkyJce2u+++m/DwcDp37kyXLl346KOPcmyvV68eM2fOZNy4cXTu3JnevXuzc+eF3/wwbdo0NmzYQOfOnXniiSeYNWvWr8q88sorREZG0rlzZzp06MCbb755wecxJVd6ZhYfrj1A/xeX8fzCnXQPr83XD/XllXHdaB5aNFfQ5tdsPpJSoDjmI5k4cSLDhw8v9Lcf5UFp+mwYR1aW8tWWw/xj8S5iks4Q0awOjw1rR88WdQvf2eTL5iMpQ2w+EmPypqos353Ai9/uYvvhE7RrWIN3b49gULv6NipvMbJEYgAK7YgPhBtuuIH9+/fnWJffHWem/NlwIJnp3+5i3f5kmtZ1buW9vktjGxMrAMp1IlFV+6ulBJs/f36xn7M8NPWWdjuPnOClRbtYsuMYoZdU4c8jOzLm8nAqV7Qu30Apt4kkODiYpKQkQkJCLJkYwEkiSUlJdmtwCXUw6QwvL9nN/Kh4LqlSkSlDL+WOPs2pVrncfo2VGOX2HQgLCyMuLo6EhIRAh2JKkODgYMLCwgIdhvEQm3yG15dFM29DHEEVhElXteR3/VtRu1rlQIdmXOU2kVSqVMmrX2UbYwIj/vhZXl8WzaeRsQjCb69oxu8GtKJBTbtiLGnKbSIxxpRMh1PO8sayvcxdH4uijL08nPsHtqJRLd/GkjP+Y4nEGFMiHDuRyhvL9/LRuoNkZSm3XN6UBwa2pkltSyAlnSUSY0xAJZxM480f9vKfNQfIyFJu7hHGAwNb07RutUCHZrxkicQYExBJp9J4a8U+PlgdQ3qmckO3Jjw4qDXNQmwok9LGEokxplglnz7HDDeBpKZnMqprEx68ug0tbCysUssSiTGmWCSdSuPdlfuZ9VMMZ9IzGdGlMQ9d3YZW9WwumNLOEokxxq+Onkjl7RX7+HDtQVIzMrnuskY8fHUb2jSoEejQTBGxRGKM8Yu4X87w5g97+SQyjswsZWTXxtw/oDWt69sVSFnj10QiIsOAfwFBwDuq+nyu7VWAD4AeQBIwRlVjRGQw8DxQGTgHTFHVpe4+y4FGwFn3MENU9Zg/62GM8d7+xNO8sSya+T/HIwKjezTld/1bER5id2GVVX5LJCISBLwODAbigPUiskBVt3sUuwv4RVVbi8hYYDowBkgErlfVQyLSCVgENPHYb7yq5pxgxBgTULuOnOT1ZdF8tfkQlYIq8NsrmnFv/5b2Q8JywJ9XJD2BaFXdByAic4CRgGciGQlMc5fnAa+JiKjqzx5ltgFVRaSKqqb5MV5jzEXYEpfCa8v2sGjbUapXDuKeq1pyd9+W1KthU9qWF/5MJE2AWI/ncUDo7NsXAAAesElEQVSv/MqoaoaIpAAhOFck2W4CNuZKIu+LSCbwX+A5zWPsbxGZBEwCZwpZY0zR2nAgmVeXRrN8VwI1gyvy0NVtuOPK5tSpboMpljclurNdRDriNHcN8Vg9XlXjRaQGTiK5DaefJQdVnQHMAGeq3WII15gyT1X5aW8Sry2NZvW+JOpWr8yUoZdyW+9m1AyuFOjwTID4M5HEA009noe56/IqEyciFYFaOJ3uiEgYMB+YoKp7s3dQ1Xj335Mi8hFOE9qvEokxpuhkZinfbj3CWyv2sjkuhfo1qvDUde25tVe4zQdi/JpI1gNtRKQFTsIYC9yaq8wC4HZgNTAaWKqqKiK1ga+BJ1R1VXZhN9nUVtVEEakEDAeW+LEOxpRrqemZzNsQx9s/7uNA0hlahFbnrzdcxo3dmxBcKSjQ4ZkSwm+JxO3zmIxzx1UQ8J6qbhORZ4FIVV0AvAvMFpFoIBkn2QBMBloDU0VkqrtuCHAaWOQmkSCcJPK2v+pgTHl1/Mw5/rPmADN/iiHx1Dm6NK3Nk9e2Y3CHhjYnuvkVKQ9zVEdERGhkpN0tbExhDh0/y7sr9/PxuoOcOZfJgEvrcV//VvRqUdempC6HRGSDqkYUVs4aN40x7DpykrdW7GVB1CEUGNGlMZOuakn7RjUDHZopBSyRGFNOqSrr9ifz5g97WbYrgaqVgritdzPu6tuCsDr2K3TjPUskxpQzmVnKd9uP8uYPe4mKPU5I9cr8fnBbfntFM/sNiLkolkiMKSdOpWXwaWQsM3+K4UDSGcLrVuPPozpxc48wuwPL+MQSiTFlXPzxs8z6KYaP1x3kZGoG3cNr89jQdgzt2ICKQRUCHZ4pAyyRGFNGbTz4C++u3M+3W48AcG2nhtzVtwXdwusEODJT1lgiMaYMycjMYtG2o7yzch8/HzxOjeCK3N23BROubE6T2jYKr/EPSyTGlAEnUtOZu87p/4g/fpZmIdWYdn0Hbo5oSvUq9t/c+Jd9wowpxQ4kneb9VTF8GhnL6XOZ9GpRl6ev78DV7RvYL9BNsbFEYkwpo6qs3Z/M+6v2s3j7UYJEuL5LY+7q24JOTWoFOjxTDlkiMaaUOJ2WwedR8Xzw0wF2HT1J7WqVuH9AKyb0bk6DmsGBDs+UY5ZIjCnh9ieeZvbqA3y6IZaTqRl0bFyTF0Z3ZkSXxvb7D1MiWCIxpgTKzFJ+2H2MWT8d4IfdCVQKEn5zWSMm9G5O9/DaNoCiKVEskRhTghw/c45PI+OYveYAB5PP0KBmFR4d3JaxPZtSv4Y1X5mSyRKJMSXA9kMn+GB1DJ9HxZOankXP5nV5bNilDO3YkEr263NTwlkiMSZA0jOz+HbrET5YHcP6mF8IrlSBG7o14bYrmtOhsQ3fbkoPSyTGFLPY5DN8vO4gn0TGkXgqjfC61Xjquvbc3KMptapVCnR4xlwwSyTGFIOMzCy+33mMj9YeZMWeBAQY1K4+43s1o3/belSwHw+aUswSiTF+FH/8LHPXHWRuZCxHT6TRoGYVHhzUhrGXN6WxjX1lygi/JhIRGQb8CwgC3lHV53NtrwJ8APQAkoAxqhojIoOB54HKwDlgiqoudffpAcwEqgLfAA9reZh43pQamVnK8l3O1ceyXcdQoH/bevx5ZDiD2tW3odtNmeO3RCIiQcDrwGAgDlgvIgtUdbtHsbuAX1S1tYiMBaYDY4BE4HpVPSQinYBFQBN3n38D9wBrcRLJMGChv+phjLeOnkhl7vpY5q6PJf74WerVqMLvBrRi7OXhNK1rU9eassurRCIinwHvAgtVNcvLY/cEolV1n3uMOcBIwDORjASmucvzgNdERFT1Z48y24Cq7tVLXaCmqq5xj/kBMApLJCZAsrKUH6MT+XDNAb7feYzMLKVfm1Ceuq4913RoYLfumnLB2yuSN4A7gFdE5FPgfVXdVcg+TYBYj+dxQK/8yqhqhoikACE4VyTZbgI2qmqaiDRxj+N5zCbkQUQmAZMAwsPDCwnVmAsTf/ws8yLj+HRDLHG/nCWkemXu7teCcZeH0zy0eqDDM6ZYeZVIVHUJsEREagHj3OVY4G3gP6qa7o/gRKQjTnPXkAvdV1VnADMAIiIirA/F+CwtI5PF247ySWQsK6MTUYW+rUN5bJgzbW2VijbulSmfvO4jEZEQ4LfAbcDPwIdAX+B2YEAeu8QDTT2eh7nr8ioTJyIVgVo4ne6ISBgwH5igqns9yocVckxjitT2Qyf4JDKWz6PiOX4mnSa1q/LQoDaM7hFmfR/G4H0fyXzgUmA2Tif4YXfTXBGJzGe39UAbEWmB82U/Frg1V5kFOIloNTAaWKqqKiK1ga+BJ1R1VXZhVT0sIidE5AqczvYJwKve1MGYC5FyJp0Fm+KZGxnL1vgTVA6qwJCODRhzeVOubBVqk0YZ48HbK5JXVHVZXhtUNSKf9RkiMhnnjqsg4D1V3SYizwKRqroApwN/tohEA8k4yQZgMtAamCoiU911Q1T1GHA//7v9dyHW0W6KSFaWsnpfEnPXx/LttiOcy8iifaOaTLu+A6O6NaF2tcqBDtGYEkm8+QmGiNyYx+oUYIv75V6iRUREaGRkfhdOprzL3XFeM7gio7o14ZaIpjbjoCnXRGRDfhcLnry9IrkL6A1kX5UMADYALUTkWVWdfVFRGhMgp9IyWLjlMPN/jmf1viRUoU/rEKYMdUbctQmjjPGet4mkEtBeVY8CiEgDnF+k9wJW4PSdGFOiZWYpq6IT+WxjHN9uO0JqehbNQqrx8NVtuKm7dZwbc7G8TSRh2UnEdQxoqqrJIuKXW3+NKSq7jpzks41xfB4Vz9ETadQMrsiN3cO4qXsTuofXsdkGjfGRt4lkuYh8BXzqPr/JXVcdOO6XyIzxQcLJNBZsOsRnG+PYdugEFSsIAy6tx9PXhzGoXX1rujKmCHmbSB4AbsT53Qg4zVr/dQdLHOiPwIy5UKnpmSzZcZTPNsbzw+4EMrOUzmG1ePr6DlzfpTGhl1QJdIjGlEmFJhJ38MUlqjoQ+K//QzLGe1lZytr9yXwRFc/XWw5zMjWDhjWDmXRVS27s1oQ2DWoEOkRjyrxCE4mqZopIlojUUtWU4gjKmIKoKlviU1gQdYgvNx/i6Ik0qlUOYlinhtzUPYwrWobYDwaNKUbeNm2dAraIyHfA6eyVqvqQX6IyJg/Rx06xYNMhvtx0iP2Jp6kUJPRvW58/XteYa9rXp1plm6fNmEDw9n/eZ+7DmGJ16PhZvtx0iAWbDrHt0AlEoHfLEO69qiXDOjW0X5sbUwJ4O/rvLBGpCoR7MXy8MT5JPn2Or7cc5suoQ6yLSQagS1gt/jS8A8M7N6JBzeAAR2iM8eTtoI3XAy/hTH3bQkS6As+q6gh/BmfKj1NpGXy3/QgLog7x455EMrKUVvWq8+jgtozo0tjm+DCmBPO2aWsazoyHywFUNUpEWvopJlNOnErL4PsdR/lq82F+2J3AuYwsmtSuyl39WjCiS2M6NKppPxY0phTwNpGkq2pKrv/U3k65a8x5J1PT+X7HMb7e8r/k0aBmFW7tGc51nRvRI7wOFeyOK2NKFW8TyTYRuRUIEpE2wEPAT/4Ly5QlJ1PTWbLjKF9vPsKKPTmTx/DOjehuycOYUs3bRPIg8EcgDfgYZ46RP/srKFP65UgeuxM4l+kkj/G9wrnuMksexpQl3t61dQYnkfzRv+GY0uxEajrf7zjK15sPs2J3Iucys2hYM5jxV1jyMKYs8/aurbbAH4Dmnvuo6iD/hGVKi2MnU/lu+1EWbTvK6r2JpGcqDWsG89srmnFd54Z0a2rJw5iyztumrU+BN4F3gEz/hWNKgwNJp1m07QiLth1l48FfUIXwutWYeGVzhnWy5GFMeeNtIslQ1X/7NRJTYqkq2w+fYNG2oyzedoSdR04C0L5RTR6+ug1DOzakXcMadquuMeWUt4nkSxG5H5iP0+EOgKomF7STiAwD/gUEAe+o6vO5tlfBGZK+B5AEjFHVGBEJAeYBlwMzVXWyxz7LgUbAWXfVkNIwb3xpk5mlbDz4C4u2HmHR9iPEJp9FBCKa1eGp69oztGNDm1HQGAN4n0hud/+d4rFOgXx/lOgOP/86MBiIA9aLyAJV3e5R7C7gF1VtLSJjgenAGCAV+BPQyX3kNl5VI72M3XgpNT2T1XuTWLz9CN9tP0riqXNUDqpAn9YhPDCgNVe3b0C9GjanhzEmJ2/v2mpxEcfuCUSr6j4AEZkDjAQ8E8lInF/Ng3MF8pqIiKqeBlaKSOuLOK+5AMdOprJs5zGW7DjGyj2JnE3PpHrlIAa2q8/Qjg0ZcGk9agRXCnSYxpgSrMBEIiKPqeoL7vLNqvqpx7a/qur/K2D3JkCsx/M4oFd+ZVQ1Q0RSgBAgsZC43xeRTJyJtp5zZ2rMHfskYBJAeHh4IYcrP7L7O5buOMaSncfYFOvMlNy4VjCje4Rxdfv6XNEyxKaiNcZ4rbArkrHAC+7yk/xvznaAYUBBicRfxqtqvIjUwEkkt+H0s+SgqjOAGQARERG/SjTlSWp6Jqv3JfH9jqMs3XGMQympiECXsNr8fnBbrm7fgPaNrLPcGHNxCkskks9yXs9ziweaejwPc9flVSZORCoCtXA63fOlqvHuvydF5COcJrRfJZLyLuFkmttkdZSV0YmcOZdJ1UpB9GsTyv9d05aB7epbf4cxpkgUlkg0n+W8nue2HmgjIi1wEsZY4NZcZRbgdOSvBkYDS/NqpsrmJpvaqpooIpWA4cCSQuIoF7KylM3xKSzfdYzluxLYFHccVafJ6qbuYQxqX5/e1mRljPGDwhJJFxE5gXP1UdVdxn1e4OxCbp/HZJxxuYKA91R1m4g8C0Sq6gLgXWC2iEQDyTjJxjmBSAxQE6gsIqOAIcABYJGbRIJwksjbF1LhsiTpVBor9iTww64EVuxJJPn0ufNNVo9eY01WxpjiIQVcAJQZERERGhlZ+u8WzsxSNsUdZ/muBH7YdYzN8SmoQkj1yvRvW4/+l9ajX5t61K1u088aY3wnIhtUNaKwct7+jsQESOKpNFbsTmD5rgR+3JPAL2fSqSDQtWltHrmmLQMurUenxrVsSBJjTMBYIilh0jOziIo9zo+7E1i+O4HNcSkAhF5SmYHt6jPg0vr0ax1KHbvqMMaUEJZIAkxV2ZtwmpV7ElgZnciafcmcSsuggkC38Dr8fnBbBlxan46Na9pVhzGmRLJEEgBJp9JYGZ3Iyj2JrIpO5FBKKuCMoDuia2P6tQ7lylah1Kpmvyg3xpR8lkiKQWp6Jutjklm5J5Ef9ySy/bBz81vN4Ir0aR3KA4NC6de6HuEhNgiiMab0sUTiB5lZyo7DJ1gVncjK6ETW7U8mLSOLSkFC9/A6/GFIW/q2qcdlTWoRZM1VxphSzhJJEcjKUnYfO8nqvUms3pvE2v3JpJxNB6Btg0sY36sZ/dqE0rNFXapXsZfcGFO22LfaRcjuIF+9L4k1e5NYvS+J5NPnAKefY1jHhvRuFULvViE0qFng7zaNMabUs0TiBVXlYPIZ54pjn3PVceykM79Xo1rBDLi0Hr1bOokjrI71cxhjyhdLJAWY/3McK/cksXrv/+6sCr2kCr1bhXBlqxB6twyhWUg1G4LEGFOuWSIpwNsr9nM45SxXtAzhvgFO8mhV7xJLHMYY48ESSQFm3nk5odWr2A8BjTGmAJZIClC/hnWUG2NMYSoEOgBjjDGlmyUSY4wxPrFEYowxxieWSIwxxvjEEokxxhifWCIxxhjjE78mEhEZJiK7RCRaRJ7IY3sVEZnrbl8rIs3d9SEiskxETonIa7n26SEiW9x9XhH7daAxxgSU3xKJiAQBrwPXAh2AcSLSIVexu4BfVLU18E9gurs+FfgT8Ic8Dv1v4B6gjfsYVvTRG2OM8ZY/r0h6AtGquk9VzwFzgJG5yowEZrnL84CrRURU9bSqrsRJKOeJSCOgpqquUVUFPgBG+bEOxhhjCuHPRNIEiPV4Hueuy7OMqmYAKUBIIceMK+SYxhhjilGZ7WwXkUkiEikikQkJCYEOxxhjyix/JpJ4oKnH8zB3XZ5lRKQiUAtIKuSYYYUcEwBVnaGqEaoaUa9evQsM3RhjjLf8mUjWA21EpIWIVAbGAgtylVkA3O4ujwaWun0feVLVw8AJEbnCvVtrAvBF0YdujDHGW34b/VdVM0RkMrAICALeU9VtIvIsEKmqC4B3gdkiEg0k4yQbAEQkBqgJVBaRUcAQVd0O3A/MBKoCC92HMcaYAJECLgDKjIiICI2MjAx0GMYYU6qIyAZVjSisXJntbDfGGFM8LJEYY4zxiSUSY4wxPrFEYowxxieWSIwxxvjEEokxxhifWCIxxhjjE0skxhhjfGKJxBhjjE8skRhjjPGJJRJjjDE+sURijDHGJ5ZIjDHG+MQSiTHGGJ9YIjHGGOMTSyTGGGN8YonEGGOMTyyRGGOM8YklEmOMMT6xRGKMMcYnfk0kIjJMRHaJSLSIPJHH9ioiMtfdvlZEmntse9Jdv0tEhnqsjxGRLSISJSKR/ozfGGNM4Sr668AiEgS8DgwG4oD1IrJAVbd7FLsL+EVVW4vIWGA6MEZEOgBjgY5AY2CJiLRV1Ux3v4Gqmuiv2I0xxnjPn1ckPYFoVd2nqueAOcDIXGVGArPc5XnA1SIi7vo5qpqmqvuBaPd4xhhjShh/JpImQKzH8zh3XZ5lVDUDSAFCCtlXgcUiskFEJuV3chGZJCKRIhKZkJDgU0WMMcbkrzR2tvdV1e7AtcADInJVXoVUdYaqRqhqRL169Yo3QmOMKUf8mUjigaYez8PcdXmWEZGKQC0gqaB9VTX732PAfKzJyxhjAsqfiWQ90EZEWohIZZzO8wW5yiwAbneXRwNLVVXd9WPdu7paAG2AdSJSXURqAIhIdWAIsNWPdTDGGFMIv921paoZIjIZWAQEAe+p6jYReRaIVNUFwLvAbBGJBpJxkg1uuU+A7UAG8ICqZopIA2C+0x9PReAjVf3WX3UwxhhTOHEuAMq2iIgIjYy0n5wYY8yFEJENqhpRWLnS2NlujDGmBLFEYowxxieWSIwxxvjEEokxxhifWCIxxhjjE0skxhhjfGKJxBhjjE8skRhjjPGJJRJjjDE+sURijDHGJ5ZIjDHG+MQSiTHGGJ9YIjHGGOMTSyTGGGN8YonEGGOMTyyRGGOM8YklEmOMMT6xRGKMMcYnlkiMMcb4xK+JRESGicguEYkWkSfy2F5FROa629eKSHOPbU+663eJyFBvj2mMMaZ4+S2RiEgQ8DpwLdABGCciHXIVuwv4RVVbA/8Eprv7dgDGAh2BYcAbIhLk5TGNMcYUo4p+PHZPIFpV9wGIyBxgJLDdo8xIYJq7PA94TUTEXT9HVdOA/SIS7R4PL45ZZB784EpiM07549DGGFMsPhm/ispVavj1HP5MJE2AWI/ncUCv/MqoaoaIpAAh7vo1ufZt4i4XdkwARGQSMAkgPDz8oioQVjWUSqlBF7WvMcaUBFIMXeH+TCQBpaozgBkAERERejHHePzmBUUakzHGlEX+TFXxQFOP52HuujzLiEhFoBaQVMC+3hzTGGNMMfJnIlkPtBGRFiJSGafzPPef+AuA293l0cBSVVV3/Vj3rq4WQBtgnZfHNMYYU4z81rTl9nlMBhYBQcB7qrpNRJ4FIlV1AfAuMNvtTE/GSQy45T7B6UTPAB5Q1UyAvI7przoYY4wpnDgXAGVbRESERkZGBjoMY4wpVURkg6pGFFbOftlujDHGJ5ZIjDHG+MQSiTHGGJ9YIjHGGOOTctHZLiIJwIGL3D0USCzCcEoDq3P5UN7qXN7qC77VORFAVYcVVrBcJBJfiEikN3ctlCVW5/KhvNW5vNUXiq/O1rRljDHGJ5ZIjDHG+MQSSeFmBDqAALA6lw/lrc7lrb5QTHW2PhJjjDE+sSsSY4wxPrFEYowxxieWSFwiMkxEdolItIg8kcf2iSKSICJR7uPuQMRZVAqrr1vmFhHZLiLbROSj4o6xqHnxHv/T4/3dLSLHAxFnUfKizuEiskxEfhaRzSLym0DEWZS8qHMzEfnere9yEQkLRJxFRUTeE5FjIrI1n+0iIq+4r8dmEele5EGoarl/4AxJvxdoCVQGNgEdcpWZCLwW6FiLsb5tgJ+BOu7z+oGO2991zlX+QZxpCgIeu5/f5xnA79zlDkBMoOMuhjp/CtzuLg8CZgc6bh/rfBXQHdiaz/bfAAsBAa4A1hZ1DHZF4ugJRKvqPlU9B8wBRgY4Jn/ypr73AK+r6i8AqnqsmGMsahf6Ho8DPi6WyPzHmzorUNNdrgUcKsb4/MGbOncAlrrLy/LYXqqo6gqc+ZzyMxL4QB1rgNoi0qgoY7BE4mgCxHo8j3PX5XaTe2k4T0Sa5rG9tPCmvm2BtiKySkTWiEihwySUcN6+x4hIM6AF//uyKa28qfM04LciEgd8g3MlVpp5U+dNwI3u8g1ADREJKYbYAsXrz/7FskTivS+B5qraGfgOmBXgePytIk7z1gCcv87fFpHaAY2o+IwF5qk7K2cZNw6YqaphOE0gs0WkrH8v/AHoLyI/A/2BeKA8vNd+U9Y/MN6KBzyvMMLcdeepapKqprlP3wF6FFNs/lBofXH+almgqumquh/YjZNYSitv6pxtLKW/WQu8q/NdwCcAqroaCMYZ6K+08ub/8iFVvVFVuwF/dNeV+hsrCnAhn/2LYonEsR5oIyItRKQyzhfJAs8CudoURwA7ijG+olZofYHPca5GEJFQnKaufcUZZBHzps6ISDugDrC6mOPzB2/qfBC4GkBE2uMkkoRijbJoefN/OdTjqutJ4L1ijrG4LQAmuHdvXQGkqOrhojxBxaI8WGmlqhkiMhlYhHPXx3uquk1EngUiVXUB8JCIjAAycDq2JgYsYB95Wd9FwBAR2Y5z2T9FVZMCF7VvvKwzOF88c9S93aU087LOv8dptnwEp+N9Ymmuu5d1HgD8TUQUWAE8ELCAi4CIfIxTp1C3r+tpoBKAqr6J0/f1GyAaOAPcUeQxlOLPjDHGmBLAmraMMcb4xBKJMcYYn1giMcYY4xNLJMYYY3xiicQYY4xPLJGYUklETnlR5v9EpFoRnnOUiHQowuP95MO+p9x/G4vIvALK1RaR+y/2PMZ4wxKJKcv+D7igRCIiQQVsHoUz4F+RUNUri+AYh1R1dAFFagOWSIxfWSIxpZqIDHDnlJgnIjtF5EP3F7wPAY2BZSKyzC07RERWi8hGEflURC5x18eIyHQR2QjcLCL3iMh6EdkkIv8VkWoiciXOiAYvuvOVtBKRru6AlptFZL6I1HGPt1ycuU0iRWSHiFwuIp+JyB4Rec4j9lMey4+LyBb3nM/nUc8Wbuxbch2jefY8FCLSUUTWufFtFpE2wPNAK3fdiyJyiThzcWx0jzXS4zg7RORtceafWSwiVd1trUVkiRvbRhFp5a6f4r5Om0XkmSJ9Y03pEuix9O1hj4t5AKfcfwcAKTjjB1XAGdqkr7stBgh1l0NxfsVc3X3+ODDVo9xjHscO8Vh+DnjQXZ4JjPbYthno7y4/C7zsLi8HprvLD+MMzd4IqIIzhllIrjpcC/wEVHOf182jvguACe7yAx77NsedhwJ4FRjvLlcGqnpud9dXBGp6vCbROPNUNMcZtaGru+0T4Lfu8lrgBnc5GOcqbwjOXCbivu5fAVcF+nNhj8A8bIgUUxasU9U4ABGJwvlSXJmrzBU4zVKrRAScL1rP8bTmeix3cv/qrw1cgjPcRg4iUguorao/uKtm4UyYlC17yJUtwDZ1xzYSkX04A+h5DjdzDfC+qp4BUNW85pboA9zkLs8GpudRZjXwR3Fm/PtMVfe4dc0ROvBXEbkKyMIZTryBu22/qka5yxuA5iJSA2iiqvPd2FLdegzBSSY/u+UvwRnUc0UecZkyzhKJKQvSPJYzyftzLcB3qjoun2Oc9lieCYxS1U0iMhF38MqLjCkrV3xZ+cTnjQLHM1LVj0RkLXAd8I2I3MuvB9ocD9QDeqhquojE4FxleMYMzutYtYDTCfA3VX3rAuI3ZZT1kZiy7CRQw11eA/QRkdYAIlJdRNrms18N4LCIVML54v3V8VQ1BfhFRPq5224DfuDifAfckX2HmYjUzaPMKpwBJckV03ki0hLYp6qvAF8Ancn5GoAzC+IxN4kMBJoVFJiqngTiRGSUe44qbpyLgDs9+pmaiEh9r2pryhxLJKYsmwF8KyLLVDUBZ8Tmj0VkM04zULt89vsTTr/AKmCnx/o5wBQR+dntcL4dp/N9M9AVp5/kgqnqtzhNYZFu09wf8ij2MPCAiGwh/9ntbgG2usfohDO9ahJOc95WEXkR+BCIcI8zIVf98nMbzujXm3H6chqq6mLgI2C1e6x55ExYphyx0X+NMcb4xK5IjDHG+MQSiTHGGJ9YIjHGGOMTSyTGGPP/26tjAQAAAIBB/taD2FsSsYgEgEUkACwiAWAJUNxQ5cZBKfYAAAAASUVORK5CYII=\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.plot(distances, np.subtract(hf_energies, energies[0][1]), label='Hartree-Fock')\n", - "for k in range(len(transformations)):\n", - " pylab.plot(distances, np.subtract(energies[k][0], energies[k][1]), label='VQE + '+transformations[k])\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Energy')\n", - "pylab.title('Energy difference from ExactEigensolver')\n", - "pylab.legend(loc='upper left');" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "for k in range(len(transformations)):\n", - " pylab.plot(distances, eval_counts[k], '-o', label='VQE + ' + transformations[k])\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Evaluations')\n", - "pylab.title('VQE number of evaluations')\n", - "pylab.legend(loc='upper left');" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "scrolled": true - }, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/chemistry/h2_qpe.ipynb b/community/chemistry/h2_qpe.ipynb deleted file mode 100644 index fc7e2b1e0..000000000 --- a/community/chemistry/h2_qpe.ipynb +++ /dev/null @@ -1,232 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## _*H2 ground state energy computation using Quantum Phase Estimation*_\n", - "\n", - "This notebook demonstrates using Qiskit Chemistry to compute ground state energy of the Hydrogen (H2) molecule using QPE (Quantum Phase Estimation) algorithm. Let's first look at how to carry out such computation programmatically. Afterwards, we will illustrate how the computation can also be carried out using json configuration dictionaries.\n", - "\n", - "This notebook has been written to use the PYSCF chemistry driver." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We first set up the H2 molecule, create the fermionic and in turn the qubit operator using PySCF." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "from collections import OrderedDict\n", - "import time\n", - "\n", - "from qiskit import BasicAer\n", - "from qiskit.transpiler import PassManager\n", - "from qiskit.aqua import AquaError\n", - "from qiskit.aqua import QuantumInstance\n", - "from qiskit.aqua.algorithms import ExactEigensolver\n", - "from qiskit.aqua.algorithms import QPE\n", - "from qiskit.aqua.components.iqfts import Standard\n", - "from qiskit.chemistry import FermionicOperator\n", - "from qiskit.chemistry import QiskitChemistry\n", - "from qiskit.chemistry.aqua_extensions.components.initial_states import HartreeFock\n", - "from qiskit.chemistry.drivers import PySCFDriver, UnitsType\n", - "\n", - "distance = 0.735\n", - "driver = PySCFDriver(atom='H .0 .0 .0; H .0 .0 {}'.format(distance),\n", - " unit=UnitsType.ANGSTROM, charge=0, spin=0, basis='sto3g')\n", - "molecule = driver.run()\n", - "\n", - "qubit_mapping = 'parity'\n", - "fer_op = FermionicOperator(h1=molecule.one_body_integrals, h2=molecule.two_body_integrals)\n", - "qubit_op = fer_op.mapping(map_type=qubit_mapping,threshold=1e-10).two_qubit_reduced_operator(2)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Using a classical exact eigenvalue solver, we can establish the reference groundtruth value of the ground state energy:" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The exact ground state energy is: -1.8572750302023817\n" - ] - } - ], - "source": [ - "exact_eigensolver = ExactEigensolver(qubit_op, k=1)\n", - "result_ee = exact_eigensolver.run()\n", - "reference_energy = result_ee['energy']\n", - "print('The exact ground state energy is: {}'.format(result_ee['energy']))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Next we set up the QPE algorithm instance using the HartreeFock initial state and a standard inverse quantum fourier transform, and execute:" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The ground state energy as computed by QPE is: -1.8571368753258866\n" - ] - } - ], - "source": [ - "num_particles = molecule.num_alpha + molecule.num_beta\n", - "two_qubit_reduction = True\n", - "num_orbitals = qubit_op.num_qubits + (2 if two_qubit_reduction else 0)\n", - "\n", - "num_time_slices = 50\n", - "n_ancillae = 9\n", - "\n", - "state_in = HartreeFock(qubit_op.num_qubits, num_orbitals,\n", - " num_particles, qubit_mapping, two_qubit_reduction)\n", - "iqft = Standard(n_ancillae)\n", - "\n", - "qpe = QPE(qubit_op, state_in, iqft, num_time_slices, n_ancillae,\n", - " expansion_mode='suzuki',\n", - " expansion_order=2, shallow_circuit_concat=True)\n", - "backend = BasicAer.get_backend('qasm_simulator')\n", - "quantum_instance = QuantumInstance(backend, shots=100, pass_manager=PassManager())\n", - "result_qpe = qpe.run(quantum_instance)\n", - "print('The ground state energy as computed by QPE is: {}'.format(result_qpe['energy']))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As can be easily seen, the QPE computed energy is quite close to the groundtruth value we computed earlier.\n", - "\n", - "Next we demonstrate how the same computation can be carried out using json dictionaries to drive the qiskit.chemistry stack. Such a dictionary can of course also be manipulated programmatically. An sibling notebook `h2_iqpe` is also provided, which showcases how the ground state energies over a range of inter-atomic distances can be computed and then plotted as well." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [], - "source": [ - "molecule = 'H .0 .0 0; H .0 .0 {}'.format(distance)\n", - "\n", - "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", - "qiskit_chemistry_qpe_dict = {\n", - " 'driver': {'name': 'PYSCF'},\n", - " 'PYSCF': {\n", - " 'atom': molecule, \n", - " 'basis': 'sto3g'\n", - " },\n", - " 'operator': {'name': 'hamiltonian', 'transformation': 'full', 'qubit_mapping': 'parity'},\n", - " 'algorithm': {\n", - " 'name': 'QPE',\n", - " 'num_ancillae': 9,\n", - " 'num_time_slices': 50,\n", - " 'expansion_mode': 'suzuki',\n", - " 'expansion_order': 2,\n", - " },\n", - " 'initial_state': {'name': 'HartreeFock'},\n", - " 'backend': {'shots': 100}\n", - "}\n", - "\n", - "qiskit_chemistry_ees_dict = {\n", - " 'driver': {'name': 'PYSCF'},\n", - " 'PYSCF': {'atom': molecule, 'basis': 'sto3g'},\n", - " 'operator': {'name': 'hamiltonian', 'transformation': 'full', 'qubit_mapping': 'parity'},\n", - " 'algorithm': {\n", - " 'name': 'ExactEigensolver',\n", - " }\n", - "}" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "With the two algorithms configured, we can then run them and check the results, as follows." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The groundtruth total ground state energy is -1.857275030202381.\n", - "The total ground state energy as computed by QPE is -1.857136875325887.\n", - "In comparison, the Hartree-Fock ground state energy is -1.8369679912029842.\n" - ] - } - ], - "source": [ - "result_qpe = QiskitChemistry().run(qiskit_chemistry_qpe_dict, backend=backend)\n", - "result_ees = QiskitChemistry().run(qiskit_chemistry_ees_dict)\n", - "\n", - "print('The groundtruth total ground state energy is {}.'.format(\n", - " result_ees['energy'] - result_ees['nuclear_repulsion_energy']\n", - "))\n", - "print('The total ground state energy as computed by QPE is {}.'.format(\n", - " result_qpe['energy'] - result_qpe['nuclear_repulsion_energy']\n", - "))\n", - "print('In comparison, the Hartree-Fock ground state energy is {}.'.format(\n", - " result_ees['hf_energy'] - result_ees['nuclear_repulsion_energy']\n", - "))" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/chemistry/h2_swaprz.ipynb b/community/chemistry/h2_swaprz.ipynb deleted file mode 100644 index 3bb2e2fc6..000000000 --- a/community/chemistry/h2_swaprz.ipynb +++ /dev/null @@ -1,208 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## _*H2 energy plot computed using SWAPRZ variational form*_\n", - "\n", - "This notebook demonstrates using Qiskit Chemistry to plot graphs of the ground state energy of the Hydrogen (H2) molecule over a range of inter-atomic distances using VQE and SWAPRZ. It is compared to the same energies as computed by the ExactEigensolver. `SWAPRZ` is a particle preserving variational form and should be used in conjunction with operator `jordan_wigner mapping` and `HarteeFock` initial state.\n", - "\n", - "This notebook populates a dictionary, that is a progammatic representation of an input file, in order to drive the Qiskit Chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here where we alter the molecule supplied to the driver in each loop.\n", - "\n", - "This notebook has been written to use the PYQUANTE chemistry driver. See the PYQUANTE chemistry driver readme if you need to install the external PyQuante2 library that this driver requires." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Processing step 20 --- complete\n", - "Distances: [0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.675 0.7 0.725 0.75 0.775\n", - " 0.8 0.825 0.85 0.875 0.9 0.925 0.95 0.975 1. ]\n", - "Energies: [[-1.05515972 -1.07591361 -1.09262986 -1.10591801 -1.11628597 -1.12416089\n", - " -1.12990475 -1.1338262 -1.13618944 -1.13722135 -1.13711706 -1.13604435\n", - " -1.13414767 -1.1315512 -1.12836187 -1.12467172 -1.12056028 -1.11609624\n", - " -1.11133942 -1.10634211 -1.10115033]\n", - " [-1.05515974 -1.07591361 -1.09262987 -1.10591802 -1.11628599 -1.12416089\n", - " -1.12990476 -1.1338262 -1.13618944 -1.13722136 -1.13711707 -1.13604436\n", - " -1.13414767 -1.13155121 -1.12836188 -1.12467175 -1.12056028 -1.11609624\n", - " -1.11133943 -1.10634212 -1.10115034]]\n", - "Hartree-Fock energies: [-1.04299622 -1.0630621 -1.0790507 -1.09157046 -1.10112822 -1.10814997\n", - " -1.11299652 -1.11597525 -1.11734902 -1.11734325 -1.11615145 -1.11393966\n", - " -1.1108504 -1.10700581 -1.10251056 -1.09745432 -1.09191405 -1.08595588\n", - " -1.07963694 -1.07300677 -1.06610866]\n", - "VQE num evaluations: [ 737. 710. 734. 793. 919. 804. 695. 731. 619. 727. 637. 743.\n", - " 708. 782. 701. 1032. 1051. 1119. 1141. 995. 884.]\n" - ] - } - ], - "source": [ - "import numpy as np\n", - "import pylab\n", - "import copy\n", - "from qiskit.chemistry import QiskitChemistry\n", - "\n", - "# Input dictionary to configure qiskit chemistry for the chemistry problem.\n", - "qiskit_chemistry_dict = {\n", - " 'problem': {'random_seed': 50},\n", - " 'driver': {'name': 'PYQUANTE'},\n", - " 'PYQUANTE': {'atoms': '', 'basis': 'sto3g'},\n", - " 'operator': {'name': 'hamiltonian', 'qubit_mapping': 'jordan_wigner',\n", - " 'two_qubit_reduction': False},\n", - " 'algorithm': {'name': ''},\n", - " 'optimizer': {'name': 'COBYLA', 'maxiter': 10000 },\n", - " 'variational_form': {'name': 'SWAPRZ'},\n", - " 'initial_state': {'name': 'HartreeFock'}\n", - "}\n", - "molecule = 'H .0 .0 -{0}; H .0 .0 {0}'\n", - "algorithms = ['VQE', 'ExactEigensolver']\n", - "\n", - "start = 0.5 # Start distance\n", - "by = 0.5 # How much to increase distance by\n", - "steps = 20 # Number of steps to increase by\n", - "energies = np.empty([len(algorithms), steps+1])\n", - "hf_energies = np.empty(steps+1)\n", - "distances = np.empty(steps+1)\n", - "eval_counts = np.empty(steps+1)\n", - "\n", - "print('Processing step __', end='')\n", - "for i in range(steps+1):\n", - " print('\\b\\b{:2d}'.format(i), end='', flush=True)\n", - " d = start + i*by/steps\n", - " qiskit_chemistry_dict['PYQUANTE']['atoms'] = molecule.format(d/2) \n", - " for j in range(len(algorithms)):\n", - " dict = copy.deepcopy(qiskit_chemistry_dict)\n", - " dict['algorithm']['name'] = algorithms[j]\n", - " if algorithms[j] == 'ExactEigensolver':\n", - " del dict['optimizer']\n", - " del dict['variational_form']\n", - " del dict['initial_state']\n", - " solver = QiskitChemistry()\n", - " result = solver.run(dict)\n", - " energies[j][i] = result['energy']\n", - " hf_energies[i] = result['hf_energy']\n", - " if algorithms[j] == 'VQE':\n", - " eval_counts[i] = result['algorithm_retvals']['eval_count']\n", - " distances[i] = d\n", - "print(' --- complete')\n", - "\n", - "print('Distances: ', distances)\n", - "print('Energies:', energies)\n", - "print('Hartree-Fock energies:', hf_energies)\n", - "print('VQE num evaluations:', eval_counts)\n" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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yhCVLltyzbcmSJTzxxBP06dOH8ePHEx4ezpEjR9i3bx/ffvttWrn008kHBQXRoEGDvA6/SNAJJRf8vd05FXmHI5eirB2KphV6AwYMYP369SQmGhe6O3v2LJcvX+bkyZNpMwIDODs7M3PmTL788ktrhlsk6ckhc6Fn40pMWn2UlYcu4eVRytrhaFre2TAerhwx7zkrNoYen2W6u0yZMvj6+rJhwwb69u3LkiVLGDRoEEePHqV58+b3lK1VqxZ3797l9u3bwL3TyQPs2bMny9mHtYejayi54FrMns71y7P28GWSUwzWDkfTCr30zV5LlixhyJAhOTru/iYvnUwsQ9dQcsnf250NIVfYceI6HeuVt3Y4mpY3sqhJWFLfvn159dVXOXjwIHFxcTRv3pxDhw6xffv2e8qdPn2asmXLUqqUbjnIS7qGkkuPeJanlLO9nopF0/JAiRIl6NixI88++2xa7WTYsGHs3LmTrVu3AsZVHV955RUmT55szVCLJJ1QcsnBzobeXpXYHHqF2IRka4ejaYXekCFDOHz4cFpCKVasGGvWrGHKlCnUrVuXcuXK4efnx7Bhw9KOSV1DPvWxe/dua4VfqOnp683gwLmb9P9uD1MHNmFAcw+zn1/T8oOCMn39qlWreO211/j777+pVq2atcMpcPT09XkgOupCpvuaVS1NtbLOrDx0MQ8j0jQtI/369eP06dM6mViBTig5MGVpTwat6IkyZHwnl4jQr6k7u0/d4EpUfB5Hp2malj/ohJIDjdy8uGQLwaHLMi3Tz9sdpfRULJqmFV06oeRA5xbjcFCKgNAFmZapUa443lVL6bu9NE0rsnRCyYESLpXoYFuKTbFnSU7KvEnL39udY1diCIuIzsPoNE3T8gedUHKoR42e3LAV9h3+OdMyvb0qY2cjupaiaVqRpBNKDrVrPpoSBsWG439kWqZMcQce8XRjddAlUgxF53ZsTcsrtra294wn+ewz843YDwoKIiAgIO11ZtPeX758mQEDBpjtug/j7NmzNGrUyKoxZERPvZJDTsVK08mxAlsTrvB+fBSOTq4ZlvP39mBr2DX2nLpB2zrl8jhKTSvcihUrRlBQkEXOHRQURGBgID179kzbNnjwYGbOnPmfssuXL7dIDHktOTkZOzvzpQFdQ3kAPev4E2sj7DzwXaZlOtcvj4ujnW720rQ8EhUVhaenJ+Hh4YBxJP3cuXMBGD16ND4+PjRs2JBJkyalHbN//37atGlDkyZN8PX1JSoqiokTJ6aNqF+6dGmm10tfO4iLi2PQoEE0aNAAf39/WrZsSerg6c2bN9O6dWuaNWvGwIEDiY2NBaB69epMmjSJZs2a0bhxY44dOwbAP//8k1YT8vb2JiYmBqUUb775Jo0aNaJx48YZxtWqVSuOHj2a9vqRRx4hMDCQO3fu8Oyzz+Lr64u3tzerV68GjDWvPn360KlTJzp37vzQn3tGrFJDEZGBwAdAfcBXKZXh8HUR6Q58C9gCPyqlPjNtF+BjYCCQAnynlJpu6bhbNh1JmZDvWX96PZ39xmdYxsnelp6NK7Eu+DIf92tEMQdbS4elaXnu832fc+zmMbOes16Zerzt+3aWZe7evUvTpk3TXr/zzjtptYjhw4czbtw4bt26xfPPPw/AlClTKFOmDCkpKXTu3Jng4GDq1avH4MGDWbp0KS1atCA6OhpnZ2c+/PBDAgMD02ok8+bNy3Da+/Rmz55N6dKlCQ0NJSQkJC2269ev8/HHH7N161aKFy/O559/zrRp05g4cSIA5cqV4+DBg8yePZupU6fy448/MnXqVGbNmoWfnx+xsbE4OTnxxx9/EBQUxOHDh7l+/TotWrSgffv298QwePBgli1bxuTJk4mIiCAiIgIfHx/effddOnXqxM8//8zt27fx9fWlS5cuABw8eJDg4GDKlCnzMH+qTFmrySsEeBz4IbMCImILzAK6AheB/SKyRikVCgwHqgD1lFIGEcmTaX7t7J141LkqK+POExsTQQmXShmW82/mztLAC2wOvZK2VLCmabmXWZNX165d+f333xkzZgyHDx9O275s2TLmzJlDcnIyERERhIaGIiJUqlSJFi1aAFCyZMlMr5dZk1eqnTt3Mm7cOAAaNWqEl5cXAHv37iU0NBQ/Pz8AEhMTad26ddpxjz/+OADNmzfnjz+M/bJ+fn689tprDBs2jMcffxwPDw927tzJkCFDsLW1pUKFCnTo0IH9+/enXQdg0KBBPProo0yePJlly5al9e9s3ryZNWvWMHXqVADi4+M5f/582udl7mQCVkooSqkwMI4wz4IvcFIpddpUdgnQFwgFRgNDlVIG0/muWTTgdHo1GMaSg5/x1/4Z9On0SYZlfKuXwb1UMVYeuqQTilYoZVeTyGsGg4GwsDCcnZ25desWHh4enDlzhqlTp7J//35Kly7N8OHDiY/Pm5kslFJ07dqVxYsXZ7jf0dERMN5kkJxsnFR2/Pjx9OrVi4CAAPz8/Ni0aVOOruXu7k7ZsmUJDg5m6dKlfP/992kxrFixAk9Pz3vK//vvvxQvXvxh31qW8nMfijuQfgKti6ZtALWAwSISKCIbRKROZicRkVGmcoGRkZG5DqpJwyFUToGAC39mWsbGRujbtDI7TlwnMiYh19fUNC1rX3/9NfXr12fRokWMGDGCpKQkoqOjKV68OK6urly9epUNGzYA4OnpSUREBPv37wcgJiaG5ORkXFxciImJeaDr+vn5sWyZcQaN0NBQjhwxrmLZqlUrdu3axcmTJwG4c+cOx48fz/Jcp06donHjxrz99tu0aNGCY8eO0a5dO5YuXUpKSgqRkZFs374dX1/f/xw7ePBgvvjiC6KiotJqL926dWPGjBmkTgB86NChB3pvD8NiCUVEtopISAaPvmY4vSMQb5r9ci6Q6eAQpdQcpZSPUsrHzc0t1xcWGxt6uHqyV93h5s2TmZbz93YnxaBYe/hyrq+paZpRah9K6mP8+PGEh4fz448/8tVXX9GuXTvat2/Pxx9/TJMmTfD29qZevXoMHTo0rfnJwcGBpUuXMnbsWJo0aULXrl2Jj4+nY8eOhIaG3tMpn9209y+99BKRkZE0aNCA999/n4YNG+Lq6oqbmxvz5s1jyJAheHl50bp167TO98x88803ac1m9vb29OjRA39/f7y8vGjSpAmdOnXiiy++oGLFiv85dsCAAWlLIqeaMGECSUlJeHl50bBhQyZMmJDbjz9bVp2+XkS2AW9k1CkvIq2BD5RS3Uyv3wFQSn0qIseAHkqpM6YO+ttKqYzv403HXNPXh59Yz4Dd43mvwiM80X1GpuV6z9iBIKwd2zbX19Q0ayso09fnpZSUFJKSknBycuLUqVN06dKF8PBwHBwcrB3aQyus09fvB+qISA0RcQCeANaY9q0COpqedwCyrkuaWd1aPaidIgRcyXqRnn5N3TlyKYqT1x6sGq1pWsEQFxdH27ZtadKkCf7+/syePbtAJ5PcskpCERF/EbkItAbWi8gm0/bKIhIAoJRKBl4GNgFhwDKlVOrN1p8B/UXkCPApMDJP47exoUe5JhySRC5fzrzG06dpZWwEPSZF0wopFxcXAgMDOXz4MMHBwfTo0cPaIVmVVRKKUmqlUspDKeWolKqQ2qyllLqslOqZrlyAUqquUqqWUmpKuu23lVK9lFKNlVKtlVKHM7qOJfXwfgmADQdmZVqmvIsTbeu4serQZQx6KhatEChKK7wWRbn9++bnJq98rUqV1ngZ7Nhw/WCW5fo3c+fS7bv8cyL3d5hpmjU5OTlx48YNnVQKKaUUN27cwMnJ6aHPoefyyoWeFVvx2bWdnDq1hVq1umZYpkejSnxa8hg/7jhNR888GX+paRbh4eHBxYsXMcft91r+5OTkhIeHx0MfrxNKLnTzeYUv1u8gIPhHxmaSUBzsbBjhV51PNxwj5FIUjdyzvRlN0/Ile3t7atSoYe0wtHxMN3nlQjm3+viKMwG3QjNdbx5gSMuqlHC0Y+6O03kYnaZpWt7SCSWXerp34KIthIStyLRMSSd7nmhRhXXBEVy6fTcPo9M0Tcs7OqHkUucWr2CvFAFHf82y3Ii2xqaCX3aeyYuwNE3T0kRE5c0PWZ1QcqmkaxXa2bqyMfYMKcmJmZZzL1WM3l6VWLzvPFF3k/IwQk3TirK1hy/T4YttbA29avFr6YRiBj2rd+e6rRAYPC/Lcs+3q8mdxBSW7DufN4FpmlakLQu8wLglh2hapRQta5p/uvr76YRiBh18XsbZoAgI/z3Lco3cXfGrXZZfdp0lMTnzTnxN07TcmrfrDG8tD8avdjnmP+uLi5O9xa+pE4oZOBUrTWeH8myJjyAxIet5u55vV5Mr0fF6FmJN0yxm1t8n+WBtKN0aVuDHZ3zybOVYnVDMpEedfsRks948QIe6bnhWcGHujtN6xLGmaWallOKLjcf4clM4/ZpWZtbQZjja5d0y5DqhmEkr75GUNig2nF6XZTkRYWS7Ghy7EsOOE9fzKDpN0wo7g0ExeW0os7edYohvVaYNaoqdbd5+xeuEYib29s48WqwK25JuEheb9YrEfZpWpryLox7oqGmaWaQYFG+tCGbe7rOMbFuDT/wbYWOT5RLrFqETihn1rD+EeBvhr8DMF90CcLSzZbhfdXacuE7o5eg8ik7TtMIoMdnAK0sOsfzARcZ1rsN7vepjXHcw7+mEYkZNGw2lYooi4PyWbMsO862Gs4MtP+paiqZpDyk+KYXRCw6wPjiC93rW59Wuda2WTEAnFLOysbWjh2td9hhiuXXzVJZlXZ3teaJFVdYcvpxno1g1TSs87iQk8+y8/fwVfo2P+zXi+fY1rR2STijm1rPRcJJF2LJ/erZlR/hVRwG/7Dpr8bg0TSs8ou4m8dRP/7L39A2+GtiEJ1tVs3ZIgE4oZudZpzc1U4SAiF3Zlq1SxpmejSux6N/zRMfr6Vg0TcvejdgEhszZy5FLUcwe1ozHmz38+iXmphOKmYmNDT3KenFAErgScSjb8s+3q0FsQjJL913Ig+g0TSvIrkTFM3jOXk5FxjL3aR+6N6pk7ZDuoROKBfT0fhGAjVmsN5/Ky6MUrWqW4eddZ0hK0dOxaJqWsQs34xj4w24ibt9l/rO+PJIPV4DVCcUCqlZtSyODHQGRgTkqP6p9TSKi4lkfHGHhyDRNK4hOXotl4Pd7iL6bzMLnW9GqZllrh5QhnVAspGcFX8JsUjh95q9syz5Stzy1y5dgznY9HYumafcKunCbgd/vJtlgYMmoVjStUsraIWVKJxQL6dZ8LKIUG4LmZlvWxkYY1a4moRHR7D51Iw+i0zStINh+PJKhc/fi4mTPitFtqF+ppLVDypJOKBZSvkIjfKUYG26FZLnefKq+3pUpV8KRH7brgY6apsGaw5d5bv5+qpUtzvIXW1OtbHFrh5QtnVAsqEfl9pyzhdDwldmWdbSzZYRfdbYfjyQsQk/HomlF2fzdZxm35BDeVUuzZFQrypd0snZIOaITigV18R2HnVIEhGS93nyqYS2rUszelh936HXnNa0oUkoxbctxJq05Spf6Ffj1WV9ci1l+YSxz0QnFglxdq9LWpiQbY05lud58qlLODgxuUYU1hy9xJSo+DyLUNC2/SDEo3l8VwvQ/TzDIx4PvhjXDyT7v1jIxB51QLKx3jR5csxV25WBMCsCzfjVIMSjm7T5r2cA0Tcs3EpJTGLv4IAv/Pc/oR2rxeX+vPF/LxBwKXsQFTKdWr1M+RbHg2OIcla9a1pkejSqx8N9zxCYkWzg6TdOsLTYhmRG/7CfgyBXe71Wft7vXs+qMwbmhE4qF2ds7M7icN3u4y6lT2U9rD8aBjjHxySzdr6dj0bTC7LppXq5/z9xk2qAmjGxn/RmDc0MnlDwwoO0kHJRi4f6vclS+SZVS+NYow8879XQsmlZYXbgZx8Dv93DiWgxzn26eryZ5fFg6oeSBMmVq08uxImvvXiTq9tkcHTOqXU0u3b5LwBE9HYumFTbHrkTT/7vd3IhNYOHIlnSqV8HaIZmFTih5ZJjPq8TbCCt2fJij8p3qlaemW3Hm7tDTsWhaYRJ49iaDvt+DCPz+YhuaVytj7ZDMxmoJRUQGishRETEtduupAAAgAElEQVSIiE8W5bqLSLiInBSR8em2dxaRgyISJCI7RaR23kT+cDzr9KKFcmRx5D6Sk7K/JdjGRni+XU1CLkWz8+T1PIhQ0zRL+zPsKsN+/JdyJRxZMboNnhVdrB2SWVmzhhICPA5sz6yAiNgCs4AeQANgiIg0MO3+DhimlGoKLALet2y4ufdk3UFcsRX+2js1R+X9vd3xKF2MKevDSNZ9KZpWoP0eeIFRvx3As6ILv7/YGo/SztYOyeysllCUUmFKqfBsivkCJ5VSp5VSicASoG/qKYDUmdJcgcuWidR8Ovj+D/cUWHgq+6lYAJzsbXmvZ32OXYlhsb7jS9MKJKUU32w9zpvLg2ldsyyLnm9F2RKO1g7LIvJ7H4o7kP6b9KJpG8BIIEBELgJPAZ9ldAIRGSUigSISGBkZadFgs2Nr58DQiq05KImEHluVo2O6N6pIq5plmLY5nNtx2Y+21zQt/0hMNvDm8mC+2XqCAc09+Hl4C0o42lk7LIuxaEIRka0iEpLBo2/2R2frVaCnUsoD+AWYllEhpdQcpZSPUsrHzc3NDJfNHf+2k3A2KBYenJ6j8iLCxN4NibqbxDdbT1g4Ok3TzCU6PokR8/ax/MBFXu1Sly8HeOFgl99/w+eORVOlUqpLLk9xCaiS7rUHcElE3IAmSql/TduXAhtzea084VLSnb7O1Vh+9xyvXj9GuXL1sj2mQeWSDPGtym97zzG0ZVXqVihcHXmaVthcun2XEb/s43TkHaYObMKA5gV/jElO5Pd0uR+oIyI1RMQBeAJYA9wCXEWkrqlcVyDMSjE+sKEt3yJJhN935uwWYoDXH/WkuIMtH60L1bcRa1o+FnIpCv9Zu4i4Hc/8Z32LTDIB69427G/q/2gNrBeRTabtlUUkAEAplQy8DGzCmDCWKaWOmrY/D6wQkcMY+1DetMb7eBjVq3egnRRn6c1gEhNicnRMmeIOvNq1LjtOXGdr2DULR6hp2sP4O/wag37Yg52NsHx0G/xql7N2SHlKitKvXR8fHxUYGGjtMADYvX8WL4R+z5Qqj9Gn0yc5OiYpxUDPb3eQmGJg86vtcbQrWFNba1phtujf80xYHUK9ii78PLwFFQrIolg5ISIHlFKZjhdMlaMaioj8ISK9RCS/N5EVGK2bj6ZmirDgXECOlggGsLe1YeJjDTh3I46fd561bICapuWIwaD4fOMx3l15hPZ1yrHshdaFKpk8iJwmiNnAUOCEiHwmIp4WjKlIEBsbhrl3JMwmhUNHFuT4uHZ13OhSvwIz/zrBtWi9CJemWVNCcgrjlgbx3bZTDG1ZlblP+1C8EN8WnJ0cJRSl1Fal1DCgGXAW2Coiu0VkhIgUnPUp85ne7SZQ0qBYEDz3gY57v1d9ElMMfL4xu3GhmqZZyu24RJ76cR9rD19mfI96TOnXqEAuimVOOX73IlIWGI5xQOEh4FuMCSZni3xo/+HsXI7+JevyV8otIi4fyPFx1csV59m2NVhx8CJBF25bMEJN0zJy/kYcj3+3m6ALt5k+xJsXO9QqsItimVNO+1BWAjsAZ+AxpVQfpdRSpdRYoIQlAyzshrR+D4DFe6Y80HFjO9XBzcWRD9YcxWAoOjdWaJq1BV24jf/sXdyITWTByJb0aVLZ2iHlGzmtoUxXSjVQSn2qlLpngY6c9PxrmatUuTmdbEuzIvo4cXE5n1W4hKMdb3XzJOjCbVYFXbJghJqmpdp09ApPzNmDs6Mtf7zUBt8ahWfqeXPIaUIpLSKP3/foLCLlLRpdEfGk1/NE2wjrdn78QMf1b+ZBEw9XPttwjDt6/XlNsxilFLP+PsmLCw7gWbEkK1/yo5abbpy5X04TynPAj8Aw02Mu8DawS0SeslBsRYZ34yepb7Bl0cW/cnwLMRjXTJn4WEOuxSQwe9tJC0aoaUXX3cQUXlkSxJebwnnMqzJLR7WiXCGdLTi3cppQ7IH6Sqn+Sqn+GNcmUUBLjIlFywWxseHJaj05ZavYc/D7Bzq2ebXS+Hu7M3fHGc7fiLNQhJpWNEVE3WXQD3tYF3yZt7p78u0TTXGy1wOKM5PThOKhlLqa7vU1oIpS6iaQZP6wip7ufu9QNkWxMPS3Bz727e71sLMRpgSEWiAyTSuaDp6/RZ+ZuzgdGcvcp3x46ZHa+k6ubOQ0oWwTkXUi8oyIPAOsNm0rDuj7Vs3AwdGFQaUbs13Fcu7cjgc6tqKrE2M61mbT0avs0ssFa1quLT9wkSd+2Esxe1tWjvGjS4MK1g6pQMhpQhmDcc2RpqbHr8AYpdQdpVRHSwVX1AxqOxE7pVj07+cPfOxzbWvgUboYH64N1csFa9pDSjEopqwP5Y3fD9O8WmlWj/HTy0U8gGwTimld97+UUiuUUq+aHstVUZpVMo+Uc6tPT4fyrLpzlpjoB7sV2Mnelvd71Sf8agyL9p23UISaVnhF3U3i2Xn7mbvjDM+0rsavz/lSuriDtcMqULJNKEqpFMAgIq55EE+RN6zZK8TZCCt3Tn7gY7s1rEjrmmX5avNxbt3RywVrWk6diozFf9Yudp28zif+jZnctxH2RXwalYeR008sFjgiIj+JyPTUhyUDK6oa1OtHM+XAoit7SEl+sKQgIkzq04CY+CS+2XrcQhFqWuHyz/FI+s3axe27SSwc2ZKhLataO6QCK6cJ5Q9gArAdOJDuoVnAsFr+XLKFf/Z988DH1qtYkmEtq7Hg3/OEX8nZ4l2aVhQppfhxx2lG/LIP91LFWD3Gj5Y1y1o7rAItp7MNzweWAXuVUvNTH5YNrejq1OoNKqUoFh5f9lDHv9a1LiUc7Zi89qheLljTMpCQnMKby4P5eH0YXRtUYMXoNlQp42ztsAq8nE4O+RgQBGw0vW4qImssGVhRZmfvxBNuvuyTBMJPrH/g40sXd+C1rnXZfeoGG0OuWCBCTSu4rsXEM2TOXpYfuMgrnevw3bDmRXoNE3PKaZPXB4AvpjEnSqkgoKaFYtKA/u0m4mRQLAp88GYvgGEtq1K/UkneXXmEy7fvmjk6TSuYDpy7Rd+ZuwiNiGbW0Ga81rUuNjZ6sKK55DShJCmlou7bpgc7WJBrqeo8VsyD9fER3Lp56oGPt7O1YdZQbxKTDby86CBJemyKVoQppfh55xkG/7AHWxth+Ytt6OVVydphFTo5TShHRWQoYCsidURkBrDbgnFpwJMt3yRRYN7fbz3U8TXdSvD5AC8Onr/N5xuOmTk6TSsYYuKTeGnhQT5cF8ojnuVZP7Ydjdz1KAhLyGlCGQs0BBKAxUA08D9LBaUZ1azRmV72biyMDudKxKGHOkdvr8o807oaP+48o/tTtCInLCKaPjN3sTn0Ku/0qMfcp5vj6qxXLbeUnN7lFaeUek8p1UIp5WN6Hm/p4DQY2/FLDAIz/37zoc/xbq/6eHm48ubyw3pGYq3IWBZ4gX6zdnEnIZlFI1vygl6m1+JyepdXXRGZIyKbReSv1Ielg9OgcmUfhpWow5rEKxw/ueGhzuFoZ8usoc0Q4KVFB4hPSjFvkJqWj8QnpfDW8sO8tTyYZlVLs/6Vdnp8SR7JaZPX78Ah4H3gzXQPLQ+M7PotLgq+3vXg07GkqlLGma8GNSXkUjQfr9fT3GuF05nrd+g3axfLAi/ycsfaLBjZEjcXvRhWXslpQklWSn2nlNqnlDqQ+rBoZFoaV9eqPO/Wip3cYe+BHx76PF0bVOCF9jVZsPc8q/U69Fohs+FIBI/N2MmV6Hh+GdGCN7p5YqtvCc5TOU0oa0XkJRGpJCJlUh8WjUy7x5AuX1EpRTEt+DsMKQ+/fvwb3TzxqVaad/44wslrsWaMUNOsIzHZwIdrQxm98CC1ypdg/Svt6OhZ3tphFUk5TSjPYGzi2s3/z+MVaKmgtP9ydHJlbI1+hNmksHHnRw99HntbG2YM9cbJ3paXFh7gbqLuT9EKrsu37/LEnD38vOsMw9tU5/cXWuNeqpi1wyqycnqXV40MHnqkfB7r1f4D6hlsmH7qDxITHn7ix0quxfhmcFNOXItlwuoQM0aoaXnnn+OR9Jq+g/ArMcwc6s0HfRriYKennLemLD99EXkr3fOB9+37xFJBaRmzsbXj1cYvcMkWlvz5eq7O1b6uG2M71WH5gYss23/BTBFqmuWlGBTTthxn+C/7KO/ixJqxbentVdnaYWlkX0N5It3zd+7b193MsWg50MbnJdpQjDlXdxMdlbtEMK5zHfxql2XC6hDCIqLNFKGmWc6Fm3EM/mEP0/88wePeHqwa40cttxLWDkszyS6hSCbPM3qt5ZFXW71PtMBPW3M3WYGtjfDNYG9ci9nz0sKDxMQnmSlCTTMvpRTLAi/Q/ZvthF+JYdqgJkwd6EUxB1trh6alk11CUZk8z+i1lkfqefbhMYfyLIgJJ+Jy7u7ednNxZMYQb87duMM7fxzR66do+c6N2AReXHCAt5YH08jdlQ3/a8fjzTz0qPd8KLuE0kREokUkBvAyPU993fhhLyoiA0XkqIgYRMQni3I/i8g1EQm5b3sZEdkiIidM/y39sLEUVC8/8iUAM7c93MSR6bWsWZY3unmyLjiC3/aey/X5NM1c/jp2lW7f7ODvY5G827Mei55vhUdpvRBWfpVlQlFK2SqlSiqlXJRSdqbnqa9zM8NaCPA4xiWFszKPjPtqxgN/KqXqAH+aXhcplSo3Z1iJOqxNvEr48XW5Pt+L7WvRqV55PloXyuELt80QoaY9vLjEZN5beYRn5wVSroQDq1/2Y1T7WnqgYj5nlXvslFJhSqnwHJTbDtzMYFdfIHUJ4vlAPzOGV2A8lzoly56HH5eSysZG+GpgE8q7ODFm0UGi4nR/imYdh87fotf0nSzad55R7Wuyaowf9SuVtHZYWg4U1Ju2KyilIkzPrwAVMisoIqNEJFBEAiMjI/Mmujzi6lqVUeXbsIs49hz4PtfnK13cgZlDvbkaHc/rvx/W/SlankpKMfD1luMM+H4PickGFo1sxbs96+NkrzveCwqLJRQR2SoiIRk8+przOsr4rZfpN59Sao5pyn0fNzc3c146XxjS5Ssqp8DXwd/nakqWVN5VS/NOj/psDbvKd/88+EqRmvYwTkXGMuC73Xz75wn6NqnMhv+1o3UtPUOwOURHXeCzZY8RGxORfeFcslhCUUp1UUo1yuCx2gynvyoilQBM/71mhnMWSA6OLoytaZySJWDHw89GnN4Iv+r09qrEFxvD+WnnGbOcU9MyopTit73n6DV9B2dvxDFraDOmDW5KSSe9CJY5HDg8nwErerA07gyBRxdZ/HoFtclrDcb5xTD91xxJqsDq2W4S9Q22zDi9KldTsqQSEaYNakqPRhX5aF0os7edNEOUmnava9HxjJi3nwmrQmhRvQyb/tder/NuJklJccxYOZhnD32JPcJvvpN4pFXuZtfICaskFBHxF5GLQGtgvYhsMm2vLCIB6cotBvYAniJyUUSeM+36DOgqIieALqbXRZaNrR2veY3msi0s3mqefzQOdjbMGOJN36aV+WJjOF9vOa77VDSzUEqxOugS3b7Zzp5TN5jcpyG/PutLRVcna4dWKFy4sIfhC9oyJzqUxxwqsmzQFho1GJj9gWYgRelLwsfHRwUGFt5Jkl+c35IjhjsEPB6Aq2tVs5wzxaAYvyKY3w9c5MUOtXi7u6ceUKY9tLPX7zBhdQg7TlzHy8OVaYOaULu8i7XDKhSUwcC6fyYw5exqbICJtQbRvf1Es5xbRA4opTIdM5jKzixX0/KFV1tPYODu8fy0ZRyvDVhplnPa2gif9/fCwc6G7/85RUJyChN7N9BJRXsgCckpzPnnNDP+PomDrQ0fPNaAp1pX1+NKzCQm+hIfrRnKhpSbNBNHPnt0DpUqN8/zOHRCKUQ86/bmscCvWRh7giGXD5jtH5SNjfBxv0Y42tny864zJCYb+KhvI2z0l4GWA3tP3+C9lUc4FXmHXo0rMaF3A928ZUaHghcwPvBzrtooXi7tzcheP2Fr52CVWHRCKWTGdpzKxk1PMXPbm0wZ+pfZzisiTOhdH0d7G77bdoqEZAOf9/fSvzC1TN28k8iU9WGsOHgRj9LF+GV4CzrW0yspmktyUjxz1o3gh6gjVEaY7/M+TRo9kf2BFqQTSiFTsZI3w1zqMi/mOE+Fr6GeZx+znVtEeKubJ052tny99TiJyQamDWqCnW1BvVlQswSDQbH8wEU+2RBGbHwyLz1Si7Gd6uiZgc3o4sW9vLP1JYIkiT4O5XnnsYWUcLH+HXI6oRRCI7t8yx9/9ODrvR/zgxkTChiTyrgudXCws+HzjcdITDYwfYi3XilPA+D41RjeXxnCvrM3aVG9NFP8G1O3gu50N6d12yYw5Yyxj/TzGv3p2cE848/MQSeUQqikaxVGVWjDl5F72B04mzY+L5n9GqMfqYWjnQ0frgvlxQUHmD2smZ4iowi7m5jCjL9OMGf7aUo42fFFfy8GNPfQ/WxmFBsTwZQ1Q1mXfB1vceTTrt/h7u5r7bDuoW8bLqQSE2Lot7ANClg+aAvFS1S0yHUW7D3H+6tCaFenHHOe8tHNGkXQ3+HXmLg6hAs379K/mQfv9qxH2RKO1g6rUAk6spDx+z/jio3ihVJNeL7XT9jZ592NDTm9bVi3UxRSDo4uTPF5m8s2is/XPmmx6zzZqhpfDvBi58nrjJi3jzsJuZ9PTCsYrkbHM2bhQUb8sh8HWxsWP9+KrwY10cnEjBITYvhmxQCeOfApAPOav8PofgvzNJk8CJ1QCjFvryd5rmR9ViZe5c/dn1vsOgN9qvDN4KbsP3uLp3/eR7ReSrhQi7qbxBcbj9Hhy7/ZEnaV17vWJWCcnszR3MJPrGfIorb8FBuOv2NlVgzaQtPGw6wdVpZ0k1chl5Rwh2GL/IggmT96LcWtfEOLXWtjSARjFx+ifqWS/PqsL6WcrXMvvGYZdxNTmLf7LN9tO0lMQjJ9mlTm9a6eVC2rV1A0p5TkROZveJGZN/ZR0gCTGzxLh1avWTWmnDZ56YRSBJw+8yeDto2jhU0JZj+1G7GxXMX0z7CrjF5wkBrlijN9iDeeFfUdPgVdUoqBpfsvMP3PE1yLSaBTvfK88agnDSrrRa/M7cKFXbz35ysckkS62Lgyodc8ypSpbe2wdB+K9v9q1ujMa5U6sJM7LN08zqLX6ly/Ar+MaMH12AQem7GTWX+fJDnFYNFrapZhMBgncewy7R/eXxVC1TLO/P5ia34e3kInEzNTBgO/b36V/ltf4KRK4JOqfZk2bHu+SCYPQtdQighlMDD6t9YcMNxhWceZ1Kj+iEWvd/NOIhNXh7AuOAIvD1emDmyixyMUEEopth2P5IuN4YRFRFOvogtvdfeko2d5PYebBUReO8qkjc+xQ92hJU58/OgcKlbytnZY99BNXhkoygkF4NrVEB4PeAIP7Pjtyd3Y21u+7TvgSAQTVoUQE5/MuC51eKF9TT2yPh8LPHuTLzaGs+/sTaqWceb1R+vymFdlPZ7EQjbt+IiPTi4lHni1YjuGPDoDG9v8NzxQJ5QMFPWEArB156e8emoRo0o2YKz/0jy55o3YBCauPsr6IxE0MdVW6ujaSr4SFhHN1E3h/HnsGm4ujrzSuQ6DfaroGRAsJCrqPJ+ue4b1yddpaLDlk0emUbNGJ2uHlSmdUDKgE4rR+4u6sDbxCvObv5OntyGuD45gwuoQYuOT+V/XOoxqp2sr1nb+Rhxfbz3OqqBLlHC048UOtRjhVx1nh/z3K7mw2B04mwnBs7lhAy+U8mJkrx/zpLUgN3RCyYBOKEaxMREM+P1RBMuOos/I9dgEJq4OIeDIFV1bsRKlFHtO32D+7rNsCb2Kva0NI/xq8GKHmvpWbwu6G3eTr9c+xeL489RIET5tPYmG9ftbO6wc0QklAzqh/L+Dh39lxKEv6OdYiclDtuT59dcFX2bi6qPExifzate6PN+uhq6tWFhcYjIrD13i193nCL8aQ2lne57wrcrwNtWpUDJ/jrwuLAKD5jHp4Fect4UnnWswrvd8nIqVtnZYOaYTSgZ0QrnXtysG8GNsON/UeZLObd7O8+tfj01gwqoQNoRcoUmVUnw10EsvB2sB52/E8euesywLvEB0fDINKpVkeJvq9GlaWU/oaWF3Yq/w9fpnWRp/AfcU+NB7HL7eI60d1gPTCSUDOqHcK3UU/RWS+aP375Rzq5/nMSilWBccwcTVIdxJTOG1rnV5vl1NvXBXLiml2HHiOvN3n+Wv8GvYiNC9UUWGt6mOT7XS+vbfPLB7/yw+OPIdV2xgmHMNxvb+BWfnctYO66HohJIBnVD+Ky9H0WclMsZYW9l41FhbGduxNh3rldeJ5QHFJiSz4sBF5u85y+nIO5Qr4cAQ36oMa1lNL7ubR6KjLjA1YAQrE69SPUX4qMXb+X4OruzohJIBnVAytnDDS3x2bQfvV+zI4G7TrRaHUoq1wRF8vC6UazEJuJcqxtCWVRnkUwU3Fz2DbVZOR8by655zLD9wkdiEZJp4uPJMm+r08qqEo51u1sorf++Zysdh87hhA8Nd6jG61084OrlaO6xc0wklAzqhZMyQksxLC/zybBR9dpJSDGwJvcqCvefYfeoG9rZCt4YVebJVNVrWKKOba0wiYxL469hV1gVHsOPEdexthV6NK/FMm+p4Vy04Hb6Fwa2bp/hsw3MEJN+gjsGGj1pNLDB3cOWETigZ0Aklc9YYRZ8TpyJjWbj3PMsPGDuU65QvwbCWVXm8uQclneytHV6eUkpx4losW0KvsjXsKkEXbqMUuJcqxkAfD4a2rEp5F92slZeUwcDmXVP45ORSogVGlfJiZI+52DsWt3ZoZqUTSgZ0Qsnalp2f8NqpxbxQsiEv+y+xdjj3uJuYwtrgyyzce47DF6MoZm9LP+/KDGtZjUbuBb9JITNJKQb2n73J1tBrbA27yvmbcQB4ebjSpX4FutSvQP1KLrrWZgXXI8P4eONI/jRE09Bgy4ftPqVu7R7WDssidELJgE4o2XtvUWfWJV5lvs+7NG001NrhZCj44m0W7D3HmsOXiU8y0LRKKZ5sVY3eXpUKxW2w0fFJ/BMeydawq/x97BrR8ck42NngV6ssXRpUoHO9CrqD3YqUwcDabe/z+bk1xAuMKevL091n59tVFM1BJ5QM6ISSPWuOon9QUXFJrDh4kQX/nuN05B1KOdszoJkHHTzdaFCpZIFaivbCzTj+DLvK1rBr7D19g2SDokxxBzrVK0+X+hVoV6ccxR31dCjWdiXiEJM3j2Ynd2iq7PnwkWlW73PMCzqhZEAnlJw5cHg+Iw59SW/78kwZstVqtxLnVOpUIgv3nmfT0SskG4z/piuWdKJB5ZI0rFySBpVK0rCyK1XKFLNa85BSiuuxiZy4FsPJa7GcuBqb9vx6bCIANd2K07V+Bbo0qECzqqX1bdP5RHJSPIu3jGPm1V0oYFzFdjzR9Vts7YrGVDU6oWRAJ5Sc+27VUGZHHWFkCU/G9V9u7XByLCouiZDLUYRejubo5ShCI6I5eS0WU47BxdGO+mkJpiQNKpekTnkXs86qq5TiWkxCWsI4cS2Wk6bnt+KS0sq5ONpRp0IJ6pR3wbOiCx083ajlVsJscWjmEXx0KR/t+4RjNgbaUpx3O31NlSqtrR1WntIJJQM6oeScMhj4cFkPlidc5o1yrXmm1xxrh/TQ4pNSCL8Sw9HL0YRGRHH0cjTHImK4m5QCgL2tUKe8Cw0rl6RcBuNdMvpfRPHfjbfvJKUlkJj45LTtrsXsqVuhBLXLu1CnfAnqVChB3QoulHdx1J3p+VhU1HmmbxjF7/EXcTPA+LpD6dJmfL6vsVuCTigZ0AnlwaQkJ/Lm4s5sMdzm4yq96NvpM2uHZDYpBsWZ63cIjTDVZC5HExYRTfTd5P8WzuQ7//7NLk521C5vrHHUqVAi7Xm5Eg46cRQgymBg3T8TmXp2FVECQ4vXYkyPH/J1f6Kl6YSSAZ1QHlxiQgxjlnRmv4rja8/hdGz9hrVD0jSLOX3mL6b88xb7JAEvgx0T2kymnmcfa4dldTlNKEWv7qY9EAdHF77tv44Gyp43wuexP+hna4ekaWYXf/cW0/8YRP9/XiFMxTOhUmd+e3q/TiYPyCoJRUQGishRETGISKZZT0R+FpFrIhJy3/YvReSYiASLyEoRKWX5qIsu5xLlmdV3OR4GG145NI2w8NXWDknTzGb7v9/Sb3F75saE0cO+PGsf+4NBj36TL9d2z++sVUMJAR4HtmdTbh7QPYPtW4BGSikv4Djwjlmj0/6jdJla/NDzV1wUvLj7Pc6d22HtkDQtV65cCeK139oy5tiPOCD85DWOT4b9Rdlyda0dWoFllYSilApTSoXnoNx24GYG2zcrpVJ7T/cCHmYOUctAxYpN+aHTTBTwwp8vce1qSLbHaFp+k5wUz68Bo+i74Um2J9/mldLerBi2p0AufJXfFIY+lGeBDZntFJFRIhIoIoGRkZF5GFbhVKP6I3zXajK3RPFCwDCibp+1dkialmP7g37miQUt+TJyD81sSrCyy1ye7/NroZvM0VosllBEZKuIhGTw6GvGa7wHJAMLMyujlJqjlPJRSvm4ubmZ69JFWsP6/Zne5BXOSQpjVj5OXNx1a4ekaVk6f34n//vNj2cPf02USuGrmoOZ/dTuIjdA0dIs1uuklOpiqXMDiMhwoDfQWRWle5/ziZbNRvFF3A1eP7mQ137vxYwn/tK/8rR8JzrqAnM2j2XhnZPYKxhb1punu07HqZheL8YSCmSTl4h0B94C+iil4qwdT1HVpe07TPLozi7ieO/3nhhSMhgUqGlWkJwUz5KNY+n9Rw9+vXOSxxwrsr7XUkb1+U0nEwuy1m3D/iJyEWgNrBeRTabtlUUkIF25xcAewFNELorIc6ZdMwEXYIuIBInI93n8FjSTx7tM5dUyLdiQcpNPl/dBGXfBZ3EAABH4SURBVAzWDkkr4nbtn8mA33yZcnUbtcWJpa2n8OGQrbiVb2jt0Ao9PVJeM4uvlvsz785JXnJtzOh+i6wdjlYEnT7zJ19uf4+d3KFKCrxe70k6tXqzSM69ZW45HSmvR+5oZvHa4yu4veRRZkcdwXXjGIZ2n2XtkLQi4tbNU8zeMpbf757HWcEb5VszpMs0HBxdrB1akaMTimYWYmPDpIHriFrcmU+vbsd120R6PfKhtcPSCrGkhDss2voqP1zbTZzAgGJVeanrdMqUqW3t0IosXRfUzMbO3okvBwXgoxx59+wf/LLuOd2nopmdMhj4a/cX9FvYiqnX9+BlU5zl7abx/uAAnUysTCcUzawcnVyZNSCALnalmXZjH28s6kBc7DVrh6UVAspgYM+B73lqvg/jTvyGHcJ39Ufx/TP/UrvWo9YOT0MnFM0CnEuUZ+rQf3itrC9bk28xdFkXPfeXliv7D/3E8F9b/F979x4dVXnucfz7S4LcIchFQCDhZpEqIsrFGyICtdKKF2prFaXW2mN7vB1be1rb2uNx1QtrVY+ttWKPtVIFW9Qj1htgQS2FAAYIQaAiDfdLBKSAEJPZz/ljb+wQBxhgkp1Jns9as/Jm9p49zzszmV/23jPvy42lj7LFPuGnnUbw/Lj5nDvo5rhLc0n8U16uRs199zfcWfIrqoD7T76e84f8R9wluSxSvORpHl30CPNVQYeEcUPnYVxxwX1+wr2W+QRbKXigxGPDhvncPv1GluckuKnVKfzbJZN8aHB3SEtKp/Drd3/B39hL24RxQ6dzGTvsPv9SYkw8UFLwQInPvr07+O8XxzKtcivnqwU/H/NHWrXuGndZro5Ztvx5Hl0wgXdsD20C45sdzuLKCx6gabPj4y6tQfNAScEDJV4WBEyZfgsPbp5N50A8PHQCvXulmu7GNTQrVk7j0aL7mW27aB0Y49udydcveJBmLTrEXZrDAyUlD5S6oXjJ09zx7oPsEdzT80ouGvrTuEtyMXl/1es8NvdeZgQ7aRkY1x1/OlcPf5AWLTvFXZpL4oGSggdK3bF1Syl3vHYti1XJN5r34pYxk8lr1CTuslwt+fuq13hi3n28UbWd5gbj8k/lmuEP+mHQOsoDJQUPlLqlsmIPD7w4lucq1jOYJkz48hTaHN8z7rJcDQkSVbyz4BEmrZxMEftoGhjXtD6Z64ZPoHV+YdzluUPwQEnBA6VuevHNO7l33au0DeChs+/h830uj7skl0Ef797KS3+9h2c2vsWaXOiQML7efiBjz7vbgyRLeKCk4IFSdy1b/jy3zb2b7Tnwk66jGXPBfT5KbJbbvGkRz865h6m73mdXjjg1yGNcjzGMOPtOGjVqFnd57gh4oKTggVK3bd++ijtfvooi9jGYJtw++Ie+t5KFlpRO4Q+Lf82Mqu0YMCKvDeP638Rpfb/m/yRkKQ+UFDxQ6r6qyn08N/N2Ht/8DjtyxBdzj+fm839O167nxF2aO4Sqyn3MnPsAkz54iZKcSloGxhUte3PV2XfRufNh34dcHeeBkoIHSvbYvWsTv5t5G5M+Wkal4Mpmhdw4/Be0bXdS3KW5JDt3ruX5t3/G5PL5bM4V3RJwdeehXHru3f4dknrEAyUFD5TsU751GY/95Q5e2Leexgbj25zGdSMe8jerGAWJKoqX/oE/L3+WV/dtZG+OGGSNGdfnKoYOvNWH1amHPFBS8EDJXv8om80v3/kxM4KdtE0YN504nMuH3+8nd2vRqg+m88riibyycwWbckXTwBjVuCPXnHELfT53SdzluRrkgZKCB0r2W1I6hV8snECxPqEgAbf0/iojz/mRn+ytIVu3lPLawv/hz1vnsyInINeMs9SC0QUjGX7mzb6n2EB4oKTggVI/WBDw9vyHefi9p1iVa5wa5HH76TczsP/1cZdWL+zetYkZ8x/ilfWzmG97MYUf+R3dcQhfGHgr7dr1ibtEV8s8UFLwQKlfElWfMO2tH/PomlfZkivOU3NuO/tuTur1xbhLyzqVFXv4a/FjvPLBNGZXbqciR3RNwJfanMLoAd+hoOC8uEt0MfJAScEDpX7at3cHk9/8Hk+UF7FbMEhNGdnxLC4ccBPt2p8cd3l1VmXFHhYvf443VvyJ1/euY2eOaBMYFzUrYPTnx9Gv75V+KNEBHigpeaDUbzs/KuMPs37I6ztKKcsFmXE6jRl5wkBG9P82HTudHneJsQoSVaxc9QpF77/MvG1LKQ72sDdHNAmMCxq15Uu9L+esAd/yDzq4z/BAScEDpWGwIGDV6unMLH2a6TuWsSonAKBfkMfI9mcwov8NdOkyJOYqa54FAWvXzaFoxVTmbS1mQdUOPsoRAN0TYnDzLgzpMpQhp42neYuOMVfr6jIPlBQ8UBqmsrK3mFnyJNO3LWF5TgKAk4NcRrbtx4h+19O9cFi8BWbQ1i2lFL03haJN8yjat5nNuWGAdEwYg5t0ZHCnwQzq+1VOOKFfzJW6bOKBkoIHilu/fh4zF/+WGeXFlORUAtAryGFkfl9GnnodvXqMyprzBpUVe1i3sYgPNsxjwYY5FO1Zx+rc8O+5dWAMymvDkA4DGNxnLN26npM1/XJ1jwdKCh4oLtnmzYt5c9HjzNiygGL2YRKtA6OARnQ9Lp+C5p3omt+Tbu1PoeDEwbEMtR4kqti8ZTFlG+ez5sP3WPvPNZTtLWdNYg8bcoxA4R5I08AYkNOcIW1PZXDvL/O5XqP9G+suYzxQUvBAcQfzYflyZi2ayIrty1lbsZ21ib1syjEsesMGaBUY3WhEt+Na061ZJ7pFYdOt80Dy87sf0R6ABQGJxCcEQSVViQo+/vhD1m1cSFl5CWs+Ws2ajzdTVrWLdSSoyPlXDU0Do5A8Chq1oqB5Zwrye1HY4TT69LqYRo2bZ/QxcW4/D5QUPFDckfikYhfrN85n7ZbFrNm2knW71rGmYhvrEnvZWC1sWgZGW8shwEgAVRgBkBBUQdgGqhS1k25bXZ4ZXYMcCvJaUNjsBLq1KqSw/SkUdB5M+/Z9/dCVq3XpBorvEzt3EMc1bkmP7hfSo/uFn1kWhs0C1m5ZxNrtK1n7z3XsqNpNLjnkKZdc5SRdcv/1M2d/O++AduO8JnRr24fCTmfQqeMZ5DVqEkOPnTs2HijOHYUwbIbTo/vwuEtxrs7wfWfnnHMZEUugSPqKpGWSAkkHPS4n6UlJWyWVHmT5HZJMUruaq9Y551w64tpDKQUuB94+zHpPARelWiCpKzAKWJvRypxzzh2VWALFzJab2co01nsb2H6QxQ8BdwIN52NqzjlXh2XlORRJY4ANZrYkjXVvlLRQ0sLy8vJaqM455xqmGvuUl6SZQKoR5+4ys5eOYbvNgB8RHu46LDObCEyE8HsoR3u/zjnnDq3GAsXMRtTQpnsC3YElCr8c1gUoljTIzDbX0H0655w7jKz7HoqZLQU+nchaUhlwppl9GFtRzjnn4hl6RdJlwC+B9sBHwGIz+4KkzsBvzeziaL3JwDCgHbAFuNvM/rfatspIM1AklQNrjrLsdkBDCy3vc8PgfW4YjqXPBWbW/nArNaixvI6FpIXpjGVTn3ifGwbvc8NQG33Oyk95Oeecq3s8UJxzzmWEB0r6JsZdQAy8zw2D97lhqPE++zkU55xzGeF7KM455zLCA8U551xGeKBUI+kiSSslrZL0nymWj5dULmlxdLkhjjoz6XB9jta5UtJ70bQDz9Z2jZmWxvP8UNJz/HdJH8VRZyal0edukmZJWiSpRNLFcdSZKWn0t0DSm1FfZ0vqEkedmZTGlB+S9Ej0mJRIGpDRAszML9EFyAU+AHoAxwFLgL7V1hkP/CruWmu5z72BRUCb6PcOcddd032utv7NwJNx110Lz/NE4Kao3Rcoi7vuGu7vn4DrovZwYFLcdWeg30OBAUDpQZZfDLwGCBgCFGXy/n0P5UCDgFVmttrMPgGmAGNirqmmpdPnbwGPmtkOADPbWss1ZtqRPs9XAZNrpbKak06fDWgVtVsDG2uxvkxLp799gb9E7VkplmcdO/SUHxD28WkLzQPyJXXK1P17oBzoRGBd0u/ro+uquyLaXZwaTfSVzdLp80nASZLmSJonKeWkZ1kk3ecZSQWEg5H+JdXyLJJOn38GXCNpPfAq4Z5Ztkqnv0sIJ/oDuAxoKaltLdQWp7Rf+0fDA+XIvQwUmlk/YAbw+5jrqQ15hIe9hhH+t/6EpPxYK6o9XwOmmlki7kJqwVXAU2bWhfDQyCRJ9fk94nvA+ZIWAecDG4CG8DzXmPr8YjkaG4DkPY4u0XWfMrNtZlYR/fpb4Ixaqq2mHLbPhP/FTDOzSjP7B/B3woDJVun0eb+vkf2HuyC9Pn8T+COAmc0FmhAOKJiN0vlb3mhml5vZ6cBd0XVZ/+GLwziS1/4R80A50AKgt6Tuko4jfDOZlrxCteONlwDLa7G+mnDYPgP/R7h3gqR2hIfAVtdmkRmWTp+R1AdoA8yt5fpqQjp9XgtcCCDpZMJAydZpTtP5W26XtAf2Q+DJWq4xDtOAa6NPew0BdprZpkxtPOvmQ6lJZlYl6d+BNwg/JfKkmS2TdA+w0MymAbdIugSoIjz5NT62gjMgzT6/AYyS9B7hIYHvm9m2+Ko+Nmn2GcI3oSkWfTwmm6XZ5zsID2feTniCfny29j3N/g4D7pNkwNvAd2MrOEOSp/yIzoXdDTQCMLPfEJ4buxhYBXwMfCOj95+lrxfnnHN1jB/ycs45lxEeKM455zLCA8U551xGeKA455zLCA8U55xzGeGB4rKapN1prHObpGYZvM9LJfXN4Pb+dgy33R397Cxp6iHWy5f0naO9H+fS4YHiGoLbgCMKFEm5h1h8KeHAghlhZmdnYBsbzWzsIVbJBzxQXI3yQHH1gqRh0ZwWUyWtkPRM9G3gW4DOwCxJs6J1R0maK6lY0p8ktYiuL5P0gKRi4CuSviVpgaQlkp6X1EzS2YQjJEyI5krpKal/NGhmiaQXJbWJtjdb4bwqCyUtlzRQ0guS3pd0b1Ltu5PaP5C0NLrP+1P0s3tU+9Jq2yjcPweGpM9Lmh/VVyKpN3A/0DO6boKkFgrnAimOtjUmaTvLJT2hcO6b6ZKaRst6SZoZ1VYsqWd0/fejx6lE0n9l9Il12SXu8fv94pdjuQC7o5/DgJ2EYxPlEA6Xcm60rAxoF7XbEX4runn0+w+Anyatd2fSttsmte8Fbo7aTwFjk5aVAOdH7XuAh6P2bOCBqH0r4XDwnYDGhOOjta3Why8CfwOaRb8fn6K/04Bro/Z3k25bSDQHBvBL4OqofRzQNHl5dH0e0CrpMVlFOEdGIeEoEP2jZX8EronaRcBlUbsJ4V7fKMJ5VBQ97n8Ghsb9uvBLPBcfesXVJ/PNbD2ApMWEb45/rbbOEMLDVXMkQfiGmzxW13NJ7VOivYB8oAXhMB4HkNQayDezt6Krfk84cdN++4dxWQoss2jcJEmrCQfpSx7CZgTwOzP7GMDMUs1rcQ5wRdSeBDyQYp25wF0KZyB8wczej/p6QOnAzyUNBQLCIcxPiJb9w8wWR+13gUJJLYETzezFqLZ9UT9GEYbKomj9FoQDh76doi5Xz3mguPqkIqmdIPXrW8AMM7vqINvYk9R+CrjUzJZIGk80QOZR1hRUqy84SH3pOOR4SWb2rKQiYDTwqqRv89nBPK8G2gNnmFmlpDLCvY7kmiF8HJse4u4E3Gdmjx9B/a6e8nMoriHYBbSM2vOAcyT1ApDUXNJJB7ldS2CTpEaEb8Cf2Z6Z7QR2SDovWjYOeIujMwP4xv5PpEk6PsU6cwgHraRaTZ+S1ANYbWaPAC8B/TjwMYBwRsatUZhcABQcqjAz2wWsl3RpdB+NozrfAK5POg91oqQOafXW1TseKK4hmAi8LmmWmZUTjhA9WVIJ4eGhPge53U8IzxvMAVYkXT8F+L6kRdGJ6esIT9KXAP0Jz6McMTN7nfAQ2cLokN33Uqx2K/BdSUs5+Ex7VwKl0TZOIZzydRvhYb5SSROAZ4Azo+1cW61/BzOOcLTtEsJzPR3NbDrwLDA32tZUDgwu14D4aMPOOecywvdQnHPOZYQHinPOuYzwQHHOOZcRHijOOecywgPFOedcRnigOOecywgPFOeccxnx/8N/bkLxDnv5AAAAAElFTkSuQmCC\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.plot(distances, hf_energies, label='Hartree-Fock')\n", - "for j in range(len(algorithms)):\n", - " pylab.plot(distances, energies[j], label=algorithms[j])\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Energy')\n", - "pylab.title('H2 Ground State Energy')\n", - "pylab.legend(loc='upper right');" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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NT2I/d838kOfeW1apQ3XD5rrdYqCizb1dStNKp7aFdOu09Xm7Sm3soVmm3Xbbdqa2LWxJ2+3Ccx8l45zLpcQTh6RxwInAMjPbMzb/OOBPQAFwt5ndWN02zOwx4DFJnYE/Aokkjo0loWmnQ+uW7Lx9623b2qs6Y2+1tTknngi8zd05l68SH1Ul6TBgHXBvReKQVAC8DxwDFAFzgBGEJDImZRPnm9my6HU3Aw+Y2es17dNHVTnnXOYazagqM5spqU/K7P2AxWb2IYCkicBwMxtDqJ1UojAW8kbg6eqShqRRwCiAXr16ZS1+55xzleWqPaU7sCT2vCiaV50rgKOBUyRdUtUKZjbWzAab2eAdd9wxe5E655yrpEl0jpvZn4E/17aeXznunHPJy1WNYynQM/a8RzTPOedcI5erxDEH2FVSX0mFwBnAlPpu1Mymmtmojh071jtA55xzVUs8cUh6EJgF7C6pSNIFZlYKXA5MAxYCD5nZ/Czsa6iksWvWrKnvppxzzlXDb3LonHMOSH84bl5dpeY1DuecS15eJQ7v43DOueTlVeLwGodzziUvrxKH1ziccy55eZU4vMbhnHPJy6vE4TUO55xLXl4lDuecc8nzxOGccy4jeZU4vI/DOeeSl1eJw/s4nHMueXmVOJxzziXPE4dzzrmMeOJwzjmXkbxKHN457pxzycurxOGd4845l7y8ShzOOeeS54nDOedcRjxxOOecy0ijTxyS9pD0V0mTJV2a63icc665SzRxSBonaZmkd1LmHyfpPUmLJV1T0zbMbKGZXQKcBhycZLzOOedql3SNYzxwXHyGpALgduB4oD8wQlJ/SXtJeiLl8Y3oNcOAJ4GnEo7XOedcLVomuXEzmympT8rs/YDFZvYhgKSJwHAzGwOcWM12pgBTJD0J/L2qdSSNAkYB9OrVKyvxO+ec21aiiaMa3YElsedFwP7VrSzpCOD7wHbUUOMws7HAWIDBgwdbNgJ1zjm3rVwkjoyY2QxgRjrrShoKDO3Xr1+SITnnXLOWi1FVS4Gesec9onnOOeeagFwkjjnArpL6SioEzgCmZGPDfssR55xLXtLDcR8EZgG7SyqSdIGZlQKXA9OAhcBDZjY/S/vzmxw651zCkh5VNaKa+U/hQ2udc65JavRXjmfCm6qccy55eZU4nHPOJS+vEof3cTjnXPLyKnF4U5VzziUvrxKH1ziccy55eZU4vMbhnHPJy6vE4ZxzLnmeOJxzzmUkrxKH93E451zy8ipxeB+Hc84lL68Sh3POueR54nDOOZcRTxzOOecykleJwzvHnXMueXmVOLxz3DnnkpdXicM551zyPHE455zLiCcO55xzGWkSiUNSO0lzJZ2Y61icc665SzRxSBonaZmkd1LmHyfpPUmLJV2TxqZ+BjyUTJTOOecy0TLh7Y8HbgPurZghqQC4HTgGKALmSJoCFABjUl5/PvBdYAHQOuFYnXPOpSHRxGFmMyX1SZm9H7DYzD4EkDQRGG5mY4BtmqIkHQG0A/oDGyU9ZWblVaw3ChgF0KtXrywehXPOubikaxxV6Q4siT0vAvavbmUz+wWApHOBr6pKGtF6YyV9DgwtLCwclL1wnXPOxTWJznEAMxtvZk/Uso5fAOiccwnLReJYCvSMPe8Rzas3v+WIc84lLxeJYw6wq6S+kgqBM4ApOYjDOedcHSQ9HPdBYBawu6QiSReYWSlwOTANWAg8ZGbzs7E/b6pyzrnkJT2qakQ1858Cnsr2/iQNBYb269cv25t2zjkXaTKd4+nwGodzziUvrxKHd44751zy8ipxeI3DOeeSl1eJwznnXPLyKnF4U5VzziUvF7ccSYyZTQWmDh48+KJcx+Kc26qkpISioiI2bdqU61Ac0Lp1a3r06EGrVq3q9Pq0EoekR4B7gKeru1eUc85Vp6ioiA4dOtCnTx8k5TqcZs3MWLFiBUVFRfTt27dO20i3qeovwJnAIkk3Stq9TntzzjVLmzZtokuXLp40GgFJdOnSpV61v7QSh5k9a2YjgX2Aj4FnJb0s6TxJdavrJMD7OJxrvDxpNB71/SzS7hyX1AU4F7gQeAP4EyGRPFOvCLLIh+M656rTvn37Ss/Hjx/P5ZdfntE25s2bx1NPZf2mF1uMHz+eHXfckYEDBzJw4EDOPvvsjLcxY8YMTjwx2V/ZTreP41Fgd+A+YKiZfR4tmiRpblLBOedcY1FaWsq8efOYO3cuJ5xwQpXLW7as/3ij008/ndtuu63e20lSujWOP5tZfzMbE0saAJjZ4ATics65BjN16lT2339/9t57b44++mi+/PJLAEaPHs1ZZ53FwQcfzFlnncV1113HpEmTGDhwIJMmTdpmeVlZGVdffTX77rsvAwYM4M4779yyj5tuumnL/Ouvvz6j+ObNm8cBBxzAgAEDOPnkk1m1ahUAixcv5uijj+a73/0u++yzDx988EGl182ZM4e99957m/n1lW567Czp+ynz1gBvm9myrEbknMtrN0ydz4LPvs7qNvt3257rh36nxnU2btzIwIEDtzxfuXIlw4YNA+CQQw7hlVdeQRJ33303f/jDH7j55psBWLBgAS+++CJt2rRh/PjxzJ07d0uNYPTo0ZWWjx07lo4dOzJnzhw2b97MwQcfzLHHHsuiRYtYtGgRs2fPxswYNmwYM2fO5LDDDtsmzkmTJvHiiy8C8OMf/5jzzjuPs88+m1tvvZXDDz+c6667jhtuuIFbbrmFkSNHcs0113DyySezadMmysvLWbIk/MDqyy+/zBVXXMHjjz+e9Z/TTjdxXAAcCDwXPT8CeA3oK+lXZnZfVqOqI787rnOuOm3atGHevHlbnlckAQjDhU8//XQ+//xziouLKw1THTZsGG3atKl2u/Hl06dP56233mLy5MkArFmzhkWLFjF9+nSmT5/O3nvvDcC6detYtGhRlYkjtalqzZo1rF69msMPPxyAc845h1NPPZW1a9eydOlSTj75ZCBcm1Fh4cKFjBo1iunTp9OtW7fM3qg0pJs4WgF7mNmXAJJ2Au4l/Fb4TELfR875BYDONX611Qxy4YorruCqq65i2LBhzJgxg9GjR29Z1q5duxpfG19uZtx6660MGTKk0jrTpk3j2muv5eKLL640//bbb+euu+4CyGqn+ze/+U02bdrEG2+8kUjiSLePo0dF0ogsA3qa2UqgJOtROedcA1qzZg3du3cHYMKECdWu16FDB9auXVvt8iFDhnDHHXdQUhKKxffff5/169czZMgQxo0bx7p16wBYunQpy5Yt47LLLmPevHnMmzev2gK+Y8eOdO7cmRdeeAGA++67j8MPP5wOHTrQo0cPHnvsMQA2b97Mhg0bAOjUqRNPPvkk1157LTNmzMjszUhDuoljhqQnJJ0j6Rzg8WheO2B11qNyzrkGNHr0aE499VQGDRpE165dq13vyCOPZMGCBVs6x1NdeOGF9O/fn3322Yc999yTiy++mNLSUo499ljOPPNMDjzwQPbaay9OOeWUGhNQqgkTJnD11VczYMAA5s2bx3XXXQeEJPLnP/+ZAQMGcNBBB/HFF19sec1OO+3EE088wWWXXcarr76awbtRO5lZ7SuFq0W+DxwSzXoJ+Iel8+IcGDx4sFW0XTrncm/hwoXsscceuQ7DxVT1mUh6LZ2RsrX2cUgqAJ41syOBf9Q5yjqSdATwa2A+MNHMZjR0DM4557aqtanKzMqAckkZX44taZykZZLeSZl/nKT3JC2WdE1tIQDrgNZAUaYxOOecy650R1WtA96W9AywvmKmmV1Zy+vGA7cRRmABW2owtwPHEBLBHElTgAJgTMrrzwdeMLPno5Fc/wuMTDNm55xzCUg3cTwSPTJiZjMl9UmZvR+w2Mw+BJA0ERhuZmOAmm6wsgrYrrqFkkYBo4CsX+zinHNuq7QSh5lNkNQG6GVm79Vzn92BJbHnRYTrQaoUXbE+BOhEqL1UF+NYSZ8DQwsLCwfVM0bnnHPVSGs4bnRF9jzgn9HzgVHzUuLM7BEzu9jMTq+tY9zvjuucc8lL9zqO0YQmptUAZjYP+FYd97kU6Bl73iOaV2/+exzOuaoceeSRTJs2rdK8W265hUsvvZT58+dz1FFHsfvuu7PLLrtw/fXXU14efug09TbnAwcOZMGCBbk4hEYl3cRRYmappXFdf0J2DrCrpL6SCoEzgAapvTjnmqcRI0YwceLESvMmTpzIGWecwbBhw7jmmmt47733ePvtt5k9ezZ/+tOftqx3+umnb7m6e968efTv37+hw2900k0c8yWdCRRI2lXSrcDLtb1I0oPALGB3SUWSLjCzUuByYBqwEHjIzObXMf5KvKnKOVeVU045hSeffJLi4mIAPv74Yz777DMWL1685Q62AG3btuW2227jpptuymW4jV66o6quAH4BbAYeJBT6v67tRWY2opr5TwFZ/xktvzuuc03A09fAF29nd5s77wXH31jt4h122IH99tuPp59+muHDhzNx4kROO+005s+fz6BBlcfS7LLLLmzcuJHVq8PdlOK3OQeYNWtWjXfLbQ7S/c3xDWb2CzPb18wGR9N1/6XzhHiNwzlXnXhz1cSJExkxosrz2m2kNlU196QB6f907G7AT4A+8deY2VHJhFU3XuNwrgmooWaQpOHDh/Nf//VfvP7662zYsIFBgwbxxhtvMHPmzErrffjhh3Tp0oVOnTrlJM6mIN0+joeBN4BfAlfHHo2K1zicc9Vp3749Rx55JOeff/6W2sbIkSN58cUXefbZZ4HwK4FXXnklN9xwQy5DbfTSTRylZnaHmc02s9cqHolG5pxzWTZixAjefPPNLYmjTZs2TJkyhd/+9rfstttudO3alYMPPpiRI7fe2ajiN8YrHi+/XOu4oLyX7m3VRxN+vOlRQgc5ANEPOTUasaaqixYtWpTrcJxzkaZyW/XHHnuMq666iueee47evXvnOpxE1ee26ukmjo+qmG1mVteLABPlv8fhXOPSVBJHc5Lo73EAmFnf2tdyzjnXHNTYxyHpp7HpU1OW/S6poOrKbzninHPJq61z/IzY9LUpy47Lciz15qOqnGu8GukvTTdL9f0sakscqma6qufOOVel1q1bs2LFCk8ejYCZsWLFClq3bl3nbdTWx2HVTFf13DnnqtSjRw+KiopYvnx5rkNxhETeo0ePOr++tsTxXUlfE2oXbaJpoud1T1fOuWalVatW9O3rY2zyRY2Jw8wKGiqQbPBbjjjnXPLSvXK8SfDOceecS15eJQ7nnHPJ88ThnHMuI544nHPOZSTdXwDMGUktCL82uD0w18wm5Dgk55xr1hKtcUgaJ2mZpHdS5h8n6T1JiyVdU8tmhgM9gBKgKKlYnXPOpSfpGsd44Dbg3ooZkgqA24FjCIlgjqQpQAEwJuX15wO7Ay+b2Z2SJgP/Sjhm55xzNUg0cZjZTEl9UmbvByw2sw8BJE0EhpvZGODE1G1IKgKKo6dlyUXrnHMuHbnoHO8OLIk9L4rmVecRYIikW4GZ1a0kaZSkuZLm+m0NnHMuOY2+c9zMNgAXpLHeWEmfA0MLCwsHJR+Zc841T7mocSwFesae94jmOeecawJykTjmALtK6iupkPCbH1OysWG/5YhzziUv6eG4DwKzgN0lFUm6wMxKgcuBacBC4CEzm5+l/fkvADrnXMKUjz+sMnjwYJs7d26uw3DOuSZF0mtmNri29fLqliNe43DOueTlVeLwPg7nnEteXiUOr3E451zy8ipxeI3DOeeSl1eJwznnXPLyKnF4U5VzziUvrxKHN1U551zy8ipxOOecS15eJQ5vqnLOueTlVeLwpirnnEteXiUO55xzyfPE4ZxzLiOeOJxzzmUkrxKHd44751zy8ipxeOe4c84lL68Sh3POueR54nDOOZcRTxzOOecy0jLXAdRG0qHASEKs/c3soByH5JxzzVqiNQ5J4yQtk/ROyvzjJL0nabGka2rahpm9YGaXAE8AE5KM1znnXO2SrnGMB24D7q2YIakAuB04BigC5kiaAhQAY1Jef76ZLYumzwQuSDhe55xztUg0cZjZTEl9UmbvByw2sw8BJE0EhpvZGODEqrYjqRewxszWJhiuc865NOSic7w7sCT2vCiaV5M5yl6cAAAYMElEQVQLgL/VtIKkUZLmSpq7fPnyeobonHOuOo2+cxzAzK5PY52xkj4HhhYWFg5qgLCcc65ZykWNYynQM/a8RzTPOedcE5CLxDEH2FVSX0mFwBnAlGxs2G854pxzyUt6OO6DwCxgd0lFki4ws1LgcmAasBB4yMzmZ2l/fpND55xLmMws1zFk3eDBg23u3Lm5DsM555oUSa+Z2eDa1surW454jcM555KXV4nD+ziccy55eZU4vMbhnHPJy6vE4TUO55xLXl4lDuecc8nLq8ThTVXOOZe8vEoc3lTlXJ4pL8t1BK4KeZU4nHN5ZNZf4A99ocivyWps8ipxeFOVc3ni7ckw7VrY9DX84wLY7L+o0JjkVeLwpirn8sCHz8Ojl0Cvg+CsR2D1p/DUT3MdlYvJq8ThnGvivngHJv0QuvSDEX+HXY6CQ38Cb/491EJco+CJwznXOKxeAg+cAoXt4YeToU3nMP/wn0GPfeGJq2DVJ7mN0QGeONyqj+GrRbmOwjV3G1bC/T+A4g0haXTssXVZQUv4/l1g5fDIKCgrzV2cDsizxOGd4xnauBrGHQe37wdPXQ0bV+U6ItcclWyCiWfCqo/gjAdgp+9su84OfeF7N8OSV+CFmxs+RldJXiWOeneOfzIL5tyT3aAas2eug3Vfwp4/gDl3w62D4fX7oLw815G55qK8DB65CD6dBSffCX0PrX7d754Oe50Gz/8ePn214WJ028irxFFvr0+AJ6+CZ0fnf+H50cxwvAdeBj+4G0bNgC67wJTL4Z6jYenruY7Q5Tsz+Oc1sHAKDBkDe36/9td874/QsTs8ciFs8paFXPHEETfsNhh8Prz4f/DoKCjdnOuIklG8AaZcCZ37whE/D/O++V04fxqc9NfQSXnXUTD1x7B+RW5jdfnrpVtg9lg48HI48EfpvaZ1R/jBPbBmKTz5k2Tjc9XyxBFX0BK+97/wH9fD2w+HzrqNqxtm3yUbG2Y/ADN+F9qTh/0ZCttunS/BwBFwxVw44Eeh2eq2QaH5zm/94LLpzYmhZr/nKXDMrzN7bc/9wkirtx+CNyclEp6rWaNPHJJ6SXpM0jhJ1zTADuHQq+DksfDpK6HzePWS5PZXvB6evgZ+1w1eHZvcfiosfQ1m3Q6DzoW+h1W9TuuOcNzv4NKXYKc9Q/Pd2CNgyezk48tna7+ERc/C8vehtDjX0eTOB/+Gxy8L37+T/gIt6lAMHfrf0OtAePK/YeVH2Y/R1SjR3xyXNA44EVhmZnvG5h8H/AkoAO42sxtr2Mb3gM5mdr+kSWZ2em37zdpvjn/4fLgYqbAdjHwYdt6r/tuM++iF0Kew6mPYYZdQCxg5Gfr9R3b3U6G0OCSAjSvhsldDgqiNGcx/BKb9EtZ+Bt89E465Adp/I5kY882mr2Hh1HB2/NHMMKQUQC2gU+9woVuXfqF/qWJ6++51K0ybgs/fhL+dAJ37wHlPpfcdrM7qT+GOQ2DH3eC8p6GgVdbCbK7S/c3xpBPHYcA64N6KxCGpAHgfOAYoAuYAIwhJZEzKJs4HyoDJgAH3mdnfattv1hIHwJfz4YFTQwFw+r3hStb62rwWnrke5t4T+hmG3x76GMYNCbWbC58N/wzZ9vxN8Nxv4IwH4dsnZBjzOph5U6ittGoDR/4c9r0oNO+5yko3w6JnQnPn+/+E0k2hoNzr1HCW/fVnsGIxrPhg69+S9Vtf37J1OJHYkkyiv113g7Y75Oyw6m3Vx3DPsVBQCBc8A9t/s/7bfHtyuJfVYT+Fo35R/+3lSlkpfDwT3nkE1n8Fx/4auu7a4GE0isQRBdIHeCKWOA4ERpvZkOj5tQBmlpo0Kl7/E2C2mc2UNNnMTqlmvVHAKIBevXoN+uSTLF5humYp/P00WP4uDLsVBp5Z920t/lfodF5TFEY0HfmLrf0Mqz8NndLbdYAL/5XdQmLZu3DnofDtE+HUWnNv9b5aBE//NDQ3fKN/iP8be4Sz5FatsxdvU1NeDp++DG89BAseh02roW3XMFJor1PDlc9S1a81g7VfREkkeqz8MPr7EZSXhPXUAo77Pew/quGOK1vWr4Bxx4ZC8YLpsOPu2dv2o5fCWxPh3Ceh90HZ227SysvCMOR3/gELpsCGr6CwQ6htlpfB0D/BXlUWd4lpzInjFOA4M7swen4WsL+ZXV7N6/cERgNfAevMrNahFFmtcVTYtAYmnQUfPR8Ky8Ourr4gqMrG1TD9F/DG/eHMcfjtoZMv1aevwoQTodcB8MNHslP9Li8LfTUrFsFlc6D9jvXbnhm8+wT88+ew5tOt89vtGBJIxx7QsWf0t/vW6XbfyK8mGDP48p2QLN75B3y9FFq1g29/DwacBt86ov6fX1lpeI9XfBAGKbz/NBz7GzjoimwcQcMo3gD3Dg/NVGc/Dr0PzO72N6+Fvx4K5aVwyYvQplN2t59NZlA0J3xf5j8G676AVm1ht+PCSUa/Y2DDCph8frjYcfD5YahyA52U5U3iyHBfQ4Gh/fr1u2jRogRuo1FaDFOvhDcfhH3ODiOw0ikY3p8GU/8zfEkO/jEcfk3NX4R5D8Jjl4Qvzff+N7MEVZVX7wy1hJPvhO+eUb9txZVsDP8Ea5aGGtSaJaHwXFMUHsXrKq/fohVs321rIuncB3Y9FrrvU/9jbEirPgnNUG8/HGqhLVrCLv8RksXux4c+sSSUlYSL5eY/Ckf9Mpy8NHZlpfDQWfDe03DavdB/WDL7KXot1Gj2GAqn/K1xfZ/M4PN5oRlq/qPh/6RgO9j1mJAsdjtu2+9MWQn8+9fw0p9C3+qpE0KTZcLSTRy5aKBeCvSMPe8RzWv8WhbCSXeEQm/mTaGt+tQJsF37qtffsDJc4PTWpNCsc8YDoZCszcARoUB66RbYcY/6NU2s+gSevQH6HQ0Dah1XkJlWbaofmWUWmmuqSyqfvBQ6jJ+/MSSS/sPDo/vgxlsrWb0kfJ7vPhGe9zwg3Aaj/8nQrkvy+y9oBd+/OxQ6//5NOJE58ueNq5CMW/lRGPX0wb/ghD8mlzQAegwK78W/fhXO2vceWfdtlZeF/7+STeE73qpNqBVU/E2nX88Mli2IksUjoemxRcvQR3rUL2H3E6D19tW/vqAVHPOrcGv5xy6BOw+H4bfCd06u+3FlUS5qHC0JneP/QUgYc4AzzWx+tvaZSFNVqrl/C/8UO+8JZz4MHXaqvHzh1HA3z40rw9DBQ38SEk+6ysth0shQW/nh5Lp1ypvB/d8Pw2h/NAs69cp8G0nauCqciS54PPSZlBVDh26hgOk/HHruDy0Kch1lOGt+9a/w3O8Ag4OuDP1cnXvnJp7ystBP9sZ9oQZ79A2NK3mUbApnyi/cHArAo0fDfhclv9/yMpgwDD57Ay55If0z9A0rw68MFs0O/ytLX9u2thzXolVIIIVtU5JKbHrZwpB81CKcXO35g9C/WJd+y9VLQtNV0ewwIGXIb6HldplvJw2NoqlK0oPAEUBX4EvgejO7R9IJwC2EkVTjzOy3Wdpfsk1Vqd6fDg+fEzpBfzg5dPit/wqe+kmoku48IBoxNaBu29+8Fu4ZEs7QL/pX5qMs5v0dHrsUjr+p8XeobloTkuSCx8OIpLLN0H4n2CNKIr0Pyk0SWfpaKKS/eBt2HRJuedEYEnB5OTx9dbjH2P6XwnFjGkfyWPRs+P6v+iicHQ/5XWiebChriuCOg2GHb4VO+NSm5PJy+Oq9kCAqEsVX74dlKgg3WOy5fxjM0KYzlGwITbJb/san11cxL/rbfqettehsDF0vKwkXTM66LYzAPHV8OMYsaxSJI1capMZRYenrYcRVWQkcfGUYrrrpazjiZ3Dwf9a/c3T1pzD2yDDe/cJn0z9jWbcMbtsXdvx2GOPeWJt/qrJ5beUkUroxdLx/+8Twj9jn0OSHAW/6OrQxz74LOuwMx/8+JLHGUDhXMINpv4BXbg/9YSfcnLvPeU0R/PPacN+pHXYJCTYbQ9frYsHj8NDZcMhVcMh/wdK5IUEsmR1qFpuje1y16bw1SfTcD7rtU32zc2Px7lOh6cosnJRmufmvWSaOBq9xVFj1Mdx/Shi11G2fcDXsN/bI3vY/fQUmDM1spNVD58B7T8ElLyVzTUhDKV4fkseCx0MyKVkPbXaAPaIk0vfw7F74ZRYKv6d/FobI7jcqtEnX1B6dS2bwrxvC/dUG/jDcRqYha2ZlJfDKX2DG78HK4LCfhKa8hJpS0jblCnj9XkCES8AU+hl77gs99gsJo8sujetEIF2rPoHJ54Xa8P6XhFu2ZNIMXoNmmTgqNGiNo8LGVfDxi7Db8cmcDVc0Ow2+AE7835rXXTg1XPF+1P+Ef+R8UbwhdLQueBze+ycUrw1njXsMhf4nhbbk+iSRVZ+E3yVZNC2MZDnxT6HTtbEzC7canzEmXDNy0l8b5sLMj18M/XzL3w3f++NvDCPlGoPi9TD9f0IzUc/9oPug+l2l3tiUFsOz14ek3W2f0HSVhT63Zpk4clbjaCjT/wde/nMYoVJdZ+PG1XD7/qFpZ9Rz+XsbhpJNIYnMfzR0sBevi9VEMkwiZSXwyh2h4EVhdM7+lzS9q+JfuDmMKuo/PNxBNqnPfu2X8Mz/hNGCHXuFZrxM70TgsmPhVHjsslCxOumOcA1RPTTLxFEhJzWOhlBeBhNHwqLp1Y+0mnJFuMjwon9Dt70bPsZcKNkYrshf8FhKEhkK3zkJ+hxWfRIomhuusfny7XDWfMJN0Kln1es2BbNuh2k/D8M9Tx2f3Saj8rJwEeK/fx3e84N/HEYMxu+w7Breyo/g4XPDtSIHXBZGsdWx6apZJo68r3HA1pFWXxfBhf+Grv22LvtwRrhC9+AfhzHgzVFFEpn/aLhPVPE6aNsldKx/5+StHeub1oSz8zn3QIdvwgl/COs0xTbvVLPvCiOb+h0Np98fhofW15I54S7JX7wVrog/4Y85uZeSq0bpZpj+y/D7Jmc+DLsdW6fNNMvEUSFvaxwVVn0S7mnVplMYadWmc2jTveOgMG780pezU1g0dSUbYfGz4dYO7z0dOtbbdgnDaj/4F6xfDvtdHG6Ot12HXEebXa9NCMOI+x4GIx7M7Gr2zevCENXl74Whq1+8E97HDjuH4bXfOTk/Emw++mwedBtY55d74sjnxAHh99EnDIU+B4dbsVeM8T73SehzSK6ja3y2JJFHQ8d6113hxP9L70r+purNiWFARc8DYORD2ybHDSu3Jofl0eOr98NV/hVatAzDa3cbAof/NP8SrKvEE0e+Jw6ANx6Ax38U7nWzaDrscw4MvSXXUTV+5eVN67qW+njnH/CPi0KC3Cu6w/NX74e/65dvXa9lm5BMd9w9PLpGf3f4Vv4OsHDbaMz3qkpMrI8j16E0jL1HwvKF8PKt4VYdx9yQ64iahuaSNCDc6qKgEB4+L9yQsnXHkBR2GxIuDu26e7jOp2Ov5vW+uHrxGkdTV14GM6OrdHvum+toXGO1bln49cH2O3n/hKtWs6xxNEstCsLtTZyrif/Ur8sir5s655zLiCcO55xzGcmrxCFpqKSxa9asyXUozjmXt/IqcZjZVDMb1bFjHt3MzDnnGpm8ShzOOeeS54nDOedcRjxxOOecy4gnDueccxnJyyvHJS0HPqnjy7sCX2UxnKbAj7l58GPOf/U93t5mtmNtK+Vl4qgPSXPTueQ+n/gxNw9+zPmvoY7Xm6qcc85lxBOHc865jHji2NbYXAeQA37MzYMfc/5rkOP1Pg7nnHMZ8RqHc865jHjicM45l5FmmzgkHSfpPUmLJV1TxfJzJS2XNC96XJiLOLOptmOO1jlN0gJJ8yX9vaFjzLY0Puf/i33G70tanYs4syWN4+0l6TlJb0h6S9IJuYgzm9I45t6S/hUd7wxJPXIRZzZJGidpmaR3qlkuSX+O3pO3JO2T1QDMrNk9gALgA+BbQCHwJtA/ZZ1zgdtyHWsDH/OuwBtA5+j5N3Idd9LHnLL+FcC4XMed8Gc8Frg0mu4PfJzruBvgmB8GzommjwLuy3XcWTjuw4B9gHeqWX4C8DQg4ADg1Wzuv7nWOPYDFpvZh2ZWDEwEhuc4pqSlc8wXAbeb2SoAM1vWwDFmW6af8wjgwQaJLBnpHK8B20fTHYHPGjC+JKRzzP2Bf0fTz1WxvMkxs5nAyhpWGQ7ca8ErQCdJ38zW/ptr4ugOLIk9L4rmpfpBVM2bLKlnw4SWmHSOeTdgN0kvSXpF0nENFl0y0v2ckdQb6MvWAqYpSud4RwM/lFQEPEWoZTVl6Rzzm8D3o+mTgQ6SujRAbLmU9ne/Lppr4kjHVKCPmQ0AngEm5DiehtCS0Fx1BOHs+y5JnXIaUcM5A5hsZmW5DiRhI4DxZtaD0Jxxn6R8Lwd+Ahwu6Q3gcGApkO+fc6Ly/QtTnaVAvAbRI5q3hZmtMLPN0dO7gUENFFtSaj1mwlnJFDMrMbOPgPcJiaSpSueYK5xB026mgvSO9wLgIQAzmwW0JtwYr6lK53/5MzP7vpntDfwimtekB0GkIZPvfsaaa+KYA+wqqa+kQkKhMSW+Qkp74DBgYQPGl4Rajxl4jFDbQFJXQtPVhw0ZZJalc8xI+jbQGZjVwPFlWzrH+ynwHwCS9iAkjuUNGmV2pfO/3DVWq7oWGNfAMebCFODsaHTVAcAaM/s8Wxtvma0NNSVmVirpcmAaYVTGODObL+lXwFwzmwJcKWkYUErohDo3ZwFnQZrHPA04VtICQlX+ajNbkbuo6yfNY4ZQ2Ey0aDhKU5Xm8f43oQnyvwgd5ec25eNO85iPAMZIMmAmcFnOAs4SSQ8Sjqtr1F91PdAKwMz+Sui/OgFYDGwAzsvq/pvwd8Y551wONNemKuecc3XkicM551xGPHE455zLiCcO55xzGfHE4ZxzLiOeOFyTIGldGuv8p6S2WdznSZL6Z3F7L9fjteuiv90kTa5hvU6SflTX/TiXDk8cLp/8J5BR4pBUUMPikwg3yMsKMzsoC9v4zMxOqWGVToAnDpcoTxyuSZF0RPSbCpMlvSvpgejq2CuBbsBzkp6L1j1W0ixJr0t6WFL7aP7Hkn4v6XXgVEkXSZoj6U1J/5DUVtJBhDsG3BT9VscukgZGN398S9KjkjpH25uh8LsecyUtlLSvpEckLZL0m1js62LTP5P0drTPG6s4zr5R7G+nbKNPxW8wSPqOpNlRfG9J2hW4EdglmneTpPYKv0XxerSt4bHtLJR0l8Jvr0yX1CZa1k/Ss1Fsr0vaJZp/dfQ+vSXphqx+sK5pyfV95f3hj3QewLro7xHAGsK9d1oQbhNySLTsY6BrNN2VcJVwu+j5z4DrYuv9NLbtLrHp3wBXRNPjgVNiy94CDo+mfwXcEk3PAH4fTf+YcKvybwLbEe7/1SXlGI4HXgbaRs93qOJ4pwBnR9OXxV7bh+g3GIBbgZHRdCHQJr48mt8S2D72niwm/EZDH8JdEQZGyx4CfhhNvwqcHE23JtTijiX8loei9/0J4LBcfy/8kZtHs7zliGvyZptZEYCkeYRC8MWUdQ4gNDO9JAlCwRq/F9Wk2PSe0Vl9J6A94fYVlUjqCHQys+ejWRMIPxBUoeL2JW8D8y26L5CkDwk3m4vfuuVo4G9mtgHAzKr6XYWDgR9E0/cBv69inVnALxR+0e4RM1sUHWul0IHfSToMKCfcWnunaNlHZjYvmn4N6COpA9DdzB6NYtsUHcexhOTxRrR+e8INMGdWEZfLc544XFO0OTZdRtXfYwHPmNmIaraxPjY9HjjJzN6UdC7RjR7rGFN5Snzl1cSXjhrvB2Rmf5f0KvA94ClJF7PtTSlHAjsCg8ysRNLHhFpEPGYI72ObGnYnYIyZ3ZlB/C5PeR+HyydrgQ7R9CvAwZL6AUhqJ2m3al7XAfhcUitCQbvN9sxsDbBK0qHRsrOA56mbZ4DzKkaASdqhinVeItx8kZSYtpD0LeBDM/sz8DgwgMrvAYRf+VsWJY0jgd41BWZma4EiSSdF+9guinMacH6sn6i7pG+kdbQu73jicPlkLPBPSc+Z2XLCHY0flPQWoVnn29W87n8I7fovAe/G5k8Erpb0RtRBfA6hs/wtYCChnyNjZvZPQtPW3Kip7SdVrPZj4DJJb1P9L7edBrwTbWNPwk+FriA0z70j6SbgAWBwtJ2zU46vOmcR7g79FqEvZmczmw78HZgVbWsylROUa0b87rjOOecy4jUO55xzGfHE4ZxzLiOeOJxzzmXEE4dzzrmMeOJwzjmXEU8czjnnMuKJwznnXEb+H5CaQYI0rpTPAAAAAElFTkSuQmCC\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.plot(distances, np.subtract(hf_energies, energies[1]), label='Hartree-Fock')\n", - "pylab.plot(distances, np.subtract(energies[0], energies[1]), label='VQE')\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Energy')\n", - "pylab.yscale('log')\n", - "pylab.title('Energy difference from ExactEigensolver')\n", - "pylab.legend(loc='center right');" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.plot(distances, eval_counts, '-o', color=[0.8500, 0.3250, 0.0980], label='VQE')\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Evaluations')\n", - "pylab.title('VQE number of evaluations')\n", - "pylab.legend(loc='upper left');" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/chemistry/h2_uccsd.ipynb b/community/chemistry/h2_uccsd.ipynb deleted file mode 100644 index 881f9d0de..000000000 --- a/community/chemistry/h2_uccsd.ipynb +++ /dev/null @@ -1,206 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## _*H2 dissociation curve using VQE with UCCSD*_\n", - "\n", - "This notebook demonstrates using Qiskit Chemistry to plot graphs of the ground state energy of the Hydrogen (H2) molecule over a range of inter-atomic distances using VQE and UCCSD. It is compared to the same energies as computed by the ExactEigensolver. `UCCSD` should be used together with `HartreeFock` initial state.\n", - "\n", - "This notebook populates a dictionary, that is a progammatic representation of an input file, in order to drive the Qiskit Chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here where we alter the molecule supplied to the driver in each loop.\n", - "\n", - "This notebook has been written to use the PYQUANTE chemistry driver. See the PYQUANTE chemistry driver readme if you need to install the external PyQuante2 library that this driver requires." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Processing step 20 --- complete\n", - "Distances: [0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.675 0.7 0.725 0.75 0.775\n", - " 0.8 0.825 0.85 0.875 0.9 0.925 0.95 0.975 1. ]\n", - "Energies: [[-1.05515973 -1.07591359 -1.09262986 -1.105918 -1.11628597 -1.12416088\n", - " -1.12990475 -1.1338262 -1.13618942 -1.13722134 -1.13711707 -1.13604434\n", - " -1.13414766 -1.1315512 -1.12836187 -1.12467173 -1.12056027 -1.11609624\n", - " -1.11133942 -1.10634211 -1.10115033]\n", - " [-1.05515974 -1.07591361 -1.09262987 -1.10591802 -1.11628599 -1.12416089\n", - " -1.12990476 -1.1338262 -1.13618944 -1.13722136 -1.13711707 -1.13604436\n", - " -1.13414767 -1.13155121 -1.12836188 -1.12467175 -1.12056028 -1.11609624\n", - " -1.11133943 -1.10634212 -1.10115034]]\n", - "Hartree-Fock energies: [-1.04299622 -1.0630621 -1.0790507 -1.09157046 -1.10112822 -1.10814997\n", - " -1.11299652 -1.11597525 -1.11734902 -1.11734325 -1.11615145 -1.11393966\n", - " -1.1108504 -1.10700581 -1.10251056 -1.09745432 -1.09191405 -1.08595588\n", - " -1.07963694 -1.07300677 -1.06610866]\n", - "VQE num evaluations: [45. 51. 51. 51. 43. 54. 50. 47. 51. 46. 42. 57. 49. 53. 49. 55. 50. 46.\n", - " 51. 56. 55.]\n" - ] - } - ], - "source": [ - "import numpy as np\n", - "import pylab\n", - "import copy\n", - "from qiskit.chemistry import QiskitChemistry\n", - "\n", - "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", - "qiskit_chemistry_dict = {\n", - " 'driver': {'name': 'PYQUANTE'},\n", - " 'PYQUANTE': {'atoms': '', 'basis': 'sto3g'},\n", - " 'operator': {'name': 'hamiltonian', 'qubit_mapping': 'jordan_wigner',\n", - " 'two_qubit_reduction': False},\n", - " 'algorithm': {'name': ''},\n", - " 'optimizer': {'name': 'COBYLA', 'maxiter': 10000 },\n", - " 'variational_form': {'name': 'UCCSD'},\n", - " 'initial_state': {'name': 'HartreeFock'}\n", - "}\n", - "molecule = 'H .0 .0 -{0}; H .0 .0 {0}'\n", - "algorithms = ['VQE', 'ExactEigensolver']\n", - "\n", - "start = 0.5 # Start distance\n", - "by = 0.5 # How much to increase distance by\n", - "steps = 20 # Number of steps to increase by\n", - "energies = np.empty([len(algorithms), steps+1])\n", - "hf_energies = np.empty(steps+1)\n", - "distances = np.empty(steps+1)\n", - "eval_counts = np.empty(steps+1)\n", - "\n", - "print('Processing step __', end='')\n", - "for i in range(steps+1):\n", - " print('\\b\\b{:2d}'.format(i), end='', flush=True)\n", - " d = start + i*by/steps\n", - " qiskit_chemistry_dict['PYQUANTE']['atoms'] = molecule.format(d/2) \n", - " for j in range(len(algorithms)):\n", - " dict = copy.deepcopy(qiskit_chemistry_dict)\n", - " dict['algorithm']['name'] = algorithms[j] \n", - " if algorithms[j] == 'ExactEigensolver':\n", - " del dict['optimizer']\n", - " del dict['variational_form']\n", - " del dict['initial_state']\n", - " solver = QiskitChemistry()\n", - " result = solver.run(dict)\n", - " energies[j][i] = result['energy']\n", - " hf_energies[i] = result['hf_energy']\n", - " if algorithms[j] == 'VQE':\n", - " eval_counts[i] = result['algorithm_retvals']['eval_count']\n", - " distances[i] = d\n", - "print(' --- complete')\n", - "\n", - "print('Distances: ', distances)\n", - "print('Energies:', energies)\n", - "print('Hartree-Fock energies:', hf_energies)\n", - "print('VQE num evaluations:', eval_counts)\n" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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yhCVLltyzbcmSJTzxxBP06dOH8ePHEx4ezpEjR9i3bx/ffvttWrn008kHBQXRoEGDvA6/SNAJJRf8vd05FXmHI5eirB2KphV6AwYMYP369SQmGhe6O3v2LJcvX+bkyZNpMwIDODs7M3PmTL788ktrhlsk6ckhc6Fn40pMWn2UlYcu4eVRytrhaFre2TAerhwx7zkrNoYen2W6u0yZMvj6+rJhwwb69u3LkiVLGDRoEEePHqV58+b3lK1VqxZ3797l9u3bwL3TyQPs2bMny9mHtYejayi54FrMns71y7P28GWSUwzWDkfTCr30zV5LlixhyJAhOTru/iYvnUwsQ9dQcsnf250NIVfYceI6HeuVt3Y4mpY3sqhJWFLfvn159dVXOXjwIHFxcTRv3pxDhw6xffv2e8qdPn2asmXLUqqUbjnIS7qGkkuPeJanlLO9nopF0/JAiRIl6NixI88++2xa7WTYsGHs3LmTrVu3AsZVHV955RUmT55szVCLJJ1QcsnBzobeXpXYHHqF2IRka4ejaYXekCFDOHz4cFpCKVasGGvWrGHKlCnUrVuXcuXK4efnx7Bhw9KOSV1DPvWxe/dua4VfqOnp683gwLmb9P9uD1MHNmFAcw+zn1/T8oOCMn39qlWreO211/j777+pVq2atcMpcPT09XkgOupCpvuaVS1NtbLOrDx0MQ8j0jQtI/369eP06dM6mViBTig5MGVpTwat6IkyZHwnl4jQr6k7u0/d4EpUfB5Hp2malj/ohJIDjdy8uGQLwaHLMi3Tz9sdpfRULJqmFV06oeRA5xbjcFCKgNAFmZapUa443lVL6bu9NE0rsnRCyYESLpXoYFuKTbFnSU7KvEnL39udY1diCIuIzsPoNE3T8gedUHKoR42e3LAV9h3+OdMyvb0qY2cjupaiaVqRpBNKDrVrPpoSBsWG439kWqZMcQce8XRjddAlUgxF53ZsTcsrtra294wn+ewz843YDwoKIiAgIO11ZtPeX758mQEDBpjtug/j7NmzNGrUyKoxZERPvZJDTsVK08mxAlsTrvB+fBSOTq4ZlvP39mBr2DX2nLpB2zrl8jhKTSvcihUrRlBQkEXOHRQURGBgID179kzbNnjwYGbOnPmfssuXL7dIDHktOTkZOzvzpQFdQ3kAPev4E2sj7DzwXaZlOtcvj4ujnW720rQ8EhUVhaenJ+Hh4YBxJP3cuXMBGD16ND4+PjRs2JBJkyalHbN//37atGlDkyZN8PX1JSoqiokTJ6aNqF+6dGmm10tfO4iLi2PQoEE0aNAAf39/WrZsSerg6c2bN9O6dWuaNWvGwIEDiY2NBaB69epMmjSJZs2a0bhxY44dOwbAP//8k1YT8vb2JiYmBqUUb775Jo0aNaJx48YZxtWqVSuOHj2a9vqRRx4hMDCQO3fu8Oyzz+Lr64u3tzerV68GjDWvPn360KlTJzp37vzQn3tGrFJDEZGBwAdAfcBXKZXh8HUR6Q58C9gCPyqlPjNtF+BjYCCQAnynlJpu6bhbNh1JmZDvWX96PZ39xmdYxsnelp6NK7Eu+DIf92tEMQdbS4elaXnu832fc+zmMbOes16Zerzt+3aWZe7evUvTpk3TXr/zzjtptYjhw4czbtw4bt26xfPPPw/AlClTKFOmDCkpKXTu3Jng4GDq1avH4MGDWbp0KS1atCA6OhpnZ2c+/PBDAgMD02ok8+bNy3Da+/Rmz55N6dKlCQ0NJSQkJC2269ev8/HHH7N161aKFy/O559/zrRp05g4cSIA5cqV4+DBg8yePZupU6fy448/MnXqVGbNmoWfnx+xsbE4OTnxxx9/EBQUxOHDh7l+/TotWrSgffv298QwePBgli1bxuTJk4mIiCAiIgIfHx/effddOnXqxM8//8zt27fx9fWlS5cuABw8eJDg4GDKlCnzMH+qTFmrySsEeBz4IbMCImILzAK6AheB/SKyRikVCgwHqgD1lFIGEcmTaX7t7J141LkqK+POExsTQQmXShmW82/mztLAC2wOvZK2VLCmabmXWZNX165d+f333xkzZgyHDx9O275s2TLmzJlDcnIyERERhIaGIiJUqlSJFi1aAFCyZMlMr5dZk1eqnTt3Mm7cOAAaNWqEl5cXAHv37iU0NBQ/Pz8AEhMTad26ddpxjz/+OADNmzfnjz+M/bJ+fn689tprDBs2jMcffxwPDw927tzJkCFDsLW1pUKFCnTo0IH9+/enXQdg0KBBPProo0yePJlly5al9e9s3ryZNWvWMHXqVADi4+M5f/582udl7mQCVkooSqkwMI4wz4IvcFIpddpUdgnQFwgFRgNDlVIG0/muWTTgdHo1GMaSg5/x1/4Z9On0SYZlfKuXwb1UMVYeuqQTilYoZVeTyGsGg4GwsDCcnZ25desWHh4enDlzhqlTp7J//35Kly7N8OHDiY/Pm5kslFJ07dqVxYsXZ7jf0dERMN5kkJxsnFR2/Pjx9OrVi4CAAPz8/Ni0aVOOruXu7k7ZsmUJDg5m6dKlfP/992kxrFixAk9Pz3vK//vvvxQvXvxh31qW8nMfijuQfgKti6ZtALWAwSISKCIbRKROZicRkVGmcoGRkZG5DqpJwyFUToGAC39mWsbGRujbtDI7TlwnMiYh19fUNC1rX3/9NfXr12fRokWMGDGCpKQkoqOjKV68OK6urly9epUNGzYA4OnpSUREBPv37wcgJiaG5ORkXFxciImJeaDr+vn5sWyZcQaN0NBQjhwxrmLZqlUrdu3axcmTJwG4c+cOx48fz/Jcp06donHjxrz99tu0aNGCY8eO0a5dO5YuXUpKSgqRkZFs374dX1/f/xw7ePBgvvjiC6KiotJqL926dWPGjBmkTgB86NChB3pvD8NiCUVEtopISAaPvmY4vSMQb5r9ci6Q6eAQpdQcpZSPUsrHzc0t1xcWGxt6uHqyV93h5s2TmZbz93YnxaBYe/hyrq+paZpRah9K6mP8+PGEh4fz448/8tVXX9GuXTvat2/Pxx9/TJMmTfD29qZevXoMHTo0rfnJwcGBpUuXMnbsWJo0aULXrl2Jj4+nY8eOhIaG3tMpn9209y+99BKRkZE0aNCA999/n4YNG+Lq6oqbmxvz5s1jyJAheHl50bp167TO98x88803ac1m9vb29OjRA39/f7y8vGjSpAmdOnXiiy++oGLFiv85dsCAAWlLIqeaMGECSUlJeHl50bBhQyZMmJDbjz9bVp2+XkS2AW9k1CkvIq2BD5RS3Uyv3wFQSn0qIseAHkqpM6YO+ttKqYzv403HXNPXh59Yz4Dd43mvwiM80X1GpuV6z9iBIKwd2zbX19Q0ayso09fnpZSUFJKSknBycuLUqVN06dKF8PBwHBwcrB3aQyus09fvB+qISA0RcQCeANaY9q0COpqedwCyrkuaWd1aPaidIgRcyXqRnn5N3TlyKYqT1x6sGq1pWsEQFxdH27ZtadKkCf7+/syePbtAJ5PcskpCERF/EbkItAbWi8gm0/bKIhIAoJRKBl4GNgFhwDKlVOrN1p8B/UXkCPApMDJP47exoUe5JhySRC5fzrzG06dpZWwEPSZF0wopFxcXAgMDOXz4MMHBwfTo0cPaIVmVVRKKUmqlUspDKeWolKqQ2qyllLqslOqZrlyAUqquUqqWUmpKuu23lVK9lFKNlVKtlVKHM7qOJfXwfgmADQdmZVqmvIsTbeu4serQZQx6KhatEChKK7wWRbn9++bnJq98rUqV1ngZ7Nhw/WCW5fo3c+fS7bv8cyL3d5hpmjU5OTlx48YNnVQKKaUUN27cwMnJ6aHPoefyyoWeFVvx2bWdnDq1hVq1umZYpkejSnxa8hg/7jhNR888GX+paRbh4eHBxYsXMcft91r+5OTkhIeHx0MfrxNKLnTzeYUv1u8gIPhHxmaSUBzsbBjhV51PNxwj5FIUjdyzvRlN0/Ile3t7atSoYe0wtHxMN3nlQjm3+viKMwG3QjNdbx5gSMuqlHC0Y+6O03kYnaZpWt7SCSWXerp34KIthIStyLRMSSd7nmhRhXXBEVy6fTcPo9M0Tcs7OqHkUucWr2CvFAFHf82y3Ii2xqaCX3aeyYuwNE3T0kRE5c0PWZ1QcqmkaxXa2bqyMfYMKcmJmZZzL1WM3l6VWLzvPFF3k/IwQk3TirK1hy/T4YttbA29avFr6YRiBj2rd+e6rRAYPC/Lcs+3q8mdxBSW7DufN4FpmlakLQu8wLglh2hapRQta5p/uvr76YRiBh18XsbZoAgI/z3Lco3cXfGrXZZfdp0lMTnzTnxN07TcmrfrDG8tD8avdjnmP+uLi5O9xa+pE4oZOBUrTWeH8myJjyAxIet5u55vV5Mr0fF6FmJN0yxm1t8n+WBtKN0aVuDHZ3zybOVYnVDMpEedfsRks948QIe6bnhWcGHujtN6xLGmaWallOKLjcf4clM4/ZpWZtbQZjja5d0y5DqhmEkr75GUNig2nF6XZTkRYWS7Ghy7EsOOE9fzKDpN0wo7g0ExeW0os7edYohvVaYNaoqdbd5+xeuEYib29s48WqwK25JuEheb9YrEfZpWpryLox7oqGmaWaQYFG+tCGbe7rOMbFuDT/wbYWOT5RLrFqETihn1rD+EeBvhr8DMF90CcLSzZbhfdXacuE7o5eg8ik7TtMIoMdnAK0sOsfzARcZ1rsN7vepjXHcw7+mEYkZNGw2lYooi4PyWbMsO862Gs4MtP+paiqZpDyk+KYXRCw6wPjiC93rW59Wuda2WTEAnFLOysbWjh2td9hhiuXXzVJZlXZ3teaJFVdYcvpxno1g1TSs87iQk8+y8/fwVfo2P+zXi+fY1rR2STijm1rPRcJJF2LJ/erZlR/hVRwG/7Dpr8bg0TSs8ou4m8dRP/7L39A2+GtiEJ1tVs3ZIgE4oZudZpzc1U4SAiF3Zlq1SxpmejSux6N/zRMfr6Vg0TcvejdgEhszZy5FLUcwe1ozHmz38+iXmphOKmYmNDT3KenFAErgScSjb8s+3q0FsQjJL913Ig+g0TSvIrkTFM3jOXk5FxjL3aR+6N6pk7ZDuoROKBfT0fhGAjVmsN5/Ky6MUrWqW4eddZ0hK0dOxaJqWsQs34xj4w24ibt9l/rO+PJIPV4DVCcUCqlZtSyODHQGRgTkqP6p9TSKi4lkfHGHhyDRNK4hOXotl4Pd7iL6bzMLnW9GqZllrh5QhnVAspGcFX8JsUjh95q9syz5Stzy1y5dgznY9HYumafcKunCbgd/vJtlgYMmoVjStUsraIWVKJxQL6dZ8LKIUG4LmZlvWxkYY1a4moRHR7D51Iw+i0zStINh+PJKhc/fi4mTPitFtqF+ppLVDypJOKBZSvkIjfKUYG26FZLnefKq+3pUpV8KRH7brgY6apsGaw5d5bv5+qpUtzvIXW1OtbHFrh5QtnVAsqEfl9pyzhdDwldmWdbSzZYRfdbYfjyQsQk/HomlF2fzdZxm35BDeVUuzZFQrypd0snZIOaITigV18R2HnVIEhGS93nyqYS2rUszelh936HXnNa0oUkoxbctxJq05Spf6Ffj1WV9ci1l+YSxz0QnFglxdq9LWpiQbY05lud58qlLODgxuUYU1hy9xJSo+DyLUNC2/SDEo3l8VwvQ/TzDIx4PvhjXDyT7v1jIxB51QLKx3jR5csxV25WBMCsCzfjVIMSjm7T5r2cA0Tcs3EpJTGLv4IAv/Pc/oR2rxeX+vPF/LxBwKXsQFTKdWr1M+RbHg2OIcla9a1pkejSqx8N9zxCYkWzg6TdOsLTYhmRG/7CfgyBXe71Wft7vXs+qMwbmhE4qF2ds7M7icN3u4y6lT2U9rD8aBjjHxySzdr6dj0bTC7LppXq5/z9xk2qAmjGxn/RmDc0MnlDwwoO0kHJRi4f6vclS+SZVS+NYow8879XQsmlZYXbgZx8Dv93DiWgxzn26eryZ5fFg6oeSBMmVq08uxImvvXiTq9tkcHTOqXU0u3b5LwBE9HYumFTbHrkTT/7vd3IhNYOHIlnSqV8HaIZmFTih5ZJjPq8TbCCt2fJij8p3qlaemW3Hm7tDTsWhaYRJ49iaDvt+DCPz+YhuaVytj7ZDMxmoJRUQGishRETEtduupAAAgAElEQVSIiE8W5bqLSLiInBSR8em2dxaRgyISJCI7RaR23kT+cDzr9KKFcmRx5D6Sk7K/JdjGRni+XU1CLkWz8+T1PIhQ0zRL+zPsKsN+/JdyJRxZMboNnhVdrB2SWVmzhhICPA5sz6yAiNgCs4AeQANgiIg0MO3+DhimlGoKLALet2y4ufdk3UFcsRX+2js1R+X9vd3xKF2MKevDSNZ9KZpWoP0eeIFRvx3As6ILv7/YGo/SztYOyeysllCUUmFKqfBsivkCJ5VSp5VSicASoG/qKYDUmdJcgcuWidR8Ovj+D/cUWHgq+6lYAJzsbXmvZ32OXYlhsb7jS9MKJKUU32w9zpvLg2ldsyyLnm9F2RKO1g7LIvJ7H4o7kP6b9KJpG8BIIEBELgJPAZ9ldAIRGSUigSISGBkZadFgs2Nr58DQiq05KImEHluVo2O6N6pIq5plmLY5nNtx2Y+21zQt/0hMNvDm8mC+2XqCAc09+Hl4C0o42lk7LIuxaEIRka0iEpLBo2/2R2frVaCnUsoD+AWYllEhpdQcpZSPUsrHzc3NDJfNHf+2k3A2KBYenJ6j8iLCxN4NibqbxDdbT1g4Ok3TzCU6PokR8/ax/MBFXu1Sly8HeOFgl99/w+eORVOlUqpLLk9xCaiS7rUHcElE3IAmSql/TduXAhtzea084VLSnb7O1Vh+9xyvXj9GuXL1sj2mQeWSDPGtym97zzG0ZVXqVihcHXmaVthcun2XEb/s43TkHaYObMKA5gV/jElO5Pd0uR+oIyI1RMQBeAJYA9wCXEWkrqlcVyDMSjE+sKEt3yJJhN935uwWYoDXH/WkuIMtH60L1bcRa1o+FnIpCv9Zu4i4Hc/8Z32LTDIB69427G/q/2gNrBeRTabtlUUkAEAplQy8DGzCmDCWKaWOmrY/D6wQkcMY+1DetMb7eBjVq3egnRRn6c1gEhNicnRMmeIOvNq1LjtOXGdr2DULR6hp2sP4O/wag37Yg52NsHx0G/xql7N2SHlKitKvXR8fHxUYGGjtMADYvX8WL4R+z5Qqj9Gn0yc5OiYpxUDPb3eQmGJg86vtcbQrWFNba1phtujf80xYHUK9ii78PLwFFQrIolg5ISIHlFKZjhdMlaMaioj8ISK9RCS/N5EVGK2bj6ZmirDgXECOlggGsLe1YeJjDTh3I46fd561bICapuWIwaD4fOMx3l15hPZ1yrHshdaFKpk8iJwmiNnAUOCEiHwmIp4WjKlIEBsbhrl3JMwmhUNHFuT4uHZ13OhSvwIz/zrBtWi9CJemWVNCcgrjlgbx3bZTDG1ZlblP+1C8EN8WnJ0cJRSl1Fal1DCgGXAW2Coiu0VkhIgUnPUp85ne7SZQ0qBYEDz3gY57v1d9ElMMfL4xu3GhmqZZyu24RJ76cR9rD19mfI96TOnXqEAuimVOOX73IlIWGI5xQOEh4FuMCSZni3xo/+HsXI7+JevyV8otIi4fyPFx1csV59m2NVhx8CJBF25bMEJN0zJy/kYcj3+3m6ALt5k+xJsXO9QqsItimVNO+1BWAjsAZ+AxpVQfpdRSpdRYoIQlAyzshrR+D4DFe6Y80HFjO9XBzcWRD9YcxWAoOjdWaJq1BV24jf/sXdyITWTByJb0aVLZ2iHlGzmtoUxXSjVQSn2qlLpngY6c9PxrmatUuTmdbEuzIvo4cXE5n1W4hKMdb3XzJOjCbVYFXbJghJqmpdp09ApPzNmDs6Mtf7zUBt8ahWfqeXPIaUIpLSKP3/foLCLlLRpdEfGk1/NE2wjrdn78QMf1b+ZBEw9XPttwjDt6/XlNsxilFLP+PsmLCw7gWbEkK1/yo5abbpy5X04TynPAj8Aw02Mu8DawS0SeslBsRYZ34yepb7Bl0cW/cnwLMRjXTJn4WEOuxSQwe9tJC0aoaUXX3cQUXlkSxJebwnnMqzJLR7WiXCGdLTi3cppQ7IH6Sqn+Sqn+GNcmUUBLjIlFywWxseHJaj05ZavYc/D7Bzq2ebXS+Hu7M3fHGc7fiLNQhJpWNEVE3WXQD3tYF3yZt7p78u0TTXGy1wOKM5PThOKhlLqa7vU1oIpS6iaQZP6wip7ufu9QNkWxMPS3Bz727e71sLMRpgSEWiAyTSuaDp6/RZ+ZuzgdGcvcp3x46ZHa+k6ubOQ0oWwTkXUi8oyIPAOsNm0rDuj7Vs3AwdGFQaUbs13Fcu7cjgc6tqKrE2M61mbT0avs0ssFa1quLT9wkSd+2Esxe1tWjvGjS4MK1g6pQMhpQhmDcc2RpqbHr8AYpdQdpVRHSwVX1AxqOxE7pVj07+cPfOxzbWvgUboYH64N1csFa9pDSjEopqwP5Y3fD9O8WmlWj/HTy0U8gGwTimld97+UUiuUUq+aHstVUZpVMo+Uc6tPT4fyrLpzlpjoB7sV2Mnelvd71Sf8agyL9p23UISaVnhF3U3i2Xn7mbvjDM+0rsavz/lSuriDtcMqULJNKEqpFMAgIq55EE+RN6zZK8TZCCt3Tn7gY7s1rEjrmmX5avNxbt3RywVrWk6diozFf9Yudp28zif+jZnctxH2RXwalYeR008sFjgiIj+JyPTUhyUDK6oa1OtHM+XAoit7SEl+sKQgIkzq04CY+CS+2XrcQhFqWuHyz/FI+s3axe27SSwc2ZKhLataO6QCK6cJ5Q9gArAdOJDuoVnAsFr+XLKFf/Z988DH1qtYkmEtq7Hg3/OEX8nZ4l2aVhQppfhxx2lG/LIP91LFWD3Gj5Y1y1o7rAItp7MNzweWAXuVUvNTH5YNrejq1OoNKqUoFh5f9lDHv9a1LiUc7Zi89qheLljTMpCQnMKby4P5eH0YXRtUYMXoNlQp42ztsAq8nE4O+RgQBGw0vW4qImssGVhRZmfvxBNuvuyTBMJPrH/g40sXd+C1rnXZfeoGG0OuWCBCTSu4rsXEM2TOXpYfuMgrnevw3bDmRXoNE3PKaZPXB4AvpjEnSqkgoKaFYtKA/u0m4mRQLAp88GYvgGEtq1K/UkneXXmEy7fvmjk6TSuYDpy7Rd+ZuwiNiGbW0Ga81rUuNjZ6sKK55DShJCmlou7bpgc7WJBrqeo8VsyD9fER3Lp56oGPt7O1YdZQbxKTDby86CBJemyKVoQppfh55xkG/7AHWxth+Ytt6OVVydphFTo5TShHRWQoYCsidURkBrDbgnFpwJMt3yRRYN7fbz3U8TXdSvD5AC8Onr/N5xuOmTk6TSsYYuKTeGnhQT5cF8ojnuVZP7Ydjdz1KAhLyGlCGQs0BBKAxUA08D9LBaUZ1azRmV72biyMDudKxKGHOkdvr8o807oaP+48o/tTtCInLCKaPjN3sTn0Ku/0qMfcp5vj6qxXLbeUnN7lFaeUek8p1UIp5WN6Hm/p4DQY2/FLDAIz/37zoc/xbq/6eHm48ubyw3pGYq3IWBZ4gX6zdnEnIZlFI1vygl6m1+JyepdXXRGZIyKbReSv1Ielg9OgcmUfhpWow5rEKxw/ueGhzuFoZ8usoc0Q4KVFB4hPSjFvkJqWj8QnpfDW8sO8tTyYZlVLs/6Vdnp8SR7JaZPX78Ah4H3gzXQPLQ+M7PotLgq+3vXg07GkqlLGma8GNSXkUjQfr9fT3GuF05nrd+g3axfLAi/ycsfaLBjZEjcXvRhWXslpQklWSn2nlNqnlDqQ+rBoZFoaV9eqPO/Wip3cYe+BHx76PF0bVOCF9jVZsPc8q/U69Fohs+FIBI/N2MmV6Hh+GdGCN7p5YqtvCc5TOU0oa0XkJRGpJCJlUh8WjUy7x5AuX1EpRTEt+DsMKQ+/fvwb3TzxqVaad/44wslrsWaMUNOsIzHZwIdrQxm98CC1ypdg/Svt6OhZ3tphFUk5TSjPYGzi2s3/z+MVaKmgtP9ydHJlbI1+hNmksHHnRw99HntbG2YM9cbJ3paXFh7gbqLuT9EKrsu37/LEnD38vOsMw9tU5/cXWuNeqpi1wyqycnqXV40MHnqkfB7r1f4D6hlsmH7qDxITHn7ix0quxfhmcFNOXItlwuoQM0aoaXnnn+OR9Jq+g/ArMcwc6s0HfRriYKennLemLD99EXkr3fOB9+37xFJBaRmzsbXj1cYvcMkWlvz5eq7O1b6uG2M71WH5gYss23/BTBFqmuWlGBTTthxn+C/7KO/ixJqxbentVdnaYWlkX0N5It3zd+7b193MsWg50MbnJdpQjDlXdxMdlbtEMK5zHfxql2XC6hDCIqLNFKGmWc6Fm3EM/mEP0/88wePeHqwa40cttxLWDkszyS6hSCbPM3qt5ZFXW71PtMBPW3M3WYGtjfDNYG9ci9nz0sKDxMQnmSlCTTMvpRTLAi/Q/ZvthF+JYdqgJkwd6EUxB1trh6alk11CUZk8z+i1lkfqefbhMYfyLIgJJ+Jy7u7ednNxZMYQb87duMM7fxzR66do+c6N2AReXHCAt5YH08jdlQ3/a8fjzTz0qPd8KLuE0kREokUkBvAyPU993fhhLyoiA0XkqIgYRMQni3I/i8g1EQm5b3sZEdkiIidM/y39sLEUVC8/8iUAM7c93MSR6bWsWZY3unmyLjiC3/aey/X5NM1c/jp2lW7f7ODvY5G827Mei55vhUdpvRBWfpVlQlFK2SqlSiqlXJRSdqbnqa9zM8NaCPA4xiWFszKPjPtqxgN/KqXqAH+aXhcplSo3Z1iJOqxNvEr48XW5Pt+L7WvRqV55PloXyuELt80QoaY9vLjEZN5beYRn5wVSroQDq1/2Y1T7WnqgYj5nlXvslFJhSqnwHJTbDtzMYFdfIHUJ4vlAPzOGV2A8lzoly56HH5eSysZG+GpgE8q7ODFm0UGi4nR/imYdh87fotf0nSzad55R7Wuyaowf9SuVtHZYWg4U1Ju2KyilIkzPrwAVMisoIqNEJFBEAiMjI/Mmujzi6lqVUeXbsIs49hz4PtfnK13cgZlDvbkaHc/rvx/W/SlankpKMfD1luMM+H4PickGFo1sxbs96+NkrzveCwqLJRQR2SoiIRk8+przOsr4rZfpN59Sao5pyn0fNzc3c146XxjS5Ssqp8DXwd/nakqWVN5VS/NOj/psDbvKd/88+EqRmvYwTkXGMuC73Xz75wn6NqnMhv+1o3UtPUOwOURHXeCzZY8RGxORfeFcslhCUUp1UUo1yuCx2gynvyoilQBM/71mhnMWSA6OLoytaZySJWDHw89GnN4Iv+r09qrEFxvD+WnnGbOcU9MyopTit73n6DV9B2dvxDFraDOmDW5KSSe9CJY5HDg8nwErerA07gyBRxdZ/HoFtclrDcb5xTD91xxJqsDq2W4S9Q22zDi9KldTsqQSEaYNakqPRhX5aF0os7edNEOUmnava9HxjJi3nwmrQmhRvQyb/tder/NuJklJccxYOZhnD32JPcJvvpN4pFXuZtfICaskFBHxF5GLQGtgvYhsMm2vLCIB6cotBvYAniJyUUSeM+36DOgqIieALqbXRZaNrR2veY3msi0s3mqefzQOdjbMGOJN36aV+WJjOF9vOa77VDSzUEqxOugS3b7Zzp5TN5jcpyG/PutLRVcna4dWKFy4sIfhC9oyJzqUxxwqsmzQFho1GJj9gWYgRelLwsfHRwUGFt5Jkl+c35IjhjsEPB6Aq2tVs5wzxaAYvyKY3w9c5MUOtXi7u6ceUKY9tLPX7zBhdQg7TlzHy8OVaYOaULu8i7XDKhSUwcC6fyYw5exqbICJtQbRvf1Es5xbRA4opTIdM5jKzixX0/KFV1tPYODu8fy0ZRyvDVhplnPa2gif9/fCwc6G7/85RUJyChN7N9BJRXsgCckpzPnnNDP+PomDrQ0fPNaAp1pX1+NKzCQm+hIfrRnKhpSbNBNHPnt0DpUqN8/zOHRCKUQ86/bmscCvWRh7giGXD5jtH5SNjfBxv0Y42tny864zJCYb+KhvI2z0l4GWA3tP3+C9lUc4FXmHXo0rMaF3A928ZUaHghcwPvBzrtooXi7tzcheP2Fr52CVWHRCKWTGdpzKxk1PMXPbm0wZ+pfZzisiTOhdH0d7G77bdoqEZAOf9/fSvzC1TN28k8iU9WGsOHgRj9LF+GV4CzrW0yspmktyUjxz1o3gh6gjVEaY7/M+TRo9kf2BFqQTSiFTsZI3w1zqMi/mOE+Fr6GeZx+znVtEeKubJ052tny99TiJyQamDWqCnW1BvVlQswSDQbH8wEU+2RBGbHwyLz1Si7Gd6uiZgc3o4sW9vLP1JYIkiT4O5XnnsYWUcLH+HXI6oRRCI7t8yx9/9ODrvR/zgxkTChiTyrgudXCws+HzjcdITDYwfYi3XilPA+D41RjeXxnCvrM3aVG9NFP8G1O3gu50N6d12yYw5Yyxj/TzGv3p2cE848/MQSeUQqikaxVGVWjDl5F72B04mzY+L5n9GqMfqYWjnQ0frgvlxQUHmD2smZ4iowi7m5jCjL9OMGf7aUo42fFFfy8GNPfQ/WxmFBsTwZQ1Q1mXfB1vceTTrt/h7u5r7bDuoW8bLqQSE2Lot7ANClg+aAvFS1S0yHUW7D3H+6tCaFenHHOe8tHNGkXQ3+HXmLg6hAs379K/mQfv9qxH2RKO1g6rUAk6spDx+z/jio3ihVJNeL7XT9jZ592NDTm9bVi3UxRSDo4uTPF5m8s2is/XPmmx6zzZqhpfDvBi58nrjJi3jzsJuZ9PTCsYrkbHM2bhQUb8sh8HWxsWP9+KrwY10cnEjBITYvhmxQCeOfApAPOav8PofgvzNJk8CJ1QCjFvryd5rmR9ViZe5c/dn1vsOgN9qvDN4KbsP3uLp3/eR7ReSrhQi7qbxBcbj9Hhy7/ZEnaV17vWJWCcnszR3MJPrGfIorb8FBuOv2NlVgzaQtPGw6wdVpZ0k1chl5Rwh2GL/IggmT96LcWtfEOLXWtjSARjFx+ifqWS/PqsL6WcrXMvvGYZdxNTmLf7LN9tO0lMQjJ9mlTm9a6eVC2rV1A0p5TkROZveJGZN/ZR0gCTGzxLh1avWTWmnDZ56YRSBJw+8yeDto2jhU0JZj+1G7GxXMX0z7CrjF5wkBrlijN9iDeeFfUdPgVdUoqBpfsvMP3PE1yLSaBTvfK88agnDSrrRa/M7cKFXbz35ysckkS62Lgyodc8ypSpbe2wdB+K9v9q1ujMa5U6sJM7LN08zqLX6ly/Ar+MaMH12AQem7GTWX+fJDnFYNFrapZhMBgncewy7R/eXxVC1TLO/P5ia34e3kInEzNTBgO/b36V/ltf4KRK4JOqfZk2bHu+SCYPQtdQighlMDD6t9YcMNxhWceZ1Kj+iEWvd/NOIhNXh7AuOAIvD1emDmyixyMUEEopth2P5IuN4YRFRFOvogtvdfeko2d5PYebBUReO8qkjc+xQ92hJU58/OgcKlbytnZY99BNXhkoygkF4NrVEB4PeAIP7Pjtyd3Y21u+7TvgSAQTVoUQE5/MuC51eKF9TT2yPh8LPHuTLzaGs+/sTaqWceb1R+vymFdlPZ7EQjbt+IiPTi4lHni1YjuGPDoDG9v8NzxQJ5QMFPWEArB156e8emoRo0o2YKz/0jy55o3YBCauPsr6IxE0MdVW6ujaSr4SFhHN1E3h/HnsGm4ujrzSuQ6DfaroGRAsJCrqPJ+ue4b1yddpaLDlk0emUbNGJ2uHlSmdUDKgE4rR+4u6sDbxCvObv5OntyGuD45gwuoQYuOT+V/XOoxqp2sr1nb+Rhxfbz3OqqBLlHC048UOtRjhVx1nh/z3K7mw2B04mwnBs7lhAy+U8mJkrx/zpLUgN3RCyYBOKEaxMREM+P1RBMuOos/I9dgEJq4OIeDIFV1bsRKlFHtO32D+7rNsCb2Kva0NI/xq8GKHmvpWbwu6G3eTr9c+xeL489RIET5tPYmG9ftbO6wc0QklAzqh/L+Dh39lxKEv6OdYiclDtuT59dcFX2bi6qPExifzate6PN+uhq6tWFhcYjIrD13i193nCL8aQ2lne57wrcrwNtWpUDJ/jrwuLAKD5jHp4Fect4UnnWswrvd8nIqVtnZYOaYTSgZ0QrnXtysG8GNsON/UeZLObd7O8+tfj01gwqoQNoRcoUmVUnw10EsvB2sB52/E8euesywLvEB0fDINKpVkeJvq9GlaWU/oaWF3Yq/w9fpnWRp/AfcU+NB7HL7eI60d1gPTCSUDOqHcK3UU/RWS+aP375Rzq5/nMSilWBccwcTVIdxJTOG1rnV5vl1NvXBXLiml2HHiOvN3n+Wv8GvYiNC9UUWGt6mOT7XS+vbfPLB7/yw+OPIdV2xgmHMNxvb+BWfnctYO66HohJIBnVD+Ky9H0WclMsZYW9l41FhbGduxNh3rldeJ5QHFJiSz4sBF5u85y+nIO5Qr4cAQ36oMa1lNL7ubR6KjLjA1YAQrE69SPUX4qMXb+X4OruzohJIBnVAytnDDS3x2bQfvV+zI4G7TrRaHUoq1wRF8vC6UazEJuJcqxtCWVRnkUwU3Fz2DbVZOR8by655zLD9wkdiEZJp4uPJMm+r08qqEo51u1sorf++Zysdh87hhA8Nd6jG61084OrlaO6xc0wklAzqhZMyQksxLC/zybBR9dpJSDGwJvcqCvefYfeoG9rZCt4YVebJVNVrWKKOba0wiYxL469hV1gVHsOPEdexthV6NK/FMm+p4Vy04Hb6Fwa2bp/hsw3MEJN+gjsGGj1pNLDB3cOWETigZ0Aklc9YYRZ8TpyJjWbj3PMsPGDuU65QvwbCWVXm8uQclneytHV6eUkpx4losW0KvsjXsKkEXbqMUuJcqxkAfD4a2rEp5F92slZeUwcDmXVP45ORSogVGlfJiZI+52DsWt3ZoZqUTSgZ0Qsnalp2f8NqpxbxQsiEv+y+xdjj3uJuYwtrgyyzce47DF6MoZm9LP+/KDGtZjUbuBb9JITNJKQb2n73J1tBrbA27yvmbcQB4ebjSpX4FutSvQP1KLrrWZgXXI8P4eONI/jRE09Bgy4ftPqVu7R7WDssidELJgE4o2XtvUWfWJV5lvs+7NG001NrhZCj44m0W7D3HmsOXiU8y0LRKKZ5sVY3eXpUKxW2w0fFJ/BMeydawq/x97BrR8ck42NngV6ssXRpUoHO9CrqD3YqUwcDabe/z+bk1xAuMKevL091n59tVFM1BJ5QM6ISSPWuOon9QUXFJrDh4kQX/nuN05B1KOdszoJkHHTzdaFCpZIFaivbCzTj+DLvK1rBr7D19g2SDokxxBzrVK0+X+hVoV6ccxR31dCjWdiXiEJM3j2Ynd2iq7PnwkWlW73PMCzqhZEAnlJw5cHg+Iw59SW/78kwZstVqtxLnVOpUIgv3nmfT0SskG4z/piuWdKJB5ZI0rFySBpVK0rCyK1XKFLNa85BSiuuxiZy4FsPJa7GcuBqb9vx6bCIANd2K07V+Bbo0qECzqqX1bdP5RHJSPIu3jGPm1V0oYFzFdjzR9Vts7YrGVDU6oWRAJ5Sc+27VUGZHHWFkCU/G9V9u7XByLCouiZDLUYRejubo5ShCI6I5eS0WU47BxdGO+mkJpiQNKpekTnkXs86qq5TiWkxCWsI4cS2Wk6bnt+KS0sq5ONpRp0IJ6pR3wbOiCx083ajlVsJscWjmEXx0KR/t+4RjNgbaUpx3O31NlSqtrR1WntIJJQM6oeScMhj4cFkPlidc5o1yrXmm1xxrh/TQ4pNSCL8Sw9HL0YRGRHH0cjTHImK4m5QCgL2tUKe8Cw0rl6RcBuNdMvpfRPHfjbfvJKUlkJj45LTtrsXsqVuhBLXLu1CnfAnqVChB3QoulHdx1J3p+VhU1HmmbxjF7/EXcTPA+LpD6dJmfL6vsVuCTigZ0AnlwaQkJ/Lm4s5sMdzm4yq96NvpM2uHZDYpBsWZ63cIjTDVZC5HExYRTfTd5P8WzuQ7//7NLk521C5vrHHUqVAi7Xm5Eg46cRQgymBg3T8TmXp2FVECQ4vXYkyPH/J1f6Kl6YSSAZ1QHlxiQgxjlnRmv4rja8/hdGz9hrVD0jSLOX3mL6b88xb7JAEvgx0T2kymnmcfa4dldTlNKEWv7qY9EAdHF77tv44Gyp43wuexP+hna4ekaWYXf/cW0/8YRP9/XiFMxTOhUmd+e3q/TiYPyCoJRUQGishRETGISKZZT0R+FpFrIhJy3/YvReSYiASLyEoRKWX5qIsu5xLlmdV3OR4GG145NI2w8NXWDknTzGb7v9/Sb3F75saE0cO+PGsf+4NBj36TL9d2z++sVUMJAR4HtmdTbh7QPYPtW4BGSikv4Djwjlmj0/6jdJla/NDzV1wUvLj7Pc6d22HtkDQtV65cCeK139oy5tiPOCD85DWOT4b9Rdlyda0dWoFllYSilApTSoXnoNx24GYG2zcrpVJ7T/cCHmYOUctAxYpN+aHTTBTwwp8vce1qSLbHaFp+k5wUz68Bo+i74Um2J9/mldLerBi2p0AufJXfFIY+lGeBDZntFJFRIhIoIoGRkZF5GFbhVKP6I3zXajK3RPFCwDCibp+1dkialmP7g37miQUt+TJyD81sSrCyy1ye7/NroZvM0VosllBEZKuIhGTw6GvGa7wHJAMLMyujlJqjlPJRSvm4ubmZ69JFWsP6/Zne5BXOSQpjVj5OXNx1a4ekaVk6f34n//vNj2cPf02USuGrmoOZ/dTuIjdA0dIs1uuklOpiqXMDiMhwoDfQWRWle5/ziZbNRvFF3A1eP7mQ137vxYwn/tK/8rR8JzrqAnM2j2XhnZPYKxhb1punu07HqZheL8YSCmSTl4h0B94C+iil4qwdT1HVpe07TPLozi7ieO/3nhhSMhgUqGlWkJwUz5KNY+n9Rw9+vXOSxxwrsr7XUkb1+U0nEwuy1m3D/iJyEWgNrBeRTabtlUUkIF25xcAewFNELorIc6ZdMwEXYIuIBInI93n8FjSTx7tM5dUyLdiQcpNPl/dBGXfBZ3EAABH4SURBVAzWDkkr4nbtn8mA33yZcnUbtcWJpa2n8OGQrbiVb2jt0Ao9PVJeM4uvlvsz785JXnJtzOh+i6wdjlYEnT7zJ19uf4+d3KFKCrxe70k6tXqzSM69ZW45HSmvR+5oZvHa4yu4veRRZkcdwXXjGIZ2n2XtkLQi4tbNU8zeMpbf757HWcEb5VszpMs0HBxdrB1akaMTimYWYmPDpIHriFrcmU+vbsd120R6PfKhtcPSCrGkhDss2voqP1zbTZzAgGJVeanrdMqUqW3t0IosXRfUzMbO3okvBwXgoxx59+wf/LLuOd2nopmdMhj4a/cX9FvYiqnX9+BlU5zl7abx/uAAnUysTCcUzawcnVyZNSCALnalmXZjH28s6kBc7DVrh6UVAspgYM+B73lqvg/jTvyGHcJ39Ufx/TP/UrvWo9YOT0MnFM0CnEuUZ+rQf3itrC9bk28xdFkXPfeXliv7D/3E8F9b/F979x4dVXnucfz7S4LcIchFQCDhZpEqIsrFGyICtdKKF2prFaXW2mN7vB1be1rb2uNx1QtrVY+ttWKPtVIFW9Qj1htgQS2FAAYIQaAiDfdLBKSAEJPZz/ljb+wQBxhgkp1Jns9as/Jm9p49zzszmV/23jPvy42lj7LFPuGnnUbw/Lj5nDvo5rhLc0n8U16uRs199zfcWfIrqoD7T76e84f8R9wluSxSvORpHl30CPNVQYeEcUPnYVxxwX1+wr2W+QRbKXigxGPDhvncPv1GluckuKnVKfzbJZN8aHB3SEtKp/Drd3/B39hL24RxQ6dzGTvsPv9SYkw8UFLwQInPvr07+O8XxzKtcivnqwU/H/NHWrXuGndZro5Ztvx5Hl0wgXdsD20C45sdzuLKCx6gabPj4y6tQfNAScEDJV4WBEyZfgsPbp5N50A8PHQCvXulmu7GNTQrVk7j0aL7mW27aB0Y49udydcveJBmLTrEXZrDAyUlD5S6oXjJ09zx7oPsEdzT80ouGvrTuEtyMXl/1es8NvdeZgQ7aRkY1x1/OlcPf5AWLTvFXZpL4oGSggdK3bF1Syl3vHYti1XJN5r34pYxk8lr1CTuslwt+fuq13hi3n28UbWd5gbj8k/lmuEP+mHQOsoDJQUPlLqlsmIPD7w4lucq1jOYJkz48hTaHN8z7rJcDQkSVbyz4BEmrZxMEftoGhjXtD6Z64ZPoHV+YdzluUPwQEnBA6VuevHNO7l33au0DeChs+/h830uj7skl0Ef797KS3+9h2c2vsWaXOiQML7efiBjz7vbgyRLeKCk4IFSdy1b/jy3zb2b7Tnwk66jGXPBfT5KbJbbvGkRz865h6m73mdXjjg1yGNcjzGMOPtOGjVqFnd57gh4oKTggVK3bd++ijtfvooi9jGYJtw++Ie+t5KFlpRO4Q+Lf82Mqu0YMCKvDeP638Rpfb/m/yRkKQ+UFDxQ6r6qyn08N/N2Ht/8DjtyxBdzj+fm839O167nxF2aO4Sqyn3MnPsAkz54iZKcSloGxhUte3PV2XfRufNh34dcHeeBkoIHSvbYvWsTv5t5G5M+Wkal4Mpmhdw4/Be0bXdS3KW5JDt3ruX5t3/G5PL5bM4V3RJwdeehXHru3f4dknrEAyUFD5TsU751GY/95Q5e2Leexgbj25zGdSMe8jerGAWJKoqX/oE/L3+WV/dtZG+OGGSNGdfnKoYOvNWH1amHPFBS8EDJXv8om80v3/kxM4KdtE0YN504nMuH3+8nd2vRqg+m88riibyycwWbckXTwBjVuCPXnHELfT53SdzluRrkgZKCB0r2W1I6hV8snECxPqEgAbf0/iojz/mRn+ytIVu3lPLawv/hz1vnsyInINeMs9SC0QUjGX7mzb6n2EB4oKTggVI/WBDw9vyHefi9p1iVa5wa5HH76TczsP/1cZdWL+zetYkZ8x/ilfWzmG97MYUf+R3dcQhfGHgr7dr1ibtEV8s8UFLwQKlfElWfMO2tH/PomlfZkivOU3NuO/tuTur1xbhLyzqVFXv4a/FjvPLBNGZXbqciR3RNwJfanMLoAd+hoOC8uEt0MfJAScEDpX7at3cHk9/8Hk+UF7FbMEhNGdnxLC4ccBPt2p8cd3l1VmXFHhYvf443VvyJ1/euY2eOaBMYFzUrYPTnx9Gv75V+KNEBHigpeaDUbzs/KuMPs37I6ztKKcsFmXE6jRl5wkBG9P82HTudHneJsQoSVaxc9QpF77/MvG1LKQ72sDdHNAmMCxq15Uu9L+esAd/yDzq4z/BAScEDpWGwIGDV6unMLH2a6TuWsSonAKBfkMfI9mcwov8NdOkyJOYqa54FAWvXzaFoxVTmbS1mQdUOPsoRAN0TYnDzLgzpMpQhp42neYuOMVfr6jIPlBQ8UBqmsrK3mFnyJNO3LWF5TgKAk4NcRrbtx4h+19O9cFi8BWbQ1i2lFL03haJN8yjat5nNuWGAdEwYg5t0ZHCnwQzq+1VOOKFfzJW6bOKBkoIHilu/fh4zF/+WGeXFlORUAtAryGFkfl9GnnodvXqMyprzBpUVe1i3sYgPNsxjwYY5FO1Zx+rc8O+5dWAMymvDkA4DGNxnLN26npM1/XJ1jwdKCh4oLtnmzYt5c9HjzNiygGL2YRKtA6OARnQ9Lp+C5p3omt+Tbu1PoeDEwbEMtR4kqti8ZTFlG+ez5sP3WPvPNZTtLWdNYg8bcoxA4R5I08AYkNOcIW1PZXDvL/O5XqP9G+suYzxQUvBAcQfzYflyZi2ayIrty1lbsZ21ib1syjEsesMGaBUY3WhEt+Na061ZJ7pFYdOt80Dy87sf0R6ABQGJxCcEQSVViQo+/vhD1m1cSFl5CWs+Ws2ajzdTVrWLdSSoyPlXDU0Do5A8Chq1oqB5Zwrye1HY4TT69LqYRo2bZ/QxcW4/D5QUPFDckfikYhfrN85n7ZbFrNm2knW71rGmYhvrEnvZWC1sWgZGW8shwEgAVRgBkBBUQdgGqhS1k25bXZ4ZXYMcCvJaUNjsBLq1KqSw/SkUdB5M+/Z9/dCVq3XpBorvEzt3EMc1bkmP7hfSo/uFn1kWhs0C1m5ZxNrtK1n7z3XsqNpNLjnkKZdc5SRdcv/1M2d/O++AduO8JnRr24fCTmfQqeMZ5DVqEkOPnTs2HijOHYUwbIbTo/vwuEtxrs7wfWfnnHMZEUugSPqKpGWSAkkHPS4n6UlJWyWVHmT5HZJMUruaq9Y551w64tpDKQUuB94+zHpPARelWiCpKzAKWJvRypxzzh2VWALFzJab2co01nsb2H6QxQ8BdwIN52NqzjlXh2XlORRJY4ANZrYkjXVvlLRQ0sLy8vJaqM455xqmGvuUl6SZQKoR5+4ys5eOYbvNgB8RHu46LDObCEyE8HsoR3u/zjnnDq3GAsXMRtTQpnsC3YElCr8c1gUoljTIzDbX0H0655w7jKz7HoqZLQU+nchaUhlwppl9GFtRzjnn4hl6RdJlwC+B9sBHwGIz+4KkzsBvzeziaL3JwDCgHbAFuNvM/rfatspIM1AklQNrjrLsdkBDCy3vc8PgfW4YjqXPBWbW/nArNaixvI6FpIXpjGVTn3ifGwbvc8NQG33Oyk95Oeecq3s8UJxzzmWEB0r6JsZdQAy8zw2D97lhqPE++zkU55xzGeF7KM455zLCA8U551xGeKBUI+kiSSslrZL0nymWj5dULmlxdLkhjjoz6XB9jta5UtJ70bQDz9Z2jZmWxvP8UNJz/HdJH8VRZyal0edukmZJWiSpRNLFcdSZKWn0t0DSm1FfZ0vqEkedmZTGlB+S9Ej0mJRIGpDRAszML9EFyAU+AHoAxwFLgL7V1hkP/CruWmu5z72BRUCb6PcOcddd032utv7NwJNx110Lz/NE4Kao3Rcoi7vuGu7vn4DrovZwYFLcdWeg30OBAUDpQZZfDLwGCBgCFGXy/n0P5UCDgFVmttrMPgGmAGNirqmmpdPnbwGPmtkOADPbWss1ZtqRPs9XAZNrpbKak06fDWgVtVsDG2uxvkxLp799gb9E7VkplmcdO/SUHxD28WkLzQPyJXXK1P17oBzoRGBd0u/ro+uquyLaXZwaTfSVzdLp80nASZLmSJonKeWkZ1kk3ecZSQWEg5H+JdXyLJJOn38GXCNpPfAq4Z5Ztkqnv0sIJ/oDuAxoKaltLdQWp7Rf+0fDA+XIvQwUmlk/YAbw+5jrqQ15hIe9hhH+t/6EpPxYK6o9XwOmmlki7kJqwVXAU2bWhfDQyCRJ9fk94nvA+ZIWAecDG4CG8DzXmPr8YjkaG4DkPY4u0XWfMrNtZlYR/fpb4Ixaqq2mHLbPhP/FTDOzSjP7B/B3woDJVun0eb+vkf2HuyC9Pn8T+COAmc0FmhAOKJiN0vlb3mhml5vZ6cBd0XVZ/+GLwziS1/4R80A50AKgt6Tuko4jfDOZlrxCteONlwDLa7G+mnDYPgP/R7h3gqR2hIfAVtdmkRmWTp+R1AdoA8yt5fpqQjp9XgtcCCDpZMJAydZpTtP5W26XtAf2Q+DJWq4xDtOAa6NPew0BdprZpkxtPOvmQ6lJZlYl6d+BNwg/JfKkmS2TdA+w0MymAbdIugSoIjz5NT62gjMgzT6/AYyS9B7hIYHvm9m2+Ko+Nmn2GcI3oSkWfTwmm6XZ5zsID2feTniCfny29j3N/g4D7pNkwNvAd2MrOEOSp/yIzoXdDTQCMLPfEJ4buxhYBXwMfCOj95+lrxfnnHN1jB/ycs45lxEeKM455zLCA8U551xGeKA455zLCA8U55xzGeGB4rKapN1prHObpGYZvM9LJfXN4Pb+dgy33R397Cxp6iHWy5f0naO9H+fS4YHiGoLbgCMKFEm5h1h8KeHAghlhZmdnYBsbzWzsIVbJBzxQXI3yQHH1gqRh0ZwWUyWtkPRM9G3gW4DOwCxJs6J1R0maK6lY0p8ktYiuL5P0gKRi4CuSviVpgaQlkp6X1EzS2YQjJEyI5krpKal/NGhmiaQXJbWJtjdb4bwqCyUtlzRQ0guS3pd0b1Ltu5PaP5C0NLrP+1P0s3tU+9Jq2yjcPweGpM9Lmh/VVyKpN3A/0DO6boKkFgrnAimOtjUmaTvLJT2hcO6b6ZKaRst6SZoZ1VYsqWd0/fejx6lE0n9l9Il12SXu8fv94pdjuQC7o5/DgJ2EYxPlEA6Xcm60rAxoF7XbEX4runn0+w+Anyatd2fSttsmte8Fbo7aTwFjk5aVAOdH7XuAh6P2bOCBqH0r4XDwnYDGhOOjta3Why8CfwOaRb8fn6K/04Bro/Z3k25bSDQHBvBL4OqofRzQNHl5dH0e0CrpMVlFOEdGIeEoEP2jZX8EronaRcBlUbsJ4V7fKMJ5VBQ97n8Ghsb9uvBLPBcfesXVJ/PNbD2ApMWEb45/rbbOEMLDVXMkQfiGmzxW13NJ7VOivYB8oAXhMB4HkNQayDezt6Krfk84cdN++4dxWQoss2jcJEmrCQfpSx7CZgTwOzP7GMDMUs1rcQ5wRdSeBDyQYp25wF0KZyB8wczej/p6QOnAzyUNBQLCIcxPiJb9w8wWR+13gUJJLYETzezFqLZ9UT9GEYbKomj9FoQDh76doi5Xz3mguPqkIqmdIPXrW8AMM7vqINvYk9R+CrjUzJZIGk80QOZR1hRUqy84SH3pOOR4SWb2rKQiYDTwqqRv89nBPK8G2gNnmFmlpDLCvY7kmiF8HJse4u4E3Gdmjx9B/a6e8nMoriHYBbSM2vOAcyT1ApDUXNJJB7ldS2CTpEaEb8Cf2Z6Z7QR2SDovWjYOeIujMwP4xv5PpEk6PsU6cwgHraRaTZ+S1ANYbWaPAC8B/TjwMYBwRsatUZhcABQcqjAz2wWsl3RpdB+NozrfAK5POg91oqQOafXW1TseKK4hmAi8LmmWmZUTjhA9WVIJ4eGhPge53U8IzxvMAVYkXT8F+L6kRdGJ6esIT9KXAP0Jz6McMTN7nfAQ2cLokN33Uqx2K/BdSUs5+Ex7VwKl0TZOIZzydRvhYb5SSROAZ4Azo+1cW61/BzOOcLTtEsJzPR3NbDrwLDA32tZUDgwu14D4aMPOOecywvdQnHPOZYQHinPOuYzwQHHOOZcRHijOOecywgPFOedcRnigOOecywgPFOeccxnx/8N/bkLxDnv5AAAAAElFTkSuQmCC\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.plot(distances, hf_energies, label='Hartree-Fock')\n", - "for j in range(len(algorithms)):\n", - " pylab.plot(distances, energies[j], label=algorithms[j])\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Energy')\n", - "pylab.title('H2 Ground State Energy')\n", - "pylab.legend(loc='upper right');" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.plot(distances, np.subtract(hf_energies, energies[1]), label='Hartree-Fock')\n", - "pylab.plot(distances, np.subtract(energies[0], energies[1]), label='VQE')\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Energy')\n", - "pylab.title('Energy difference from ExactEigensolver')\n", - "pylab.legend(loc='upper left');" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.plot(distances, eval_counts, '-o', color=[0.8500, 0.3250, 0.0980], label='VQE')\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Evaluations')\n", - "pylab.title('VQE number of evaluations')\n", - "pylab.legend(loc='upper left');" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/chemistry/h2_var_forms.ipynb b/community/chemistry/h2_var_forms.ipynb deleted file mode 100644 index f386f756f..000000000 --- a/community/chemistry/h2_var_forms.ipynb +++ /dev/null @@ -1,212 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## _*H2 energy with various RY and RYRZ variational forms*_\n", - "\n", - "This notebook demonstrates using Qiskit Chemistry to plot graphs of the ground state energy of the Hydrogen (H2) molecule using VQE with different variation form configurations. The results are compared to the same energy as computed by the ExactEigensolver\n", - "\n", - "This notebook populates a dictionary, that is a progammatic representation of an input file, in order to drive the Qiskit Chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here. \n", - "\n", - "This notebook has been written to use the PYSCF chemistry driver." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Hartree-Fock energy: -1.1173432691225829\n", - "FCI energy: -1.1372213770723014\n" - ] - } - ], - "source": [ - "import numpy as np\n", - "import pylab\n", - "from qiskit.chemistry import QiskitChemistry\n", - "\n", - "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", - "qiskit_chemistry_dict = {\n", - " 'problem': {'random_seed': 50},\n", - " 'driver': {'name': 'PYSCF'},\n", - " 'PYSCF': {'atom': 'H .0 .0 -0.3625; H .0 .0 0.3625', 'basis': 'sto3g'},\n", - " 'operator': {'name': 'hamiltonian', 'qubit_mapping': 'jordan_wigner',\n", - " 'two_qubit_reduction': False},\n", - " 'algorithm': {'name': 'ExactEigensolver'}\n", - "}\n", - "var_forms = ['RYRZ', 'RY']\n", - "entanglements = ['full', 'linear']\n", - "depths = [x for x in range(3, 11)]\n", - "\n", - "energies = np.empty([len(var_forms), len(entanglements), len(depths)])\n", - "hf_energy = None\n", - "energy = None\n", - "eval_counts = np.empty([len(var_forms), len(entanglements), len(depths)])\n", - "\n", - "solver = QiskitChemistry()\n", - "result = solver.run(qiskit_chemistry_dict)\n", - "hf_energy = result['hf_energy']\n", - "energy = result['energy']\n", - "print('Hartree-Fock energy:', hf_energy)\n", - "print('FCI energy:', energy)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "With a reference FCI energy computed from ExactEigensolver we now compute the ground state energy with VQE and different variational form setups" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Processing step 7 --- complete\n", - "Depths: [3, 4, 5, 6, 7, 8, 9, 10]\n", - "Energies: [[[-1.11734306 -1.13720243 -1.13720372 -1.13722021 -1.13722135\n", - " -1.13722136 -1.13722136 -1.13722136]\n", - " [-1.13722127 -1.13722069 -1.13722133 -1.13711301 -1.13715782\n", - " -1.13717939 -1.13722016 -1.13717511]]\n", - "\n", - " [[-1.13722034 -1.13722128 -1.13722094 -1.13722098 -1.13722135\n", - " -1.13722136 -1.13722137 -1.13722136]\n", - " [-1.1372213 -1.13722138 -1.13722136 -1.13722137 -1.13722137\n", - " -1.13722137 -1.13722137 -1.13722137]]]\n", - "Num evaluations: [[[ 8011. 10000. 10000. 10000. 4405. 3554. 3410. 3097.]\n", - " [ 5603. 10000. 5328. 10000. 10000. 10000. 10000. 10000.]]\n", - "\n", - " [[ 7455. 2840. 4351. 3553. 1145. 1944. 1053. 1052.]\n", - " [ 1956. 380. 1052. 841. 1024. 1016. 675. 702.]]]\n" - ] - } - ], - "source": [ - "qiskit_chemistry_dict['algorithm']['name'] = 'VQE' \n", - "qiskit_chemistry_dict['optimizer'] = {'name': 'COBYLA', 'maxiter': 10000 }\n", - "qiskit_chemistry_dict['variational_form'] = {'name': 'RYRZ', 'depth': 3, 'entanglement': 'full'}\n", - "qiskit_chemistry_dict['initial_state'] = {'name': 'ZERO'}\n", - " \n", - "print('Processing step __', end='')\n", - "for i, d in enumerate(depths):\n", - " print('\\b\\b{:2d}'.format(i), end='', flush=True)\n", - " qiskit_chemistry_dict['variational_form']['depth'] = d\n", - " for j in range(len(entanglements)):\n", - " qiskit_chemistry_dict['variational_form']['entanglement'] = entanglements[j] \n", - " for k in range(len(var_forms)):\n", - " qiskit_chemistry_dict['variational_form']['name'] = var_forms[k] \n", - " solver = QiskitChemistry()\n", - " result = solver.run(qiskit_chemistry_dict)\n", - " energies[k][j][i] = result['energy']\n", - " eval_counts[k][j][i] = result['algorithm_retvals']['eval_count']\n", - "print(' --- complete')\n", - "\n", - "print('Depths: ', depths)\n", - "print('Energies:', energies)\n", - "print('Num evaluations:', eval_counts)" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "for k in range(len(var_forms)):\n", - " for j in range(len(entanglements)):\n", - " pylab.plot(depths, energies[k][j]-energy, label=var_forms[k]+' + '+entanglements[j])\n", - "pylab.xlabel('Variational form depth')\n", - "pylab.ylabel('Energy difference')\n", - "pylab.yscale('log')\n", - "pylab.title('H2 Ground State Energy Difference from Reference')\n", - "pylab.legend(loc='upper right');" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The above plot shows how close the ground state energy result from VQE was to the reference. The next plot shows how many evaluations (calls to the objective/cost function) were needed by the optimizer before it stopped and returned. Note that the optimzer was configured with a maximum number of iterations of 10,000. The COBYLA optimizer makes one evaluation per iteration and it can be seen that for some points that the iteration limit was reached which caused the optimizer to return." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "for k in range(len(var_forms)):\n", - " for j in range(len(entanglements)):\n", - " pylab.plot(depths, eval_counts[k][j], '-o', label=var_forms[k]+' + '+entanglements[j])\n", - "pylab.xlabel('Variational form depth')\n", - "pylab.ylabel('Evaluations')\n", - "pylab.title('VQE number of evaluations')\n", - "pylab.legend(loc='upper right');" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/chemistry/h2_vqe_initial_point.ipynb b/community/chemistry/h2_vqe_initial_point.ipynb deleted file mode 100644 index 2e83c3549..000000000 --- a/community/chemistry/h2_vqe_initial_point.ipynb +++ /dev/null @@ -1,291 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## _*Initializing next computation from prior result*_\n", - "\n", - "This notebook demonstrates using Qiskit Chemistry to plot graphs of the ground state energy of the Hydrogen (H2) molecule over a range of inter-atomic distances using VQE and RYRZ. It is compared to the same energies as computed by the ExactEigensolver and we also compare using the previous computed optimal solution as the starting initial point for the next distance.\n", - "\n", - "This notebook populates a dictionary, that is a progammatic representation of an input file, in order to drive the Qiskit Chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here where we alter the molecule supplied to the driver in each loop.\n", - "\n", - "This notebook has been written to use the PYQUANTE chemistry driver. See the PYQUANTE chemistry driver readme if you need to install the external PyQuante2 library that this driver requires." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "scrolled": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Processing step 20 --- complete\n", - "Distances: [0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.675 0.7 0.725 0.75 0.775\n", - " 0.8 0.825 0.85 0.875 0.9 0.925 0.95 0.975 1. ]\n", - "Energies: [[-1.05515974 -1.07591361 -1.09262987 -1.10591801 -1.11628598 -1.12416089\n", - " -1.12990476 -1.1338262 -1.13618944 -1.13722136 -1.13711707 -1.13604436\n", - " -1.13414767 -1.1315512 -1.12836188 -1.12467175 -1.12056028 -1.11609624\n", - " -1.11133942 -1.10634212 -1.10115033]\n", - " [-1.05515974 -1.07591361 -1.09262987 -1.10591801 -1.11628598 -1.12416089\n", - " -1.12990476 -1.1338262 -1.13618944 -1.13722135 -1.13711706 -1.13604436\n", - " -1.13414767 -1.1315512 -1.12836188 -1.12467175 -1.12056028 -1.11609624\n", - " -1.11133942 -1.10634212 -1.10115033]\n", - " [-1.05515974 -1.07591361 -1.09262987 -1.10591802 -1.11628599 -1.12416089\n", - " -1.12990476 -1.1338262 -1.13618944 -1.13722136 -1.13711707 -1.13604436\n", - " -1.13414767 -1.13155121 -1.12836188 -1.12467175 -1.12056028 -1.11609624\n", - " -1.11133943 -1.10634212 -1.10115034]]\n", - "Hartree-Fock energies: [-1.04299622 -1.0630621 -1.0790507 -1.09157046 -1.10112822 -1.10814997\n", - " -1.11299652 -1.11597525 -1.11734902 -1.11734325 -1.11615145 -1.11393966\n", - " -1.1108504 -1.10700581 -1.10251056 -1.09745432 -1.09191405 -1.08595588\n", - " -1.07963694 -1.07300677 -1.06610866]\n", - "VQE num evaluations: [[377 418 377 357 374 380 361 376 365 353 350 353 351 360 378 342 345 365\n", - " 344 341 349]\n", - " [377 300 262 263 281 293 286 273 292 259 288 266 265 241 301 280 283 273\n", - " 296 291 266]\n", - " [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n", - " 0 0 0]]\n" - ] - } - ], - "source": [ - "import numpy as np\n", - "import pylab\n", - "import copy\n", - "from qiskit.chemistry import QiskitChemistry\n", - "\n", - "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", - "qiskit_chemistry_dict = {\n", - " 'problem': {'random_seed': 50},\n", - " 'driver': {'name': 'PYQUANTE'},\n", - " 'PYQUANTE': {'atoms': '', 'basis': 'sto3g'},\n", - " 'operator': {'name': 'hamiltonian', 'qubit_mapping': 'parity',\n", - " 'two_qubit_reduction': True},\n", - " 'algorithm': {'name': ''},\n", - " 'optimizer': {'name': 'COBYLA', 'maxiter': 10000 },\n", - " 'variational_form': {'name': 'RYRZ', 'depth': 5, 'entanglement': 'linear'}\n", - "}\n", - "molecule = 'H .0 .0 -{0}; H .0 .0 {0}'\n", - "algorithms = [{'name': 'VQE'},\n", - " {'name': 'VQE'},\n", - " {'name': 'ExactEigensolver'}]\n", - "titles= ['VQE Random Seed', 'VQE + Initial Point', 'ExactEigensolver']\n", - "\n", - "start = 0.5 # Start distance\n", - "by = 0.5 # How much to increase distance by\n", - "steps = 20 # Number of steps to increase by\n", - "energies = np.empty([len(algorithms), steps+1])\n", - "hf_energies = np.empty(steps+1)\n", - "distances = np.empty(steps+1)\n", - "eval_counts = np.zeros([len(algorithms), steps+1], dtype=np.intp)\n", - "\n", - "print('Processing step __', end='')\n", - "for i in range(steps+1):\n", - " print('\\b\\b{:2d}'.format(i), end='', flush=True)\n", - " d = start + i*by/steps\n", - " qiskit_chemistry_dict['PYQUANTE']['atoms'] = molecule.format(d/2) \n", - " for j in range(len(algorithms)):\n", - " dict = copy.deepcopy(qiskit_chemistry_dict)\n", - " dict['algorithm'] = algorithms[j] \n", - " if algorithms[j]['name'] == 'ExactEigensolver':\n", - " del dict['optimizer']\n", - " del dict['variational_form']\n", - " solver = QiskitChemistry()\n", - " result = solver.run(dict)\n", - " energies[j][i] = result['energy']\n", - " hf_energies[i] = result['hf_energy']\n", - " if algorithms[j]['name'] == 'VQE':\n", - " eval_counts[j][i] = result['algorithm_retvals']['eval_count']\n", - " if j == 1:\n", - " algorithms[j]['initial_point'] = result['algorithm_retvals']['opt_params'].tolist()\n", - " distances[i] = d\n", - "print(' --- complete')\n", - "\n", - "print('Distances: ', distances)\n", - "print('Energies:', energies)\n", - "print('Hartree-Fock energies:', hf_energies)\n", - "print('VQE num evaluations:', eval_counts)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The plot of ground energies from VQE, whether starting from a random initial point or the optimal solution from the prior point are indistinguisable here." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.plot(distances, hf_energies, label='Hartree-Fock')\n", - "for j in range(len(algorithms)):\n", - " pylab.plot(distances, energies[j], label=titles[j])\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Energy')\n", - "pylab.title('H2 Ground State Energy')\n", - "pylab.legend(loc='upper right');" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "for i in range(2):\n", - " pylab.plot(distances, np.subtract(energies[i], energies[2]), label=titles[i])\n", - "pylab.plot(distances, np.subtract(hf_energies, energies[2]), label='Hartree-Fock')\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Energy')\n", - "pylab.title('Energy difference from ExactEigensolver')\n", - "pylab.legend(loc='upper left');" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Lets plot the difference of the VQE ground state energies from the ExactEigensolver. They are both in the same ballpark and both very small." - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "for i in range(len(algorithms)-1):\n", - " pylab.plot(distances, np.subtract(energies[i], energies[2]), label=titles[i])\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Energy')\n", - "pylab.yscale('log')\n", - "pylab.title('H2 Ground State Energy')\n", - "pylab.legend(loc='upper right');" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Finally lets plot the number of evaluations taken at each point. Both start out at the same number since we start them the same. But we can see, as we step along small distances, that the prior solution is a better guess as the starting point for the next step leading to fewer evaluations." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "for i in range(2):\n", - " pylab.plot(distances, eval_counts[i], '-o', label=titles[i])\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Evaluations')\n", - "pylab.title('VQE number of evaluations')\n", - "pylab.legend(loc='center left');" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Total evaluations for 'VQE Random Seed' = 7616\n", - "Total evaluations for 'VQE + Initial Point' = 5936\n", - "\n", - "Total evaluations for 'VQE + Initial Point' are 77.94% of 'VQE Random Seed'\n" - ] - } - ], - "source": [ - "for i in range(2):\n", - " print(\"Total evaluations for '{}' = {}\".format(titles[i], np.sum(eval_counts[i])))\n", - "\n", - "percent = np.sum(eval_counts[1])*100/np.sum(eval_counts[0])\n", - "print(\"\\nTotal evaluations for '{}' are {:.2f}% of '{}'\".format(titles[1], percent, titles[0]))" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/chemistry/h2_vqe_spsa.ipynb b/community/chemistry/h2_vqe_spsa.ipynb deleted file mode 100644 index a8538f625..000000000 --- a/community/chemistry/h2_vqe_spsa.ipynb +++ /dev/null @@ -1,181 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## _*H2 ground state energy with VQE and SPSA*_\n", - "\n", - "This notebook demonstrates using Qiskit Chemistry to plot graphs of the ground state energy of the Hydrogen (H2) molecule over a range of inter-atomic distances using VQE with SPSA optimizer. It is compared to the same energies as computed by the ExactEigensolver. SPSA is designed to work well with probabalistic/noisy measurements. And with RYRZ variational form makes this a suitable configuration to run on a near term device.\n", - "\n", - "This notebook populates a dictionary, that is a progammatic representation of an input file, in order to drive the qiskit.chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here where we alter the molecule supplied to the driver in each loop.\n", - "\n", - "This notebook has been written to use the PYSCF chemistry driver." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Processing step 20 --- complete\n", - "Distances: [0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.675 0.7 0.725 0.75 0.775\n", - " 0.8 0.825 0.85 0.875 0.9 0.925 0.95 0.975 1. ]\n", - "Energies: [[-1.06086904 -1.07138175 -1.09113875 -1.10744489 -1.11953674 -1.13116184\n", - " -1.13320145 -1.13667867 -1.13892688 -1.13662612 -1.13536438 -1.13603326\n", - " -1.13339153 -1.1308772 -1.12739979 -1.12469779 -1.12047399 -1.11336415\n", - " -1.11008319 -1.10846154 -1.10181643]\n", - " [-1.05515979 -1.07591366 -1.09262991 -1.10591805 -1.11628601 -1.12416092\n", - " -1.12990478 -1.13382622 -1.13618945 -1.13722138 -1.13711707 -1.13604436\n", - " -1.13414767 -1.13155121 -1.12836188 -1.12467175 -1.12056028 -1.11609624\n", - " -1.11133942 -1.10634211 -1.10115033]]\n", - "Hartree-Fock energies: [-1.04299627 -1.06306214 -1.07905074 -1.0915705 -1.10112824 -1.10814999\n", - " -1.11299655 -1.11597526 -1.11734903 -1.11734327 -1.11615145 -1.11393966\n", - " -1.1108504 -1.10700581 -1.10251055 -1.09745432 -1.09191404 -1.08595587\n", - " -1.07963693 -1.07300676 -1.06610865]\n" - ] - } - ], - "source": [ - "import numpy as np\n", - "import pylab\n", - "from qiskit.chemistry import QiskitChemistry\n", - "\n", - "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", - "qiskit_chemistry_dict = {\n", - " 'problem': {'random_seed': 750},\n", - " 'driver': {'name': 'PYSCF'},\n", - " 'PYSCF': {'atom': '', 'basis': 'sto3g'},\n", - " 'operator': {'name': 'hamiltonian', 'transformation': 'full', \n", - " 'qubit_mapping': 'parity', 'two_qubit_reduction': True},\n", - " 'algorithm': {},\n", - "}\n", - "molecule = 'H .0 .0 -{0}; H .0 .0 {0}'\n", - "algorithms = [{'name': 'VQE', 'operator_mode': 'paulis'},\n", - " {'name': 'ExactEigensolver'}\n", - " ]\n", - "optimizer = {'name': 'SPSA', 'max_trials': 200}\n", - "variational_form = {'name': 'RYRZ', 'depth': 3, 'entanglement': 'full'}\n", - "backend = {'provider': 'qiskit.BasicAer', 'name': 'qasm_simulator', 'shots': 1024}\n", - "\n", - "start = 0.5 # Start distance\n", - "by = 0.5 # How much to increase distance by\n", - "steps = 20 # Number of steps to increase by\n", - "energies = np.empty([len(algorithms), steps+1])\n", - "hf_energies = np.empty(steps+1)\n", - "distances = np.empty(steps+1)\n", - "\n", - "print('Processing step __', end='')\n", - "for i in range(steps+1):\n", - " print('\\b\\b{:2d}'.format(i), end='', flush=True)\n", - " d = start + i*by/steps\n", - " qiskit_chemistry_dict['PYSCF']['atom'] = molecule.format(d/2) \n", - " for j in range(len(algorithms)):\n", - " qiskit_chemistry_dict['algorithm'] = algorithms[j]\n", - " if algorithms[j]['name'] == 'VQE':\n", - " qiskit_chemistry_dict['optimizer'] = optimizer\n", - " qiskit_chemistry_dict['variational_form'] = variational_form\n", - " qiskit_chemistry_dict['backend'] = backend\n", - " else:\n", - " qiskit_chemistry_dict.pop('optimizer')\n", - " qiskit_chemistry_dict.pop('variational_form')\n", - " qiskit_chemistry_dict.pop('backend')\n", - " solver = QiskitChemistry()\n", - " result = solver.run(qiskit_chemistry_dict)\n", - " energies[j][i] = result['energy']\n", - " hf_energies[i] = result['hf_energy']\n", - " distances[i] = d\n", - "print(' --- complete')\n", - "\n", - "print('Distances: ', distances)\n", - "print('Energies:', energies)\n", - "print('Hartree-Fock energies:', hf_energies)" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "scrolled": false - }, - "outputs": [ - { - "data": { - "image/png": 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8kiYuTpkyhTp16lCnTh0CAwPveF2tW7fG09Mzaa2VJ554wuYYZsyYcUc5muz2wQcf5Ni509K6dWvSm6/WunVrTpw4kWYbW34HGeHu7s6VK5ZqHU2bNk23baJRo0bh5eXFmjVr7B5TIpNQMiHIvzI3ImNZE3o5p0PJ1/bs2cOlS5fYs2cPVapUyelw7ou7uztVq1ZNKsECEBoaSkREBI0aNWLp0qV88803rF+/ntDQUKZMmcJTTz3F2bP/VGuYM2dOUqmXxAKWuUF6a8ncb0JR1XsSb363YcMGm9uOHz+et99+m2+//TbL4jEJJROa1yxDWZdCLNhhur34dTR819m+j19H23TqGzduUK5cuTu2ubq6UrBgQcDyof3222/j7+9P/fr1CQ0NBWDLli00adKEBg0a0LRpUw4ePAhYvrk//vjjtGvXDnd3dyZMmMD48eNp0KABjRs35tq1awAcPXqUDh06EBAQQIsWLZKOW6xYsTQrGQMULFgQV1dXAPr27cu8efOSnps3bx59+vQB4KOPPuKTTz5JKh3j7+/PoEGDmDhxYprHtyWGIkWKJK14eeLECR5++GF8fHx45JFHOHXqFGC50hs2bBiBgYHUrl2bpUuXAqS6RszatWtp0aIF3bp1w9vbG4DHH3+cgIAA6taty5QpUwAYPXp00tID/fr1AywfePXq1aNevXp8/vnnSXF5enoyYMAA6tWrl3QFmtLrfe2116hbty5t27Zly5YttG7dGg8PD5YsWQJAdHQ0gwYNon79+jRo0CDpm3pUVBR9+vTBy8uL7t27ExUVlXTclStX0qRJE/z9/enZs2dS3bZSpUrh6Oho8++gdevWvPTSS/j5+VGvXj22bNkCpP03mHzl0S5duqR4xZ34+zt//jwtW7ZMOn7iF5SyZcve0b5ChQrcuHEjzbgzRVXzzSMgIEDt7b2l+7TmW8v06s0Yux87t9u/f/8/Pyx/Q/XbTvZ9LH/DpjhWr16tXbt2TfX5atWq6ZdffqmqqhMnTtTBgwerqmpYWJjGxsaqqurvv/+uQUFBqqr63XffaY0aNTQ8PFwvXbqkxYsX10mTJqmq6ssvv6yfffaZqqo+/PDDeujQIVVV3bRpk7Zp0+aec0+aNClp39RcuHBBK1SokBRLnTp1dM+ePaqqWrJkSb1x48Yd7RctWqSPPfaYqqq2atVKa9eurb6+vurr66uvvvpqmudKTZcuXXTGjBmqqjp9+vSk4w8cOFDbt2+v8fHxeujQIa1cubJGRUXpN998o++++66qqkZHR2tAQIAeO3ZM16xZo87Oznrs2LGkY1+9elVVVSMjI7Vu3bp65coVVVUtWrRoUptt27ZpvXr19ObNmxoREaHe3t66Y8cOPX78uIqIbty4Mc34AV2+fLmqqj7++OParl07vX37toaEhKivr6+qqo4bN04HDRqkqqoHDhzQKlWqaFRUlH766adJ23ft2qWOjo66detWvXz5srZo0UJv3rypqqoffvihvvPOO/ece/Dgwbp169Y042vVqpUOGTJEVVX//PNPrVu3rqqm/Tc4fPjwpP07d+6sa9asUVXL3/Ply5fveA/HjRun7733nqqqxsXFaXh4eIpx/Pnnn9qxY8c0Y73j/2srYJva8Bmbv4tR2UGQvxtT1x3nl13nGNjUPafDyTkdP8yxU4eEhODm5pZmm6CgIAACAgJYsGABYKlGPHDgQA4fPoyIJFUTBkvBSBcXF1xcXHB1daVr164A1K9fn927d3Pz5k02bNhAz549k/aJiYm557zDhg1LN/7y5ctTr149Vq9eTfny5SlQoAD16tVL/4VbzZkzh8DAdMsspWnjxo1J70v//v15/fXXk57r1asXDg4O1KpVCw8PD0JDQ1NdI6ZgwYI0bNjwjrVnvvzySxYuXAjA6dOnOXz4MKVLl77j/OvXr6d79+5JywYEBQWxbt06unXrRrVq1WjcuHGa8RcsWJAOHToAlt9RoUKFcHJyon79+kljHevXr2fEiBEA1KlTh2rVqnHo0CH++usvRo4cCYCPjw8+Pj4AbNq0if3799OsWTMAbt++TZMmTe4597Rp09J7ewHLlShAy5YtCQ8P58aNG0RERKT6N3g/HnroIZ555hliY2N5/PHH71h0LrnKlStz6NAhoqOj71hrx15MQskkr4rF8a5YnAU7zuTvhJJDnnzySZYuXZruAHyhQoUAcHR0TOrb/+9//0ubNm1YuHAhJ06coHXr1ve0B3BwcEj62cHBgbi4OBISEihRosQdi3tlRmK3V/ny5ZM+eAC8vb3Zvn07Dz/8cNK27du3ZzqB3A8RuednTWWNmLVr196xlszatWtZtWoVGzduxNnZmdatWxMdHX1f509v7RoAJyenpDhT+n1lhKrSrl07fvjhhwztf7eU3sfU/gYLFChwx3hReu9Zy5Yt+euvv1i2bBlPP/00o0aNYsCAAfe0q1GjBt7e3lStWpXVq1dTv379zL+wZMwYih0E+Vdm15kwjlyyvXS5YR9z587lk08+Sepzvx/J10u537txihcvTvXq1fnpp58Ay4fPrl277juGREFBQSxfvpzg4OCk8ROA119/nTfeeIOrV68ClquxhQsX3rOoV1omTJhwx2qRKWnatGnSOM6cOXNo0aJF0nM//fQTCQkJHD16lGPHjuHp6ZnqGjF3CwsLo2TJkjg7OxMaGsqmTZuSnnNyckrav0WLFixatIjIyEhu3brFwoUL74jBHlq0aMGcOXOS4j116hSenp60bNmSuXPnArB37152794NQOPGjfn77785cuQIALdu3eLQoUMZPn/i0gjr16/H1dUVV1fXVP8G3d3dCQkJSVr+OXHMJTUnT56kfPnyPPvsswwZMoQdO3ak2G7Xrl0cO3aMs2fP2j2ZgEkodtHNrxKODmLWSckhnp6eSQPl9+P111/nzTffpEGDBhn6FjtnzhymT5+Or68vdevWZfHixfe0mTx5MpMnT073WCVKlKBJkyaUL18eDw+PpO3dunVj8ODBNGvWjJo1a9K8eXMWLVp0x2Brv379km4bbtu27T3HDg0NvaeL6W5fffUV3333HT4+PsyaNYsvvvgi6bmqVavSsGFDOnbsyOTJkylcuHCqa8TcrUOHDsTFxeHl5cXo0aPv6LoaOnQoPj4+9OvXD39/f55++mkaNmxIo0aNGDJkSNLSyvbywgsvkJCQQP369enduzczZsygUKFCPP/889y8eRMvLy/GjBlDQEAAYBnQnjFjBn379sXHx4cmTZok3XiR3JAhQ9K9zRgsyzk3aNCAYcOGMX36dCD1v8FmzZpRvXp1vL29GTlyJP7+/mkee+3atfj6+tKgQQOCg4N56aWXUmx3/fp13N3dcXJySjfeDLFloCWvPDI6KL/z4k794cAPabZ5+tvN2viDVRofn5ChczyIUhq8ywmbN2/Whg0bakJC3n7vY2Nj9amnntInn3zyvl5r586dNSYmYzeNDBw4UH/66acM7Wv8o1WrVukO3GeH4OBg7dWrV5ptMjMob65QbLDixAo+3voxYTGpl1kJ8nfjfFg0G49dzcbIDLBMAqxSpQp+fn6p3laaFxQoUIBZs2YxZ86ce/rj07J06dKkW6iN/GvUqFF8/PHHDBkyJMvOYQblbdDZozOzD8xm1clV9KjdI8U27bzL41K4APN3nKFZzdSXmzXsr2DBgrlqQl9ekhUzvTOjUaNG99xNN2vWrCwZD7CnnKrakNz48eOz/Bwmodigbum6VCtejWXHl6WaUAo7OdLFpyKLQ87x7mNxFM3nywMbRlZILEdj5E6my8sGIkLn6p3ZdmEbF26lvvRvkL8bkbfjWbHPLA9sGEb+YxKKjTp7dEZRfj3+a6ptAquVpEqpIuZuL8Mw8iWTUGxUtXhVfMr4sOzYslTbiAhBDdz4++gVzt2ISrWdYRhGXmQSyn3o5NGJg9cPcuT6kVTb9PB3QxUWhZirlOzyIJevB8vAd9myZZPmkvj5+bF//367xTNjxgzOnftnuerUSt5PnjyZ77//3m7nzYixY8cybtw4ux0r8fewZs0avLy8eOWVV+xybCNlOZJQRKSniOwTkQQRSbWGhIh0EJGDInJEREYn2y4i8r6IHBKRAyIyMjvi7uDeAUdxZNnx1K9SqpZ25iH3kizYcRbL7dtGVnuQy9cn6t27d1IJ+pCQkKRKvfZwd0KBlEveDxs2LMVyHQ+iuydZtmnTht27d/Pdd99luF6Wkb6cukLZCwQBf6XWQEQcgYlAR8Ab6Csiif+XPQ1UAeqoqhcwL8WD2FnpIqVpXKkxy44tI0FTX5chyN+NI5dusuesWR44Ozzo5etTs3DhQh555BFUlfPnz1O7dm0uXLjAiRMnaNGiBf7+/vj7+9+xJsZHH31E/fr18fX1ZfTo0fz8889s27YtaTZ98tLsd0t+dbB161Z8fHzw8/PjtddeSypWmVbZ+tatW/PEE09Qp04d+vXrl/SFavTo0Xh7e+Pj48Orr74KpF4uP1FoaCgNGzZM+vnEiRNJtwZv376dVq1aERAQQPv27Tl//jxgufJ6+eWXCQwM5Isvvrjn9+Dk5ESJEiUIDw9P8303Mi5H7m1V1QNwb7G0uzQEjqjqMWvbecBjwH7geeBJVcunuqpeytKAk+lcvTNvrX+LnZd2ElA+IMU2nepX5O0l+5i//Qw+biWyK7Qc9dGWjwi9dm9ZisyoU6oObzR8I9128fHxODjc+d0oeekQgDJlyrBjxw6+/vprxo0bx7Rp06hTpw7r1q2jQIECrFq1irfeeov58+cDlppOO3fuJDo6mpo1a/LRRx+xc+dOXnnlFb7//ntefvllhg4dyuTJk6lVqxabN2/mhRde4I8//kj60ASSyq7cXXW4adOmd6y2FxwczPr165N+3rhxI927d2f+/PlMnDiR3377jXfeeYcKFSoQGRnJ77//TuHChTl8+DB9+/Zl27Zt/PrrryxevJjNmzfj7OzMtWvXKFWqFBMmTGDcuHF3FJTs169f0odtu3bt+OSTT+6Ib9CgQUydOpUmTZowevQ/69JMnz4dV1dXtm7dSkxMDM2aNePRRx8FYOfOnezbt49KlSrRrFkz/v77b7y8vFi4cCGhoaGISNJaHCNGjGDgwIEMHDiQb7/9lpEjR7Jo0aKk89SpU4fbt29z/PhxqlevTnBwML179yY2NpYRI0awePFiypYtS3BwMP/+97+TFo26fft2mmVQHBwciI83K6xmldw8WaIykHza8xmgkfXfNYDeItIduAyMVNXDKR1ERIYCQ8FSkyizHqn6CEUKFGHZsWWpJhTXIk608y7Pkl3n+HdnbwoWMENVWelBL18Pli6vlAo4fvXVV9SrV4/GjRsnVSGOjY3lxRdfJCQkBEdHx6SChatWrWLQoEE4OzsDlkWgUpNWyfvEsuqJpdoTKzoD6ZatT/w9+Pn5ceLECRo3bkzhwoUZPHgwXbp0oUuXLkDa5fIT9erVi+DgYEaPHk1wcDDBwcEcPHiQvXv30q5dO8DyZaJixYp3vI9pqVy5Mrt3706x5pmReVmWUERkFVAhhaf+rar3VtG7P4WAaFUNFJEg4FsgxdKkqjoFmAIQGBiYsUGNXfPg6BroPhlnJ2daV2nNypMrebPhmzg5plxk7Ql/N5btPs/ag5d4tG5Kb0PeYsuVRFbIK+XrU3PmzBkcHBy4ePEiCQkJODg48Nlnn1G+fHl27dpFQkJClqxrkRpNo2x98vcs8X0uUKAAW7ZsYfXq1fz8889MmDCBP/74w6Zz9e7dm549exIUFISIUKtWLfbs2UPdunXZuHFjivukV+p+5MiRdO3alTfffJMxY8bYFIdhuyz76qyqbVW1XgoPW5PJWSzjJIncrNvAcrWywPrvhYCPfaJOxa3LsHse7JwNQBePLoTFhLH+7PpUd2lRqwxlihU0c1KyWF4pX5+SuLg4nnnmGX744Qe8vLySSmeEhYVRsWJFHBwcmDVrVlIXTrt27fjuu++IjIwESBrrcXFxISLC9qUVSpQogYuLS9Ks9OTLE9tatj7RzZs3CQsLo1OnTnz22WdJ71Fa5fIT1ahRA0dHR959992kKw9PT08uX76clFBiY2PZt2+fza8We5ooAAAgAElEQVTtgw8+4I8//jDJJIvk5r6YrUAtEakuIgWBPsAS63OLgDbWf7cCMr5IgS0aDwf3FvDrG3DtGE0qNaFkoZJp3u1VwNGBx/wqszr0Ijcib2dpePldXihfHxwcfMdtwxs2bOCDDz6gRYsWNG/enPHjxzNt2jQOHDjACy+8wMyZM/H19SU0NDTpW3mHDh3o1q0bgYGB+Pn5JQ2wJ64Ln3xQPr2S99OnT+fZZ5/Fz8+PW7duJd1AYGvZ+kQRERF06dIFHx+fpNcBaZfLT653797Mnj2bXr16Af/UbXvjjTfw9fVNeq9sdf36dWrVqmVze+M+2VKS2N4PoDuWq4wY4CKwwrq9ErA8WbtOWJLFUSxdZYnbSwDLgD3ARsDXlvNmak35G6dV/1dFdeojqnGx+u7GdzVgVoBGxESkusvesze02htL9fsNxzN+3lzMlK/PuyIi/vm7/t///qcjR47MwWjsIyYmRkuWLKm3bt3K6VBytQeufL2qLlRVN1UtpKrlVbW9dfs5Ve2UrN1yVa2tqjVU9f1k22+oamdVra+qTVTVvn0NKXF1gy6fwZmtsO5Tunh0ISY+htWnVqe6i3fF4tSp4MJ80+2VpfJL+frstGzZMvz8/KhXrx7r1q3jP//5T06HlClr1qwhMDCQp59+OummBcP+cvNdXrlPvR5w8Df48yN8azxM5WKVWXZsGY/VfCzF5iJCD3833l9+gNAL4dSpUDybA84fTPl6++vdu3e6d0w9SBInNhpZKzePoeROnT6B4pWQhUPpVLUdmy9s5krUlVSb9wx0o4iTI1P+OpaNQWYfNdUADCPPyOz/zyah3K8iJaD7ZLh2nC5nD5CgCWlWIC7hXJA+DauwJORcnisYWbhwYa5evWqSimHkAarK1atXM3Ubuunyygj35tDsJTz+/hyvuk1YdmwZ/b37p9p8cPPqfL/xJNPXH+e/XexXoymnubm5cebMGS5fvpzToRiGYQeFCxdOd5JwWkxCyag2/4ajq+l88RjjXApxPOw41V2rp9jUraQz3Xwr8cOWU4x8uBauzilPhnzQODk5Ub16yq/ZMIz8x3R5ZVSBghA0jY7hEQikuU4KwNCWHkTejmf25pPZE59hGIZV1O3sqV9mEkpmlKtDuUfeoWFUNMsOzEtzLMGrYnFa1S7Ld38fJzrWFKczDCN7bDl+jRYfr2HzsatZfi6TUDKr4bN0dq7Kmdgwdh9J+yrluVYeXLl5m/k7zmRTcIZh5GdrQi/Rf/pmihcpQJVSWT//xiSUzBKhbedvKKjKsr/GQnzqi/c08SiNr5srU/86RnyCuTPKMIys88uuczz7/TZqlivGj881oVKJtNfosQeTUOzApXRNWpWqzwqJJHbNB6m2ExGea1WDE1cjWbnvQjZGaBhGfjJ38ylGztuJf9WS/DC0MWWKFUp/JzswCcVOOvsN4ZqjI5t2TIaTKZfWBmhftwLVSjsz+c+jZv6GYRh2N2ntUd5auIfWtcsy85mGFC+cfXeVmoRiJy0qt8DFyYVlJcvAwqEQnfIyo44OwrMtPNh1JoxNx+6/Qq5hGEZKVJWPfgvlo99C6epbiW/6B1KkoGO2xmASip0UdCzIo+6P8keRQkSGn7WUuk/FEwFulClWkG/+OpqNERqGkVfFJyj/WbSXSWuP8mSjqnze2y9HVoo1CcWOOnt0Jio+hjX+T8CuubBvUYrtCjs58nRTd9YevMyB8ylfyRiGYdgiNj6Bl4NDmLP5FM+3rsH7j9fD0UFyJBaTUOwooHwAFYpWYFkhR6jkD0tfhvBzKbZ9qnE1nAs6MjWPFo00DCPrRd2OZ+j32/hl1zne6FCHNzrUQSRnkgmYhGJXDuJAp+qd2HB+I9c6j4O4GFj0AiQk3NO2hHNB+jxUlSW7znE2jxWNNAwj64VHxzLw2y2sPXSZ97vX4/nWNXI6JJNQ7K2zR2fiNZ4VEYeg/QdwbA1s+SbFtoNbWOpgTV93PDtDNAzjAXf1ZgxPTt3EjlPX+aJPA/o1qpbTIQEmodhd7ZK1qVWyFkuPLYWAp6F2R/j9bQi7d9XGyiWK0M23EvO2njLrzhuGYZNzN6Lo9c1GDl+8ydQBgXTzrZTTISWxKaGISEkRqSsiHiJiklA6OlfvzO7LuzkdcQY6fADxMbB7Xopth7ayFI2ctdEUjTQMI23Hr9yi5+SNXAqPYdbgRrSpUy6nQ7pDqslBRFxF5C0R2QNsAr4BfgROishPItImu4J80HSq3gmAZceXQSkPqNYMQuZCChMZ61QoTmvPsszYcMIUjTQMI1X7z4XTc/IGomPj+WFoYxpWL5XTId0jrauNn4HTQAtV9VTV5qoaqKpVgA+Bx0RkcLZE+YCpWKwiAeUDWHZsmWU2vG9fuHoEzmxLsf2wVjW4eus2P283RSMNw7jXthPX6D1lIwUdHfhxWBPqVXbN6ZBSlGpCUdV2qjpLVW+k8Nx2VX1ZVadnbXgPrs4enTkRfoL91/ZD3cfByRlC5qTYtlH1UvhWKcHUdaZopGEYd1qx7wL9pm2mbLFC/PR8U2qULZbTIaUq3fEQsXhKRMZYf64qIg2zPrQH26PVHqWAQwHLwluFXMCrG+xdALH33iIsIgxr6cHJq5H8ttcUjTQMw2LO5pM8P3s7XhWL8/PzTamcDRWDM8OWAfavgSZAX+vPEcDELIsoj3At5EqLyi347fhvxCfEg19fiAmDg8tTbP9o3QpUL1PUFI00DANVZfzvh/j3wr20ql2Wuc82olTRgjkdVrpsSSiNVHU4EA2gqteB3P/KcoHOHp25HHWZLRe2gHtLKO5mGZxPQWLRyD1nw9iYDSurGYaRO8XFJ/Dmgj18ufowvQLdmDogEOeCBXI6LJvYklBiRcQRUAARKQvcO/XbuEcrt1YUdSpq6fZycLBcpRz9A8LPp9g+yL+ypWjkn6Yci2HkR1G34xk2ezvztp5mxMM1+aiHDwUcH5yZGrZE+iWwECgvIu8D64HUV5EykhQuUJi2Vduy6tQqouKiLHd7aQLsDk65vZMjg5pV589Dl9l/zhSNNIz85Pqt2/SbtonVoZd497G6/OtRzxyty5UR6SYUVZ0DvI4liZwHHlfVn7I6sLzisZqPcSv2luUqpXQNqNI41TkpAE81qkbRgo5MMaXtDSPfOHM9kh6TN7D3XDiT+vnTv4l7ToeUIbZeS5UBIlV1AnBFRKpnYUx5SmD5QOqUqsPs/bMtg+1+T8KVg3B2R4rtXZ2d6NuwKr/sPs+Z65HZHK1hGNntwPlwgr7ewJWIGGYPbkSHehVzOqQMs+W24beBN4A3rZucgNlZGVReIiL09+7P0bCjbDi3wTInpUBhy3opqXimeXUEmGaKRhpGnrbx6FV6Td6Igwg/DWuaK2e/3w9brlC6A92AWwCqeg5wycqg8pqO7h0pU6QMs/bPgsKu4NUV9vwMsdEptq9Uogjd/CoRvPU012+ZopGGkRct232egd9uoYJrYRa80BTPCg/+x6otCeW2WiZGJN7lVTRrQ8p7nByd6OPZh7/P/c3RG0ct3V7RN+DQr6nu81zLGkTFxjNrkykaaRh5zYy/j/PiDzvwreLKT8OaUCmXT1i0lS0J5UcR+QYoISLPAquAqZk9sYj0FJF9IpIgIoFptOsgIgdF5IiIjE62/RER2SEiISKyXkRqZjamrNTLsxeFHAtZrlKqt4LilSHkh1Tbe1Zw4eE65UzRSMPIQ1SVj34LZewv+2nnVZ5ZgxtRwjnvTOuz5S6vcVgKRc4HPIExqvqVHc69FwgC/kqtgXX+y0SgI+AN9BURb+vTk4B+quoHzAX+Y4eYskzJwiXpWqMrvxz9hWu3w8CnNxxZBRGpl1p5rqUH127dZuaGE9kXqGEYWSI2PoF//bSLSWuP8mSjqkx6KoDCTo45HZZdpZlQRMRRRNao6u+q+pqqvqqqv9vjxKp6QFUPptOsIXBEVY+p6m1gHvBY4iGA4tZ/uwIpL96ei/T36s/thNv8ePBHS7eXxsPuH1Nt38ijNA/XKceXqw9zKTzl8RbDMHK/8OhYnpmxlQU7zjKqXW3ef7wejg4P1hwTW6SZUFQ1HkgQkZyqlVwZSwn9RGes2wCGAMtF5AzQH0tJ/XuIyFAR2SYi2y5fvpylwabHo4QHzSo3Y17oPG6XrAZuDdOckwIwpos3sfHKh7+GZmOkhmHYy5nrkTwxaQMbj17lox71GflIrQduwqKtbBlDuQnsEZHpIvJl4sOWg4vIKhHZm8LjsfT3TtcrQCdVdQO+A8an1EhVp1jXcQksW7asHU6bOQO8BnA1+iq/Hv/VUorl8gE4H5Jqe/cyRRnSojoLdp5l+8lr2RipYRiZFXL6Bo9P3MD5sGhmPtOQ3g9VzemQspQtCWUB8F8sYx3brY+UV4q6i6q2VdV6KTwW2xjfWaBKsp/dgLPWemK+qrrZuj0YaGrjMXNUk0pNqFmiJrP2z0K9u4NjoVQLRiYa3qYmFYoXZszifWa9FMN4QPy65zx9pmykSEEHFr7QlGY1y+R0SFnOloRSQlVnJn8AJbM6MKutQC0RqS4iBYE+wBLgOuAqIrWt7doBB7IppkwREZ7yeoqD1w+yNewweHWBPT9BXEyq+xQtVIC3Onux71w487aeysZoDcO4X6rK5D+P8vycHXhXLM7CF5pRs9yDP8fEFrYklIEpbHs6sycWke7W8Y8mwDIRWWHdXklElgOoahzwIrACS8L4UVX3Wbc/C8wXkV1YxlBey2xM2aWzR2dKFippuYXY90mIug6HVqS5T1efijSqXopxKw5yI9JMdjSM3CjWWnr+w19D6eJTkbnPNqZMsUI5HVa2STWhiEhfEfkF8BCRJckea4BMd+ar6kJVdVPVQqpaXlXbW7efU9VOydotV9XaqlpDVd+/a//6quqrqq1V9YGp+V64QGF6efbizzN/crKsB7hUTLfbS0QY260uYVGxfLryUDZFahiGrcKiYhn03VbmbT3N8DY1+LJPgzx3W3B60rpC2QB8iuXK4NNkj38B7bM+tLytT50+FHAowOzQHyxzUg6vhJuX0tzHq2Jx+jeuxpzNJ015e8PIRU5fs9zJtfn4VT55wofX2tfBIQ/eFpyeVBOKqp4E1gHRqvpnsscOa5eTkQllipShU/VOLD66mDDvrpY5KXvSXxVgVDtPSjgXZOySfWapYMPIBXacuk73r//mYng03z/TiJ6BVdLfKY/K7fNQ8rT+3v2Jiovi52u7oHIA7JyT5pwUsJS3f629J1tOXGPJrlw/l9Mw8rRlu8/Td8omnAsWYOHwZjSpUTqnQ8pRWToPxUibZylPGlVoxNzQucT69oZL++DC7nT36xVYhfqVXflg+QFuxZiLRcPIbqrKxDVHGD53B/Uqu7LwhabUKFssp8PKcRmdh7I9K4PKT/p79+dS5CV+L14SHAumWTAykaOD8M5jdbkYHsNXfxzJhigNw0h0Oy6BN+bv5pMVB+nmW4k5QxpROh/dyZWWAuk1sM47MbJIC7cWuBd3Z9aRhXSs3RHZ8yO0+z8okHYFUv+qJenh78b09cfoFeiGh/l2ZBhZLiwylufnbGfD0auMfLgmr7SrnWfLqGSELSs21hKRn0Vkv4gcS3xkR3D5gYM40M+rH3uv7iWkRjOIvGq548sGb3T0pFABR/5v6X4zQG8YWezo5Zt0n/Q3W09c49Oevox61NMkk7vY0uX1HZZS8XFAG+B7zBLAdtWtRjeKFyzOrIgDUKw87Eq/2wugnEthXm5bi7UHL7P6QNq3HBuGkXF/hF7k8Ql/cyMyltmDG9EjwC2nQ8qVbEkoRVR1NSCqelJVxwKdszas/MXZyZknaj/B6tNrOOPdGQ79Breu2LTvwKbu1CxXjP9but8sxGUYdqaqTPjjMINnbqNqaWd+GdGcRh75+06utNiSUGJExAE4LCIvikh3wHTY21nfOn1xwIG5zoUgIc6mOSkATo4OjO1al1PXIpm2zvREGoa93IqJY/jcHYxbeYiuPpX4eVhTKueRpXqzii0J5SXAGRgJBGCpm5VSfS8jEyoUrcCj7o+y4NxablbyTbcUS3LNa5WhQ90KTFxzlHM3orIuSMPIJ05djaTHpA38tvcC/+7kxRd9/ChSMH+VUckIW5YA3qqqN1X1jKoOUtUgVd2UHcHlNwO8B3Ar9hYLqtS1zEe5sMfmff/d2YsEVd5f/kAUXTaMXGv94St0nbCe82HRzBjUkGdbepjBdxuletuwtTBkqrcOqWq3LIkoH6tbpi7+5fyZe/MI/RyccAz5ATrUt2nfKqWceb51DT5fdZh+ja7QtEbeX3vBMOxJVZm+/jgfLD9ArXIuTBkQQLXSRXM6rAdKWlco47AUgxwPeHFngchPsz60/Km/d3/ORl7gj5pNYM+PEB9r877DWtXArWQR3lmyn7j4hCyM0jDylujYeEb9uIv3lh3gUe8KLHihqUkmGZBWccjEYpBrgZt3FYj8M/tCzF/aVGlD5WKVmVUYuHUZjqyyed/CTo78p7M3By9GMGvTyawL0jDykLM3onhi8gYW7jzLv9rV5ut+/hQtlO6cbyMFtgzKQxpdX4Z9OTo40s+rHzsjTrDXtRyEzLmv/dvXLU+LWmUY//shrtxMfRVIwzBgy/FrdPtqPSeuRDJtQCAjHqmVL8vO20taC2yVSnwAjiJS8q5tRhbpXrM7RZ2K8n2lGnDwN4i0fT0zEeHtrnWJuh3PJ78dzMIoDePBparM2nSSJ6duwrWIE4uGN6Otd/mcDuuBl9YVynZgm/W/xYEd/FMYclvWh5Z/FStYjKBaQfwec4ELkgA7768wQc1yxXimeXV+3H6akNM3sihKw3gwxcTF8+aCPfx30V5a1CrDwuHNqFnOTK2zh7TGUKqrqof1v3c/PLIzyPyon1c/ElDmVvGCzZPva3AeYMTDNSnnUohRwSFERN/fvoaRV50Pi6LvlE3M23qaF9vUZNrAh3At4pTTYeUZaXV5uae1o1iYgjZZpHKxyjxS9RF+LhBLZMQ52LfwvvZ3KezEl30acPJaJG/M322KRxr53pqDl+j0xToOXohg4pP+vNreE0czXmJXaXV5fSIi80VkgIjUFZFyIlJVRB4WkXeBv7HcTmxkkQHeA4iIjyK4ogds+DLd1Rzv1sijNG908GT5ngtMX388i6I0jNwtNj6BD38NZdB3WylfvDC/jGhOZ5+KOR1WnpTqvXGq2lNEvIF+wDNARSASOAAsB95X1ehsiTKf8ivnR/PKzZl6fivdj++jxPE/waP1fR3j2RYe7Dh5g//9GoqPWwkaVjf3Uxj5x/mwKEbM3cm2k9fp27Aqb3f1prCTKaGSVSQ/dYUEBgbqtm0P1v0ER64foccvPXjy1m3ecPGGp+bf9zHCo2N5bMLf3IqJY+nI5pRzKZwFkRpG7rLm4CVGBYdwOy6BD4Lq85hf5ZwO6YElIttVNTC9drbOQzFySM2SNQmqFcQ8ZydOnlgLF/ff9zGKF3Zi0lP+hEfHMmLuTjOL3sjT7u7iWjKiuUkm2cQklAfAcL/hODkW5vPSpWHjhAwdo06F4nzQvT6bj19j3MpDdo7QMHKHxLu4Jv95lL4Nq7JoeDNqmOWxs41JKA+AMkXK8Ez9Z1jlXIgdBxdC+PkMHSfI341+jaoy+c+jrNh3wc5RGkbOSryL68D5cL7o48f/guqb8ZJsZsua8gtEpLN1kS0jhwysO5ByhUsxrmRxdPPkDB9nTFdvfNxcefXHXZy4csuOERpGzoiLT+Cj30wXV25gS5L4GngSy4qNH4qIZxbHZKSgSIEijAh4hT2FCvLbvtkQE5Gh4xQq4MjX/fxxdBSGzd5O1G2zbLDx4DofFkWfKZuYtNZ0ceUGtiywtUpV+wH+wAlglYhsEJFBImKmmGajrh5d8SxWhc+LFSRm+4wMH8etpDOf9/bj4MUI/rNor5n0aDyQEru49p8P5/PeposrN7CpG0tESgNPA0OAncAXWBLM71kWmXEPRwdHXm06hnNOBfhh1xSIj8vwsVp7lmPkw7WYv+MM87aetmOUhpG1Yu/q4vplRHMeb2C6uHIDW8ZQFgLrsKwr31VVu6lqsKqOAMy1ZTZrXLExLUp4MqVQAjf2/JCpY418pBYta5fl7cX72H3GFJE0cr8jlyLoMWmDtYuriuniymVsuUL5UlW9VfV/qnrH7UW2THQx7G9Uiw+45eDA5O33X44lOUcH4fPefpR1KcTzs3dwI/K2HaM0DPtJSFCmrTtGpy/Xc/paJF/38+d/QT6miyuXsSWhlBSRoLsej4hIuSyPzkhRzVK1CSpVn2DHKE4euL+ikXcrVbQgX/fz53JEDC8Hh5CQYMZTjNzl9LVI+k7dxHvLDtCiZhlWvNKSTvVNLa7cyJaEMhiYhqWmVz9gKvAG8LeI9M/ISUWkp4jsE5EEEUn1KkdEvhWRSyKy967tpUTkdxE5bP1vyYzE8SAb3vojCip8vm1cpo/lW6UEY7p6s/bgZSasOWKH6Awj81SV4K2n6PD5X+w7F87HPXyYNjDQlA7KxWxJKE6Al6r2UNUegDeWJYEbYUksGbEXCAL+SqfdDKBDCttHA6tVtRaw2vpzvlKmeBWeKenLKo1g+8FFmT5ev0ZV6d6gMp+tOsRfhy7bIULDyLhL4dEMnrmNN+bvob6bK7++1IJeD1VBxJSbz81sSShuqnox2c+XgCqqeg3I0MpNqnpAVdNdn1ZV/wJSWv/2MWCm9d8zgcczEseDbkCbjygXF8+4rR+ToJmrzyUivN+9HrXLufDSvJ2cvRFlpygN4/4s3X2ORz//i7+PXGFMF2/mDmlMlVLOOR2WYQNbEspaEVkqIgNFZCCw2LqtKJBTtwaVT3aDwAUg1cWgRWSoiGwTkW2XL+etb95FXN0Y6VqfvfERrAj9MdPHcy5YgElP+RMbr7wwZwcxcWbSo5F9bkTeZsQPO3lx7k6qlXJm2cgWPNO8Og5mEawHhi0JZTjwHeBnfXwPDFfVW6raJrWdRGSViOxN4fGYfUK3UMusvFRHklV1iqoGqmpg2bJl7XnqXKFLq/+jTsxtPt/+GTHxMZk+nkfZYozr6cOu0zcYs2ifGaQ3ssWag5d49LO/+HXPeUa1q83855uadd7t5FjYMYasHMKFW1lfvy/VBbYARMQRWGVNHPe1EIeqts1MYOm4KCIVVfW8iFTE0g2XLzmW9eRfxTx5NvY4c/fOYJDvc5k+Zod6FXmxTU0mrDlCgiof9vAxS6UaWeJWTBzvLTvAD1tOUatcMb59+iHqVXbN6bDyBFVl3sF5jN82nsIIZ8JPUaFohSw9Z5pXKKoaDySISG77DS8BBlr/ndgNl281bv4WLSOjmLp7Ctejr9vlmP96tDYjH6nFT9vP8NK8ncSaNVQMO9t64hodv1jHvK2neK6lB7+MaG6SiZ1cibrCC6tf4IPNHxBAYRYcP0zg1ayviGFLl9dNYI+ITBeRLxMfmTmpiHQXkTNAE2CZiKywbq8kIsuTtfsB2Ah4isgZERlsfepDoJ2IHAbaWn/Ov6o0YpSTG7fib/PNrkl2OaSIMKpdbd7sWIelu88zbNZ2omPNmIqReRHRsYxdso9e32wEIHhoE97s5GUmKdrJH6f+IGhxEFsvbOEtKcukI7sp2+otqBuU5edOdwlg60D8PVR1Zkrbc7MHcQlgm+1fzP+tfomFrq4sfGwx7q7udjv0rE0n+e+ivTStUZqpAwIpWijNnlLDSJGqsmTXOd5bdoArN2N4qlE1RnesY/6e7CQyNpKPt37M/MPz8SpRkw8vXcbj3H7o+jn4D8jUsW1dAtimNeVFpAhQ1ZZbfXOzPJ1QEuK5MqEBnYtDk2oP83mbz+16+Pnbz/Daz7vwq1KC7wY1xLWIKTRt2O7IpZuMWbyXDUev4uPmyruP1cO3SomcDivP2H15N2+ue5PTEad5pmYQw7cvwin8AvScAZ4pTeW7P3ZbU15EugIhwG/Wn/1EZEmmIzTsy8GRMo1HMPj6dVafWs32i9vtevgeAW5MfNKfPWfDeHLqJq7ezPwdZUbeF3U7nk9WhNLxi7/YezaMdx+vx8IXmplkYidxCXFMCpnEgF8HEJsQy7eBb/Hyhtk4Rd2AgUvskkzuhy1jKGOBhljnnKhqCOCRhTEZGeX3JP1vO1IOJ8ZtHZfpyY5361i/IlMHBHLk0k16T9nEhbBoux7fyFtW7b9I2/F/MnHNUbr5VuaPV1vTv3E1c8egnZwKP8XAXwfy9a6v6Vi9I/Prv0zg4n9BgcLwzAqo0jDbY7IlocSqathd28wtP7lRwaIUeWgIIy9fYO/Vvfx2/De7n6K1ZzlmPtOQ8zei6PXNRk5fi7T7OYwH2+lrkQyZuZUh32+jaCFHgoc25tNevpQpViinQ8sTVJUFhxfwxC9PcDz8OJ+0/IT/lQjAJXgAlKgKg1dC2ZxZWNeWhLJPRJ4EHEWkloh8BWzI4riMjHroWbpGxVLH0YUvdnxhl8mOd2vsUZrZQxpxI/I2PSdv5Ojlm3Y/h/HgiYmLZ+KaI7T77E82HL3KW53qsGxkCxp5lM7p0PKM69HXeXnNy7y94W18yviwoNsCOlw4CvMHW65IBv0KxSvlWHy2JJQRQF0gBvgBCAdezsqgjExwKY+DT29ePX+Kc7fOMXNf1tyM16BqSYKfa0JcQgK9v9nI/nPhWXIe48Hw95ErdPxiHZ+sOEgbz3KsGtWKoS1r4ORo06Kwhg3WnVlH0JIg1p1dx6uBrzKl7WQq/D0RVrwFXl3hqQVQJGfHpmy6yyuvyNN3eSV3KRS+bsSous1ZE32OOZ3m4F3aO0tOdfTyTZ6atplbMXHMfKYhDarmu5UE8rVL4dG8t+wAS3ado1ppZ97pVpfWnmapJHuKjI1k/PbxBB8MpmaJmnzY4kM8XT1g8XDYHQwPDYGOH4ND1s3jsdttwyJSG/bDaI4AACAASURBVHgVcCdZqRZVfTiTMWa7fJNQAOb0IuzcdoKquePs5Exwl2CcnbKmYuvpa5H0m7aZqzdjmDbwIZrUMF0ceV10bDyzNp7ki9WHuR2fwAutazCsVQ0zOdHOtl3Yxn///i9nb56lv3d/RvqPpFBcLPw4AI6uhof/Ay1ehSwu62/PhLILmAxsB5KmSquqfe9LzQb5KqEcXwczu7C59Ss8e3IBT9R+gjFNxmTZ6S6GR9Nv2mZOX4tkcv8A2phvqXlSbHwCP247zVerj3AhPJrWnmUZ27Uu7mWK5nRoeUp0XDRf7vyS2ftnU7lYZd5r/h4B5QPg5mWY2xPO77bLhEVb2TOhbFfVALtFloPyVUJRhW/bw9WjjG85mO8O/sDnbT7nkaqPZNkpr96MYcC3Wzh0MYIv+jQwy7TmIfEJyuKQs3y+6jCnrkUSUK0krz7qaa5Gs8Duy7v59/p/cyL8BL09ezMqYJSld+HacZgdBOHn7TZh0Vb2TChjsVTzXYhlYB4A6wJbD5R8lVDA8i1mSiti/QfQj/Ocv3We+d3mU845664ewqJieWbGVrafvM5TjasyuqPX/7d33uFRVOsf/7zpCSmQQEJISKETFAEhgIAgAaUoIhaa7RZsiOK9du7Pfq9yFStibyhSRL0ionRUakBKKKFDQgiQkEYKSTa75/fHjBhwAwE2u9nkfJ5nnj0z5+yZ98zszndOew+B2rWG26KU4qdtR3l18W72ZBXRoVkwD1/dln5tm+jVEx1MubWcaZun8cn2T4gIiOC5Xs/Ro/FlcGQLHEqG1W+CrQLGzHH6HBNHCsoBO4eVUsrtJjfWO0EB+OkJWPsO+0d/zsj1z9E5vDPvDnwXD6m50Tcny61MWbSLj1YdoFmIP/8ZcSl929S9tWjqMkopft6dzZRFu9l6uICWTRrwz6vbMqhDU73gVQ2wI2cHk1ZOYm/+XkaEdeIRGhOYuQmObjVEBCC8A9z8iUvmmDjUl1ddoV4KSukJeDsRAsOZ03c8z697gYe7PswdHez6/HQov6Xl8ejcLezLLubmy6P519AEQgK0D7DaTvKBXF5euJP1B/OIbuTPxAFtuKFzlJ7h7mjKCrFkbODDbR/xfv4WGlltPJN9nCtPloJ3A4jqAtHd/tgCXfdSdtGCIiKPKqX+a4ZvVkp9VSnuP0qpJx1mrZOol4ICsO0bmPsX1KD/8mDJdlYeXsmXQ7+kXWi7Gj91qcXKW8v28O7P+wlr4MO/b7iUgQlVrtiscSEpGfm8smg3v+zOJjzIlwn9WzGyWww+XnouiUMoPAp7l0JGMmRsYE/ebiY1DiXV14ehFg+eCE0kJKanIR5N2oNn7WkqdoSgbFRKdTkzbG/fXai3gqIUfH4DHP6NvHFLuXHZPQT5BDHr2ln4e/k7xYRthwt4+Kst7DxayLDLmvH0dQmEaVcctYLdxwqZsmgXC7cfo1GAN/f2a8ltPeLw99FDgB3CkS2wZhps+xpsFqy+IXwa1YK3VR5BXgE8lfgYSa2Hu9rKs+IIQdmklOp8ZtjevrtQbwUF4PheeKcnJAxndc+/cPfiuxnZdiT/6vEvp5lQXmHjnRX7mLp8D0F+3jw7rAPXdozUnbsuQCnF5kP5fLLqIN+nZNLAx4txfVrw195xBPnpZsmLxmaDPQthzdtw8FejCavLbRxsO4BJqZ+ScjyFgbED+VePfxHqF+pqa89JdQXlbHUqVUXY3r6mttO4FfR+CH6ezBWdb+X2hNuZvmM6faL60Ld5X6eY4OPlwYMDWnPNJRE8OjeFCTM3MT8lk+evv4TwYD+n2FDfKbVYmbclk8/XpLH1cAGBvl7cdWUL7rmyJY0a+LjaPPenvBi2zDRqJLn7IDgKBj6HtdOtzDj4A2+tfhIfTx8m95nM4PjBde5l6mw1FCtQDAjgD/zuVlYAP6WU273G1OsaCoDlJEzrAR7elN+1gjEL7ySrJItvrv+Gxv6NnWpKhdXGhysP8Ori3fh7e/LUtQmM6BJV5/5gtYX0nBK+WJfGnA2HyC+x0Do8kNt7xnJDl2g9rNsRnDgCye/Dho+hNB+adYGe4yHhenafOMAzq59h6/Gt9Ivux1M9n6JJgHuNetSjvOxQ7wUFYM9imHETJD3FvkuHM3L+SLpGdGXagGk1OpS4KvZlF/Ho3BR+S8ujX9sm/OeGS2nW0Dn9OnUdm80Y+jt9zUFW7M7GQ4RrOkRwW484erQI1eLtCE7rH6mA9tdCz/uheXfKbRbeS3mPj7d+TLBvMI8nPs6guEFued21oNhBC4rJ7NsMYRm/llnH1vLvdf/m8cTHGdt+rEvMsdoU09cc5L8/7cLTQ3h8cDtGdmuuPdVeIPkl5czZcIgv1qaTnltCkyBfRifGMCYxhqYhumnxojmzf8QnEDrfBt3vhtB4ADZlbeLp1U9zoOAAw1oO45Guj9DQz31XqdSCYgctKCYFGTA1EeKvRI2eyYRlE1iTuYaZ186kTaM2LjMrPaeEx75OYc3+HMKDfBnZrTkjuzUnulHNOLWsa2w7XMD0NQf5bnMmZRU2EuNCua1nLNd0aKqH/jqKlDmw4iWzfyTaEJEut59yG19sKeb1315n9q7ZRDaI5KmeT9ErqpeLjb54tKDYQQtKJVa/BYv+BaNmkhPbnRvn3Ugjv0bMHDoTPy/XvcUqpViamsWMdWms2J0NwFVtwxmTGMNV7cL15LozOFFqYcmOY3y+No1N6fn4e3syvHMUt/eMpX1ksKvNq1v88gosex4iO0GvB6D9MPD8oyv5l4xfeH7t8xwrPsbY9mOZ0HlCjXn4djZaUOygBaUSVgu8dyWUFcL4dazM3sS9S+5lbPuxPJ74uKutAyAjr4TZ6w8xa/0hsgvLiAzxY2S35ozqVr+bbg4eL2bpziyWph4j+UAuFTZFi8YNuLVHLDdeHk2Iv9uNl6ndKAXLXoBfX4GOI+H6aadNOswtzWVy8mQWHFhAq4ateOaKZ7isyWUuNNjxaEGxgxaUM0hbA58MMoYTD3iGycmT+SL1C6YlTaNPdB9XW3cKi9XG0tRjzFiXzq97juPpIfRvF86Y7jFc2bpJna+1VFht/JaWx7KdWSxJPca+7GIAWocHktQ+gqT24Vwe00j72KoJlDJq8mumQpc74NrXwcPDjFLM3z+f/67/L0WWIu669C7+funf8fase4KuBcUOWlDs8L/xkDIL7llFWVg8o+aPIrc0l2+GfUOYf+1zTZ6eU8LM9el8teEQx4vKiWroz5juMdzcNZrwoLpTayk4aeHn3dksSz3Git3Z5JdY8PYUuseHkdQ+nKR2EcSE1Y3mlFqLzQYLHoYNH0Hi3TB48qmFrDKLMnl+7fOsPLySjk068mzPZ2nVqJWLDa45tKDYQQuKHYqPw1uXQ9NL4Y7v2ZO/l1HzR9GjWQ+m9p9aa4c4llfYWLTjKF+uS2f1vhy8PISBCRGM6R5DjxZhbjlC7MDxYpamHmNpahbrDxpNWaENfLiqbThJ7cPp07qxnsXuLGxWmDcBNs+AXg/CgGdBBKvNyqxds3hj4xsAPNjlQUa1HYVnDS6/WxvQgmIHLShVsOETmD8RbngfLhvJjNQZvJT8Ek8kPsGY9mNcbd052Z9dxKz1h/hqwyHySiz4eHrQKjyQhGbBtI8MJsHcaounY4vVRlpOCXuzitiXXcSeY4WkZBSw/7jRlNU2IsiohbQPp1PzRnW+Sa/WYbXAN3fB9m+g3xPQ9zEQITUnlRfWvUBKdgq9onrxVI+naBbYzNXWOgUtKHbQglIFNht8NBDy0+D+DSi/EO5fdj+rDq/i1X6v0j+mv6strBalFivLd2axOSOf1COF7Mg8wfGiU2vCEdXQ3xCYZsEkRAaREBlCdCP/Gut7KLVY2ZddxN6s07eDOcVYrH/875qF+NG2aRD92obTv104zUN1U5bLqCiDuX+FnfONWknviZwoP8HUTVOZvWs2DX0b8nDXh7m2xbW1tvZeE2hBsYMWlLNwZAu83w+6/hWGTqHYUsy4RePYmbuTaQOm0SOyh6stvCCyCktPiUvqkRPsOHKC/dlF2MyffaCvF+0jg0iINGozje14QLb3D7H3v8kvsbDXFJA9WYVk5J3k92QeArFhDWgVHmhsTQJpHRFIyyaBNNCuT2oHlpMw+1bYuwQGv4xKHMf8/fOZsmEKeWV53NLmFiZ0mUCwT/0bjq0FxQ5aUM7Bj4/Buvdg3DKI6kJBWQF3/nQnh4sO8+HVH9KxSUdXW+gQTpZb2X2skB1HTpwSmtQjJygut1503j6eHrRoUkk4wgNpHR5EXOMAfL3qdju7W1NWBDNHwcGVcN0b7GlxBS+sfYGNWRvp2Lgjk3pMIiEswdVWugwtKHbQgnIOSk/A1G4QHAl/XwoenmSXZHP7j7dzovwEnwz6xKUz6WsSm02RnltCYWnFn+Kq27IR6OtF89AA3efhbpQWwIxbIGM9xcPeYFrFUWakziDIJ4iJXSZyQ+sbXOLnrjahBcUOWlCqwda58PXfYMgrkDgOgIzCDO748Q6sysr0wdOJCY5xsZEajYMoyYUvRqCObuWnqybyypEVZJ/MZkTrEUzsMtGt/W85kuoKiktkV0RuFpHtImITkSqNFJGPRSRLRLadcfxlEdkpIiki8q2I6LvuKC65EVr0g6XPQ1EWANFB0bx/9ftYlZVxi8ZxtPioS03UaBxCUTZ8dh37c3YxrmNfHt0/hzD/ML4Y8gXPXPGMFpMLwFX1uG3ACOCXc6T7FBhk5/hi4BKlVEdgN/CEQ62rz4jAkClQcdKYIWzSsmFL3h34LgXlBdy1+C5yS3NdaKRGc5GcOELJp4N5veIoN0ZFsOPkUSZ1n8TMoTPrTF+hK3CJoCilUpVSu6qR7hfgT08updQipdTvjd1rgWgHm1i/+X11x5TZsHfpqcMdwjowtf9UMosyuWfxPRSWF7rQSI3mwlB5aSz5YhDX+5fwUXAAQ1tcy/fDv2dUu7o/QbGmqQs9TX8FfqwqUkTuEpENIrIhOzvbiWa5Ob3/AWGtYf5DUF5y6nDXpl15td+r7Mnbw/1L7+dkxUkXGqnRnAdKsX/TJ9w7dygPNbAR3DCOzwZ9xgu9X6iVbobckRoTFBFZIiLb7GzXO/Ack4AKYEZVaZRS7yuluiqlujZp4l7LbroUbz+47g1jsuOKF0+LujL6Sl7s8yKbsjbxjxX/wGK1uMhIjaZ6HE9byfPTezFiyxRSvIVH297K7Bvm0SWii6tNq1PU2IwqpdSAmsobQETuBK4FklR9GqrmTOJ6GR5W17wNl94EkX+45B4UP4giSxHPrnmWJ1Y+weQ+k3VzgabWUVqQwecL7+ej4j2UiXBL6GXcm/Q6jRrol8uawC2n6IrIIOBRoK9SquRc6TUXwcDnYPdPMO8BY25KpXUgbmpzE0XlRUz5bQqB3oE83fPpeuWOQlN7sVlK+WHpI7yRuYxjnh5c5RfJQ/2nEB9Rt9YpqW24atjwDSKSAfQEfhCRhebxZiKyoFK6mcAaoK2IZIjI38yoqUAQsFhENovIu04uQv3Bv6HhtvvIZlj358t85yV3Mu7ScXy952umbJhi1yWJRuM0lGJ98puM+rwbTx5bQZhnAB93f443Ry/RYuIEXFJDUUp9C3xr53gmMKTS/ugqvl93Fx6ojSQMhzaDYfm/of210CjutOgJnSdQWF7IZzs+I9g3mLs63uUaOzX1mv37FvHayv9jBSU0FeHF1mMZ0vORej/L3Zm4ZZOXxsmIwNBX4O3u8MM/Yezc0/yRiAhPdH+CIksRb216i0DvQLdwe6+pG+Tm7mXaognMLT2En4IHI3pxa9IU/HwDXW1avUMLiqZ6hERD0lPw46OGe5aON58W7SEePN/reYotxbyY/CKBPoEMaznMRcZq6gNlZYV8sXgiH2av46TATQFx3DvgDcJCW7ratHqL9uWlqT42K3x0NeQdhPvXQ0Don5KUWcsYv3Q8yUeSufeye7n7srt1k4PGodhsVn5c/RJv7JnFEQ/oJ4E81OfftIh3j3V73JFa7ctL46Z4eMKwN6E0HxZOspvE19OXt/q/xXUtr2PalmmMXzqegrICJxuqqYvYcvax6If7uPHTTjy+bxYNlfBhh/t46/Y1WkxqCbqGojl/lj4Hv06B278zHEnaQSnFV7u/4sXkF4kIiODVfq/W6/UkNBfIyXxs275hydbPeMd6lL0+PsThxT0xQxnc5//w8Przgmgax6Pd19tBC4qDsJTCO1eAssF9a8Dbv8qkKdkp/GPFP8grzWNSj0mMaD3CiYZq3BKrBfYuwbZ5JosPLefdkABDSLxDuKfj3QxKGKMn0ToZLSh20ILiQA78Ap9dB70mwsBnz5o0tzSXx355jLVH1jKi9Qie7P4kvp76zVJTCaUgcxOkzMa2dS6LKebdsDD2enkQ3yCSe7o8yDVxg7SQuIjqCooe5aW5MOKvhM63wuq3DLcsTS+tMmmoXyjvDniXtze/zQdbPyA1J5XXrnqNqMAoJxqsqZUUZEDKHNgyC9vxXSwODObdpk3ZqwKID45j8mX3ck3cNVpI3ARdQ9FcOCW58HYihDSHvy8xOu3PwfL05UxaOQkPDw9e6vMSvaN6O8FQTa3CZoXU72HDR3DgV2woFsd04t0AYW9ZDvEh8dzT8R4tJLUIPcpLU/MEhMKglyBzI6x7r1pfuSrmKmZdO4uIgAjuW3If72x+B5uy1bChmlpBRRlsnG68hHx1B7b8NBZ2G8ONHXvzsGcuVr9gJveZzLfDvmVIiyFaTNwQXUPRXBxKwZe3wMFVMH4tNKzeevMnK07ywtoXmLdvHr2jevNSn5cI8Q2pYWM1LqGsCH771PBaXZhJeWRHFrZP4uPczewt2KdrJG6A7pS3gxaUGiI/Hd7uYbi7HzPnNLcsZ0MPLa7jFOdA8ntG7bU0n+NxVzAnpgNzsjeQU5pDi5AW3N3xbi0kboAWFDtoQalB1kyDhU/AjR8ZnfTngR5aXMcoyIDVU2HjZ2ApYXub/nwR2oSfstdTYaugT1QfxrYfS89mPbUXBTdBC4odtKDUIDYrfJhkPEzGJ9t1y3I2zhxa/HDXhwnyCaohYzU1QvZuWPU6pMzGAixt148vfGFL/m4CvAIY3mo4o9uNJi4kztWWas4TLSh20IJSwxzdCu/1hU6j4fq3z/vrVpv11NDiEN8Qxl06jpFtR+Ln5VcDxmocxuHf4NdXYecP5Pr483XrK5hlyyGrNIfmQc0Z024M17e6Xr8guDFaUOygBcUJLH7aeEu943tjrsoFsCNnB29ufJNVmauM0WCd7mNYy2F4eehpU7WGinLYtxTWvgMHfmZXYCNmxHXkh5MZlNss9Ijswa3tb6V3VG/dP1IH0IJiBy0oTqC8BN7pabhn6TQGWiVBdCJ4+Zx3VslHknlj4xukHE8hLjiOB7o8wICYAXqZYVdhrYADP8O2b2Dn91hLC1gRGskXETFsKD2Cn6cf17W8jrHtx9KyoXYhX5fQgmIHLShO4vBGWPgkHEoGZQWfQIjrY4hLy/4Q2uK8RoItO7SMNze+yf6C/XQI68CDXR6kZ7OeNVwIDWD0jaWtMkQkdR6qJIcdDRqyIKotP1FMluUEkQ0iGd1uNCNaj9BDv+soWlDsoAXFyZQWwIFfjaaRvUshP8043jDWFJckiO8Dfud+CFltVr7f/z3TNk/jSPERukd2Z2KXiVzS+JIaLkQ9xGaDjGTY9jXs+A6KjpHmH8iC5pewwLOcg6XH8fLwok9UH4a1HEa/5v10c2QdRwuKHbSguBClIHc/7FtmiMvBX6G8CMQTmica4tKyPzTrdFYXLmXWMubsmsMHKR+QV5bHwNiB3N/5flqEtHBiYeogShk1y+3fwPZv4cRhsnz8+Sn2Mhb4wPaSTAShW9NuDIkfwoDYAbo2Uo/QgmIHLSi1iIpy4y1471JDZI5sNo77NzLEJXEcxPSo8utF5UVM3zGdz7Z/Rqm1lOGthnPvZffStEFTJxWgDqCUMTJv29eGiOSnccLThyXxnVng70tyURoKRUJYAkPihzAobhARDSJcbbXGBWhBsYMWlFpM8XHYt9wQl90/wsk8iLkCej8ErQdW2eeSW5rLBykfMHvXbARhVLtRjG43muigaCcXwI3IT4etXxlefrN3Uurhyc9xl7MgKIhfiw5isVmIDY5lSPwQBscPJj4k3tUWa1yMFhQ7aEFxE8qLYePnhmv8ExkQcYkhLAnDwdN+W31mUSbTNk/j+/3fY1M22oW2IykmiYGxA2kR0kKPDCvJNfpDUuZA+moyvTxZ16wDaxtF8HPJIYorSmji34RB8YMYGj+UhLAEfc00p9CCYgctKG6G1WK8Sa98HY7vgkZxcMUD0GkseNuf7JhRmMHS9KUsSVvC5myjGS0uOI6kmCQGxA6gQ1iH+vOgtJTC7p9g61dk71tMso8n6xtGsC7An4yKIsBYq6ZvdF+GthhK14iues6Ixi5aUOygBcVNsdlg1wJY+aoxK7tBOPS8D7r+DfyCq/xaVkkWy9OXsyR9CeuPrseqrDRt0JSkmCSSYpLoEt6ldjxAywqh8Cj4hxp9SB4X4d/KZoO0leRvnsH6g4tJ9rKRHNCA/V5GnkE+QXSL6EZiZCLdm3anZcOW9UdgNReMFhQ7aEFxc5QyRof9+irsXw6+IZD4d+h+LwQ2OetXC8oKWHFoBUvSl7Amcw1l1jJC/UK5qvlVJMUk0T2yOz6e5z/58rywlMLx3ZCVClk7jM/sVKNP43c8vKBBE2MLDDfEM7AJBEb8EW4QbsT5h54Sn6KMZDZu/IB1matJ9qhgl483SgR/Dx8ub9qN7pE9SIxMpG2jtrVDRDVuhRYUO2hBqUNkboKVr8GOeeDlC51vgysmQKPYc361xFLCysMrWZK+hF8yfqHYUkygdyBXRl/J5RGXExMcQ0xQDBEBERf28LVaIGefIRaVxSN3P/y+mJiHNzRuA+HtILy9serlyTwoyoLiLCjKNj/NzWYBoFiEdG8v0ry9SfP2Id2/Afu8PNnpqbCK4IPQOSiOxPhrSIzqRYfGHfD28D7/Mmg0ldCCYgctKHWQ43sN32FbZhkP60tuNNa6j70CPM/9IC23lrP2yFqWpi9lefpy8sryTsV5e3gTFRh1SmCaBzUnJtj4bBbY7I8HdcFho0kufa0hHMd3nxIAxMPwDBDeHsIToEk74zOsZZX2naw4yaHCQ6SfSOfgiYOkn0gnLX8f6YXpHC/LPy1tuPgQJz50Dk0gMWE0l8X0wdfT98KupUZTBVpQ7KAFpQ5zItNYEXDDJ2ApNprDWg+EtoOh1QDwb3jOLGzKRlZJFukn0kkvNLaMwoxT+ycrTp5K6ykeRHoGEFNeRvOiXJpbKgjzCcEWEoU1OJKKwKbYgiKoCAjDKoJN2ahQFVhtVrvhEksJhwoPkXYijWMlx06zK8wvjNjgWGKCY4gNjjXCQTHEBMfg7+Xv8Eup0ZyJFhQ7aEGpB5QXw/4VRo1h109Qctzol4jtBW2HQNtBxmix80RZK8jZt4RDu/5HesYa0svyOOTtxaGAENK8PCi0lZ9XfoLg6eGJl3jhIR74efkRHRRNbNCfhSPQJ/C87dVoHIkWFDtoQaln2KzGqLBdC2DXj5C90zge3sGoubQdAs06Vz2qynLSEKedPxjfLzkOnj6GW/52Q6HNYAiOBIxO/7zSvNNE4lTYwwMv8cLTw9M4Lp56pUKNW6EFxQ5aUOo5OfuMeRm7foS01YYn5MAIaDPIEJcWfQ0R2bMIds433MJYSsA3GFpfbYhIqwFnHaqs0dRFarWgiMjNwDNAeyBRKWX3KS8iHwPXAllKqT+5lRWRfwKvAE2UUsfPdV4tKJpTlOTC3iVG7WXPEigvBC9/sJYbQhMUaQhIu6EQ2/uC1nPRaOoK1RUUV/mc3gaMAN47R7pPganA9DMjRKQ5cDWQfmacRnNOAkKh4y3GVlEOaSthz2Lw9jdEJPIsTWEajcYuLhEUpVQqcM4ZukqpX0Qkroro14BHge8caZumHuLlY7jOb9nf1ZZoNG6NW76Cicj1wGGl1JZqpL1LRDaIyIbs7GwnWKfRaDT1kxqroYjIEsDe4hSTlFIXXKsQkQDgSYzmrnOilHofeB+MPpQLPa9Go9Fozk6NCYpSakANZd0SiAe2mE1m0cBGEUlUSh2toXNqNBqN5hy43ULQSqmtQPjv+yJyEOhanVFeGo1Go6k5XNKHIiI3iEgG0BP4QUQWmsebiciCSulmAmuAtiKSISJ/c4W9Go1Gozk3rhrl9S3wrZ3jmcCQSvujq5FXnEON02g0Gs0F4ZajvDQajUZT+9CCotFoNBqHUK98eYlINpB2gV9vDNS3jn9d5vqBLnP94GLKHKuUOvuyqNQzQbkYRGRDdXzZ1CV0mesHusz1A2eUWTd5aTQajcYhaEHRaDQajUPQglJ93ne1AS5Al7l+oMtcP6jxMus+FI1Go9E4BF1D0Wg0Go1D0IKi0Wg0GoegBeUMRGSQiOwSkb0i8rid+DtFJFtENpvb311hpyM5V5nNNLeIyA4R2S4iXzrbRkdTjfv8WqV7vFtE8l1hpyOpRpljRGS5iGwSkRQRGWIvH3ehGuWNFZGlZllXiEi0K+x0JCLysYhkici2KuJFRN40r0mKiHRxqAFKKb2ZG+AJ7ANaAD7AFiDhjDR3AlNdbauTy9wa2AQ0MvfDXW13TZf5jPQTgI9dbbcT7vP7wL1mOAE46Gq7a7i8XwF3mOH+wOeuttsB5b4S6AJsqyJ+CPAjIEAPYJ0jz69rKKeTCOxVSu1XSpUDs4DrXWxTTVOdMo8D3lZK5QEopbKcbKOjOd/7PBqY6RTLao7qlFkBwWY4BMh0on2OpjrlTQCWmeHlduLdDqXUL0DuWZJcD0xXBmuBhiIS6ajza0E5nSjgUKX9DPPYmdxoVhfnikhz55hWwN2OPgAACGdJREFUY1SnzG2ANiKySkTWisggp1lXM1T3PiMisRgLui2zF+9GVKfMzwC3mktLLMCombkr1SnvFmCEGb4BCBKRMCfY5kqq/du/ELSgnD/fA3FKqY7AYuAzF9vjDLwwmr36YbytfyAiDV1qkfMYBcxVSlldbYgTGA18qpSKxmga+VxE6vIz4mGgr4hsAvoCh4H6cJ9rjLr8Y7kQDgOVaxzR5rFTKKVylFJl5u6HwOVOsq2mOGeZMd5i5imlLEqpA8BuDIFxV6pT5t8Zhfs3d0H1yvw3YA6AUmoN4IfhUNAdqc5/OVMpNUIp1RmYZB5z+8EX5+B8fvvnjRaU01kPtBaReBHxwXiYzKuc4Iz2xmFAqhPtqwnOWWbgfxi1E0SkMUYT2H5nGulgqlNmRKQd0Ahj1VB3pzplTgeSAESkPYagZDvVSsdRnf9y40o1sCeAj51soyuYB9xujvbqARQopY44KnO3W1O+JlFKVYjI/cBCjFEiHyultovIc8AGpdQ84AERGQZUYHR+3ekygx1ANcu8ELhaRHZgNAk8opTKcZ3VF0c1ywzGQ2iWMofHuDPVLPM/MZozH8LooL/TXctezfL2A14UEQX8Aox3mcEOwlw2vR/Q2OwLexrwBlBKvYvRNzYE2AuUAH9x6Pnd9Pei0Wg0mlqGbvLSaDQajUPQgqLRaDQah6AFRaPRaDQOQQuKRqPRaByCFhSNRqPROAQtKBqHICJF1UgzUUQCHHjO4SKS4MD8Vl/Ed4vMz2YiMvcs6RqKyH0Xep6LxZx/sExEgisdGy4iypx34+jzxYnIGEfnWyn/+0XkrzWVv+b80IKicSYTgfMSFBHxPEv0cAwHfw5BKXWFA/LIVErddJYkDQGXCQrGHIQtSqkTlY6NBlaan44mDrArKCLiiHlwH+PePsfqFFpQNA5FRPqZa0vMFZGdIjLDfCt+AGgGLBeR5Wbaq0VkjYhsFJGvRCTQPH5QRCaLyEbgZhEZJyLrRWSLiHwtIgEicgWGp4KXxVizpKWIdDKdV6aIyLci0sjMb4UY65tsEJFUEekmIt+IyB4ReaGS7UWVwo+JyFbznC/ZKWe8afvWM/KIE3MtChHpICLJpn0pItIaeAloaR57WUQCxViTY6OZ1/WV8kkVkQ/EWINmkYj4m3GtRGSJadtGEWlpHn/EvE4pIvJsFbdoLPBdJXsDgd4YbldGnes+mnFDzGO/ibG2xnzzeF/5Yw2ZTSISZJa3j3nsITHWE5onIsuApeZv42UR2WaWf2Sl8/8sIt+JyH4ReUlExprXc+vvZVZKlQAHRSTxbL9LjZNwtf9+vdWNDSgyP/sBBRg+gjww3Jb0NuMOAo3NcGOM2ckNzP3HgKcqpXu0Ut5hlcIvABPM8KfATZXiUoC+Zvg54HUzvAKYbIYfxHDLHgn4YvgpCzujDIOB1UCAuR9qp7zzgNvN8PhK343DXIsCeAsYa4Z9AP/K8eZxLyC40jXZi7FWRRyGN4ZOZtwc4FYzvA64wQz7YdT6rsZYz0TM6z4fuNKO3WlAUKX9scBHZng1cPnZ7qN5vkNAvJluJjDfDH8P9DLDgWbZ+v0ebx6/07zmoeb+jRhOVj2BCAz3L5Hm9/Ir3afDwLOV7uHrlfKcBPzT1f8Bven1UDQ1Q7JSKkMpZQM2Yzwcz6QHRnPVKhHZDNwBxFaKn10pfImI/CoiWzEegB3OzExEQoCGSqmfzUOfYSw29Du/u1PZCmxXSh1RhpPP/ZzuLA9gAPCJMt5+UUrZW1+iF384jfzcTjwYD+EnReQxIFYpddJOGgH+IyIpwBIMV+IRZtwBpdRmM/wbEGe+9Ucppb41bSs17bza3DYBG4F22HfgGaqUKqy0PxpjrRDMz8rNXvbuYztgvzKchMLpjjNXAa+atdGGSqmKKq7L4krXtDcwUyllVUodA34Guplx6yvdp33AIvP4Vk7/TWVh1H41Lkb78tLUBGWVwlbs/84E48FSVbt9caXwp8BwpdQWEbkT01HlBdpkO8M+WxX2VYez+i1SSn0pIuuAocACEbmbPzvVHAs0wagZWETkIEYtoLLNYFxH/7OcToAXlVLvncPmChHxUErZRCQUY6XCS8XwZ+UJKBF5pIrzn/U6KaVeEpEfMPppVonINVUkLa7i+JmceZ8q38PKtvgB9sRa42R0DUXjTAqBIDO8FuglIq0ARKSBiLSp4ntBwBER8cZ4AP8pP6VUAZAnIn3MuNsw3nYvhMXAX8QckWY+eM9kFX/0OYy1E4+ItMB4m38To9+iI6dfAzBWRswyxeQqTq+l/QmzdpEhIsPNc/iadi4E/ip/9ENFiUi4nSx2YSyLC3ATxrK3sUqpOKVUc+AA0MfO9077vojEmfsjK5W3pVJqq1JqMoa333Z2ynsmvwIjRcRTRJpg1CqTz5LeHm0Au2uoa5yLFhSNM3kf+ElEliulsjHa02eazT1rMB5A9vg/jH6DVcDOSsdnAY+YHcAtMZrNXjbz64TRj3LeKKV+wmgi22A2xz1sJ9mDwHizGa6qFe9uAbaZeVyCsfRqDsbb+zYReRmYAXQ187n9jPJVxW0YXq9TMPo9miqlFgFfAmvMvOZi/0H+A3/U8EYD354R/zVnGe1lNtvdh3Eff8MQjAIzeqJZrhTAgrF2eQpgNQcQPGQny2/NNFswVsV8VCl19GyFt0MvjJcAjYvR3oY1mnqEGOv5TFdKDbyIPAKVUkXmqK+3gT1KqdccZuT52dIZ+IdS6jZXnF9zOrqGotHUI5SxmNIHUmli4wUwzqx1bcdosjtXv01N0hijBqupBegaikaj0Wgcgq6haDQajcYhaEHRaDQajUPQgqLRaDQah6AFRaPRaDQOQQuKRqPRaBzC/wNIgMoxefwvhQAAAABJRU5ErkJggg==\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.plot(distances, hf_energies, label='Hartree-Fock')\n", - "for j in range(len(algorithms)):\n", - " pylab.plot(distances, energies[j], label=algorithms[j])\n", - "pylab.xlabel('Interatomic distance (Angstrom)')\n", - "pylab.ylabel('Energy (Hartree)')\n", - "pylab.title('H2 Ground State Energy')\n", - "pylab.legend(loc='upper right');" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.plot(distances, np.subtract(hf_energies, energies[1]), label='Hartree-Fock')\n", - "pylab.plot(distances, np.subtract(energies[0], energies[1]), label=algorithms[0])\n", - "pylab.xlabel('Interatomic distance (Angstrom)')\n", - "pylab.ylabel('Energy (Hartree)')\n", - "pylab.title('Energy difference from ExactEigensolver')\n", - "pylab.legend(loc='upper left');" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/chemistry/h2o.ipynb b/community/chemistry/h2o.ipynb deleted file mode 100644 index f028e74d7..000000000 --- a/community/chemistry/h2o.ipynb +++ /dev/null @@ -1,512 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## _*Qiskit Chemistry, H2O ground state computation*_\n", - "\n", - "This notebook demonstrates how to use Qiskit Chemistry to compute the ground state energy of a water (H2O) molecule using VQE and UCCSD.\n", - "\n", - "While the molecule has been input below to the driver in xyz format, the Z-matrix format is also support. H2O in Z-matrix format would look like this \n", - "```\n", - "H; O 1 1.08; H 2 1.08 1 104.5\n", - "```\n", - "and is convenient when the goal is to change bond angle, or plot the energy changing distance(s) while preserving the angle.\n", - "\n", - "This notebook has been written to use the PYSCF chemistry driver. " - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "# imports needed by declarative approach here. List is short as classes are dynamically\n", - "# loaded based on dictionary names which are registered to our pluggable framework.\n", - "# The name of a given algorithm or component can be found in its CONFIGURATION dictonary\n", - "from qiskit.chemistry import QiskitChemistry\n", - "\n", - "# imports needed by programmatic approach\n", - "from qiskit import BasicAer\n", - "\n", - "from qiskit.aqua import Operator, QuantumInstance\n", - "from qiskit.aqua.algorithms.adaptive import VQE\n", - "from qiskit.aqua.algorithms.classical import ExactEigensolver\n", - "from qiskit.aqua.components.optimizers import SLSQP\n", - "\n", - "from qiskit.chemistry.drivers import PySCFDriver, UnitsType\n", - "from qiskit.chemistry.core import Hamiltonian, TransformationType, QubitMappingType \n", - "from qiskit.chemistry.aqua_extensions.components.variational_forms import UCCSD\n", - "from qiskit.chemistry.aqua_extensions.components.initial_states import HartreeFock" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Using a declarative dictionary approach with QiskitChemistry\n", - "\n", - "Lets format up a dictionary and run the experiment this way. The operator will default to `parity` mapping and `two_qubit_reduction` of True.\n", - "\n", - "With the input problem dictionary for water we now create an QiskitChemistry object and call run on it passing in the dictionary to get a result. We use ExactEigensolver first as a reference." - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [], - "source": [ - "qiskit_chemistry_dict = {\n", - " 'driver': {'name': 'PYSCF'},\n", - " 'PYSCF': {'atom': 'O 0.0 0.0 0.0; H 0.757 0.586 0.0; H -0.757 0.586 0.0', 'basis': 'sto-3g'},\n", - " 'operator': {'name': 'hamiltonian', 'freeze_core': True},\n", - " 'algorithm': {'name': 'ExactEigensolver'}\n", - "}\n", - "solver = QiskitChemistry()\n", - "result = solver.run(qiskit_chemistry_dict)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The `run` method returns a result dictionary. Some notable fields include 'energy' which is the computed ground state energy." - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Ground state energy: -75.0123592858051\n" - ] - } - ], - "source": [ - "print('Ground state energy: {}'.format(result['energy']))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "There is also a 'printable' field containing a complete ready to print readable result" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "=== GROUND STATE ENERGY ===\n", - " \n", - "* Electronic ground state energy (Hartree): -84.206272446428\n", - " - computed part: -23.544497240436\n", - " - frozen energy part: -60.661775205992\n", - " - particle hole part: 0.0\n", - "~ Nuclear repulsion energy (Hartree): 9.193913160623\n", - "> Total ground state energy (Hartree): -75.012359285805\n", - " Measured:: Num particles: 8.000, S: 0.000, M: 0.00000\n", - " \n", - "=== DIPOLE MOMENT ===\n", - " \n", - "* Electronic dipole moment (a.u.): [0.0 1.57867263 0.0]\n", - " - computed part: [0.0 1.57778798 0.0]\n", - " - frozen energy part: [0.0 0.00088465 0.0]\n", - " - particle hole part: [0.0 0.0 0.0]\n", - "~ Nuclear dipole moment (a.u.): [0.0 2.21475902 0.0]\n", - "> Dipole moment (a.u.): [0.0 0.63608639 0.0] Total: 0.63608639\n", - " (debye): [0.0 1.61677018 0.0] Total: 1.61677018\n" - ] - } - ], - "source": [ - "for line in result['printable']:\n", - " print(line)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Lets do the same programmatically\n", - "\n", - "First we create and run a driver to produce our molecule object. The molecule object holds data from the drivers in a common way so it can then be used independently of which specific driver created it.\n", - "\n", - "And let's print some of fields it has. You can refer to qiskit.aqua.qmolecule.py for more information or look at the API documentation." - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Hartree-Fock energy: -74.96294665653834\n", - "Nuclear repulsion energy: 9.193913160623385\n", - "Number of molecular orbitals: 7\n", - "Number of alpha electrons: 5\n", - "Number of beta electrons: 5\n" - ] - } - ], - "source": [ - "driver = PySCFDriver(atom='O 0.0 0.0 0.0; H 0.757 0.586 0.0; H -0.757 0.586 0.0',\n", - " unit=UnitsType.ANGSTROM, charge=0, spin=0, basis='sto3g')\n", - "molecule = driver.run()\n", - "\n", - "print('Hartree-Fock energy: {}'.format(molecule.hf_energy))\n", - "print('Nuclear repulsion energy: {}'.format(molecule.nuclear_repulsion_energy))\n", - "print('Number of molecular orbitals: {}'.format(molecule.num_orbitals))\n", - "print('Number of alpha electrons: {}'.format(molecule.num_alpha))\n", - "print('Number of beta electrons: {}'.format(molecule.num_beta))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We now need to create a qubit operator as input to compute the ground state energy. The Hamilitonian object can be used. This wraps a `FermionicOperator` class, which can be used directly but entails more steps. Other tutorials here show FermionicOperator being used.\n", - "\n", - "The Hamiltonian class not only gives us a qubit operator for the main Hamiltonian but also auxilliary operators including dipole operators and others to measure spin and num particles. The algorithm, if it supports aux_ops, which ExactEignesolver and VQE both do, will evaluate these at the ground state where the minimum energy is found." - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Representation: paulis, qubits: 10, size: 551\n" - ] - } - ], - "source": [ - "core = Hamiltonian(transformation=TransformationType.FULL, qubit_mapping=QubitMappingType.PARITY, \n", - " two_qubit_reduction=True, freeze_core=True)\n", - "qubit_op, aux_ops = core.run(molecule)\n", - "\n", - "print(qubit_op)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We now pass these to the ExactEigensolver and run it to produce a result. This result will include the computed electronic part of the ground state energy. We can pass this result back to the Hamiltonian object from above and it will combine it with values it stored such as the frozen core energy to form a complete result for the molecule. As can be seen this matches the result from the declarative approach above.\n", - "\n", - "Note: the num particles printed here is that which is observed from the spin operator that is in the aux_ops. It says 8 which matches what we expect; the molecule has 10 (5 alpha and 5 beta) but the operator was left with 8 after we took away 2 from freezing the core. The molecule has a core_orbitals property which lists the orbitals comprising the core ones that can be frozen so we can easily figure how many electrons that is (2 per orbital in that list)." - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "=== GROUND STATE ENERGY ===\n", - " \n", - "* Electronic ground state energy (Hartree): -84.206272446429\n", - " - computed part: -23.544497240436\n", - " - frozen energy part: -60.661775205992\n", - " - particle hole part: 0.0\n", - "~ Nuclear repulsion energy (Hartree): 9.193913160623\n", - "> Total ground state energy (Hartree): -75.012359285805\n", - " Measured:: Num particles: 8.000, S: 0.000, M: 0.00000\n", - " \n", - "=== DIPOLE MOMENT ===\n", - " \n", - "* Electronic dipole moment (a.u.): [0.0 1.57867263 0.0]\n", - " - computed part: [0.0 1.57778798 0.0]\n", - " - frozen energy part: [0.0 0.00088465 0.0]\n", - " - particle hole part: [0.0 0.0 0.0]\n", - "~ Nuclear dipole moment (a.u.): [0.0 2.21475902 0.0]\n", - "> Dipole moment (a.u.): [0.0 0.63608639 0.0] Total: 0.63608639\n", - " (debye): [0.0 1.61677018 0.0] Total: 1.61677018\n" - ] - } - ], - "source": [ - "ee = ExactEigensolver(qubit_op, aux_operators=aux_ops)\n", - "algo_result = ee.run()\n", - "result = core.process_algorithm_result(algo_result)\n", - "for line in result[0]:\n", - " print(line)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Using VQE. First declaratively with the dictionary.\n", - "\n", - "We update the dictionary, for VQE with UCCSD, and run the computation again. By default, if a backend is not explicitly provided, as is the case here, it will use the `statevector_simulator` from `BasicAer`. \n", - "\n", - "_*Please note that with 10 qubits the simulation can take a while.*_" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Ground state energy: -75.0122585919439\n", - "=== GROUND STATE ENERGY ===\n", - " \n", - "* Electronic ground state energy (Hartree): -84.206171752567\n", - " - computed part: -23.544396546575\n", - " - frozen energy part: -60.661775205992\n", - " - particle hole part: 0.0\n", - "~ Nuclear repulsion energy (Hartree): 9.193913160623\n", - "> Total ground state energy (Hartree): -75.012258591944\n", - " Measured:: Num particles: 8.000, S: 0.000, M: 0.00000\n", - " \n", - "=== DIPOLE MOMENT ===\n", - " \n", - "* Electronic dipole moment (a.u.): [-0.00000112 1.57887918 0.00000014]\n", - " - computed part: [-0.00000112 1.57799453 0.00000014]\n", - " - frozen energy part: [0.0 0.00088465 0.0]\n", - " - particle hole part: [0.0 0.0 0.0]\n", - "~ Nuclear dipole moment (a.u.): [0.0 2.21475902 0.0]\n", - "> Dipole moment (a.u.): [0.00000112 0.63587984 -0.00000014] Total: 0.63587984\n", - " (debye): [0.00000284 1.61624518 -0.00000036] Total: 1.61624518\n" - ] - } - ], - "source": [ - "qiskit_chemistry_dict['algorithm']['name'] = 'VQE'\n", - "qiskit_chemistry_dict['optimizer'] = {'name': 'SLSQP', 'maxiter': 2500}\n", - "qiskit_chemistry_dict['variational_form'] = {'name': 'UCCSD'}\n", - "qiskit_chemistry_dict['initial_state'] = {'name': 'HartreeFock'}\n", - "\n", - "solver = QiskitChemistry()\n", - "result = solver.run(qiskit_chemistry_dict)\n", - "\n", - "print('Ground state energy: {}'.format(result['energy']))\n", - "\n", - "for line in result['printable']:\n", - " print(line)" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Actual VQE evaluations taken: 666\n" - ] - } - ], - "source": [ - "print('Actual VQE evaluations taken: {}'.format(result['algorithm_retvals']['eval_count']))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Using VQE, programmatically\n", - "\n", - "The solver above, with the complete dictionary, will recompute the molecule internally again with the driver. Here we will start with the qubit operator that we computed above. We need to setup an optimizer, variational form and initial state for use with VQE.\n", - "\n", - "The variational form and UCCSD are a little more complex since they need information about numbers of orbitals and numbers of electrons, as well as what qubit mapping etc was used for the qubit operator. However we have some help from the Hamiltonian class that we can use (which internally is what the declarative form takes advantage of too). \n", - "\n", - "Note: If you use FermionicOperator directly to make a qubit operator then you need to keep track of electrons removed etc. The molecule object from the driver has the original values but if you freeze out orbitals then the electrons remaining in the operator is what is required." - ] - }, - { - "cell_type": "code", - "execution_count": 47, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Ground state energy: -75.0122585919439\n", - "=== GROUND STATE ENERGY ===\n", - " \n", - "* Electronic ground state energy (Hartree): -84.206171752567\n", - " - computed part: -23.544396546575\n", - " - frozen energy part: -60.661775205992\n", - " - particle hole part: 0.0\n", - "~ Nuclear repulsion energy (Hartree): 9.193913160623\n", - "> Total ground state energy (Hartree): -75.012258591944\n" - ] - } - ], - "source": [ - "init_state = HartreeFock(num_qubits=qubit_op.num_qubits, \n", - " num_orbitals=core._molecule_info['num_orbitals'],\n", - " num_particles=core._molecule_info['num_particles'],\n", - " qubit_mapping=core._qubit_mapping,\n", - " two_qubit_reduction=core._two_qubit_reduction)\n", - "\n", - "var_form = UCCSD(num_qubits=qubit_op.num_qubits,\n", - " depth=1,\n", - " num_orbitals=core._molecule_info['num_orbitals'], \n", - " num_particles=core._molecule_info['num_particles'],\n", - " qubit_mapping=core._qubit_mapping,\n", - " two_qubit_reduction=core._two_qubit_reduction, \n", - " initial_state=init_state)\n", - "\n", - "optimizer = SLSQP(maxiter=2500)\n", - "\n", - "# setup backend on which we will run\n", - "backend = BasicAer.get_backend('statevector_simulator')\n", - "quantum_instance = QuantumInstance(backend=backend)\n", - "\n", - "vqe = VQE(qubit_op, var_form, optimizer, 'matrix')\n", - "algo_result = vqe.run(quantum_instance)\n", - "lines, result = core.process_algorithm_result(algo_result)\n", - "\n", - "print('Ground state energy: {}'.format(result['energy']))\n", - "\n", - "for line in lines:\n", - " print(line)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Internally the core, when processing the algorithm result, stores the result dictionary from the algorithm under the `algorithm_retvals` key. We used this above in declarative approach, to get the eval count, and since we process the result the same way here, using the core, we can do this here too. But here we have direct access to the algorithm result since we ran it. Hence we can access the count directly from the above algo_result. To show these are the same they are both printed below." - ] - }, - { - "cell_type": "code", - "execution_count": 48, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Actual VQE evaluations taken: 666\n", - "Actual VQE evaluations taken: 666\n" - ] - } - ], - "source": [ - "print('Actual VQE evaluations taken: {}'.format(result['algorithm_retvals']['eval_count']))\n", - "\n", - "print('Actual VQE evaluations taken: {}'.format(algo_result['eval_count']))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Z-matrix format\n", - "\n", - "Z-matrix was mentioned in the introduction. Lets show it in use in a quick final example here. We'll use ExactEigensolver as the goal here is just to show the technique. We will keep the bond angle between the Hydrogen atoms and Oxygen constant while varying the interatomic distance of one the Hydrogen atoms. This is simple to do in Z-matrix format, though can of course be done using xyz format but that needs more work to compute the coordinates each time." - ] - }, - { - "cell_type": "code", - "execution_count": 44, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "import pylab\n", - "\n", - "h2o = 'H; O 1 1.08; H 2 {} 1 104.5'\n", - "qiskit_chemistry_dict = {\n", - " 'driver': {'name': 'PYSCF'},\n", - " 'PYSCF': {'atom': '', 'basis': 'sto-3g'},\n", - " 'operator': {'name': 'hamiltonian', 'freeze_core': True},\n", - " 'algorithm': {'name': 'ExactEigensolver'}\n", - "}\n", - "\n", - "distances = [x * 0.01 + 1.00 for x in range(17)]\n", - "energies = np.empty(len(distances))\n", - "\n", - "for i, distance in enumerate(distances):\n", - " qiskit_chemistry_dict['PYSCF']['atom'] = h2o.format(distance)\n", - " solver = QiskitChemistry()\n", - " result = solver.run(qiskit_chemistry_dict)\n", - " energies[i] = result['energy']" - ] - }, - { - "cell_type": "code", - "execution_count": 46, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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kBBwBrDezxQllPSXNlPSxpCOKWa+DmaWH6XVAhzDdBViVsNxqoIuZTQU+BNLD410zW1DUhiVdISlVUmpGRsYeHpZzzlWdDVnZXD9pJvu3b8atp1bvdqBElVpZKGkK0LGIWTeb2Wth+jy+fxaUDnQ3s02ShgKvSupnZlnF7cfMTJKVEsv+wEFAwc+DyZKOMLNPitjeI8AjACkpKSVu1znn4pabl8+vnp3J9pw8Jl5e/duBElVqpGY2sqT5kpKB04GhCevkADlhOk3SUqA3kFpo9fWSOplZeqhu2xDK1wCJ/RG7hrILgM/NbFvY99vAocAPkpBzztUkf35rAdNWZPLAuYM4oAa0AyWKuzpuJPCVma0uKJDUXlJSmO5F1MFgWRHrvg6MDtOjgdcSyi8KveQOAbaEaruvgaMkJUuqT9QpocjqOOecqylenbmGJ/67gkt/1JNTB3WJO5xyizsJncsPOyQcCcwJXbZfBK4ys0wASY9KSgnL3QkcJ2kxUTK7M5S/RZS0lgD/An4Zyl8ElgJzgdnAbDN7o1KOyjnnqsC8tVsY+/IcRvRsw00n9Yk7nD0iM2/yKElKSoqlphauCXTOuXht3rGLnz70Kbm7jTeuOZz2zRvGHdK3JKWZWUrpS/rYcc45V+Pk5RvXPjeL9VtymHTlIdUqAZWXJyHnnKth7p+yiP8syuDPpw1gcPfWcYezV+JuE3LOOVcO785bx98+WMK5w7px/ojucYez1zwJOedcDbE0Yxu/eX42B3dtyS0/qzkXpJbEk5BzztUA23J2c+VTaTRMrsfDFwylUf2kuEOqEN4m5Jxz1ZyZ8dsXZrN843aeGjOczq0axx1ShfEzIeecq+bGfbyMt79cx00n9uGw/drFHU6F8iTknHPV2CeLM7j73a/46cGdGXN4z7jDqXCehJxzrppalbmDayfO5IB9mvOXMwZQG+/D6UnIOeeqoezcPK56Oo3d+cY/Lxxao0bGLo/aeVTOOVeDmRm/f2Uu89OzeGx0Cj3aNY07pErjZ0LOOVfNPP35Sl6esYbrj+3NMX06lL5CDeZJyDnnqpHUFZn83xvzObbPPlxzzP5xh1PpPAk551w1sSErm188M4OurRtz3zmDqFev9nVEKMzbhJxzrhrYtTufXz4zg+05u3l6zAhaNq4fd0hVwpOQc85VA7f/ez6pK7/hofMHc2DHmnWL7r3h1XHOORezl9JWM2HqSq44shenDOwcdzhVypOQc87F6Ms1W/j9K3M5bL+2/O4nB8YdTpXzJOScczH5ZvsurnwqjbZNG/C38waTnFT3vpK9Tcg552KQm5fP1c/OIGNbDi9edShtm9XcW3TvjbqXdp1zLmZmxv++Po/Plm7ijtMGMLBrq7hDio0nIeecq2ITPlvBs198zS+O3o8zhnaNO5xYeRJyzrkq9NHCDdz65nyO79uB3x5f9zoiFOZJyDnnqsji9Vu55tmZ9OnYgr/WkRERSuNJyDnnqkDm9l2MmZBKowZJPDo6haYNvV8YxJSEJE2SNCs8VkiaFcp7SNqZMG9cMeu3kTRZ0uLwt3Uo7yNpqqQcSTcUWucESQslLZE0tvKP0jnnIrt253PVU2msz8rmXxel0LlV47hDqjZiScVmdk7BtKR7gS0Js5ea2aBSNjEWeN/M7gwJZSxwI5AJXAuMSlxYUhLwd+A4YDUwXdLrZjZ/rw/GOedKYGbc/Mpcpq3I5MHzBjOoW93tCVeUWKvjFN2r9mxgYjlXPRWYEKYnEJKOmW0ws+lAbqHlhwNLzGyZme0CngvbcM65SvWvT5bxQtpqrj32AH52cN0akqcs4m4TOgJYb2aLE8p6Spop6WNJRxSzXgczSw/T64DS7vrUBViV8Hx1KCuSpCskpUpKzcjIKGXTzjlXtCnz13PH219x8sBOXH/sAXGHUy1VWnWcpClAxyJm3Wxmr4Xp8/j+WVA60N3MNkkaCrwqqZ+ZZRW3HzMzSVZhgUfbfAR4BCAlJaVCt+2cqxsWpGdx3XMzGdClJfecebD3hCtGpSUhMxtZ0nxJycDpwNCEdXKAnDCdJmkp0BtILbT6ekmdzCxdUidgQynhrAG6JTzvGsqcc67CZWzN4bIJqTRrlMy/LkqhcYOkuEOqtuKsjhsJfGVmqwsKJLUPnQiQ1As4AFhWxLqvA6PD9GjgtSKWSTQdOEBST0kNgHPDNpxzrkJl5+Zx5VOpbNqew6MXDaNDi0Zxh1StxdlR/Vx+2CHhSOBWSblAPnCVmWUCSHoUGGdmqcCdwPOSxgAriTo3IKkj0VlTCyBf0vVAXzPLkvQr4F0gCXjczOZV+hE65+oUM+Oml+cy4+vNPPzzIQzo2jLukKo9mXmTR0lSUlIsNbVwbaBzzv3Q3z9cwt3vLuSG43vzq2PqbkcESWlmllKWZePuHeecc7XCO1+mc/e7Cxk1qDNX/3j/uMOpMTwJOefcXvpyzRZ+PWk2g7u34s4zBhJdAunKwpOQc87thfVZ2Vw2IZXWTerzyIUpNKrvPeHKw0fQc865PbRzVx6XP5lKVnYuL/3iMNo3r5t3R90bnoScc24P5OcbN7w4m7lrtvDIhSkc1KlF3CHVSF4d55xze+CB9xfz7znpjD2hD8f1LW3kMFccT0LOOVdOr89eywPvL+asoV254shecYdTo3kScs65cpi1ajO/fWE2w3u04bbT+ntPuL3kScg558poxcbtjBk/nX1aNOThC4bQMNl7wu0tT0LOOVcGG7flMPqJaeSbMf6S4bRt5j3hKoL3jnPOuVJsz9nNpeOnsz4rm4mXH8J+7ZvFHVKt4UnIOedKkJuXzy+emcG8tVk8cuFQBndvHXdItYpXxznnXDHMjBtfmsN/FmVw+6j+HHuQd8WuaJ6EnHOuGHe9u5CXZ6zh1yN7c+7w7nGHUyt5EnLOuSJM+GwFD3+0lPNHdOfaY31U7MriScg55wp5a246t7wxj+P6duBPp/q1QJXJk5BzziX4Ytkmrp80iyHdW/O38waTVM8TUGXyJOScc8HCdVu57MlUurVuzGOj/bYMVcGTkHPOAWs372T049No0iCJCZcOp1WTBnGHVCd4EnLO1Xmbd+xi9OPT2J6zm/GXDKdr6yZxh1RnlCkJSXpZ0smSPGk552qV7NzoxnQrN+3gkYv8vkBVraxJ5R/A+cBiSXdKOrASY3LOuSqRl29c99xMUld+w33nHMyh+7WNO6Q6p0xJyMymmNnPgSHACmCKpM8kXSKpfmUG6JxzlcHMuOX1ebw7bz1/PLkvpwzsHHdIdVKZq9cktQUuBi4DZgIPECWlyZUSmXPOVaJ/fLSUpz5fyZVH9uLSw3vGHU6dVaYBTCW9AhwIPAX81MzSw6xJklIrKzjnnKsML6Su4u53F3La4C7ceEKfuMOp08p6JvSgmfU1szsSEhAAZpZS3p1KmiRpVniskDQrlPeQtDNh3rhi1m8jabKkxeFv61DeR9JUSTmSbkhYvpukDyXNlzRP0nXljdk5Vzt8uHADY1+eyxEHtOMvZwyknl+MGquy3sqhtaTTC5VtAeaa2Yby7tTMzimYlnRv2FaBpWY2qJRNjAXeN7M7JY0Nz28EMoFrgVGFlt8N/MbMZkhqDqRJmmxm88sbu3Ou5pq1ajO/fHoGB3VqzsMXDKVBsnf4jVtZk9AY4FDgw/D8aCAN6CnpVjN7ak92rmhAprOBY8q56qkhBoAJwEfAjSEhbpB0cuLC4ewtPUxvlbQA6AJ4EnKujli+cTuXjp9Ou+YNePziYTRr6LdTqw7K+jOgPnCQmZ1hZmcAfQEDRhCdgeypI4D1ZrY4oaynpJmSPpZ0RDHrdUioFlwHlPkmH5J6AIOBL0pY5gpJqZJSMzIyyrpp51w1lbE1h4sej/7ln7x0BPs0bxRzRK5AWX8KdDWz9QnPNwDdzCxTUm5RK0iaAnQsYtbNZvZamD4PmJgwLx3obmabJA0FXpXUz8yyigvMzEySleUgJDUDXgKuL2WbjwCPAKSkpJRp28656qlgNISNW3cx8YpD6NmuadwhuQRlTUIfSXoTeCE8PyOUNQU2F7WCmY0saYOSkoHTgaEJ6+QAOWE6TdJSoDdQuAfeekmdzCxdUieipFiicD3TS8AzZvZyacs752q+rOxcRj8+jSUbtvHo6BQGdWsVd0iukLJWx10NPAEMCo8ngavNbLuZ/XgP9z0S+MrMVhcUSGovKSlM9wIOAJYVse7rwOgwPRp4rYhlvhXanh4DFpjZfXsYr3OuBtmes5tLn5jOvLVZPHzBEI7s3T7ukFwRSj0TCklhSkg2L1Xgvs/l+1VxAEcCt4YqvnzgKjPLDHE8Cowzs1TgTuB5SWOAlUSdG5DUkeisqQWQL+l6ovargcCFwNyC7uDA783srQo8HudcNbFzVx5jJkxn5qrNPHTeYI49qMzNxq6Kyaz0Jg9J7wOnm9mWUheuZVJSUiw11a/Hda6myNmdx2UTUvl0yUbuP2cQpw7qEndIdY6ktLJeQ1rWNqFtRGcRk4HtBYVmdu0exOecc5Vi1+58rn5mBp8s3shdZw70BFQDlDUJvRwezjlXLe3Oy+f6STOZsmADfxrVn7NTusUdkiuDMiUhM5sgqTFR9+mFlRyTc86VS16+ccMLs3lr7jr+cPJBXHjIvnGH5MqorDe1+ykwC3gnPB8k6fXKDMw558oiP9/4/ctzeXXWWn77kwO57IhecYfkyqGsXbRvAYYTrgkys1mAv9POuViZGbe8MY9Jqau49pj9ufrH+8cdkiunsiah3CJ6xuVXdDDOOVdWZsaf31rAk1OjewL9+rjecYfk9kBZOybMk3Q+kCTpAKKRqj+rvLCcc65k901exL8+Wc7Fh/Vg7Il9iK5JdzVNWc+ErgH6EQ2pMxHIAq6vrKCcc64kD32wmL99sITzhnfjf07p6wmoBitr77gdwM3h4ZxzsfnXf5Zxz3uLOH1wF24fNcBvSlfDlfX23r2BG4AeieuYWXnvA+Scc3vsyakruP2tBZw8sBN3nel3Ra0Nytom9AIwDngUyKu8cJxzrmjPTfua/3ltHsf17cD95wwiOcnviloblDUJ7Tazhys1EuecK8YrM1dz0ytzOap3ex46fzD1PQHVGmV9J9+Q9EtJnSS1KXhUamTOOQf8e046v3l+Nof2ass/LxxKw+SkuENyFaisZ0IF9+75bUKZ4ResOucq0eT567nuuZkM3bc1j45OoVF9T0C1TVl7x/Ws7ECccy7RRws3cPUzM+jXpSWPXzyMJg3K+pvZ1SQlVsdJ+l3C9FmF5v25soJyztVt73y5jiueTGP/fZrx5CXDad6oftwhuUpSWpvQuQnTNxWad0IFx+Kcc7wyczVXPzuDfl1aMPHyQ2jZxBNQbVZaElIx00U9d865vfLU5yv59aTZjOjZhqfHjPAEVAeUVslqxUwX9dw55/bYwx8t5S/vfMXIg/bhofOHeCeEOqK0JHSwpCyis57GYZrwvFGlRuacqxPMjHveW8jfP1zKzw7uzL1nH+zXAdUhJSYhM/OfIs65SpOfb/zfG/OYMHUl5w3vxm2jBpDkQ/HUKd7n0TkXi915+dz40lxemrGay4/oye9POshHw66DPAk556pczu48rn9uFm9/uY7/d1xvrjlmf09AdZQnIedcldq5K48rn07jP4sy+OMpfRlzuF8LX5d5EnLOVZms7FwuG5/K9JWZ/OWMAZwzrHvcIbmYxdIFRdIkSbPCY4WkWaG8h6SdCfPGFbN+G0mTJS0Of1uH8j6SpkrKkXRDEeslSZop6c3KPULnXGGZ23fx8399wYyvv+HBcwd7AnJATGdCZnZOwbSke4EtCbOXmtmgUjYxFnjfzO6UNDY8vxHIBK4FRhWz3nXAAqDFnsbunCu/9VnZXPDoF3yduYNHLhrKMX06xB2SqyZi7YyvqCXybGBiOVc9FZgQpicQko6ZbTCz6UBuEfvqCpxMdGM+51wVWZW5g7PGTWXt5p2Mv2S4JyD3PXFfEXYEsN7MFieU9QxVZh9LOqKY9TqYWXqYXgeU5VN9P/A7IL+0BSVdISlVUmpGRkYZNu2cK8qSDds4a9xUtuzM5ZnLD+HQ/drGHZKrZiqtOk7SFKBjEbNuNrPXwvR5fP8sKB3mYNvSAAAamklEQVTobmabJA0FXpXUz8yyfrCVwMxMUolDCEk6BdhgZmmSji4tdjN7BHgEICUlxYcncm4PfLlmCxc9Po16EpOuPIQ+Hb0W3P1QpSUhMxtZ0nxJycDpwNCEdXKAnDCdJmkp0BtILbT6ekmdzCxdUidgQynh/Aj4maSTiIYbaiHpaTO7oFwH5Zwrk9QVmVwyfjotGtXn6ctG0LNd07hDctVUnNVxI4GvzGx1QYGk9pKSwnQv4ABgWRHrvs53d3sdDbxWxDLfMrObzKyrmfUguj3FB56AnKscnyzO4MLHptGuWUOev+pQT0CuRHFeJ3QuP+yQcCRwq6Rcorabq8wsE0DSo8A4M0sF7gSelzQGWEnUuQFJHYnOmloA+ZKuB/qWVJ3nnKs473y5jmsnzqRX+6Y8NWYE7Zs3jDskV83JzJs8SpKSkmKpqYVrA51zicyMRz9Zzp/fXsCgbq0Yf/FwvxdQHSYpzcxSyrKsj5jgnNsruXn5/M9r85g47WtOGtCRe88aROMGPgC/KxtPQs65PbZlZy6/fCaN/y7ZxNU/3o/fHHcg9fxWDK4cPAk55/bIyk3buXT8dL7O3ME9Zx3MmUO7xh2Sq4E8CTnnym36ikyueDIVA54aM4JDevlFqG7PeBJyzpXLKzNXc+OLc+naujGPXTzMu2C7veJJyDlXJmbGXycv4sEPlnBIrzaMu2AorZo0iDssV8N5EnLOlSo7N4/fvjiHN2av5eyUrtw2agANkuMeetLVBp6EnHMlytiawxVPpTLz682MPbEPVx7Zy2/F7SqMJyHnXLEWrtvKpeOns2l7DuMuGMIJ/TvFHZKrZTwJOeeK9PGiDK5+ZgZNGiTx/JWHMrBrq7hDcrWQJyHn3A88NXUFt7wxn94dmvP4xSl0atk47pBcLeVJyDn3rbx847Z/z+eJ/67g2D778OB5g2na0L8mXOXxT5dzDoBtObu5duJMPvhqA2MO78nvTzqIJB+Cx1UyT0LOOdZs3smY8dNZvGEbt43qzwWH7Bt3SK6O8CTkXB03a9VmLpuQSs7uPMZfMowjDmgfd0iuDvEk5FwdZWZM+GwFf37rKzq0bMjEy0dwQIfmcYfl6hhPQs7VQVt25PK7l2bz7rz1jDxoH+4+82BaN/UheFzV8yTkXB0za9VmfvXsDNZtyeYPJx/EmMN7+ggILjaehJyrI8yMxz5dzp1vf0WHFo144apDGdy9ddxhuTrOk5BzdcDmHbu44YXZTFmwgeP7duDuMw+mZZP6cYflnCch52q7tJWZXPPsTDZu28UtP+3L6MN6ePWbqzY8CTlXS+XnG498soy7311Il1aNeekXhzGga8u4w3LuezwJOVcLbdqWw29emM1HCzM4eUAn7jhjAC0aefWbq348CTlXy0xbnsk1E2fwzY5c/jSqPxeM6O7Vb67a8iTkXC2Rn2/846Ml3Dd5Efu2bcrjFw+jX2evfnPVWyz355U0SdKs8FghaVYo7yFpZ8K8ccWs30bSZEmLw9/WobyPpKmSciTdUGidVpJelPSVpAWSDq38I3WuamRszWH0E9O4571FnDKwM29cc7gnIFcjxHImZGbnFExLuhfYkjB7qZkNKmUTY4H3zexOSWPD8xuBTOBaYFQR6zwAvGNmZ0pqADTZm2Nwrrr4bOlGrntuFlk7c7nz9AGcM6ybV7+5GiPW6jhF/ylnA8eUc9VTgaPD9ATgI+BGM9sAbJB0cqH9tASOBC4GMLNdwK49jdu56iAv3/jbB4t58P3F9GzXlKfGDKdPxxZxh+VcucTdJnQEsN7MFieU9ZQ0E8gC/mBmnxSxXgczSw/T64AOpeynJ5ABPCHpYCANuM7Mthe1sKQrgCsAunfvXuaDca6qbMjK5rrnZjF12SZOH9KFP53a328+52qkSvvUSpoCdCxi1s1m9lqYPg+YmDAvHehuZpskDQVeldTPzLKK24+ZmSQrJZxkYAhwjZl9IekBoiq8PxazzUeARwBSUlJK27ZzVcbMeDFtNbe/tYDs3DzuPnMgZ6V0izss5/ZYpSUhMxtZ0nxJycDpwNCEdXKAnDCdJmkp0BtILbT6ekmdzCxdUidgQynhrAZWm9kX4fmLREnIuRpjxcbt/P6VuXy2dBPDerTmjtMHsv8+zeIOy7m9Euf5+0jgKzNbXVAgqT2QaWZ5knoBBwDLilj3dWA0cGf4+1oRy3zLzNZJWiXpQDNbCBwLzK+g43CuUuXm5fPIf5bx4PuLaZBUj9tP6895w7pTz2+97WqBOJPQuXy/Kg6izgO3SsoF8oGrzCwTQNKjwDgzSyVKPs9LGgOsJOrcgKSORGdNLYB8SdcDfUN13jXAM6Fn3DLgkso+QOf21syvv+Gml+fy1bqtnNi/I7f8rB8dWjSKOyznKozMvMmjJCkpKZaaWrg20LnKtS1nN/e8u5AJU1fQoXkjbj21H8f3K6qJ1bnqR1KamaWUZVnvTuNcNfP+gvX88dUvSc/K5qJD9uWGnxxIcx/3zdVSnoScqyY2bM3m/96Yz7/npNO7QzNePP8whu7rN51ztZsnIedilp9vPJ+6ij+/tYDs3fnccHxvrjhyPxokxzKqlnNVypOQczFamrGNm16ey7TlmYzo2YY7Th9Ar/be7drVHZ6EnIvBrt35jPt4KQ99sIRG9evxlzMGcHaKj/nm6h5PQs5VsbSV33DTy3NYtH4bpwzsxP/8tC/7NPdu165u8iTkXBXZmp3LXe8s5OkvVtK5ZWMevziFY/qUNuyhc7WbJyHnKll2bh7PfPE1D3+0hMztu7jksJ785vjePuCoc3gScq7S7Nqdz/Opq3jogyWsy8rmR/u35cYT+jCwa6u4Q3Ou2vAk5FwF252Xz6uz1vLA+4tYlbmTofu25r5zDuaw/drFHZpz1Y4nIecqSH6+8e+56fx1yiKWZWynf5cW3HpJf47u3d57vTlXDE9Czu0lM2PKgg3c+95Cvlq3ld4dmjHugqH8pF8HTz7OlcKTkHN7yMz4dMlG7nlvEbNXbaZH2yY8cO4gThnYmSS/zYJzZeJJyLk9MG15Jve8t5BpyzPp0qoxd50xkNOHdCE5yYfaca48PAk5Vw6zV23m3smL+M+iDNo3b8itp/bjnGHdaJicFHdoztVInoScK4MF6VncN3kRk+evp3WT+vz+pD5ceEgPGjfw5OPc3vAk5FwJFq/fyoMfLOHNOWtp1jCZ3xzXm0sO70kzv9DUuQrh/0nOFbJzVx7/npvOpOlfM33FNzRpkMQvj96Py4/oRasmDeIOz7laxZOQc0Q93b5ck8Vz07/m9Vlr2Zqzm57tmjL2xD6cNbQrbZs1jDtE52olT0KV5NqJM+nbuQWnDe5ChxY+QnJ1tWVHLq/NXsNz01YxPz2Lhsn1OHlAJ84Z1o3hPdv4dT7OVTJPQpVge85u1m7eyeuz13LXO19xVO/2nJXSjWMP2sd7UVUDZsYXyzOZNH0Vb81NJ2d3Pv06t+BPo/rzs4M707Jx/bhDdK7OkJnFHUO1lpKSYqmpqXu07vKN23kxbRUvpa1hXVY2rZrU59SDO3Pm0G7079LCf2VXsQ1bs3kpbQ3Pp65i+cbtNG+UzKhBXThnWDf6d2kZd3jO1RqS0swspUzLehIq2d4koQJ5+cZ/l2zkhbTVvDtvHbt259OnY3POHNqVUYO70M7bGyrN7rx8/rM4g+emreL9rzaQl28M79mGc4d148T+nbyLtXOVwJNQBaqIJJRoy45c3pizlhfSVjN71WaS64kf99mHs4Z25cd99qG+X3FfIVZl7uD51FW8kLqadVnZtGvWgDOGduXslG7s175Z3OE5V6t5EqpAFZ2EEi1av5WX0lbz8sw1ZGzNoW3TBowa3IUzh3bloE4tKmWftVXO7jxmfb2Zz5Zu4rOlG5m+4hvqCY7q3Z5zhnXjmD4daJDsCd65qlDtk5CkScCB4WkrYLOZDZLUA1gALAzzPjezq4pYvw0wCegBrADONrNvJPUBngCGADeb2T0J6/wauAwwYC5wiZlllxZrZSahArvz8vl4UQYvpq1myoL15OYZ/bu04Kyh3fjZwZ1p3dSvTSlsd14+c9ZsYerSTUxduonUlZlk5+YjQf/OLRl5UAfOSulK51aN4w7VuTqn2ieh7wUg3QtsMbNbQxJ608z6l7LOXUCmmd0paSzQ2sxulLQPsC8wCvimIAlJ6gJ8CvQ1s52SngfeMrPxpcVXFUkoUeb2Xbw2aw0vpq1m3tosGiTVY2TfffjxgftwcLdW7Ne+WZ0coTkv31iQnsVnSzcydekmpi3PZPuuPAD6dGzOofu15dBebRnRsy0tm3jvNufiVJ4kFGsXbUXdw84GjinnqqcCR4fpCcBHwI1mtgHYIOnkItZJBhpLygWaAGv3JObK1qZpAy75UU8u+VFP5q/N4sW01bw6aw1vzV0HQOP6SfTv0oIBXVoxsGtLBnZtSY+2TalXyxKTmbFo/bZvk87nyzaRlb0bgF7tm3LakC4ctl87RvRs4xeSOleDxXomJOlI4L6CjBnOhOYBi4As4A9m9kkR6202s1ZhWkRnPa0S5t8CbCtUHXcdcDuwE3jPzH5eQlxXAFcAdO/efejKlSv37kD3Un6+sWzjduas3syc1VuYu2YL89ZuITs3H4DmDZPp3yVKSAO6tuTgrq3o2rpxjeoCbmYs37idz5ZuYuqyTXy+dBObtu8CoHubJhzaq210trNfW7/417lqrlqcCUmaAnQsYtbNZvZamD4PmJgwLx3obmabJA0FXpXUz8yyituPmZmkEjOppNZEZ089gc3AC5IuMLOni9nmI8AjEFXHlbTtqlCvnth/n2bsv08zTh/SFYjaRBZv2Mbc1VuYs2Yzc1dv4Yn/rmBXXpSYWjWpz4CCxNSlFQd3a0nHFo1iS0zZuXmkb8kmffPO6O+Wnazdks26Ldms3byTtZt3fnum07FFI47q3Z5DQhVbtzZNYonZOVf5Ki0JmdnIkuZLSgZOB4YmrJMD5ITpNElLgd5A4UaZ9ZI6mVm6pE7AhlLCGQksN7OMsO+XgcOAIpNQTZCcVI+DOrXgoE4tOHtYNyDqIbZo3bZvk9Ls1VsY9/Ey8vKjPNquWUMGdm1Jx5aNaFI/icYNwqN+Ek0aJNGofhJNGiTTOMxrkjivQRJN6icVedO27Nw81mdls3ZzlFwKkkyUYKLpb3bk/mC9Nk0b0KllI7q2bkxKj9Yc1KkFh+3Xjh5tm9Soszjn3J6Ls01oJPCVma0uKJDUnqjDQZ6kXsABwLIi1n0dGA3cGf6+VsQyib4GDpHUhKg67lh+mNhqvIbJSQwIVXKMiMqyc/OYn54VktJmvlyzhTmrN7NjVx47c/Mob21s/SR9m6Qa109ia/bub6vNErVqUp9OLRvTqWUjBndvRedWjenYohGdWjWic8vGdGzZiEb1/UJR5+q6OJPQuXy/Kg7gSODW0HkgH7jKzDIBJD0KjDOzVKLk87ykMcBKos4NSOpIlFxaAPmSrifqEfeFpBeBGcBuYCahuq22a1Q/iSHdWzOke+sfzDMzcnbns3NXHjty89i5Kzxy89ixazfZuXnfJquCeTsKTTdrmEznlo3o2LIRnVtFSadjy0Y0aeDDEjrnShd7F+3qrqq7aDvnXE1Xno4Jfgm5c8652HgScs45FxtPQs4552LjScg551xsPAk555yLjSch55xzsfEk5JxzLjaehJxzzsXGL1YthaQMolEZ9kQ7YGMFhlNRPK7y8bjKx+Mqn9oY175m1r4sC3oSqkSSUst61XBV8rjKx+MqH4+rfOp6XF4d55xzLjaehJxzzsXGk1Dlqq4jdXtc5eNxlY/HVT51Oi5vE3LOORcbPxNyzjkXG09CzjnnYuNJaA9IelzSBklfFjNfkh6UtETSHElDEuaNlrQ4PEZXh7gkDZI0VdK8UH5OdYgrYX4LSaslPVRd4pLUXdJ7khZImi+pRzWJ667wPi4Iy6gK4+oTPkc5km4oNO8ESQtDzGMrKqa9iUtSN0kfhvdvnqTrqkNcCfOTJM2U9GZ1iUtSK0kvSvoqfMYO3euAzMwf5XwQ3YZ8CPBlMfNPAt4GBBwCfBHK2wDLwt/WYbp1NYirN3BAmO4MpAOt4o4rYf4DwLPAQ9XhfQzzPgKOC9PNgCZxxwUcBvwXSAqPqcDRVRjXPsAw4HbghoTyJGAp0AtoAMwG+laDuDoBQ8J0c2BRdYgrYf7/C5/7Nysqpr2NC5gAXBamG1TE94SfCe0BM/sPkFnCIqcCT1rkc6CVpE7AT4DJZpZpZt8Ak4ET4o7LzBaZ2eKwjbXABqBMVztXZlwAkoYCHYD3KiqevY1LUl8g2cwmh+1sM7MdcccFGNCI6MuhIVAfWF9VcZnZBjObDuQWmjUcWGJmy8xsF/BcOIZY4zKzdDObEaa3AguALnHHBSCpK3Ay8GhFxbO3cUlqSZTAHgvL7TKzzXsbjyehytEFWJXwfHUoK6487ri+JWk40ZfY0rjjklQPuBf4QVVFFSnu9eoNbJb0cqguuVtSUtxxmdlU4EOiM9l04F0zW1CFcRUn7s99qUJ16mDgi3gj+db9wO+A/LgDSdATyACeCJ/7RyU13duNehJy3wq/pp8CLjGz6vDh/yXwlpmtjjuQQpKBI4iS4zCiaqaL4wwIQNL+wEFAV6Iv+WMkHRFvVNWfpGbAS8D1ZpZVDeI5BdhgZmlxx1JIMlE13sNmNhjYDux1+54nocqxBuiW8LxrKCuuPO64kNQC+Ddwc6jiqUrFxXUo8CtJK4B7gIsk3VkN4loNzArVS7uBV4n+OeOO6zTg81A9uI2o3WjvG473Xtyf+2JJqk+UgJ4xs5fjjif4EfCz8Ll/jujHxNPxhgREn/vVZlZwtvgiFfC59yRUOV4n+sKUpEOALWaWDrwLHC+ptaTWwPGhLNa4JDUAXiFqZ3ixCuMpMS4z+7mZdTezHkRnHU+aWYX2rNqTuIDpRO0wBe1mxwDzq0FcXwNHSUoOX65HEbVzxG06cICknuGzdi7RMcQq9Bx8DFhgZvfFHU8BM7vJzLqGz/25wAdmdkHMYWFm64BVkg4MRcdSEZ/7ve3ZUBcfwESiOvdcol8HY4CrgKvCfAF/J2pXmQukJKx7KbAkPC6pDnEBF4R1ZiU8BsUdV6FtXEzF947bm/fxOGBOKB8PNIg7LqJeaP8kSjzzgfuq+PXqGMqzgM1hukWYdxJR77OlRGfbsccFHE7UmWNOwuf+pLjjKrSNo6n43nF78z4OAlLDa/YqFdC714ftcc45FxuvjnPOORcbT0LOOedi40nIOedcbDwJOeeci40nIeecc7HxJORqDEl5kmaFEY9nS/pNGNoHSSmSHixh3R6Szq+6aMtG0rVhNOJnCpUfXXj0ZEnjJZ1Zjm1frAoeebyiKRrB/aS443DxSY47AOfKYaeZDQKQtA/RCMMtgP81s1Si6xeK0wM4P6xTnfwSGGlVODSRpGSLRnqoDgYBKcBbcQfi4uFnQq5GMrMNwBVEw/oo8cxB0lHhjGlWGGixOXAncEQo+3U4M/pE0ozwOCyse7SkjxLumfJMuLIeScMkfRbOwqZJaq7oni93S5qu6N4+VxYVr6T/J+nL8Lg+lI0jGnfubUm/LuuxSzpG0qsJz4+T9EqYvkTSIknTiIZ/KVhmvKRxkr4A7pLURtKrIebPJQ0My7WXNDmcbT4qaaWkdmHeBeG4Z0n6p8KgrZK2Sbo9vC6fS+pQRMzDFd2jZmZ4DQ8MoyfcCpwTtnlOCXHdImlCeM9WSjpd0b2T5kp6J4wQ4WqiirwS1x/+qMwHsK2Iss1Et3o4mnBlOfAG8KMw3YzojP/b+aG8CdAoTB8ApIbpo4EtROOb1SO6J8/hRCOLLwOGheVahO1eAfwhlDUkOhvrWSjGoUQjGzQN8cwDBod5K4B2RRxXQRyJo1hkAmcSjZjwFdA+LPss8FOi++N8TXQbjgZE9xZ6KCwzHngTSArP/0Z0BgnRsEOzwvRDwE1h+gSiEQXaEQ2M+gZQP8z7B3BRmDbgp2H6roLXo9DxtCC6/QXASOClMH0xCSNhlBDXLcCnRLenOBjYAZwY5r0CjIr78+mPPXt4dZyrjf4L3BfaWV42s9X64Q1G6wMPSRoE5BHdnqHANAvVY5JmEVXlbQHSLbrPChZGW5Z0PDAwoa2mJVFSW56wvcOBV8xse1jnZaJRuGeWchyfmNkpBU8kjQ/7NklPARdIeoJokNKLgFOAj8wsIyw/qdBxvWBmeQkxnRG294GktooGsT2caCBUzOwdSd+E5Y8lSqbTw2vZmOi+UwC7iBIcQBrRkEaFtQQmSDqAKGkVd+ZSXFwAb5tZrqS5REMUvRPK5xK9R64G8iTkaixJvYgSyAaiX+oAmNmdkv5NNF7ZfyX9pIjVf010w7eDic54shPm5SRM51Hy/4mAa8ysKgeiBXiC6Mwkmyi57C4i0Ra2fS/2J2CCmd1UxLxcMysY/6u41+tPwIdmdpqie/d8tAcx5ACYWb6kxH3mF7NPVwN4m5CrkRSNYD2OqCrHCs3bz8zmmtlfiEZw7gNsJbqFc4GWRGc2+cCFRL+sS7IQ6CRpWNhHc0nJRKOg/6KgTUJSb/3wRl+fAKMkNQnzTgtle8yiO+CuBf5AlJAguiHbUeHsoT5wVgmb+AT4eYj5aGBjOLv7L3B2KD+e6Db0AO8DZyrqEEJou9m3HCG35LvbN1ycUF74fSkuLldL+a8HV5M0DtVj9YHdRDfgK2oI/usl/ZjoF/I8ovvq5AN5kmYTtY/8A3hJ0kVE1TolniWY2S5J5wB/k9QY2EnUtvEoUVXQjNCBIQMYVWjdGaEqbVooetTMSquKK4tniNqFFoT9pEu6hagdazNRO1JxbgEelzSHqH1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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.plot(distances, energies)\n", - "pylab.xlabel('Distance of Hydrogen atom')\n", - "pylab.ylabel('Energy')\n", - "pylab.title('H2O molecule, one H atom distance varied');" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/chemistry/input_files/gaussian_h2_0.735_sto-3g.txt b/community/chemistry/input_files/gaussian_h2_0.735_sto-3g.txt deleted file mode 100644 index 81d5e84d2..000000000 --- a/community/chemistry/input_files/gaussian_h2_0.735_sto-3g.txt +++ /dev/null @@ -1,43 +0,0 @@ -&name -Gaussian H2 experiment -&end - -&driver - name=GAUSSIAN -&end - -&gaussian -# rhf/sto-3g scf(conventional) - -h2 molecule - -0 1 -H 0.0 0.0 -0.3675 -H 0.0 0.0 0.3675 - - -&end - -&operator - name=hamiltonian - qubit_mapping=parity -&end - -&algorithm - name=VQE - operator_mode=matrix -&end - -&optimizer - name=L_BFGS_B - factr=10 -&end - -&variational_form - name=RYRZ -&end - -&backend - provider=qiskit.BasicAer - name=statevector_simulator -&end diff --git a/community/chemistry/input_files/gaussian_lih_1.6_sto-3g.txt b/community/chemistry/input_files/gaussian_lih_1.6_sto-3g.txt deleted file mode 100644 index cb2eb7211..000000000 --- a/community/chemistry/input_files/gaussian_lih_1.6_sto-3g.txt +++ /dev/null @@ -1,49 +0,0 @@ -&name -Gaussian LiH experiment -&end - -&driver - name=GAUSSIAN -&end - -&gaussian -# rhf/sto-3g scf(conventional) - -lih molecule - -0 1 -Li 0.0 0.0 -0.8 -H 0.0 0.0 0.8 - - -&end - -&operator - name=hamiltonian - qubit_mapping=parity - freeze_core=True - orbital_reduction=[-3, -2] -&end - -&algorithm - name=VQE - operator_mode=matrix -&end - -&optimizer - name=L_BFGS_B - factr=10 -&end - -&variational_form - name=UCCSD -&end - -&initial_state - name=HartreeFock -&end - -&backend - provider=qiskit.BasicAer - name=statevector_simulator -&end diff --git a/community/chemistry/input_files/h2_on_device.txt b/community/chemistry/input_files/h2_on_device.txt deleted file mode 100644 index 512898bd9..000000000 --- a/community/chemistry/input_files/h2_on_device.txt +++ /dev/null @@ -1,47 +0,0 @@ -&name -H2 molecule experiment. This configuration shows what might be used on a near-term real device. -The device (backend) has been set to qasm_simulator so it can be run. On a real device -the Qconfig.py would need to be set with token etc. This experiment will make many evaluations -on the device during its variational approach to finding the minimum eigenvalue of the -Hamiltonian, i.e. the ground state energy. -&end - -&driver - name=HDF5 -&end - -&hdf5 - hdf5_input=../h2_0.735_sto-3g.hdf5 -&end - -&operator - name=hamiltonian - qubit_mapping=parity - two_qubit_reduction=True -&end - -&algorithm - name=VQE - operator_mode=paulis -&end - -&initial_state - name=ZERO -&end - -&optimizer - name=SPSA - max_trials=200 -&end - -&variational_form - name=RYRZ - depth=3 - entanglement=full -&end - -&backend - provider=qiskit.BasicAer - name=qasm_simulator - shots=1024 -&end diff --git a/community/chemistry/input_files/hdf5_h2_0.735_sto-3g.txt b/community/chemistry/input_files/hdf5_h2_0.735_sto-3g.txt deleted file mode 100644 index c2b6a594d..000000000 --- a/community/chemistry/input_files/hdf5_h2_0.735_sto-3g.txt +++ /dev/null @@ -1,35 +0,0 @@ -&name -HDF5 H2 experiment -&end - -&driver - name=HDF5 -&end - -&hdf5 - hdf5_input=../h2_0.735_sto-3g.hdf5 -&end - -&operator - name=hamiltonian - qubit_mapping=parity -&end - -&algorithm - name=VQE - operator_mode=matrix -&end - -&optimizer - name=L_BFGS_B - factr=10 -&end - -&variational_form - name=RYRZ -&end - -&backend - provider=qiskit.BasicAer - name=statevector_simulator -&end diff --git a/community/chemistry/input_files/hdf5_lih_1.6_sto-3g.txt b/community/chemistry/input_files/hdf5_lih_1.6_sto-3g.txt deleted file mode 100644 index 99882238e..000000000 --- a/community/chemistry/input_files/hdf5_lih_1.6_sto-3g.txt +++ /dev/null @@ -1,41 +0,0 @@ -&name -HDF5 LiH experiment -&end - -&driver - name=HDF5 -&end - -&hdf5 - hdf5_input=../lih_1.6_sto-3g.hdf5 -&end - -&operator - name=hamiltonian - qubit_mapping=parity - freeze_core=True - orbital_reduction=[-3, -2] -&end - -&algorithm - name=VQE - operator_mode=matrix -&end - -&initial_state - name=HartreeFock -&end - -&optimizer - name=L_BFGS_B - factr=10 -&end - -&variational_form - name=UCCSD -&end - -&backend - provider=qiskit.BasicAer - name=statevector_simulator -&end diff --git a/community/chemistry/input_files/input_file_sample.txt b/community/chemistry/input_files/input_file_sample.txt deleted file mode 100644 index 7f248282f..000000000 --- a/community/chemistry/input_files/input_file_sample.txt +++ /dev/null @@ -1,100 +0,0 @@ -# Sample input file for Qiskit Chemistry stack. -# -# This is a simple sample to show representative sections but not -# all fields are shown. Consult the documentation for further -# information and complete list of sections and field names. -# Many sections and fields default to suitable values in order to -# simplify editing this input file. However using the GUI to edit -# an input file is recommended as it simplifies the editing task -# by presenting only appropriate sections according to problem type -# and algorithm selected. The input file is also validated against -# the combined schema of all the constituent sections - -# NAME is an optional section for the user to describe this file's purpose -# -&name -H2 molecule experiment. In order to be to run this, with no further -driver installation requirements this will use the HDF5 file driver. -&end - -# Problem to be solved. Defaults to energy -# -&problem - name=energy -&end - -# External library DRIVER used for electronic structure computation. -# The DRIVER is named here and matching section should contain the -# molecular configuration for the driver. This molecular configuration -# is driver dependent so please consult the driver documentation -# for more information. The configuration will include the molecule and -# and basis set plus any additional configuration needed. From the -# driver computation one and two electron integrals are extracted from -# the result. -# -&driver - name=HDF5 -&end - -# -- Molecule and config in driver specific format -# Drivers need an external chemistry program or library to be installed. -# Qiskit Chemistry provides the interfacing logic but the actual -# program or library it interfaces with needs to be separately installed. -# The configuration needed in this section depends on the specific driver. -# Please see the particular driver documentation for more information. -# This sample, as it uses the HDF5 driver, just needs to refer to an -# hdf5 file that was written from a prior chemistry driver usage. See the -# HDF5 driver documentation for more detail on this. -&hdf5 - hdf5_input=../h2_0.735_sto-3g.hdf5 -&end - -# Absolute bare minimum input file is just the driver info. With just -# this a default OPERATOR and ALGORITHM will be used for the computation -# OPERATOR and ALGORITHM may be given here to select a specific chosen -# configuration other than the default. -# -# At this point we have integral matrices which we are passed on down the -# chemistry stack to create the fermionic and qubit hamiltonians and run the -# energy computation using the algorithm which defaults to VQE. -# -&operator - name=hamiltonian - qubit_mapping=parity -&end - -# Algorithm is named here. Default is VQE. -# -# VQE has some parameters and an Optimizer and Variational form can be specifically -# defined in this input file to replace the default ones that would otherwise be used -# -&algorithm - name=VQE - operator_mode=matrix -&end - -# Below are specific configuration sections that depend on choice of ALGORITHM -# For VQE this is OPTIMIZER, VARIATIONAL_FORM and INITIAL_STATE -# Each specific entity to be used is named here -# - -&initial_state - name=ZERO -&end - -&optimizer - name=L_BFGS_B -&end - -&variational_form - name=RYRZ -&end - -# BACKEND specifies the particular quantum computing backend, whether real -# device or simulator that wll be used. The BACKEND will default to a QISkit -# local simulator without this section. -# -&backend - provider=qiskit.BasicAer - name=statevector_simulator -&end diff --git a/community/chemistry/input_files/iqpe_h2.txt b/community/chemistry/input_files/iqpe_h2.txt deleted file mode 100644 index 3043ead2a..000000000 --- a/community/chemistry/input_files/iqpe_h2.txt +++ /dev/null @@ -1,56 +0,0 @@ -&name - H2 molecule experiment -&end - -&problem - name=energy - auto_substitutions=True - random_seed=None -&end - -&driver - name=PYQUANTE - hdf5_output=None -&end - -&pyquante - atoms=H .0 .0 .0; H .0 .0 0.735 - units=Angstrom - charge=0 - multiplicity=1 - basis=sto3g -&end - -&operator - name=hamiltonian - transformation=full - qubit_mapping=parity - two_qubit_reduction=True - freeze_core=False - orbital_reduction=[] - max_workers=4 -&end - -&algorithm - name=IQPE - num_time_slices=200 - expansion_mode=suzuki - expansion_order=2 - num_iterations=9 -&end - -&initial_state - name=HartreeFock - qubit_mapping=jordan_wigner - two_qubit_reduction=True - num_particles=2 - num_orbitals=4 -&end - -&backend - provider=qiskit.BasicAer - name=qasm_simulator - shots=100 - skip_transpiler=False - noise_params=None -&end diff --git a/community/chemistry/input_files/psi4_h2_0.735_sto-3g.txt b/community/chemistry/input_files/psi4_h2_0.735_sto-3g.txt deleted file mode 100644 index 6869a2c36..000000000 --- a/community/chemistry/input_files/psi4_h2_0.735_sto-3g.txt +++ /dev/null @@ -1,44 +0,0 @@ -&name -PSI4 H2 experiment -&end - -&driver - name=PSI4 -&end - -&psi4 -molecule h2 { - 0 1 - H 0.0 0.0 -0.3675 - H 0.0 0.0 0.3675 -} - -set { - basis sto-3g - scf_type pk -} -&end - -&operator - name=hamiltonian - qubit_mapping=parity -&end - -&algorithm - name=VQE - operator_mode=matrix -&end - -&optimizer - name=L_BFGS_B - factr=10 -&end - -&variational_form - name=RYRZ -&end - -&backend - provider=qiskit.BasicAer - name=statevector_simulator -&end diff --git a/community/chemistry/input_files/psi4_lih_1.6_sto-3g.txt b/community/chemistry/input_files/psi4_lih_1.6_sto-3g.txt deleted file mode 100644 index 6253a52d5..000000000 --- a/community/chemistry/input_files/psi4_lih_1.6_sto-3g.txt +++ /dev/null @@ -1,50 +0,0 @@ -&name -PSI4 LiH experiment -&end - -&driver - name=PSI4 -&end - -&psi4 -molecule lih { - 0 1 - Li 0.0 0.0 -0.8 - H 0.0 0.0 0.8 -} - -set { - basis sto-3g - scf_type pk -} -&end - -&operator - name=hamiltonian - qubit_mapping=parity - freeze_core=True - orbital_reduction=[-3, -2] -&end - -&algorithm - name=VQE - operator_mode=matrix -&end - -&optimizer - name=L_BFGS_B - factr=10 -&end - -&variational_form - name=UCCSD -&end - -&initial_state - name=HartreeFock -&end - -&backend - provider=qiskit.BasicAer - name=statevector_simulator -&end diff --git a/community/chemistry/input_files/psi4_save_hdf5.txt b/community/chemistry/input_files/psi4_save_hdf5.txt deleted file mode 100644 index 925a1f9a3..000000000 --- a/community/chemistry/input_files/psi4_save_hdf5.txt +++ /dev/null @@ -1,30 +0,0 @@ -# Sample input file for Qiskit Chemistry stack -# To show how to save an hdf5 file -# -&name -H2 molecule experiment -&end - -# To the external library DRIVER used for electronic structure computation -# we add an hdf5_output=*filename* This will run the stack and after -# the molecular information is extracted from the driver it will be -# written to the hdf5 file. At this point the stack ends and no further -# processing is done. -# -&driver - name=PSI4 - hdf5_output=molecule.hdf5 -&end - -&PSI4 -molecule h2 { - 0 1 - H 0.0 0.0 0.0 - H 0.0 0.0 0.735 -} - -set { - basis sto-3g - scf_type pk -} -&END diff --git a/community/chemistry/input_files/pyquante_h2_0.735_sto-3g.txt b/community/chemistry/input_files/pyquante_h2_0.735_sto-3g.txt deleted file mode 100644 index f3434bef4..000000000 --- a/community/chemistry/input_files/pyquante_h2_0.735_sto-3g.txt +++ /dev/null @@ -1,39 +0,0 @@ -&name -PyQuante H2 experiment -&end - -&driver - name=PYQUANTE -&end - -&pyquante - atoms=H 0.0 0.0 -0.3675; H 0.0 0.0 0.3675 - units=Angstrom - charge=0 - multiplicity=1 - basis=sto3g -&end - -&operator - name=hamiltonian - qubit_mapping=parity -&end - -&algorithm - name=VQE - operator_mode=matrix -&end - -&optimizer - name=L_BFGS_B - factr=10 -&end - -&variational_form - name=RYRZ -&end - -&backend - provider=qiskit.BasicAer - name=statevector_simulator -&end diff --git a/community/chemistry/input_files/pyquante_lih_1.6_sto-3g.txt b/community/chemistry/input_files/pyquante_lih_1.6_sto-3g.txt deleted file mode 100644 index 0dba669cf..000000000 --- a/community/chemistry/input_files/pyquante_lih_1.6_sto-3g.txt +++ /dev/null @@ -1,45 +0,0 @@ -&name -PyQuante LiH experiment -&end - -&driver - name=PYQUANTE -&end - -&pyquante - atoms=Li 0.0 0.0 -0.8; H 0.0 0.0 0.8 - units=Angstrom - charge=0 - multiplicity=1 - basis=sto3g -&end - -&operator - name=hamiltonian - qubit_mapping=parity - freeze_core=True - orbital_reduction=[-3, -2] -&end - -&algorithm - name=VQE - operator_mode=matrix -&end - -&optimizer - name=L_BFGS_B - factr=10 -&end - -&variational_form - name=UCCSD -&end - -&initial_state - name=HartreeFock -&end - -&backend - provider=qiskit.BasicAer - name=statevector_simulator -&end diff --git a/community/chemistry/input_files/pyscf_h2_0.735_sto-3g.txt b/community/chemistry/input_files/pyscf_h2_0.735_sto-3g.txt deleted file mode 100644 index d7ea2b2c2..000000000 --- a/community/chemistry/input_files/pyscf_h2_0.735_sto-3g.txt +++ /dev/null @@ -1,39 +0,0 @@ -&name -PySCF H2 experiment -&end - -&driver - name=PYSCF -&end - -&pyscf - atom=H 0.0 0.0 -0.3675; H 0.0 0.0 0.3675 - unit=Angstrom - charge=0 - spin=0 - basis=sto3g -&end - -&operator - name=hamiltonian - qubit_mapping=parity -&end - -&algorithm - name=VQE - operator_mode=matrix -&end - -&optimizer - name=L_BFGS_B - factr=10 -&end - -&variational_form - name=RYRZ -&end - -&backend - provider=qiskit.BasicAer - name=statevector_simulator -&end diff --git a/community/chemistry/input_files/pyscf_lih_1.6_sto-3g.txt b/community/chemistry/input_files/pyscf_lih_1.6_sto-3g.txt deleted file mode 100644 index dca5b057b..000000000 --- a/community/chemistry/input_files/pyscf_lih_1.6_sto-3g.txt +++ /dev/null @@ -1,45 +0,0 @@ -&name -PySCF LiH experiment -&end - -&driver - name=PYSCF -&end - -&pyscf - atom=Li 0.0 0.0 -0.8; H 0.0 0.0 0.8 - unit=Angstrom - charge=0 - spin=0 - basis=sto3g -&end - -&operator - name=hamiltonian - qubit_mapping=parity - freeze_core=True - orbital_reduction=[-3, -2] -&end - -&algorithm - name=VQE - operator_mode=matrix -&end - -&optimizer - name=L_BFGS_B - factr=10 -&end - -&variational_form - name=UCCSD -&end - -&initial_state - name=HartreeFock -&end - -&backend - provider=qiskit.BasicAer - name=statevector_simulator -&end diff --git a/community/chemistry/input_files/pyscf_minimal.txt b/community/chemistry/input_files/pyscf_minimal.txt deleted file mode 100644 index 9b9cdffdc..000000000 --- a/community/chemistry/input_files/pyscf_minimal.txt +++ /dev/null @@ -1,18 +0,0 @@ -# Sample input file for Qiskit Chemistry stack -# This demonstrates the bare minimum configuration. This is to specify a driver -# along with the required driver specific configuration -# All other sections are optional and being omitted fallback to their default -# values, such as VQE for the algorithm with itself having a default optimizer -# and a default variational form. - -# PySCF driver. -# -&DRIVER - name=PYSCF -&END - -# Molecule atoms and basis set are required -&PYSCF - atom=H .0 .0 .0; H .0 .0 0.735 - basis=sto3g -&END diff --git a/community/chemistry/input_files/qpe_h2.txt b/community/chemistry/input_files/qpe_h2.txt deleted file mode 100644 index b72c0b228..000000000 --- a/community/chemistry/input_files/qpe_h2.txt +++ /dev/null @@ -1,60 +0,0 @@ -&name - H2 molecule experiment with QPE -&end - -&problem - name=energy - auto_substitutions=True - random_seed=None -&end - -&driver - name=PYQUANTE - hdf5_output=None -&end - -&pyquante - atoms=H .0 .0 .0; H .0 .0 0.735 - units=Angstrom - charge=0 - multiplicity=1 - basis=sto3g -&end - -&operator - name=hamiltonian - 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.plot(distances, dipoles)\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Moment debye')\n", - "pylab.title('LiH Dipole Moment');" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/chemistry/lih_uccsd.ipynb b/community/chemistry/lih_uccsd.ipynb deleted file mode 100644 index c5b8cbd1b..000000000 --- a/community/chemistry/lih_uccsd.ipynb +++ /dev/null @@ -1,234 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## _*LiH dissociation curve using VQE with UCCSD variational form*_\n", - "\n", - "This notebook demonstrates using Qiskit Chemistry to plot graphs of the ground state energy of the Lithium Hydride (LiH) molecule over a range of inter-atomic distances using VQE and UCCSD. It is compared to the same energies as computed by the ExactEigensolver\n", - "\n", - "This notebook populates a dictionary, that is a progammatic representation of an input file, in order to drive the Qiskit Chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here where we alter the molecule supplied to the driver in each loop.\n", - "\n", - "This notebook has been written to use the PYSCF chemistry driver." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Processing step 22 --- complete\n", - "Distances: [0.6 0.7 0.8 0.9 1. 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9\n", - " 2. 2.25 2.5 2.75 3. 3.25 3.5 3.75 4. ]\n", - "Energies: [[-7.3133458 -7.50092206 -7.63097823 -7.7208124 -7.78224239 -7.82359927\n", - " -7.85069837 -7.86756328 -7.87700148 -7.8810157 -7.88107203 -7.87826815\n", - " -7.87344011 -7.86723367 -7.86015319 -7.84104235 -7.82307636 -7.80861236\n", - " -7.79836328 -7.79175303 -7.78771683 -7.7853196 -7.78391829]\n", - " [-7.31334583 -7.50092209 -7.63097825 -7.72081241 -7.7822424 -7.82359928\n", - " -7.85069838 -7.86756329 -7.87700149 -7.88101572 -7.88107204 -7.87826817\n", - " -7.87344029 -7.86723396 -7.86015321 -7.84104271 -7.82307664 -7.8086124\n", - " -7.79836343 -7.79175325 -7.78771697 -7.78531972 -7.78391847]]\n", - "Hartree-Fock energies: [-7.29954105 -7.48594487 -7.61577016 -7.70575334 -7.76736214 -7.80874318\n", - " -7.83561583 -7.85195386 -7.86053866 -7.86335762 -7.86186477 -7.85714496\n", - " -7.8500187 -7.84111204 -7.83090558 -7.80193896 -7.77087367 -7.74000074\n", - " -7.7108299 -7.68437642 -7.6612016 -7.64145387 -7.62497563]\n", - "VQE num evaluations: [71. 62. 71. 71. 71. 71. 71. 71. 71. 71. 71. 62. 60. 60. 61. 60. 70. 71.\n", - " 70. 80. 90. 90. 90.]\n" - ] - } - ], - "source": [ - "import numpy as np\n", - "import pylab\n", - "import copy\n", - "from qiskit.chemistry import QiskitChemistry\n", - "\n", - "# Input dictionary to configure Qiskit Chemistry for the chemistry problem.\n", - "qiskit_chemistry_dict = {\n", - " 'driver': {'name': 'PYSCF'},\n", - " 'PYSCF': {'atom': '', 'basis': 'sto3g'},\n", - " 'operator': {'name': 'hamiltonian', 'qubit_mapping': 'parity',\n", - " 'two_qubit_reduction': True, 'freeze_core': True, 'orbital_reduction': [-3, -2]},\n", - " 'algorithm': {'name': ''},\n", - " 'optimizer': {'name': 'SLSQP', 'maxiter': 1000},\n", - " 'variational_form': {'name': 'UCCSD'},\n", - " 'initial_state': {'name': 'HartreeFock'}\n", - "}\n", - "molecule = 'H .0 .0 -{0}; Li .0 .0 {0}'\n", - "algorithms = ['VQE', 'ExactEigensolver']\n", - "\n", - "pts = [x * 0.1 for x in range(6, 20)]\n", - "pts += [x * 0.25 for x in range(8, 16)]\n", - "pts += [4.0]\n", - "energies = np.empty([len(algorithms), len(pts)])\n", - "hf_energies = np.empty(len(pts))\n", - "distances = np.empty(len(pts))\n", - "dipoles = np.empty([len(algorithms), len(pts)])\n", - "eval_counts = np.empty(len(pts))\n", - "\n", - "print('Processing step __', end='')\n", - "for i, d in enumerate(pts):\n", - " print('\\b\\b{:2d}'.format(i), end='', flush=True)\n", - " qiskit_chemistry_dict['PYSCF']['atom'] = molecule.format(d/2) \n", - " for j in range(len(algorithms)):\n", - " dict = copy.deepcopy(qiskit_chemistry_dict)\n", - " dict['algorithm']['name'] = algorithms[j] \n", - " if algorithms[j] == 'ExactEigensolver':\n", - " del dict['optimizer']\n", - " del dict['variational_form']\n", - " del dict['initial_state']\n", - " solver = QiskitChemistry()\n", - " result = solver.run(dict)\n", - " energies[j][i] = result['energy']\n", - " hf_energies[i] = result['hf_energy']\n", - " dipoles[j][i] = result['total_dipole_moment'] / 0.393430307\n", - " if algorithms[j] == 'VQE':\n", - " eval_counts[i] = result['algorithm_retvals']['eval_count']\n", - " distances[i] = d\n", - "print(' --- complete')\n", - "\n", - "print('Distances: ', distances)\n", - "print('Energies:', energies)\n", - "print('Hartree-Fock energies:', hf_energies)\n", - "print('VQE num evaluations:', eval_counts)" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.plot(distances, hf_energies, label='Hartree-Fock')\n", - "for j in range(len(algorithms)):\n", - " pylab.plot(distances, energies[j], label=algorithms[j])\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Energy')\n", - "pylab.title('LiH Ground State Energy')\n", - "pylab.legend(loc='upper right');" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.plot(distances, np.subtract(hf_energies, energies[1]), label='Hartree-Fock')\n", - "pylab.plot(distances, np.subtract(energies[0], energies[1]), label='VQE')\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Energy')\n", - "pylab.title('Energy difference from ExactEigensolver')\n", - "pylab.legend(loc='upper left');" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "for j in reversed(range(len(algorithms))):\n", - " pylab.plot(distances, dipoles[j], label=algorithms[j])\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Moment in debye')\n", - "pylab.title('LiH Dipole Moment')\n", - "pylab.legend(loc='upper right');" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.plot(distances, eval_counts, '-o', color=[0.8500, 0.3250, 0.0980], label='VQE')\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Evaluations')\n", - "pylab.title('VQE number of evaluations')\n", - "pylab.legend(loc='upper left');" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/chemistry/nah_1.9_sto-3g.hdf5 b/community/chemistry/nah_1.9_sto-3g.hdf5 deleted 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.plot(distances, np.subtract(hf_energies, energies[1]), label='Hartree-Fock')\n", - "pylab.plot(distances, np.subtract(energies[0], energies[1]), label='VQE')\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Energy')\n", - "pylab.title('Energy difference from ExactEigensolver')\n", - "pylab.legend(loc='upper left');" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "for j in reversed(range(len(algorithms))):\n", - " pylab.plot(distances, dipoles[j], label=algorithms[j])\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Moment in debye')\n", - "pylab.title('NaH Dipole Moment')\n", - "pylab.legend(loc='upper right');" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.plot(distances, eval_counts, '-o', color=[0.8500, 0.3250, 0.0980], label='VQE')\n", - "pylab.xlabel('Interatomic distance')\n", - "pylab.ylabel('Evaluations')\n", - "pylab.title('VQE number of evaluations')\n", - "pylab.legend(loc='upper left');" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/finance/README.md b/community/finance/README.md deleted file mode 100644 index 6bb2400b6..000000000 --- a/community/finance/README.md +++ /dev/null @@ -1,19 +0,0 @@ -# Qiskit Aqua Finance Tutorials, Samples and Input Files - -Qiskit Finance is a set of tools, algorithms and software for use with quantum computers to -carry out research and investigate how to take advantage of quantum computing power to solve problems -in the financial domain. - -Qiskit Finance translates finance-specific problems into inputs -for a quantum algorithm residing in Qiskit Aqua, which in turn uses [Qiskit](https://www.qiskit.org/) for the relevant -quantum computation. - -This folder contains some Jupyter Notebook examples. There are Python code files too. - -For more detail see the main [index](../aqua/index.ipynb#optimization) - -## Input files - -The folder [input_files](input_files) contains example JSON input files that can be loaded -and run by the Qiskit Aqua [GUI](https://github.com/Qiskit/aqua/README.md#gui) or by the Qiskit Aqua -[command line](https://github.com/Qiskit/aqua/README.md#command-line) tool. diff --git a/community/finance/input_files/portfolio.json b/community/finance/input_files/portfolio.json deleted file mode 100644 index 9b7e20629..000000000 --- a/community/finance/input_files/portfolio.json +++ /dev/null @@ -1,129 +0,0 @@ -{ - "problem": { - "name": "ising", - "random_seed": 50 - }, - "algorithm": { - "name": "VQE", - "operator_mode": "matrix" - }, - "optimizer": { - "name": "COBYLA", - "maxiter": 25000 - }, - "variational_form": { - "name": "RYRZ", - "depth": 3, - "entanglement": "full" - }, - "backend": { - "provider": "qiskit.BasicAer", - "name": "statevector_simulator" - }, - "input": { - "aux_ops": [], - "name": "EnergyInput", - "qubit_op": { - "paulis": [ - { - "coeff": { - "imag": 0.0, - "real": -0.24403472627604428 - }, - "label": "IIIZ" - }, - { - "coeff": { - "imag": 0.0, - "real": 0.3881691708820725 - }, - "label": "IIZI" - }, - { - "coeff": { - "imag": 0.0, - "real": 1.9473142336529263 - }, - "label": "IIZZ" - }, - { - "coeff": { - "imag": 0.0, - "real": -0.2667811512679368 - }, - "label": "IZII" - }, - { - "coeff": { - "imag": 0.0, - "real": 2.3988667437794624 - }, - "label": "IZIZ" - }, - { - "coeff": { - "imag": 0.0, - "real": 1.8728983411674296 - }, - "label": "IZZI" - }, - { - "coeff": { - "imag": 0.0, - "real": -4.440892098500626e-16 - }, - "label": "IZZZ" - }, - { - "coeff": { - "imag": 0.0, - "real": 0.3158601888295829 - }, - "label": "ZIII" - }, - { - "coeff": { - "imag": 0.0, - "real": 1.8821687969396752 - }, - "label": "ZIIZ" - }, - { - "coeff": { - "imag": 0.0, - "real": 2.0525084750150535 - }, - "label": "ZIZI" - }, - { - "coeff": { - "imag": 0.0, - "real": -5.551115123125783e-17 - }, - "label": "ZIZZ" - }, - { - "coeff": { - "imag": 0.0, - "real": 1.73738172527763 - }, - "label": "ZZII" - }, - { - "coeff": { - "imag": 0.0, - "real": 1.1102230246251565e-16 - }, - "label": "ZZIZ" - }, - { - "coeff": { - "imag": 0.0, - "real": 5.551115123125783e-17 - }, - "label": "ZZZZ" - } - ] - } - } -} \ No newline at end of file diff --git a/community/finance/simulation/iron_condor.ipynb b/community/finance/simulation/iron_condor.ipynb deleted file mode 100644 index 96d23bc5f..000000000 --- a/community/finance/simulation/iron_condor.ipynb +++ /dev/null @@ -1,401 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# _*Pricing Iron Condor Option*_ \n", - "\n", - "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", - "\n", - "***\n", - "### Contributors\n", - "Stefan Woerner[1], Daniel Egger[1]\n", - "### Affliation\n", - "- [1]IBMQ" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Introduction\n", - "
\n", - "Suppose a iron condor option with strike prices $K_1 < K_2 < K_3 < K_4$ and an underlying asset whose spot price at maturity $S_T$ follows a given random distribution.\n", - "The corresponding payoff function is defined as:\n", - "
\n", - "
\n", - "$$ F(S_T) = \n", - "\\begin{cases}\n", - "0 ,& S_T < K_1 \\\\\n", - "S_T - K_1 ,& K_1 \\leq S_T < K_2 \\\\\n", - "K_2 - K_1 ,& K_2 \\leq S_T < K_3 \\\\\n", - "K_3 - S_T ,& K_3 \\leq S_T < K_4 \\\\\n", - "0 ,& S_T \\geq K_4. \n", - "\\end{cases}$$\n", - "
\n", - "In the following, a quantum algorithm based on amplitude estimation is used to estimate the expected payoff, i.e., the fair price before discounting, for the option:\n", - "
\n", - "
\n", - "$$\\mathbb{E}\\left[ F(S_T) \\right].$$\n", - "
\n", - "The approximation of the objective function is explained in detail in the following paper:
\n", - "Quantum Risk Analysis. Woerner, Egger. 2018." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import matplotlib.pyplot as plt\n", - "%matplotlib inline\n", - "import numpy as np\n", - "\n", - "from qiskit import BasicAer\n", - "from qiskit.aqua.algorithms import AmplitudeEstimation\n", - "from qiskit.aqua.components.uncertainty_models import LogNormalDistribution\n", - "from qiskit.aqua.components.uncertainty_problems import UnivariateProblem\n", - "from qiskit.aqua.components.uncertainty_problems import UnivariatePiecewiseLinearObjective as PwlObjective" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Uncertainty Model\n", - "\n", - "We construct a circuit factory to load a log-normal random distribution into a quantum state.\n", - "The distribution is truncated to a given interval $[low, high]$ and discretized using $2^n$ grid points, where $n$ denotes the number of qubits used.\n", - "The unitary operator corresponding to the circuit factory implements the following: \n", - "$$\\big|0\\rangle_{n} \\mapsto \\big|\\psi\\rangle_{n} = \\sum_{i=0}^{2^n-1} \\sqrt{p_i}\\big|i\\rangle_{n},$$\n", - "where $p_i$ denote the probabilities corresponding to the truncated and discretized distribution and where $i$ is mapped to the right interval using the affine map:\n", - "$$ \\{0, \\ldots, 2^n-1\\} \\ni i \\mapsto \\frac{high - low}{2^n - 1} * i + low \\in [low, high].$$" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "# number of qubits to represent the uncertainty\n", - "num_uncertainty_qubits = 3\n", - "\n", - "# parameters for considered random distribution\n", - "S = 2.0 # initial spot price\n", - "vol = 0.4 # volatility of 40%\n", - "r = 0.05 # annual interest rate of 4%\n", - "T = 40 / 365 # 40 days to maturity\n", - "\n", - "# resulting parameters for log-normal distribution\n", - "mu = ((r - 0.5 * vol**2) * T + np.log(S))\n", - "sigma = vol * np.sqrt(T)\n", - "mean = np.exp(mu + sigma**2/2)\n", - "variance = (np.exp(sigma**2) - 1) * np.exp(2*mu + sigma**2)\n", - "stddev = np.sqrt(variance)\n", - "\n", - "# lowest and highest value considered for the spot price; in between, an equidistant discretization is considered.\n", - "low = np.maximum(0, mean - 3*stddev)\n", - "high = mean + 3*stddev\n", - "\n", - "# construct circuit factory for uncertainty model\n", - "uncertainty_model = LogNormalDistribution(num_uncertainty_qubits, mu=mu, sigma=sigma, low=low, high=high)" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "

" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# plot probability distribution\n", - "x = uncertainty_model.values\n", - "y = uncertainty_model.probabilities\n", - "plt.bar(x, y, width=0.2)\n", - "plt.xticks(x, size=15, rotation=90)\n", - "plt.yticks(size=15)\n", - "plt.grid()\n", - "plt.xlabel('Spot Price at Maturity $S_T$ (\\$)', size=15)\n", - "plt.ylabel('Probability ($\\%$)', size=15)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Payoff Function\n", - "\n", - "The payoff function equals zero as long as the spot price at maturity $S_T$ is less than the strike price $K_1$, then increases linearly, and is bounded by $K_2$.\n", - "The implementation uses two comparators, that flip an ancilla qubit each from $\\big|0\\rangle$ to $\\big|1\\rangle$ if $S_T \\geq K_1$ and $S_T \\leq K_2, and these ancillas are used to control the linear part of the payoff function.\n", - "\n", - "The linear part itself is then approximated as follows.\n", - "We exploit the fact that $\\sin^2(y + \\pi/4) \\approx y + 1/2$ for small $|y|$.\n", - "Thus, for a given approximation scaling factor $c_{approx} \\in [0, 1]$ and $x \\in [0, 1]$ we consider\n", - "$$ \\sin^2( \\pi/2 * c_{approx} * ( x - 1/2 ) + \\pi/4) \\approx \\pi/2 * c_{approx} * ( x - 1/2 ) + 1/2 $$ for small $c_{approx}$.\n", - "\n", - "We can easily construct an operator that acts as \n", - "$$\\big|x\\rangle \\big|0\\rangle \\mapsto \\big|x\\rangle \\left( \\cos(a*x+b) \\big|0\\rangle + \\sin(a*x+b) \\big|1\\rangle \\right),$$\n", - "using controlled Y-rotations.\n", - "\n", - "Eventually, we are interested in the probability of measuring $\\big|1\\rangle$ in the last qubit, which corresponds to\n", - "$\\sin^2(a*x+b)$.\n", - "Together with the approximation above, this allows to approximate the values of interest.\n", - "The smaller we choose $c_{approx}$, the better the approximation.\n", - "However, since we are then estimating a property scaled by $c_{approx}$, the number of evaluation qubits $m$ needs to be adjusted accordingly.\n", - "\n", - "For more details on the approximation, we refer to:\n", - "Quantum Risk Analysis. Woerner, Egger. 2018." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [], - "source": [ - "# set the strike price (should be within the low and the high value of the uncertainty)\n", - "strike_price_1 = 1.438\n", - "strike_price_2 = 1.896\n", - "strike_price_3 = 2.126\n", - "strike_price_4 = strike_price_3 + strike_price_2 - strike_price_1\n", - "\n", - "# set the approximation scaling for the payoff function\n", - "c_approx = 0.25\n", - "\n", - "# setup piecewise linear objective fcuntion\n", - "breakpoints = [uncertainty_model.low, strike_price_1, strike_price_2, strike_price_3, strike_price_4]\n", - "slopes = [0, 1, 0, -1, 0]\n", - "offsets = [0, 0, strike_price_2 - strike_price_1, strike_price_2 - strike_price_1, 0]\n", - "f_min = 0\n", - "f_max = strike_price_2 - strike_price_1\n", - "iron_condor_objective = PwlObjective(\n", - " uncertainty_model.num_target_qubits, \n", - " uncertainty_model.low, \n", - " uncertainty_model.high,\n", - " breakpoints,\n", - " slopes,\n", - " offsets,\n", - " f_min,\n", - " f_max,\n", - " c_approx\n", - ")\n", - "\n", - "# construct circuit factory for payoff function\n", - "iron_condor = UnivariateProblem(\n", - " uncertainty_model,\n", - " iron_condor_objective\n", - ")" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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pY3HWrg2dxuUoLyQu/9x9N6xZY43sruaKi20Z3vvvD53E5SgvJC6/bNxol7VOOAEOPzx0mvxwwglw2GHWFdjXKnEV8ELi8ssTT8C8eT4AsTaJ2Nndhx/CCy+ETuNykBcSl18GD4Z994UzzgidJL906wa77uoDFF2FvJC4/PHOO/DGG9bTqL6v1Fyrtt3WesA9/zx89FHoNC7HeCFx+aOkBJo3t7EPrvZddRVst52flbiteCFx+eHLL+Hhh200drNmodPkp513hksugXHjYNmy0GlcDvFC4vLD8OFQVmaXtVzdGTgQvvsORo0KncTlEC8kLv6+/dbe2M45B4qKQqfJb4ccYjMpDx8O69eHTuNyhBcSF3/jxsHKlT4AMVuKi2HRInjoodBJXI7wQuLirazMGn+POMJW9XN1r1MnOOgg62rtAxQdXkhc3D3/PHzyiX1K9jVHsqNePRgwwNYpee210GlcDvBC4uJt8GDYfXc477zQSQpLjx6www6+VokDvJC4OPvgA5g8Gfr1swFzLnsaN7ZxJU88AbNnh07jAvNC4uJryBBbtKp379BJClPfvjaDwLBhoZO4wLyQuHhautSmNe/Rw5bTddm3xx5wwQUwejSsXh06jQvIC4mLpxEjYN067/IbWnExfPONLSTmClbWC4mItBGRl0SkVEQWisgtIlLlDHsicoiIPB/tv05E5ovI3SLiy98VonXrbOnXzp2tG6oL54gjoF07GDoUNm0KncYFktVCIiItgcmAAmcBtwC/BG5OcWgLYA5wHdAJuBHoCDwrIg3qLLDLTRMmwJIlfjaSKwYOhDlz4MknQydxgWT7TbgP0AjooqqrgRdFpDlwk4jcFm3biqq+AbyRsGmqiHwJvAD8CPh3Hed2uULVupyWT9Xhwjv7bJuapqQEunQJncYFkO1LW52BSUkFYwJWXE7M8Gctj756v89CMm0avP++fQr2AYi5oX59myzz1VdhxozQaVwA2S4kBwGzEjeo6nygNHqsSiJST0S2FZEDgb8A7wLv1EVQl6MGD4addoLu3UMncYl69oSmTX2AYoESzeJcOSKyAfiVqpYkbf8SGKeq16c4/nmsjQRgBvBzVV1ayb69gd4ArVq1ajthwoRqZV6zZg1Nmzat1rEhxClvplkbLVjAUZdcwryLL2ZugMWr8vm5rQ37Dx/O7k88wVsPPsj6nXfO6Fh/butOTfK2b99+hqoekXJHVc3aDdgADKhg+wJgUBrH/wA4GrgYO7OZATRMdVzbtm21uqZMmVLtY0OIU96Ms/bvr7rNNqoLF9ZJnlTy+rmtDZ9/riqiev31GR/qz23dqUleYLqm8d6e7UtbK4HtK9jeAliV6mBV/VRV31bV+7Ezk8OAi2o3ostJq1bZWIVu3WA37/Wdk/bdF846y8b4lJaGTuOyKNuFZBZJbSEishfQhKS2k1RUdR6wAti31tK53HX33baAVXFx6CSuKsXFsGIF3Hdf6CQui7JdSJ4DOolI4qLaXYG1wLRMflDU4L4jNr7E5bONG20+pxNPhMMOC53GVeX44+Hww60rcFlZ6DQuS7JdSEYA64DHRKRj1CB+E/BPTegSLCKficjohPt/F5G/iMg5ItJeRK4BJgGfY92HXT57/HGYP98HIMaBiP07zZoFL7wQOo3LkqwWElVdCZwE1Aeexka0D8ZGqidqEO1TbjpwPDAa+BdwLfAo8FNV/baOY7vQBg+26+9nnBE6iUtH167WjuVdgQtG1qcXUdUPgQ4p9ilKuj8BP/MoTG+/DW++aVPG169ySjaXK7bd1qaY//3vYeZMm4XA5TWf/dfltpISaN4cLr88dBKXiauugoYN7QOAy3teSFzu+uILePhhuOIKaNYs9f4ud+y0E1xyifXeWrYsdBpXx1IWEhHpISK+cpDLvttvt0ka+/cPncRVx8CB8N13MHJk6CSujqVzRjIG2A9ARDaJyFF1G8k5bMzIqFFwzjk2s6yLnzZt4JRT7APB+vWh07g6lE4hWQnsHn0v2FoiztWte++FlSt9AGLcFRfDokUwcWLoJK4OpdNrazJwn4h8jBWRsSJSaZdbVfUzFlczZWXWSHvkkXDssaHTuJro1AkOPti6Al98sU/9n6fSKSQ9gWuAA4HDsZHkX9VlKFfgnnsOPvkExo/3N564E4EBA6BPH1uv5IQTQidydSBlIVHVUuDvACLSEbhBVd+v62CugA0eDHvsAeefHzqJqw2XXALXX2//rl5I8lI6vbY2iciR0d2pQIXL4TpXKz74AF56Cfr1g222CZ3G1YbGje2M5Mkn4fPPQ6dxdSCdxvb1wHbR9z2AzFascS4TJSXQqBH07h06iatN11xjMxMMGxY6iasD6bSRfAjcJCJPYL22zhORylbMUlW9s9bSucKydKm1i1x+OeywQ+g0rjbtsYfNwTV6NNx8M7RoETqRq0XpFJL+wEhsckUFrqtiXwW8kLjqGTEC1q2zxlmXf4qL7YPC6NHwi1+ETuNqUcpLW6r6hqr+UFW3wc5Ifqqq9Sq5+ax6rnrWrYM77oDOneGgg1Lv7+KnbVto1w6GDrU1ZlzeyHSurfbYpS7nateDD8KSJT4AMd8VF8O8edbw7vJGRtPIq+o0ABE5GmgH7IAtd/uaqr5d+/FcQVC1RvZDDoGOHUOncXXprLNgn32sK/C554ZO42pJRoVERJoADwOdgE3Acmy52/oi8jxwfjTuxLn0TZ0K778Pd93lAxDzXf36cO21dmby7rs2e4GLvUwvbd0GHAN0Axqq6m5Aw+j+McBfazeeKwiDB9u04927h07isqFnT1sWoKQkdBJXSzItJOcCv1HVh1W1DEBVy1T1YeC3gA9Fdpn59FN45hm4+mobP+LyX/Pm0KsXPPQQLFgQOo2rBZkWkhbAF5U89gXQvGZxXMEZOhQaNLBC4grHtdfa5Jy33x46iasFmRaS94GrRba8kB3dvzp63Lm0NFizBsaMgQsvhN12Cx3HZdM++1jD+8iRUOrNqnGXaSG5HmtonyUifxGRYhH5M/ARcEr0uHNVGz8eioo47owzbAGrAw4InciFUFwMK1bAXntxYocOtoDZ+PGhU7lqyLT778sichjwB6w9ZDdgEfA20EVVfYyJq9r48TaPVmkp35/W/ulP9ibije2FZf5866W3YoW9FubN2zzHmr8WYiXTMxJU9UNV7aaq+6lq4+jrRV5EXFpuuGHrSxmlpbbdFZYbbrAxRIn8tRBLGRUSEfm7iLSpqzCuAMyfn9l2l7/8tZA3qtP99wMReUdE+oiIT+HpMrP33pltd/nLXwt5I6NCoqr7AB2BWcDfgEUi8kC0cqJzqQ0aZKObEzVubNtdYRk0yP7tE/lrIZaq00YyRVV7YA3t/YE9gUkiMk9EbhaRfWs7pMsjJ5xg4weaNUNFoHVrGDXKG1cLUffu9m/fujXft5T84x/+WoihjAtJOVVdo6qjgRuB14G9gN8Bn4jIkyLSupYyunwyfLj11Pnvf5n28sswd66/cRSy7t1h7lzeHTPG7i9bFjaPq5ZqFRIRKRKRG0VkNvACsAbrDtwMOBMoAibUVkiXJ7791j6Bduli3X2di5QWFUGnTjbSff360HFchjLttXWJiLwMfAZcCowB9lHVn6vqo6q6TlWfBa4FKluO1xWqe++FVatg4MDQSVwuGjgQFi+GiRNDJ3EZyvSMZBSwGOikqvuq6q2q+mUF+30C/LGiHyAibUTkJREpFZGFInKLiFS5sqKIHCkiY0Tks+i4j6MzooYZ5nehlJXBkCE2bfixx4ZO43JRp05w8ME2G3Ty+BKX0zIa2Q7srqorU+2kqouAm5O3i0hLYDK2yuJZwH7AP7CC9vsqfmTXaN+/Ap8CPwJujb766jhx8Nxz8MknNrLd1xxxFRGBAQOgTx949VXrmOFiIdMpUlIWkRT6AI2w6VRWAy+KSHPgJhG5LdpWkb+q6lcJ96eKyHfASBFprarzapjL1bWSEth9dzjfVxpwVbjkErj+ejsr8UISGxk3totIVxGZLCLzRWRp8i3F4Z2BSUkFYwJWXE6s7KCkIlLuvejrLhn9AS77PvgAJk+Gfv1gm21Cp3G5rHFjOyN58kmYPTt0GpemTBvbLwLuxRrb9wSeAp6Jfs5qYHiKH3EQNpjxe6o6HyiNHsvEsUAZ8HGGx7lsKymxRavKJ+RzrirXXGODVocODZ3EpSnTM5JfYW0TfaP7d6hqT2AfYBlWEKrSElhVwfaV0WNpEZFdgRuA+6q4HOZywdKl1i7SowfsuGPoNC4O9tgDunaFe+6B1f7fOw5EM+gdISJrgNNVdaqIbABOVtWp0WPnAINVtaiK4zcA16nqkKTtC4Cxqppy2k8R2RZrsN8TaFtZu42I9AZ6A7Rq1arthAnVG9ayZs0amjZtWq1jQ8i1vK3vvZd9xo7lnXvvpTRpDqVcy5pKnPLGKStsnbfZxx/Ttk8fPrvmGr7MsXa1uD+3mWjfvv0MVU09lENV074BC7CuvwBzgasTHusCfJPi+KXAjRVsXwP8Ko3fL1ibynLgoHRzt23bVqtrypQp1T42hJzK+913qq1aqXbuXOHDOZU1DXHKG6esqpXkbddOtahIdePGrOepSl48t2kCpmsa77GZXtqajnW5BWsf+YOIXCkil2KTOL6d4vhZJLWFiMheQBOS2k4qMRjrNnyWqqazvwtpwgRYssQHILrqGTjQptB58snQSVwKmRaSPwPliwX8AXgHuAMb4b6M6FJSFZ4DOolIs4RtXYG1wLSqDhSR32GTRF6sqq9lmNtlm6o1srdpAyefHDqNi6Ozz7apdEpKQidxKaRVSESkkYicCxwHNBCRVqq6SlXPApoC26vq0aqaqr/eCGAd8JiIdIzaMW4C/qkJjebRCPbRCfcvAv4EjAMWiMhPE247Z/D3umyZNg3+8x/7VOkDEF111K8P/fvb4MQZM0KncVVIWUiiaeFnAg9jl6/uAz4WkVMA1ObXSqtrhVrD+ElAfeBpbPT7YGwG4UQNon3KnRJ9vQx4M+l2Wjq/22VZSYn10rr44tBJXJz16gVNm9oARZez0jkjuQ0br3E80Bg4BBsMOLI6v1BtzfcOqtpIVXdT1f9T1U1J+xSp6mUJ9y9TVankNrY6OVwd+uwzeOopG1jWqFHoNC7OWrSwYjJxIixcGDqNq0Q6heQY4Peq+rqqfqeqHwFXAXuLyG51G8/F0tCh0KAB9O2bel/nUunfHzZtsinmXU5Kp5DsBiS3fXyOdcXdtdYTuXhbtcoGknXrBrv55wxXC/bbD846C0aOhNJUY55dCOn22vI5nV16Ro+2Bay8y6+rTQMHwvLlcP/9oZO4CqRbSCYlTcy4KNr+UoaTNrp8tnEjDBtms7YefnjoNC6fnHACHHaYdeLwtUpyTjrTyG+1rohzFXriCZg3z3vYuNonYmcll14KL7xgi2C5nJGykKiqFxKXnpIS2GcfOPPM0ElcPuraFX7zG3udeSHJKRmvR+Jchd59F15/Ha691gaSOVfbttvOpph//nn46KPQaVwCLySudpSUQLNm0LNn6CQun/XpYwVlyJDU+7qs8ULiam7BAnjoIbjiCmjePHQal8923tmW4x03znpxuZzghcTV3PDhUFZmA8ecq2sDBsDatTauxOUELySuZkpL7T/02WdbQ7tzde3QQ21G6dtvh/XrQ6dxeCFxNTVuHKxc6QMQXXYNHGhzbz38cOgkDi8kribKyqzRs21baNcudBpXSE49FQ480Aco5ggvJK76Jk2CWbN8zRGXffXqWVvJ9OnW7dwF5YXEVV9JiU3MeMEFoZO4QtSjB7Rs6Sso5gAvJK56Zs60qSr69YNttw2dxhWiJk2gd294/HGYMyd0moLmhcRVT0kJNGxo/5GdC6VfP7vMNXx46CQFzQuJy9xXX8F999mlhZ12Cp3GFbI994Tzz4e774ZvvgmdpmB5IXGZGzkS1q2zxk7nQhs4EFavhjFjQicpWF5IXGbWr7eBYJ06QZs2odM4B0cdBccea13RN20KnaYgeSFxmZk4ERYv9gGILrcMHAizZ8PTT4dOUpC8kLj0qdqiVQcf7OtBuNxyzjmw997eFTgQLyQufa++Cu+95wMQXe5p0MCo1nPKAAAfqUlEQVQmDZ02zV6jLqu8kLj0lZTADjvAxReHTuLc1q64wsaW+FlJ1nkhcemZPdvWZO/TBxo3Dp3Gua1tvz1cfjk8+CAsWhQ6TUHxQuLSM3SoLaF7zTWhkzhXuQEDYONGuPPO0EkKihcSl9rq1XDPPdC1K+yxR+g0zlVu//3hjDOskKxdGzpNwfBC4lIbPdpGDXuXXxcHAwfCsmXwwAOhkxQMLySuaps22WWtdu3giCNCp3EutZ/9DH78Y+uq7muVZIUXEle1J5+EuXP9bMTFh4i9XmfOhJdeCp2mIHghcVUrKYGiIluT3bm4uPBC2GUXOytxdS7rhURE2ojISyJSKiILReQWEamf4phtReRvIvKqiKwVET9fzYYZM2wQ4rXXWo8t5+Jiu+2sh+Gzz9oqnq5OZbWQiEhLYDKgwFnALcAvgZtTHNoYuAIoBd6oy4wuQUkJNG0KPXuGTuJc5q6+2hZdGzo0dJK8l+0zkj5AI6CLqr6oqiOwIvILEWle2UGqugrYQVU7AY9nJ2qBW7gQJkyAXr2gRYvQaZzL3C67QPfucO+9sGJF6DR5LduFpDMwSVVXJ2ybgBWXE6s6UNW7X2TV7bdbj63+/UMnca76Bg6E0lK4667QSfJatgvJQcAWFyxVdT52yeqgLGdxlSkttcWrzjoL9tsvdBrnqu9HP4IOHWDYMNiwIXSavNUgy7+vJbCqgu0ro8dqjYj0BnoDtGrViqlTp1br56xZs6bax4ZQG3l3e/ppDly+nPdOPJGv6/BvL8TnNlvilBXqNu+OHTvyw5df5sNbb2Vphw41/nn+3FZAVbN2AzYAAyrYvgAYlObP6Ed0pSvdW9u2bbW6pkyZUu1jQ6hx3rIy1YMPVj3sMPu+DhXcc5tFccqqWsd5N21S/cEPVI86qlZe04X03ALTNY332Gxf2loJbF/B9hZUfKbisu2FF+Cjj6C42NcccfmhXj2bzPGdd+Ctt0KnyUvZLiSzSGoLEZG9gCYktZ24QEpKYNddbYJG5/LFpZfaNPM+QLFOZLuQPAd0EpFmCdu6AmuBaVnO4pJ99BE8/zz07Wv9753LF02bwpVXwqOPwrx5odPknWwXkhHAOuAxEekYNYjfBPxTE7oEi8hnIjI68UAR6Swi5wE/ie6fF91aZy9+nhsyxEYEX3VV6CTO1b5+/exy7fDhoZPknawWElVdCZwE1AeexgYjDgZuTNq1QbRPojuBh4Fe0f2Ho1v7uspbUJYvh3Hj4JJLYOedQ6dxrvbtvTece66NKVmzJnSavJLt7r+o6odAlX3wVLUonW2uFo0caQsBDRgQOolzdae4GB56CMaOtTMUVyt89l8H69fbSPaTT4ZDDw2dxrm689OfwtFH22XcsrLQafKGFxIHDz9sc2sVF4dO4lzdKy6Gzz6Df/0rdJK84YWk0Klal98DD4ROnUKnca7unXsu7LWXdwWuRV5ICt3rr8P06Ta5XT1/ObgC0KCBtY9MmQLvvx86TV7wd45CV1ICLVtaby3nCsWVV0Ljxvb6dzXmhaSQzZkDjz9u40aaNAmdxrnsadkSLrsMHngAliwJnSb2vJAUsmHD7HJW376hkziXfQMGWI/FO+8MnST2vJAUqtWr4e674fzzYc89Q6dxLvsOOABOO80KyXffhU4Ta15ICtWYMfDNN9bI7lyhKi6GpUvhwQdDJ4k1LySFaNMmGDoUjj0WjjoqdBrnwunQAX74Q+sK7Kt5V5sXkkL09NMwe7YPQHROxM7KP/jAugO7avFCUohKSqB1azj77NBJnAvvootsolIfoFhtXkgKzXvvwbRp0L+/DcxyrtA1bAhXXw3PPAOffho6TSx5ISk0JSU2ZqRXr9T7Olcorr7aFnMbMiR0kljyQlJIFi2y3ik9e9qyo845s+uucOGF1ptx5crQaWLHC0khueMO2LgRrr02dBLncs/AgVBaauOrXEa8kBSKtWthxAg44wzYf//QaZzLPT/5CfzsZzbjw8aNodPEiheSQjF+PCxb5l1+natKcTF88QU89ljoJLHihaQQlK858uMfw4knhk7jXO467TTYbz+fFThDXkgKweTJMHOmfdoSCZ3GudxVv75N5vjmm/D226HTxIYXkkJQUgKtWkG3bqGTOJf7Lr8cWrTwAYoZ8EKS72bNgmefhWuuge22C53GudzXtClccQU88oi1l7iUvJDku6FDrYD06RM6iXPx0b+/tS0OHx46SSx4IclnK1bAvfdC9+6wyy6h0zgXH61bQ5cuMGoUfPtt6DQ5zwtJPhs1ygZY+ZojzmWuuBhWrbIPY65KXkjy1YYNdlp+0km23oJzLjPHHANHHmnzb5WVhU6T07yQ5KtHHoEFC3wAonPVJWL/fz75BJ57LnSanOaFJB+pWtfFAw6Azp1Dp3Euvs47D/bYwwcopuCFJB+9+Sa8+64NrKrn/8TOVds220C/fjao94MPQqfJWf4uk49KSmya+B49QidxLv5694ZGjXytkipkvZCISBsReUlESkVkoYjcIiL10ziuhYiMEZGVIvK1iIwXkR2zkTlOtlu8GB591F78TZuGjuNc/O2wA1x6Kdx/PyxdGjpNTspqIRGRlsBkQIGzgFuAXwI3p3H4ROBnwBXAZcCRwBN1kTPO9njiCWsk7NcvdBTn8seAAbBunS3F4LaS7TOSPkAjoIuqvqiqI7Ai8gsRaV7ZQSJyDNAJuFRVH1XVx4GLgXYi0rFOko4fD0VFnNihAxQV2f1cNn487L03e02caCPZX3kldCLn8sdBB8GPfgQ33xyv94QsvYdlu5B0Biap6uqEbROw4lLV/OadgSWq+v27o6q+A8yJHqtd48fbpaF58xBVmDfP7ufqC6c87xdfIGCDEHM5r3NxM348fPwxlJXF6z0hS+9hDerkp1buIODlxA2qOl9ESqPHnq7iuFkVbP8oeqx23XCDvRknKi2Fyy6DP/2p1n9djX3yydYrupWW2t/RvXuYTM7lkxtusEtbifw94XvZLiQtgVUVbF8ZPVad4/at6AAR6Q30BmjVqhVTp05NO+SJ8+dT0aodunEjX+28c9o/J1t2/vDDivPOn8+0DP7ubFuzZk1G/y6hxSlvnLJC7uf194QUVDVrN2ADMKCC7QuAQVUc9yLweAXbxwOvp/q9bdu21Yy0bq1qw/q2vLVundnPyZa45Y1MmTIldISMxClvnLKqxiBv3P6P1VJeYLqm8d6e7TaSlcD2FWxvQcVnHKmO2z7FcdUzaBA0brzltsaNbXsuilte5+Imbv/Hspw324VkFkltGiKyF9CEittAKj0uUlnbSc10724z57ZujYrYlNKjRuVue0Pc8joXN3H7P5blvNkuJM8BnUSkWcK2rsBaYFqK43YVkXblG0TkCKx9pG5mU+veHebOZdrLL8Pcubn7gikXt7zOxU3c/o9lMW+2C8kIYB3wmIh0jBrEbwL+qQldgkXkMxEZXX5fVd8EJgHjRKSLiJyNtY+8pqqTs/oXOOec20JWC4mqrgROAupjXX1vBgYDNybt2iDaJ1E37KzlHmAcMAM4py7zOuecSy3b3X9R1Q+BDin2Kapg2yrg8ujmnHMuR/jsv84552rEC4lzzrkaERtzkt9E5CtgXjUP3wlYVotx6lqc8sYpK8Qrb5yyQrzyxikr1Cxva1VNOXS/IApJTYjIdFU9InSOdMUpb5yyQrzyxikrxCtvnLJCdvL6pS3nnHM14oXEOedcjXghSW1U6AAZilPeOGWFeOWNU1aIV944ZYUs5PU2EuecczXiZyTOOedqxAuJc865GvFC4pxzrka8kDjnnKsRLyTOOedqJOuz/7raEa0s+XNAgIdVdbmI7AlcB+wHzAVGqeoH4VKCiPwGeDZ0jnSJSCOggap+k7BtZ6Af0AYoA/4D3KGqX4dJ6Vxu8e6/ERERbH2T04CDgR2ATcAS4C1grKp+Ei7hZiJyFPAC0BTYCKwAOgHPYplnAocCuwIdVfXVQFERkTJAsSWRHwAmqupnofKkIiLPAp+q6oDo/jHYKpxl2Bo4ArQF1gMdVHVmwKyHAY1U9Y2EbacCv2Nz0XsfuClxn1wR/Z87Azgce41Mxz505PSbkog0x+au6qCqr4XOA99n6gBsC/xLVb+NPgD1xVaSnY19sFxYJ78/x//NsiJ6wp/F3iCWYKs47oG9uJ/D/iEOBG5V1VtD5SwnIi9iZ5PnAN9ii4Odjb3RnaeqG0RkO+AJoKGqtg+YtQz4K/BD4GQs97+xovKQqi4Ila0iIrIM6KWqT0b338Ke47PLz1JEpAXwFPCdqnYKmPUt4GlVHRTd7wncDUwBXsaK3knA8cC55X9ToKxvYM/rR9H9ltiHobbAmmi3ptiHtk6JZ4QhiMg1VTzcCPgbMAT4FEBV78hGroqIyP7AS8Be0aY5wCnAi8D2wOfY+9daoK2qflnrIVS14G/Ag9gL4ocJ23YHngceje6fiL3ge+ZA3uVA54T7u2CfPk9J2u80YFngrGXAUdH3LYHe0Yt+Y3SbGm3bMfTzGmUsBU5IuL8++XlNeG6/DZx1dWI24DNgWAX7jQDez5XXQXR/NHYmfWrCtlOBlcDgHHgdlGFn92WV3BIf2xQ460PYmef+2JWU+6L3szeAZtE+O0X7jKyLDN7YbjoDv9WE6/hqp4B9gLNFZDdVnQb8CRgQKGMijW6J90naVtH9oFR1paqOUtWTgD2BX2Kn4iOAhSLyr6ABzf+AxDO4Jdh/zmQ7YkUnpLKk+62BRyrY7xHsE2kuORO4RVWfL98QfT8I6BIs1WZPAUuBXkB9Va1XfsNeDwL8LNqWvCx4trUDBqnqZ6q6Avg91k76d43O7FR1GVDClq/tWuOFxAj2CSPZpuixFtH9t4EDshWqCjOA60SkmYjUA64HFgBXi0h9ABFpAFyDvTHmHFVdrKpDVPVYYB/gRuwsMLS/AL8VkZ7RczgI+JuInCwi24rIdlE7xJ+xT4IhvQp0T7g/E6houvAjsddHLtkeaxNJNgNr2wtKVc8GLgV+BbwrIsclPhwmVaVaAosT7pf/WyevwTQb+wBX67zXlpkM/FFE/quqs+H7a7hDsX+g8kb2pkAu9NS5Abv+uQK7PFSKNbQ9AnwqIuWN7btjlwtymqrOw97A/5IDWR4Tkf7Yp7fBwMfYB4nyT86Kfbh4CnuTCel64PXow8QwrJH9XhHZAbtkCNZGMhD4bZCEWzpXRMoL3UqgogWTdsIu2QWnqi+IyI+w5+9fIvI81isyaPtNBZZiZ6PlNgEjsbPpRLtQR9m9sR2Ius0+j53+z8Oui++DNbpfqKrPRfvdhq0Y1jVU1nJR5tOxDwOPquoiEdkV+DWb/467VfXfAWMiIjcCd2kd9RapKyKyI9AVOAr7hFwPK9wfAc+o6oyA8b4nIj8B7gSOZnORI+H7ldglpCFhEpqo00WysaraM2m/kUAbVT0+O8nSE/3fug277DYSKy7tVfWVoMEAEXkCWJH8XFaw3zDgYFXtWOsZvJCY6JLQBcCPgYZYw+UD0TVH53KaiByMFZPkoveGqm4ImS0TInIl8Lmqvhw6S0Wi7uCDsQ9rp2kOdKsWkVZAY1Wdk2K/X2CdLl6q9QxeSPKPiNRX1YrafHKGiDTEGgTLgM9y8c0uaiPZl4QxRao6P2wq53KPN7YnEZFDRORcEblCRHpF3x8SOlcyEekiIk+IyLMicka0rauIzAXWi8i86NNdUCJycTS+ofx+AxH5C/aJ+b9YZ4AVIpIL1/ABEJG2IvIUdj35I+B1bHzDHBFZICK3iEjjoCHziERC56iIiDRK/rcWkZ9E7wttQ+XKOSH7P+fSDeiJtStU1Hd8EzblyOWhc0ZZL4hyvQY8iTW2X4m17YzGRrM+GOXuFDjrh8DVCff/EeX9P+A4rOviTdhgqetz4Lk9BWsbm471zLoJG5S6Psr8S6x31H+AljmQ93RsXM4HwEQSxsAk7HM04cc6nEI0piFh29nY4NSNwIboOT8t9HMaZWsBPB7l2gjcBdQH7k16X3gd2Cl03jT/pnPr6nUQ/I/LhRvQP3rB3I6NAt4petHUj75vBwyP3mD65kDed4ERCfe7R9n+kbTfGGBy4KylwIkJ95cCAyrY7zpgXg48tzOAeyt5jczFzuIbRm+AdwTOenLCm9nwKPumqFhLwn65UEg2seWAxHOiN+M3on/766LvN1LBANAAeYdi06D0B3pEHx4eBb6IiuLO2PizBcCdofOm+TfVWSHxNhJARGZjb8y3pdjv10AfVd03O8kqzbEa6KKqk6P7LbDeOR01oZEyuuQ1UlWDjc8QkUVAP1V9NLq/DjtLmpq038nAU6raKPspt8ixFjhTVV9M2t4Sm1HgEFX9SER6AH9V1d1C5IwyvYbNC3Z5wrae2Jvgi1iPw+9E5Gis0T3YwLmo19ZPVfWd6P6/gQWqekbSfs8CTVT1xAAxE3PMAf6kqndF9w/DCvXlqnpvwn5XYmfS+4RJCiJyT5q7tsYGUdb668DbSMyuwDtp7PcOOTBYCuvamfhiKJ+raFXSfmuwgV8hPYUNntw2uj8ZuLCC/S7EPvWFthTruZfsx9jzXj6OaB6bB6qGcihwf+IGVb0Hm87np8DL0ZiSXHQo1o022ShsEsfQdmHz+DGI5tTC5q1K9BkVj4fJpkuxs6Qfpri1ruwH1JQPSDT/Ba4UkVdUtaL+7uUzlV4Z7RvaPGx210kAqrop6pb4UdJ++7LliNcQfoeNwP6fiNwNPA38VUQOZfOguQ7AYdhMsKGNAm4VkSZY28N6bGT4DcAU3TweZl8gdA+u74AmyRtVdUY0EnsSdrnopiznqkzi5Y+v2fwBKNG35MYH3DlYQZ4W3T8euxR3LNY2We44wr8OPgXeUdUeVe0kIudh7Wi1zguJ+SU2IPFDEXkMm/J8FfbC3x44CLumuye5MVL8MZKmOlDVtyvY7yK2fNFnnaquEJGfYm/Ev8A+6QEcE93WY5dhjlfVd8Ok3ExVB0WXYX6LTdsC9jp4EBuEVm4DNvdaSP/FrtM/lfyAqs6OismzwNgs56rMJBHZGH3fAvgJmz9MlDsIWJTNUJUYAQwRkR9iRe8C7EPRH0SkKTYB4uFAMRB6RvC3sAKXSuKA1VrlbSQREdkPGxV+KpunYy73BdZz52+qmnxqm7NEZG9glarmxJQTACJSxJaD5j7X3BxDsg02zqUhMDuXnsNyInIVNk3KYVrJwNnozOpxrP0s2Cf9aIaDZJ+q6gNJ+02NtudC1/VrsUuu22CzRIwQkQuxNqjySTtHAb8J+RqOuiEfp6pDU+y3E9bGN62q/aqVwQvJ1qJ+4+VtC6tUNfQsr865HBFd5t5JVb8KnSVXeCHJM9Fp97+B7rlwqUhiuHStxGQZY+dyhReSBNEbyC7Ax6q6VUNgdGr4c1Udl/VwW+b4eRUPN8Ea1H5LNIW8qj6bjVwVkRgtXQvxWsY4XdE8XOer6i2BcwRdDramojORxKWBZ2B/R/A3UbFZlc/F/j+NVdVZIvJj4GY2f/i5XRPWf6lVoQfJ5MIN2A54GHuj2IQ1pI4GWiTtF3xgV5QjTqu3LQPOSrj/FtYbqlnCthZY75hJOfDcvogtVbs9dm18OPAlNoPANgmvl+ewXlzBX79p/E11NhAtgwz7Y70Ny1+Xn2NvcLOxYv0uNn38EmDPHHjO3sBmyi2/3zLKWBblXM3mAZXNQuWMsnXCPogtjp7X1dgCViuxwaq3R//vNmFLRtd+htD/YLlwA/6A9dK6ElsYaED0gv4U+EHCfrlSSGZgPVsux/qGJ95+FL3ALyjfFjhrbJaujXLEaRnjvdO89Qn9uiUHloPNMG9slgaOisXD2EqOYB0wVgKjk/a7D3irTjKE/gfLhRvW3bdf0rZdgVeAr4Bjom25UkgEW+d8KTZtwz4Jj7WI/hNsNedSoKzvADcm3P8C6FbBfj2Ar3Ig77KkN4udo+fz5KT9fp4DhaT87DPVLRfOTBcCFyTcbx3l6pK03+XAJznwOkguJF8BAyvYL/jUPlj35I4J91tG+Tsk7XcK1nmo1jP4OBKzF0kDDVV1sYichFXxySLSndzo347aq2KUiDwE/BH4r4gMj77PNX8BxovIF8A4Ni9duxy7nCXYaXguLF0Lm5cxfh0bHJe4jPHLaoM/c2UZ42+Al4G7U+zXDuvaHlLw5WBrKJeXBl7LlgNTy79Pnm6oMTaItdZ5ITELgR9gZyDfU+sb3k1ESrBTx6CN7MlUdRXQT0RGYX3bPwX+Sg6tKa3xWroW4rWM8TtYO96/qtopWvsltODLwVZDXJYGfh0bKPlplOXv2Kzbv4lm6/gmmo/v11jhq3Xea4vvJz3bV1V/VsU+v8M+TasGnPyuKiLSDVsOdE9scrbgy4CWk5gsXQuxWsb4/4Deqpo8gDZ5vxOAm1W1fXaSVZgh+HKwmZAYLQ0sIvtjc9iVvw7mYmf5j2AzBcwDirAPRu1V9T+1nsELyfdd57oCf1HV5VXsdxF2rfzyyvYJLbrs0gRYozm+SqIrHJIDy8HWBcmRpYGj8WPHYT0NX1LVtdHA6ivY/OHnAVX9sk5+vxcS55xzNZELs2y6OiIid4nI6NA50hGnrBC/vM7VJW9sz4CI3AXUU9VeobOkqT3x+bAQp6wQo7wiMhm7+nBS6CypxCkrxCtvXWb1QpKZ2Lx5AKjq/qEzpCtOWSF2eYX4vG7jlBXilbfOsnobSR6Lun3uoqqhF95JKU5ZIX55natLcamkOUFEGkZrfMTFadhKb3EQp6wQo7wisk1cXrdxygrxyluXWb2QZCY2bx6uMIhIXxH5XES+EZG3ReSSCnY7nBx43cYpK8Qrb+is3kYSQyKSbp/1ikbiZlWcskK88kYDUIdhywC/h40jGCsiZwGXqOrakPkSxSkrxCtvLmT1NhIyfvNoE3pku9i61x9j0yBUZQ/g6JB545QV4pVXRKYDL6vqrxO2nQSMx0Y3n6a2KNfRwBueNX1xypsLWb2QEK83DwAR+Q+2+FbXFPudB0wM/CKPTdYoR2zyisg3wBmqOjVpexG2Xkp9oDM2H1ToN7vYZIV45c2FrN5GYv4H/E9Vz6/qBvwzdNDI28BP09ivfELEkOKUFeKV92vszWELqjoXOBabEv8N4MjsxqpQnLJCvPIGz+pnJHw/8dqpqto6xX7nYmt4By3AIrIfcIiqPpViv0ZYF9XkqbqzJk5ZoxyxySsiTwLfqOrFlTzeCJu4rzOBJxuNU9YoT2zy5kJWLyTE683DuXIicj5QDJyuqisq2ac+cCc22eg+2cyXlCM2WaMsscmbC1m9kDjnnKsRbyNxzjlXI15InHPO1YgXEldQROQyEZkRjQBeKSLviUid9MYTkQNE5CYR2T6NfW8SEU24LRSRR6P2u1THXhYd07R2kjuXGS8krmCILZd8NzAJ6AL0AJ4EzqyjX3kAcCOQspBEvgaOiW7XAT8BXhKRJimO+1d0TGk1czpXIz5Fiisk/YCRqnp9wranReTmUIGSbFTVt6Lv3xKR+cCrwM+Bh5N3jnri1FfVr4CvshfTuS35GYkrJNsDi5M3akLXRREpii4TXSQi90WXwJaKyI3Jx4lIh2iCvO9EZImI3FF+eUlEfgY8He06J/qZczPMOyP6WhT9zLEiMl1EzhaRmcB3wNEVXdoSkUYicpuIzBORdSIyR0T+nJT/ChGZGT0+T0R+jXPV4GckrpD8G+gffdJ/RlWXV7Hv34BngPOAE4AbRWSZqt4OICJtgOeBF4Fzgb2AvwD7AqdGv+s64O/YZbRFwLoM8xZFXxcnbbsNuAVYgs3mukU7iogIdsnuGOBWrCDtARyfsM+vgD9FP2sq0Ba4VURKVXV4hjldoVNVv/mtIG7Aj4DZ2PQmZcBM7A25ecI+RdHjLyQdexewAFtqGWAC8Cl2aal8nwuiY4+J7p8e3S9KI9tN2FQWDaLbAcAUYDWwW7TP2Ojn/STp2Mui7U2j+52i+2dW8ruaA2uAG5O234IVrfqp8vrNb4k3v7TlCoaq/hc4GGtcvwObK+v/gOkV9Hh6POn+Y8DuwJ7R/aOAx1V1U8I+jwIbgXbVjLgjsCG6fYyd3XRV1UUJ+yxQ1f+k+DkdgBVa+UwNxwBNgIdFpEH5DXgZaMXmv9G5tPilLVdQVHUd1nbxNICI9MJ6cvUChiTsujTp0PL7uwHzo69Lkn72JhFZDuxQzXhfAx2xs4nFwEJVTZ56YslWR21tR+xSWmXKJ/ibWcnjewE+DZBLmxcSV9BUdbSI3AYclPTQLpXcX5TwdYt9ol5UOwIVzneUho2qOj3FPunMabQcK3SVKc93OhUXpo/T+B3Ofc8vbbmCISLJxQER2RlowdZvqOck3S9vMP8yuv82cE5UPBL3aQC8Ft1fH31tWIPY1fESsIOInF7J428Ca4HdVXV6BbdvshfV5QM/I3GF5INoyu0XsEtVrbGeVaXAvUn7HhItL/Ao1murFzBAVcuix/+ILWv6hIjcibUr/BWYpKpvRvuUf7K/SkQmAKWq+kHd/GlbeBEbdPmAiNyC9SDbDThBVa9S1VUichMwRERaA69gHyoPANqranIRda5KXkhcIbkFOAsYirVjLMYW/OmqqnOS9v01dunnUWy8xq3A991iVXWmiHTGutA+hvWuejA6rnyfeSJyHXAt0B87mymqiz8skaqqiJwTZR6ILRG9EHggYZ/bRGQhNv34L7G/8RNgYl3nc/nHp5F3LkG0POkcbOnSZ8KmcS4evI3EOedcjXghcc45VyN+acs551yN+BmJc865GvFC4pxzrka8kDjnnKsRLyTOOedqxAuJc865Gvl/T2D1lNDCAdoAAAAASUVORK5CYII=\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# plot exact payoff function (evaluated on the grid of the uncertainty model)\n", - "x = uncertainty_model.values\n", - "def payoff(x):\n", - " if x <= strike_price_1:\n", - " return 0\n", - " elif x < strike_price_2:\n", - " return x - strike_price_1\n", - " elif x < strike_price_3:\n", - " return strike_price_2 - strike_price_1\n", - " elif x < strike_price_4:\n", - " return strike_price_2 - strike_price_1 + strike_price_3 - x\n", - " else:\n", - " return 0\n", - "y = [payoff(x_) for x_ in x]\n", - "plt.plot(x, y, 'ro-')\n", - "plt.grid()\n", - "plt.title('Payoff Function', size=15)\n", - "plt.xlabel('Spot Price', size=15)\n", - "plt.ylabel('Payoff', size=15)\n", - "plt.xticks(x, size=15, rotation=90)\n", - "plt.yticks(size=15)\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "exact expected value:\t0.3569\n" - ] - } - ], - "source": [ - "# evaluate exact expected value (normalized to the [0, 1] interval)\n", - "exact_value = np.dot(uncertainty_model.probabilities, y)\n", - "print('exact expected value:\\t%.4f' % exact_value)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Evaluate Expected Payoff" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [], - "source": [ - "# set number of evaluation qubits (=log(samples))\n", - "m = 5\n", - "\n", - "# construct amplitude estimation \n", - "ae = AmplitudeEstimation(m, iron_condor)" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [], - "source": [ - "# result = ae.run(quantum_instance=BasicAer.get_backend('qasm_simulator'), shots=100)\n", - "result = ae.run(quantum_instance=BasicAer.get_backend('statevector_simulator'))" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Exact value: \t0.3569\n", - "Estimated value:\t0.3428\n", - "Probability: \t0.9697\n" - ] - } - ], - "source": [ - "print('Exact value: \\t%.4f' % exact_value)\n", - "print('Estimated value:\\t%.4f' % result['estimation'])\n", - "print('Probability: \\t%.4f' % result['max_probability'])" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# plot estimated values for \"a\"\n", - "plt.bar(result['values'], result['probabilities'], width=0.5/len(result['probabilities']))\n", - "plt.xticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", - "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", - "plt.title('\"a\" Value', size=15)\n", - "plt.ylabel('Probability', size=15)\n", - "plt.ylim((0,1))\n", - "plt.grid()\n", - "plt.show()\n", - "\n", - "# plot estimated values for option price (after re-scaling and reversing the c_approx-transformation)\n", - "plt.bar(result['mapped_values'], result['probabilities'], width=1/len(result['probabilities']))\n", - "plt.plot([exact_value, exact_value], [0,1], 'r--', linewidth=2)\n", - "plt.xticks(size=15)\n", - "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", - "plt.title('Estimated Option Price', size=15)\n", - "plt.ylabel('Probability', size=15)\n", - "plt.ylim((0,1))\n", - "plt.grid()\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "qiskit_master", - "language": "python", - "name": "qiskit_master" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/finance/simulation/long_butterfly.ipynb b/community/finance/simulation/long_butterfly.ipynb deleted file mode 100644 index 52c9ae6f6..000000000 --- a/community/finance/simulation/long_butterfly.ipynb +++ /dev/null @@ -1,397 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# _*Pricing Long Butterfly Options*_ \n", - "\n", - "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", - "\n", - "***\n", - "### Contributors\n", - "Stefan Woerner[1], Daniel Egger[1]\n", - "### Affliation\n", - "- [1]IBMQ" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Introduction\n", - "
\n", - "Suppose a long butterfly option with strike prices $K_1 < K_2 < K_3$, with $K_2 - K_1 = K_3 - K_2$ and an underlying asset whose spot price at maturity $S_T$ follows a given random distribution.\n", - "The corresponding payoff function is defined as:\n", - "
\n", - "
\n", - "$$ F(S_T) = \n", - "\\begin{cases}\n", - "0 ,& S_T < K_1 \\\\\n", - "S_T - K_1 ,& K_1 \\leq S_T < K_2 \\\\\n", - "2K_2 - K_1 - S_T ,& K_2 \\leq S_T < K_3 \\\\\n", - "0 ,& S_T \\geq K_3. \n", - "\\end{cases}$$\n", - "
\n", - "In the following, a quantum algorithm based on amplitude estimation is used to estimate the expected payoff, i.e., the fair price before discounting, for the option:\n", - "
\n", - "
\n", - "$$\\mathbb{E}\\left[ F(S_T) \\right].$$\n", - "
\n", - "The approximation of the objective function is explained in detail in the following paper:
\n", - "Quantum Risk Analysis. Woerner, Egger. 2018." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import matplotlib.pyplot as plt\n", - "%matplotlib inline\n", - "import numpy as np\n", - "\n", - "from qiskit import BasicAer\n", - "from qiskit.aqua.algorithms import AmplitudeEstimation\n", - "from qiskit.aqua.components.uncertainty_models import LogNormalDistribution\n", - "from qiskit.aqua.components.uncertainty_problems import UnivariateProblem\n", - "from qiskit.aqua.components.uncertainty_problems import UnivariatePiecewiseLinearObjective as PwlObjective" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Uncertainty Model\n", - "\n", - "We construct a circuit factory to load a log-normal random distribution into a quantum state.\n", - "The distribution is truncated to a given interval $[low, high]$ and discretized using $2^n$ grid points, where $n$ denotes the number of qubits used.\n", - "The unitary operator corresponding to the circuit factory implements the following: \n", - "$$\\big|0\\rangle_{n} \\mapsto \\big|\\psi\\rangle_{n} = \\sum_{i=0}^{2^n-1} \\sqrt{p_i}\\big|i\\rangle_{n},$$\n", - "where $p_i$ denote the probabilities corresponding to the truncated and discretized distribution and where $i$ is mapped to the right interval using the affine map:\n", - "$$ \\{0, \\ldots, 2^n-1\\} \\ni i \\mapsto \\frac{high - low}{2^n - 1} * i + low \\in [low, high].$$" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "# number of qubits to represent the uncertainty\n", - "num_uncertainty_qubits = 3\n", - "\n", - "# parameters for considered random distribution\n", - "S = 2.0 # initial spot price\n", - "vol = 0.4 # volatility of 40%\n", - "r = 0.05 # annual interest rate of 4%\n", - "T = 40 / 365 # 40 days to maturity\n", - "\n", - "# resulting parameters for log-normal distribution\n", - "mu = ((r - 0.5 * vol**2) * T + np.log(S))\n", - "sigma = vol * np.sqrt(T)\n", - "mean = np.exp(mu + sigma**2/2)\n", - "variance = (np.exp(sigma**2) - 1) * np.exp(2*mu + sigma**2)\n", - "stddev = np.sqrt(variance)\n", - "\n", - "# lowest and highest value considered for the spot price; in between, an equidistant discretization is considered.\n", - "low = np.maximum(0, mean - 3*stddev)\n", - "high = mean + 3*stddev\n", - "\n", - "# construct circuit factory for uncertainty model\n", - "uncertainty_model = LogNormalDistribution(num_uncertainty_qubits, mu=mu, sigma=sigma, low=low, high=high)" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# plot probability distribution\n", - "x = uncertainty_model.values\n", - "y = uncertainty_model.probabilities\n", - "plt.bar(x, y, width=0.2)\n", - "plt.xticks(x, size=15, rotation=90)\n", - "plt.yticks(size=15)\n", - "plt.grid()\n", - "plt.xlabel('Spot Price at Maturity $S_T$ (\\$)', size=15)\n", - "plt.ylabel('Probability ($\\%$)', size=15)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Payoff Function\n", - "\n", - "The payoff function equals zero as long as the spot price at maturity $S_T$ is less than the strike price $K_1$, then increases linearly, and is bounded by $K_2$.\n", - "The implementation uses two comparators, that flip an ancilla qubit each from $\\big|0\\rangle$ to $\\big|1\\rangle$ if $S_T \\geq K_1$ and $S_T \\leq K_2, and these ancillas are used to control the linear part of the payoff function.\n", - "\n", - "The linear part itself is then approximated as follows.\n", - "We exploit the fact that $\\sin^2(y + \\pi/4) \\approx y + 1/2$ for small $|y|$.\n", - "Thus, for a given approximation scaling factor $c_{approx} \\in [0, 1]$ and $x \\in [0, 1]$ we consider\n", - "$$ \\sin^2( \\pi/2 * c_{approx} * ( x - 1/2 ) + \\pi/4) \\approx \\pi/2 * c_{approx} * ( x - 1/2 ) + 1/2 $$ for small $c_{approx}$.\n", - "\n", - "We can easily construct an operator that acts as \n", - "$$\\big|x\\rangle \\big|0\\rangle \\mapsto \\big|x\\rangle \\left( \\cos(a*x+b) \\big|0\\rangle + \\sin(a*x+b) \\big|1\\rangle \\right),$$\n", - "using controlled Y-rotations.\n", - "\n", - "Eventually, we are interested in the probability of measuring $\\big|1\\rangle$ in the last qubit, which corresponds to\n", - "$\\sin^2(a*x+b)$.\n", - "Together with the approximation above, this allows to approximate the values of interest.\n", - "The smaller we choose $c_{approx}$, the better the approximation.\n", - "However, since we are then estimating a property scaled by $c_{approx}$, the number of evaluation qubits $m$ needs to be adjusted accordingly.\n", - "\n", - "For more details on the approximation, we refer to:\n", - "Quantum Risk Analysis. Woerner, Egger. 2018." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [], - "source": [ - "# set the strike price (should be within the low and the high value of the uncertainty)\n", - "strike_price_1 = 1.438\n", - "strike_price_2 = 1.896\n", - "strike_price_3 = 2*strike_price_2 - strike_price_1\n", - "\n", - "# set the approximation scaling for the payoff function\n", - "c_approx = 0.25\n", - "\n", - "# setup piecewise linear objective fcuntion\n", - "breakpoints = [uncertainty_model.low, strike_price_1, strike_price_2, strike_price_3]\n", - "slopes = [0, 1, -1, 0]\n", - "offsets = [0, 0, strike_price_2 - strike_price_1, 0]\n", - "f_min = 0\n", - "f_max = strike_price_2 - strike_price_1\n", - "butterfly_objective = PwlObjective(\n", - " uncertainty_model.num_target_qubits, \n", - " uncertainty_model.low, \n", - " uncertainty_model.high,\n", - " breakpoints,\n", - " slopes,\n", - " offsets,\n", - " f_min,\n", - " f_max,\n", - " c_approx\n", - ")\n", - "\n", - "# construct circuit factory for payoff function\n", - "butterfly = UnivariateProblem(\n", - " uncertainty_model,\n", - " butterfly_objective\n", - ")" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# plot exact payoff function (evaluated on the grid of the uncertainty model)\n", - "x = uncertainty_model.values\n", - "def payoff(x):\n", - " if x <= strike_price_1:\n", - " return 0\n", - " elif x < strike_price_2:\n", - " return x - strike_price_1\n", - " elif x < strike_price_3:\n", - " return 2*strike_price_2 - strike_price_1 - x\n", - " else:\n", - " return 0\n", - "y = [payoff(x_) for x_ in x]\n", - "plt.plot(x, y, 'ro-')\n", - "plt.grid()\n", - "plt.title('Payoff Function', size=15)\n", - "plt.xlabel('Spot Price', size=15)\n", - "plt.ylabel('Payoff', size=15)\n", - "plt.xticks(x, size=15, rotation=90)\n", - "plt.yticks(size=15)\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "exact expected value:\t0.2598\n" - ] - } - ], - "source": [ - "# evaluate exact expected value (normalized to the [0, 1] interval)\n", - "exact_value = np.dot(uncertainty_model.probabilities, y)\n", - "print('exact expected value:\\t%.4f' % exact_value)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Evaluate Expected Payoff" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [], - "source": [ - "# set number of evaluation qubits (=log(samples))\n", - "m = 5\n", - "\n", - "# construct amplitude estimation \n", - "ae = AmplitudeEstimation(m, butterfly)" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [], - "source": [ - "# result = ae.run(quantum_instance=BasicAer.get_backend('qasm_simulator'), shots=100)\n", - "result = ae.run(quantum_instance=BasicAer.get_backend('statevector_simulator'))" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Exact value: \t0.2598\n", - "Estimated value:\t0.2290\n", - "Probability: \t0.7939\n" - ] - } - ], - "source": [ - "print('Exact value: \\t%.4f' % exact_value)\n", - "print('Estimated value:\\t%.4f' % result['estimation'])\n", - "print('Probability: \\t%.4f' % result['max_probability'])" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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rnZrtNPAmSVsA2xbTSzzxs9ZcbBoifX2ZLwFfyCX1S3oZ+I6k90TEwjrla4j09WVfB1wHMH78+Ojr66tf+5L6+/vpVFm9zO1U25Rz79hoedpBa7n8yQ3/XZd9vK/iGo0MPp7K6VY7NTvwU5LOkbQUeB34Q41XPQPAzjXSR1P7zKeem7L39+bKpkb565ebLd/MzDqo2XE4ZwLnAt8jnTn8E3Ax8DSwjOzSVB1LSPdq3iRpH2B7Bt97aSQK78+QguC4Qr5xwLqsjmZm1iXNBpxPAxcCl2XLt0bERcCBpIDxjgbbzwaOk7RjLm0S6fEHzd4rOi17fwwgItaQxgl9tJBvEvCIe6iZmXVXs/dw3gYsjIg3JL1OdrkqItZJ+g7wXdIZ0FCuIZ0l3SLpUmA/YDpwRb6rdHbJbl5EnJEtTwd2JA36XAF8EDgbuCUifpYr/2uk+ztXkcYJTcxexze5n2Zm1mHNnuH8Htgh+/wc8Fe5dbuQBnUOKSIGgKNIY3VuAy4CriSdNeVtxcbjeZaQxunMAO4ETge+mb3ny59POvM5GpgDfBg43bMMmJl1X7NnOA8B7yP96P+QNEPArsCfgM8D9zYqICIWAR9qkGdsYXkWaQBnQxFxK+nsxszMNiHNBpzpwN7Z50tIl9SmkM5s5gJf7FTFzMystzQVcCLiKeCp7PMa0rNwzhqGepmZWY9pZ+DnnwN7AS9GxAudq5KZmfWiVh4x/TlJvwaeBX4EPCfpeUn/u+O1MzOzntHsTAMXAFeTxtOcCIzP3mcD387Wm5mZDdLsJbXPA5dExFcL6Xdlc5t9njTzgJmZ2UaavaQ2iqGf6jmPGpN5mpmZQfMB51bg1CHWfQS4vb3qmJlZryrziOmJucXZwGWSxjL4EdMHAv/Y+SqamVkvKHMP53YGP0p6b+C4Gnm/T3oSp5mZ2UbKBJy3DXstzMys55V5xPSzVVTEzMx6W9MzDUjaitRB4AhgV+C/gQdJjwpYW29bMzPbfDUVcCTtAdwNHEx6wufLwOGk8TdPSDo2In7X6UqamdnI12y36CuAtwLvj4j9IuLwiNgPeH+WfkWnK2hmZr2h2YAzETgnIn6ST8yWv0ya5sbMzGyQZgPONsAfhlj3B+At7VXHzMx6VbMB51HgHEnb5xOz5XOy9WZmZoM020ttGnA/8GtJd5M6DexBGgQqoK+jtTMzs57R1BlORCwE3gFcB+wOHEMKONcA74iIJzpeQzMz6wmlz3AkbQ0cCvwqIs4dviqZmVkvauYM5w3gPuDdw1QXMzPrYaUDTkSsA34BjBm+6piZWa9qtpfaV4ALJB00HJUxM7Pe1WwvtfNJMwoslPQCqZda5DNExKEdqpuZmfWQZgPOz7OXmZlZU0oFHEmjSNPa/Bz4DXBPRLw8nBUzM7PeUuYR0/sB9wBjc8krJH0sIu4eroqZmVlvKdNp4DJgHfA3wHbAgcDjwLXDWC8zM+sxZQLO4cD5EfFQRLwWEYuBzwB/IWmv4a2emZn1ijIBZy/gl4W0Z0hzp+3Z8RqZmVlPKjsOJxpnMTMzG1rZbtFzJK2tkX5vMT0i9mi/WmZm1mvKBJyLhr0WZmbW8xoGnIhwwDEzs7Y1O5eamZlZSxxwzMysEg44ZmZWCQccMzOrhAOOmZlVwgHHzMwqUXnAkXSApHslrZL0oqSLJW3ZYJv3SZohaWm23VOSLpS0bSHfdElR43X88O6VmZk10uwD2NoiaRfSow4WAScB+wOXkwLf+XU2nZTlvRT4BXAw8LXs/SOFvMuBYoBZ3G7dzcysPZUGHOCzwCjg1IhYAcyVtBMwXdJlWVotl0bE73LL/ZJeA66VtG9EPJtbtzYiHh2e6puZWauqvqR2AjCnEFhmkYLQkUNtVAg26z2evXvuNjOzEaDqgDMOWJJPiIjngFXZumZ8gPRguKcK6TtLekXS65Iel3Rqy7U1M7OOUUR1Tx6Q9DpwdkRcVUh/HrghIs4rWc6ewM+AOyNiSi79E6QznoXADqQHxU0EPhIRtwxR1lRgKsCYMWMOmTVrVrO7VdPKlSvZYYcdOlJWL3M71fbkC8s3Wh4zCl5evWH5oL1HV1yjkcHHUzmdbKcJEyY8FhHjy+TtRsD5UkR8q5D+AnB9RHylRBlvIXU8+HPgkIgYqJNXwMPAqIh4T6Oyx48fHwsWLGiUrZT+/n76+vo6UlYvczvVNvbcOzZannbQWi5/csMt12XfOLHqKo0IPp7K6WQ7SSodcKq+pDYA7FwjfTTwaqONswByA3AgMLFesAGIFE1vAQ5u1PXazMyGV9W91JZQuFcjaR9gewr3doZwJak79TERUSb/en5iqZlZl1V9hjMbOE7Sjrm0ScBqYF69DSV9Gfgi8ImImF/my7IzolOAJyLijdaqbGZmnVD1Gc41wJnALZIuBfYDpgNX5LtKS1oKzIuIM7Ll04FLgOuBFyQdlivzmfXdpiXNA24mnS1tD3waOAw4eXh3y8zMGqk04ETEgKSjgKuB20j3ba4kBZ1ivfL3XI7N3qdkr7xPkgIRwFLg74G9SF2mfwqcGBGzO1F/MzNrXdVnOETEIuBDDfKMLSxPYXCgqbXdGW1UzczMhpFnizYzs0o44JiZWSUccMzMrBIOOGZmVgkHHDMzq4QDjpmZVcIBx8zMKuGAY2ZmlXDAMTOzSjjgmJlZJRxwzMysEg44ZmZWCQccMzOrhAOOmZlVwgHHzMwq4YBjZmaVcMAxM7NKOOCYmVklHHDMzKwSDjhmZlYJBxwzM6uEA46ZmVXCAcfMzCrhgGNmZpVwwDEzs0ps1e0KmFn3jT33joZ5ln3jxApqYr3MZzhmZlYJBxwzM6uEA46ZmVXCAcfMzCrhgGNmZpVwwDEzs0o44JiZWSUccMzMrBIOOGZmVgkHHDMzq4QDjpmZVcIBx8zMKuGAY2ZmlfBs0WYNNJpJ2bMom5XjMxwzM6uEA46ZmVWi8oAj6QBJ90paJelFSRdL2rLEdqMlzZA0IGm5pB9IemuNfCdJelLSa5IWSZo0PHtiZmbNqPQejqRdgHuARcBJwP7A5aTAd36DzW8E3gV8ClgHXArcCvxNrvwjgJuB7wBnAhOBmZIGIuLuju6MmbXMTxjdPFXdaeCzwCjg1IhYAcyVtBMwXdJlWdogkg4HjgOOjIgHsrQXgB9JOjoi7smyfhV4ICLOzJbvl3QgcAHggNMj/GNlNjJVHXBOAOYUAsss0tnKkcBtdbZ7eX2wAYiIH0v6VbbuHknbABNIZzZ5s4AZkkZHxPIO7YeZjQDuYbhpqTrgjAPuyydExHOSVmXrhgo444AlNdIXZ+sgXZ7buka+xaRLdu8EftJatZsz9tw7mHbQWqaU+Et8KLX+I3TqP89wnSH4zMM2F5081lv5f13m++uZdtBa+toqoTWKiOq+THodODsiriqkPw/cEBHnDbHdXOCPEXFyIf37wH4R8QFJfw3MB/4qIhbm8rwd+AVwXK37OJKmAlOzxXcBT7W8gxvbDXilQ2X1MrdTOW6nctxO5XSynfaNiN3LZOzGwM9aEU5DpLeyXXFZdbYnIq4Drmvw3U2TtCAixne63F7jdirH7VSO26mcbrVT1d2iB4Cda6SPBl5tYbudc9sN5NKKeWhQvpmZDbOqA84SNtxzAUDSPsD21L5HM+R2mfy9nWeA12vkG0fqRv10C/U1M7MOqTrgzAaOk7RjLm0SsBqY12C7PbNxNgBIGg/sl60jItYA9wMfLWw7CXikCz3UOn6Zrke5ncpxO5XjdiqnK+1UdaeBXUiDPn9O6gq9H3AFcFVEnJ/LtxSYFxFn5NLuIvU0+xIbBn7+NiKKAz/7gatJg0InZvmP98BPM7PuqvQMJyIGgKOALUldoC8CrgQuLGTdKsuTN5l0FvSvwA3AY8AphfLnA6cBRwNzgA8DpzvYmJl1X6VnOGZmtvnybNENeLLRxlppI0nvy9pnabbdU5IulLRtId90SVHjdfzw7lXntdhOY4fY/1k18o74YwlabqehjpOQ9OVcvuuHyFOrU9ImTdLbJV0r6QlJb0jqL7ld136b/AC2OjzZaGNttNGkLO+lpIG5BwNfy94/Usi7HCgGmMXt1r1KbR5LkO5FPpRb3mjQXi8cS9BWO30XuKuQdjJwDlnHopwlwCcLactaq3FXHUj6d34UeEsT23Xvtyki/BriBXyZNL5np1zaPwKr8mk1tjucNND0g7m0Q7O0o3Npc4D7CtveCczv9r5X0Ea710ibmrXRvrm06cAr3d7PLrbT2KxN/keD8kf8sdROOw1R1h3A4kLa9cCCbu9nh9pqi9znm4D+Ett09bfJl9TqG2qy0VGkyUbrbTdoslFg/WSj5CYb/bfCtrOAwyWNbr/6lWipjSLidzWSH8/e9+hc9TYZrR5LDfXQsQQdaidJuwLHADM7W71NR0Ssa2Gzrv42OeDUN2jS0Ih4jvTXVr1rvp2abHQkaLWNavkA6RS/OJ/dzpJekfS6pMclndpybbun3XaakV2nf0nSFZJG5db1yrEEnTueTiO1yaB7XcABklZIWiNpvqS2Av4I09XfJgec+nah9pQ4A9m6drZb/17MN1BYv6lrtY02ImlP4CvA/y38dbuUdEnlY6R7Oy8CN4/AoNNqO60B/gU4gzSk4Frgc2z8Q9orxxJ06HgiDaP4aUQUZxh5HJgG/E/g46ThF3MlHdpCXUeirv42udNAY5vUZKObqFbbKGWU3kI6fV8J/MNGBUd8v5D3NuBh0kP1bmmlsl3UdDtFxEvAF3JJ/ZJeBr4j6T2Rmxm9Rjkj8ViC9o+nvUiX384ZVHDEtwp57yB1UDiP1Mlgc9C13yaf4dTnyUYba7WNAJAk0kDeA4GJkQYHDynS3ctbgIPLdE/fhLTVTgU3Ze/vzZVNjfJH2rEEnWmnj5F+HG9slDEiVpNuhr+3Ud4e0dXfJgec+jzZaGOtttF6V5K6v54UEWXyrzfS/mpvt53yovDeK8cSdKadJpN6U/26ie8dacdTq7r62+SAU9/mNNloq1ptI7IBeV8EPhFpWqKGsjOiU4AnIuKN1qrcFS23Uw2nZe+PQU8dS9BmO0kaCxxGyd5pWeeLE8jacjPQ3d+mbvcl35RfpJtjLwFzSfOzTSXdZ/h6Id9S4HuFtLuAXwKnkq4NPwU8WMhzBLAWuAroAy4j/QVxbLf3fbjbCDid9FflDNIPRP61ey7fPNLAs2NJgebOrI0+3O19r6idppMGPp6abXcx6cf35l47ltppp1z6uaS/zmuN8xoNPAh8htQBYxJp0OQaYHy3972FttqO9MfHacAjwH/llrcbqp26+dvU9Ubb1F/AAcB92X/yl0ij4bcs5FkGXF9I2zn7MX0VWAH8ENitRvknk2bPXkM6pZ3c7X2uoo1IA/BiiNeUXL7vZf85VgN/zH4wTuj2PlfYTpOBBaTZFv6U/YBcDGzTi8dSq+2US18I3DVEuduS7v/9Omuj5dmP72Hd3ucW22lsnf9DY4dqp27+NnnyTjMzq4Tv4ZiZWSUccMzMrBIOOGZmVgkHHDMzq4QDjpmZVcIBx8zMKuGAY2ZmlXDAMTOzSvx/yX3D0Td3Kb0AAAAASUVORK5CYII=\n", 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# plot estimated values for \"a\"\n", - "plt.bar(result['values'], result['probabilities'], width=0.5/len(result['probabilities']))\n", - "plt.xticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", - "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", - "plt.title('\"a\" Value', size=15)\n", - "plt.ylabel('Probability', size=15)\n", - "plt.ylim((0,1))\n", - "plt.grid()\n", - "plt.show()\n", - "\n", - "# plot estimated values for option price (after re-scaling and reversing the c_approx-transformation)\n", - "plt.bar(result['mapped_values'], result['probabilities'], width=1/len(result['probabilities']))\n", - "plt.plot([exact_value, exact_value], [0,1], 'r--', linewidth=2)\n", - "plt.xticks(size=15)\n", - "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", - "plt.title('Estimated Option Price', size=15)\n", - "plt.ylabel('Probability', size=15)\n", - "plt.ylim((0,1))\n", - "plt.grid()\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "qiskit_master", - "language": "python", - "name": "qiskit_master" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/finance/simulation/short_butterfly.ipynb b/community/finance/simulation/short_butterfly.ipynb deleted file mode 100644 index 227ec7e2c..000000000 --- a/community/finance/simulation/short_butterfly.ipynb +++ /dev/null @@ -1,397 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# _*Pricing Short Butterfly Options*_ \n", - "\n", - "The latest version of this notebook is available on https://github.com/Qiskit/qiskit-tutorials.\n", - "\n", - "***\n", - "### Contributors\n", - "Stefan Woerner[1], Daniel Egger[1]\n", - "### Affliation\n", - "- [1]IBMQ" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Introduction\n", - "
\n", - "Suppose a short butterfly option with strike prices $K_1 < K_2 < K_3$, with $K_2 - K_1 = K_3 - K_2$ and an underlying asset whose spot price at maturity $S_T$ follows a given random distribution.\n", - "The corresponding payoff function is defined as:\n", - "
\n", - "
\n", - "$$ F(S_T) = \n", - "\\begin{cases}\n", - "0 ,& S_T < K_1 \\\\\n", - "K_1 - S_T ,& K_1 \\leq S_T < K_2 \\\\\n", - "S_T - 2K_2 + K_1 ,& K_2 \\leq S_T < K_3 \\\\\n", - "0 ,& S_T \\geq K_3. \n", - "\\end{cases}$$\n", - "
\n", - "In the following, a quantum algorithm based on amplitude estimation is used to estimate the expected payoff, i.e., the fair price before discounting, for the option:\n", - "
\n", - "
\n", - "$$\\mathbb{E}\\left[ F(S_T) \\right].$$\n", - "
\n", - "The approximation of the objective function is explained in detail in the following paper:
\n", - "Quantum Risk Analysis. Woerner, Egger. 2018." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import matplotlib.pyplot as plt\n", - "%matplotlib inline\n", - "import numpy as np\n", - "\n", - "from qiskit import BasicAer\n", - "from qiskit.aqua.algorithms import AmplitudeEstimation\n", - "from qiskit.aqua.components.uncertainty_models import LogNormalDistribution\n", - "from qiskit.aqua.components.uncertainty_problems import UnivariateProblem\n", - "from qiskit.aqua.components.uncertainty_problems import UnivariatePiecewiseLinearObjective as PwlObjective" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Uncertainty Model\n", - "\n", - "We construct a circuit factory to load a log-normal random distribution into a quantum state.\n", - "The distribution is truncated to a given interval $[low, high]$ and discretized using $2^n$ grid points, where $n$ denotes the number of qubits used.\n", - "The unitary operator corresponding to the circuit factory implements the following: \n", - "$$\\big|0\\rangle_{n} \\mapsto \\big|\\psi\\rangle_{n} = \\sum_{i=0}^{2^n-1} \\sqrt{p_i}\\big|i\\rangle_{n},$$\n", - "where $p_i$ denote the probabilities corresponding to the truncated and discretized distribution and where $i$ is mapped to the right interval using the affine map:\n", - "$$ \\{0, \\ldots, 2^n-1\\} \\ni i \\mapsto \\frac{high - low}{2^n - 1} * i + low \\in [low, high].$$" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "# number of qubits to represent the uncertainty\n", - "num_uncertainty_qubits = 3\n", - "\n", - "# parameters for considered random distribution\n", - "S = 2.0 # initial spot price\n", - "vol = 0.4 # volatility of 40%\n", - "r = 0.05 # annual interest rate of 4%\n", - "T = 40 / 365 # 40 days to maturity\n", - "\n", - "# resulting parameters for log-normal distribution\n", - "mu = ((r - 0.5 * vol**2) * T + np.log(S))\n", - "sigma = vol * np.sqrt(T)\n", - "mean = np.exp(mu + sigma**2/2)\n", - "variance = (np.exp(sigma**2) - 1) * np.exp(2*mu + sigma**2)\n", - "stddev = np.sqrt(variance)\n", - "\n", - "# lowest and highest value considered for the spot price; in between, an equidistant discretization is considered.\n", - "low = np.maximum(0, mean - 3*stddev)\n", - "high = mean + 3*stddev\n", - "\n", - "# construct circuit factory for uncertainty model\n", - "uncertainty_model = LogNormalDistribution(num_uncertainty_qubits, mu=mu, sigma=sigma, low=low, high=high)" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# plot probability distribution\n", - "x = uncertainty_model.values\n", - "y = uncertainty_model.probabilities\n", - "plt.bar(x, y, width=0.2)\n", - "plt.xticks(x, size=15, rotation=90)\n", - "plt.yticks(size=15)\n", - "plt.grid()\n", - "plt.xlabel('Spot Price at Maturity $S_T$ (\\$)', size=15)\n", - "plt.ylabel('Probability ($\\%$)', size=15)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Payoff Function\n", - "\n", - "The payoff function equals zero as long as the spot price at maturity $S_T$ is less than the strike price $K_1$, then increases linearly, and is bounded by $K_2$.\n", - "The implementation uses two comparators, that flip an ancilla qubit each from $\\big|0\\rangle$ to $\\big|1\\rangle$ if $S_T \\geq K_1$ and $S_T \\leq K_2, and these ancillas are used to control the linear part of the payoff function.\n", - "\n", - "The linear part itself is then approximated as follows.\n", - "We exploit the fact that $\\sin^2(y + \\pi/4) \\approx y + 1/2$ for small $|y|$.\n", - "Thus, for a given approximation scaling factor $c_{approx} \\in [0, 1]$ and $x \\in [0, 1]$ we consider\n", - "$$ \\sin^2( \\pi/2 * c_{approx} * ( x - 1/2 ) + \\pi/4) \\approx \\pi/2 * c_{approx} * ( x - 1/2 ) + 1/2 $$ for small $c_{approx}$.\n", - "\n", - "We can easily construct an operator that acts as \n", - "$$\\big|x\\rangle \\big|0\\rangle \\mapsto \\big|x\\rangle \\left( \\cos(a*x+b) \\big|0\\rangle + \\sin(a*x+b) \\big|1\\rangle \\right),$$\n", - "using controlled Y-rotations.\n", - "\n", - "Eventually, we are interested in the probability of measuring $\\big|1\\rangle$ in the last qubit, which corresponds to\n", - "$\\sin^2(a*x+b)$.\n", - "Together with the approximation above, this allows to approximate the values of interest.\n", - "The smaller we choose $c_{approx}$, the better the approximation.\n", - "However, since we are then estimating a property scaled by $c_{approx}$, the number of evaluation qubits $m$ needs to be adjusted accordingly.\n", - "\n", - "For more details on the approximation, we refer to:\n", - "Quantum Risk Analysis. Woerner, Egger. 2018." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [], - "source": [ - "# set the strike price (should be within the low and the high value of the uncertainty)\n", - "strike_price_1 = 1.438\n", - "strike_price_2 = 1.896\n", - "strike_price_3 = 2*strike_price_2 - strike_price_1\n", - "\n", - "# set the approximation scaling for the payoff function\n", - "c_approx = 0.25\n", - "\n", - "# setup piecewise linear objective fcuntion\n", - "breakpoints = [uncertainty_model.low, strike_price_1, strike_price_2, strike_price_3]\n", - "slopes = [0, -1, 1, 0]\n", - "offsets = [1, 1, 1+strike_price_1 - strike_price_2, 1]\n", - "f_min = 0\n", - "f_max = strike_price_2 - strike_price_1\n", - "butterfly_objective = PwlObjective(\n", - " uncertainty_model.num_target_qubits, \n", - " uncertainty_model.low, \n", - " uncertainty_model.high,\n", - " breakpoints,\n", - " slopes,\n", - " offsets,\n", - " f_min,\n", - " f_max,\n", - " c_approx\n", - ")\n", - "\n", - "# construct circuit factory for payoff function\n", - "butterfly = UnivariateProblem(\n", - " uncertainty_model,\n", - " butterfly_objective\n", - ")" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# plot exact payoff function (evaluated on the grid of the uncertainty model)\n", - "x = uncertainty_model.values\n", - "def payoff(x):\n", - " if x <= strike_price_1:\n", - " return 1\n", - " elif x < strike_price_2:\n", - " return 1+strike_price_1 - x\n", - " elif x < strike_price_3:\n", - " return 1+x - 2*strike_price_2 + strike_price_1\n", - " else:\n", - " return 1\n", - "y = [payoff(x_) for x_ in x]\n", - "plt.plot(x, y, 'ro-')\n", - "plt.grid()\n", - "plt.title('Payoff Function', size=15)\n", - "plt.xlabel('Spot Price', size=15)\n", - "plt.ylabel('Payoff', size=15)\n", - "plt.xticks(x, size=15, rotation=90)\n", - "plt.yticks(size=15)\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "exact expected value:\t0.7402\n" - ] - } - ], - "source": [ - "# evaluate exact expected value (normalized to the [0, 1] interval)\n", - "exact_value = np.dot(uncertainty_model.probabilities, y)\n", - "print('exact expected value:\\t%.4f' % exact_value)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Evaluate Expected Payoff" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [], - "source": [ - "# set number of evaluation qubits (=log(samples))\n", - "m = 6\n", - "\n", - "# construct amplitude estimation \n", - "ae = AmplitudeEstimation(m, butterfly)" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [], - "source": [ - "# result = ae.run(quantum_instance=BasicAer.get_backend('qasm_simulator'), shots=100)\n", - "result = ae.run(quantum_instance=BasicAer.get_backend('statevector_simulator'))" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Exact value: \t0.7402\n", - "Estimated value:\t0.6413\n", - "Probability: \t0.4953\n" - ] - } - ], - "source": [ - "print('Exact value: \\t%.4f' % exact_value)\n", - "print('Estimated value:\\t%.4f' % result['estimation'])\n", - "print('Probability: \\t%.4f' % result['max_probability'])" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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\n", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# plot estimated values for \"a\"\n", - "plt.bar(result['values'], result['probabilities'], width=0.5/len(result['probabilities']))\n", - "plt.xticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", - "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", - "plt.title('\"a\" Value', size=15)\n", - "plt.ylabel('Probability', size=15)\n", - "plt.ylim((0,1))\n", - "plt.grid()\n", - "plt.show()\n", - "\n", - "# plot estimated values for option price (after re-scaling and reversing the c_approx-transformation)\n", - "plt.bar(result['mapped_values'], result['probabilities'], width=1/len(result['probabilities']))\n", - "plt.plot([exact_value, exact_value], [0,1], 'r--', linewidth=2)\n", - "plt.xticks(size=15)\n", - "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", - "plt.title('Estimated Option Price', size=15)\n", - "plt.ylabel('Probability', size=15)\n", - "plt.ylim((0,1))\n", - "plt.grid()\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "qiskit_master", - "language": "python", - "name": "qiskit_master" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/optimization/3-Coloring Oracle via Reduction to SAT.ipynb b/community/optimization/3-Coloring Oracle via Reduction to SAT.ipynb deleted file mode 100644 index 3ff37dcf9..000000000 --- a/community/optimization/3-Coloring Oracle via Reduction to SAT.ipynb +++ /dev/null @@ -1,225 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Constructing Quantum Oracles for 3-Coloring Problems via NP-Reduction\n", - "\n", - "In this notebook, we demonstrate how to easily construct quantum oracles for [3-Coloring problems](https://en.wikipedia.org/wiki/Graph_coloring) using Qiskit Aqua via simple NP-Reduction to [SAT problems](https://en.wikipedia.org/wiki/Boolean_satisfiability_problem).\n", - "\n", - "3-Coloring is the decision problem of determining whether a graph's vertices can be colored using only 3 different colors s.t. no neighboring vertices share the same color. SAT is also a decision problem where we want to see if an \n", - "given conjunctive normal form (CNF) has a satisfying assignment.\n", - "\n", - "Aqua already provides an `LogicExpressionOracle` class capable of building Quantum Oracle circuits from arbitrary logic expressions, with support for the [DIMACS CNF format](https://www.satcompetition.org/2009/format-benchmarks2009.html). So, to take advantage of that, we in this notebook aim to reduce 3-coloring problems to SAT problems, and then directly use the `LogicExpressionOracle` class to build the Oracle circuit.\n", - "\n", - "For 3-coloring problem instances, we work with the [DIMACS graph coloring format](https://mat.tepper.cmu.edu/COLOR/instances.html), which basically indicates the number of vertices and edges on the `'p edge'` line, followed by the `'e'` lines listing all edges (vertex pairs). For example we can have the following toy instance, and easily parse it." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The input 3-coloring instance has 3 vertices and 3 edges: [[1, 2], [1, 3], [2, 3]].\n" - ] - } - ], - "source": [ - "three_coloring_instance = '''\n", - "c This is an example DIMACS 3-coloring file\n", - "p edge 3 3\n", - "e 1 2\n", - "e 1 3\n", - "e 2 3\n", - "'''\n", - "\n", - "import itertools\n", - "\n", - "def parse_3_coloring_instance(instance):\n", - " ls = [\n", - " l.strip() for l in instance.split('\\n')\n", - " if len(l) > 0 and not l.strip()[0] == 'c'\n", - " ]\n", - " headers = [l for l in ls if l[0] == 'p']\n", - " if len(headers) == 1:\n", - " p, sig, nv, ne = headers[0].split()\n", - " assert p == 'p' and sig == 'edge'\n", - " elif len(headers) > 1:\n", - " raise RuntimeError('Invalid input format for 3-Coloring.')\n", - " h_nv, h_ne = int(nv), int(ne)\n", - " edges = [[int(v) for v in l.split()[1:]] for l in ls if l[0] == 'e']\n", - " nv = len(set(list(itertools.chain.from_iterable(edges))))\n", - " ne = len(edges)\n", - " if not h_nv == nv:\n", - " print((\n", - " 'Warning: inaccurate vertex count {} in header. '\n", - " 'Actual vertex count is {}.'\n", - " ).format(h_nv, nv))\n", - " if not h_ne == ne:\n", - " print((\n", - " 'Warning: inaccurate edge count {} in header. '\n", - " 'Actual edge count is {}.'\n", - " ).format(h_ne, ne))\n", - "\n", - " return nv, ne, edges\n", - "\n", - "nv, ne, edges = parse_3_coloring_instance(three_coloring_instance)\n", - "\n", - "print('The input 3-coloring instance has {} vertices and {} edges: {}.'.format(nv, ne, edges))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "For any 3-coloring problem instance, we can use the following simple strategy to reduce it to a SAT problem:\n", - "\n", - "- For each vertex $v$, we create three boolean variables $v_r$, $v_g$, and $v_b$, corresponding to the vertex $v$ being of color red, green, and blue, respectively.\n", - "- For each vertex $v$, we then have the constraint that it needs to be of one and only one color. Therefore, $v_r \\vee v_g \\vee v_b = True$, and $v_i \\wedge v_j = False$ for $i,j \\in \\{r,g,b\\}, i \\ne j$.\n", - "- For each edge $(v, t)$, we have the constraint that they cannot both be of the same color. Therefore, $v_i \\wedge t_i = False$ for $i \\in \\{r, g, b\\}$.\n", - "\n", - "With this simple strategy and the help of the [De Morgan's Law](https://en.wikipedia.org/wiki/De_Morgan%27s_laws), we can carry out the reduction as follows." - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The input 3-Coloring instance can be reduced to the following SAT instance:\n", - "\n", - "p cnf 9 21\n", - "1 2 3 0\n", - "-1 -2 0\n", - "-1 -3 0\n", - "-2 -3 0\n", - "4 5 6 0\n", - "-4 -5 0\n", - "-4 -6 0\n", - "-5 -6 0\n", - "7 8 9 0\n", - "-7 -8 0\n", - "-7 -9 0\n", - "-8 -9 0\n", - "-1 -4 0\n", - "-2 -5 0\n", - "-3 -6 0\n", - "-1 -7 0\n", - "-2 -8 0\n", - "-3 -9 0\n", - "-4 -7 0\n", - "-5 -8 0\n", - "-6 -9 0\n" - ] - } - ], - "source": [ - "def reduce_to_sat(nv, ne, edges):\n", - "\n", - " def _get_vertex_rgb(v):\n", - " return 3 * v - 2, 3 * v - 1, 3 * v\n", - "\n", - " def _get_vertex_constraints(v):\n", - " r, g, b = _get_vertex_rgb(v)\n", - " return [\n", - " '{0} {1} {2} 0'.format(r, g, b),\n", - " '{} {} 0'.format(-r, -g),\n", - " '{} {} 0'.format(-r, -b),\n", - " '{} {} 0'.format(-g, -b)\n", - " ]\n", - "\n", - " def _get_edge_constraints(v1, v2):\n", - " r1, g1, b1 = _get_vertex_rgb(v1)\n", - " r2, g2, b2 = _get_vertex_rgb(v2)\n", - " return [\n", - " '{0} {1} 0'.format(-r1, -r2),\n", - " '{0} {1} 0'.format(-g1, -g2),\n", - " '{0} {1} 0'.format(-b1, -b2)\n", - " ]\n", - "\n", - " buf = list()\n", - " buf.append('p cnf {0} {1}'.format(nv * 3, nv * 4 + ne * 3))\n", - " buf.extend(itertools.chain.from_iterable([\n", - " _get_vertex_constraints(v)\n", - " for v in range(1, nv + 1)])\n", - " )\n", - " buf.extend(itertools.chain.from_iterable([\n", - " _get_edge_constraints(v1, v2)\n", - " for v1, v2 in edges])\n", - " )\n", - " return '\\n'.join(buf)\n", - "\n", - "sat_instance_cnf = reduce_to_sat(nv, ne, edges)\n", - "print('The input 3-Coloring instance can be reduced to the following SAT instance:\\n\\n{}'.format(sat_instance_cnf))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we have successfully reduced the 3-Coloring problem instance to its equivalent SAT instance, we can go ahead using Aqua's `LogicExpressionOracle` to build the oracle and construct the quantum circuit." - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "from qiskit.aqua.components.oracles import LogicExpressionOracle\n", - "\n", - "oracle = LogicExpressionOracle(expression=sat_instance_cnf)\n", - "oracle.circuit.draw(output='mpl', scale=0.3)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.2" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/community/optimization/3sat2-3.cnf b/community/optimization/3sat2-3.cnf deleted file mode 100644 index 2d2944119..000000000 --- a/community/optimization/3sat2-3.cnf +++ /dev/null @@ -1,5 +0,0 @@ -c This is an example DIMACS 3-sat file with unique satisfying solution: 1 2 0 -p cnf 2 3 -1 2 0 -1 -2 0 --1 2 0 diff --git a/community/optimization/README.md b/community/optimization/README.md deleted file mode 100644 index 5106864fd..000000000 --- a/community/optimization/README.md +++ /dev/null @@ -1,19 +0,0 @@ -# Qiskit Aqua Optimization Tutorials, Samples and Input Files - -Qiskit Aqua Optimization is a set of tools, algorithms and software for use with quantum computers to -carry out research and investigate how to take advantage of quantum computing power to solve optimization -problems. - -Qiskit Aqua Optimization translates optimization-specific problems into inputs -for a quantum algorithm residing in Qiskit Aqua, which in turn uses [Qiskit](https://www.qiskit.org/) for the relevant -quantum computation. - -This folder contains some Jupyter Notebook examples. There are Python code files too. - -For more detail see the main [index](../aqua/index.ipynb#optimization) - -## Input files - -The folder [input_files](input_files) contains a number of example JSON input files that can be loaded -and run by the Qiskit Aqua [GUI](https://github.com/Qiskit/aqua/README.md#gui) or by the Qiskit Aqua -[command line](https://github.com/Qiskit/aqua/README.md#command-line) tool. diff --git a/community/optimization/clique.ipynb b/community/optimization/clique.ipynb deleted file mode 100644 index 802bbeb8e..000000000 --- a/community/optimization/clique.ipynb +++ /dev/null @@ -1,319 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## _*Using Qiskit Aqua for clique problems*_\n", - "\n", - "This Qiskit Aqua Optimization notebook demonstrates how to use the VQE quantum algorithm to compute the clique of a given graph. \n", - "\n", - "The problem is defined as follows. A clique in a graph $G$ is a complete subgraph of $G$. That is, it is a subset $K$ of the vertices such that every two vertices in $K$ are the two endpoints of an edge in $G$. A maximal clique is a clique to which no more vertices can be added. A maximum clique is a clique that includes the largest possible number of vertices. \n", - "\n", - "We will go through three examples to show:\n", - "1. How to run the optimization using the declarative approach\n", - "2. How to run the optimization using the programmatic approach\n", - "3. How how to run the optimization with the VQE.\n", - "\n", - "Note that the solution may not be unique." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### The problem and a brute-force method." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "\n", - "from qiskit import BasicAer\n", - "\n", - "from qiskit.aqua import run_algorithm\n", - "from qiskit.aqua.input import EnergyInput\n", - "from qiskit.aqua.translators.ising import clique\n", - "from qiskit.aqua.algorithms import ExactEigensolver" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "first, let us have a look at the graph, which is in the adjacent matrix form." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[ 0. 4. 5. 3. -5.]\n", - " [ 4. 0. 7. 0. 6.]\n", - " [ 5. 7. 0. -4. 0.]\n", - " [ 3. 0. -4. 0. 8.]\n", - " [-5. 6. 0. 8. 0.]]\n" - ] - } - ], - "source": [ - "K = 3 # K means the size of the clique\n", - "np.random.seed(100)\n", - "num_nodes = 5\n", - "w = clique.random_graph(num_nodes, edge_prob=0.8, weight_range=10)\n", - "print(w) " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let us try a brute-force method. Basically, we exhaustively try all the binary assignments. In each binary assignment, the entry of a vertex is either 0 (meaning the vertex is not in the clique) or 1 (meaning the vertex is in the clique). We print the binary assignment that satisfies the definition of the clique (Note the size is specified as K)." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Solution is [1, 0, 0, 1, 1]\n" - ] - } - ], - "source": [ - "def brute_force():\n", - " # brute-force way: try every possible assignment!\n", - " def bitfield(n, L):\n", - " result = np.binary_repr(n, L)\n", - " return [int(digit) for digit in result]\n", - "\n", - " L = num_nodes # length of the bitstring that represents the assignment\n", - " max = 2**L\n", - " has_sol = False\n", - " for i in range(max):\n", - " cur = bitfield(i, L)\n", - " cur_v = clique.satisfy_or_not(np.array(cur), w, K)\n", - " if cur_v:\n", - " has_sol = True\n", - " break\n", - " return has_sol, cur\n", - "\n", - "has_sol, sol = brute_force()\n", - "if has_sol:\n", - " print(\"Solution is \", sol)\n", - "else:\n", - " print(\"No solution found for K=\", K)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Part I: Run the optimization using the declarative approach\n", - "\n", - "Here the steps are:\n", - "* Create the qubit operator i.e. Ising Hamiltonian, using clique ising translator\n", - "* Create an EnergyInput object and a dictionary describing the algorithm and the components for Aqua to solve the problem\n", - "* Run the algorithm and get the result\n", - "* Use the result with the clique object to determine a solution" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Solution is [1. 0. 1. 1. 0.]\n" - ] - } - ], - "source": [ - "qubit_op, offset = clique.get_clique_qubitops(w, K)\n", - "\n", - "algo_input = EnergyInput(qubit_op)\n", - "params = {\n", - " 'problem': {'name': 'ising'},\n", - " 'algorithm': {'name': 'ExactEigensolver'}\n", - "}\n", - "result = run_algorithm(params, algo_input)\n", - "\n", - "x = clique.sample_most_likely(len(w), result['eigvecs'][0])\n", - "ising_sol = clique.get_graph_solution(x)\n", - "if clique.satisfy_or_not(ising_sol, w, K):\n", - " print(\"Solution is\", ising_sol)\n", - "else:\n", - " print(\"No solution found for K=\", K)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Part II: Run the optimization using the programmatic approach\n", - "\n", - "The main difference here is running the Aqua algorithm. Here we directly construct the algorithm and then run() it to get the result. The post computation on the result is identical." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Solution is [1. 0. 1. 1. 0.]\n" - ] - } - ], - "source": [ - "# We will use the qubit_op and offset from above and not re-compute them here\n", - "\n", - "algo = ExactEigensolver(qubit_op)\n", - "result = algo.run()\n", - "\n", - "x = clique.sample_most_likely(len(w), result['eigvecs'][0])\n", - "ising_sol = clique.get_graph_solution(x)\n", - "if clique.satisfy_or_not(ising_sol, w, K):\n", - " print(\"Solution is\", ising_sol)\n", - "else:\n", - " print(\"No solution found for K=\", K) " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Part III: Run the optimization with the VQE\n", - "\n", - "##### Declarative\n", - "\n", - "We reuse the EnergyInput object we created above. VQE algorithm needs an optimizer and a variational form. Then also we need a quantum backend on which the algorithm will run." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Solution is [1. 0. 1. 1. 0.]\n" - ] - } - ], - "source": [ - "params = {\n", - " 'problem': {'name': 'ising', 'random_seed': 10598},\n", - " 'algorithm': {'name': 'VQE'},\n", - " 'optimizer': {'name': 'COBYLA'},\n", - " 'variational_form': {'name': 'RY', 'depth': 5, 'entanglement': 'linear'}\n", - "}\n", - "backend = BasicAer.get_backend('statevector_simulator')\n", - "result = run_algorithm(params, algo_input, backend=backend)\n", - "\n", - "x = clique.sample_most_likely(len(w), result['eigvecs'][0])\n", - "ising_sol = clique.get_graph_solution(x)\n", - "\n", - "if clique.satisfy_or_not(ising_sol, w, K):\n", - " print(\"Solution is\", ising_sol)\n", - "else:\n", - " print(\"No solution found for K=\", K)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Programmatic\n", - "\n", - "We can create the objects directly ourselves too and run VQE for the result" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Solution is [1. 0. 1. 1. 0.]\n" - ] - } - ], - "source": [ - "from qiskit.aqua import aqua_globals\n", - "from qiskit.aqua.algorithms import VQE\n", - "from qiskit.aqua.components.optimizers import COBYLA\n", - "from qiskit.aqua.components.variational_forms import RY\n", - "\n", - "aqua_globals.random_seed = 10598\n", - "\n", - "optimizer = COBYLA()\n", - "var_form = RY(qubit_op.num_qubits, depth=5, entanglement='linear')\n", - "vqe = VQE(qubit_op, var_form, optimizer)\n", - "\n", - "backend = BasicAer.get_backend('statevector_simulator')\n", - "result = vqe.run(backend)\n", - "\n", - "x = clique.sample_most_likely(len(w), result['eigvecs'][0])\n", - "ising_sol = clique.get_graph_solution(x)\n", - "\n", - "if clique.satisfy_or_not(ising_sol, w, K):\n", - " print(\"Solution is\", ising_sol)\n", - "else:\n", - " print(\"No solution found for K=\", K)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/community/optimization/exact_cover.ipynb b/community/optimization/exact_cover.ipynb deleted file mode 100644 index 172b6110a..000000000 --- a/community/optimization/exact_cover.ipynb +++ /dev/null @@ -1,299 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## _*Using Qiskit Aqua for exact cover problems*_\n", - "\n", - "In mathematics, given a collection $S$ of subsets of a set $X$.\n", - "An exact cover is a subcollection $S_{ec} \\subseteq S$ such that each element in $X$ is contained in exactly one subset $\\in S_{ec}$. \n", - "\n", - "We will go through three examples to show:\n", - "1. How to run the optimization using the declarative approach\n", - "2. How to run the optimization using the programmatic approach\n", - "3. How how to run the optimization with the VQE." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### The problem and the brute-force method.\n", - "\n", - "First, let us take a look at the list of subsets." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[2, 3, 4], [1, 2], [3, 4], [1, 2, 3]]\n" - ] - } - ], - "source": [ - "import numpy as np\n", - "import json\n", - "\n", - "from qiskit import BasicAer\n", - "from qiskit.aqua import run_algorithm\n", - "from qiskit.aqua.input import EnergyInput\n", - "from qiskit.aqua.translators.ising import exact_cover\n", - "from qiskit.aqua.algorithms import ExactEigensolver\n", - "\n", - "input_file = 'sample.exactcover'\n", - "with open(input_file) as f:\n", - " list_of_subsets = json.load(f)\n", - " print(list_of_subsets)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Then we apply the brute-force method. Basically, we exhaustively try all the binary assignments. In each binary assignment, the entry of a subset is either 0 (meaning the subset is not in the cover) or 1 (meaning the subset is in the cover). We print the binary assignment that satisfies the definition of the exact cover." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Solution is [0, 1, 1, 0]\n" - ] - } - ], - "source": [ - "def brute_force():\n", - " # brute-force way: try every possible assignment!\n", - " has_sol = False\n", - "\n", - " def bitfield(n, L):\n", - " result = np.binary_repr(n, L)\n", - " return [int(digit) for digit in result] # [2:] to chop off the \"0b\" part\n", - "\n", - " L = len(list_of_subsets)\n", - " max = 2**L\n", - " for i in range(max):\n", - " cur = bitfield(i, L)\n", - " cur_v = exact_cover.check_solution_satisfiability(cur, list_of_subsets)\n", - " if cur_v:\n", - " has_sol = True\n", - " break\n", - " return has_sol, cur\n", - "\n", - "has_sol, cur = brute_force()\n", - "if has_sol:\n", - " print(\"Solution is\", cur)\n", - "else:\n", - " print(\"No solution is found\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Part I: Run the optimization using the declarative approach\n", - "\n", - "Here the steps are:\n", - "* Create the qubit operator i.e. Ising Hamiltonian, using `exact_cover` ising translator\n", - "* Create an EnergyInput object and a dictionary describing the algorithm and the components for Aqua to solve the problem\n", - "* Run the algorithm and get the result\n", - "* Use the result with the `exact_cover` object to determine a solution" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Solution is [0. 1. 1. 0.]\n" - ] - } - ], - "source": [ - "qubit_op, offset = exact_cover.get_exact_cover_qubitops(list_of_subsets)\n", - "algo_input = EnergyInput(qubit_op)\n", - "\n", - "params = {\n", - " 'problem': {'name': 'ising'},\n", - " 'algorithm': {'name': 'ExactEigensolver'}\n", - "}\n", - "result = run_algorithm(params, algo_input)\n", - "\n", - "x = exact_cover.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", - "ising_sol = exact_cover.get_solution(x)\n", - "np.testing.assert_array_equal(ising_sol, [0, 1, 1, 0])\n", - "if exact_cover.check_solution_satisfiability(ising_sol, list_of_subsets):\n", - " print(\"Solution is\", ising_sol)\n", - "else:\n", - " print(\"No solution is found\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Part II: Run the optimization using the programmatic approach\n", - "\n", - "The main difference here is running the Aqua algorithm. Here we directly construct the algorithm and then run() it to get the result. The post computation on the result is identical." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Solution is [0. 1. 1. 0.]\n" - ] - } - ], - "source": [ - "algo = ExactEigensolver(algo_input.qubit_op, k=1, aux_operators=[])\n", - "result = algo.run()\n", - "\n", - "x = exact_cover.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", - "ising_sol = exact_cover.get_solution(x)\n", - "np.testing.assert_array_equal(ising_sol, [0, 1, 1, 0])\n", - "\n", - "if exact_cover.check_solution_satisfiability(ising_sol, list_of_subsets):\n", - " print(\"Solution is\", ising_sol)\n", - "else:\n", - " print(\"No solution is found\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Part III: Run the optimization with the VQE\n", - "\n", - "##### Declarative\n", - "\n", - "We reuse the EnergyInput object we created above. VQE algorithm needs an optimizer and a variational form. Then also we need a quantum backend on which the algorithm will run." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Solution is [0. 1. 1. 0.]\n" - ] - } - ], - "source": [ - "params = {\n", - " 'problem': {'name': 'ising', 'random_seed': 10598},\n", - " 'algorithm': {'name': 'VQE'},\n", - " 'optimizer': {'name': 'COBYLA'},\n", - " 'variational_form': {'name': 'RYRZ', 'depth': 5}\n", - "}\n", - "backend = BasicAer.get_backend('statevector_simulator')\n", - "result = run_algorithm(params, algo_input, backend=backend)\n", - "\n", - "x = exact_cover.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", - "ising_sol = exact_cover.get_solution(x)\n", - "if exact_cover.check_solution_satisfiability(ising_sol, list_of_subsets):\n", - " print(\"Solution is\", ising_sol)\n", - "else:\n", - " print(\"No solution is found\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Programmatic\n", - "\n", - "We can create the objects directly ourselves too and run VQE for the result" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Solution is [0. 1. 1. 0.]\n" - ] - } - ], - "source": [ - "from qiskit.aqua import aqua_globals\n", - "from qiskit.aqua.algorithms import VQE\n", - "from qiskit.aqua.components.optimizers import COBYLA\n", - "from qiskit.aqua.components.variational_forms import RY\n", - "\n", - "aqua_globals.random_seed = 10598\n", - "\n", - "optimizer = COBYLA()\n", - "var_form = RY(qubit_op.num_qubits, depth=5, entanglement='linear')\n", - "vqe = VQE(qubit_op, var_form, optimizer)\n", - "\n", - "backend = BasicAer.get_backend('statevector_simulator')\n", - "result = vqe.run(backend)\n", - "\n", - "x = exact_cover.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", - "ising_sol = exact_cover.get_solution(x)\n", - "if exact_cover.check_solution_satisfiability(ising_sol, list_of_subsets):\n", - " print(\"Solution is\", ising_sol)\n", - "else:\n", - " print(\"No solution is found\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.2" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/community/optimization/graph_partition.ipynb b/community/optimization/graph_partition.ipynb deleted file mode 100644 index e64c44514..000000000 --- a/community/optimization/graph_partition.ipynb +++ /dev/null @@ -1,282 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## _*Using Qiskit Aqua for graph partition problems*_\n", - "\n", - "Here we consider a simplified graph partition problem.\n", - "Consider a graph $G = (V, E)$, where $V$ denotes the set of n vertices and $E$ the set of edges. \n", - "The objective of graph partition is to partition $G$ into two sets of the same size (let us assume we have even number of vertices), \n", - "while minimizing the capacity of the edges across the two sets.\n", - "\n", - "We will go through three examples to show:\n", - "1. How to run the optimization using the declarative approach\n", - "2. How to run the optimization using the programmatic approach\n", - "3. How how to run the optimization with the VQE.\n", - "\n", - "Note the objective_value below is defined as the the number of crossing edges. The goal is to minimize this value.\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### The problem and the brute-force method\n", - "\n", - "The graph involved in our example is as follows. The graph is in the adjacent matrix form." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[ 0. 4. 5. 3.]\n", - " [ 4. 0. -5. 7.]\n", - " [ 5. -5. 0. 0.]\n", - " [ 3. 7. 0. 0.]]\n" - ] - } - ], - "source": [ - "import numpy as np\n", - "from qiskit import BasicAer\n", - "from qiskit.aqua import run_algorithm\n", - "from qiskit.aqua.input import EnergyInput\n", - "from qiskit.aqua.translators.ising import graph_partition\n", - "from qiskit.aqua.algorithms import ExactEigensolver\n", - "\n", - "np.random.seed(100)\n", - "num_nodes = 4\n", - "w = graph_partition.random_graph(num_nodes, edge_prob=0.8, weight_range=10)\n", - "print(w)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The brute-force method is as follows. Basically, we exhaustively try all the binary assignments. In each binary assignment, the entry of a vertex is either 0 (meaning the vertex is in the first partition) or 1 (meaning the vertex is in the second partition). We print the binary assignment that satisfies the definition of the graph partition and corresponds to the minimial number of crossing edges." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Objective value computed by the brute-force method is 3\n" - ] - } - ], - "source": [ - "def brute_force():\n", - " # use the brute-force way to generate the oracle\n", - " def bitfield(n, L):\n", - " result = np.binary_repr(n, L)\n", - " return [int(digit) for digit in result] # [2:] to chop off the \"0b\" part\n", - "\n", - " L = num_nodes\n", - " max = 2**L\n", - " minimal_v = np.inf\n", - " for i in range(max):\n", - " cur = bitfield(i, L)\n", - "\n", - " how_many_nonzero = np.count_nonzero(cur)\n", - " if how_many_nonzero * 2 != L: # not balanced\n", - " continue\n", - "\n", - " cur_v = graph_partition.objective_value(np.array(cur), w)\n", - " if cur_v < minimal_v:\n", - " minimal_v = cur_v\n", - " return minimal_v\n", - "\n", - "sol = brute_force()\n", - "print(\"Objective value computed by the brute-force method is\", sol)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Part I: Run the optimization using the declarative approach" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Objective value computed by ExactEigensolver is 3.0\n" - ] - } - ], - "source": [ - "qubit_op, offset = graph_partition.get_graph_partition_qubitops(w)\n", - "algo_input = EnergyInput(qubit_op)\n", - "\n", - "params = {\n", - " 'problem': {'name': 'ising'},\n", - " 'algorithm': {'name': 'ExactEigensolver'}\n", - "}\n", - "result = run_algorithm(params, algo_input)\n", - "\n", - "x = graph_partition.sample_most_likely(result['eigvecs'][0])\n", - "# check against the oracle\n", - "ising_sol = graph_partition.get_graph_solution(x)\n", - "np.testing.assert_array_equal(ising_sol, [0, 1, 0, 1])\n", - "print(\"Objective value computed by ExactEigensolver is\", graph_partition.objective_value(x, w))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Part II: Run the optimization using the programmatic approach" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Objective value computed by the ExactEigensolver is 3.0\n" - ] - } - ], - "source": [ - "algo = ExactEigensolver(algo_input.qubit_op, k=1, aux_operators=[])\n", - "result = algo.run()\n", - "\n", - "x = graph_partition.sample_most_likely(result['eigvecs'][0])\n", - "# check against the oracle\n", - "ising_sol = graph_partition.get_graph_solution(x)\n", - "np.testing.assert_array_equal(ising_sol, [0, 1, 0, 1])\n", - "print(\"Objective value computed by the ExactEigensolver is\", graph_partition.objective_value(x, w))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Part III: Run the optimization with the VQE\n", - "\n", - "##### Declarative\n", - "\n", - "We reuse the EnergyInput object we created above. VQE algorithm needs an optimizer and a variational form. Then also we need a quantum backend on which the algorithm will run." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Objective value computed by VQE is 3.0\n" - ] - } - ], - "source": [ - "params = {\n", - " 'problem': {'name': 'ising', 'random_seed': 10598},\n", - " 'algorithm': {'name': 'VQE'},\n", - " 'optimizer': {'name': 'COBYLA'},\n", - " 'variational_form': {'name': 'RY', 'depth': 5, 'entanglement': 'linear'}\n", - "}\n", - "backend = BasicAer.get_backend('statevector_simulator')\n", - "result = run_algorithm(params, algo_input, backend=backend)\n", - "\n", - "x = graph_partition.sample_most_likely(result['eigvecs'][0])\n", - "# check against the oracle\n", - "ising_sol = graph_partition.get_graph_solution(x)\n", - "np.testing.assert_array_equal(ising_sol, [1, 0, 1, 0])\n", - "print(\"Objective value computed by VQE is\", graph_partition.objective_value(x, w))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Programmatic\n", - "\n", - "We can create the objects directly ourselves too and run VQE for the result." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Objective value computed by VQE is 3.0\n" - ] - } - ], - "source": [ - "from qiskit.aqua import aqua_globals\n", - "from qiskit.aqua.algorithms import VQE\n", - "from qiskit.aqua.components.optimizers import COBYLA\n", - "from qiskit.aqua.components.variational_forms import RY\n", - "\n", - "aqua_globals.random_seed = 10598\n", - "\n", - "optimizer = COBYLA()\n", - "var_form = RY(qubit_op.num_qubits, depth=5, entanglement='linear')\n", - "vqe = VQE(qubit_op, var_form, optimizer)\n", - "\n", - "backend = BasicAer.get_backend('statevector_simulator')\n", - "result = vqe.run(backend)\n", - "\n", - "x = graph_partition.sample_most_likely(result['eigvecs'][0])\n", - "# check against the oracle\n", - "ising_sol = graph_partition.get_graph_solution(x)\n", - "np.testing.assert_array_equal(ising_sol, [1, 0, 1, 0])\n", - "print(\"Objective value computed by VQE is\", graph_partition.objective_value(x, w))" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.2" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/community/optimization/grover.ipynb b/community/optimization/grover.ipynb deleted file mode 100644 index 0dba7d671..000000000 --- a/community/optimization/grover.ipynb +++ /dev/null @@ -1,332 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": { - "collapsed": true - }, - "source": [ - "# _*Using Grover's Algorithm to Perform Quantum Search*_\n", - "\n", - "This notebook demonstrates how to use the `Qiskit Aqua` library `Grover` search algorithm and process the result." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import pylab\n", - "import numpy as np\n", - "from qiskit import BasicAer\n", - "from qiskit.tools.visualization import plot_histogram\n", - "from qiskit.aqua import QuantumInstance\n", - "from qiskit.aqua import run_algorithm\n", - "from qiskit.aqua.algorithms import Grover\n", - "from qiskit.aqua.components.oracles import LogicalExpressionOracle, TruthTableOracle" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Use Quantum Search to Find Solutions to 3-SAT Problems\n", - "\n", - "Let's look at an example 3-Satisfiability (3-SAT) problem and walkthrough how we can use Quantum Search to find its satisfying solutions. 3-SAT problems are usually expressed in [Conjunctive Normal Forms (CNF)](https://en.wikipedia.org/wiki/Conjunctive_normal_form) and written in the [DIMACS-CNF](https://www.satcompetition.org/2009/format-benchmarks2009.html) format. For example:" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "input_3sat_instance = '''\n", - "c example DIMACS-CNF 3-SAT\n", - "p cnf 3 5\n", - "-1 -2 -3 0\n", - "1 -2 3 0\n", - "1 2 -3 0\n", - "1 -2 -3 0\n", - "-1 2 3 0\n", - "'''" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The CNF of this 3-SAT instance contains 3 variables and 5 clauses:\n", - "\n", - "$(\\neg v_1 \\vee \\neg v_2 \\vee \\neg v_3) \\wedge (v_1 \\vee \\neg v_2 \\vee v_3) \\wedge (v_1 \\vee v_2 \\vee \\neg v_3) \\wedge (v_1 \\vee \\neg v_2 \\vee \\neg v_3) \\wedge (\\neg v_1 \\vee v_2 \\vee v_3)$\n", - "\n", - "It can be verified that this 3-SAT problem instance has three satisfying solutions:\n", - "\n", - "$(v_1, v_2, v_3) = (T, F, T)$ or $(F, F, F)$ or $(T, T, F)$\n", - "\n", - "Or, expressed using the DIMACS notation:\n", - "\n", - "`1 -2 3`, or `-1 -2 -3`, or `1 2 -3`.\n", - "\n", - "With this example problem input, we then create the corresponding `oracle` for our `Grover` search. In particular, we use the `LogicalExpressionOracle` component provided by Aqua, which supports parsing DIMACS-CNF format strings and constructing the corresponding oracle circuit." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "oracle = LogicalExpressionOracle(input_3sat_instance)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The `oracle` can now be used to create an Grover instance:" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [], - "source": [ - "grover = Grover(oracle)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can then configure the backend and run the Grover instance to get the result:" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[1, -2, 3]\n" - ] - } - ], - "source": [ - "backend = BasicAer.get_backend('qasm_simulator')\n", - "quantum_instance = QuantumInstance(backend, shots=1024)\n", - "result = grover.run(quantum_instance)\n", - "print(result['result'])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As seen above, a satisfying solution to the specified 3-SAT problem is obtained. And it is indeed one of the three satisfying solutions.\n", - "\n", - "Since we used the `'qasm_simulator'`, the complete measurement result is also returned, as shown in the plot below, where it can be seen that the binary strings `000`, `011`, and `101` (note the bit order in each string), corresponding to the three satisfying solutions all have high probabilities associated with them." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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t3TVQ3P1e4N421p3Q3usObv+SOHGJiIgkQ3PhioiIxKAEKiIiEoMSqIiISAxKoCIiIjEogYqIiMSgBCoiIhKDEqiIiEgMSqAiIiIxKIGKiIjEkFQCNbNzovtvNr2+0cxWm9nzZpbam+yJiIhkkWRroDc3PTGzI4EbgP8CegJ3dV1YIiIi2S3ZuXCHAE331/wH4Cl3v8PMXgCe79LIREREsliyNdAdQN/o+UnArOj55oTlIiIie71ka6BzgbvM7GVgLDA5Wv5p4P2uDExERCSbJVsDvRKoJyTOy9x9bbT8VNSEKyIi3UhSNVB3Xw2c3sryq7ssIhERkRyQ9DhQM9vXzCab2fVmdkC07BAzK+j68ERERLJTUjVQMxtO6Di0P3AA8CTwV+Dy6PXXuzpAERGRbJRsDfRu4AVgELA9YfnTwOe6KigREZFsl2wv3M8Cx7p7o5klLl8FFHdZVCIiIlkuzly4PVtZVkIYCyoiItItJJtAXwCuSXjtZtYPmAI802VRiYiIZLlkm3CvAV40sxpgX+BxYDiwDjini2MTERHJWsmOA11rZp8BvgIcSajB/hz4b3ff3u6bRURE9iLJ1kCJEuUD0UNERKRb2mMCNbOzgN+7+67oeZvcfUaXRSYiIpLFOlID/Q3wKeAv0fO2OJDXFUGJiIhkuz0mUHffp7XnIiIi3VlSCdHMKszsY0nXzPLMrKLrwhIREcluydYoXwRamzT+gGidiIhIt5BsAjXCtc6WBgJbOx+OiIhIbujQMBYzezp66sCjZrYzYXUecBgwr4tjExERyVodHQe6IfrXgE3sfieWeuBlYFoXxiUiIpLVOpRA3f2rAGa2AviRu6u5VkREurVkp/KbkqpAREREcklHZiJ6E5jg7pvM7C1a70QEgLsf0ZXBiYiIZKuO1ECnA02dhtqbiUhERKTb6MhMRFNaey4iItKdaWo+ERGRGDpyDbTd656JdA1URES6i47ejUVEREQSJHUNVERERAJdAxUREYlB40BFRERi0DhQERGRGDQOVEREJIak5sJtYmaHAGXRy2p3f6/rQhIREcl+SSVQMxsI/BL4EvC3vy+2mcDX3H1Dm28WERHZiyTbC/cXwHBgPLBv9KgADkb3AxURkW4k2SbcU4CT3H1+wrJXzOyfgVldF5aIiEh2S7YGuh5o7Wba2wA134qISLeRbAK9BbjbzA5sWhA9vytaJyIi0i3EmUz+YGCFma2JXh8I7AA+SbhGKiIistdL+2TyZnYF8G9AEbAEuNrd57ZRtohQuz0SGAE84u6XtFKuH/ADYDIwEHgfuMHdn+jK2EVERJqkdTJ5MzsXuAe4Ang5+vc5Mxvp7qtaeUtv4EPgP4FL29hmT+B/gY3AOcBqYDB/nz1JRESky8WaSKETrgEedPemIS9Xmdkk4HLguy0Lu/sK4FsAZja5jW1+FSgExrt7fbRsRRfGLCIi8jFJdSIys15mNsXM3jGzHWbWmPjY03uBMcALLVa9AHw2ubB3cybwCvBTM/vAzJaa2c1RzVRERCQlkq2Bfh84F7gd+AnhWuZQ4DzgP/bw3k8AecC6FsvXAROTjCPRMOBE4DHgtCienwH7A9e2LGxmlxI1BxcVFVFVVQVAcXEx+fn5vPvuuwD079+fYcOGsXDhQgDy8vIYPXo0NTU1bN0aRvKUlZWxceNGYEAnwt+z+vp6Fi9eDEDv3r0ZNWoUS5YsYefO0Ep92GGHUVdXx4YNYSTR0KFDcXdWrlwJQGFhIYWFhSxduhSA/fbbj7KyMt566y127doFwOjRo1m1ahWbNm0CYNiwYdTX17N69WoABg0aREFBAdXV1QD06dOH0tJSFi1aRGNjOHcqLy+ntraWzZs3AzB8+HC2bdvG2rVrgfB59+vXj5qaGgD69u3LiBEjWLhwIe6OmVFeXs6yZcvYsmULAKWlpXz00UfU1dUBnfue1q0LP73BgwfTq1cvamtrARgwYAAlJSUsWrQIgJ49e3L44YdTXV3N9u3bARg5ciTr169n/fr1AAwZMgQzY8WKFQAMHDiQoqKipL4nOCm5H0KSqqqq9D218T2lUlVVlf6eMvD31JXHvY4y9zbvTvbxwmbLgcvd/Q9mtgX4jLu/Z2aXEyZYaKuZFTMrBtYQbo1WmbD8RuB8dy/dw/89E/iwZSciM3uHMCPSwe7eGC27lJDg9/d2drC8vNxnz57d/k53wHUPpTaB3nHxppRuXzJDv5vMSeVnr8899xUUFCxw97F7KpfsONBBwNLo+f8BB0TP/wB8fg/v/RBojLbRcpsfJBlHojrgnabkGakG8gm1XhERkS6XbAJdBRRHz98lTO0HMA7Y3t4bow4+C4CTW6w6GZiXZByJXgGGm1nivnyaMDvSh53YroiISJuSTaC/5e8Xbu4BpkTNug/SsUkUfgxcYmZfN7MyM7uHkJDvBzCzh83s4cQ3mNlnzOwzQD+gIHo9MqHIfUABcI+ZlZrZKcAU4N72mm9FREQ6I6lORO7+3YTnvzGz1YQetO+4+8wOvP/x6JZo3yNMpLAY+IK7r4yKlLTytoUtXp8OrCR0FsLd3zezzxOS858JzcEPECZWEBERSYlOjQN19z8Bf0ryPfcC97ax7oRWllkH4+jMUBgREZGkJNuEi5kdGTW1vhE9HjGzI1MRnIiISLZKdiKF84HXCc2vz0aPQcBrZnZB14cnIiKSnZJtwr0V+A93vy1xoZl9l3DN8dGuCkxERCSbJduEWwi0doeTJwm3MxMREekWkk2gLwIntLL8BGBOZ4MRERHJFR25ofZZCS+fA243s7H8vfftscBZwM1dHp2IiEiWintD7eYJ2RP8lDaGp4iIiOxtOnJD7aSHuoiIiOztlBxFRERiiDORwmlmVmlmH5rZejObY2ZfSEVwIiIi2SrZiRS+TphQ/j3geuA7wHLgt2b2ta4PT0REJDslO5HC9cA17v7/Epb90swWEJLpA10WmYiISBZLtgm3hHDz7JaeA4Z0PhwREZHcEOeG2i1viA3wecItxkRERLqFZJtwfwT8NLr7yrxo2XHAhcBVXRmYiIhINkv2htpTzewvwL8SZh8CqAbOcfffdXVwIiIi2arDCdTMehCaaivd/bepC0lERCT7dfgaqLs3ADOAvqkLR0REJDck24loETA8FYGIiIjkkmQT6M3AXWZ2ppkdZGYFiY8UxCciIpKVku2F+0z07wzAE5Zb9DqvK4ISERHJdskm0M+lJAoREZEc06EEamb5wJ3AmUBPYBbwLXf/MIWxiYiIZK2OXgOdAlxCaML9H8JsRPelKCYREZGs19Em3LOAf3L3XwOY2X8Dr5hZnrs3piw6ERGRLNXRGuhBwNymF+7+GtAAFKciKBERkWzX0QSaB9S3WNZA8p2QRERE9godTYAGPGpmOxOW7QtMM7NtTQvc/UtdGZyIiEi26mgCfaiVZY92ZSAiIiK5pEMJ1N2/mupAREREckmyU/mJiIgISqAiIiKxKIGKiIjEoAQqIiISgxKoiIhIDEqgIiIiMSiBioiIxKAEKiIiEoMSqIiISAxKoCIiIjEogYqIiMSgBCoiIhKDEqiIiEgMSqAiIiIxKIGKiIjEoAQqIiISgxKoiIhIDEqgIiIiMSiBioiIxKAEKiIiEoMSqIiISAxKoCIiIjGkPYGa2RVmttzMdpjZAjMbv4fyE6JyO8ys1swua7E+z8y+n7DN5Wb2AzPrkdo9ERGR7iytCdTMzgXuAW4DyoF5wHNmVtJG+YOBZ6Ny5cDtwE/N7OyEYtcD3wS+BRwKfDt6/d0U7YaIiAjprqVdAzzo7tOi11eZ2STgclpPeJcBa939quh1tZkdA1wLTI+WfRb4vbv/Pnq9wsyeBo5JyR6IiIiQxhqomfUCxgAvtFj1AiEJtmZcK+WfB8aaWc/o9cvA58zs0Oj/GQmcSKi5ioiIpEQ6a6CfAPKAdS2WrwMmtvGeTwGzWinfI9peHfBDoC+w1Mwao3W3uvu9rW3QzC4FLgUoKiqiqqoKgOLiYvLz83n33XcB6N+/P8OGDWPhwoUA5OXlMXr0aGpqati6dSsAZWVlbNy4ERjQoQ8grvr6ehYvXgxA7969GTVqFEuWLGHnzp0AHHbYYdTV1bFhwwYAhg4diruzcuVKAAoLCyksLGTp0qUA7LfffpSVlfHWW2+xa9cuAEaPHs2qVavYtGkTAMOGDaO+vp7Vq1cDMGjQIAoKCqiurgagT58+lJaWsmjRIhobGwEoLy+ntraWzZs3AzB8+HC2bdvG2rVrgfB59+vXj5qaGgD69u3LiBEjWLhwIe6OmVFeXs6yZcvYsmULAKWlpXz00UfU1dUBnfue1q0LP73BgwfTq1cvamtrARgwYAAlJSUsWrQIgJ49e3L44YdTXV3N9u3bARg5ciTr169n/fr1AAwZMgQzY8WKFQAMHDiQoqKipL4nOCm5H0KSqqqq9D218T2lUlVVlf6eMvD31JXHvY4yd+9w4c4ws2JgDTDB3SsTlt8InO/upa285x3gUXe/JWFZBTAHKHb3OjM7D7gT+DdgCfAZwnXWf3P3X7YXU3l5uc+ePbvT+3bdQ6lNoHdcvCml25fM0O8mc1L52etzz30FBQUL3H3snsqlswb6IdAIDGqxfBDwQRvv+aCN8g3R9iAkzx+5+6+j12+Z2RDCNdV2E6iIiEhcabsG6u71wALg5BarTib0sm3N/DbKv+Huu6LX+YTEnKgRjXEVEZEUSncv3B8Dj5jZa8ArhF62xcD9AGb2MIC7XxSVvx+40szuBqYCxwGXAF9J2Obvge+Y2XJCE245obfvw6neGRER6b7SmkDd/XEzGwh8DygCFgNfcPeVUZGSFuWXm9kXgJ8QhrqsBb7l7tMTil0FfB+4F/gkoWPRNOAWREREUiTts/VEvWNb7SHr7ie0smwOcGQ729sCXB09RERE0kLXCUVERGJQAhUREYlBCVRERCQGJVAREZEYlEBFRERiUAIVERGJQQlUREQkBiVQERGRGJRARUREYlACFRERiUEJVEREJAYlUBERkRiUQEVERGJQAhUREYlBCVRERCQGJVAREZEYlEBFRERiUAIVEZG0mDVrFkcffTRjxozh7rvv/tj6nTt38rWvfY0xY8YwceJEVq1aBcCCBQuoqKigoqKC8ePHM3PmTACWLVvWvLyiooKSkhLuu+++tO2PEqiIJK2rD4QAo0eP5rjjjqOiooITTzwxbfsi6dHY2Mh1113HE088wfz585k+fTpvv/32bmUeffRRDjjgABYsWMDll1/OzTffDEBZWRmzZ8+msrKSJ598kmuuuYaGhgZGjBhBZWUllZWVvPjii+Tn5/PFL34xbfukBCoiSUnFgbDJ008/TWVlJbNnz07nLkkaLFiwgIMPPpihQ4fSq1cvzjrrLJ577rndyjz77LOcd955AJxxxhlUVlbi7uTn59OjRw8gnJyZ2ce2P2fOHIYOHcpBBx2U+p2JKIF2c11dk9ixYwcTJ05k/PjxjBs3jttvvz2t+yOpl+oDoeyd6urqOPDAA5tfFxcXU1dX12aZHj160K9fPzZu3AjAG2+8wbhx4zj++OO56667mn9HTWbMmMHZZ5+d4r3YnRJoN5aKmkTv3r156qmnmDt3LpWVlfzxj3/k9ddfz8DeSaqk6kBoZpx99tl87nOf48EHH0zPzkjOGDt2LPPnz2fWrFncfffd7Nixo3ldfX09f/jDHzjjjDPSGpMSaDeWipqEmbH//vsDsGvXLhoaGlJWy0jFdbg9bVM6r60D4bPPPstLL73EE088wS9/+UvmzZuX4UilKxUVFbFmzZrm12vXrqWoqKjNMg0NDXz00UcUFBTsVqa0tJQ+ffpQXV3dvGzWrFkcccQRfPKTn0zhHnycEmg3lqqaRGNjIxUVFZSWlnLCCScwduzYLo89FbXnjmxTUncgLC4uBqCwsJDTTjuNBQsWpHI3JM2OPPJIamtrWblyJfX19cyYMYNJkybtVubUU0/l17/+NQC/+93vGD9+PGbGypUrm6+Vv//++yxbtoySkpLm902fPj3tzbegBCqd0FZNIi8vj8rKShYvXkxVVRVLly7t8v87FbXnjmxTUnMg3Lp1K1u2bAFg69atvPjii5SVlaVt7syvAAASrklEQVR3xySlevTowR133MHkyZM59thjOfPMMykrK+O2225r/ju74IIL2LhxI2PGjOG+++7jpptuAuBPf/oT48ePp6KiggsvvJA777yTgQMHAuH38tJLL3H66aenf5/S/j9K1kimJnHggQd2qCZRXl7evLx///4cf/zx/PGPf2TkyJFdGntrteeWNZa2as8DBw7kjTfe4KqrrmL16tXcd9999OjRo0PblN0PhI2NjZx//vnNB8Ly8nJOPfVULrjgAi677DLGjBnDgAED+MUvfgGEA+Hdd99Nz5492WeffZoPhCtWrODCCy8EQo118uTJTJw4MZO7KSlw8sknc/LJJ++27IYbbmh+vu+++7Z6/fvcc8/l3HPPbXWbffr04b333uvSODtKCbQbS6xJFBUVMWPGDH7+85/vVqapJnH00Ud/rCZx4IEH0qNHj91qEh9++CE9e/akf//+bN++nZdeeolvf/vbGdrDtjXVnmtqavjmN7+pg3WSuvpAOHToUObOndvlce5tZs2axQ033EBjYyMXXnghV1999W7rd+7cyeWXX86iRYsYMGAADzzwACUlJbz44ovccsst1NfX06tXL6ZMmUJFRQUAp59+OuvWrWPfffcFQnNoYWFh2vctFymBdmOpqEksWbKEK664gsbGRv72t79x5plncsopp3R57KmoPXdkmyKZ0nSNfsaMGRQXF3PSSScxadIkDj300OYyidf9p0+fzs0338wDDzzAwIEDeeyxxygqKmLp0qV8+ctfZsmSJc3vmzp16m6tR9IxSqDdXFfXJEaNGsWcOXO6PM6WUlF77t+//x63KZIpidfogeZr9IkJ9Nlnn+X6668HwnX/66+/HnfniCOOaC5TVlbG9u3b2blzJ717907rPlz30ICUbv+OizeldPstKYFKTkpF7RlodZvycXvbgTAXdPa6f5Onn36a0aNH75Y8r7zySvLy8jj99NO59tprNcFFBymBSs5KRYeE1rYpsreorq5mypQpTJ8+vXnZ1KlTKS4uZsuWLVx88cU8/vjjzb3XpX1KoN2cahIiuaGz1/3XrFnDRRddxL333svBBx/c/J6m8bd9+/Zl8uTJVFVVKYF2kMaBiojkgM6Mv928eTPnnXceN954I8cee2xz+YaGBjZs2ACEmcOef/55XbZIgmqgktNSWYNW7VmySWeu+0+bNo3ly5dz5513cueddwJhuEp+fj6TJ09m165dNDY2MmHCBC666KJM7mZOUQIVEckRca/7X3vttVx77bWtbvPFF1/s0hi7EzXhioiIxKAEKiIiEoOacEVEcoh6zmcP1UBFRERiUAIVERGJQQlUREQkBiVQERGRGJRARUREYlACFRERiUEJVEREJAYlUBERkRiUQEVERGJQAhUREYlBCVRERCQGJVAREZEYlEBFRERiUAIVERGJQQlUREQkhrQnUDO7wsyWm9kOM1tgZuP3UH5CVG6HmdWa2WWd3aaIiEhnpTWBmtm5wD3AbUA5MA94zsxK2ih/MPBsVK4cuB34qZmdHXebIiIiXSHdNdBrgAfdfZq7V7v7VUAdcHkb5S8D1rr7VVH5acBDwLWd2KaIiEinpS2BmlkvYAzwQotVLwCfbeNt41op/zww1sx6xtymiIhIp5m7p+c/MisG1gAT3L0yYfmNwPnuXtrKe94BHnX3WxKWVQBzgGLAYmzzUuDS6GUpUNMFu5esTwAfZuD/7QqKPXNyOf5cjh1yO37Fnrwh7l64p0I90hFJNnH3nwM/z2QMZvaGu4/NZAxxKfbMyeX4czl2yO34FXvqpDOBfgg0AoNaLB8EfNDGez5oo3xDtD2LsU0REZFOS9s1UHevBxYAJ7dYdTKh52xr5rdR/g133xVzmyIiIp2W7ibcHwOPmNlrwCuEXrbFwP0AZvYwgLtfFJW/H7jSzO4GpgLHAZcAX+noNrNURpuQO0mxZ04ux5/LsUNux6/YUyRtnYia/0OzK4DrgCJgMfAvTR2AzOwlAHc/IaH8BOAnwChgLfBDd7+/o9sUERFJhbQnUBERkb2B5sIVERGJQQlUREQkBiXQDDAzy3QM3ZE+dxHpSkqgGeC68JwRTZ+7Emn6mZmONRmS+Nnrt9+11IkoTcysN3AE8A/AZmAJ8C7wvrtvNTPL9sRqZnmEPPS3TMeSDDPbH6gAzgM2AcuAd4DF7r42k7F1lJn1AP6Wa5+9ZAcz6+vuWzIdx95GCTRNzOy/gLMId4oZAAwlDMt5Crjb3WszF137zGyMuy9osSyPcEDP+h+QmT1ESKDLCJ/9QYRE+mdgmrvPzmB47TKz49395RbLciaZmtlBwNeAo4D3CHNPLwHedPdN2XrimBhXLn3eicysjHC3qnLCyfoqYBFQ6e7vR2Wy8vPPFUqgaWBmI4E/AZOBBe6+wcwKgX8C/hn4FPBtwsE8q74QMxtBOOgtJdzl5hF3X5iw3ggTcpQDf45mh8oa0Wf/KmF2qtfdvdHM+gPnAF8HxgK3AD8gy04IzOxQwue+FXgG+Km7v5Kw3oCewCnAa+6+LiOBtiG6n+90YD/gdeAwwjSbG4C5wI/d/b3MRdi26O+zrMVNKgzIAxqz6XfSGjM7hHAv5XWECWYOJRxnehOS6S/cveVdrLKCmQ0i/L0+6+4b2ynX0913pS+yVri7Hil+ADcQzvqaXvdosf424G2gONOxthL7jYSa208I0yOuIZwMXAccFJU5EPgbMDjT8bYS/9XAywmve7VYfxnwPvDpTMfaxu9mIfBdQsJpIMzx/CPgkKjMJ6PP/qBMx9tK/PcDvwc+lbCsBLgeWAmsB87IdJxtxP6z6HP9IHo+ssX6faJ9+TKQl+l4W4n/vuiz75uwbBBhJrdKwknZP2U6zjZi/2n02W8EngS+APRuUaaEcF/o3pmIsemhC/vpUQ0UmdlwAHdvMLMeZrZvtH4asI1QQ802pYQz2R8C3yAc1BcDFwDzzez3hGkWq919dcaibNsiYIiZnQRhTubos98vWv8k4WD+lbY2kEEHEmoPU4EzgBOBB4DTgGVm9ibwa8Jn/37GomzbKGCOu38Q3b+3h7uvcvcfuvsQYBZwmZntk4WdW44inADcBxwPLDazd83sBjMr8NCcezFhZrTGTAbahiFAlbtvMbM8M8tz93Xu/qC7VxD27Rtmlp/hOFszlnC8+VfCJZffAsvN7KdmdmRU5hvAZe6+M0MxAuqFmy6VhNrDTDM7x8x6u3uDu+8AcPflhKahjP4YWoqu/TwDfODuH7j7End/iFD7/GfgP4HthDPEH2cu0nbNJ9TuHzWzy8xsv+iz3w7g7huA/cmy+yVG15ifAZa6+8boUQncTGiy/RKhafoEQo00G/0RuCDqwLIrOnHsmXDy8jPg08DRHlUrsoGZDSFcI38N+D7h930q8DyhxeJDM3sF+BdCbSkbPQ981cwOdfdGD5cueplZr2j9Lwk10mMyF+LHRfeNXg0sd/dfAZOA0cA9wHjgdTN7i3BtN+Ofva6Bpkn0w/gJcDjhB/IaMDt6/k3gH4Gh7r41Y0HuQWvXHMzsLOA3wP7uvi0zkbUvOmDfSqjhbyc0Qf8O+D/gq4QaRmm2xg9hKIK36MRiZqcAz5Gln72ZjSE0I34A3OzuT7dYfyihI1dBNsVvZv0IveVXuPuchOX7EW5UMQa4gvC76dt0MpZNouvPM4ADgO+7+wMt1h8GVAEHZNln34fQ0vIXd3+1xbp8wnX0awkdMjP+2SuBppGZDQS+SLhAPozQPDoAmANMdfdfZzC8j2ntoB0t70HUkcLMfgSM9YQbAGSTqOmqMRrKcjzhLPZY4EhCrX8WofPWcxkM82OiJk1r7fNPKHMzMM7dT0lbYB3U1LszumxxB+Ezb+o89BwwknBCs9zdz8lcpO1r6jjk7g0tlv83cGC2/u4hDF0BbgfOJ3Q2e4Hwez+M8LfwZ//7na+yUmu9hM3sQUIfgPGZiSohFiXQ1DKzwcDw6OVWQq/K7YQEuj/h2ueH3k5vs0xJiN0IF/Vr3P2DhPVGuDa3xt1fz0yUyYmasAoJ38G+wOZsrvW3x8xOANa7+5JMx9Ke6Fr/RMKJ49GEa6MbCdf+H3X3lRkMr0MSe+ASehVXAre7+/SMBtaKKNZ9ohPHfQmtXhWEmt2RwHLgUWBG4t9zNogmffC2mvSjVoDfAfe5+2/TGlxr8SiBpo6ZXU4YAzeakChrCU22LwK/ydKOH8DHYt9K6Pq+mtD8+ZS712QwvD2KrnVuT3jd7h9mNmkZe66JPuszCCcq+xHGf851983RAd0JzW9Zdd0ZPhZ7PqHX+Rx3/0tCmd7ARHd/JjNRJi9x3LaZ9Xf3zZmOKQ4z60lo8Zqf6VhACTRloubad4G7CD35Cgln4ScQmq/WAt9y96XZNph5D7GXERLpv0Sx52VbL0QzG0DoffsM4Ux7XtPnm5hIo4Hmqz2LZmjZQ+yJg/vLgDp3/2vGgm1F1Gz4S+BzhFaLNYQWjG2E5sNH3X1ZVLbVSwSZ0krsqwnJfgfhMssj7v525iJsX5RcDgZWttY7NduOM4n2FHvWajmuRY8uG8t0FfBqG+uOJ1wLqgU+kelY96bYE+LfSeio1UioAd1C6CjUVOYgwhjLYZmOd2+JPYrt3wknAEdFrw8lDHm6D1hA6FRUmOk4Y8T+OvB0tsYexXs1obXoV8DphIkT8lqU6UfoUdwz0/HGjP00WozlzuRDw1hSpx7oG/V2w8x6N3Uh9zA12/mEM9vPZy7ENuVy7BDmHP4VocNWOfAEYZznUjP7k5ldSjgwjvDsm0Ixl2OHMOzgIY+uibv72+7+KHAlYdjHocAjGYyvPe3F/q+E1pdsjR3gXMKJ13DCFKHzgTvN7HgLs29B6O1/k2d6Bp+P62js/+FZNNuZEmjq/IbQDHR1NA5up4dB/PsAuPsq4K/A4EwG2YacjT26PrWUMEn/X9z9TXf/LmFw9inRupsJw1p+mLFAW5HLsUNz7+zFwNkWpsIjGsS/j4exiJWEcZSDzWx0JmNtKZdjh+apB3cRepSPJ0yk8EvCiVglMNvMrifU9F5tc0MZkMuxZ7wKvDc+CNd8DDiTMMvNFsIPYgx/nwLsgmj50EzHu7fEnrAPvYmmjyP0nNynxfoTyN6pB3M29ii+YwnNzj8EBrWy/iDC+NsDMx3rXhZ7EaGGf0or68oJk1ZsiH47WRV/LseuTkQpZGYHEBLOZwkDs4+LVn1ASFKPuPvNmYmufbkae8L4w2HAVk+YYD1h3Y3AJe4+LHORflwuxw7NHbT2IUxOcRvhJgPTgccJdwI5glCrGOnuR2UqztbkcuxNoiEe7u47oqEswG73wb0V+IK7l2cqxrbkauxKoF3MzD4JXEi4ZvIhYbzhX4GXCUNAehLa+f/g7u9kKs7W5HLssFv81wB/IUyfWEeY73aGR/ddJcyjudbdZ2Ys2BZyOfbWRCdglxCuW32G0GKxg9AZ53ZvMctMNsnx2FvtaWthFp8q4FfunnXN/5CbsSuBdrFoloxRhN6GG4ECwkDmTxMOjN/L1j/AXI4d2oy/nNBxZTVwp2fvLZweJEdjh+bp77YkHgCjWt2+hAlDDiPUqrPu95PLsUPr8bdSZl9CR53/8SzqhJPLsYMSaJeKaghbCE0NlQnLSgiTNn+dMAPROe5elbFAW5HLsUO78Q8mXNv6BqFzwleyLf5cjr2JmU0l9KJ8jTCW76NWygzwLLyJdi7HDh2O/wDPsjHDkNuxA+pE1JUPQg3iLeDYNtb3Bt4gNANlPN69JfYOxt8rW+PP5dij+L5C6ODxV8L44KmEyb6HA/tFZfYnDE84PNPx7i2xtxP/PwCHJMTfNP3dYZmOd2+JvemhGmgXii6EzyRMAXYR8J5//A4aVxFuZPuZDITYplyOHXI7/lyOHcDMphEmfbiDkHwuJhwEawj3kv0j4cYJ97h7r7a2kwm5HDvkdvy5HHsTjQPtQh7mL/13wlnTw8BFZnaQhTuBNF0Mn0AYb5ZVcjl2yO34czn2aPzkcuCv7l7r7j9y98MJN6SeQzgoPkG4d2NWTUKQy7FDbsefy7EnUg00BSzM4PMfhJsebyXMqrGeMJ9sHfB1d38rcxG2LZdjh9yOP1djtzB/7yB3f9vCjFW7POHAYmbnAv8DHOnuf85UnK3J5dght+PP5dibKIGmUDQ04TTCpAQ7CDWIJz2LJ6RuksuxQ27Hn8uxN4l6sZqHW2p9g9AMl5/puDoil2OH3I4/12JXAk0Ty7I7TyQjl2OH3I4/l2NvYmbXECYGvzPTsSQrl2OH3I4/F2JXAhWRlLJwq6rGXDwRyOXYIbfjz4XYlUBFRERiUC9cERGRGJRARUREYlACFRERiUEJVEREJAYlUBERkRiUQEVERGL4/6Eq2mwcLGS1AAAAAElFTkSuQmCC\n", - "text/plain": [ - "
" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "plot_histogram(result['measurement'])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The above step-by-step programatic approach can also be achieved by using a json configuration dictionary with the parameters for the algorithm and any other dependent objects it requires, as follows:" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "execution_count": 7, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "params = {\n", - " 'problem': {\n", - " 'name': 'search',\n", - " },\n", - " 'algorithm': {\n", - " 'name': 'Grover'\n", - " },\n", - " 'oracle': {\n", - " 'name': 'LogicalExpressionOracle',\n", - " 'expression': input_3sat_instance\n", - " },\n", - " 'backend': {\n", - " 'shots': 1000,\n", - " },\n", - "}\n", - "\n", - "result_dict = run_algorithm(params, backend=backend)\n", - "plot_histogram(result_dict['measurement'])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Quantum Search with Arbitrary Boolean Logical Expressions\n", - "\n", - "Aqua's `Grover` can also be used to perform Quantum Search on `Oracle` constructed from means in addition to DIMACS. For example, the `LogicalExpressionOracle` can actually be configured using arbitrary Boolean logical expressions, as demonstrated below." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "execution_count": 8, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "expression = '(w ^ x) & ~(y ^ z) & (x & y & z)'\n", - "oracle = LogicalExpressionOracle(expression)\n", - "grover = Grover(oracle)\n", - "result = grover.run(QuantumInstance(BasicAer.get_backend('qasm_simulator'), shots=1024))\n", - "plot_histogram(result['measurement'])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In the example above, the input Boolean logical expression `'(w ^ x) & ~(y ^ z) & (x & y & z)'` should be quite self-explanatory, where `^`, `~`, and `&` represent the Boolean logical XOR, NOT, and AND operators, respectively. It should be quite easy to figure out the satisfying solution by examining its parts: `w ^ x` calls for `w` and `x` taking different values; `~(y ^ z)` requires `y` and `z` be the same; `x & y & z` dictates all three to be `True`. Putting these together, we get the satisfying solution `(w, x, y, z) = (False, True, True, True)`, which our `Grover`'s result agrees with." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Quantum Search with Oracles from TruthTable\n", - "\n", - "With Aqua, `Oracle`s can also be constructed from truth tables, meaning we can also perform Quantum Search on truth tables. Even though this might seem like a moot point as we would be essentially searching for entries of a truth table with the $1$ value, it'd a good example for demonstrative purpose." - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [], - "source": [ - "truthtable = '1000000000000001'" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As shown, the `truthtable` is specified with a bitstring containing values of all entries in the table. It has length $16$, so the corresponding truth table is of $4$ input bits. Since the very first and last values are $1$, the corresponding truth table target entries are `0000` and `1111`.\n", - "\n", - "Next, we can setup the `Oracle` and `Grover` objects to perform Quantum Search as usual." - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "oracle = TruthTableOracle(truthtable)\n", - "grover = Grover(oracle)\n", - "result = grover.run(QuantumInstance(BasicAer.get_backend('qasm_simulator'), shots=1024))\n", - "plot_histogram(result['measurement'])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As shown, the search result coincides with our expectation." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.2" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/optimization/input_files/grover.json b/community/optimization/input_files/grover.json deleted file mode 100644 index 84d511af7..000000000 --- a/community/optimization/input_files/grover.json +++ /dev/null @@ -1,17 +0,0 @@ -{ - "algorithm": { - "name": "Grover" - }, - "backend": { - "provider": "qiskit.BasicAer", - "name": "qasm_simulator", - "shots": 1000 - }, - "oracle": { - "expression": "c example DIMACS-CNF 3-SAT\np cnf 3 5\n-1 -2 -3 0\n1 -2 3 0\n1 2 -3 0\n1 -2 -3 0\n-1 2 3 0", - "name": "LogicalExpressionOracle" - }, - "problem": { - "name": "search" - } -} diff --git a/community/optimization/input_files/maxcut.json b/community/optimization/input_files/maxcut.json deleted file mode 100644 index f14958c22..000000000 --- a/community/optimization/input_files/maxcut.json +++ /dev/null @@ -1,179 +0,0 @@ -{ - "algorithm": { - "initial_point": null, - "name": "VQE", - "operator_mode": "matrix" - }, - "backend": { - "provider": "qiskit.BasicAer", - "name": "statevector_simulator", - "skip_transpiler": false - }, - "initial_state": { - "name": "ZERO" - }, - "input": { - "aux_ops": [], - "name": "EnergyInput", - "qubit_op": { - "paulis": [ - { - "coeff": { - "imag": 0.0, - "real": 1.0 - }, - "label": "ZIIIZIIIII" - }, - { - "coeff": { - "imag": 0.0, - "real": 1.0 - }, - "label": "ZIIIIIIIZI" - }, - { - "coeff": { - "imag": 0.0, - "real": 1.0 - }, - "label": "IZIZIIIIII" - }, - { - "coeff": { - "imag": 0.0, - "real": 1.0 - }, - "label": "IZIIIIZIII" - }, - { - "coeff": { - "imag": 0.0, - "real": 1.0 - }, - "label": "IZIIIIIIZI" - }, - { - "coeff": { - "imag": 0.0, - "real": 1.0 - }, - "label": "IIZIZIIIII" - }, - { - "coeff": { - "imag": 0.0, - "real": 1.0 - }, - "label": "IIZIIIIZII" - }, - { - "coeff": { - "imag": 0.0, - "real": 1.0 - }, - "label": "IIZIIIIIIZ" - }, - { - "coeff": { - "imag": 0.0, - "real": 1.0 - }, - "label": "IIIZIIIIZI" - }, - { - "coeff": { - "imag": 0.0, - "real": 1.0 - }, - "label": "IIIZIIIIIZ" - }, - { - "coeff": { - "imag": 0.0, - "real": 1.0 - }, - "label": "IIIIZIIZII" - }, - { - "coeff": { - "imag": 0.0, - "real": 1.0 - }, - "label": "IIIIZIIIIZ" - }, - { - "coeff": { - "imag": 0.0, - "real": 1.0 - }, - "label": "IIIIIZZIII" - }, - { - "coeff": { - "imag": 0.0, - "real": 1.0 - }, - "label": "IIIIIZIZII" - }, - { - "coeff": { - "imag": 0.0, - "real": 1.0 - }, - "label": "IIIIIZIIZI" - }, - { - "coeff": { - "imag": 0.0, - "real": 1.0 - }, - "label": "IIIIIZIIIZ" - }, - { - "coeff": { - "imag": 0.0, - "real": 1.0 - }, - "label": "IIIIIIZIZI" - }, - { - "coeff": { - "imag": 0.0, - "real": 1.0 - }, - "label": "IIIIIIZIIZ" - }, - { - "coeff": { - "imag": 0.0, - "real": 1.0 - }, - "label": "IIIIIIIZZI" - }, - { - "coeff": { - "imag": 0.0, - "real": 1.0 - }, - "label": "IIIIIIIZIZ" - } - ] - } - }, - "optimizer": { - "factr": 10, - "iprint": -1, - "maxfun": 2000, - "name": "L_BFGS_B" - }, - "problem": { - "name": "ising", - "random_seed": null - }, - "variational_form": { - "depth": 10, - "entanglement": "linear", - "entangler_map": null, - "name": "RYRZ" - } -} \ No newline at end of file diff --git a/community/optimization/max_cut.ipynb b/community/optimization/max_cut.ipynb deleted file mode 100644 index fcc88a02c..000000000 --- a/community/optimization/max_cut.ipynb +++ /dev/null @@ -1,294 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": { - "collapsed": true - }, - "source": [ - "## _*Using Qiskit Aqua for max-cut problems*_\n", - "\n", - "This Qiskit Aqua Optimization notebook demonstrates how to use the VQE quantum algorithm to compute the max cut of a given graph. \n", - "\n", - "The problem is defined as follows. Given a graph $G = (V,E)$ with weights $w_{ij}$ on the edges, we are looking for a subset $S \\subseteq V$ such that $\\sum_{(i,j) \\in E : i \\in S, j \\not\\in S} w_{ij}$ is maximized.\n", - "\n", - "The graph provided as an input is used first to generate an Ising Hamiltonian, which is then passed as an input to VQE. As a reference, this notebook also computes the max cut using the Exact Eigensolver classical algorithm and the solver embedded in the commercial non-quantum IBM CPLEX product (if it is available in the system and the user has followed the necessary configuration steps in order for Qiskit Aqua to find it). Please refer to the Qiskit Aqua Optimization documentation for installation and configuration details for CPLEX." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "\n", - "from qiskit.aqua import Operator, run_algorithm\n", - "from qiskit.aqua.input import EnergyInput\n", - "from qiskit.aqua.translators.ising import max_cut\n", - "from qiskit.aqua.algorithms.classical.cplex.cplex_ising import CPLEX_Ising\n", - "from qiskit import Aer" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here an Operator instance is created for our Hamiltonian. In this case the paulis are from an Ising Hamiltonian translated from the max-cut problem. We load a small sample instance of the max-cut problem." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "w = max_cut.parse_gset_format('sample.maxcut')\n", - "qubitOp, offset = max_cut.get_max_cut_qubitops(w)\n", - "algo_input = EnergyInput(qubitOp)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We also offer a function to generate a random graph as a input." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[ 0. 8. -9. 0.]\n", - " [ 8. 0. 7. 9.]\n", - " [-9. 7. 0. -8.]\n", - " [ 0. 9. -8. 0.]]\n" - ] - } - ], - "source": [ - "if True:\n", - " np.random.seed(8123179)\n", - " w = max_cut.random_graph(4, edge_prob=0.5, weight_range=10)\n", - " qubitOp, offset = max_cut.get_max_cut_qubitops(w)\n", - " algo_input.qubit_op = qubitOp\n", - "print(w)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here we test for the presence of algorithms we want to use in this notebook. If Aqua is installed correctly `ExactEigensolver` and `VQE` will always be found. `CPLEX.Ising` is dependent on IBM CPLEX being installed (see introduction above). CPLEX is *not required* but if installed then this notebook will demonstrate the `CPLEX.Ising` algorithm , that uses CPLEX, to compute max-cut as well." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "['ExactEigensolver', 'CPLEX.Ising', 'VQE']\n" - ] - } - ], - "source": [ - "to_be_tested_algos = ['ExactEigensolver', 'CPLEX.Ising', 'VQE']\n", - "print(to_be_tested_algos)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can now use the Operator without regard to how it was created. First we need to prepare the configuration params to invoke the algorithm. Here we will use the ExactEigensolver first to return the smallest eigenvalue. Backend is not required since this is computed classically not using quantum computation. We then add in the qubitOp Operator in dictionary format. Now the complete params can be passed to the algorithm and run. The result is a dictionary." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "energy: -20.5\n", - "max-cut objective: -24.0\n", - "solution: [1. 0. 1. 1.]\n", - "solution objective: 24.0\n" - ] - } - ], - "source": [ - "algorithm_cfg = {\n", - " 'name': 'ExactEigensolver',\n", - "}\n", - "\n", - "params = {\n", - " 'problem': {'name': 'ising'},\n", - " 'algorithm': algorithm_cfg\n", - "}\n", - "result = run_algorithm(params,algo_input)\n", - "# print('objective function:', max_cut.max_cut_obj(result, offset))\n", - "x = max_cut.sample_most_likely(result['eigvecs'][0])\n", - "print('energy:', result['energy'])\n", - "print('max-cut objective:', result['energy'] + offset)\n", - "print('solution:', max_cut.get_graph_solution(x))\n", - "print('solution objective:', max_cut.max_cut_value(x, w))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "*Note*: IBM CPLEX is an _optional_ installation addition for Aqua. If installed then the Aqua CPLEX.Ising algorithm will be able to be used. If not, then solving this problem using this particular algorithm will simply be skipped. \n", - "\n", - "We change the configuration parameters to solve it with the CPLEX backend. The CPLEX backend can deal with a particular type of Hamiltonian called Ising Hamiltonian, which consists of only Pauli Z at most second order and often for combinatorial optimization problems that can be formulated as quadratic unconstrained binary optimization problems, such as the max-cut problem.\n", - "\n", - "Note that for a max-cut problem, since we are computing a bipartition of the graph, every binary vector $x$ and its complement (i.e., the vector $y$ such that $y_j = 1 - x_j$ for all $j$) represent exactly the same solution, and will have the same objective function value. Different solution methods may return solutions that look different, but in fact have the same objective function value." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPXPARAM_TimeLimit 600\n", - "CPXPARAM_Read_DataCheck 1\n", - "CPXPARAM_Threads 1\n", - "CPXPARAM_MIP_Tolerances_MIPGap 0\n", - "CPXPARAM_MIP_Tolerances_Integrality 0\n", - "CPXPARAM_MIP_Display 0\n", - "energy: -20.5\n", - "time: 0.026632682000126806\n", - "max-cut objective: -24.0\n", - "solution: [1 0 1 1]\n", - "solution objective: 24.0\n" - ] - } - ], - "source": [ - "cplex_installed = True\n", - "try:\n", - " CPLEX_Ising.check_pluggable_valid()\n", - "except Exception as e:\n", - " cplex_installed = False\n", - "\n", - "\n", - "if cplex_installed:\n", - " algorithm_cfg = {\n", - " 'name': 'CPLEX.Ising',\n", - " 'display': 0\n", - " }\n", - "\n", - " params = {\n", - " 'problem': {'name': 'ising'},\n", - " 'algorithm': algorithm_cfg\n", - " }\n", - "\n", - " result = run_algorithm(params, algo_input)\n", - "\n", - " x_dict = result['x_sol']\n", - " print('energy:', result['energy'])\n", - " print('time:', result['eval_time'])\n", - " print('max-cut objective:', result['energy'] + offset)\n", - " x = np.array([x_dict[i] for i in sorted(x_dict.keys())])\n", - " print('solution:', max_cut.get_graph_solution(x))\n", - " print('solution objective:', max_cut.max_cut_value(x, w))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we want VQE and so change it and add its other configuration parameters. VQE also needs and optimizer and variational form. While we can omit them from the dictionary, such that defaults are used, here we specify them explicitly so we can set their parameters as we desire." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "energy: -20.499999999997623\n", - "time: 12.321285724639893\n", - "max-cut objective: -23.999999999997623\n", - "solution: [1. 0. 1. 1.]\n", - "solution objective: 24.0\n" - ] - } - ], - "source": [ - "algorithm_cfg = {\n", - " 'name': 'VQE',\n", - " 'operator_mode': 'matrix'\n", - "}\n", - "\n", - "optimizer_cfg = {\n", - " 'name': 'L_BFGS_B',\n", - " 'maxfun': 6000\n", - "}\n", - "\n", - "var_form_cfg = {\n", - " 'name': 'RYRZ',\n", - " 'depth': 3,\n", - " 'entanglement': 'linear'\n", - "}\n", - "\n", - "params = {\n", - " 'problem': {'name': 'ising'},\n", - " 'algorithm': algorithm_cfg,\n", - " 'optimizer': optimizer_cfg,\n", - " 'variational_form': var_form_cfg\n", - "}\n", - "\n", - "backend = Aer.get_backend('statevector_simulator')\n", - "result = run_algorithm(params, algo_input, backend=backend)\n", - "\n", - "x = max_cut.sample_most_likely(result['eigvecs'][0])\n", - "print('energy:', result['energy'])\n", - "print('time:', result['eval_time'])\n", - "print('max-cut objective:', result['energy'] + offset)\n", - "print('solution:', max_cut.get_graph_solution(x))\n", - "print('solution objective:', max_cut.max_cut_value(x, w))" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.2" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/optimization/partition.ipynb b/community/optimization/partition.ipynb deleted file mode 100644 index c619277a4..000000000 --- a/community/optimization/partition.ipynb +++ /dev/null @@ -1,301 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": { - "collapsed": true - }, - "source": [ - "## _*Using Qiskit Aqua for partition problems*_\n", - "\n", - "This Qiskit Aqua Optimization notebook demonstrates how to use the VQE algorithm to compute a balanced partition of a set of numbers. This problem is known as \"number partitioning\" or simply \"partition\" in computer science.\n", - "\n", - "The problem is defined as follows. We are given a set of numbers $S$, and we want to determine a partition of $S$ into disjoint sets $S_1, S_2$ such that $|\\sum_{a \\in S_1} - \\sum_{a \\in S_2}|$ is minimized.\n", - "\n", - "The list of numbers provided as an input is used first to generate an Ising Hamiltonian, which is then passed as an input to VQE. As a reference, this notebook also computes the maximum stable set using the Exact Eigensolver classical algorithm and the solver embedded in the commercial IBM CPLEX product (if it is available in the system and the user has followed the necessary configuration steps in order for Qiskit Aqua to find it). Please refer to the Qiskit Aqua Optimization documentation for installation and configuration details for CPLEX." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "from qiskit.aqua import Operator, run_algorithm\n", - "from qiskit.aqua.input import EnergyInput\n", - "from qiskit.aqua.translators.ising import partition\n", - "from qiskit import Aer\n", - "from qiskit.aqua.algorithms.classical.cplex.cplex_ising import CPLEX_Ising" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here an Operator instance is created for our Hamiltonian. In this case the Paulis are from an Ising Hamiltonian of the number partitioning problem (expressed in minimization form). Rather than minimizing the absolute value of the difference of the sum of numbers into two sets, we minimize the difference square.\n", - "\n", - "We load a small instance of the problem." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ 1 3 4 7 10 13 15 16]\n" - ] - } - ], - "source": [ - "number_list = partition.read_numbers_from_file('sample.partition')\n", - "qubitOp, offset = partition.get_partition_qubitops(number_list)\n", - "algo_input = EnergyInput(qubitOp)\n", - "print(number_list)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We also offer a function to generate a set of numbers as a input." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ 9 8 23 4 2]\n" - ] - } - ], - "source": [ - "if True:\n", - " np.random.seed(8123179)\n", - " number_list = partition.random_number_list(5, weight_range=25)\n", - " qubitOp, offset = partition.get_partition_qubitops(number_list)\n", - " algo_input.qubit_op = qubitOp\n", - " print(number_list)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here we test for the presence of algorithms we want to use in this notebook. If Aqua is installed correctly `ExactEigensolver` and `VQE` will always be found. `CPLEX.Ising` is dependent on IBM CPLEX being installed (see introduction above). CPLEX is *not required* but if installed then this notebook will demonstrate the `CPLEX.Ising` algorithm , that uses CPLEX, to compute partition as well." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "['ExactEigensolver', 'CPLEX.Ising', 'VQE']\n" - ] - } - ], - "source": [ - "to_be_tested_algos = ['ExactEigensolver', 'CPLEX.Ising', 'VQE']\n", - "print(to_be_tested_algos)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can now use the Operator without regard to how it was created. First we need to prepare the configuration params to invoke the algorithm. Here we will use the ExactEigensolver first to return the smallest eigenvalue. Backend is not required since this is computed classically not using quantum computation. We then add in the qubitOp Operator in dictionary format. Now the complete params can be passed to the algorithm and run. The result is a dictionary." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "energy: -694.0\n", - "partition objective: 0.0\n", - "solution: [1. 1. 0. 1. 1.]\n", - "solution objective: 0\n" - ] - } - ], - "source": [ - "algorithm_cfg = {\n", - " 'name': 'ExactEigensolver',\n", - "}\n", - "\n", - "params = {\n", - " 'problem': {'name': 'ising'},\n", - " 'algorithm': algorithm_cfg\n", - "}\n", - "result = run_algorithm(params,algo_input)\n", - "\n", - "x = partition.sample_most_likely(result['eigvecs'][0])\n", - "print('energy:', result['energy'])\n", - "print('partition objective:', result['energy'] + offset)\n", - "print('solution:', x)\n", - "print('solution objective:', partition.partition_value(x, number_list))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "*Note*: IBM CPLEX is an _optional_ installation addition for Aqua. If installed then the Aqua CPLEX.Ising algorithm will be able to be used. If not, then solving this problem using this particular algorithm will simply be skipped. \n", - "\n", - "We change the configuration parameters to solve it with the CPLEX backend. The CPLEX backend can deal with a particular type of Hamiltonian called Ising Hamiltonian, which consists of only Pauli Z at most second order and often for combinatorial optimization problems that can be formulated as quadratic unconstrained binary optimization problems, such as the Number Partitioning problem.\n", - "\n", - "Note that for a Number Partitioning problem, since we are computing a bipartition of the set $S$, every binary vector $x$ and its complement (i.e., the vector $y$ such that $y_j = 1 - x_j$ for all $j$) represent exactly the same solution, and will have the same objective function value. Different solution methods may return solutions that look different, but in fact have the same objective function value." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPXPARAM_TimeLimit 600\n", - "CPXPARAM_Read_DataCheck 1\n", - "CPXPARAM_Threads 1\n", - "CPXPARAM_MIP_Tolerances_MIPGap 0\n", - "CPXPARAM_MIP_Tolerances_Integrality 0\n", - "CPXPARAM_MIP_Display 0\n", - "energy: -694.0\n", - "time: 0.007695371999943745\n", - "partition objective: 0.0\n", - "solution: [1 1 0 1 1]\n", - "solution objective: 0\n" - ] - } - ], - "source": [ - "cplex_installed = True\n", - "try:\n", - " CPLEX_Ising.check_pluggable_valid()\n", - "except Exception as e:\n", - " cplex_installed = False\n", - " \n", - "if cplex_installed:\n", - " algorithm_cfg = {\n", - " 'name': 'CPLEX.Ising',\n", - " 'display': 0\n", - " }\n", - "\n", - " params = {\n", - " 'problem': {'name': 'ising'},\n", - " 'algorithm': algorithm_cfg\n", - " }\n", - "\n", - " result = run_algorithm(params, algo_input)\n", - "\n", - " x_dict = result['x_sol']\n", - " print('energy:', result['energy'])\n", - " print('time:', result['eval_time'])\n", - " print('partition objective:', result['energy'] + offset)\n", - " x = np.array([x_dict[i] for i in sorted(x_dict.keys())])\n", - " print('solution:', x)\n", - " print('solution objective:', partition.partition_value(x, number_list))\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we want VQE and so change it and add its other configuration parameters. VQE also needs and optimizer and variational form. While we can omit them from the dictionary, such that defaults are used, here we specify them explicitly so we can set their parameters as we desire." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "energy: -693.9999999996322\n", - "time: 378.3389091491699\n", - "partition objective: 3.6777692002942786e-10\n", - "solution: [1. 1. 0. 1. 1.]\n", - "solution objective: 0\n" - ] - } - ], - "source": [ - "\n", - "algorithm_cfg = {\n", - " 'name': 'VQE',\n", - " 'operator_mode': 'matrix'\n", - "}\n", - "\n", - "optimizer_cfg = {\n", - " 'name': 'L_BFGS_B',\n", - " 'maxfun': 6000\n", - "}\n", - "\n", - "var_form_cfg = {\n", - " 'name': 'RYRZ',\n", - " 'depth': 3,\n", - " 'entanglement': 'linear'\n", - "}\n", - "\n", - "params = {\n", - " 'problem': {'name': 'ising'},\n", - " 'algorithm': algorithm_cfg,\n", - " 'optimizer': optimizer_cfg,\n", - " 'variational_form': var_form_cfg\n", - "}\n", - "\n", - "backend = Aer.get_backend('statevector_simulator')\n", - "result = run_algorithm(params, algo_input, backend=backend)\n", - "\n", - "x = partition.sample_most_likely(result['eigvecs'][0])\n", - "print('energy:', result['energy'])\n", - "print('time:', result['eval_time'])\n", - "print('partition objective:', result['energy'] + offset)\n", - "print('solution:', x)\n", - "print('solution objective:', partition.partition_value(x, number_list))" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "mykernel", - "language": "python", - "name": "mykernel" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.7" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/optimization/sample.exactcover b/community/optimization/sample.exactcover deleted file mode 100644 index 325e206dc..000000000 --- a/community/optimization/sample.exactcover +++ /dev/null @@ -1 +0,0 @@ -[[2,3,4], [1, 2], [3,4], [1,2,3]] diff --git a/community/optimization/sample.maxcut b/community/optimization/sample.maxcut deleted file mode 100644 index 84d5352f4..000000000 --- a/community/optimization/sample.maxcut +++ /dev/null @@ -1,21 +0,0 @@ -10 20 -1 5 1 -1 9 1 -2 4 1 -2 7 1 -2 9 1 -3 5 1 -3 8 1 -3 10 1 -4 9 1 -4 10 1 -5 8 1 -5 10 1 -6 7 1 -6 8 1 -6 9 1 -6 10 1 -7 9 1 -7 10 1 -8 9 1 -8 10 1 diff --git a/community/optimization/sample.partition b/community/optimization/sample.partition deleted file mode 100644 index acfe57e6f..000000000 --- a/community/optimization/sample.partition +++ /dev/null @@ -1,8 +0,0 @@ -1 -3 -4 -7 -10 -13 -15 -16 diff --git a/community/optimization/sample.setpacking b/community/optimization/sample.setpacking deleted file mode 100644 index 99340e656..000000000 --- a/community/optimization/sample.setpacking +++ /dev/null @@ -1 +0,0 @@ -[[4,5], [4], [5]] diff --git a/community/optimization/set_packing.ipynb b/community/optimization/set_packing.ipynb deleted file mode 100644 index 4d435e1e2..000000000 --- a/community/optimization/set_packing.ipynb +++ /dev/null @@ -1,277 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## _*Using Qiskit Aqua for set packing problems*_\n", - "\n", - "Given a collection $S$ of subsets of a set $X$, the set packing problem tries to find the subsets that are pairwise disjoint (in other words, no two of them share an element). The goal is to maximize the number of such subsets.\n", - "\n", - "We will go through three examples to show:\n", - "1. How to run the optimization using the declarative approach\n", - "2. How to run the optimization using the programmatic approach\n", - "3. How how to run the optimization with the VQE." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### The problem and the brute-force method.\n", - "\n", - "The problem is as follows. First, let us print the list of subsets." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[4, 5], [4], [5]]\n" - ] - } - ], - "source": [ - "import numpy as np\n", - "import json\n", - "\n", - "from qiskit import BasicAer\n", - "\n", - "from qiskit.aqua import run_algorithm\n", - "from qiskit.aqua.input import EnergyInput\n", - "from qiskit.aqua.translators.ising import set_packing\n", - "from qiskit.aqua.algorithms import ExactEigensolver\n", - "\n", - "\n", - "input_file = 'sample.setpacking'\n", - "with open(input_file) as f:\n", - " list_of_subsets = json.load(f)\n", - " print(list_of_subsets)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The brute-force method is as follows. Basically, we exhaustively try all the binary assignments. In each binary assignment, the entry of a subset is either 0 (meaning the subset is not taken) or 1 (meaning the subset is taken). We print the binary assignment that satisfies the definition of the set packing. " - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Size of set packing 2\n" - ] - } - ], - "source": [ - "def brute_force():\n", - " # brute-force way: try every possible assignment!\n", - " def bitfield(n, L):\n", - " result = np.binary_repr(n, L)\n", - " return [int(digit) for digit in result] # [2:] to chop off the \"0b\" part\n", - "\n", - " L = len(list_of_subsets)\n", - " max = 2**L\n", - " max_v = -np.inf\n", - " for i in range(max):\n", - " cur = bitfield(i, L)\n", - " cur_v = set_packing.check_disjoint(cur, list_of_subsets)\n", - " if cur_v:\n", - " if np.count_nonzero(cur) > max_v:\n", - " max_v = np.count_nonzero(cur)\n", - " return max_v\n", - "\n", - "size = brute_force()\n", - "print(\"Size of set packing\", size)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Part I: Run the optimization using the declarative approach\n", - "\n", - "Here the steps are:\n", - "* Create the qubit operator i.e. Ising Hamiltonian, using `set_packing` ising translator\n", - "* Create an EnergyInput object and a dictionary describing the algorithm and the components for Aqua to solve the problem\n", - "* Run the algorithm and get the result\n", - "* Use the result with the `set_packing` object to determine a solution" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Size of set packing 2\n" - ] - } - ], - "source": [ - "qubit_op, offset = set_packing.get_set_packing_qubitops(list_of_subsets)\n", - "\n", - "algo_input = EnergyInput(qubit_op)\n", - "params = {\n", - " 'problem': {'name': 'ising'},\n", - " 'algorithm': {'name': 'ExactEigensolver'}\n", - "}\n", - "result = run_algorithm(params, algo_input)\n", - "\n", - "x = set_packing.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", - "ising_sol = set_packing.get_solution(x)\n", - "np.testing.assert_array_equal(ising_sol, [0, 1, 1])\n", - "print(\"Size of set packing\", np.count_nonzero(ising_sol))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Part II: Run the optimization using the programmatic approach\n", - "\n", - "The main difference here is running the Aqua algorithm. Here we directly construct the algorithm and then run() it to get the result. The post computation on the result is identical." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Size of set packing 2\n" - ] - } - ], - "source": [ - "algo = ExactEigensolver(qubit_op)\n", - "result = algo.run()\n", - "\n", - "x = set_packing.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", - "ising_sol = set_packing.get_solution(x)\n", - "np.testing.assert_array_equal(ising_sol, [0, 1, 1])\n", - "oracle = brute_force()\n", - "print(\"Size of set packing\", np.count_nonzero(ising_sol))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Part III: Run the optimization with the VQE\n", - "\n", - "##### Declarative\n", - "\n", - "We reuse the EnergyInput object we created above. VQE algorithm needs an optimizer and a variational form. Then also we need a quantum backend on which the algorithm will run." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Size of set packing 2\n" - ] - } - ], - "source": [ - "params = {\n", - " 'problem': {'name': 'ising', 'random_seed': 100},\n", - " 'algorithm': {'name': 'VQE'},\n", - " 'optimizer': {'name': 'COBYLA'},\n", - " 'variational_form': {'name': 'RY', 'depth': 5, 'entanglement': 'linear'}\n", - "}\n", - "backend = BasicAer.get_backend('statevector_simulator')\n", - "result = run_algorithm(params, algo_input, backend=backend)\n", - "\n", - "x = set_packing.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", - "ising_sol = set_packing.get_solution(x)\n", - "print(\"Size of set packing\", np.count_nonzero(ising_sol))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Programmatic\n", - "\n", - "We can create the objects directly ourselves too and run VQE for the result" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Size of set packing 2\n" - ] - } - ], - "source": [ - "from qiskit.aqua import aqua_globals\n", - "from qiskit.aqua.algorithms import VQE\n", - "from qiskit.aqua.components.optimizers import COBYLA\n", - "from qiskit.aqua.components.variational_forms import RY\n", - "\n", - "aqua_globals.random_seed = 100\n", - "\n", - "optimizer = COBYLA()\n", - "var_form = RY(qubit_op.num_qubits, depth=5, entanglement='linear')\n", - "vqe = VQE(qubit_op, var_form, optimizer)\n", - "\n", - "backend = BasicAer.get_backend('statevector_simulator')\n", - "result = vqe.run(backend)\n", - "\n", - "x = set_packing.sample_most_likely(len(list_of_subsets), result['eigvecs'][0])\n", - "ising_sol = set_packing.get_solution(x)\n", - "print(\"Size of set packing\", np.count_nonzero(ising_sol))" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.2" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/community/optimization/stable_set.ipynb b/community/optimization/stable_set.ipynb deleted file mode 100644 index dfe91fa4f..000000000 --- a/community/optimization/stable_set.ipynb +++ /dev/null @@ -1,293 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": { - "collapsed": true - }, - "source": [ - "## _*Using Qiskit Aqua for stable-set problems*_\n", - "\n", - "This Qiskit Aqua Optimization notebook demonstrates how to use the VQE algorithm to compute the maximum stable set of a given graph. \n", - "\n", - "The problem is defined as follows. Given a graph $G = (V,E)$, we want to compute $S \\subseteq V$ such that there do not exist $i, j \\in S : (i, j) \\in E$, and $|S|$ is maximized. In other words, we are looking for a maximum cardinality set of mutually non-adjacent vertices.\n", - "\n", - "The graph provided as an input is used first to generate an Ising Hamiltonian, which is then passed as an input to VQE. As a reference, this notebook also computes the maximum stable set using the Exact Eigensolver classical algorithm and the solver embedded in the commercial IBM CPLEX product (if it is available in the system and the user has followed the necessary configuration steps in order for Qiskit Aqua to find it). Please refer to the Qiskit Aqua Optimization documentation for installation and configuration details for CPLEX." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "\n", - "from qiskit.aqua import Operator, run_algorithm\n", - "from qiskit.aqua.translators.ising import stable_set\n", - "from qiskit.aqua.input import EnergyInput\n", - "from qiskit.aqua.algorithms.classical.cplex.cplex_ising import CPLEX_Ising\n", - "from qiskit import Aer" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here an Operator instance is created for our Hamiltonian. In this case the Paulis are from an Ising Hamiltonian of the maximum stable set problem (expressed in minimization form). We load a small instance of the maximum stable set problem." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "w = stable_set.parse_gset_format('sample.maxcut')\n", - "qubitOp, offset = stable_set.get_stable_set_qubitops(w)\n", - "algo_input = EnergyInput(qubitOp)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We also offer a function to generate a random graph as a input." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[0. 1. 1. 1. 0.]\n", - " [1. 0. 0. 0. 1.]\n", - " [1. 0. 0. 1. 1.]\n", - " [1. 0. 1. 0. 0.]\n", - " [0. 1. 1. 0. 0.]]\n" - ] - } - ], - "source": [ - "if True:\n", - " np.random.seed(8123179)\n", - " w = stable_set.random_graph(5, edge_prob=0.5)\n", - " qubitOp, offset = stable_set.get_stable_set_qubitops(w)\n", - " algo_input.qubit_op = qubitOp\n", - "print(w)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here we test for the presence of algorithms we want to use in this notebook. If Aqua is installed correctly `ExactEigensolver` and `VQE` will always be found. `CPLEX.Ising` is dependent on IBM CPLEX being installed (see introduction above). CPLEX is *not required* but if installed then this notebook will demonstrate the `CPLEX.Ising` algorithm , that uses CPLEX, to compute stable set as well." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "['ExactEigensolver', 'CPLEX.Ising', 'VQE']\n" - ] - } - ], - "source": [ - "to_be_tested_algos = ['ExactEigensolver', 'CPLEX.Ising', 'VQE']\n", - "print(to_be_tested_algos)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can now use the Operator without regard to how it was created. First we need to prepare the configuration params to invoke the algorithm. Here we will use the ExactEigensolver first to return the smallest eigenvalue. Backend is not required since this is computed classically not using quantum computation. We then add in the qubitOp Operator in dictionary format. Now the complete params can be passed to the algorithm and run. The result is a dictionary." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "energy: -5.5\n", - "stable set objective: -2.0\n", - "solution: [0. 1. 1. 0. 0.]\n", - "solution objective and feasibility: (2.0, True)\n" - ] - } - ], - "source": [ - "algorithm_cfg = {\n", - " 'name': 'ExactEigensolver',\n", - "}\n", - "\n", - "params = {\n", - " 'problem': {'name': 'ising'},\n", - " 'algorithm': algorithm_cfg\n", - "}\n", - "result = run_algorithm(params,algo_input)\n", - "\n", - "x = stable_set.sample_most_likely(result['eigvecs'][0])\n", - "print('energy:', result['energy'])\n", - "print('stable set objective:', result['energy'] + offset)\n", - "print('solution:', stable_set.get_graph_solution(x))\n", - "print('solution objective and feasibility:', stable_set.stable_set_value(x, w))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "*Note*: IBM CPLEX is an _optional_ installation addition for Aqua. If installed then the Aqua CPLEX.Ising algorithm will be able to be used. If not, then solving this problem using this particular algorithm will simply be skipped.\n", - "\n", - "We change the configuration parameters to solve it with the CPLEX backend. The CPLEX backend can deal with a particular type of Hamiltonian called Ising Hamiltonian, which consists of only Pauli Z at most second order and can be used for combinatorial optimization problems that can be formulated as quadratic unconstrained binary optimization problems, such as the stable set problem. Note that we may obtain a different solution - but if the objective value is the same as above, the solution will be optimal." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPXPARAM_TimeLimit 600\n", - "CPXPARAM_Read_DataCheck 1\n", - "CPXPARAM_Threads 1\n", - "CPXPARAM_MIP_Tolerances_MIPGap 0\n", - "CPXPARAM_MIP_Tolerances_Integrality 0\n", - "CPXPARAM_MIP_Display 0\n", - "energy: -5.5\n", - "time: 0.011368974000106391\n", - "stable set objective: -2.0\n", - "solution: [0 0 0 1 1]\n", - "solution objective and feasibility: (2, True)\n" - ] - } - ], - "source": [ - "cplex_installed = True\n", - "try:\n", - " CPLEX_Ising.check_pluggable_valid()\n", - "except Exception as e:\n", - " cplex_installed = False\n", - "\n", - "\n", - "if cplex_installed:\n", - " algorithm_cfg = {\n", - " 'name': 'CPLEX.Ising',\n", - " 'display': 0\n", - " }\n", - "\n", - " params = {\n", - " 'problem': {'name': 'ising'},\n", - " 'algorithm': algorithm_cfg\n", - " }\n", - "\n", - " result = run_algorithm(params, algo_input)\n", - "\n", - " x_dict = result['x_sol']\n", - " print('energy:', result['energy'])\n", - " print('time:', result['eval_time'])\n", - " print('stable set objective:', result['energy'] + offset)\n", - " x = np.array([x_dict[i] for i in sorted(x_dict.keys())])\n", - " print('solution:', stable_set.get_graph_solution(x))\n", - " print('solution objective and feasibility:', stable_set.stable_set_value(x, w))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we want VQE and so change it and add its other configuration parameters. VQE also needs and optimizer and variational form. While we can omit them from the dictionary, such that defaults are used, here we specify them explicitly so we can set their parameters as we desire." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "energy: -5.499999999924708\n", - "time: 95.46273922920227\n", - "stable set objective: -1.9999999999247082\n", - "solution: [0. 0. 0. 1. 1.]\n", - "solution objective and feasibility: (2.0, True)\n" - ] - } - ], - "source": [ - "algorithm_cfg = {\n", - " 'name': 'VQE',\n", - " 'operator_mode': 'matrix'\n", - "}\n", - "\n", - "optimizer_cfg = {\n", - " 'name': 'L_BFGS_B',\n", - " 'maxfun': 2000\n", - "}\n", - "\n", - "var_form_cfg = {\n", - " 'name': 'RYRZ',\n", - " 'depth': 3,\n", - " 'entanglement': 'linear'\n", - "}\n", - "\n", - "params = {\n", - " 'problem': {'name': 'ising'},\n", - " 'algorithm': algorithm_cfg,\n", - " 'optimizer': optimizer_cfg,\n", - " 'variational_form': var_form_cfg\n", - "}\n", - "\n", - "backend = Aer.get_backend('statevector_simulator')\n", - "result = run_algorithm(params, algo_input, backend=backend)\n", - "\n", - "x = stable_set.sample_most_likely(result['eigvecs'][0])\n", - "print('energy:', result['energy'])\n", - "print('time:', result['eval_time'])\n", - "print('stable set objective:', result['energy'] + offset)\n", - "print('solution:', stable_set.get_graph_solution(x))\n", - "print('solution objective and feasibility:', stable_set.stable_set_value(x, w))" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.2" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/optimization/vertex_cover.ipynb b/community/optimization/vertex_cover.ipynb deleted file mode 100644 index 00aec67c9..000000000 --- a/community/optimization/vertex_cover.ipynb +++ /dev/null @@ -1,277 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## _*Using Qiskit Aqua for the vertex-cover problems*_\n", - "\n", - "A vertex cover of a graph is a set of vertices such that each edge of the graph is incident to at least one vertex of the set. The goal of NPC problem is to minimize the size of the vertex cover. \n", - "\n", - "We will go through three examples to show:\n", - "1. How to run the optimization using the declarative approach\n", - "2. How to run the optimization using the programmatic approach\n", - "3. How how to run the optimization with the VQE." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### The problem and the brute-force method\n", - "\n", - "The problem is as follows. the graph is in the adjacent matrix form." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[0. 4. 5.]\n", - " [4. 0. 3.]\n", - " [5. 3. 0.]]\n" - ] - } - ], - "source": [ - "import numpy as np\n", - "from qiskit import BasicAer\n", - "from qiskit.aqua import run_algorithm\n", - "from qiskit.aqua.input import EnergyInput\n", - "from qiskit.aqua.translators.ising import vertex_cover\n", - "from qiskit.aqua.algorithms import ExactEigensolver\n", - "\n", - "np.random.seed(100)\n", - "num_nodes = 3\n", - "w = vertex_cover.random_graph(num_nodes, edge_prob=0.8, weight_range=10)\n", - "print(w)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The brute-force method is as follows. Basically, we exhaustively try all the binary assignments. In each binary assignment, the entry of a vertex is either 0 (meaning the vertex is not in the cover) or 1 (meaning the vertex is in the cover). We print the binary assignment that satisfies the definition of the vertex cover and corresponds to the minimial size. " - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Size of the vertex cover 2\n" - ] - } - ], - "source": [ - "def brute_force():\n", - " # brute-force way\n", - " def bitfield(n, L):\n", - " result = np.binary_repr(n, L)\n", - " return [int(digit) for digit in result] # [2:] to chop off the \"0b\" part\n", - "\n", - " L = num_nodes\n", - " max = 2**L\n", - " minimal_v = np.inf\n", - " for i in range(max):\n", - " cur = bitfield(i, L)\n", - "\n", - " cur_v = vertex_cover.check_full_edge_coverage(np.array(cur), w)\n", - " if cur_v:\n", - " nonzerocount = np.count_nonzero(cur)\n", - " if nonzerocount < minimal_v:\n", - " minimal_v = nonzerocount\n", - "\n", - " return minimal_v\n", - "\n", - "size = brute_force()\n", - "print('Size of the vertex cover', size)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Part I: Run the optimization using the declarative approach\n", - "\n", - "Here the steps are:\n", - "* Create the qubit operator i.e. Ising Hamiltonian, using `vertex_cover` ising translator\n", - "* Create an EnergyInput object and a dictionary describing the algorithm and the components for Aqua to solve the problem\n", - "* Run the algorithm and get the result\n", - "* Use the result with the `vertex_cover` object to determine a solution" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Size of the vertex cover 2\n" - ] - } - ], - "source": [ - "qubit_op, offset = vertex_cover.get_vertex_cover_qubitops(w)\n", - "\n", - "algo_input = EnergyInput(qubit_op)\n", - "params = {\n", - " 'problem': {'name': 'ising'},\n", - " 'algorithm': {'name': 'ExactEigensolver'}\n", - "}\n", - "result = run_algorithm(params, algo_input)\n", - "\n", - "x = vertex_cover.sample_most_likely(len(w), result['eigvecs'][0])\n", - "sol = vertex_cover.get_graph_solution(x)\n", - "np.testing.assert_array_equal(sol, [0, 1, 1])\n", - "print('Size of the vertex cover', np.count_nonzero(sol))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Part II: Run the optimization using the programmatic approach\n", - "\n", - "The main difference here is running the Aqua algorithm. Here we directly construct the algorithm and then run() it to get the result. The post computation on the result is identical." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Size of the vertex cover 2\n" - ] - } - ], - "source": [ - "algo = ExactEigensolver(qubit_op)\n", - "result = algo.run()\n", - "\n", - "x = vertex_cover.sample_most_likely(len(w), result['eigvecs'][0])\n", - "sol = vertex_cover.get_graph_solution(x)\n", - "np.testing.assert_array_equal(sol, [0, 1, 1])\n", - "print('Size of the vertex cover', np.count_nonzero(sol))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Part III: Run the optimization with the VQE\n", - "\n", - "##### Declarative\n", - "\n", - "We reuse the EnergyInput object we created above. VQE algorithm needs an optimizer and a variational form. Then also we need a quantum backend on which the algorithm will run." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Size of the vertex cover 2\n" - ] - } - ], - "source": [ - "params = {\n", - " 'problem': {'name': 'ising', 'random_seed': 100},\n", - " 'algorithm': {'name': 'VQE', 'operator_mode': 'paulis'},\n", - " 'optimizer': {'name': 'SPSA', 'max_trials': 200},\n", - " 'variational_form': {'name': 'RYRZ', 'depth': 3}\n", - "}\n", - "backend = BasicAer.get_backend('qasm_simulator')\n", - "result = run_algorithm(params, algo_input, backend=backend)\n", - "\n", - "x = vertex_cover.sample_most_likely(len(w), result['eigvecs'][0])\n", - "sol = vertex_cover.get_graph_solution(x)\n", - "print('Size of the vertex cover', np.count_nonzero(sol))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Programmatic\n", - "\n", - "We can create the objects directly ourselves too and run VQE for the result" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Size of the vertex cover 2\n" - ] - } - ], - "source": [ - "from qiskit.aqua import aqua_globals\n", - "from qiskit.aqua.algorithms import VQE\n", - "from qiskit.aqua.components.optimizers import SPSA\n", - "from qiskit.aqua.components.variational_forms import RYRZ\n", - "\n", - "aqua_globals.random_seed = 100\n", - "\n", - "optimizer = SPSA(max_trials=200)\n", - "var_form = RYRZ(qubit_op.num_qubits, depth=3)\n", - "vqe = VQE(qubit_op, var_form, optimizer, operator_mode='paulis')\n", - "\n", - "backend = BasicAer.get_backend('qasm_simulator')\n", - "result = vqe.run(backend)\n", - "\n", - "x = vertex_cover.sample_most_likely(len(w), result['eigvecs'][0])\n", - "sol = vertex_cover.get_graph_solution(x)\n", - "print('Size of the vertex cover', np.count_nonzero(sol))" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.2" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/qiskit/algorithm_introduction_with_vqe.ipynb b/qiskit/algorithm_introduction_with_vqe.ipynb deleted file mode 100644 index e74cbabe9..000000000 --- a/qiskit/algorithm_introduction_with_vqe.ipynb +++ /dev/null @@ -1,298 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": { - "collapsed": true - }, - "source": [ - "## _*Using Qiskit Aqua algorithms, a how to guide*_\n", - "\n", - "This notebook demonstrates how to use the `Qiskit Aqua` library to invoke an algorithm and process the result.\n", - "\n", - "Further information may be found for the algorithms in the online [Aqua documentation](https://qiskit.org/documentation/aqua/algorithms.html).\n", - "\n", - "Algorithms in Aqua can be created and run as usual in Python by constructing instances and calling methods. There is also a high level `run_algorithm` method that takes a configuration dictionary with data describing which algorithm to use, which components etc along with an InputInstance type to supply data to the algorithm. This latter approach is what we call `declarative` with the former, the regular Python way, `programmatic`. This tutorial will show both approaches.\n", - "\n", - "Aqua has many `algorithms` for solving different problems. For some we also have classical algorithms, that take the exact same input data, to solve the problem. This can be useful in the near term as Quantum algorithms are developed since we are still at a stage where we can do classical comparison of the result.\n", - "\n", - "Aqua also has various `components` which are dependent objects used by algorithms, such as variational forms, qfts, initial states etc. We will see more on this below.\n", - "\n", - "Lastly for developers we also have a collections of `circuits` and gates which can be used to help build out new components and algorithms.\n", - "\n", - "Here we will choose to show some of the main aspects of Aqua by solving a ground state energy problem." - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [], - "source": [ - "from qiskit.aqua import Operator" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As input, for an energy problem, we need a Hamiltonian and so we first create a suitable `Operator ` instance. In this case we have a paulis list, as below, from a previously computed Hamiltonian, that we saved, so as to focus this notebook on using the algorithms. We simply load these paulis to create the original Operator.\n", - "\n", - "This Hamiltonian was created originally using Qiskit Chemistry for an H2 molecule at 0.735A interatomic distance. Please refer to the chemistry tutorials here if you are interested in understanding more. Suffice to say at this level Aqua does not really care about the source of the Operator." - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [], - "source": [ - "pauli_dict = {\n", - " 'paulis': [{\"coeff\": {\"imag\": 0.0, \"real\": -1.052373245772859}, \"label\": \"II\"},\n", - " {\"coeff\": {\"imag\": 0.0, \"real\": 0.39793742484318045}, \"label\": \"ZI\"},\n", - " {\"coeff\": {\"imag\": 0.0, \"real\": -0.39793742484318045}, \"label\": \"IZ\"},\n", - " {\"coeff\": {\"imag\": 0.0, \"real\": -0.01128010425623538}, \"label\": \"ZZ\"},\n", - " {\"coeff\": {\"imag\": 0.0, \"real\": 0.18093119978423156}, \"label\": \"XX\"}\n", - " ]\n", - "}\n", - "\n", - "qubit_op = Operator.load_from_dict(pauli_dict)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Let's start with a classical algorithm\n", - "\n", - "We can now use the Operator without regard to how it was created. We chose to start this tutorial with a classical algorithm as it involves a little less setting up than the `VQE` quantum algorithm we will use later. Here we will use `ExactEigensolver` to compute the minimum eigenvalue of the Operator (Hamiltonian).\n", - "\n", - "#### First let's show the `programmatic` approach.\n", - "\n", - "We construct an `ExactEigensolver` instance, passing in the Operator, and then call `run()` on in order to compute the result. All Aqua algorithms have the run method (it is defined by a base class which all algorithms extend) and while no parameters are need for classical algorithms a quantum algorithm will require a backend (quantum simulator or real device) on which it will be run. The `result` object returned is a dictionary. While the results fields can be different for algorithms solving different problems, and even within a given problem type there may be algorithm specific data returned, for a given problem the fields core to that problem are common across algorithms in order that different algorithms can be chosen to solve the same problem in a consistent fashion." - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "-1.857275030202378\n" - ] - } - ], - "source": [ - "from qiskit.aqua.algorithms import ExactEigensolver\n", - "\n", - "ee = ExactEigensolver(qubit_op)\n", - "result = ee.run()\n", - "print(result['energy'])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Now let's show the `declarative` approach. \n", - "\n", - "Here we need to prepare a configuration dictionary of parameters to define the algorithm. Again we we will use the ExactEigensolver and need to create an `algorithm` where it is named by `name`. The name comes from a `CONFIGURATION` dictionary in the algorithm and this name is registered to the Aqua discovery framework so we can load the corresponding class and run it during the exceution of `run_algorithm`. `run_algorithm` requires the configuration dictionary and input data passed via an InputInstance class. For an energy problem the data is supplied via an EnergyInput (extends InputInstance), other problem types have their own specific InputInstance. `run_algorithm` returns the same dictionary as above (internally it calls the run() method of the algorithm and passes back the result)\n", - "\n", - "Note: there are other fields such `problem` that could have been added below. This field defaults to `energy`, which is what we want so it has been omitted. Defaults are convenient in the declarative form too as algorithms can define for both their properties as well as defaults for dependent components." - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "-1.8572750302023808\n" - ] - } - ], - "source": [ - "from qiskit.aqua import run_algorithm\n", - "from qiskit.aqua.input import EnergyInput\n", - "\n", - "aqua_cfg_dict = {\n", - " 'algorithm': {\n", - " 'name': 'ExactEigensolver'\n", - " }\n", - "}\n", - "\n", - "algo_input = EnergyInput(qubit_op)\n", - "result = run_algorithm(aqua_cfg_dict, algo_input)\n", - "print(result['energy'])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Lets switch now to using a Quantum algorithm.\n", - "\n", - "We will use the Variational Quantum Eigensolver (VQE) to solve the same problem as above. As its name implies its uses a variational approach. An ansatz (a variational form) is supplied and using a quantum/classical hybrid technique the energy resulting from evaluating the Operator with the variational form on a quantum backend is taken down to a minimum using a classical optimizer that varies the parameters of the variational form.\n", - "\n", - "#### Lets do the `declarative` approach first this time\n", - "\n", - "In the description above we talked about `VQE` a `variational form` and an `optimizer`. We can now set this up as a dictionary. While we can omit them from the dictionary, such that defaults are used, here we specify them explicitly so we can set their parameters as we desire.\n", - "\n", - "As this is a quantum algorithm we need to specify a backend. Here we use the `statevector_simpulator` from the `qiskit.BasicAer` provider from `Qiskit Terra`. As this is a variational algorithm going from quantum to classical and looping until it finds a minimum it takes a few seconds. The result here is very close to our classical result above." - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "-1.8572750302012253\n" - ] - } - ], - "source": [ - "aqua_cfg_dict = {\n", - " 'algorithm': {\n", - " 'name': 'VQE',\n", - " 'operator_mode': 'matrix'\n", - " },\n", - " 'variational_form': {\n", - " 'name': 'RYRZ',\n", - " 'depth': 3,\n", - " 'entanglement': 'linear'\n", - " },\n", - " 'optimizer': {\n", - " 'name': 'L_BFGS_B',\n", - " 'maxfun': 1000\n", - " },\n", - " 'backend': {\n", - " 'name': 'statevector_simulator',\n", - " 'provider': 'qiskit.BasicAer'\n", - " }\n", - "}\n", - "\n", - "algo_input = EnergyInput(qubit_op)\n", - "result = run_algorithm(aqua_cfg_dict, algo_input)\n", - "print(result['energy'])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### And now `programmatic`\n", - " \n", - "Here we create the variational form and optimizer and then pass them to VQE along with the Operator. The backend is created and passed to the algorithm so it can be run there." - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "-1.8572750301886618\n" - ] - } - ], - "source": [ - "from qiskit import BasicAer\n", - "from qiskit.aqua.algorithms import VQE\n", - "from qiskit.aqua.components.variational_forms import RYRZ\n", - "from qiskit.aqua.components.optimizers import L_BFGS_B\n", - "\n", - "var_form = RYRZ(qubit_op.num_qubits, depth=3, entanglement='linear')\n", - "optimizer = L_BFGS_B(maxfun=1000)\n", - "vqe = VQE(qubit_op, var_form, optimizer)\n", - "backend = BasicAer.get_backend('statevector_simulator')\n", - "result = vqe.run(backend)\n", - "print(result['energy'])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "While a backend can be passed directly to the quantum algorithm run(), internally it will be detected as such and wrapped as a QuantumInstance. However by doing this explicitly yourself, as below, various parameters governing the execution can be set, including in more advanced cases ability to set noise models, coupling maps etc. The following shows the above but using a QuantumInstance and setting up a default transpiler PassManager for circuit processing." - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "-1.8572750302012366\n" - ] - } - ], - "source": [ - "from qiskit.aqua import QuantumInstance\n", - "from qiskit.transpiler import PassManager\n", - "\n", - "var_form = RYRZ(qubit_op.num_qubits, depth=3, entanglement='linear')\n", - "optimizer = L_BFGS_B(maxfun=1000)\n", - "vqe = VQE(qubit_op, var_form, optimizer)\n", - "backend = BasicAer.get_backend('statevector_simulator')\n", - "qi = QuantumInstance(backend=backend, pass_manager=PassManager())\n", - "result = vqe.run(qi)\n", - "print(result['energy'])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Concluding\n", - "\n", - "This completes an introduction to programming and using Aqua algorithms. There are plenty of other tutorials showing Aqua being used to solve other problems, including AI, Finance, Optimization and Chemistry. We encourage you to explore these further and see that various capabilities and techniques employed." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/qiskit/artificial_intelligence/index.ipynb b/qiskit/artificial_intelligence/index.ipynb index 30d03091c..645421d35 100644 --- a/qiskit/artificial_intelligence/index.ipynb +++ b/qiskit/artificial_intelligence/index.ipynb @@ -4,17 +4,15 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Qiskit Aqua Artificial Intelligence\n", + "# Qiskit Artificial Intelligence\n", "\n", - "Qiskit Aqua Artificial Intelligence is a set of tools, algorithms and software for use with quantum computers to \n", - "carry out research and investigate how to take advantage of quantum computing power to solve artificial intelligence\n", - "problems. \n", + "Qiskit Artificial Intelligence is a set of tools, algorithms and software for use with quantum computers to carry out research and investigate how to take advantage of quantum computing power to solve artificial intelligence problems. \n", "\n", "## Contents\n", "\n", "* [Quantum SVM for Classification](qsvm_classification.ipynb)\n", "* [qGANs for Learning & Loading Random Distributions](qgans_for_loading_random_distributions.ipynb)\n", - "* More examples can be found in [commuity/aqua/artificial_intelligence](../../../community/aqua/artificial_intelligence)" + "* More examples can be found in [community/artificial_intelligence](https://github.com/Qiskit/qiskit-tutorials-community/tree/master/artificial_intelligence)" ] }, { @@ -43,7 +41,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.3" + "version": "3.6.1" } }, "nbformat": 4, diff --git a/qiskit/artificial_intelligence/qsvm_datasets.py b/qiskit/artificial_intelligence/qsvm_datasets.py deleted file mode 100644 index 1688b524a..000000000 --- a/qiskit/artificial_intelligence/qsvm_datasets.py +++ /dev/null @@ -1,559 +0,0 @@ -# -*- coding: utf-8 -*- - -# Copyright 2018 IBM. -# -# Licensed under the Apache License, Version 2.0 (the "License"); -# you may not use this file except in compliance with the License. -# You may obtain a copy of the License at -# -# http://www.apache.org/licenses/LICENSE-2.0 -# -# Unless required by applicable law or agreed to in writing, software -# distributed under the License is distributed on an "AS IS" BASIS, -# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -# See the License for the specific language governing permissions and -# limitations under the License. -# ============================================================================= - -import numpy as np -import scipy -from scipy.linalg import expm -import matplotlib.pyplot as plt -from mpl_toolkits.mplot3d import Axes3D -from sklearn import datasets -from sklearn.model_selection import train_test_split -from sklearn.preprocessing import StandardScaler, MinMaxScaler -from sklearn.decomposition import PCA - - -def ad_hoc_data(training_size, test_size, n, gap, PLOT_DATA): - class_labels = [r'A', r'B'] - if n == 2: - N = 100 - elif n == 3: - N = 20 # courseness of data seperation - - label_train = np.zeros(2*(training_size+test_size)) - sample_train = [] - sampleA = [[0 for x in range(n)] for y in range(training_size+test_size)] - sampleB = [[0 for x in range(n)] for y in range(training_size+test_size)] - - sample_Total = [[[0 for x in range(N)] for y in range(N)] for z in range(N)] - - interactions = np.transpose(np.array([[1, 0], [0, 1], [1, 1]])) - - steps = 2*np.pi/N - - sx = np.array([[0, 1], [1, 0]]) - X = np.asmatrix(sx) - sy = np.array([[0, -1j], [1j, 0]]) - Y = np.asmatrix(sy) - sz = np.array([[1, 0], [0, -1]]) - Z = np.asmatrix(sz) - J = np.array([[1, 0], [0, 1]]) - J = np.asmatrix(J) - H = np.array([[1, 1], [1, -1]])/np.sqrt(2) - H2 = np.kron(H, H) - H3 = np.kron(H, H2) - H = np.asmatrix(H) - H2 = np.asmatrix(H2) - H3 = np.asmatrix(H3) - - f = np.arange(2**n) - - my_array = [[0 for x in range(n)] for y in range(2**n)] - - for arindex in range(len(my_array)): - temp_f = bin(f[arindex])[2:].zfill(n) - for findex in range(n): - my_array[arindex][findex] = int(temp_f[findex]) - - my_array = np.asarray(my_array) - my_array = np.transpose(my_array) - - # Define decision functions - maj = (-1)**(2*my_array.sum(axis=0) > n) - parity = (-1)**(my_array.sum(axis=0)) - dict1 = (-1)**(my_array[0]) - if n == 2: - D = np.diag(parity) - elif n == 3: - D = np.diag(maj) - - Basis = np.random.random((2**n, 2**n)) + 1j*np.random.random((2**n, 2**n)) - Basis = np.asmatrix(Basis).getH()*np.asmatrix(Basis) - - [S, U] = np.linalg.eig(Basis) - - idx = S.argsort()[::-1] - S = S[idx] - U = U[:, idx] - - M = (np.asmatrix(U)).getH()*np.asmatrix(D)*np.asmatrix(U) - - psi_plus = np.transpose(np.ones(2))/np.sqrt(2) - psi_0 = 1 - for k in range(n): - psi_0 = np.kron(np.asmatrix(psi_0), np.asmatrix(psi_plus)) - - sample_total_A = [] - sample_total_B = [] - sample_total_void = [] - if n == 2: - for n1 in range(N): - for n2 in range(N): - x1 = steps*n1 - x2 = steps*n2 - phi = x1*np.kron(Z, J) + x2*np.kron(J, Z) + (np.pi-x1)*(np.pi-x2)*np.kron(Z, Z) - Uu = scipy.linalg.expm(1j*phi) - psi = np.asmatrix(Uu)*H2*np.asmatrix(Uu)*np.transpose(psi_0) - temp = np.asscalar(np.real(psi.getH()*M*psi)) - if temp > gap: - sample_Total[n1][n2] = +1 - elif temp < -gap: - sample_Total[n1][n2] = -1 - else: - sample_Total[n1][n2] = 0 - - # Now sample randomly from sample_Total a number of times training_size+testing_size - tr = 0 - while tr < (training_size+test_size): - draw1 = np.random.choice(N) - draw2 = np.random.choice(N) - if sample_Total[draw1][draw2] == +1: - sampleA[tr] = [2*np.pi*draw1/N, 2*np.pi*draw2/N] - tr += 1 - - tr = 0 - while tr < (training_size+test_size): - draw1 = np.random.choice(N) - draw2 = np.random.choice(N) - if sample_Total[draw1][draw2] == -1: - sampleB[tr] = [2*np.pi*draw1/N, 2*np.pi*draw2/N] - tr += 1 - - sample_train = [sampleA, sampleB] - - for lindex in range(training_size+test_size): - label_train[lindex] = 0 - for lindex in range(training_size+test_size): - label_train[training_size+test_size+lindex] = 1 - label_train = label_train.astype(int) - sample_train = np.reshape(sample_train, (2*(training_size+test_size), n)) - training_input = {key: (sample_train[label_train == k, :])[:training_size] - for k, key in enumerate(class_labels)} - test_input = {key: (sample_train[label_train == k, :])[training_size:( - training_size+test_size)] for k, key in enumerate(class_labels)} - - if PLOT_DATA: - img = plt.imshow(np.asmatrix(sample_Total).T, interpolation='nearest', - origin='lower', cmap='copper', extent=[0, 2*np.pi, 0, 2*np.pi]) - plt.show() - fig2 = plt.figure() - for k in range(0, 2): - plt.scatter(sample_train[label_train == k, 0][:training_size], - sample_train[label_train == k, 1][:training_size]) - - plt.title("Ad-hoc Data") - plt.show() - - elif n == 3: - for n1 in range(N): - for n2 in range(N): - for n3 in range(N): - x1 = steps*n1 - x2 = steps*n2 - x3 = steps*n3 - phi = x1*np.kron(np.kron(Z, J), J) + x2*np.kron(np.kron(J, Z), J) + x3*np.kron(np.kron(J, J), Z) + \ - (np.pi-x1)*(np.pi-x2)*np.kron(np.kron(Z, Z), J)+(np.pi-x2)*(np.pi-x3)*np.kron(np.kron(J, Z), Z) + \ - (np.pi-x1)*(np.pi-x3)*np.kron(np.kron(Z, J), Z) - Uu = scipy.linalg.expm(1j*phi) - psi = np.asmatrix(Uu)*H3*np.asmatrix(Uu)*np.transpose(psi_0) - temp = np.asscalar(np.real(psi.getH()*M*psi)) - if temp > gap: - sample_Total[n1][n2][n3] = +1 - sample_total_A.append([n1, n2, n3]) - elif temp < -gap: - sample_Total[n1][n2][n3] = -1 - sample_total_B.append([n1, n2, n3]) - else: - sample_Total[n1][n2][n3] = 0 - sample_total_void.append([n1, n2, n3]) - - # Now sample randomly from sample_Total a number of times training_size+testing_size - tr = 0 - while tr < (training_size+test_size): - draw1 = np.random.choice(N) - draw2 = np.random.choice(N) - draw3 = np.random.choice(N) - if sample_Total[draw1][draw2][draw3] == +1: - sampleA[tr] = [2*np.pi*draw1/N, 2*np.pi*draw2/N, 2*np.pi*draw3/N] - tr += 1 - - tr = 0 - while tr < (training_size+test_size): - draw1 = np.random.choice(N) - draw2 = np.random.choice(N) - draw3 = np.random.choice(N) - if sample_Total[draw1][draw2][draw3] == -1: - sampleB[tr] = [2*np.pi*draw1/N, 2*np.pi*draw2/N, 2*np.pi*draw3/N] - tr += 1 - - sample_train = [sampleA, sampleB] - - for lindex in range(training_size+test_size): - label_train[lindex] = 0 - for lindex in range(training_size+test_size): - label_train[training_size+test_size+lindex] = 1 - label_train = label_train.astype(int) - sample_train = np.reshape(sample_train, (2*(training_size+test_size), n)) - training_input = {key: (sample_train[label_train == k, :])[:training_size] - for k, key in enumerate(class_labels)} - test_input = {key: (sample_train[label_train == k, :])[training_size:( - training_size+test_size)] for k, key in enumerate(class_labels)} - - if PLOT_DATA: - - sample_total_A = np.asarray(sample_total_A) - sample_total_B = np.asarray(sample_total_B) - x1 = sample_total_A[:, 0] - y1 = sample_total_A[:, 1] - z1 = sample_total_A[:, 2] - - x2 = sample_total_B[:, 0] - y2 = sample_total_B[:, 1] - z2 = sample_total_B[:, 2] - - fig1 = plt.figure() - ax1 = fig1.add_subplot(1, 1, 1, projection='3d') - ax1.scatter(x1, y1, z1, c='#8A360F') - plt.show() - # - fig2 = plt.figure() - ax2 = fig2.add_subplot(1, 1, 1, projection='3d') - ax2.scatter(x2, y2, z2, c='#683FC8') - plt.show() - - sample_training_A = training_input['A'] - sample_training_B = training_input['B'] - - x1 = sample_training_A[:, 0] - y1 = sample_training_A[:, 1] - z1 = sample_training_A[:, 2] - - x2 = sample_training_B[:, 0] - y2 = sample_training_B[:, 1] - z2 = sample_training_B[:, 2] - - fig1 = plt.figure() - ax1 = fig1.add_subplot(1, 1, 1, projection='3d') - ax1.scatter(x1, y1, z1, c='#8A360F') - ax1.scatter(x2, y2, z2, c='#683FC8') - plt.show() - - return sample_Total, training_input, test_input, class_labels - - -def sample_ad_hoc_data(sample_Total, test_size, n): - tr = 0 - - class_labels = [r'A', r'B'] # copied from ad_hoc_data() - if n == 2: - N = 100 - elif n == 3: - N = 20 - - label_train = np.zeros(2*test_size) - sampleA = [[0 for x in range(n)] for y in range(test_size)] - sampleB = [[0 for x in range(n)] for y in range(test_size)] - while tr < (test_size): - draw1 = np.random.choice(N) - draw2 = np.random.choice(N) - if sample_Total[draw1][draw2] == +1: - sampleA[tr] = [2*np.pi*draw1/N, 2*np.pi*draw2/N] - tr += 1 - - tr = 0 - while tr < (test_size): - draw1 = np.random.choice(N) - draw2 = np.random.choice(N) - if sample_Total[draw1][draw2] == -1: - sampleB[tr] = [2*np.pi*draw1/N, 2*np.pi*draw2/N] - tr += 1 - sample_train = [sampleA, sampleB] - for lindex in range(test_size): - label_train[lindex] = 0 - for lindex in range(test_size): - label_train[test_size+lindex] = 1 - label_train = label_train.astype(int) - sample_train = np.reshape(sample_train, (2 * test_size, n)) - test_input = {key: (sample_train[label_train == k, :])[:] for k, key in enumerate(class_labels)} - return test_input - - -def Breast_cancer(training_size, test_size, n, PLOT_DATA): - class_labels = [r'A', r'B'] - data, target = datasets.load_breast_cancer(True) - sample_train, sample_test, label_train, label_test = train_test_split(data, target, test_size=0.3, random_state=12) - - # Now we standarize for gaussian around 0 with unit variance - std_scale = StandardScaler().fit(sample_train) - sample_train = std_scale.transform(sample_train) - sample_test = std_scale.transform(sample_test) - - # Now reduce number of features to number of qubits - pca = PCA(n_components=n).fit(sample_train) - sample_train = pca.transform(sample_train) - sample_test = pca.transform(sample_test) - - # Scale to the range (-1,+1) - samples = np.append(sample_train, sample_test, axis=0) - minmax_scale = MinMaxScaler((-1, 1)).fit(samples) - sample_train = minmax_scale.transform(sample_train) - sample_test = minmax_scale.transform(sample_test) - - # Pick training size number of samples from each distro - training_input = {key: (sample_train[label_train == k, :])[:training_size] for k, key in enumerate(class_labels)} - test_input = {key: (sample_train[label_train == k, :])[training_size:( - training_size+test_size)] for k, key in enumerate(class_labels)} - - if PLOT_DATA: - for k in range(0, 2): - plt.scatter(sample_train[label_train == k, 0][:training_size], - sample_train[label_train == k, 1][:training_size]) - - plt.title("PCA dim. reduced Breast cancer dataset") - plt.show() - - return sample_train, training_input, test_input, class_labels - - -def Digits(training_size, test_size, n, PLOT_DATA): - class_labels = [r'A', r'B', r'C', r'D', r'E', r'F', r'G', r'H', r'I', r'J'] - data = datasets.load_digits() - sample_train, sample_test, label_train, label_test = train_test_split( - data.data, data.target, test_size=0.3, random_state=22) - - # Now we standarize for gaussian around 0 with unit variance - std_scale = StandardScaler().fit(sample_train) - sample_train = std_scale.transform(sample_train) - sample_test = std_scale.transform(sample_test) - - # Now reduce number of features to number of qubits - pca = PCA(n_components=n).fit(sample_train) - sample_train = pca.transform(sample_train) - sample_test = pca.transform(sample_test) - - # Scale to the range (-1,+1) - samples = np.append(sample_train, sample_test, axis=0) - minmax_scale = MinMaxScaler((-1, 1)).fit(samples) - sample_train = minmax_scale.transform(sample_train) - sample_test = minmax_scale.transform(sample_test) - - # Pick training size number of samples from each distro - training_input = {key: (sample_train[label_train == k, :])[:training_size] for k, key in enumerate(class_labels)} - test_input = {key: (sample_train[label_train == k, :])[training_size:( - training_size+test_size)] for k, key in enumerate(class_labels)} - - if PLOT_DATA: - for k in range(0, 9): - plt.scatter(sample_train[label_train == k, 0][:training_size], - sample_train[label_train == k, 1][:training_size]) - - plt.title("PCA dim. reduced Digits dataset") - plt.show() - - return sample_train, training_input, test_input, class_labels - - -def Iris(training_size, test_size, n, PLOT_DATA): - class_labels = [r'A', r'B', r'C'] - data, target = datasets.load_iris(True) - sample_train, sample_test, label_train, label_test = train_test_split(data, target, test_size=1, random_state=42) - - # Now we standarize for gaussian around 0 with unit variance - std_scale = StandardScaler().fit(sample_train) - sample_train = std_scale.transform(sample_train) - sample_test = std_scale.transform(sample_test) - - # Scale to the range (-1,+1) - samples = np.append(sample_train, sample_test, axis=0) - minmax_scale = MinMaxScaler((-1, 1)).fit(samples) - sample_train = minmax_scale.transform(sample_train) - sample_test = minmax_scale.transform(sample_test) - - # Pick training size number of samples from each distro - training_input = {key: (sample_train[label_train == k, :])[:training_size] for k, key in enumerate(class_labels)} - test_input = {key: (sample_train[label_train == k, :])[training_size:( - training_size+test_size)] for k, key in enumerate(class_labels)} - - if PLOT_DATA: - for k in range(0, 3): - plt.scatter(sample_train[label_train == k, 0][:training_size], - sample_train[label_train == k, 1][:training_size]) - - plt.title("Iris dataset") - plt.show() - - return sample_train, training_input, test_input, class_labels - - -def Wine(training_size, test_size, n, PLOT_DATA): - class_labels = [r'A', r'B', r'C'] - - data, target = datasets.load_wine(True) - sample_train, sample_test, label_train, label_test = train_test_split(data, target, test_size=0.1, - random_state=7) - - # Now we standarize for gaussian around 0 with unit variance - std_scale = StandardScaler().fit(sample_train) - sample_train = std_scale.transform(sample_train) - sample_test = std_scale.transform(sample_test) - - # Now reduce number of features to number of qubits - pca = PCA(n_components=n).fit(sample_train) - sample_train = pca.transform(sample_train) - sample_test = pca.transform(sample_test) - - # Scale to the range (-1,+1) - samples = np.append(sample_train, sample_test, axis=0) - minmax_scale = MinMaxScaler((-1, 1)).fit(samples) - sample_train = minmax_scale.transform(sample_train) - sample_test = minmax_scale.transform(sample_test) - # Pick training size number of samples from each distro - training_input = {key: (sample_train[label_train == k, :])[:training_size] for k, key in enumerate(class_labels)} - test_input = {key: (sample_train[label_train == k, :])[training_size:( - training_size+test_size)] for k, key in enumerate(class_labels)} - - if PLOT_DATA: - for k in range(0, 3): - plt.scatter(sample_train[label_train == k, 0][:training_size], - sample_train[label_train == k, 1][:training_size]) - - plt.title("PCA dim. reduced Wine dataset") - plt.show() - - return sample_train, training_input, test_input, class_labels - - -def Gaussian(training_size, test_size, n, PLOT_DATA): - sigma = 1 - if n == 2: - class_labels = [r'A', r'B'] - label_train = np.zeros(2*(training_size+test_size)) - sample_train = [] - sampleA = [[0 for x in range(n)] for y in range(training_size+test_size)] - sampleB = [[0 for x in range(n)] for y in range(training_size+test_size)] - randomized_vector1 = np.random.randint(2, size=n) - randomized_vector2 = (randomized_vector1+1) % 2 - for tr in range(training_size+test_size): - for feat in range(n): - if randomized_vector1[feat] == 0: - sampleA[tr][feat] = np.random.normal(-1/2, sigma, None) - elif randomized_vector1[feat] == 1: - sampleA[tr][feat] = np.random.normal(1/2, sigma, None) - else: - print('Nope') - - if randomized_vector2[feat] == 0: - sampleB[tr][feat] = np.random.normal(-1/2, sigma, None) - elif randomized_vector2[feat] == 1: - sampleB[tr][feat] = np.random.normal(1/2, sigma, None) - else: - print('Nope') - - sample_train = [sampleA, sampleB] - for lindex in range(training_size+test_size): - label_train[lindex] = 0 - for lindex in range(training_size+test_size): - label_train[training_size+test_size+lindex] = 1 - label_train = label_train.astype(int) - sample_train = np.reshape(sample_train, (2*(training_size+test_size), n)) - training_input = {key: (sample_train[label_train == k, :])[:training_size] - for k, key in enumerate(class_labels)} - test_input = {key: (sample_train[label_train == k, :])[training_size:( - training_size+test_size)] for k, key in enumerate(class_labels)} - - if PLOT_DATA: - fig1 = plt.figure() - for k in range(0, 2): - plt.scatter(sample_train[label_train == k, 0][:training_size], - sample_train[label_train == k, 1][:training_size]) - - plt.title("Gaussians") - plt.show() - - return sample_train, training_input, test_input, class_labels - elif n == 3: - class_labels = [r'A', r'B', r'C'] - label_train = np.zeros(3*(training_size+test_size)) - sample_train = [] - sampleA = [[0 for x in range(n)] for y in range(training_size+test_size)] - sampleB = [[0 for x in range(n)] for y in range(training_size+test_size)] - sampleC = [[0 for x in range(n)] for y in range(training_size+test_size)] - randomized_vector1 = np.random.randint(3, size=n) - randomized_vector2 = (randomized_vector1+1) % 3 - randomized_vector3 = (randomized_vector2+1) % 3 - for tr in range(training_size+test_size): - for feat in range(n): - if randomized_vector1[feat] == 0: - sampleA[tr][feat] = np.random.normal(2*1*np.pi/6, sigma, None) - elif randomized_vector1[feat] == 1: - sampleA[tr][feat] = np.random.normal(2*3*np.pi/6, sigma, None) - elif randomized_vector1[feat] == 2: - sampleA[tr][feat] = np.random.normal(2*5*np.pi/6, sigma, None) - else: - print('Nope') - - if randomized_vector2[feat] == 0: - sampleB[tr][feat] = np.random.normal(2*1*np.pi/6, sigma, None) - elif randomized_vector2[feat] == 1: - sampleB[tr][feat] = np.random.normal(2*3*np.pi/6, sigma, None) - elif randomized_vector2[feat] == 2: - sampleB[tr][feat] = np.random.normal(2*5*np.pi/6, sigma, None) - else: - print('Nope') - - if randomized_vector3[feat] == 0: - sampleC[tr][feat] = np.random.normal(2*1*np.pi/6, sigma, None) - elif randomized_vector3[feat] == 1: - sampleC[tr][feat] = np.random.normal(2*3*np.pi/6, sigma, None) - elif randomized_vector3[feat] == 2: - sampleC[tr][feat] = np.random.normal(2*5*np.pi/6, sigma, None) - else: - print('Nope') - - sample_train = [sampleA, sampleB, sampleC] - for lindex in range(training_size+test_size): - label_train[lindex] = 0 - for lindex in range(training_size+test_size): - label_train[training_size+test_size+lindex] = 1 - for lindex in range(training_size+test_size): - label_train[training_size+test_size+training_size+test_size+lindex] = 2 - label_train = label_train.astype(int) - sample_train = np.reshape(sample_train, (3*(training_size+test_size), n)) - training_input = {key: (sample_train[label_train == k, :])[:training_size] - for k, key in enumerate(class_labels)} - test_input = {key: (sample_train[label_train == k, :])[training_size:( - training_size+test_size)] for k, key in enumerate(class_labels)} - - if PLOT_DATA: - fig1 = plt.figure() - for k in range(0, 3): - plt.scatter(sample_train[label_train == k, 0][:training_size], - sample_train[label_train == k, 1][:training_size]) - - plt.title("Gaussians") - plt.show() - - return sample_train, training_input, test_input, class_labels - else: - print("Gaussian presently only supports 2 or 3 qubits") - - -if __name__ == '__main__': - - _, train_data, test_data, label = ad_hoc_data(training_size=4, test_size=4, n=2, gap=0.3, PLOT_DATA=False) - print(train_data) - print(test_data) - print(label) diff --git a/qiskit/bernstein_vazirani.ipynb b/qiskit/bernstein_vazirani.ipynb deleted file mode 100644 index 24d5ae62f..000000000 --- a/qiskit/bernstein_vazirani.ipynb +++ /dev/null @@ -1,213 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": { - "collapsed": true - }, - "source": [ - "# _*Experiment with the Bernstein-Vazirani Algorithm in Aqua*_\n", - "\n", - "This notebook demonstrates how to experiment with the `Bernstein-Vazirani` algorithm in `Qiskit Aqua`.\n", - "\n", - "We first import all necessary modules." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import math\n", - "from qiskit import BasicAer\n", - "from qiskit.aqua import QuantumInstance\n", - "from qiskit.aqua import run_algorithm\n", - "from qiskit.aqua.algorithms import BernsteinVazirani\n", - "from qiskit.aqua.components.oracles import TruthTableOracle" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The Bernstein-Vazirani algorithm is explained in more detail in the corresponding notebook located in the directory `community/algorithms`. We can experiment with it in Aqua by feeding it oracles created using truth tables. For example, we can create a `TruthTableOracle` instance as follows." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "bitstr = '00111100'\n", - "oracle = TruthTableOracle(bitstr)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As shown, the truthtable is specified with the `bitstr` containing values of all entries in the table. It has length $8$, so the corresponding truth table is of $3$ input bits. The truthtable represents the function mappings as follows.\n", - "\n", - "- $\\mathbf{a} \\cdot 000 \\mod 2 = 0$\n", - "- $\\mathbf{a} \\cdot 001 \\mod 2 = 0$\n", - "- $\\mathbf{a} \\cdot 010 \\mod 2 = 1$\n", - "- $\\mathbf{a} \\cdot 011 \\mod 2 = 1$\n", - "- $\\mathbf{a} \\cdot 100 \\mod 2 = 1$\n", - "- $\\mathbf{a} \\cdot 101 \\mod 2 = 1$\n", - "- $\\mathbf{a} \\cdot 110 \\mod 2 = 0$\n", - "- $\\mathbf{a} \\cdot 111 \\mod 2 = 0$\n", - "\n", - "And obviously the goal is to find the bitstring $\\mathbf{a}$ that satisfies all the inner product equations.\n", - "\n", - "We can inspect the circuit corresponding to the binary function encoded in the `TruthTableOracle` instance." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "execution_count": 3, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "oracle.circuit.draw(output='latex')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As seen, the $v_i$'s correspond to the 3 input bits; the $o_0$ is the oracle's output qubit; the $a_0$ is an ancilla qubit.\n", - "\n", - "Let us first compute the groundtruth $\\mathbf{a}$ classically:" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The groundtruth result bitstring is 110.\n" - ] - } - ], - "source": [ - "a_bitstr = \"\"\n", - "num_bits = math.log2(len(bitstr))\n", - "for i in reversed(range(3)):\n", - " bit = bitstr[2 ** i]\n", - " a_bitstr += bit\n", - "print(f'The groundtruth result bitstring is {a_bitstr}.')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Next we can create a `BernsteinVazirani` instance using the oracle, and run it to check the result against the groundtruth." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The result bitstring computed using Bernstein-Vazirani is 110.\n" - ] - } - ], - "source": [ - "bv = BernsteinVazirani(oracle)\n", - "backend = BasicAer.get_backend('qasm_simulator')\n", - "result = bv.run(QuantumInstance(backend, shots=1024))\n", - "print('The result bitstring computed using Bernstein-Vazirani is {}.'.format(result['result']))\n", - "assert(result['result'] == a_bitstr)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The above step-by-step programatic approach can also be achieved by using a json configuration dictionary with the parameters for the algorithm and any other dependent objects it requires, as follows:" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The result bitstring computed using Bernstein-Vazirani is 110.\n" - ] - } - ], - "source": [ - "params = {\n", - " 'problem': {\n", - " 'name': 'hiddenstringfinding',\n", - " },\n", - " 'algorithm': {\n", - " 'name': 'BernsteinVazirani'\n", - " },\n", - " 'oracle': {\n", - " 'name': 'TruthTableOracle',\n", - " 'bitmaps': [bitstr]\n", - " },\n", - " 'backend': {\n", - " 'shots': 1024,\n", - " },\n", - "}\n", - "\n", - "result_dict = run_algorithm(params, backend=backend)\n", - "print('The result bitstring computed using Bernstein-Vazirani is {}.'.format(result_dict['result']))\n", - "assert(result_dict['result'] == a_bitstr)" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.2" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/qiskit/chemistry/H2/.ipynb_checkpoints/w8_02-checkpoint.ipynb b/qiskit/chemistry/H2/.ipynb_checkpoints/w8_02-checkpoint.ipynb deleted file mode 100644 index 3b9c29e80..000000000 --- a/qiskit/chemistry/H2/.ipynb_checkpoints/w8_02-checkpoint.ipynb +++ /dev/null @@ -1,338 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# _*Qiskit Aqua: Experiment with classification problem with quantum-enhanced support vector machines*_\n", - "\n", - "This notebook is based on an official notebook by Qiskit team, available at https://github.com/qiskit/qiskit-tutorial under the [Apache License 2.0](https://github.com/Qiskit/qiskit-tutorial/blob/master/LICENSE) license. \n", - "The original notebook was developed by Vojtech Havlicek[1], Kristan Temme[1], Antonio Córcoles[1], Peng Liu[1], Richard Chen[1], Marco Pistoia[1] and Jay Gambetta[1] ([1]IBMQ)\n", - "\n", - "Your **TASK** is to execute every step of this notebook while learning to use qiskit-aqua and also understanding how this SVM implementation can be used for classifying breast cancer analysis." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Introduction\n", - "Classification algorithms and methods for machine learning are essential for pattern recognition and data mining applications. Well known techniques such as support vector machines and neural networks have blossomed over the last two decades as a result of the spectacular advances in classical hardware computational capabilities and speed. This progress in computer power made it possible to apply techniques, that were theoretically developed towards the middle of the 20th century, on classification problems that were becoming increasingly challenging.\n", - "\n", - "A key concept in classification methods is that of a kernel. Data cannot typically be separated by a hyperplane in its original space. A common technique used to find such a hyperplane consists on applying a non-linear transformation function to the data. This function is called a feature map, as it transforms the raw features, or measurable properties, of the phenomenon or subject under study. Classifying in this new feature space -and, as a matter of fact, also in any other space, including the raw original one- is nothing more than seeing how close data points are to each other. This is the same as computing the inner product for each pair of data in the set. So, in fact we do not need to compute the non-linear feature map for each datum, but only the inner product of each pair of data points in the new feature space. This collection of inner products is called the kernel and it is perfectly possible to have feature maps that are hard to compute but whose kernels are not.\n", - "\n", - "In this notebook we provide an example of a classification problem that requires a feature map for which computing the kernel is not efficient classically -this means that the required computational resources are expected to scale exponentially with the size of the problem. We show how this can be solved in a quantum processor by a direct estimation of the kernel in the feature space. The method we used falls in the category of what is called supervised learning, consisting of a training phase (where the kernel is calculated and the support vectors obtained) and a test or classification phase (where new unlabelled data is classified according to the solution found in the training phase).\n", - "\n", - "References and additional details:\n", - "\n", - "[1] Vojtech Havlicek, Antonio D. C´orcoles, Kristan Temme, Aram W. Harrow, Abhinav Kandala, Jerry M. Chow, and Jay M. Gambetta1, \"Supervised learning with quantum enhanced feature spaces,\" [arXiv: 1804.11326](https://arxiv.org/pdf/1804.11326.pdf)" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "from qsvm_datasets import *\n", - "from qiskit.aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name\n", - "from qiskit.aqua.input import get_input_instance\n", - "from qiskit.aqua import run_algorithm\n", - "\n", - "# setup aqua logging\n", - "import logging\n", - "from qiskit.aqua._logging import set_logging_config, build_logging_config\n", - "# set_logging_config(build_logging_config(logging.DEBUG)) # choose INFO, DEBUG to see the log" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### [Optional] Setup token to run the experiment on a real device\n", - "If you would like to run the experiement on a real device, you need to setup your account first.\n", - "\n", - "Note: If you do not store your token yet, use `IBMQ.save_accounts()` to store it first." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "from qiskit import IBMQ\n", - "IBMQ.load_accounts()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "First we prepare the dataset, which is used for training, testing and the finally prediction.\n", - "\n", - "*Note: You can easily switch to a different dataset, such as the Breast Cancer dataset, by replacing 'ad_hoc_data' to 'Breast_cancer' below.*" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{'A': 0, 'B': 1}\n" - ] - } - ], - "source": [ - "feature_dim=2 # we support feature_dim 2 or 3\n", - "sample_Total, training_input, test_input, class_labels = ad_hoc_data(\n", - " training_size=20, test_size=10, n=feature_dim, gap=0.3, PLOT_DATA=True\n", - ")\n", - "\n", - "datapoints, class_to_label = split_dataset_to_data_and_labels(test_input)\n", - "print(class_to_label)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "With the dataset ready we initialize the necessary inputs for the algorithm:\n", - "- the input dictionary (params) \n", - "- the input object containing the dataset info (algo_input)." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [], - "source": [ - "params = {\n", - " 'problem': {'name': 'classification', 'random_seed': 10598},\n", - " 'algorithm': {\n", - " 'name': 'QSVM'\n", - " },\n", - " 'backend': {'name': 'qasm_simulator', 'shots': 1024},\n", - " 'feature_map': {'name': 'SecondOrderExpansion', 'depth': 2, 'entanglement': 'linear'}\n", - "}\n", - "\n", - "algo_input = get_input_instance('ClassificationInput')\n", - "algo_input.training_dataset = training_input\n", - "algo_input.test_dataset = test_input\n", - "algo_input.datapoints = datapoints[0] # 0 is data, 1 is labels" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "With everything setup, we can now run the algorithm.\n", - "\n", - "For the testing, the result includes the details and the success ratio.\n", - "\n", - "For the prediction, the result includes the predicted labels. " - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "testing success ratio: 1.0\n", - "predicted classes: ['A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B']\n" - ] - } - ], - "source": [ - "result = run_algorithm(params, algo_input)\n", - "print(\"testing success ratio: \", result['testing_accuracy'])\n", - "print(\"predicted classes:\", result['predicted_classes'])" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "kernel matrix during the training:\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "print(\"kernel matrix during the training:\")\n", - "kernel_matrix = result['kernel_matrix_training']\n", - "img = plt.imshow(np.asmatrix(kernel_matrix),interpolation='nearest',origin='upper',cmap='bone_r')\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### The breast cancer dataset\n", - "Now we run our algorithm with the real-world dataset: the breast cancer dataset, we use the first two principal components as features." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{'A': 0, 'B': 1} {0: 'A', 1: 'B'}\n" - ] - } - ], - "source": [ - "sample_Total, training_input, test_input, class_labels = Breast_cancer(\n", - " training_size=20, test_size=10, n=2, PLOT_DATA=True\n", - ")\n", - "# n =2 is the dimension of each data point\n", - "\n", - "datapoints, class_to_label = split_dataset_to_data_and_labels(test_input)\n", - "label_to_class = {label:class_name for class_name, label in class_to_label.items()}\n", - "print(class_to_label, label_to_class)" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "testing success ratio: 0.95\n", - "ground truth: ['A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B']\n", - "predicted: ['A', 'B', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B']\n" - ] - } - ], - "source": [ - "algo_input = get_input_instance('ClassificationInput')\n", - "algo_input.training_dataset = training_input\n", - "algo_input.test_dataset = test_input\n", - "algo_input.datapoints = datapoints[0]\n", - "result = run_algorithm(params, algo_input)\n", - "print(\"testing success ratio: \", result['testing_accuracy'])\n", - "print(\"ground truth: {}\".format(map_label_to_class_name(datapoints[1], label_to_class)))\n", - "print(\"predicted: {}\".format(result['predicted_classes']))" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "kernel matrix during the training:\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "print(\"kernel matrix during the training:\")\n", - "kernel_matrix = result['kernel_matrix_training']\n", - "img = plt.imshow(np.asmatrix(kernel_matrix),interpolation='nearest',origin='upper',cmap='bone_r')\n", - "plt.show()" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.2" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/qiskit/chemistry/H2/.ipynb_checkpoints/w8_03-checkpoint.ipynb b/qiskit/chemistry/H2/.ipynb_checkpoints/w8_03-checkpoint.ipynb deleted file mode 100644 index 7e4bf44be..000000000 --- a/qiskit/chemistry/H2/.ipynb_checkpoints/w8_03-checkpoint.ipynb +++ /dev/null @@ -1,504 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# _*Qiskit Aqua: Experimenting with Max-Cut problem with variational quantum eigensolver*_ \n", - "\n", - "\n", - "This notebook is based on an official notebook by Qiskit team, available at https://github.com/qiskit/qiskit-tutorial under the [Apache License 2.0](https://github.com/Qiskit/qiskit-tutorial/blob/master/LICENSE) license. \n", - "The original notebook was developed by Antonio Mezzacapo[1], Jay Gambetta[1], Kristan Temme[1], Ramis Movassagh[1], Albert Frisch[1], Takashi Imamichi[1], Giacomo Nannicni[1], Richard Chen[1], Marco Pistoia[1], Stephen Wood[1]([1]IBMQ)\n", - "\n", - "Your **TASK** is to execute every step of this notebook while learning to use qiskit-aqua and also how to leverage general problem modeling into know problems that qiskit-aqua can solve, namely the [Maximum Cut problem](https://en.wikipedia.org/wiki/Maximum_cut) problem." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Introduction\n", - "\n", - "Many problems in quantitative fields such as finance and engineering are optimization problems. Optimization problems lay at the core of complex decision-making and definition of strategies. \n", - "\n", - "Optimization (or combinatorial optimization) means searching for an optimal solution in a finite or countably infinite set of potential solutions. Optimality is defined with respect to some criterion function, which is to be minimized or maximized. This is typically called cost function or objective function. \n", - "\n", - "**Typical optimization problems**\n", - "\n", - "Minimization: cost, distance, length of a traversal, weight, processing time, material, energy consumption, number of objects\n", - "\n", - "Maximization: profit, value, output, return, yield, utility, efficiency, capacity, number of objects \n", - "\n", - "We consider here max-cut problem of practical interest in many fields, and show how they can mapped on quantum computers.\n", - "\n", - "\n", - "### Weighted Max-Cut\n", - "\n", - "Max-Cut is an NP-complete problem, with applications in clustering, network science, and statistical physics. To grasp how practical applications are mapped into given Max-Cut instances, consider a system of many people that can interact and influence each other. Individuals can be represented by vertices of a graph, and their interactions seen as pairwise connections between vertices of the graph, or edges. With this representation in mind, it is easy to model typical marketing problems. For example, suppose that it is assumed that individuals will influence each other's buying decisions, and knowledge is given about how strong they will influence each other. The influence can be modeled by weights assigned on each edge of the graph. It is possible then to predict the outcome of a marketing strategy in which products are offered for free to some individuals, and then ask which is the optimal subset of individuals that should get the free products, in order to maximize revenues.\n", - "\n", - "The formal definition of this problem is the following:\n", - "\n", - "Consider an $n$-node undirected graph *G = (V, E)* where *|V| = n* with edge weights $w_{ij}>0$, $w_{ij}=w_{ji}$, for $(i, j)\\in E$. A cut is defined as a partition of the original set V into two subsets. The cost function to be optimized is in this case the sum of weights of edges connecting points in the two different subsets, *crossing* the cut. By assigning $x_i=0$ or $x_i=1$ to each node $i$, one tries to maximize the global profit function (here and in the following summations run over indices 0,1,...n-1)\n", - "\n", - "$$\\tilde{C}(\\textbf{x}) = \\sum_{i,j} w_{ij} x_i (1-x_j).$$\n", - "\n", - "In our simple marketing model, $w_{ij}$ represents the probability that the person $j$ will buy a product after $i$ gets a free one. Note that the weights $w_{ij}$ can in principle be greater than $1$, corresponding to the case where the individual $j$ will buy more than one product. Maximizing the total buying probability corresponds to maximizing the total future revenues. In the case where the profit probability will be greater than the cost of the initial free samples, the strategy is a convenient one. An extension to this model has the nodes themselves carry weights, which can be regarded, in our marketing model, as the likelihood that a person granted with a free sample of the product will buy it again in the future. With this additional information in our model, the objective function to maximize becomes \n", - "\n", - "$$C(\\textbf{x}) = \\sum_{i,j} w_{ij} x_i (1-x_j)+\\sum_i w_i x_i. $$\n", - " \n", - "In order to find a solution to this problem on a quantum computer, one needs first to map it to an Ising Hamiltonian. This can be done with the assignment $x_i\\rightarrow (1-Z_i)/2$, where $Z_i$ is the Pauli Z operator that has eigenvalues $\\pm 1$. Doing this we find that \n", - "\n", - "$$C(\\textbf{Z}) = \\sum_{i,j} \\frac{w_{ij}}{4} (1-Z_i)(1+Z_j) + \\sum_i \\frac{w_i}{2} (1-Z_i) = -\\frac{1}{2}\\left( \\sum_{i" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# Generating a graph of 4 nodes \n", - "\n", - "n=4 # Number of nodes in graph\n", - "G=nx.Graph()\n", - "G.add_nodes_from(np.arange(0,n,1))\n", - "elist=[(0,1,1.0),(0,2,1.0),(0,3,1.0),(1,2,1.0),(2,3,1.0)]\n", - "# tuple is (i,j,weight) where (i,j) is the edge\n", - "G.add_weighted_edges_from(elist)\n", - "\n", - "colors = ['r' for node in G.nodes()]\n", - "pos = nx.spring_layout(G)\n", - "default_axes = plt.axes(frameon=True)\n", - "nx.draw_networkx(G, node_color=colors, node_size=600, alpha=.8, ax=default_axes, pos=pos)" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[0. 1. 1. 1.]\n", - " [1. 0. 1. 0.]\n", - " [1. 1. 0. 1.]\n", - " [1. 0. 1. 0.]]\n" - ] - } - ], - "source": [ - "# Computing the weight matrix from the random graph\n", - "w = np.zeros([n,n])\n", - "for i in range(n):\n", - " for j in range(n):\n", - " temp = G.get_edge_data(i,j,default=0)\n", - " if temp != 0:\n", - " w[i,j] = temp['weight'] \n", - "print(w)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Brute force approach\n", - "\n", - "Try all possible $2^n$ combinations. For $n = 4$, as in this example, one deals with only 16 combinations, but for n = 1000, one has 1.071509e+30 combinations, which is impractical to deal with by using a brute force approach. " - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "case = [0, 0, 0, 0] cost = 0.0\n", - "case = [1, 0, 0, 0] cost = 3.0\n", - "case = [0, 1, 0, 0] cost = 2.0\n", - "case = [1, 1, 0, 0] cost = 3.0\n", - "case = [0, 0, 1, 0] cost = 3.0\n", - "case = [1, 0, 1, 0] cost = 4.0\n", - "case = [0, 1, 1, 0] cost = 3.0\n", - "case = [1, 1, 1, 0] cost = 2.0\n", - "case = [0, 0, 0, 1] cost = 2.0\n", - "case = [1, 0, 0, 1] cost = 3.0\n", - "case = [0, 1, 0, 1] cost = 4.0\n", - "case = [1, 1, 0, 1] cost = 3.0\n", - "case = [0, 0, 1, 1] cost = 3.0\n", - "case = [1, 0, 1, 1] cost = 2.0\n", - "case = [0, 1, 1, 1] cost = 3.0\n", - "case = [1, 1, 1, 1] cost = 0.0\n", - "\n", - "Best solution = [1, 0, 1, 0] cost = 4.0\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "best_cost_brute = 0\n", - "for b in range(2**n):\n", - " x = [int(t) for t in reversed(list(bin(b)[2:].zfill(n)))]\n", - " cost = 0\n", - " for i in range(n):\n", - " for j in range(n):\n", - " cost = cost + w[i,j]*x[i]*(1-x[j])\n", - " if best_cost_brute < cost:\n", - " best_cost_brute = cost\n", - " xbest_brute = x \n", - " print('case = ' + str(x)+ ' cost = ' + str(cost))\n", - "\n", - "colors = ['r' if xbest_brute[i] == 0 else 'b' for i in range(n)]\n", - "nx.draw_networkx(G, node_color=colors, node_size=600, alpha=.8, pos=pos)\n", - "print('\\nBest solution = ' + str(xbest_brute) + ' cost = ' + str(best_cost_brute)) " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Mapping to the Ising problem" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [], - "source": [ - "qubitOp, offset = max_cut.get_max_cut_qubitops(w)\n", - "algo_input = EnergyInput(qubitOp)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Checking that the full Hamiltonian gives the right cost " - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "energy: -1.5\n", - "max-cut objective: -4.0\n", - "solution: [0. 1. 0. 1.]\n", - "solution objective: 4.0\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "#Making the Hamiltonian in its full form and getting the lowest eigenvalue and eigenvector\n", - "\n", - "algorithm_cfg = {\n", - " 'name': 'ExactEigensolver',\n", - "}\n", - "\n", - "params = {\n", - " 'problem': {'name': 'ising'},\n", - " 'algorithm': algorithm_cfg\n", - "}\n", - "result = run_algorithm(params,algo_input)\n", - "x = max_cut.sample_most_likely(result['eigvecs'][0])\n", - "print('energy:', result['energy'])\n", - "print('max-cut objective:', result['energy'] + offset)\n", - "print('solution:', max_cut.get_graph_solution(x))\n", - "print('solution objective:', max_cut.max_cut_value(x, w))\n", - "\n", - "colors = ['r' if max_cut.get_graph_solution(x)[i] == 0 else 'b' for i in range(n)]\n", - "nx.draw_networkx(G, node_color=colors, node_size=600, alpha = .8, pos=pos)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Running it on quantum computer\n", - "We run the optimization routine using a feedback loop with a quantum computer that uses trial functions built with Y single-qubit rotations, $U_\\mathrm{single}(\\theta) = \\prod_{i=1}^n Y(\\theta_{i})$, and entangler steps $U_\\mathrm{entangler}$." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "energy: -1.4995485513056617\n", - "time: 8.994375944137573\n", - "max-cut objective: -3.9995485513056614\n", - "solution: [0. 1. 0. 1.]\n", - "solution objective: 4.0\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "algorithm_cfg = {\n", - " 'name': 'VQE',\n", - " 'operator_mode': 'matrix'\n", - "}\n", - "\n", - "optimizer_cfg = {\n", - " 'name': 'SPSA',\n", - " 'max_trials': 300\n", - "}\n", - "\n", - "var_form_cfg = {\n", - " 'name': 'RY',\n", - " 'depth': 5,\n", - " 'entanglement': 'linear'\n", - "}\n", - "\n", - "params = {\n", - " 'problem': {'name': 'ising', 'random_seed': 10598},\n", - " 'algorithm': algorithm_cfg,\n", - " 'optimizer': optimizer_cfg,\n", - " 'variational_form': var_form_cfg,\n", - " 'backend': {'name': 'statevector_simulator'}\n", - "}\n", - "\n", - "result = run_algorithm(params, algo_input)\n", - "\n", - "x = max_cut.sample_most_likely(result['eigvecs'][0])\n", - "print('energy:', result['energy'])\n", - "print('time:', result['eval_time'])\n", - "print('max-cut objective:', result['energy'] + offset)\n", - "print('solution:', max_cut.get_graph_solution(x))\n", - "print('solution objective:', max_cut.max_cut_value(x, w))\n", - "\n", - "colors = ['r' if max_cut.get_graph_solution(x)[i] == 0 else 'b' for i in range(n)]\n", - "nx.draw_networkx(G, node_color=colors, node_size=600, alpha = .8, pos=pos)" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "energy: -1.5\n", - "time: 18.19207787513733\n", - "max-cut objective: -4.0\n", - "solution: [1 0 1 0]\n", - "solution objective: 4.0\n" - ] - }, - { - "data": { - "image/png": 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\n", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# run quantum algorithm with shots\n", - "params['algorithm']['operator_mode'] = 'grouped_paulis'\n", - "params['backend']['name'] = 'qasm_simulator'\n", - "params['backend']['shots'] = 1024\n", - "\n", - "result = run_algorithm(params, algo_input)\n", - "x = max_cut.sample_most_likely(result['eigvecs'][0])\n", - "print('energy:', result['energy'])\n", - "print('time:', result['eval_time'])\n", - "print('max-cut objective:', result['energy'] + offset)\n", - "print('solution:', max_cut.get_graph_solution(x))\n", - "print('solution objective:', max_cut.max_cut_value(x, w))\n", - "plot_histogram(result['eigvecs'][0])\n", - "\n", - "colors = ['r' if max_cut.get_graph_solution(x)[i] == 0 else 'b' for i in range(n)]\n", - "nx.draw_networkx(G, node_color=colors, node_size=600, alpha = .8, pos=pos)" - ] - } - ], - "metadata": { - "anaconda-cloud": {}, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.2" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/qiskit/chemistry/H2/.ipynb_checkpoints/w8_04-checkpoint.ipynb b/qiskit/chemistry/H2/.ipynb_checkpoints/w8_04-checkpoint.ipynb deleted file mode 100644 index dc0b353e9..000000000 --- a/qiskit/chemistry/H2/.ipynb_checkpoints/w8_04-checkpoint.ipynb +++ /dev/null @@ -1,478 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# _*Qiskit Aqua: Experimenting with Traveling Salesman problem with variational quantum eigensolver*_ \n", - "\n", - "\n", - "This notebook is based on an official notebook by Qiskit team, available at https://github.com/qiskit/qiskit-tutorial under the [Apache License 2.0](https://github.com/Qiskit/qiskit-tutorial/blob/master/LICENSE) license. \n", - "The original notebook was developed by Antonio Mezzacapo[1], Jay Gambetta[1], Kristan Temme[1], Ramis Movassagh[1], Albert Frisch[1], Takashi Imamichi[1], Giacomo Nannicni[1], Richard Chen[1], Marco Pistoia[1], Stephen Wood[1]([1]IBMQ)\n", - "\n", - "Your **TASK** is to execute every step of this notebook while learning to use qiskit-aqua and also how to leverage general problem modeling into know problems that qiskit-aqua can solve, namely the [Travelling salesman problem](https://en.wikipedia.org/wiki/Travelling_salesman_problem)." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Introduction\n", - "\n", - "Many problems in quantitative fields such as finance and engineering are optimization problems. Optimization problems lay at the core of complex decision-making and definition of strategies. \n", - "\n", - "Optimization (or combinatorial optimization) means searching for an optimal solution in a finite or countably infinite set of potential solutions. Optimality is defined with respect to some criterion function, which is to be minimized or maximized. This is typically called cost function or objective function. \n", - "\n", - "**Typical optimization problems**\n", - "\n", - "Minimization: cost, distance, length of a traversal, weight, processing time, material, energy consumption, number of objects\n", - "\n", - "Maximization: profit, value, output, return, yield, utility, efficiency, capacity, number of objects \n", - "\n", - "We consider here max-cut problem of practical interest in many fields, and show how they can mapped on quantum computers.\n", - "\n", - "\n", - "### Weighted Max-Cut\n", - "\n", - "Max-Cut is an NP-complete problem, with applications in clustering, network science, and statistical physics. To grasp how practical applications are mapped into given Max-Cut instances, consider a system of many people that can interact and influence each other. Individuals can be represented by vertices of a graph, and their interactions seen as pairwise connections between vertices of the graph, or edges. With this representation in mind, it is easy to model typical marketing problems. For example, suppose that it is assumed that individuals will influence each other's buying decisions, and knowledge is given about how strong they will influence each other. The influence can be modeled by weights assigned on each edge of the graph. It is possible then to predict the outcome of a marketing strategy in which products are offered for free to some individuals, and then ask which is the optimal subset of individuals that should get the free products, in order to maximize revenues.\n", - "\n", - "The formal definition of this problem is the following:\n", - "\n", - "Consider an $n$-node undirected graph *G = (V, E)* where *|V| = n* with edge weights $w_{ij}>0$, $w_{ij}=w_{ji}$, for $(i, j)\\in E$. A cut is defined as a partition of the original set V into two subsets. The cost function to be optimized is in this case the sum of weights of edges connecting points in the two different subsets, *crossing* the cut. By assigning $x_i=0$ or $x_i=1$ to each node $i$, one tries to maximize the global profit function (here and in the following summations run over indices 0,1,...n-1)\n", - "\n", - "$$\\tilde{C}(\\textbf{x}) = \\sum_{i,j} w_{ij} x_i (1-x_j).$$\n", - "\n", - "In our simple marketing model, $w_{ij}$ represents the probability that the person $j$ will buy a product after $i$ gets a free one. Note that the weights $w_{ij}$ can in principle be greater than $1$, corresponding to the case where the individual $j$ will buy more than one product. Maximizing the total buying probability corresponds to maximizing the total future revenues. In the case where the profit probability will be greater than the cost of the initial free samples, the strategy is a convenient one. An extension to this model has the nodes themselves carry weights, which can be regarded, in our marketing model, as the likelihood that a person granted with a free sample of the product will buy it again in the future. With this additional information in our model, the objective function to maximize becomes \n", - "\n", - "$$C(\\textbf{x}) = \\sum_{i,j} w_{ij} x_i (1-x_j)+\\sum_i w_i x_i. $$\n", - " \n", - "In order to find a solution to this problem on a quantum computer, one needs first to map it to an Ising Hamiltonian. This can be done with the assignment $x_i\\rightarrow (1-Z_i)/2$, where $Z_i$ is the Pauli Z operator that has eigenvalues $\\pm 1$. Doing this we find that \n", - "\n", - "$$C(\\textbf{Z}) = \\sum_{i,j} \\frac{w_{ij}}{4} (1-Z_i)(1+Z_j) + \\sum_i \\frac{w_i}{2} (1-Z_i) = -\\frac{1}{2}\\left( \\sum_{i0,$$ \n", - "\n", - "where it is assumed the boundary condition of the Hamiltonian cycle $(p=N)\\equiv (p=0)$. However, here it will be assumed a fully connected graph and not include this term. The distance that needs to be minimized is \n", - "\n", - "$$C(\\textbf{x})=\\sum_{i,j}w_{ij}\\sum_{p} x_{i,p}x_{j,p+1}.$$\n", - "\n", - "Putting this all together in a single objective function to be minimized, we get the following:\n", - "\n", - "$$C(\\textbf{x})=\\sum_{i,j}w_{ij}\\sum_{p} x_{i,p}x_{j,p+1}+ A\\sum_p\\left(1- \\sum_i x_{i,p}\\right)^2+A\\sum_i\\left(1- \\sum_p x_{i,p}\\right)^2,$$\n", - "\n", - "where $A$ is a free parameter. One needs to ensure that $A$ is large enough so that these constraints are respected. One way to do this is to choose $A$ such that $A > \\mathrm{max}(w_{ij})$.\n", - "\n", - "Once again, it is easy to map the problem in this form to a quantum computer, and the solution will be found by minimizing a Ising Hamiltonian. " - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "distance\n", - " [[ 0. 91. 55.]\n", - " [91. 0. 39.]\n", - " [55. 39. 0.]]\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Generating a graph of 3 nodes\n", - "\n", - "n = 3\n", - "num_qubits = n ** 2\n", - "ins = tsp.random_tsp(n)\n", - "G = nx.Graph()\n", - "G.add_nodes_from(np.arange(0, n, 1))\n", - "colors = ['r' for node in G.nodes()]\n", - "pos = {k: v for k, v in enumerate(ins.coord)}\n", - "default_axes = plt.axes(frameon=True)\n", - "nx.draw_networkx(G, node_color=colors, node_size=600, alpha=.8, ax=default_axes, pos=pos)\n", - "print('distance\\n', ins.w)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Brute force approach" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "order = (0, 1, 2) Distance = 185.0\n", - "Best order from brute force = (0, 1, 2) with total distance = 185.0\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "from itertools import permutations\n", - "\n", - "def brute_force_tsp(w, N):\n", - " a=list(permutations(range(1,N)))\n", - " last_best_distance = 1e10\n", - " for i in a:\n", - " distance = 0\n", - " pre_j = 0\n", - " for j in i:\n", - " distance = distance + w[j,pre_j]\n", - " pre_j = j\n", - " distance = distance + w[pre_j,0]\n", - " order = (0,) + i\n", - " if distance < last_best_distance:\n", - " best_order = order\n", - " last_best_distance = distance\n", - " print('order = ' + str(order) + ' Distance = ' + str(distance))\n", - " return last_best_distance, best_order\n", - " \n", - "best_distance, best_order = brute_force_tsp(ins.w, ins.dim)\n", - "print('Best order from brute force = ' + str(best_order) + ' with total distance = ' + str(best_distance))\n", - "\n", - "def draw_tsp_solution(G, order, colors, pos):\n", - " G2 = G.copy()\n", - " n = len(order)\n", - " for i in range(n):\n", - " j = (i + 1) % n\n", - " G2.add_edge(order[i], order[j])\n", - " default_axes = plt.axes(frameon=True)\n", - " nx.draw_networkx(G2, node_color=colors, node_size=600, alpha=.8, ax=default_axes, pos=pos)\n", - "\n", - "draw_tsp_solution(G, best_order, colors, pos)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Mapping to the Ising problem" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [], - "source": [ - "qubitOp, offset = tsp.get_tsp_qubitops(ins)\n", - "algo_input = get_input_instance('EnergyInput')\n", - "algo_input.qubit_op = qubitOp" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Checking that the full Hamiltonian gives the right cost " - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "energy: -600092.5\n", - "feasible: True\n", - "solution: [0, 1, 2]\n", - "solution objective: 185.0\n" - ] - }, - { - "data": { - "image/png": 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AYGCgrlC1QginO3/+PNOmTePIkSNMmTKFO+64w+iSfkdrzcSJEwkMDKR///5Gl+PSytOBNYT/dNUAfAYMs/08DPjUUUUJISqf1prPP/+cwYMH06pVK+Lj410y4AFWrFhBRkYGb731ltGluDy7WvJKKV+gL/DKVZujgESl1IvASWCA48sTQlSG1NRUJk+eTFZWFvPmzaNjx45Gl3RdO3bsID4+ntjY2Co7s2R52BXyWus8oME1285jHW0jhHBTFouFxMREFi1axHPPPcfQoUPx9nbdayRTU1OZMGECUVFRLjE+3x247r+mEMKpjh07RmRkJF5eXixdupRWrVoZXdINFRQUEBoayvDhw+nRo4fR5bgNCXkhqpjCwkJiY2NZs2YNr776Kv/zP//j8uPLtdZERUXRsmVLhgwZYnQ5bkVCXogq5MCBA4SHh9OkSRNWrVpFkyZNjC7JLuvWrePAgQMsX77cZS7CchcS8kJUAfn5+SxcuJAvvviC0aNH8/DDD7tNWP70008sWLCAJUuWUKtWLaPLcTuu/RlNCFFhu3btYvDgwaSnp5OQkMAjjzziNgGfmZnJ2LFjeffdd2nZsqXR5bglackL4aFycnKYO3cuSUlJhIWF0bt3b6NLKpeioiLCwsJ44oknuOeee4wux21JS14ID7RlyxYGDhwIQGJiotsFPMDcuXPx8fHh5ZdfNroUtyYteSE8SGZmJtHR0Rw8eJDIyEi3HWq4adMmvv32W+Li4lx+5I+rk1dPCA+gtWbjxo0MHjyYpk2bEh8f77YBf+TIEaZPn86MGTPw9/c3uhy3Jy15Idzc2bNnmTJlChkZGcyePZsuXboYXdJNu3TpEiEhIYwePZoOHToYXY5HkJa8EG7qypQEQ4cOpXv37sTFxbl1wFssFt59912CgoJ49NFHjS7HY0hLXgg39NtvvxEREYHFYmHx4sXcdtttRpdUYUuXLuXSpUuMGjXK6FI8ioS8EG6kqKiIuLg4Vq5cySuvvMIzzzzjEScmk5OTWbduHbGxsVSvXt3ocjyKhLwQbuKXX34hPDycBg0asHLlSgICAowuySFSUlKYOHEiM2bMoGHDhkaX43Ek5IVwcQUFBcTExPD5558zcuRIHn30Ube5YrUs+fn5hIaG8tJLL9GtWzejy/FIEvJCuLA9e/YQGRlJx44diY+Pp379+kaX5DBaayZPnky7du0YMEDWHHIWCXkhXFBubi7vv/8+W7ZsITQ0lPvuu8/okhwuMTGRo0ePsnTpUo/5ZOKK3P+MjRAeJikpiYEDB1JUVERCQoJHBvzevXtZsmQJM2bMwMfHx+hyPJq05IVwERcuXOC9997jp59+4h//+Ad33XWX0SU5RUZGBuPGjWPixIk0a9bM6HI8nrTkhTCY1pqvvvqKQYMG0aBBA+Lj4z024AsLCxk7dizPPPMMQUFBRpdTJdjVkldK1QMWA10BDbwAPAy8DGTY7jZea73RGUUK4anS09OZOnUqqampzJo1iz/84Q9Gl+RUs2bNol69ejz//PNGl1Jl2NuSnwN8qbXuBHQDDtq2z9Jad7d9ScALYSeLxcLHH39McHAwXbp0YeXKlR4f8Bs3bmT79u2Eh4d7xAVc7qLMlrxSyh/oDQwH0FqbAbOcDRfi5pw8eZLIyEjMZjMxMTG0adPG6JKc7tChQ8ycOZOFCxfi5+dndDlVij1vp22wdsksU0r9oJRarJSqbfvd35VS+5RSS5VStzivTCHcX3FxMbGxsTz//PPcd999LF26tEoEfHZ2NiEhIYSGhtK2bVujy6ly7Al5b6AHMF9rfQeQC4QB84G2QHfgDPBeaQ9WSo1QSu1SSu3KyMgo7S5CeLzDhw8zbNgwtm/fTlxcHMHBwVWiy8JisfD2229z//3389BDDxldTpVkz4nXFCBFa73DdvsjIExrnXblDkqpRcCG0h6stY4BYgACAwN1xcoVwr2YzWYWL17M+vXreeONN3j88cer1IU/CxcuxGw28+abbxpdSpVVZshrrc8qpU4ppTpqrQ8BDwAHlFIBWusztrs9Bex3ZqFCuJsff/yRiIgI2rRpw5o1a6rc5Ftbtmxhw4YNxMXF4eXlZXQ5VZa9F0O9AaxSStUAjgHPA3OVUt2xDqk8AbzilAqFcDN5eXnMmzePzZs3ExoaSp8+fYwuqdKdPHmSiIgIZs2a5VHz7bgju0Jea70XCLxm87OOL0cI95acnMzUqVP505/+RGJiYpVcozQvL48xY8bw2muv0bVrV6PLqfJkWgMhHODixYvMnDmTH374gbfffpuePXsaXZIhtNZERETQtWtXnnrqKaPLEci0BkJUiNaaf/3rXwwcOBB/f3/i4+OrbMADrF69mpSUFMLCwqrUCWZXJi15IW5SRkYGUVFRnDx5khkzZnD77bcbXZKhdu/ezYoVK1ixYgU1atQwuhxhIy15IcpJa80nn3xCcHAw7du3Z9WqVVU+4NPT0xk/fjyRkZEesyyhp5CWvBDlkJKSwuTJk8nNzeXDDz+kffv2RpdkOLPZTEhICMHBwR47e6Y7k5AXwg4Wi4XVq1ezbNkynn/+eYYMGSJjv22io6Np0qQJzz33nNGliFJIyAtRhiNHjhAeHk6tWrVYvnw5LVq0MLokl/HZZ5+xZ88eVqxYISdaXZSEvBDXYTabWbZsGWvXruVvf/sbTz75pATZVQ4cOMD777/PokWLqF27dtkPEIaQkBeiFD/99BMRERE0b96c1atX07hxY6NLcilZWVmMHTuWcePG0bp1a6PLETcgIS/EVS5fvsz8+fP56quvGDNmDA8++KC03q9RXFzM+PHjeeihh6rklA3uRoZQCmGzc+dOBg0aRFZWFomJifTt21cCvhQffvghAK+//rrBlQh7SEteVHnZ2dnMnj2bnTt3Mn78eFlg+gY2b97Mpk2bZGZJNyIteVGlbd68mUGDBuHj40NiYqIE/A0cP36cKVOmMG3aNOrVq2d0OcJO0pIXVdL58+eZNm0aR48eZerUqXTv3t3oklxabm4uISEhvPnmm3Tp0sXockQ5SEteVClaaz7//HMGDx5M69atWbNmjQR8GbTWTJo0iR49etC/f3+jyxHlJC15UWWkpqYyefJkLl68yAcffECHDh2MLsktxMbGkp6eTmRkpNGliJsgIS88nsViISEhgcWLFzNs2DCGDh0qJw3ttHPnTtasWUNsbKzMLOmmJOSFRzt27BgRERFUr16dZcuW0bJlS6NLchtnzpzhnXfeYerUqXIxmBuTkBceqbCwkOXLl5OQkMBrr73GU089RbVqcgrKXmazmdDQUIYNG8add95pdDmiAiTkhcc5cOAAkyZNIiAggFWrVtGkSROjS3IrWmuioqJo0aIFwcHBRpcjKkhCXniM/Px8FixYwMaNGxk9ejQPP/ywXLF6E9avX8/+/ftZvny5vH4ewK7Pr0qpekqpj5RSvyilDiql7lZK1VdKfa2U+tX2/RZnFyvE9ezatYvBgwdz7tw5EhISeOSRRySgbsJPP/3E/PnziY6OxtfX1+hyhAPY25KfA3yptX5GKVUD8AXGA//WWkcppcKAMGCsk+oUolSXLl1izpw5bNu2jbCwMO655x6jS3JbmZmZjB07lgkTJsgJag9SZkteKeUP9AaWAGitzVrrLOAJYIXtbiuAJ51VpBCl+fbbbxk0aBBeXl4kJiZKwFdAcXExYWFh9O/fn969extdjnAge1rybYAMYJlSqhuwGxgJNNFanwHQWp9RSskYK1EpMjMzmTFjBocOHSIyMpIePXoYXZLbmzt3Lj4+PowYMcLoUoSD2dMn7w30AOZrre8AcrF2zdhFKTVCKbVLKbUrIyPjJssUwjrqY+PGjQwePJhbb72VNWvWSMA7wKZNm/jmm2+IjIyUYaYeyJ6WfAqQorXeYbv9EdaQT1NKBdha8QFAemkP1lrHADEAgYGB2gE1iyrozJkzTJ06lXPnzjFnzhw6d+5sdEke4ejRo0yfPp0PP/wQf39/o8sRTlDm27bW+ixwSinV0bbpAeAA8BkwzLZtGPCpUyoUVZrFYiExMZFnn32W7t27ExsbKwHvIJcuXSIkJITRo0fLPD4ezN7RNW8Aq2wja44Bz2N9g0hUSr0InAQGOKdEUVWdOHGCiIgIABYvXixriTqQxWLhH//4Bz179uTRRx81uhzhRHaFvNZ6LxBYyq8ecGw5QkBRURGxsbGsWrWKV155hWeeeUb6ih1s2bJlXLx4kWnTphldinAyueJVuJSDBw8SERFBw4YNWblyJQEBAUaX5HGSk5P56KOPiIuLo3r16kaXI5xMQl64hIKCAhYuXMiGDRsYNWoU/fr1kytWneD06dNMnDiR6dOn07BhQ6PLEZVAQl4Ybs+ePURGRtKxY0fi4+OpX7++0SV5pPz8fEJCQnjxxRdlNawqREJeGCY3N5e5c+fy3XffERoayn333Wd0SR5La82UKVNo164dAwcONLocUYnkbJYwxHfffcfAgQNLVm2SgHeutWvXcuTIEcaPHy/dYFWMtORFpbpw4QLR0dHs37+fiRMn8qc//cnokjze3r17Wbx4McuWLcPHx8fockQlk5a8qBRaa7788ksGDRpEo0aNSEhIkICvBOfOnWPcuHFMnDiRZs2aGV2OMIC05IXTpaWlMXXqVM6ePcvs2bPp0qWL0SVVCYWFhYwdO5ann36aoKAgo8sRBpGWvHAai8XCxx9/zNChQ+natStxcXES8JVo9uzZ1K1blxdeeMHoUoSBpCUvnOLkyZNERkZSWFhITEwMbdq0MbqkKmXjxo0kJycTGxsrVwtXcRLywqGKi4tZtWoVK1as4KWXXmLQoEESMpXs8OHDzJw5k4ULF1KnTh2jyxEGk5AXDnP48GHCw8OpW7cucXFx3HrrrUaXVOVkZ2cTEhJCaGgobdu2Nboc4QIk5EWFmc1mFi9ezPr163nzzTf5y1/+ImOxHSErCw4ehMOHITMTlILGjaFTJ+vXNQttWywW3nnnHe69914eeughg4oWrkZCXlTI3r17iYiIoG3btsTHx9OgQQOjS3JvFgt89x0sWgTbt4O3N5jN1u0AXl5QvToUF0O/fjB8ONxxByhFTEwM+fn5vPnmm4b+CcK1SMiLm5KXl8e8efPYvHkzoaGh9OnTx+iS3N/x4zBqFBw4YL3t7w/XO59RXAxffAH//Cc88ADJjz3GZ599xsqVK/H2lv/W4j/kjJgot+TkZAYOHEh+fj6JiYkS8I7w2WfwyCPw88/WcK9b9/oBD9YW/S23QJ06FH75JU2Cg5kzbJhM7iZ+R97yhd0uXrzIe++9x969e5kwYQJ//vOfjS7JM6xbByEh1j72mjXL9dBi4GR2No3q1sV/4kRo2xYCS1vfR1RV0pIXZdJas2nTJgYOHEi9evVISEiQgHeUvXth7FioXbvcAa+xLnBeq1Yt6jRtaj0x+/zzcPasc2oVbkla8uKG0tPTiYqKIiUlhejoaP74xz8aXZLnyM+HkSOt3TI1apT74ZmZmZjNZlq3bo0C6yeBrCwIC4Nly6yhL6o8acmLUmmtWb9+PcHBwXTs2JGVK1dKwDvaypWQkgI3ccFSbl4e58+do3nz5lS7Oszr1oWkJNiyxYGFCncmLXnxO6dOnWLy5Mnk5eWxYMEC2rVrZ3RJnsdigZgYqFXrhnczWyxEnT3Lzrw8souLaV69Oq82aEDT9HRubdaMGteu0aqU9WvRIrj3Xif+AcJd2NWSV0qdUEr9pJTaq5TaZds2USl12rZtr1LqUeeWKpytuLiYlStXMnz4cO655x6WL18uAe8sO3ZYu1bKmN+9GGhavToxLVvyTYcOvNKoEWNOnMDs749f7dqlP6hOHevzS9+8oHwt+fu11ueu2TZLax3tyIKEMY4cOUJ4eDi+vr6sWLGC5s2bG12SZ/vhBygqKvNutapVY0SjRiW3O+Tm0tTLi7Rateh6vQdVq2b9+uknaNrUMfUKtyXdNVWc2Wxm6dKlfPzxx/z973+nf//+MiVBZdixw3o1azlkZWVx+tIlMry9aVvWSByzGfbtg759K1Ck8AT2nnjVwCal1G6l1Iirtv9dKbVPKbVUKXVLaQ9USo1QSu1SSu3KyMix7nN+AAAWD0lEQVSocMHCcfbt28fQoUP59ddfWb16NU888YQEfGU5fdruETUauHTpEqfT0ljk7c3jdevSuqyQ9/aG336reJ3C7dnblDBprVOVUo2Br5VSvwDzgQisx2AE8B7wu9UJtNYxQAxAYGCgdkjVokLy8vKYP38+mzZtIiQkhAceeEDCvbJdmYvmOoqLi8nNzSUnJ4ecnByUlxfLa9akZrVqhNrbBVNc7IBChbuzK+S11qm27+lKqfXAXVrrkjFaSqlFwAbnlCgcafv27UyZMoU77riDxMRE6tata3RJVZOfH5w5U3JTAwX5+dZQz80lPz8fX19f/Pz8aNCwIVHnzpFdWMjc5s3xtucN2WKBevWcV79wG2WGvFKqNlBNa33J9vNDQLhSKkBrfeUofQrY78Q6RQVlZ2cza9Ysvv/+e8aPHy9rfhqtRw8s+/aRY7GUtNarVauGn58fDRs2xNfXt2T8+5QzZzhuNvNhy5bUtHcBFqWgWzcn/gHCXdjTkm8CrLd9nPcGVmutv1RKxSmlumNthJwAXnFalaJCNm/ezPTp0+nTpw+JiYn4XjMPuagcWmuOHj1KcnIyl7Zto39aGto2FLJBgwbULKWP/kxhIeuysqihFA//+mvJ9vFNm9LvRp/CvLygc2dn/BnCzZQZ8lrrY8DvmgRa62edUpFwmHPnzjF9+nSOHTvGtGnT6CYtu0qXl5fHzp072bp1K1u3bsXb25tevXrRe+RImh09SrU6dayBfB0B1auzq7xhnZ9vvfJVFk0XyBBKj6S15vPPP+f999/nqaeeIjIykho3MTeKKD+tNcePHyc5OZmtW7fy888/07VrV3r16sVf//pXWrZs+Z+T3Js2WacYdvT0wJcvW+fEucGbh6g6JOQ9zOnTp5k8eTLZ2dl88MEHdOjQweiSPN7ly5f5/vvvS4Jda43JZGLIkCEEBgZev3vsb3+DjRuhsNC62pMj5OVZ56MfMMAxzyfcnoS8h7BYLMTHx7NkyRKGDRvG0KFD8ZKWnFNorTl16hRJSUkkJyezb98+unTpgslkYs6cOdx22232DUlt397a4p450zoSpqLDWC0WKCiA99+XkTWihIS8Bzh27Bjh4eHUqFGDZcuW0bJlS6NL8jgFBQXs3r2bpKQktm7dSmFhIUFBQTz99NNMmzaN2tebR6Ysr7wCW7dar4CtSNBbLHDxIgQHwwMP3NxzCI8kIe/GCgsLWb58OQkJCbz++us8+eSTVLN3iJ0oU0pKSskJ071799KpUydMJhPR0dG0a9fOMReQeXvD4sXw4ovWoPf3L/d0BxQUWLtpBgyASZMqXpPwKBLyburnn38mPDycW2+9ldWrV9O4cWOjS3J7ZrOZPXv2lAR7bm4uJpOJJ554gsmTJ1PnJuZ9t4uvL6xYYe1mWbAAtL7xIt5XFBdDdrZ1eoTJk2HgwLIfI6ocpXXlzTQQGBiod+3aVWn780SXL19mwYIF/POf/2TMmDH07dtXpiSogNTUVLZu3UpycjK7d++mffv2mEwmTCYT7du3r/xPRvv3w4wZ1i4ci8Xaqvfx+c9ImcJC6xBJra3b+vWzrg8rs4Z6NKXUbq31TS3eKyHvRr7//nsiIyO5/fbbeeutt6gnJ9fKzWw2s3fv3pJgz8rKIigoCJPJRM+ePfH39ze6RKtTp+Crr6xdOPv2waVL1v76W26BHj3g7rvh4YcdP/xSuCQJeQ936dIl5syZw7Zt2xg3bhy9evUyuiS3kpaWVtIFs2vXLtq0aVMS7J06dZLzGMLlVSTkpU/exX3zzTdMmzaNe++9l8TExJsfxVGFFBUV8eOPP5YE+7lz5wgKCuLBBx9kwoQJ8glIVCkS8i4qMzOT6dOnc/jwYSZPnkyPHj2MLsmlZWRklFyMtHPnTlq2bInJZGLChAl06dJFWuuiypKQdzFaazZu3MicOXN4/PHHmTRpEjXLWiCiCiouLmbfvn0lwX727Fl69uzJvffeS1hYGPWlr1oIQELepaSmpjJlyhQyMzOZO3cunTp1Mrokl3L+/Pn/aq0HBARgMpkYO3YsXbt2lSt8hSiFhLwLsFgsrF27lpiYGP7617/y7LPP4l3eC2I8kMViYf/+/SV966dPn+auu+7CZDIxZswYGjZsaHSJQrg8SRKDHT9+nIiICJRSLFmyhNatWxtdkqEuXLjAtm3b2Lp1K9u2baNJkyaYTCZGjx7N7bffLm9+QpST/I8xSFFREbGxsaxatYpXX32Vp59+ukqeHLRYLBw8eLCktX7ixImS1vrIkSPlSl4hKkhC3gAHDx4kPDycRo0asWrVKprauzCzh7h48SLbtm0jOTmZ5ORk6tevj8lk4o033qBbt25Ud9S0u0IICfnKVFBQwMKFC9mwYQOjRo2iX79+VWJKAovFwqFDh0quMj1y5AiBgYGYTCZee+01AgICjC5RCI8lIV9Jdu/eTWRkJJ07dyY+Pt7jh/hlZ2ezY8eOkmD39/cnKCiIV199le7du8tKVUJUEgl5J8vJyWHu3LkkJSURFhZG7969jS7JKbTW/PrrryV964cPH6ZHjx4EBQXx8ssv06xZM6NLFKJKsivklVIngEtAMVCktQ5UStUHEoDWwAlgoNb6gnPKdE9btmwhKiqKXr16kZiYiJ+fn9ElOVROTg47d+4kKSmJbdu24ePjg8lk4oUXXuDOO++Ui7iEcAHlacnfr7U+d9XtMODfWusopVSY7fZYh1bnpi5cuEB0dHTJnO+BgTc1r5DL0Vpz9OhRkpOTSUpK4pdffqF79+4EBQUxfPhwWZFKCBdUke6aJ4D7bD+vAL6hioe81povv/ySWbNm8dhjjzFhwgR8fHyMLqtC8vLy2LlzZ0mwe3t706tXL5577jkCAwPd/u8TwtPZG/Ia2KSU0sBCrXUM0ERrfQZAa31GKVWlBzSnpaUxZcoU0tLSmD17Nl26dDG6pJuiteb48eMl0wf8/PPPdO3alV69ehEcHEyrVq2qxIggITyFvSFv0lqn2oL8a6XUL/buQCk1AhgBeOTHeYvFwrp161iwYAFDhgzhueeec7tx3pcvX+b7778vCXatNUFBQQwZMoTAwEB8fX2NLlEIcZPsCnmtdarte7pSaj1wF5CmlAqwteIDgPTrPDYGiAHroiGOKds1/Pbbb0RGRlJcXExMTAxt2rQxuiS7aK05deoUSUlJJCcns2/fPrp06YLJZGLOnDncdttt0loXwkOUGfJKqdpANa31JdvPDwHhwGfAMCDK9v1TZxbqSoqKili5ciVxcXG8/PLLDBw40OWnJCgoKGD37t0kJSWxdetWCgsLCQoK4umnn2batGmyGIkQHsqelnwTYL2tZecNrNZaf6mU+h5IVEq9CJwEBjivTNdx6NAhwsPDqVevHnFxcdx6661Gl3RdKSkpJePW9+7dS6dOnQgKCiI6Opp27dpJa12IKkDWeLWT2Wxm0aJFfPLJJ4wcOZLHHnvM5ULSbDazZ8+ekmDPzc3FZDJhMpm46667qFOnjtElCiFugqzx6mR79+4lPDyc9u3bEx8fT4MGDYwuqURqamrJCdPdu3fTvn17TCYTU6dOpX379i7fjSSEcC4J+RvIzc1l3rx5fPPNN4SGhnL//fcbXRJms5m9e/eWzAmTlZVFUFAQ/fr1Y9KkSfj7+xtdohDChUjIX8fWrVuZOnUqf/7zn0lISDA0PNPS0kq6YHbt2sVtt92GyWRi0qRJdOrUSVrrQojrkpC/RlZWFjNnzmTv3r28++673HXXXZVeQ1FRET/++GNJsJ87d467776bBx98kAkTJlCvXr1Kr0kI4Z4k5G201nz99de89957PPzwwyQkJFCrVq1K239GRsZ/LVLdsmVLTCYT77zzDn/4wx+ktS6EuCkS8kB6ejpRUVGkpKQQHR3NH//4R6fvs7i4mH379pUE+9mzZ+nZsyf33nsvYWFhHj/fvBCiclTpkLdYLHzyySd8+OGHDBw4kKioKKcuZnH+/Pn/aq0HBARgMpkYO3YsXbt2xcvLy2n7FkJUTVU25E+dOkVkZCT5+fksXLiQtm3bOnwfFouF/fv3l/Stnz59umSR6jFjxtCwYUOH71MIIa7m+iFfUADp6VBcDLVqQePGUIGLkIqLi1m1ahUrVqzgxRdfZPDgwQ7t775w4QLbtm1j69atbN++ncaNGxMUFMTo0aO5/fbb8fZ2/ZdcCOE5XDNxDh2CNWtgyxb47Tfw8rIGu8UCNWpAly7wxBPQvz+UY2jj4cOHiYiIwM/Pj9jYWIcsSWexWDh48GBJa/3EiRMlrfWRI0fSuHGVnoFZCGEw15rW4PBhGDcOfvwRtAYfH6hZE65uaRcVQX6+tWXv5QXPPw8jR1rvex1ms5klS5bw8ccf88Ybb9C/f/8KTUlw8eJFtm3bRnJyMsnJydSvX79k+oBu3bq53VTDQgjX5v7TGlgssHAhzJplDfe6da/fJePtDVfWSi0qgkWLYONG+OAD6Nr1d3fft28fERERtGrVijVr1tCoUaObKM/CoUOHSq4yPXLkCIGBgZhMJl577TUCAgLK/ZxCCFEZjA95i8Xaev/oI2t4l6cV7O0N9erBmTMwYAAsXw5//jNgXbbuww8/5F//+hchISH06dOnXK337OxsduzYURLsderUwWQy8eqrr9K9e3enjsIRQghHMT7kp02DtWutYX2zJ0D9/SEvz9p1s3492y9cYMqUKfTo0YOEhATq1q1b5lNorfn1119L+tYPHz5Mjx49CAoK4uWXX3ZI/70QQlQ2Y0P+++9h8WJr90xFR7j4+lJ84QInHn2UaZ06Me6dd7j77rtv+JCcnBx27txJUlIS27Ztw8fHB5PJxAsvvMCdd95JzZo1K1aTEEIYzLiQN5th1Chr90wFLwLSwKVLlzibkUGj6tWJ79uXmqUEvNaao0ePkpycTFJSEr/88gvdunXDZDIxfPhwj1yDVghRtRkX8ps3W8e/l9GVkl1cTPiZM2zPyaGetzd/b9SIR656TGFREWfPnsVcUEDzFi3w9fKCZcvg9dehRg3y8vLYuXNnSbB7e3tjMpl47rnnCAwMxOcGo3KEEMLdGRfyCxfa1UUTdfYs1ZViU4cOHM7PZ+SpU3Tw8eG2mjW5mJVFeno69W65hWbNmlFNKTRQeO4cSePHszY3l59//pmuXbvSq1cvgoODadWqlcut6CSEEM5iTMjn5FjHwt9yyw3vdtliYfOlSyS2aYNvtWp09/Xl3jp1+DQzk/8pLKS4uJiWLVtSo0YNcnNzycnJIScnh9qFhfglJzMkKorAwEB8fX0r6Q8TQgjXYkzIHzpkvcipjBb1SbOZakBL23BFDQQUFrLj4kWCmzTBu3p10tPTybt8mVo+Pvj5+dGyRQtqaM2tXl7Qu7fz/xYhhHBhxoT8iRPWC5nKkGex4Gfr0rmcn8+pU6coys/nMnAxOxs/Pz9rV03z5nhd3fWjNaSkWMfgyzzsQogqzO6QV0p5AbuA01rrvyillgP3Ahdtdxmutd5r15MVFFgDuAy+1aqRa7vf8ePH8fbywrtOHRoD7Vu35rqfA658QjCbbzjdgRBCeLrytORHAgeBq2cEC9Faf1T+vXrbNZNkyxo1KMbabdO5c2cUsDI1lQ7e3tcPeLC25LUu39WzQgjhgezqy1BKNQceAxY7ZK/Nm1uDvgy1qlWjT506LMjIIN9i4ce8PL69dInHyrqCtbAQmjSp8Ph7IYRwd/Z2WM8GQoFr+1gmK6X2KaVmKaXsvzy0c2drENsxA2ZY06YUWCz0PXyY8adPM65pU9qUdSXq5cvQrZvd5QghhKcqszmtlPoLkK613q2Uuu+qX40DzgI1gBhgLBBeyuNHACOA/1xResst0KqVdWKx2rVvuH9/Ly/ea9HCnr/lv/XpU/7HCCGEh7GnJW8C+iulTgDxQB+l1Eqt9RltVQAsA+4q7cFa6xitdaDWOvC/pvkdMcKuETblVlRk7aZ57DHHP7cQQriZMkNeaz1Oa91ca90aGAxs1lr/VSkVAKCsl48+Cewv157/8hfrcn75+eWv+kYuXYLBg6FOHcc+rxBCuKGKDCJfpZT6CfgJaAhEluvRfn4wdaq1/9xRq1Pl5kL9+jB6tGOeTwgh3Fy5LobSWn8DfGP7ueKd3o8+Cp9/Dl9/bZ1PviJzypjN1q6a2bPLte6rEEJ4MmMvB1XKuuRfYCBkZdl1gVSp8vOti4ZMnQomk2NrFEIIN2b8Nf+1asGKFdY++osXrWFtL62tbw5aw7x58MwzzqtTCCHckNKO6g+3Z2dKZQC/VdoOHa8hcM7oIlyUvDY3Jq/P9clrc2MNgdpa60Zl3rMUlRry7k4ptUtrHWh0Ha5IXpsbk9fn+uS1ubGKvj7Gd9cIIYRwGgl5IYTwYBLy5RNjdAEuTF6bG5PX5/rktbmxCr0+0icvhBAeTFryQgjhwSTkS6GUaqGU+j+l1EGl1M9KqZG27fWVUl8rpX61fb/xSuQeTCnlpZT6QSm1wXb7NqXUDttrk6CUqmF0jUZRStVTSn2klPrFdgzdLceOlVLqf23/p/YrpdYopXyq8rGjlFqqlEpXSu2/alupx4qymquUOmKb4r2HPfuQkC9dEfCW1roz0BP4m1KqCxAG/Ftr3R74t+12VXVlpbArpgGzbK/NBeBFQ6pyDXOAL7XWnYBuWF+nKn/sKKWaAW8CgVrrroAX1kkPq/Kxsxx45Jpt1ztW+gHtbV8jgPl27UFrLV9lfAGfAn2BQ0CAbVsAcMjo2gx6PZrbDr4+wAZAYb2Yxdv2+7uBr4yu06DXxh84ju1811Xbq/yxAzQDTgH1sc6btQF4uKofO0BrYH9ZxwqwEBhS2v1u9CUt+TIopVoDdwA7gCZa6zMAtu+NjavMUNeuFNYAyNJaX1kgIAXrf+iqqA2QASyzdWctVkrVRo4dtNangWjgJHAGuAjsRo6da13vWLnyJnmFXa+VhPwNKKX8gI+BUVrrbKPrcQVXrxR29eZS7lpVh215Az2A+VrrO4BcqmDXTGlsfctPALcBtwK1sXZBXKuqHjtluan/ZxLy16GUqo414FdprdfZNqddtVhKAJBuVH0G+t1KYVhb9vWUUlemrm4OpBpTnuFSgBSt9Q7b7Y+whr4cO/AgcFxrnaG1LgTWAUHIsXOt6x0rKcDVa6Ha9VpJyJfCttrVEuCg1nrmVb/6DBhm+3kY1r76KkWXvlLYUOD/gCvTgFbJ1wZAa30WOKWU6mjb9ABwADl2wNpN01Mp5Wv7P3bltZFj579d71j5DHjONsqmJ3DxSrfOjcjFUKVQSvUCvsO66tWVfufxWPvlE4GWWA/YAVrrTEOKdAG2hd3HaK3/opRqg7VlXx/4Afirtq7/W+UopboDi7Eucn8MeB5rg6rKHztKqUnAIKwj2H4AXsLar1wljx2l1BrgPqwzTaYB/wA+oZRjxfbGOA/raJw84Hmt9a4y9yEhL4QQnku6a4QQwoNJyAshhAeTkBdCCA8mIS+EEB5MQl4IITyYhLwQQngwCXkhhPBgEvJCCOHB/h/hWxXMyOiL5wAAAABJRU5ErkJggg==\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "#Making the Hamiltonian in its full form and getting the lowest eigenvalue and eigenvector\n", - "\n", - "algorithm_cfg = {\n", - " 'name': 'ExactEigensolver',\n", - "}\n", - "\n", - "params = {\n", - " 'problem': {'name': 'ising'},\n", - " 'algorithm': algorithm_cfg\n", - "}\n", - "\n", - "result = run_algorithm(params,algo_input)\n", - "print('energy:', result['energy'])\n", - "#print('tsp objective:', result['energy'] + offset)\n", - "x = tsp.sample_most_likely(result['eigvecs'][0])\n", - "print('feasible:', tsp.tsp_feasible(x))\n", - "z = tsp.get_tsp_solution(x)\n", - "print('solution:', z)\n", - "print('solution objective:', tsp.tsp_value(z, ins.w))\n", - "draw_tsp_solution(G, z, colors, pos)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Running it on quantum computer\n", - "We run the optimization routine using a feedback loop with a quantum computer that uses trial functions built with Y single-qubit rotations, $U_\\mathrm{single}(\\theta) = \\prod_{i=1}^n Y(\\theta_{i})$, and entangler steps $U_\\mathrm{entangler}$." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "energy: -598732.7787240263\n", - "time: 88.01577425003052\n", - "feasible: True\n", - "solution: [1, 2, 0]\n", - "solution objective: 185.0\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "algorithm_cfg = {\n", - " 'name': 'VQE',\n", - " 'operator_mode': 'matrix'\n", - "}\n", - "\n", - "optimizer_cfg = {\n", - " 'name': 'SPSA',\n", - " 'max_trials': 300\n", - "}\n", - "\n", - "var_form_cfg = {\n", - " 'name': 'RY',\n", - " 'depth': 5,\n", - " 'entanglement': 'linear'\n", - "}\n", - "\n", - "params = {\n", - " 'problem': {'name': 'ising', 'random_seed': 10598},\n", - " 'algorithm': algorithm_cfg,\n", - " 'optimizer': optimizer_cfg,\n", - " 'variational_form': var_form_cfg,\n", - " 'backend': {'name': 'statevector_simulator'}\n", - "}\n", - "\n", - "result = run_algorithm(params,algo_input)\n", - "print('energy:', result['energy'])\n", - "print('time:', result['eval_time'])\n", - "#print('tsp objective:', result['energy'] + offset)\n", - "x = tsp.sample_most_likely(result['eigvecs'][0])\n", - "print('feasible:', tsp.tsp_feasible(x))\n", - "z = tsp.get_tsp_solution(x)\n", - "print('solution:', z)\n", - "print('solution objective:', tsp.tsp_value(z, ins.w))\n", - "draw_tsp_solution(G, z, colors, pos)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "# run quantum algorithm with shots\n", - "params['algorithm']['operator_mode'] = 'grouped_paulis'\n", - "params['backend']['name'] = 'qasm_simulator'\n", - "params['backend']['shots'] = 1024\n", - "result = run_algorithm(params,algo_input)\n", - "print('energy:', result['energy'])\n", - "print('time:', result['eval_time'])\n", - "#print('tsp objective:', result['energy'] + offset)\n", - "x = tsp.sample_most_likely(result['eigvecs'][0])\n", - "print('feasible:', tsp.tsp_feasible(x))\n", - "z = tsp.get_tsp_solution(x)\n", - "print('solution:', z)\n", - "print('solution objective:', tsp.tsp_value(z, ins.w))\n", - "plot_histogram(result['eigvecs'][0])\n", - "draw_tsp_solution(G, z, colors, pos)" - ] - } - ], - "metadata": { - "anaconda-cloud": {}, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.2" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/community/chemistry/h2_0.735_sto-3g.hdf5 b/qiskit/chemistry/H2/0.7_sto-3g.hdf5 similarity index 57% rename from community/chemistry/h2_0.735_sto-3g.hdf5 rename to qiskit/chemistry/H2/0.7_sto-3g.hdf5 index ab4be2d2f7fe18940e154354a798620d07800b8d..1e7fc17d056e9acccd50532628ad72fba0683b52 100644 GIT binary patch delta 844 zcmdl`wV`T52s0G&q74f;Lx%owvwto3}scRT_B(CIo@NxhBONNUd8N8T$n?q7R z|E*LsTkb=9ky*TaIfh^M=Roe2@3Dp6!h|UdrAaui?0{OIQOUhv4 z1vXCn!mDau9?dw?liaZ9 zretn=ulQU08&Dde>cC_}b4fQ5qm&MVe<{4OH7Qn zC$AP&WClk0=JTS)OpK3V+{x!fCxW7X^96}tOpLE#!kgbq166&7aVNi*o;mq~Y!Ksb z6p;_|RZPsBlXDalKqgP_SGdinJULqtVo$%KGz*h4=j1h_VA;**RgIaLtl@l^kxb5L zLYh&G-jlVpAcpvB?Pg^3oy@HR;p*!cvoO^n+gLa`L4aeE;VnkSxsz`jK~()WN@iw~ z}isl zpOczgnv<%KVWd#arJ$f-pkN51Jb)}c12EP#&@(nOH$@W#N`Xadxwwi`OTc=Q5{om7 z6^cvpb&b=3s*97;;!7$EQWXlaxoS^6VGOsr|8c*|s;?P;IG@`y0bS+{avdYsi3nOq z({25R?uYj6-&v2l)P1%`%Kkenf=6#9s>98XI?tL;jR4xD7|?h*M8QC2dp)MJIydee(s0 zUrda5V8WZNV+eQ#Y|BaHFnfSPnoK-ma0V~_)e`b3ane-6i_bpyC e`60OPEpG#jK5Ydt Trusted Notebook\" width=\"500 px\" align=\"left\">" + "\"Note: Trusted Notebook\" width=\"500 px\" align=\"left\">" ] }, { @@ -113,6 +113,7 @@ "source": [ "# useful additional packages \n", "import matplotlib.pyplot as plt\n", + "import copy\n", "%matplotlib inline\n", "import numpy as np\n", "from qiskit import Aer\n", @@ -154,7 +155,7 @@ "\n", "In this first part of the notebook, we show the optimization of the H$_2$ Hamiltonian in the `STO-3G` basis at the bond length of 0.735 Angstrom. After mapping it to a four-qubit system with a parity transformation, two spin-parity symmetries are modded out, leading to a two-qubit Hamiltonian. The energy of the mapped Hamiltonian obtained is then minimized using the variational ansatz described in the introduction, and a stochastic perturbation simultaneous approximation (SPSA) gradient descent method. We stored the precomputed one- and two-body integrals and other molecular information in the `hdf5` file.\n", "\n", - "Here we use the [*declarative approach*](https://github.com/Qiskit/qiskit-tutorials/blob/master/qiskit/aqua/chemistry/declarative_approach.ipynb) to run our experiement, but the same is doable in a [fully programmatic way](https://github.com/Qiskit/qiskit-tutorials/blob/master/qiskit/aqua/chemistry/programmatic_approach.ipynb), especially for those users who are interested in learning the Qiskit Aqua and Qiskit Chemistry APIs as well as contributing new algorithmic components." + "Here we use the [*declarative approach*](https://github.com/Qiskit/qiskit-tutorials/blob/master/qiskit/chemistry/declarative_approach.ipynb) to run our experiement, but the same is doable in a [fully programmatic way](https://github.com/Qiskit/qiskit-tutorials/blob/master/qiskit/chemistry/programmatic_approach.ipynb), especially for those users who are interested in learning the Qiskit Aqua and Qiskit Chemistry APIs as well as contributing new algorithmic components." ] }, { @@ -167,27 +168,27 @@ "output_type": "stream", "text": [ "Ground state energy (classical): -1.137306035753\n", - "Ground state energy (quantum) : -1.137287121511\n", + "Ground state energy (quantum) : -1.137304610765\n", "====================================================\n", "=== GROUND STATE ENERGY ===\n", " \n", - "* Electronic ground state energy (Hartree): -1.85725611279\n", - " - computed part: -1.85725611279\n", + "* Electronic ground state energy (Hartree): -1.857273602044\n", + " - computed part: -1.857273602044\n", " - frozen energy part: 0.0\n", " - particle hole part: 0.0\n", "~ Nuclear repulsion energy (Hartree): 0.719968991279\n", - "> Total ground state energy (Hartree): -1.137287121511\n", + "> Total ground state energy (Hartree): -1.137304610765\n", " Measured:: Num particles: 2.000, S: 0.000, M: 0.00000\n", " \n", "=== DIPOLE MOMENT ===\n", " \n", - "* Electronic dipole moment (a.u.): [0.0 0.0 -0.00514828]\n", - " - computed part: [0.0 0.0 -0.00514828]\n", + "* Electronic dipole moment (a.u.): [0.0 0.0 0.00070479]\n", + " - computed part: [0.0 0.0 0.00070479]\n", " - frozen energy part: [0.0 0.0 0.0]\n", " - particle hole part: [0.0 0.0 0.0]\n", "~ Nuclear dipole moment (a.u.): [0.0 0.0 0.0]\n", - "> Dipole moment (a.u.): [0.0 0.0 -0.00514828] Total: 0.00514828\n", - " (debye): [0.0 0.0 -0.01308562] Total: 0.01308562\n" + "> Dipole moment (a.u.): [0.0 0.0 0.00070479] Total: 0.00070479\n", + " (debye): [0.0 0.0 0.0017914] Total: 0.0017914\n" ] } ], @@ -231,7 +232,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -251,62 +252,69 @@ "# select H2 or LiH to experiment with\n", "molecule='H2'\n", "\n", - "qiskit_chemistry_dict = {\n", + "qiskit_chemistry_dict_ee = {\n", " 'driver': {'name': 'HDF5'},\n", " 'HDF5': {'hdf5_input': ''},\n", " 'operator': {'name':'hamiltonian', \n", " 'qubit_mapping': 'parity', \n", " 'two_qubit_reduction': True},\n", - " 'algorithm': {'name': ''},\n", - " 'optimizer': {'name': 'SPSA', 'max_trials': 350},\n", - " 'variational_form': {'name': 'RYRZ', 'depth': 3, 'entanglement':'full'}\n", + " 'algorithm': {'name': 'ExactEigensolver'}\n", "}\n", "\n", "# choose which backend want to use\n", "# backend = Aer.get_backend('statevector_simulator')\n", "backend = Aer.get_backend('qasm_simulator')\n", - "backend_cfg = {'shots': 1024}\n", - "algos = ['ExactEigensolver', 'VQE']\n", + "\n", + "qiskit_chemistry_dict_vqe = {\n", + " 'driver': {'name': 'HDF5'},\n", + " 'HDF5': {'hdf5_input': ''},\n", + " 'operator': {'name':'hamiltonian', \n", + " 'qubit_mapping': 'parity', \n", + " 'two_qubit_reduction': True},\n", + " 'algorithm': {'name': 'VQE'},\n", + " 'optimizer': {'name': 'SPSA', 'max_trials': 350},\n", + " 'variational_form': {'name': 'RYRZ', 'depth': 3, 'entanglement':'full'},\n", + " 'backend': {'shots': 1024}\n", + "}\n", "\n", "if molecule == 'LiH':\n", " mol_distances = np.arange(0.6, 5.1, 0.1)\n", - " qiskit_chemistry_dict['operator']['freeze_core'] = True\n", - " qiskit_chemistry_dict['operator']['orbital_reduction'] = [-3, -2]\n", - " qiskit_chemistry_dict['optimizer']['max_trials'] = 2500\n", - " qiskit_chemistry_dict['variational_form']['depth'] = 5\n", + " qiskit_chemistry_dict_vqe['operator']['freeze_core'] = True\n", + " qiskit_chemistry_dict_vqe['operator']['orbital_reduction'] = [-3, -2]\n", + " qiskit_chemistry_dict_vqe['optimizer']['max_trials'] = 2500\n", + " qiskit_chemistry_dict_vqe['variational_form']['depth'] = 5\n", "else:\n", " mol_distances = np.arange(0.2, 4.1, 0.1)\n", "\n", + "algos = ['ExactEigensolver', 'VQE']\n", "energy = np.zeros((len(algos), len(mol_distances)))\n", "\n", - "for j, algo in enumerate(algos):\n", - " qiskit_chemistry_dict['algorithm']['name'] = algo\n", - " if algo == 'ExactEigensolver':\n", - " qiskit_chemistry_dict.pop('backend', None)\n", - " elif algo == 'VQE':\n", - " qiskit_chemistry_dict['backend'] = backend_cfg\n", - " print(\"Using {}\".format(algo))\n", + "for j, algo in enumerate([qiskit_chemistry_dict_ee, qiskit_chemistry_dict_vqe]):\n", + " algo_name = algo['algorithm']['name']\n", + " print(\"Using {}\".format(algo_name))\n", " for i, dis in enumerate(mol_distances):\n", " print(\"Processing atomic distance: {:1.1f} Angstrom\".format(dis), end='\\r')\n", - " qiskit_chemistry_dict['HDF5']['hdf5_input'] = \"{}/{:1.1f}_sto-3g.hdf5\".format(molecule, dis)\n", - " result = solver.run(qiskit_chemistry_dict, backend=backend if algo == 'VQE' else None)\n", + " algo['HDF5']['hdf5_input'] = \"{}/{:1.1f}_sto-3g.hdf5\".format(molecule, dis)\n", + " result = solver.run(algo, backend=backend if algo_name == 'VQE' else None)\n", " energy[j][i] = result['energy']\n", " print(\"\\n\")" ] }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 7, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -330,9 +338,9 @@ "metadata": { "anaconda-cloud": {}, "kernelspec": { - "display_name": "Python 3", + "display_name": "Quantum (Stable)", "language": "python", - "name": "python3" + "name": "quantum-stable" }, "language_info": { "codemirror_mode": { @@ -344,7 +352,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.4" + "version": "3.7.3" } }, "nbformat": 4, diff --git a/qiskit/deutsch_jozsa.ipynb b/qiskit/deutsch_jozsa.ipynb deleted file mode 100644 index 662dda185..000000000 --- a/qiskit/deutsch_jozsa.ipynb +++ /dev/null @@ -1,203 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": { - "collapsed": true - }, - "source": [ - "# _*Experiment with the Deutsch-Jozsa Algorithm in Aqua*_\n", - "\n", - "This notebook demonstrates how to experiment with the `Deutsch-Jozsa` algorithm in `Qiskit Aqua`.\n", - "\n", - "We first import all necessary modules." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [ - ], - "source": [ - "from qiskit import BasicAer\n", - "from qiskit.aqua import QuantumInstance\n", - "from qiskit.aqua import run_algorithm\n", - "from qiskit.aqua.algorithms import DeutschJozsa\n", - "from qiskit.aqua.components.oracles import TruthTableOracle" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The [Deutsch-Jozsa algorithm](https://en.wikipedia.org/wiki/Deutsch-Jozsa_algorithm) is explained in more detail in the corresponding notebook located in the directory `community/algorithms`. We can experiment with it in Aqua by feeding it oracles created using truth tables. For example, we can create a `TruthTableOracle` instance as follows." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "bitstr = '11110000'\n", - "oracle = TruthTableOracle(bitstr)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As shown, the truthtable is specified with the `bitstr` containing values of all entries in the table. It has length $8$, so the corresponding truth table is of $3$ input bits. We can of course see that this truth table represents a `'balanced'` function as half of values are $1$ and the other half $0$.\n", - "\n", - "It might seem like a moot point running Deutsch-Jozsa on a truthtable as the function outputs are literally listed as the truthtable's values. The intention is to create an oracle circuit whose groundtruth information is readily available to us but obviously not to the quantum Deutsch-Jozsa algorithm that is to act upon the oracle circuit. In more realistic situations, the oracle circuit would be provided as a blackbox to the algorihtm.\n", - "\n", - "Above said, we can inspect the circuit corresponding to the function encoded in the `TruthTableOracle` instance." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "execution_count": 3, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "oracle.circuit.draw(output='latex')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As seen, the $v_i$'s correspond to the 3 input bits; the $o_0$ is the oracle's output qubit; the $a_0$ is an ancilla qubit.\n", - "\n", - "Next we can simply create a `DeutschJozsa` instance using the oracle, and run it to check the result." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The truth table 11110000 represents a balanced function.\n" - ] - } - ], - "source": [ - "dj = DeutschJozsa(oracle)\n", - "backend = BasicAer.get_backend('qasm_simulator')\n", - "result = dj.run(QuantumInstance(backend, shots=1024))\n", - "print('The truth table {} represents a {} function.'.format(bitstr, result['result']))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The above step-by-step programatic approach can also be achieved by using a json configuration dictionary with the parameters for the algorithm and any other dependent objects it requires, as follows:" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The truth table 11110000 represents a balanced function.\n" - ] - } - ], - "source": [ - "bitstr = '11110000'\n", - "params = {\n", - " 'problem': {\n", - " 'name': 'functionevaluation',\n", - " },\n", - " 'algorithm': {\n", - " 'name': 'DeutschJozsa'\n", - " },\n", - " 'oracle': {\n", - " 'name': 'TruthTableOracle',\n", - " 'bitmaps': [bitstr]\n", - " },\n", - " 'backend': {\n", - " 'shots': 1024,\n", - " },\n", - "}\n", - "\n", - "result_dict = run_algorithm(params, backend=backend)\n", - "print('The truth table {} represents a {} function.'.format(bitstr, result_dict['result']))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can of course quickly put together another example for a `'constant'` function, as follows." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The truth table 1111111111111111 represents a constant function.\n" - ] - } - ], - "source": [ - "bitstr = '1' * 16\n", - "oracle = TruthTableOracle(bitstr)\n", - "dj = DeutschJozsa(oracle)\n", - "backend = BasicAer.get_backend('qasm_simulator')\n", - "result = dj.run(QuantumInstance(backend, shots=1024))\n", - "print('The truth table {} represents a {} function.'.format(bitstr, result['result']))" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.2" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/qiskit/shors.ipynb b/qiskit/shors.ipynb deleted file mode 100644 index a3d29375f..000000000 --- a/qiskit/shors.ipynb +++ /dev/null @@ -1,118 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": { - "collapsed": true - }, - "source": [ - "# _*Experiment with the Shor's Algorithm in Aqua*_\n", - "\n", - "This notebook demonstrates how to experiment with the `Shor`'s algorithm in `Qiskit Aqua`.\n", - "\n", - "We first import all necessary modules." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "from qiskit import BasicAer\n", - "from qiskit.aqua import QuantumInstance\n", - "from qiskit.aqua import run_algorithm\n", - "from qiskit.aqua.algorithms import Shor" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The [Shor's Factoring Algorithm](https://en.wikipedia.org/wiki/Shor's_algorithm) is explained in more detail in the corresponding notebook located in the directory `community/algorithms`. With Aqua, we can create a `Shor` instance by simply providing the target integer to be factored and run it, as follows." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The list of factors of 15 as computed by the Shor's algorithm is [3, 5].\n" - ] - } - ], - "source": [ - "N = 15\n", - "shor = Shor(N)\n", - "backend = BasicAer.get_backend('qasm_simulator')\n", - "quantum_instance = QuantumInstance(backend, shots=1024)\n", - "ret = shor.run(quantum_instance)\n", - "print(\"The list of factors of {} as computed by the Shor's algorithm is {}.\".format(N, ret['factors'][0]))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The above step-by-step programatic approach can also be achieved by using a json configuration dictionary with the parameters for the algorithm and any other dependent objects it requires, as follows:" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The list of factors of 15 as computed by the Shor's algorithm is [3, 5].\n" - ] - } - ], - "source": [ - "params = {\n", - " 'problem': {\n", - " 'name': 'factoring',\n", - " },\n", - " 'algorithm': {\n", - " 'name': 'Shor',\n", - " 'N': N,\n", - " },\n", - " 'backend': {\n", - " 'shots': 1024,\n", - " },\n", - "}\n", - "result_dict = run_algorithm(params, backend=backend)\n", - "print(\"The list of factors of {} as computed by the Shor's algorithm is {}.\".format(N, result_dict['factors'][0]))" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.2" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/qiskit/simon.ipynb b/qiskit/simon.ipynb deleted file mode 100644 index e5c2ac1a7..000000000 --- a/qiskit/simon.ipynb +++ /dev/null @@ -1,222 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": { - "collapsed": true - }, - "source": [ - "# _*Experiment with the Simon's Algorithm in Aqua*_\n", - "\n", - "This notebook demonstrates how to experiment with the `Simon`'s algorithm in `Qiskit Aqua`.\n", - "\n", - "We first import all necessary modules." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "from qiskit import BasicAer\n", - "from qiskit.aqua import QuantumInstance\n", - "from qiskit.aqua import run_algorithm\n", - "from qiskit.aqua.algorithms import Simon\n", - "from qiskit.aqua.components.oracles import TruthTableOracle" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The [Simon's algorithm](https://en.wikipedia.org/wiki/Simon's_problem) is explained in more detail in the corresponding notebook located in the directory `community/algorithms`. We can experiment with it in Aqua by feeding it oracles created using truth tables. For example, we can create a `TruthTableOracle` instance as follows." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "bitmaps = [\n", - " '01101001', \n", - " '10011001', \n", - " '01100110'\n", - "]\n", - "oracle = TruthTableOracle(bitmaps)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As shown, the truthtable is specified with three length-8 bitstrings, each containing the values of all entries for a particular output column in the table. Each bitstring has length $8$, so the truthtable has $3$ input bits; There are $3$ bitstrings, so the truthtable has $3$ output bits.\n", - "\n", - "The function $f$ represented by the truthtable is promised to be either 1-to-1 or 2-to-1. Our goal is to determine which. For the case of 2-to-1, we also need to compute the mask $\\mathbf{s}$, which satisfies $\\forall \\mathbf{x},\\mathbf{y}$: $\\mathbf{x} \\oplus \\mathbf{y} = \\mathbf{s}$ iff $f(\\mathbf{x}) = f(\\mathbf{y})$. Apparently, if $f$ is 1-to-1, the corresponding mask $\\mathbf{s} = \\mathbf{0}$.\n", - "\n", - "Let us first compute the groundtruth mask $\\mathbf{s}$ classically:" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The groundtruth mask is 011.\n" - ] - } - ], - "source": [ - "def compute_mask(input_bitmaps):\n", - " vals = list(zip(*input_bitmaps))[::-1]\n", - " def find_pair():\n", - " for i in range(len(vals)):\n", - " for j in range(i + 1, len(vals)):\n", - " if vals[i] == vals[j]:\n", - " return i, j\n", - " return 0, 0\n", - "\n", - " k1, k2 = find_pair()\n", - " return np.binary_repr(k1 ^ k2, int(np.log2(len(input_bitmaps[0]))))\n", - "\n", - "mask = compute_mask(bitmaps)\n", - "print(f'The groundtruth mask is {mask}.')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Next we can create a `Simon` instance using the oracle, and run it to check the result against the groundtruth." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The mask computed using Simon is 011.\n" - ] - } - ], - "source": [ - "simon = Simon(oracle)\n", - "backend = BasicAer.get_backend('qasm_simulator')\n", - "result = simon.run(QuantumInstance(backend, shots=1024))\n", - "print('The mask computed using Simon is {}.'.format(result['result']))\n", - "assert(result['result'] == mask)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The above step-by-step programatic approach can also be achieved by using a json configuration dictionary with the parameters for the algorithm and any other dependent objects it requires, as follows:" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The mask computed using Simon is 011.\n" - ] - } - ], - "source": [ - "params = {\n", - " 'problem': {\n", - " 'name': 'periodfinding',\n", - " },\n", - " 'algorithm': {\n", - " 'name': 'Simon'\n", - " },\n", - " 'oracle': {\n", - " 'name': 'TruthTableOracle',\n", - " 'bitmaps': bitmaps\n", - " },\n", - " 'backend': {\n", - " 'shots': 1024,\n", - " },\n", - "}\n", - "\n", - "result_dict = run_algorithm(params, backend=backend)\n", - "print('The mask computed using Simon is {}.'.format(result_dict['result']))\n", - "assert(result_dict['result'] == mask)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can also quickly try a truthtable that represents a 1-to-1 function (i.e., the corresponding mask is $\\mathbf{0}$), as follows." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The groundtruth mask is 000.\n", - "The mask computed using Simon is 000.\n" - ] - } - ], - "source": [ - "bitmaps = [\n", - " '00011110', \n", - " '01100110', \n", - " '10101010'\n", - "]\n", - "mask = compute_mask(bitmaps)\n", - "print(f'The groundtruth mask is {mask}.')\n", - "oracle = TruthTableOracle(bitmaps)\n", - "simon = Simon(oracle)\n", - "result = simon.run(QuantumInstance(backend, shots=1024))\n", - "print('The mask computed using Simon is {}.'.format(result['result']))\n", - "assert(result['result'] == mask)" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.2" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/qiskit/simulations_with_noise.ipynb b/qiskit/simulations_with_noise.ipynb deleted file mode 100644 index 72d52d925..000000000 --- a/qiskit/simulations_with_noise.ipynb +++ /dev/null @@ -1,308 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## _*Running simulations with noise in Aqua*_\n", - "\n", - "This notebook demonstrates using the [Qiskit Aer](https://qiskit.org/aer) `qasm_simulator` to run a simulation with noise, based on a noise model, in Aqua. This can be useful to investigate behavior under different noise conditions. Aer not only allows you to define your own custom noise model, but also allows a noise model to be easily created based on the properties of a real quantum device. The latter is what this notebook will demonstrate since the goal is to show how to do this in Aqua not how to build custom noise models.\n", - "\n", - "Further information on Qiskit Aer noise model can be found in the online Qiskit Aer documentation [here](https://qiskit.org/documentation/aer/device_noise_simulation.html) as well as in the [Qiskit Aer tutorials](https://github.com/Qiskit/qiskit-tutorials/tree/master/qiskit/aer).\n", - "\n", - "Note: this tutorial requires Qiskit Aer if you intend to run it. This can be installed using pip if you do not have it installed using `pip install qiskit-aer`" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "import pylab\n", - "\n", - "from qiskit import Aer, IBMQ\n", - "from qiskit.aqua import Operator, QuantumInstance, aqua_globals\n", - "from qiskit.aqua.algorithms.adaptive import VQE\n", - "from qiskit.aqua.algorithms.classical import ExactEigensolver\n", - "from qiskit.aqua.components.optimizers import SPSA\n", - "from qiskit.aqua.components.variational_forms import RY" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Noisy simulation will be demonstrated here with VQE, finding the minimum (ground state) energy of an Hamiltonian, but the technique applies to any quantum algorithm from Aqua.\n", - "\n", - "So for VQE we need a qubit operator as input. Here we will take a set of paulis that were originally computed by qiskit-chemistry, for an H2 molecule, so we can quickly create an Operator." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Number of qubits: 2\n" - ] - } - ], - "source": [ - "pauli_dict = {\n", - " 'paulis': [{\"coeff\": {\"imag\": 0.0, \"real\": -1.052373245772859}, \"label\": \"II\"},\n", - " {\"coeff\": {\"imag\": 0.0, \"real\": 0.39793742484318045}, \"label\": \"ZI\"},\n", - " {\"coeff\": {\"imag\": 0.0, \"real\": -0.39793742484318045}, \"label\": \"IZ\"},\n", - " {\"coeff\": {\"imag\": 0.0, \"real\": -0.01128010425623538}, \"label\": \"ZZ\"},\n", - " {\"coeff\": {\"imag\": 0.0, \"real\": 0.18093119978423156}, \"label\": \"XX\"}\n", - " ]\n", - "}\n", - "\n", - "qubit_op = Operator.load_from_dict(pauli_dict)\n", - "num_qubits = qubit_op.num_qubits\n", - "print('Number of qubits: {}'.format(num_qubits))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As the above problem is still easily tractable classically we can use ExactEigensolver to compute a reference value so we can compare later the results. \n", - "\n", - "_(A copy of the operator is used below as what is passed to ExactEigensolver will be converted to matrix form and we want the operator we use later, on the Aer qasm simuator, to be in paulis form.)_" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Reference value: -1.85727503020238\n" - ] - } - ], - "source": [ - "ee = ExactEigensolver(qubit_op.copy())\n", - "result = ee.run()\n", - "ref = result['energy']\n", - "print('Reference value: {}'.format(ref))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Performance *without* noise\n", - "\n", - "First we will run on the simulator without adding noise to see the result. I have created the backend and QuantumInstance, which holds the backend as well as various other run time configuration, which are defaulted here, so it easy to compare when we get to the next section where noise is added. There is no attempt to mitigate noise or anything in this notebook so the latter setup and running of VQE is identical." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "VQE on Aer qasm simulator (no noise): -1.8662346923695476\n", - "Delta from reference: -0.008959662167167703\n" - ] - } - ], - "source": [ - "backend = Aer.get_backend('qasm_simulator')\n", - "quantum_instance = QuantumInstance(backend=backend, seed=167, seed_transpiler=167) \n", - "\n", - "counts = []\n", - "values = []\n", - "def store_intermediate_result(eval_count, parameters, mean, std):\n", - " counts.append(eval_count)\n", - " values.append(mean)\n", - "\n", - "aqua_globals.random_seed = 167\n", - "optimizer = SPSA(max_trials=200)\n", - "var_form = RY(num_qubits)\n", - "vqe = VQE(qubit_op, var_form, optimizer, 'paulis', callback=store_intermediate_result)\n", - "vqe_result = vqe.run(quantum_instance)\n", - "print('VQE on Aer qasm simulator (no noise): {}'.format(vqe_result['energy']))\n", - "print('Delta from reference: {}'.format(vqe_result['energy']-ref))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We captured the energy values above during the convergence so we can see what went on in the graph below." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": { - "scrolled": false - }, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.rcParams['figure.figsize'] = (12, 4)\n", - "pylab.plot(counts, values)\n", - "pylab.xlabel('Eval count')\n", - "pylab.ylabel('Energy')\n", - "pylab.title('Convergence with no noise');" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Performance *with* noise\n", - "\n", - "Now we will add noise. Here we will create a noise model for Aer from an actual device. You can create custom noise models with Aer but that goes beyond the scope of this notebook. Links to further information on Aer noise model, for those that may be interested in doing this, were given in instruction above.\n", - "\n", - "First we need to get an actual device backend and from its `configuration` and `properties` we can setup a coupling map and a noise model to match the device. While we could leave the simulator with the default all to all map, this shows how to set the coupling map too. Note: We can also use this coupling map as the entanglement map for the variational form if we choose.\n", - "\n", - "Note: simulation with noise takes significantly longer than without noise." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "VQE on Aer qasm simulator (with noise): -1.6539436913665533\n", - "Delta from reference: 0.20333133883582666\n" - ] - } - ], - "source": [ - "from qiskit.providers.aer import noise\n", - "\n", - "IBMQ.load_accounts(hub=None)\n", - "device = IBMQ.get_backend('ibmqx4')\n", - "coupling_map = device.configuration().coupling_map\n", - "noise_model = noise.device.basic_device_noise_model(device.properties())\n", - "basis_gates = noise_model.basis_gates\n", - "\n", - "backend = Aer.get_backend('qasm_simulator')\n", - "quantum_instance = QuantumInstance(backend=backend, seed=167, seed_transpiler=167,\n", - " coupling_map=coupling_map,\n", - " noise_model=noise_model,\n", - " basis_gates=basis_gates)\n", - "\n", - "counts1 = []\n", - "values1 = []\n", - "def store_intermediate_result1(eval_count, parameters, mean, std):\n", - " counts1.append(eval_count)\n", - " values1.append(mean)\n", - "\n", - "aqua_globals.random_seed = 167\n", - "optimizer = SPSA(max_trials=200)\n", - "var_form = RY(num_qubits)\n", - "vqe = VQE(qubit_op, var_form, optimizer, 'paulis', callback=store_intermediate_result1)\n", - "vqe_result1 = vqe.run(quantum_instance)\n", - "print('VQE on Aer qasm simulator (with noise): {}'.format(vqe_result1['energy']))\n", - "print('Delta from reference: {}'.format(vqe_result1['energy']-ref))" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.rcParams['figure.figsize'] = (12, 4)\n", - "pylab.plot(counts1, values1)\n", - "pylab.xlabel('Eval count')\n", - "pylab.ylabel('Energy')\n", - "pylab.title('Convergence with noise');" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Declarative approach and noise model\n", - "\n", - "Note: if you are running an experiment using the declarative approach, with a dictionary/json, there are keywords in the `backend` section that let you define the noise model based on a device, as well as setup the coupling map too. The basis gate setup, that is shown above, will automatically be done. Here is an example of such a `backend` configuration:\n", - "```\n", - " 'backend': { \n", - "\t 'provider': 'qiskit.Aer',\n", - " 'name': 'qasm_simulator',\n", - "\t 'coupling_map_from_device': 'qiskit.IBMQ:ibmqx4',\n", - " 'noise_model': 'qiskit.IBMQ:ibmqx4',\n", - " 'shots': 1024\n", - "\t },\n", - "```\n", - "\n", - "If you call `run_algorithm` and override the `backend` section by explicity supplying a backend instance as a parameter to run_algorithm, please note that you can provide a QuantumInstance type there instead of BaseBackend. A QuantumInstance allows you to setup and define your own custom noise model and other run time configuration. \n", - "\n", - "(Note when a BaseBackend type is supplied to run_algorithm it is internally wrapped into a QuantumInstance, with default values supplied for noise, run time parameters etc., so you do not get the opportunity that way to set a noise model etc. But by explicitly providing a QuantumInstance you can setup these aspects to your choosing.)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.8" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/qiskit/vqe_convergence.ipynb b/qiskit/vqe_convergence.ipynb deleted file mode 100644 index 1f720d96a..000000000 --- a/qiskit/vqe_convergence.ipynb +++ /dev/null @@ -1,247 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## _*VQE; using its callback to monitor optimization progress*_\n", - "\n", - "This notebook demonstrates using Qiskit Aqua's VQE algorithm to plot graphs of the convergence path to ground state energy with different optimizers.\n", - "\n", - "This notebook uses the callback capability of VQE to capture information at each objective functional evaluation where it is computing the energy using the parameterized variational form. While the params themselves are also part of the callback we are only interested in the energy value here to plot the convergence. \n", - "\n", - "Note: other variational algorithms such as QAOA and QSVM have similar callbacks." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "import pylab\n", - "\n", - "from qiskit import BasicAer\n", - "from qiskit.aqua import Operator, QuantumInstance, aqua_globals\n", - "from qiskit.aqua.algorithms.adaptive import VQE\n", - "from qiskit.aqua.algorithms.classical import ExactEigensolver\n", - "from qiskit.aqua.components.initial_states import Zero\n", - "from qiskit.aqua.components.optimizers import COBYLA, L_BFGS_B, SLSQP\n", - "from qiskit.aqua.components.variational_forms import RY" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "First we create a qubit operator for VQE. Here we have taken a set of paulis that were originally computed by qiskit-chemistry for an H2 molecule." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "pauli_dict = {\n", - " 'paulis': [{\"coeff\": {\"imag\": 0.0, \"real\": -1.052373245772859}, \"label\": \"II\"},\n", - " {\"coeff\": {\"imag\": 0.0, \"real\": 0.39793742484318045}, \"label\": \"ZI\"},\n", - " {\"coeff\": {\"imag\": 0.0, \"real\": -0.39793742484318045}, \"label\": \"IZ\"},\n", - " {\"coeff\": {\"imag\": 0.0, \"real\": -0.01128010425623538}, \"label\": \"ZZ\"},\n", - " {\"coeff\": {\"imag\": 0.0, \"real\": 0.18093119978423156}, \"label\": \"XX\"}\n", - " ]\n", - "}\n", - "\n", - "qubit_op = Operator.load_from_dict(pauli_dict)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we loop over the set of optimizers. The defaults for maxiters/evals for the respective optimizers is more than sufficient to converge the above H2 problem so we do not need to add any logic to set accordingly." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Optimization complete \n" - ] - } - ], - "source": [ - "optimizers = [COBYLA, L_BFGS_B, SLSQP]\n", - "converge_cnts = np.empty([len(optimizers)], dtype=object)\n", - "converge_vals = np.empty([len(optimizers)], dtype=object)\n", - "num_qubits = qubit_op.num_qubits\n", - "\n", - "for i in range(len(optimizers)):\n", - " aqua_globals.random_seed = 250\n", - " optimizer = optimizers[i]()\n", - " print('\\rOptimizer: {} '.format(type(optimizer).__name__), end='')\n", - " init_state = Zero(num_qubits)\n", - " var_form = RY(num_qubits, initial_state=init_state)\n", - "\n", - " counts = []\n", - " values = []\n", - " def store_intermediate_result(eval_count, parameters, mean, std):\n", - " counts.append(eval_count)\n", - " values.append(mean)\n", - " \n", - " algo = VQE(qubit_op, var_form, optimizer, 'matrix', callback=store_intermediate_result)\n", - " backend = BasicAer.get_backend('statevector_simulator')\n", - " quantum_instance = QuantumInstance(backend=backend) \n", - " algo_result = algo.run(quantum_instance)\n", - " converge_cnts[i] = np.asarray(counts)\n", - " converge_vals[i] = np.asarray(values)\n", - "print('\\rOptimization complete ');" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now from the callback data we stored we can plot the energy value at each objective function call each optimzer makes. An optimizer using a finite difference method for computing gradient has that characteristic step like plot where for a number of evaluations it is computing the value for close by points to establish a gradient (the close by points having very similiar values whose difference cannot be seen on the scale of the graph here)." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": { - "scrolled": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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zeuaZZ/Tcc8/p4IMP1q9//evJvaEpIHADAAAgcGamG264QWvXrtWKFSt09NFH61Of+pQWLVqkG2+8UZdeeqlWrlypVatW6WUve5kuvPDC6nOvu+46rV69Wscee6zuu+8+ffrTnx739S699FItW7as+nXttdfq7LPPHnHMW97ylmlpK7HKLMOZpLe3161bt266LwMAAGBaPPLIIzryyCOn+zJmlEafqZmtd871jvdcKtwAAABAiAjcEbv/ud067rO/0Av9uem+FAAAAESAwB2xx7fv1Z6hgjbtGpruSwEAAEAECNwRG8yXJEl7s4VpvhIAAABEgcAdsf5c0fvfbHGarwQAAABRIHBHbDDvBe29BG4AAIC2QOCO2EDObynJEbgBAADaAYE7YsMVbnq4AQDAzNXV1dXScZdccomWLl2q1atX64gjjtD73/9+lctlSdIFF1yggw8+WKtXr9bq1av1la98RZLU39+v97///VqxYoVOOOEEnXjiifrGN74hSSqXy/rQhz6kY445prqpztNPP9309ZcvX65Vq1Zp9erVWrVqlW688cYpvvPREoGfEWOqVLjp4QYAAPD8zd/8jT72sY+pXC7rta99rX71q1/plFNOkSRdccUVeutb3zri+L/8y7/UIYccoscff1yxWEw7duzQv/3bv0nydqncsmWLHnjgAcViMW3atEmdnZ1jvv6tt96q+fPna+PGjTrttNN01llnBfr+CNwRG6CHGwAAROm/LpK2PRjsORetkt54ebDnlJTP55XNZjV37tymxzz55JO655579B//8R+KxbxmjQULFuiTn/ykJGnr1q1avHhx9bFly5a1/Pp9fX1jvvZk0VISscFqDzctJQAAAJJ05ZVXavXq1Vq8eLEOP/xwrV69uvrYxz/+8WpLyYMPPqgNGzbouOOOqwbqen/yJ3+in/70p1q9erU++tGP6r777hv39U855RQdc8wxOvnkk3XppZcG9r4qqHBHrDIWkAo3AACIRAiV6KBVWkoKhYLe+ta36vvf/77OP/98SaNbSur7sS+77DL98Ic/1PPPP68tW7Zo2bJl2rhxo2655RbdcsstOvXUU/XDH/5Qp556atPXr7SUPPnkkzr11FO1Zs2alnvQW0GFO2KMBQQAAGgsmUzq9NNP1+233970mKOOOkq///3vqwsrL774Yt1///3q6+urHpNOp/XGN75RV1xxhf72b/9WP/7xj1t6/RUrVmjhwoV6+OGHp/ZG6hC4Izbg7zTZz1hAAACAEZxzuvPOO7VixYqmxxx66KHq7e3V3/3d36lU8nJVNpuVc06SdO+992rLli2SvIklDzzwgA466KCWXv/555/X008/3fLxraKlJGKDOcYCAgCAmW9wcHDEgsWPfOQj+shHPtLw2CuvvFLXXHONCoWCjj32WH3gAx8Y89zf/OY39fGPf1yHHnqo5s2bp46ODn3pS1+S5IXm97znPcrlcpKkl7/85brwwgvHPN8pp5yieDyuQqGgyy+/XAsXLpzIWx2XVf4amEl6e3vdunXrpvsyRimXnQ7525slSZ2puDZ87vRpviIAADATPfLIIzryyCOn+zJmlEafqZmtd871jvdcWkoiNFTw/tmjMxXXQL6kUnnm/bEDAACAkWgpiVBlBvfC2Rk9tWNA/bmiZnckp/mqAAAAwleZJlLr3HPP1cUXXxzJ67/iFa+otplUfO9739OqVatCf20Cd4Qqu0wu7PYC995sgcANAADawsUXXxxZuG7k7rvvnrbXpqUkQgP+gslFszOSmFQCAADQDgjcERr0RwIu7PECN7O4AQAAZj4Cd4SqFe6etCSpn8ANAAAw4xG4I1RdNOlXuPuYxQ0AAGawyy67TEcffbSOPfZYrV69WnfffbfWrFmj+vHNg4ODesc73qFVq1bpmGOO0atf/Wr19/dLkjZt2qSzzjpLhx12mA455BBdeOGF1cWPt912m2bPnq3Vq1fryCOP1Gc/+9nI32MrCNwRGqwsmpxNSwkAAJjZfvOb3+imm27SvffeqwceeEBr167VAQcc0PDYL3/5y1q4cKEefPBBPfTQQ7r66quVTCblnNM555yjN7/5zXr88cf1+OOPa2hoSJ/4xCeqz33Na16j+++/X+vWrdM111yje++9N6q32DICd4QqFe5FPSyaBAAAM9vWrVs1f/58pdNeK+38+fO1ZMmSpscuXbq0envlypVKp9O65ZZblMlk9O53v1uSFI/HdeWVV+q73/1utQJe0dnZqRNPPFFPPPFESO9o8hgLGKFKD/e8rpTiMWN7dwAAELov3vNFPfrio4Ge84j9jtAnX/7JMY857bTT9LnPfU6HH364Xv/61+u8887TySef3PDYP//zP9dpp52m66+/Xqeeeqre9a536bDDDtOGDRt04oknjji2p6dHy5cvHxWsd+7cqd/+9rf69Kc/PbU3FwICd4QG8iUl46Z0Iq7uTIJFkwAAYMbq6urS+vXr9etf/1q33nqrzjvvPF1++eUNj129erWeeuop/eIXv9DatWv1spe9TL/5zW9aep1f//rXOv744xWLxXTRRRfp6KOPDvJtBILAHaHBXFGzUt5H3pVO0MMNAABCN14lOkzxeFxr1qzRmjVrtGrVKn3nO99pemxXV5fOOeccnXPOOYrFYrr55pt13HHH6frrrx9xXF9fn7Zt26aVK1fq7rvv1mte8xrddNNNYb+VKaGHO0L9uZK60l7g7s4ktZcebgAAMENt3LhRjz/+ePX2/fffr4MOOqjhsXfeead27dolScrn83r44Yd10EEH6dRTT9Xg4KC++93vSpJKpZI++tGP6sILL1RHR0f4byIgBO4IDeaLmpWKS5K60wl6uAEAwIzV39+vd73rXTrqqKN07LHH6uGHH9Yll1wiSXrTm96kZcuWadmyZTr33HP15JNP6uSTT9aqVat0/PHHq7e3V295y1tkZrrhhht0/fXX67DDDtO8efMUi8WmdYv4yaClJEID+ZJmVSvcCW3fm53mKwIAAAjHiSeeqLvuumvU/bfddlvD4//sz/6s4f0HHHCAfvKTn0iS7rrrLr3tbW/TvffeqxNOOKHarvJSR+CO0GCuqK60V+HuyiT0xA5aSgAAAFr1yle+Us8+++x0X8aE0VISof6aRZNMKQEAAGgPBO4IDeZL6vR7uLvSSaaUAAAAtAECd4QG88URPdz5Ulm5YmmarwoAAMxEzrnpvoQZY6qfJYE7Qv25Ys1YQO9/qXIDAICgZTIZ7dy5k9AdAOecdu7cqUwmM+lzsGgyIqWyU7ZQHh4LWBO453elp/PSAADADLNs2TJt2rRJO3bsmO5LmREymYyWLVs26ecTuCMymPcq2Z3VnSaTksTCSQAAELhkMqmDDz54ui8DPlpKIjKY93q1O0e1lLD5DQAAwExG4I5Iv7+Ne2dlDrcfvNneHQAAYGYjcEdkMOdVuCtzuHsyXksJiyYBAABmNgJ3RAaqPdwjF03201ICAAAwoxG4IzJQbSnxF00yFhAAAKAtELgjMlBdNOlVuJPxmDLJWLW3GwAAADMTgTsig36wrvRwS95owD4q3AAAADMagTsiA3VjASWpJ5Ogwg0AADDDEbgjMlCtcMer93VlEszhBgAAmOEI3BEZyBeVSsSUjA9/5N2ZBIsmAQAAZjgCd0QGc6XqSMCKrnSCrd0BAABmOAJ3RAZyxRH925LUnUnSUgIAADDDEbgjMpAvqjM1MnB3pRNs7Q4AADDDEbgjMpgvaVZ6ZEtJZUpJueym6aoAAAAQNgJ3RAZyRXXVtZR0ZRJyThoslKbpqgAAABA2AndEBnKlESMBJa+HWxJ93AAAADMYgTsijXq4uzPebSaVAAAAzFwE7og06uGutJiwvTsAAMDMNS2B28zONbMNZlY2s94xjjvdzDaa2RNmdlGU1xi0/iZjASuPAQAAYGaargr3Q5LOkXR7swPMLC7pnyS9UdJRkt5mZkdFc3nBKpTKyhfLTVtK6OEGAACYuRLjHxI859wjkmRmYx32cklPOOee8o/9vqSzJD0c+gUGbDDvTSEZvWiSHm4AAICZ7qXcw71U0nM1tzf59+1zBvNeoB41FjBdqXATuAEAAGaq0CrcZrZW0qIGD13snLsxhNd7r6T3StKBBx4Y9OmnZMDv0Z5VF7g7UwmZ0VICAAAwk4UWuJ1zr5/iKTZLOqDm9jL/vmavd5WkqySpt7f3JbV140DOaynprGspicVMXSm2dwcAAJjJXsotJb+TdJiZHWxmKUnnS/rJNF/TpAz4LSWzUqP/vunOJGgpAQAAmMGmayzg2Wa2SdJJkn5mZj/3719iZjdLknOuKOlCST+X9IikHzjnNkzH9U5VpcJd38Mtedu7s2gSAABg5pquKSU3SLqhwf1bJJ1Rc/tmSTdHeGmhqCyarN/4RvJmce/N0cMNAAAwU72UW0pmjOEe7gYV7vTUK9w33LdJZ3/9Tjn3kmpdBwAAgAjckahUuDsbVrin3sO9YXOf7vvDbhZfAgAAvAQRuCNQ2bq96aLJKQbloYJXQd++Jzul8wAAACB4BO4IDOZLyiRjisdG76zZnUlOeQ53tlCWJG3rI3ADAAC81BC4IzCQKzbs35ak7nRC2UJZhVJ50ufP+hXubS1UuLOFEr3eAAAAESJwR2AgV1Rng5GAkjcWUNKUFk5WAvf2cSrcuwbyOuHzv9SvHtsx6dcCAADAxBC4IzCQL2lWavSCSclrKZGG+7wno9rD3Zcb87inXujXYL6kLbtpPQEAAIgKgTsCg/kxKtz+/X1T6OOutpSMU+GuBO1iefLtKwAAAJgYAncEBnKlpoG7x28pmcpowCF/0eR4LSVbdg9JkgolergBAACiQuCOgLdosnFLSRA93LkWF01WAndxCgs0AQAAMDEE7ggM5ksNZ3BLwz3cU9nevdLD/UJ/bswwvbnaUkKFGwAAICoE7ggM5IsNd5mUhnu4p1LhHiqUlIrHVHbSjv7mCye37qm0lFDhBgAAiAqBOwJjjQXszlQWTU5tLOCB82ZJGntSyXBLCRVuAACAqBC4Q5YvllUouaY93OlETMm4TXosoHNO2UJZy/3A3ayPezBf1K5Br22FlhIAAIDoELhDNpj3gnSzHm4zm9L27rmi1x6yfF6npOaTSmpnb7NoEgAAIDoE7pAN5L0FjV1NWkoqj022h3vIP//iOR1Kxq3pLO5KO4lEhRsAACBKBO6QDfitIrOaLJqUvD7uyc7hzha9wD0rFdf+3Rltb9JSUlkwKbFoEgAAIErNy64IRCVwdzZpKZG8CvfeSfZwVyrcHcm4Fvakm1a4N+/OKmbSfp0pFk0CAABEiAp3yAb9QNxsSokkv4d7khVuf5fJTDKuRbMzY7aULOzJKJ2Iq8DW7gAAAJEhcIesMn1kVpMpJZK3vftkF01WNr3JJGNa2JPR803GAm7ZPaTFszNKxI0KNwAAQIQI3CGrTCkZq8LdlUlMeixgZVv3jmRci3oy6s8VG55r656slszpUCJmKrFoEgAAIDIE7pAN5PyWkjEq3JVFk85NPAgPV7i9lhJp9Cxu55w27x7S0jkdSsZjLJoEAACIEIE7ZC1VuNNJlcqu2o89EZXndPhTSqTRs7h3DuSVL5a9CnfcGAsIAAAQIQJ3yPpzwy0fzVS2d59MH3e1wp1oXuGuzOBePDujRIwKNwAAQJQI3CEbzBU1KxVXLGZNj6kG7kn0cWcrgTsV06IeP3D3NQ7cS/zNcVg0CQAAEB0Cd8gG8qUx20mk2gr3FAJ3Mq6OVFw9mYSeHxW4vdtL53QoEYupyFhAAACAyBC4QzaQK465YFLyerglTWp799qNbyQ1nMW9ZfeQOpJxzZmVVCJuKlDhBgAAiAyBO2SD+aJmjbHLpDS1Hu5ssaR4zJSMez/KhT0Zbaubxb1lz5AWz8nIzJSIGRVuAACACBG4QzaQK6kzPXaFe35XWpL07IuDEz7/UL48YkHmwp6Mttctmty8O6ulczokSYl4jB5uAACACBG4QzaYL47bw72gO60jFnXrVxt3TPj82WJJmeTwj3FRT0Y7+nMjNrfZuntIS2Z7gTvJWEAAAIBIEbhD1p8rqnOclhJJWrNyf/3umRcn3FaSzZcTTV9/AAAgAElEQVSUqa1wz86oVHZ6od9rK8kVS3p+b05LKhXuWExFxgICAABEhsAdssF8SbPGWTQpSaesXKBi2enOJ16Y0PmzxdKIlpLqaEC/rWT7Hi94L57j3c+iSQAAgGgRuEM2kBu/pUSSTjxorrozCd366MTaSobqKtyVwF3ZbXKzP4O70sOdZCwgAABApAjcIXLO+XO4x69wJ+IxvfbwBbp14/NyrvUKdLZQv2jSW4BZCdxb9wxveuO9DhvfAAAARInAHaJcsaxS2Y07FrDilJX76/m9OT28ta/l1xgqlJSuWTQ5ryuteMyqs7hrt3WXpGScrd0BAACiROAO0aC/Kc14G99UnHz4AknSbROYVpItjOzhjsdM+3entc3v3d68O6t5nalq20k8xpQSAACAKBG4QzSQ83aObKWHW/LGAx67bLZuefT5ll8jWxjZwy35s7hrKtyVdhLJbykhcAMAAESGwB2igfzEArfkjQe87w+7tGsg39Lx9T3ckrdwctuIwJ2pPpZkLCAAAECkCNwhGsh5LSWtjAWsOGXlApWddPvjrbWVDBVGbnwjSYtmexVu51zDCnfZSWWq3AAAAJEgcIdo0K9wd02gwn3ssjnarzPVch93tlBSpi7Q79+T1t5sUdv7chrIl6q7TEreoklJKjAaEAAAIBIE7hBVerhbnVIieYsaTz58gX712I4R27M3Ui475YplZRKjW0ok6d4/7JKkkRXumEkSowEBAAAiQuAOUaWlpJU53LXWrFygFwfyemDT7jGPyxa983ekGgfu+6qBe7iHO+FXuAncAAAA0SBwh6jSUjKRCrckvfawBYqZdOs4bSXZgtcWkkmM/DEunF2pcHuBfWmDCjctJQAAANEgcIdowJ/DPZEebkma25nS8QfO1W0bxx4POFQYu8L94OY9SsZN87vS1ccScS9wj9euAgAAgGAQuEM0kCvKTKOmiLTilJUL9MCmPdqxN9f0mKwfuOvncHemE+pOJ5QvlrVodkYxv6oteWMBJbHbJAAAQEQI3CHaNZjX7I6kzGz8g+usWbm/JOlXjzVvKxnKNw7ckjepRNKICSXScIWbHm4AAIBoELhDtG1PrtreMVFHL+lRdyah3z/XfOFkrrJoskHgXuT3cdf2b0s1iybp4QYAAIgEgTtE2/uyWjjJwG1mmjsrpX5/tGAjQ3l/0WSDwF153cVzRr5+srJokgo3AABAJAjcIdrWl510hVvyFlvuzTYP3JUe7oYVbv91lzSrcBO4AQAAIkHgDkmhVNYL/bnqiL7J6Mok1J8rNH18qLpocvSPsdJSMjpwMxYQAAAgSgTukOzYm5NzmlKFu7vFCnejlpKjFvcoFY/p8IXdI+5np0kAAIBoTWxANFq2dU9WkrR4qhXuHZML3L3L99ODnz1N6bpt3xMxFk0CAABEiQp3SLb3eYF7sosmJa+Hu3/MCrcXmus3vqmoD9uSlGQsIAAAQKQI3CHZ5le4F02hwt2dSWrvWFNKKhXuROs/RsYCAgAARIvAHZLtfVmlEjHNnZWc9Dm6M95ukZV52/WGCiUl41YN0a1IMBYQAAAgUgTukGzry2phT3pSu0xWdKW9FvuBXOPAnS2UlGnQNjKWJGMBAQAAIkXgDsm2PVObwS0NB+5mfdzZQkmZJv3bzVS3dqelBAAAIBIE7pBMZZfJiq6MF7j7so1ncWcL5YYzuMdCSwkAAEC0CNwhcM5p657slEYCSt4cbklNt3cfypca7jI5luGdJqlwAwAARIHAHYI9QwXliuXAKtxNW0qKEw/cycrGN2Uq3AAAAFEgcIdgW9/URwJKNT3cY1S401S4AQAAXtII3CGozuCeYoW7O+ONFGw2iztbLE+ipYQKNwAAQJQI3CEIYpdJyZvDLY3RUpIvTXjRZNLf2p1FkwAAANEgcIdg256cpKkH7nQipkTM1J9rMqVkEj3c1Qo3LSUAAACRIHCHYFtfVvM6U0pNYMv1RsxMXZmE9japcA/lS8pMNHBXxgLSUgIAABAJAncItu0ZmnJ1u6IrnRh745sJBm4zUzxmVLgBAAAiQuAOwba+3JRncFd0pRPNF00WyhMO3JJX5S5R4QYAAIgEgTsE2/uyWhhQ4O7ONK5wl8pO+dLEp5RIUjIeY9EkAABARAjcAcsVS3pxID/lkYAV3Zlkwznc2UJJkiY8pUTyFk4Wy7SUAAAARIHAHbDn+7wJJUEF7q50omHgHvIDd0dqMi0lVLgBAACiMi2B28zONbMNZlY2s94mxxxgZrea2cP+sX8d9XVORmWXyaBaSppNKalWuBOTaSlh0SQAAEBUpqvC/ZCkcyTdPsYxRUkfdc4dJel/SfqgmR0VxcVNRVC7TFZ0pxPamx09h7sauCdT4Y4bO00CAABEJDEdL+qce0TyRtSNccxWSVv97/ea2SOSlkp6OIprnKygA3dXOqFcsax8sTxirne24FWoM5OY9e21lFDhBgAAiMI+0cNtZsslHS/p7um9kvFt68uqIxlXT0cwf8t0+du7D9T1cU+th9tUpIcbAAAgEqFVuM1sraRFDR662Dl34wTO0yXpR5I+7JzrG+O490p6ryQdeOCBE7za4Gzry2rR7MyY1fuJ6Ep7P6L+XFFzO1PV+ystJZMZC5iIx2gpAQAAiEhogds59/qpnsPMkvLC9r875/5znNe7StJVktTb2zttaXL7nqwW9qQDO193JilJoxZODuUrYwEnuWiSsYAAAACReMm2lJhXIr5a0iPOuf9/uq+nVdv6soH1b0vexjeSRo0GzBb9Hu5J7jRJSwkAAEA0pmss4NlmtknSSZJ+ZmY/9+9fYmY3+4e9StI7Jb3OzO73v86YjuttlXNOz/flAhsJKNW2lIycVJLNT2XjGxZNAgAARGW6ppTcIOmGBvdvkXSG//0dkoJphI7IiwN55UvlQCvclUWT9S0l2eLke7iTcatOOQEAAEC4XrItJfuirQGPBJS8OdxSsD3ciViMjW8AAAAiQuAO0PaAd5mUhivco3q4C1Pr4WZrdwAAgGgQuANU2dZ9cYCBuyMZVzxm6q+vcBdKSsVjiscm3nWTYEoJAABAZAjcAdq+J6uYSQu6ghsLaGbqSicaVLhLk1owKTGHGwAAIEoE7gBt68tqfldaiXiwH2tXOjF60WShNKl2EklKMhYQAAAgMgTuAG3ry2lRgO0kFd2ZxKixgEOF0qS2dZf8CjeLJgEAACJB4A6Qt8tk8IG7aUtJYpIV7ripQEsJAABAJAjcAQp6l8mKrszolpKhQlmZyVa4GQsIAAAQGQJ3QIbyJe0ZKoTSUtKVToyaUpItlNQxyUWTcXq4AQAAIkPgDkhlJGAYFe7uTEJ7G04pmUpLCRVuAACAKBC4A7KtsstkKIsmk00q3JNfNFmihxsAACASBO6AVHeZDGnR5FChNKLvemiKYwELJSfnCN0AAABhI3AHpNpSElIPtyQN5ErV+7KF8qQDd2VOOFVuAACA8BG4A7JtT1Zd6UQ1HAepK+Odc2/NLO5sfio7TXrbwbPbJAAAQPhsJrYV9Pb2unXr1kX6mh/717dpd3GrDpnfGfi592YL2rR7SAfP71Im4YXsR7f1ab/OtPbvnuA28rG4Ntoh+u1zg3r7yw9UMhGTyXT2YWfriP2OCPzaAQAAZiozW++c6x3vuODLsW3qBT2pxzsG9OjgCyGc3cl1S0/nX5TyXnXadTs9KckGbULnkXMqxrco2RPXL/7wsMykvlyfiuWiPn3Sp0O4dgAAgPZG4A7It//3PXLOyWwiAbg19/1hl87++l361gUv0ylH7K/+XFHHfObnuviMI/We1x7S+on6d0j/cKjuPvJTOu++Vbrl4lO1f3dGb7j+DcqVcoFfNwAAAOjhDlQYYVvyxgJKqs7iHsp7iycn3MOdSEmSks7rBa9sfpOKpZQv54O4VAAAANQhcO8Duv1Fk5VZ3NlCJXBPcEpJ3Ov3TsoL3JUpJal4SoVSoenTAAAAMHkE7n1AZfJJvz+lZPKBe2SFu+DP9U7GklS4AQAAQkLg3gfMSsVlNlzhHvID94R3mozFpFhSiUpLSU2FO18icAMAAISBwL0PMDN1pRPqq7aUeJXpSW18k0hXA3elwk3gBgAACA+Bex/RnU6oP1dX4U5N4scXTynhvHBdu2iyUKaHGwAAIAwE7n1EVyYx9UWTkpRIK15tKfF7uONJKtwAAAAhIXDvI7pqKtxTCtzxlOLlSksJYwEBAADCRuDeR3RnktU53NnJLpqUvAp3ua6lhB5uAACA0BC49xFeS4lXmR7e+GYyFe6awF0eXjTJHG4AAIBwELj3EbWLJrNFLyhPrsKdGlXhTsaSypXZ2h0AACAMBO59RFd6eNFkpcKdTkxmSklasQYVblpKAAAAwkHg3kd0ZRIayJdUKjtliyWlEzHFYjbxEyVS1cBdu2iSlhIAAIBwELj3EcPbuxeVzZcm178tNa1wF11RZVcO5FoBAAAwjMC9j+jO1ATuQnly/duSV+Eu1VW44ylJoq0EAAAgBATufUR3JilJ6s8WNVQoKZOc5I8unpaVRi+alMQsbgAAgBAQuPcRwy0lBT9wT7bCPRy4SzUtJRIVbgAAgDAQuPcRXX5Lyd5sUdmpBO54StZg0aR3m4WTAAAAQSNw7yO6axdNFkpT6OFOy0rezO1ifYWblhIAAIDAEbj3ESMr3GV1pCZf4VZxZIU7Gfd7uGkpAQAACByBex9R7eGe6qLJaoXbVRdNVlpKqHADAAAEj8C9j+hMJWQm7c1NtYc7LUlKWWlUSwk93AAAAMEjcO8jYjFTV8rb3n1KgTvhhetZseKoRZO0lAAAAASvpcBtZv9pZm8yMwL6NOrKJNSfK0xt4xu/wt0RK6lYYtEkAABA2FoN0F+X9HZJj5vZ5Wa2MsRrQhNd6YT6c1Pt4fYr3PGSimUWTQIAAIStpdTmnFvrnHuHpBMkPSNprZndZWbvNrNkmBeIYV2ZhHYNFFQquylXuGfFanq4WTQJAAAQmpbLpGY2T9IFkv5S0n2SviwvgP8ylCvDKF3phHb0ezO0p7LTpCR1xIrDU0pYNAkAABCaRCsHmdkNklZK+p6kM51zW/2HrjOzdWFdHEbqziT0wKYpBu54ZdFkiUWTAAAAEWgpcEv6inPu1kYPOOd6A7wejKErndCeIa8KPdUKdyZWrLaUVHu4aSkBAAAIXKuBe66ZnVN33x5JDzrnng/4mtBEd2a4XX7yPdxeNTtjNWMB41S4AQAAwtJq4P4LSSdJqlS510haL+lgM/ucc+57IVwb6lR2m5Q0pZ0mJanDihosjVw0WSjTww0AABC0VgN3UtKRzrntkmRmCyV9V9IrJN0ur7cbIevODP+4pjqlJB0rVscCUuEGAAAIT6tl0mWVsO17XtIBzrkXJVEWjUhthTs9xZ0mMzWBO2YxJSxB4AYAAAhBqxXu28zsJkk/9G+/xb+vU9LuUK4Mo3QFWOHOqFjdaVLyFk6yaBIAACB4rQbuD0o6R9Kr/dvflfQj55yTdEoYF4bRaivcHampVbjTNXO4Ja+thAo3AABA8MYN3GYWl7TWOXeKpB+Ff0lopraHe9KLJisVbiuqUB6ucKdiKRZNAgAAhGDc1OacK0kqm9nsCK4HYwhkLKA/pSStAhVuAACACLTaUtIv6UEz+6WkgcqdzrkPhXJVaGjkWMCpzeFOqahCbQ93LEngBgAACEGrgfs//S9Mo9pFk+nE1OZwp6xBDzeLJgEAAALXUuB2zn3HzDokHeic2xjyNaGJzpT348okYzKzyZ0klpBkSqmgUrkmcMdSKpTo4QYAAAhaS2VSMztT0v2S/tu/vdrMfhLmhWG0eMzUmYpPvn9bksykRFrpupYSKtwAAADhaLUv4RJJL5c/c9s5d7+kQ0K6JoyhK5OYfP92RTytZN2iyWScHm4AAIAwtBq4C865PXX3lRseiVB1pRNTq3BLUiKllAoq1o0FJHADAAAEr9VFkxvM7O2S4mZ2mKQPSborvMtCM92ZpHLFKf6t41e4C3WLJpnDDQAAELxWK9x/JeloSTlJ10rqk/ThsC4KzS2endH+3empnSSRUtKN3NqdCjcAAEA4Wp1SMijpYv8L0+jyc45V2bnxDxxLPK1kMa9Cua6Hm0WTAAAAgWspcJvZ4ZI+Jml57XOcc68L57LQzOxZyfEPGk8ipUShMLLCzU6TAAAAoWi1h/uHkv5F0jcllcK7HEQinlbSFVR2UrnsFIsZc7gBAABC0mrgLjrn/jnUK0F0Emkl3F5JUrHslIoZc7gBAABC0uqiyZ+a2QfMbLGZ7Vf5CvXKEJ54SgnnVbMrowGTMW8Ot5tqfzgAAABGaLXC/S7/fz9ec58Tm9/smxJpxZ1Xza6MBkzFU3JyKrqikhZAnzgAAAAktT6l5OCwLwQRiqeU8GduVxZOpuIpSVKhVFAyRuAGAAAIypgtJWb2iZrvz6177O8n+6Jmdq6ZbTCzspn1jnNs3MzuM7ObJvt6qFNT4S76owFTMS9wM6kEAAAgWOP1cJ9f8/2n6h47fQqv+5CkcyTd3sKxfy3pkSm8FurFU4r7Fe5CXYWbhZMAAADBGi9wW5PvG91umXPuEefcxvGOM7Nlkt4kbxwhgpJIK+YH66Lfw11pI6HCDQAAEKzxArdr8n2j22H4v5I+Iak83oGYgHha8XJdSwkVbgAAgFCMt2jyODPrk1fN7vC/l387M9YTzWytpEUNHrrYOXfjeBdmZn8k6Xnn3HozW9PC8e+V9F5JOvDAA8c7vL0lUoqVR44FrF00CQAAgOCMGbidc/HJntg59/rJPtf3Kkl/bGZnyAv3PWZ2jXPuT5u83lWSrpKk3t5ehkmPJZFRzBVlKldbStLxtCRaSgAAAILW6sY3kXPOfco5t8w5t1ze4s1bmoVtTJBfzU6pWF00We3hpqUEAAAgUNMSuM3sbDPbJOkkST8zs5/79y8xs5un45raSsKrZqdVGN3DTYUbAAAgUK3uNBko59wNkm5ocP8WSWc0uP82SbeFfmHtokGFuzKHu1CmhxsAACBIL9mWEoTIr3CnVKj2cFPhBgAACAeBux35CyRTVlDJbylJxpnDDQAAEAYCdztKNG8pYdEkAABAsAjc7She01LCokkAAIBQEbjb0RgVbhZNAgAABIvA3Y78CnfaWDQJAAAQNgJ3O6pOKSlWt3Zn0SQAAEA4CNztqDqHu6CCX+FOWEImY9EkAABAwAjc7ai2wu33cJuZUvGUCiV6uAEAAIJE4G5HNRXuypQSyVs4SYUbAAAgWATudlSpcFtxROBOxpP0cAMAAASMwN2Oaudw+y0lkjephMANAAAQLAJ3O0qMXjQp0VICAAAQBgJ3O/Ir3BkbHgsoiUWTAAAAISBwtyN/0WQmVqxufCNJyViSCjcAAEDACNztKBaTYkllrDiypYQebgAAgMARuNtVIt2wpYTADQAAECwCd7uKp5SuGwuYiqVUKNPDDQAAECQCd7uqVLhrxgIyhxsAACB4BO52FU95G98wFhAAACBUBO525Ve4C2UWTQIAAISJwN2u4umGO00yhxsAACBYBO52lUgppZFjAZnDDQAAEDwCd7uqVLgZCwgAABAqAne78ivcpTKLJgEAAMJE4G5XfoW7UNfDXSwXVXblMZ4IAACAiSBwt6tESkkVRo4FjKckic1vAAAAAkTgblfxtJIqjBgLmIwlJYk+bgAAgAARuNtVIq2kGz0WUCJwAwAABInA3a7iDVpKYrSUAAAABI3A3a4SaSVcQYUyFW4AAIAwEbjbVTylhBtZ4U7G6eEGAAAIGoG7XfkV7lJtD7ffUsIsbgAAgOAQuNtVPK2YnMql4X5tWkoAAACCR+BuVwkvXMdqqtksmgQAAAgegbtdxdOSJKsN3FS4AQAAAkfgbleVCndNuGbRJAAAQPAI3O3Kr3DHG7SUsGgSAAAgOATudpXwAnesnJdz3mhAWkoAAACCR+BuV364TqmoUtkP3CyaBAAACByBu135Fe6UCir6gZsebgAAgOARuNtVTYW7ErhpKQEAAAgegbtdVSrcVlDR322SRZMAAADBI3C3q3ilpaSoQmlkhbtQoocbAAAgKATudpWotJQUVCx7Fe6YxZSwBBVuAACAABG425Vf4U6rqKJf4Za8hZP0cAMAAASHwN2uKhVuK6jg93BLXlsJgRsAACA4BO52VdPDXZnDLXkLJ5nDDQAAEBwCd7uqmcNdqGkpocINAAAQLAJ3u4qPXjQpSclYkkWTAAAAASJwt6vE6LGAEhVuAACAoBG421UsIScbsfGN5PVwU+EGAAAIDoG7XZnJxVMjtnaXvAo3G98AAAAEh8DdxsrxlNIaORaQOdwAAADBInC3MRdLexXu0sixgLSUAAAABIfA3ca8lpLCqJYSKtwAAADBIXC3s0RKKSuOGAvIxjcAAADBInC3s3jaq3DXtJTQww0AABAsAnc786eU1C6apKUEAAAgWATudpZIj+7hZtEkAABAoAjc7azSw11X4WYONwAAQHAI3G3M4ml/DndND3csSYUbAAAgQATudpbw53CXR1a4y66sYrk4jRcGAAAwcxC421gs2aCHO56SJBZOAgAABITA3cYsMXosYCrmBW5mcQMAAASDwN3GLJFuuGhSosINAAAQFAJ3G6tUuAvlkYsmJbFwEgAAICAE7nYWTystKtwAAABhInC3s0TKq3CXWDQJAAAQFgJ3O4unlbSSSqXhEYAsmgQAAAjWtARuMzvXzDaYWdnMesc4bo6ZXW9mj5rZI2Z2UpTXOeMlvHCtmmp2Mu71cOdKuem4IgAAgBlnuircD0k6R9Lt4xz3ZUn/7Zw7QtJxkh4J+8LaSjwtSXLF4XBdqXDTUgIAABCMxHS8qHPuEUkys6bHmNlsSa+VdIH/nLwkUmCQEl7gVm3gjtNSAgAAEKSXcg/3wZJ2SPqWmd1nZt80s87pvqgZJT66pYRFkwAAAMEKLXCb2Voze6jB11ktniIh6QRJ/+ycO17SgKSLxni995rZOjNbt2PHjgDeQRvwK9xGSwkAAEBoQmspcc69foqn2CRpk3Pubv/29RojcDvnrpJ0lST19va6Zsehhl/NtgaLJtn4BgAAIBgv2ZYS59w2Sc+Z2Ur/rlMlPTyNlzTzVHq4a8I1FW4AAIBgTddYwLPNbJOkkyT9zMx+7t+/xMxurjn0ryT9u5k9IGm1pL+P/mpnsHiDlhIWTQIAAARquqaU3CDphgb3b5F0Rs3t+yU1ndONKfLncMdqwjWLJgEAAIL1km0pQQT8CnesNHrR5O+efV7/+qsnp+WyAAAAZhICdzurVriHq9mJmPePHg9u3qkf3btpWi4LAABgJpmWlhK8RFR6uGtaSsxMqVhKe3NZFYaK03VlAAAAMwaBu535U0ridf3ayXhK/cWc8lkWTgIAAEwVLSXtzF8gGXMjA3fckpKVNJgvqVAqT8eVAQAAzBgE7nZWqXDXbXITU0JmXjtJ3xBVbgAAgKkgcLczv8Idr5+57RJSJXBn6eMGAACYCgJ3O6tUuN3IwO3K8Wrg3jNOhXvXQF6fufEhZQulcK4RAABgH0fgbmf+lJJEXUtJqRyXmRegx2spueOJF/Sd3zyrBzfvCecaAQAA9nEE7nYWi6mkuBJ1Fe5iMaZk0lss2TfOpJLdfiB/YW9uzOMAAADaFYG7zZViKcXrppTkizHNSjtJ47eU7Bn0nvvCAFvBAwAANELgbnOlWHJEhTtXLClfiCmT9AJ33zib3+wepMINAAAwFgJ3mytZSklXkHNewN66Oyu5hBKJshIxa7mlZOcAgRsAAKARAnebK8VSSllRhZIXuDfvHpJz3hzu2R3JcRdNDle4aSkBAABohMDd5sqxlFIqqFj2Fklu3jUkOW8sYE9Hcvwe7iEvaFPhBgAAaIzA3ebK8aTSKqpY9ircm3YNSi6hkiuoJ5MYd+ObaoW7nwo3AABAIwTuNletcPstJZt2D2lWMq1CuaCeFlpKKhXwF/qpcAMAADRC4G5zLp5SSkUVS15LyaZdQ+pOZ5Qv5ccN3M457R4qKGbS3myR3SYBAAAaIHC3uXIspZQVVPBbSjbvGlJPukP5cl49meSYU0qyhbLyxbIO2G+WJOlFZnEDAACMQuBucy6e9ltKyiqWytrWl9Xsjg4Vy0V1Z2LqGypWRwbW2+0vmFyxoEsSbSUAAACNELjbXKWlpFBy2taXVansNLejQ5LU1WHKl8rKFsoNn1tZMLliQackaScLJwEAAEYhcLc5L3B7YwE37RqSJM2b5QXozpR3TLO2kkrgPnR/r8K9gwo3AADAKATudhdPK2VFFUvOm8EtaV6X15PdkfYOabZwck9dSwkVbgAAgNEI3O0uUalwu2qFe4EfuGelvd7tZpvfVO5fPKdDs1JxergBAAAaSEz3BWCaxdPexjelsjbvHtT+3WnNSnrj/TJJr3d7vJaSOR1JzetKaSeBGwAAYBQCd7vze7gLJa/CvWxuh1Ixb3fJdMqrcPcNNd5tcvdQQcm4aVYqrvldae1kLCAAAMAotJS0u0Ta3/impM27h7R07iwl40lJUjrpB+4xKtyzO5IyM83rTGvHXircAAAA9Qjcbc6SacXMqVDIa8vuSoXbG0+STHitJXsGmy+anN3hhfMF3Skq3AAAAA0QuNucxb1RJNt37VWh5LR0TodScX8eoJWUScbGrHDPmeUdO68zrRcH8iqXG2+SAwAA0K4I3G3Okl7g3vzCbknS0rnDgTtf8irYTXu4Bwua41e453elVCo77W4y0QQAAKBdEbjbXCzhBe6tO73AfUBNS0m+lFdPJjnmWMDZs7zAPa/LOw+jAQEAAEYicLe5SuDevqtPkrRkTkd10WS+nFdPR7JpS8meoYLmdHjhfD6BGwAAoCECd5urtJS8sGuv5nWmNCuVGFHhnt0kcBdKZfXnipoza7ilRJJeYKGqbMkAAB7qSURBVLdJAACAEQjcbS6WzEiSrJzX0rkdklTt4S6UC+rJJBq2lFTum13t4faCO5vfAAAAjMTGN20u5le4UyqMCtz5kt9S0mDRZHWXSb/CPbsjqXjMaCkBAACoQ4W7zSX8CndKRS2d4wXuZMzv4fYXTe7NFkaN+9sz5LWOVCrcsZhpv86UdtJSAgAAMAKBu81VK9xWqAbuaoW77PVwl53Unx9Z5R6ucKeq983vSlPhBgAAqEPgbnPx1HCFe9ncWd73/qLJQqmgng6v66ivro+70sNdmcMteQsnWTQJAAAwEoG7zQ23lAz3cMdjcSUs4Y0FzHiBur6Pu76HW6LCDQAA0AiBu81VppSkVawGbklKxpPVsYCSRo0G3D1UkJnUnRkO3PPo4QYAABiFwN3uEl77SE+qXK1mS14fd2VKiaRRowH3DHrV73jMqvfN705rqFDSQK7xVvAAAADtiMDd7uLeosmFs2zE3alYyp/DXWkpGV3hnl3Tvy15FW5JVLkBAABqELjbnb+1+/yOkXdXKtzDLSWje7hr+7clr8ItSTvo4wYAAKgicLc7fwTgirkjw3MyllS+nFdXxptSUt9S0qjCPb+T3SYBAADqEbjbnV/hfvkBXSPurlS44zFTdzoxqqWkb6gwYga3JM3v9m5PZDTg937zjP7p1icmceEAAAD7BgJ3u4slJJlUGlmVTsVSype94NzTkRw9pWQwP2IGtyTtV+3hbq3CXSiVdeXax/WtO5+Z3LW39BoF/eixH+n0H52uD6z9QGivAwAA0Exiui8A08zMq3IX6wJ3PKVCyQvZPR3JERXuctlpz9DoHu50Iq6eTKLlWdx3PvGCXhzwQv2LA/lqYA9CoVTQj5/8sb75wDe1ZWCL0vG0+gv9gZ0fAACgVeacm+5rCFxvb69bt27ddF/GvuMLB0rzD5MOe0P1rr/c/j96ttCnc7pWaMOWPjlJxyzpkSQVy06/e/pFHTS/U0tmZ0ac6r7ndqszldDhC0e2qDTyxPP92rHXC+dHLe3R7Exy7CfEk9Ki46Rkx5iH5ct5/eypn2nrwFatmr9K7zvufXps12P68r1f1m/f/lt1JjvHvTYAAIDxmNl651zveMdR4Ya08GjpD3dJm4f/SDl8vzm6e3aPvr7nQcnPp7fvqXnOfOk+Saq9T5K8TK619fc3kva/JN2X2yK1Uhh/8d4WDpKOW3CcPnPSZ/TKJa+UmWmwMChJ/6+9O4+Oq7zTPP791aa9ZEuWZJUsZIMtwDbGAbOnScDsHZaeSQI5JBOSSfqEQ5qESeiGpE9neqb7pDPhdDqdDplhSEI4JJAESFjCHkJgQrAxu4yxDbbBlmVbXiRZey3v/HFvWbJUWiyrVGXX8zlHlurWXd6r62s/evW778v27u0smr1oUvsQERERmQ4K3AKfe2zUor8FbvZ/+/H1X7/Bn97bzZ9vWQnAm9s6uPL2P3HHp1dw4eK6g7a7/p5X2NjezTM3fWTcQz7RsoPrf/EKP7vudL5836tcsSzGP1110vjt3PU2PH4zvP8iNJwCl97mfc7A7OBxxevL6wEFbhEREZl5Ctzi1XFnXOwtrywtYn9/Egt4z9h29ieBALPLiw4sS6uJlrBqy75Ry0d6tGUH1WXFnLOohua6Sjbu6p1wG+Yuheseg7d+DU/9Pdy5Ek79LDSeOeEpNvj129vXPwx7tk+4/rSrnAcL/mLmjysiIiI5p8AtE4qWhOgZTJJIpggFAwfG5B45SglAdXmEfb1x4skU4WDmAN0zkOD363byiVMbCQUDNNdV8HhLG865UT3To5jBsk9C88Xw3L/Aqv8Dr9w14TlUAZGmRravvR/23Tnh+tPOAnDLB1BUMfPHFhERkZxS4JYJDZ9tsqosQocfuCtLMwVuryh7X88gtdHiUe8DPLNuJ/3xFJefHAOgua6ce1fHae8eoLYi8zajFFfCJd+Gv/g6DHRNuHoAiD17Pdsb5sOKv5vcMabLxqe9UpjObVB74sweW0RERHJOgVsmFPVHD+nqi1NVFqGz1xvKb+RMkwA15d7Qfu3dA2MG7kfe2E59ZTErmmYDcHyd1+u7YUf3mIG7sy/OnS9s4obzFlIcDg69UVbtfUxCrLKJ7QOdULVgUutPm9hy73PHVgVuERGRAqSJb2RC0QM93F7PdkdvnNJIkKJQcNS66R7uPWPMNtnZG+ePG9r52LJ6AgGvfGRROnDv3D9mGx59czs/ePZdHm9pm/J51JfVs70nR/XbAJ1bZ/7YIiIiknMK3DKhAyUlfQkAOvriGeu3Aeb4gXusyW+eWNtGPOkOlJN420SYXRoeN3Cv3rzX275lx6GfgK+hvIG9/XvpS/RNeR9TUj4XAmEFbhERkQKlwC0TipZ4lUfphyU7euMHer1Hqi5PT++euYf7kTfaaKou5aSGygPLzIzmuooxA7dzjlWbvMD9xw3t9A0mp3QesXIv5Ld1T72XfEoCAYjGvBpuERERKTgK3DKhAzXcfklJZ9/gqGnd0yqKQkRCgYw93O37B3jxvd1ccXJs1GgkzXUVbNzZTaaZT7ft62NHVz+XLp1LfzzF8xvbp3Qe6cDd2t06pe0Py6xjvBpuERERKTgK3DKhoZKSdOCOM6skknFdM2NOWYTdGXq4H29pI+U4qJwkrXluBfsHErR19o96b5VfTvLl8xdSWRLmySmWlcTK/B7unhnu4Qavjls93CIiIgVJgVsmVBoJEgzYQSUlY/VwA8ypKBrVw+2c48FXWzm+roLmutFjUTfXlgOZH5xcvXkPs0vDnDg3ysoTa3lm3U7iydQhn0dNaQ2hQCg3PdyVjbB/OyTjM39sERERySkFbpmQmREtDtHVH8c5R0dfPOMY3GnVZRH29BwcuO9Z9QGvb+3gM2c1ZdymeZyRSlZv3stp86sIBIxLlsylqz9xoKb7UAQs4I1U0p2jkUpcCvbnoHddREREckqBWyalsiRMV1+C/niKwURqzJIS8EYq2b1/qKTk3V37+adH3+YjzTVce8YxGbeZXRahpqKIDTu7D1q+s6ufLXt6OX1BFQDnNtdQEg7yxNqxg+sTLW2sa8s8GU6sPJaboQFnNXqfVcctIiJScBS4ZVKiJWE6++J09HlBerySkuryIvb0DOCcYyCR5G/ufZ2yohDf/cSycadub64rH9XDnR4O8IwF3uQ2xeEgH2mu4am1O0mlRj9g+frWDq7/+at87+kNGY/RUN6Qox5uP3CrjltERKTgKHDLpESLw3T1x+no9ad1H2NYQPDG1Y4nHV19CW57cj3r2rr47seXTThte3qkkuFBevXmvZRFgpxYP1T3ffHSOnbtH+D1bR0HbZ9Iprj1wbdwDtZuz9zDXV9Wz+6+3QwkM48TnjXRBu+zxuIWEREpOArcMileSclQ4B5r4hsYmvzmoTda+b8vbOYzZzax8sS6CY/RXFdBXzzJtn1DE9Os3ryXU+dXEQoO/VU9/4Q6QgEbNVrJT/60mXVtXZw+v4rWjj729YweKaWh3Au+Mz4Wd6QUSucocIuIiBQgBW6ZlGhJiM6+xIGRSsZ7aDIduP/HI2+zsLacb1x24qSO0Vx38Egl+3oGWb9zP2f49dtplSVhzjqumifX7jgwbvfWvb187+mNXHBiHX+zciEAb2eo464vqwfI3YOTKikREREpOArcMinpkpLOAzXcYz80mZ5tMmDG969ZTkkkOKljLEqPVLLLC9wvb/Hqt08fEbgBLl4yly17etngT5bzDw+1YAb/eOUSlsS8WSzXbu8ctV26hztnD07qoUkREZGCo8AtkxItCTOYSLGzy6t9Hq+kZN7sEiqKQnzjshMOhN9JHaM4TH1lMRt2eIF79ea9REIBls0bvY+LFtdhBk+07OB3b7Xxh/XtfO2i42mYVUJVWYRYZTEtraN7uGtKawhZKHcPTnZugwyzaYqIiMjRK5TrBsiRIeoH7A/29hIOGqXj9FpXFId57R8uPKjuerKa6yoODA24estePtQ4i6LQ6GPVRos55ZjZPPxGK139CZY2RPnssDG+F8cqM/ZwhwIh6srqcjf5TbwH+vZB6eheexERETk6qYdbJiVa7P1s9sGeXipLIuMO7wdMKWyDV8f9bns3nX1xWlo7R9VvD3fxkjrea+9hT/cA3/6rZQcdc2lDlE27e+gZSIzaLlYey9307qAHJ0VERApMTgK3mX3CzNaaWcrMVoyz3k3+ei1mdq+ZjT+unGTN8B7u8cbgPlyL6ioYTKT4zavbSDk43R9/O5NLltQTMLju7AWcNKLsZEmsEufgnR2jy0piZbHc9HBr8hsREZGClKse7hbgPwHPj7WCmTUANwIrnHNLgSBwzcw0T0ZKj7u9o6t/3DG4D9fx/oOT96z6gFDAOKVp1pjrHlNdylM3ncs3Ljth1HtLYlEg83jcsfIY7b3txJPxaWr1JGnyGxERkYKUk8DtnFvnnFs/iVVDQImZhYBSIAdPugl4DzSmjffA5OFaWOsNDfjurm6WNlRSGhn/MYOFtRUZy1fqK4upKovQ0jq6jjtWHsPh2NGzY9R7WVVaDaESlZSIiIgUmLyt4XbOtQK3AR8AbUCnc+6p3LaqcEVLhoLveGNwH66yohCNVSUA49ZvT8TMWBKLZuzhTg8N2Nozw2UlZv5Y3ArcIiIihSRrgdvMnvFrr0d+XDnJ7WcDVwILgBhQZmafHmf9vzazNWa2pr29fXpOQg44uId77DG4p0NzrVdWkmn87UOxJFbJhp37GUykDlqenvxmxmebBE1+IyIiUoCyFridcxc455Zm+Hhokru4ANjsnGt3zsWBB4GzxzneHc65Fc65FTU1NdNxCjJMcThIUcj765LNhyYBFseihALGiqbDDdxR4kl3YObKtLqyOgIWyN2Dk3poUkREpKDkbUkJXinJmWZWat4YdCuBdTluU0FLj1SS7cD9xXOP5YHrzz7s0pWlDd7IJW+PKCsJB8LUltbmbvKbnl0Q75/5Y4uIiEhO5GpYwL8ys23AWcDvzOxJf3nMzB4DcM6tAu4HXgXe8tt6Ry7aK5706CTZHKUEvPKVkxvHHp1kspqqSikvCtGSYQKcWFksN9O7p0cq6cpB77qIiIjkRE5mmnTO/Qb4TYbl24HLhr3+FvCtGWyajCM9+U22A/d0CQSME+srxnxwcs3ONTPfqOGT31QfN/PHFxERkRmXzyUlkmeGSkqy+9DkdFoSq2RdWxfJlDtoeX15Pbt6d5FIjZ6JcqREMsWP/99mtnf0HX6DNPmNiIhIwVHglklLj1SSzXG4p9uSWJTewSSbd/cctLyhvIGkS7Kzd+eE+7j9uff4n4++zd//tuXwG1QRA0wjlYiIiBQQBW6ZtMoZemhyOqUfnFw7oo47Vh4DmPDByVc/2Mf3f7+RumgRz76zi5e37D28BoUiUFGvsbhFREQKiAK3TFpdtIiScJCK4iMncC+sLScSCoyq446VTRy4uwcSfPW+15kbLeaRL3+Y2ooivvP4OzjnxtxmUjT5jYiISEFR4JZJu+6cBfz2hnMIBizXTZm0cDDACXMrRvVwzy2bi2HjBu7//vBatu3r5XtXL6c2WsyNKxex5v19/GH9rsNrlMbiFhERKSgK3DJp5UUhjp9bketmHLL0FO/De6YjwQg1pTVjTn7zuzfbuP+Vbdxw3sIDM15efVojTdWl/K8n1pNKHUYvd+U8b1jAVGridUVEROSIp8AtR73FsUo6euO0jhhlJFYWo61n9PTu2zv6uPXBNzm5cRY3rlx0YHk4GOC/XdjMOzv288ibhzGGd2UjJAehp33q+xAREZEjhgK3HPWWxqIAo+u4y2Ojerj3dA/wtV+9QSLl+LerlxMOHnyLXL4sxon1Uf716Q3Ek1PsoU5PfqM6bhERkYKQk4lvRGbSCXOjBAzWtnZy8ZK5ADjnqCqaS2v3Yyy/+xRSzlvmHBCGyELj449nrlVPzXbEk47Tfm4EbSr17A6aGuHZL4JN/Wfe0+tP5wfn/4BQQLexiIhIPtP/1HLUK4kEWVhbzgOvtvLyln20dfbR1tnPIDWEZ58HpKgoClEbLaK2opj6WcXURYvH3qGD377eSld3nGvOaCIUPMTQnRiAl26H+efCvFOndE6dA508sPEB7lp7F1846QtT2oeIiIjMDAVuKQiXL4tx38tbGUymWNJQyYWL66ivPIHGqgs5eV4lteMF7Aw+PGcvn/jff2bjO3V85qwmzjy2elT5ybie/SGEY3DqTYd4JkO6Bru4/fXbOa/xPI6bpWniRURE8pUd9pjCeWjFihVuzZo1uW6GHOW+88Q73P3iFnoGk8wuDXPR4rlcetJczj5uDpHQBOH79rNhdhN86t4pH39P3x6ueugqGisaufvSu1VaIiIiMsPM7BXn3IqJ1tP/0CJT9HeXnMBXVi7i+Q3tPN6yg8feauOXa7ZSGglyatNszlhQxRnHVrNsXiVFoeDBG48x+U08mZp0T3l1STXfPOOb3Pz8zdz99t18funnp+O0REREZJopcIschuJwkIuWzOWiJXMZSCR5YcNuXtjYzqrNe7ntqQ0AFIUCLJtXyYI5ZTRVl9FUXcpZ4Tpm71vFn9/dTUtrJy3bu1jb2smm3T0sm1fJp89o4vKTY5REguMe/+L5F/Pklif54Ws/5JzYucwKzaOmvIjAETQ5kYiIyNFOJSUiWbKvZ5DVW/ayatNe3tzWwZY9vezuHgDgS8GHuSV8H0v6f0wPJTTMKmFpQ5QFc8p59p2dbNjZTbQ4xMdPbeTaM4/huJryUfvvGUjw+tYO/vjuJn6140YSA9V0b/4SRaEQC+aUMb+6jAU1ZTRVlVJWFKI4HKQ4HKAoFKQkHKQ2WjTpcD6YSPFWayerNu9h9ea9bGrvoaI4xOzSCLNKw8wqDTOnvIgVTVWsmD+b4vD4PyiIiIgcDSZbUqLALTKDegYSfLC3l4HXf8XyVV9jd+PFVERnHVRy4nDs7h5kU3s3rR19pBxE0iOhmJGOx4OJFOm7972qfu6p2sGnEnM5rS9K72CCnoEkffEE402KGTAoCYcoCQcoKQoStADOeW1weEMldsRDtPRUsjk5h22uhsjsRubXzaJvMEFnX5z9fXE6++N09SdwDiLBACc3VnLafC98l0ZC9Awk6B1MHmiXwxEKBAgFjFDQCAUCFIXCRCPllEfKKAqFiISMYCBA0IxAAIIBI2Dex/DRGA1w/ve2sy9OR2+cjr44nb2DJFKOcDBA2D9GOBSgOBQgWhImWhwmWhIiWhKmPBLSbwVEROSQKXArcEs+2/c+/OKTMNg77mpJ5+gdTJBIORhxqwYCRlEoQCQYwMz4ajk8G8lim2eIOUeJg7KUozgFhxODHeCwoQ9nI7+Nww6cPtbQn0PrumF/Ztw0o5Azgg6CzggCQTf2umZDx800vPuoY6cX2PjfIxv2rhuxl2G7mFCxM766b9bkNzhcLv1pqM020clOg59W3cSeUG12DyIi0+4/n9LAlcsbZvy4emhSJJ/NboIbVk24WhComOQuvx3v5bmtzxFPxQ+raaM5GOiG7l3Qswu626G/Ayb4YX0wmWJ/fwLnnNdTPayX2sxwzpHC+0Ei5SDuUnSTpIckPZakO5CgL5BKt4BhCWx4yw7wer8Z6gUPeOEdl8K5JKRS4JLgnDfJEd4ppL/GpU9p6HU63Hmh1Q/E/rKJ+iockDBHwiAZcMT915nyohvjnA7V0H7G24tlDPQTbR/AKE7tH/P7fyhGHj7TfmycFbPZTdTTP0BXcLrvIRHJtoH4FGd/niEK3CJHidJwKZcde1mumyFyRLsj1w0QkaPS1OeVFhERERGRCSlwi4iIiIhkkQK3iIiIiEgWKXCLiIiIiGSRAreIiIiISBYpcIuIiIiIZJECt4iIiIhIFilwi4iIiIhkkQK3iIiIiEgWKXCLiIiIiGSRAreIiIiISBYpcIuIiIiIZJECt4iIiIhIFilwi4iIiIhkkQK3iIiIiEgWKXCLiIiIiGSRAreIiIiISBYpcIuIiIiIZJE553LdhmlnZu3A+1k+zBxgd5aPIVOn65PfdH3ym65PftP1yW+6Pvltuq9Pk3OuZqKVjsrAPRPMbI1zbkWu2yGZ6frkN12f/Kbrk990ffKbrk9+y9X1UUmJiIiIiEgWKXCLiIiIiGSRAvfU3ZHrBsi4dH3ym65PftP1yW+6PvlN1ye/5eT6qIZbRERERCSL1MMtIiIiIpJFCtyHyMwuMbP1Zvaumd2S6/YUOjNrNLM/mNnbZrbWzL7iL68ys6fNbKP/eXau21rIzCxoZq+Z2aP+6wVmtsq/j35pZpFct7FQmdksM7vfzN4xs3Vmdpbun/xhZjf5/7a1mNm9Zlas+ye3zOwnZrbLzFqGLct4z5jn3/1r9aaZnZK7lheGMa7Pd/1/4940s9+Y2axh793qX5/1ZnZxttqlwH0IzCwI/BC4FFgMfMrMFue2VQUvAXzNObcYOBO4wb8mtwC/d84tAn7vv5bc+Qqwbtjr7wDfc84tBPYB/zUnrRKA7wNPOOdOAE7Gu066f/KAmTUANwIrnHNLgSBwDbp/cu0u4JIRy8a6Zy4FFvkffw38aIbaWMjuYvT1eRpY6pxbBmwAbgXw88I1wBJ/m9v9rDftFLgPzenAu865Tc65QeA+4Moct6mgOefanHOv+l/vxwsLDXjX5Wf+aj8DrspNC8XM5gF/CdzpvzbgfOB+fxVdnxwxs0rgXODHAM65QedcB7p/8kkIKDGzEFAKtKH7J6ecc88De0csHuueuRK423leAmaZWf3MtLQwZbo+zrmnnHMJ/+VLwDz/6yuB+5xzA865zcC7eFlv2ilwH5oGYOuw19v8ZZIHzGw+8CFgFVDnnGvz39oB1OWoWQL/BvwtkPJfVwMdw/7x032UOwuAduCnfsnPnWZWhu6fvOCcawVuAz7AC9qdwCvo/slHY90zyg355/PA4/7XM3Z9FLjlqGBm5cADwFedc13D33PeUDwajicHzOxjwC7n3Cu5botkFAJOAX7knPsQ0MOI8hHdP7nj1wFfifeDUQwoY/SvyiXP6J7JX2b2TbxS1J/P9LEVuA9NK9A47PU8f5nkkJmF8cL2z51zD/qLd6Z/bed/3pWr9hW4c4ArzGwLXgnW+Xg1w7P8X5GD7qNc2gZsc86t8l/fjxfAdf/khwuAzc65dudcHHgQ757S/ZN/xrpnlBvyhJldB3wMuNYNjYk9Y9dHgfvQvAws8p8Qj+AV2j+c4zYVNL8e+MfAOufcvw5762Hgs/7XnwUemum2CTjnbnXOzXPOzce7X551zl0L/AH4uL+ark+OOOd2AFvN7Hh/0UrgbXT/5IsPgDPNrNT/ty59fXT/5J+x7pmHgf/ij1ZyJtA5rPREZoiZXYJX2niFc6532FsPA9eYWZGZLcB7uHV1VtqgiW8OjZldhleTGgR+4pz75xw3qaCZ2YeBF4C3GKoR/gZeHfevgGOA94FPOudGPuQiM8jMPgp83Tn3MTM7Fq/Huwp4Dfi0c24gl+0rVGa2HO+B1giwCfgcXmeM7p88YGb/CFyN92vw14Av4NWY6v7JETO7F/goMAfYCXwL+C0Z7hn/B6X/wCsF6gU+55xbk4t2F4oxrs+tQBGwx1/tJefcl/z1v4lX153AK0t9fOQ+p6VdCtwiIiIiItmjkhIRERERkSxS4BYRERERySIFbhERERGRLFLgFhERERHJIgVuEREREZEsUuAWEclzZpY0s9eHfdwy8VYZ9/Ocma2Y7vZN4rhXmdnimT6uiEi+CE28ioiI5Fifc255rhtxGK4CHsWbtEVEpOCoh1tE5AhkZpeY2a+Hvf6omT3qf/0jM1tjZmv9iVMm2tdpZvaimb1hZqvNrMLMis3sp2b2lpm9Zmbn+eteZ2b/MWzbR/1JjTCzbjP7Z38/L5lZnZmdDVwBfNfvnT9umr8VIiJ5T4FbRCT/lYwoKbkaeAY4w8zK/HWuxpt9EOCbzrkVwDLgI2a2bKwdm1kE+CXwFefcycAFQB9wA+CccycBnwJ+ZmbFE7SzDG8Gt5OB54EvOudexJs++Wbn3HLn3HtTOH8RkSOaAreISP7r88Nq+uOXzrkE8ARwuZmFgL8EHvLX/6SZvYo37fcSYLz66eOBNufcywDOuS5/3x8G7vGXvYM3XXXzBO0cxCsdAXgFmH+I5ykiclRSDbeIyJHrPuDLwF5gjXNuv5ktAL4OnOac22dmdwET9UwfigQHd9YM33fcOef8r5Po/xgREUA93CIiR7I/AqcAX2SonCQK9ACdZlYHXDrBPtYD9WZ2GoBfvx0CXgCu9Zc1A8f4624BlptZwMwagdMn0c79QMUhnJeIyFFFgVtEJP+NrOH+FwDnXBKvhONS/zPOuTfwSkneAX4B/Gm8HTvnBvHqv39gZm8AT+P1Wt8OBMzsLbwa7+uccwP+/jbjjTjy78Crk2j/fcDN/sOXemhSRAqODf32T0REREREppt6uEVEREREskiBW0REREQkixS4RURERESySIFbRERERCSLFLhFRERERLJIgVtEREREJIsUuEVEREREskiBW0REREQki/4/7zJ1INev+dQAAAAASUVORK5CYII=\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.rcParams['figure.figsize'] = (12, 8)\n", - "for i in range(len(optimizers)):\n", - " pylab.plot(converge_cnts[i], converge_vals[i], label=optimizers[i].__name__)\n", - "pylab.xlabel('Eval count')\n", - "pylab.ylabel('Energy')\n", - "pylab.title('Energy convergence for various optimizers')\n", - "pylab.legend(loc='upper right')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Finally since the above problem is still easily tractable classically we can use ExactEigensolver to compute a reference value for the solution. We can now plot the difference from the resultant exact solution as the energy converges with VQE towards the minimum value which should be that exact classical solution." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Reference value: -1.85727503020238\n" - ] - } - ], - "source": [ - "ee = ExactEigensolver(qubit_op)\n", - "result = ee.run()\n", - "ref = result['energy']\n", - "print('Reference value: {}'.format(ref))" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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44IEOz/fwww8TGxvb+Fq4cCGXXHJJkzaXXXZZr6WYSEOtw75kwoQJZv369b09DKWUUkqpXrFjxw5GjhzZ28PoU1q7pyKywRgzwZnjdaa7F9Rb+94XHaWUUkop1TYNuk+w9OxiJj2yhN+9s4maOmtvD0cppZRSSp0AGnSfQHvzy7juxbXUWQ3vbzzM9S+tpbiytreHpZRSSimlXEyD7hPkcFEl17ywBoD3f3kG/7gqjfUHjnL5v1dzuKiyl0enlFJKKaVcSYPuEyC/tJprXlhDaXUdr908iXhLABePjeHVmyZxpKSKS55ZxbbDxV3uf0dOCRMe/po/vL+V3JKqNtvtLyjngQ+38f7GrC6fSymllFJKdZ4G3S5WXFHLdS+t5UhxFa/cOJGU6ODGfWfEh/PebWfg4SZc+d/veXHlPjYfKqK6rt7p/o0xPPLpDipq6lm04RDTHl/G41/upKTqeNpKRl4pd771IzP+vpzXfzjAy6v29+QlKqWUUkqpDuiKlC5UUFbNL15bT2ZeGS/eMIHxQ0JbtBkeGcgHvzqTX7y2nr8u3g6Ap7swPDKQ0bHB/CRlINOTIto8x4o9BazMKOCBC5KZNTKSv3+9i2eWZfLGmoP8fGoc27NL+GxbDj4e7twyNY780mq+2HYEq9Xg5nbiV2NSSimllOqPdKbbBaxWw5trDjLjieVsPVzMv65OY2qipc32kUE+fPirM1l579n855px/HxqHKH+Xny29Qg3vbKO7zMLWz2u3mqY/9kOBof6ce3pQxgc5sc/541l8a+nMDo2hMe/3MW3u/O5bVo8K+89m/933kgmDQulsrZe88iVUkop5VIBAQFOtXvwwQeJiYkhLS2NESNGcNttt2G12iq83XDDDQwbNoy0tDTS0tL417/+BUBZWRm33XYb8fHxjBs3jvHjx/P8888DYLVaueOOOxg1alTjwjv79u1r8/xDhw4lNTWVtLQ0UlNT+eijj7p55a3Tme4etutIKf/vg61sOHCM04aF8sglqSREdPxLJyLEDvAjdoAfc0ZFAVBeXcfcp1dyx1s/8tkdU7EEejc55r2NWew8UsrTPx2Ll8fx70+jYoJ57aZJ7M4tJSLQmxA/r8Z9ifax7MkrZVCoX09cslJKKaVUt/z2t7/l97//PVarlbPOOotvv/2Ws88+G4DHH3+cyy+/vEn7W265hbi4OPbs2YObmxv5+fm89NJLgG01y+zsbLZs2YKbmxtZWVn4+/u3e/5ly5YRHh7Orl27mD17NhdddFGPX6MG3T1k38G1LPzuE9bvP4a3pxv3nWYhOTqInP3ryNnf9X5vT6vmzbUHeHjBl1w6NrYxJaS23srHq/YxJ8aDoMoMvlvbeqpIbrP3VbX1DPAvY8m+cjwDohq3Dw4azJCgIV0fqFJKKaVOTp/fB0e29myfA1Ph3Ed7tk+gpqaGqqoqBgwY0GabzMxM1q5dy5tvvombm23S0WKxcO+99wKQk5NDVFRU477Y2Finz19SUtLuubtDg+4e8vryZ3nXbAD757qtBCjpoc6jYRewdFez7faMlVU7O9nfYPgkDz755vimMJ8wll25DBHN81ZKKaXUifXkk0+yYMECDhw4wLnnnktaWlrjvrvvvpuHH34YgNdff519+/YxZsyYxqC6uSuvvJIpU6bw3XffMXPmTK655hrGjh3b7vnPPvtsjDHs3buXd955p+cuzIEG3T3kxll3M3r3D8SFO5e/1BnGGN5ef4gfDxbx86lxRAb78NgXO4m3BHDDGUM719nmtyg7uImHgh7i8Stsv9DLDi3jha0vkFuRy0D/gT0+fqWUUkr1IhfMSPe0hvSS2tpaLr/8ct566y3mzZsHtEwvaZ6f/cgjj/Duu++Sl5dHdnY2sbGx7Nq1i6VLl7J06VJmzpzJu+++y8yZM9s8f0N6SWZmJjNnzmT69OlO56Q7S4PuHjIoKoVBUSku6z9xeB0XPr2K/11Vy+T4MLaVDeDvt5zlVL54E6XHYPdSKis8SQ1PRUSwGisvbH2BnUd3atCtlFJKqV7j6enJnDlzWLFiRWPQ3VxycjKbN2/GarXi5ubG/fffz/33398kSPb29ubcc8/l3HPPJTIykg8//LDdoLtBfHw8kZGRbN++nUmTJvXYdYFWLzll+Hl58MxPx1FWXcsnm7OZN3FQ5wNusOVgAXF1e8kuti2kkzggEUHYebSzeSpKKaWUUj3HGMOqVauIj49vs01CQgITJkzgj3/8I/X1trVNqqqqMMYAsHHjRrKzswFbJZMtW7YwZIhzz63l5eWxb98+p9t3hgbdp5CkgYH87bLRjIoJ4s5zhnetk4GjAEiWA+zOLQXA39OfwUGD2XW0edK4UkoppVTXVFRUEBsb2/j6v//7vzbbPvnkk6SlpTFq1Cjq6+v55S9/2W7fL7zwAoWFhY0B+KxZs3jssccAW+A8d+5cRo0axejRo/Hw8OD2229vt7+zzz6btLQ0zj77bB599FEiIyM7f8EdkIZvBX3JhAkTzPr163t7GCet+idH8/nRKHJm/ZufnxUHwF3L72J74XY+v+zzXh6dUkoppbprx44djBw5sreH0ae0dk9FZIMxZoIzx+tMdz/kHpVKqvtB9uSVNm4bETqCrLIsSmtK2zlSKaWUUkp1hT5I2R8NHM2gnZ9y6Eh+46ak0CQAdh/bzfjI8b01MqWUUkr1UQ1VRhxdccUV3H///Sfk/KeddhrV1dVNtr3++uukpqaekPNr0N0fDUzFDYN7/g6MmYmIMCJ0BAA7j+7UoFsppZRSPa6hykhvWbNmTa+dGzS9pH+yVzAZWpfJkRJbBROLr4VQn1B9mFIppZRSygU06O6PgmOp8womWQ6wJ7cMABEhaUCSlg1USimllHIBDbr7IxFMZCrJbsfLBoLtYcqMogxqrbW9ODillFJKqb5Hg+5+yjNmDCPcDrE3t6hxW1JoErXWWvYV72vnSKWUUkop5zzyyCOkpKQwevRo0tLSWLNmDdOnT6d5aeeKigp+9rOfkZqayqhRo5gyZQplZba/xmdlZXHRRReRmJhIXFwct99+e+MDkcuXLyc4OJi0tDRGjhzJQw89dMKv0VkadPdXA1PxoYaynN2NmxoeptS8bqWUUkp11/fff8/ixYvZuHEjW7ZsYcmSJQwaNKjVtv/85z+JjIxk69atbNu2jRdffBFPT0+MMVx66aVcfPHF7Nmzhz179lBZWck999zTeOzUqVPZtGkT69evZ8GCBWzcuPFEXWKnaNDdX9kfpvQtTG9cNnVI0BC83b01r1sppZRS3ZaTk0N4eDje3t4AhIeHEx0d3WbbmJiYxvdJSUl4e3uzdOlSfHx8uPHGGwFwd3fnySef5LXXXmucCW/g7+/P+PHjycjIcNEVdY+WDOyvwodTL54Mq91HXmk1kUE+eLh5kBiSyK6juyitqmXlngLOTY3q7ZEqpZRSqhv+tvZvPT6hNiJ0BPdOurfdNrNnz+Yvf/kLw4cP55xzzuGqq65i2rRprba96aabmD17NosWLWLmzJlcf/31JCYmkp6ezvjxTUsZBwUFMXTo0BbBdWFhIT/88AMPPPBA9y7ORXSmu7/y8KJywHCSZX9jBROw5XXvPLaT+Z/t4LY3NrKvoLzDrmrrrY2z5UoppZRSAAEBAWzYsIHnnnsOi8XCVVddxSuvvNJq27S0NPbu3cvdd9/N0aNHmThxIjt27HDqPN999x1jx45l9uzZ3HfffaSkpPTgVfQcnenux9yjx5BcuJhPckuYkhgOwMjQkby35z3e3bENCCYjr4xh4f5t9lFvNUz92zJumTqMW6bGnaCRK6WUUspZHc1Iu5K7uzvTp09n+vTppKam8uqrr7bZNiAggEsvvZRLL70UNzc3PvvsM8aMGcOiRYuatCspKeHIkSMkJSWxZs0apk6dyuLFi119Kd2mM939mE/sGMKlhCPZBxq3NSwH7+6dA8De/LJWj22QdayCIyVVfL7tiOsGqpRSSqlTzq5du9izZ0/j+02bNjFkyJBW265atYpjx44BUFNTw/bt2xkyZAgzZ86koqKC1157DYD6+nruuusubr/9dnx9fV1/ET1Ig+5+TKJGA2DN2dK4zdsagzHCmPhywgO82JvffnpJRp4tKN90qIiSKq3vrZRSSimbsrIyrr/+epKTkxk9ejTbt2/nwQcfBOD8888nNjaW2NhYrrjiCjIzM5k2bRqpqamMHTuWCRMmcNlllyEifPDBByxatIjExETCwsJwc3Pr1eXku0rTS/qzSFvOU8CxnRhjEBGe+/Yw1IYRFlOAsQSQ2cFMd0PQXW81/JBZyOyUgS4ftlJKKaVOfuPHj2f16tUtti9fvrzV9tddd12r2wcNGsTHH38MwOrVq7n66qvZuHEj48aNa0xdORXoTHd/5hNMiW8s8fV7KSirISOvlI82HWZIYCL7SvYQb/FnbwcPUmbklRHq74WvpzsrMwpO0MCVUkop1R+dccYZHDhwgHHjxvX2UDpNg+5+riY8hZFygD25pfxjyR58PN35ScI4ssqyiA0TjpbXcKy8ps3jM/LLGB4ZwGlxoazco0G3UkoppVRrNOju53wGpTFMjvDlj5ks3pLDDWcMZexAW9qJl28uAHsLWk8xMcaQkVdGQkQAUxLC2VtQzuGiyhM2dqWUUkqpU4UG3f2c/+A03MSwdeNqAr09+MVZcY3LwVfJIQAy81pPMckvraa0qo7EiECmJloAWKWz3UoppdRJQdfQ6Dk9cS816O7nGiqYJLsd4KYpwwjx8yLcN5xQn1Byq/fi5e5GZhsz3Q0PUSZEBDA8MgBLoDffaV63Ukop1et8fHwoLCzUwLsHGGMoLCzEx8enW/1o9ZL+LiiGCvcgxkoWs6YOA0BEGBE6gt3HdjEk7Jw2ywZm5B8PukWEKQnhfLs7H6vV4OYmTp0+PbuY9zYc5p45Sfh4uvfMNTmos9ZxqPQQe47tobKukgvjL0TEubEppZRSp6rY2FiysrLIz8/v7aH0CT4+PsTGxnarD+mL34AmTJhg1q9f39vDOGXUvzwXCjNwT7mocdv/le1gQcV+JleFU11rJTEioMVxOcVVFFXWMmJgIAIcq6wl+1glcRZ/fJ0IoGvqrewrKKeu3jAo1JcgH8+OB+sTDIEDwS8MpO0/1BRXF5NRlEFmUSY11uMPgi6au6hxASCllFJKqe4QkQ3GmAlOtT3Zg24RiQPuB4KNMZc7c4wG3Z209nlY+ldw+FVY5+XOXQP8qBXA0OrssLEfIBzfZ4wBabqtLU1+95w6xhwfowDiDm4erQbfvm6eJPiEk+gdTqJPON5uHtx9aDGPxp7P+SEjOxxbj/PwhuSLwPPUWj1LKaWUUm3rTNDt0vQSEXkJuADIM8aMctg+B/gn4A68YIx5tK0+jDF7gZtFZJErx9qvTfq57eVgIrACWLQhi9+/u5lv7ppGvKXpbPekR5Zw1nALT1wxpnHb7Ce/JTLIh9dvPq3N09XWW7nplXV8n1nIazdN4qNN2Xy6NYf1fzyn3RSTjNxSoqUQv9z1kLUODq2BnC1g6ju8xBrAfeggMre9CceKO2zvEm4ekOrU90allFJK9TGuzul+BXgaeK1hg4i4A88As4AsYJ2IfIwtAJ/f7PibjDF5Lh6jake8xR+AvfnlTYLukqpa8kqrSWiWdjIlwcIbaw5QVVvfagBtjOGBD7fx3Z4CHrt8NGckhFNTb+Xt9YdYuaeAc5IjWx1HQVk15z+1kulJFv577eXHg9eaCqg81uF1eAGDltxCZvRgOO1PTl59D6kpg2cmQVnuiT2vUkoppU4aLg26jTErRGRos82TgAz7DDYi8hZwkTFmPrZZcXUSibMH2nvzy4DjAXFj5ZJms99TE8N5adU+1u8/xpTE8Bb9/XfFXt5ad4jbz07gygmDADgjPpwgHw8+25bTZtD99rpDVNdZ+TI9l2U78zh7RIRth5ef7eWEhNAR7CnaA8ExTrXvMcbYUmEqCk/seZVSSil10uiNkoExwCGH91n2ba0SkTAR+Q8wVkT+0E67X4jIehFZr0/q9pxgX0/CA7zJzG9aNtCxXKCjScNC8XQXvsto+Rm8s+4Qj36+k7ljovndrOGN27083JiVPJCoBCOpAAAgAElEQVSvt+dSU2dtcVxdvZU3fjjApGGhxFv8+fPH6VTVdpxS0lx8SDyHSg9RXV/d6WO7RcT24KcG3UoppVS/ddLX6TbGFBpjbjXGxNtnw9tq95wxZoIxZoLFYjmRQ+zz4iz+LcoGZuaV4eXhxqDQprPM/t4ejB08oMmS8FW19dz33hbueW8LZyaE8fjlo1uUFDwvdSClVXWsymxZ5/ubnXlkF1dx05nD+OtFozh4tIJnl2e2Od4NB47x8ebsFtvjQ+KxGiv7i/c7c9k9yy9Ug26llFKqH+uNoPswMMjhfax9mzpJxVv8W53pjgv3x72VetxTE8JJzy7haHkNmfllXPzMqsaUkldvnNRqrveUxHACvD34fGtOi32vf3+A6GAfzhkZwRkJ4Vw4Jpr/fJvJvoKW9cO/TD/C1c/9wG/f3tRiNjw+JN429qKMTl1/j/ALg4qOc8+VUkop1Tf1RtC9DkgUkWEi4gXMAz7uhXEoJ8VbAjhWUcux8uP1rjPyy4hvpXY30JjL/fCn25n71ErySqt59aZJ/P4nSXi4t/4r5+3hzjkjI/hqey619cdTTDLyyliZUcBPTxvceOwfzx+Jl7sbf/44vUnZwfc2ZPHLNzbi7+1OvdWwJ7fpF4WhQUNxF3cyi9qeJXcZnelWSiml+jWXBt0ishD4HkgSkSwRudkYUwfcDnwJ7ADeMcaku3IcqnviGiqY2JeDr6qt59DRihYPUTYYHRtCkI8H7288TEp0EJ/eMYVpwztO+Tk3NYqiilp+2Hs8OF3wwwE83YWrJg5u3BYR5MPvZg1nxe58vth2BIBXVu3jrnc3c3pcKAtusZUr3J7TtDSgl7sXgwIH9VLQrTndSimlVH/m6uolV7ex/TPgM1eeW/WcuHBbcJ2ZV874IaHsKyjHalo+RNnA3U24e84IiitquHVafJuz281NG27Bz8udz7YeYWqihfLqOt7bkMV5qVFYAr2btL1u8hDe3ZDFQ59sJz27hKeXZTA7OZJ/XT0WL3c3/L3cSc8uaXGOhJAEWwWTE60h6DbG9mClUkoppfqVk/5BStX7Ygf44uXuRqZ9prutyiWOrj19CLfPSHQ64Abw8XRnxogIvko/Qr3V8MGPhymtruO6yUNatPVwd+Phi1M4UlLF08syuHRcDM/+bBw+nu64uQkjo4LY3krQ3WsVTHxDbYv4VPXSwjxKKaWU6lUadKsOebi7MSTMj8w824OLGXlluAkMC/fv8XOdnxpFYXkNa/YV8vr3B0iJDmLc4AGtth0/JJR754zgt+cM54nLxzQJ8FOig9iRU4LVapoc02sVTPzCbP9WHj2x51VKKaXUSUGDbuWUeEtAY053Rl4Zg0L92l2yvaumJ0Xg6+nO/M92siu3lOsmD0HaSce4bXo8vzknsUUJwuToIMpr6jlwtKLpddgrmJzwvO6GoLtCg26llFKqP9KgWzklzuLPwcIKauutZOSVtfkQZXf5erlz9ggLWw8XE+zryYVjurZ6ZHJUMECLFJOGCiYnvGxgY9CtD1MqpZRS/ZEG3copcZYA6qyG/QXl7Csobzefu7vOHRUFwBXjY/H16tpsemJkAB5ucvJUMPELtf2rQbdSSinVL7m0eonqO+LtZQOX78qnpt7aZo3unjArOZJfTo/nxjOHdbkPH093EiICWn2YMiEkoRdmujXoVkoppfoznelWTomzp5N8td1WF9uVM90+nu7cM2dEizKBnZUcFdRq2cD4kHgOlh48sRVMvIPAzUNzupVSSql+SoNu5ZRgX0/CA7xZf8C2lLkrg+6ekhwdRF5pNfmlTYPrXqlgIqIL5CillFL9mAbdymlxFn+Mgcggb4J8PHt7OB1Kjg4CYEdO09nurlQw+T6zkLX7ujlLrUG3Ukop1W9p0K2c1pDXfSrMcoMtvQRokWLS2QomZdV13PbGBu56dxPGmI4PaItfmKaXKKWUUv2UBt3KafH2vG5XlQvsaSF+XsSE+LK92Ux3QwWTvcV7nepnwQ8HKKqo5dDRSnbllnZ9QL4DdKZbKaWU6qc06FZOizvFZrrBlmKyPbvl0usJIQlOpZdU1tTzwnd7GRMbjAh8lZ7b9cH4hemKlEoppVQ/pUG3ctr4waFMTQxn2vCI3h6K05KjgthbUE5FTV2T7XEhcU5VMFm49iAFZTXcf34y4wYPaKze0iUN6SVWa9f7UEoppdQpSYNu5bRgP09ev/k0Bof59fZQnJYSHYQxsPNI07SQhJCEDiuYVNXW898VmZw2LJRJw0KZnRzJtsMlHC6q7Npg/MLA1EN1y5l3pZRSSvVtGnSrPq2hgknzRXKcqWCyaEMWuSXV/HpGImBbtAdgyfYuppg0LpCjKSZKKaVUf6NBt+rTYkJ8CfLxaLOCSWZx60F3bb2Vfy/PZOzgEM5MCANsCwQlRAR0PcXEz9aPBt1KKaVU/6NBt+rTRMT2MGUbFUzamun+YONhDhdV8usZCYhI4/bZyZH8sPcoxRW1nR+MLgWvlFJK9VsadKs+LyU6mJ05JdTVN32Asa0KJnX1Vp5dnkFKdBBnJzV9aHR2ykDqrYalu7qQYtI4061Bt1JKKdXfaNCt+rzkqCCq66zsLyxvsr2hgklNfU2T7Yu35LC/sKLFLDfA6JhgIoO8u1Y6UINupZRSqt/y6O0BKOVqDQ9TpmeXkBAR2Li9oYLJkgNLiAmMwVgNa/cf5cWV+xka7cZASy6b8/Na9DcusYRvd2eyLscNL49OfG81Bnz8oGgP5G/u9nUFegUSFxzX7X6UUkop5XoadKs+LyEiAC93N7Znl3BRWkzj9hGhIwC497t7mx4QDhXAtV+03ad7LNz0VRcGExUOBcvhs+VdOLilzy/9nNjA2B7pSymllFKuo0G36vM83d0YPjCgycOUxhhqq8K5OOJRPk3fS3FlLUPD/DgvNYoJQ0Nxd5M2+6urN/z6zY1MHBbKTVOGdW4wi38HgQNh2j1dvRzAVurwifVPkFWWpUG3UkopdQrQoFv1C8lRQXy9PZcPfzzMij35rMooILfEthrl1MRJ3HpxPGfEh7XI4W7L9CEBfL+ngMlXnNlugN6CdwRU1UDMlK5cRqPBgYN5Yv0T5Ffkd6sfpZRSSp0YGnSrfmFUTDDvrM/izrc3McDPkzMSwpmaEM6UxHBiB3R+hc3ZyZF8sjmbHw8eY8LQUOcP9AuDvO2dPl9z4b7hAORVtMw5V0oppdTJR4Nu1S9cOi4WdzdhdEwIKdFBuHVmdroV05MseLoLX23P7WTQHdoj1Uv8PP0I8Awgv1JnupVSSqlTgZYMVP1CgLcHPzttCKmxwd0OuAECfTyZHB/Op1tyKKuuc/5AvzCoPAZWa8dtO2Dxs2h6iVJKKXWK0KBbqS76xdQ4jpRUcduCDdTUORlE+4WBsUJVUbfPb/G16Ey3UkopdYrQoFupLpqSGM78S1P5bk8Bdy/ajNVqOj6ocYGco90+v8XPojndSiml1ClCc7qV6oYrJwyioKyax77YRXiAN388f2T7FVB87fnfFYVAQrfOHeEbQUFlAcYYp6uuKKWUUqp3aNCtVDfdNi2evJJqXly5j4hAb/5nWnzbjf3sQXdlz8x0V9dXU1JTQrB3cLf7U0oppZTraNCtVDeJCH+6IJmCsmrmf76TsABvLh/fxoI1jekl3a9gYvG1AJBfka9Bt1JKKXWS05xupXqAm5vw9yvHcGZCGPe+t4UVu9t4wLEng24/W9CdV6l53UoppdTJToNupXqIt4c7/7lmPIkRAfzyjY3sOlLaspGXP7h790jQHeEbAUBBZUG3+1JKKaWUa3UYdIuIn4g8ICLP298nisgFrh+aUqeeQB9PXr5xIv7e7tz48lrySqqaNhDpsQVywv10VUqllFLqVOHMTPfLQDUw2f7+MPCwy0ak1CkuKtiXF6+fSFFlLTe/up6KmmaL5/iFQcWxbp/H18OXQM9AXSBHKaWUOgU4E3THG2MeA2oBjDEVgNYnU6odo2KCeerqsaRnF3PHwk3UO9bwbmem+4ttOSzZnuv0eSx+ukCOUkopdSpwJuiuERFfwACISDy2mW+lVDtmjozkz3NTWLIjl4c/3X58h19Yq0H3ku253PbGRv7wwVbnFtrBviqlznQrpZRSJz1ngu4/A18Ag0TkDeAb4B6XjkqpPuL6M4Zy05nDeHnVfv7+1S6MMa0G3TuPlPCbt34kwMuD/NJq0rNLnOpfZ7qVUkqpU0OHdbqNMV+LyEbgdGxpJb8xxmi5BKWcdP/5IymvruOppRnklVQzf8AA3CqPgbUe3NwpKKvm5lfWE+Djwcs3TOL8p77jm525pMZ2XHu7YSl4XZVSKaWUOrk5U73kLCAFKAVKgGT7NqWUE9zdhEcvS+WOGQm8vf4Qb6VXAAaqiqmuq+d/Xt9AYXk1z183geToINIGhbBsp3MVSSy+FmqttZTUODczrpRSSqne4cyKlHc7/OwDTAI2ADNcMiKl+iAR4Xezk4gM9mHtx6v4qScUFR7hL98fZMOBYzzz03GMjg0BYOaICJ74ajd5pVVEBPq022/jAjkVeQR7B+uMt1JKKXWS6nCm2xgz1+E1CxgFdL/emVL90M9OG8K1M8YBcOdLS3h/42F+e85wzh8d1dhmxohIAJbv7DhXu2GBnPyKfLKOVTB5/lIWrj3ogpErpZRSqju6siJlFjCypweiVH8xfmQ8AAOklIvTorljZkKT/SOjAokK9mGpEykmFl/bTHd+ZT6v/3CAIyVV/OmjbWw4cLTnB+6gqrbe9lCoUkoppZzSYXqJiDyFvVwgtiA9DdjoykEp1af5hQHw2HmxeIxPa5EOIiKcPSKCj348THVdPd4e7m121bAqZXZZLm+v82VqYjgHj1Zw24KNLP71FCKC2k9P6YrDRZWc8/dvOT0ulIcvSSUmxLfHz6GUUkr1Nc7MdK/HlsO9AfgeuNcYc41LR6VUX2YPuj2rjrWZfz0jKYLymnrW7Ws/k8vXw5dAr0DWHdxPUUUtv5yewH+uGU9pVR2/fGMjNXXWHh/+J5uzqayt54e9R5n1f9/y8qp9TRf/UUoppVQLzuR0v+rwesMYs+pEDEypPsvTDzx82lyVEuDMhHC8Pdz4ZmfHq1NG+EawLfcQSZGBnB4XysioIB69LJX1B47xv5/t6MmRA7agO21QCF//7iwmDQvloU+2c9m/V7PziFZQUUoppdrSZtAtIltFZEsrr60isuVEDlKpPkXEvkBO23nXvl7unBEfxtKdeR3mTntLCGV1R7nujCGNM+cXpcVw85RhvLJ6P+9vzOqxoe/NLyM9u4QLRkcRO8CPl2+YyD/npXHwaAUX/Gsln23N6bFzKaWUUn1JezndF5ywUSjV3/iGtjvTDTBjRATLPkpnb0E58ZaANtsVlvjg7lnKxWkxTbbfd+4Ith0u5g/vb2WAnxfThltwc+teOcHFW2xBdUO1FRHhorQYzkq0cOEzK1m0IYvzUqPa60IppZTql9qc6TbGHGjvdSIHqVSf4xcKle1XGDl7hK0c4NIdbVcxySupIivfEzfPUvy8mj5w6enuxtM/HYcl0JsbX1nHWY8v48mvd3PoaEWXh714SzaThoYSFdz04ckB/l5MHBJKenZxl/tWSiml+jJnVqQ8XUTWiUiZiNSISL2IaPKmUt3hF9bhTHfsAD+SIgPbLR345tqD1NcGYKWO4uqWAa8l0JuvfzuNf85LY2iYP/9auoepjy3j6ud+YHVmQaeGvOtIKbtzy7hgTOsz2SkxweSWVJNXWtWpfpVSSqn+wJnqJU8DVwN7AF/gFuAZVw5KqT7PiaAbYMbICNbtP0pJVW2LfTV1Vt5Yc5DkiFgA8ipbD859vdy5KC2GBbecxsp7Z3DXrOEcKCzn1tc3UFzZst+2LN6SjZvAuaPaCLqjgwBIz9bv5EoppVRzTi2OY4zJANyNMfXGmJeBOa4dllJ9nF8YVBZBfV27zWaMiKDOavhud8tZ6S/Sj5BfWs2Fo2xrVeVXdLyCZUyIL7+emcjz10+gpKqOF77b69RwjTEs3pLD5PgwLIHerbZJtgfd2zXoVkoppVpwJuiuEBEvYJOIPCYiv3XyOKVUW/xCAQNVRe02GzsohBA/z1ZLB762ej9DwvyYNTwRgLyKjlewbJASHcz5o6N4aeU+CsuqO2yfnl3CvoJyLhgd3WabIB9PhoT5se2w5nUrpZRSzXW4IiVwLbYg+3bgt8Ag4DJXDkqpPs++QA4VR8E/vM1mHu5uTB9u4f2Nh/li2xH8vT0I8PbAz8ud9OwS/nj+SCL8bUvBF1R2Lkf7t+cM5/OtOfx7eSZ/vCC53bafbMnGw02YkzKw3XajooPZqkG3Ukop1YIzQfd44FNjTAnwkIvHo1T/4Bdq+9eJvO67ZicxLDyAsupayqrrKKuup7y6jpgQX66cOAgfD0+CvII6NdMNkBARwKXjYnnthwPcMjWOgcGtLxlvjGHx5hymJIYzwN+r3T6To4P4dGsOxZW1BPt6dmo8SimlVF/mTNA9F3hSRFYAbwNfGGPaT0RVSrWvcaa746B7UKgfvzknsd02Fl8L+ZUd53Q395uZiXy06TBPLd3DI5ekttrmx0NFHC6q5LezhnfY36iYYMCW1z05PqzT41FKKaX6KmeWgb8RSADexVbFJFNEXnD1wJTq03ydn+l2hsWva0H3oFA/5k0czNvrDnGwsPX63Ys35+Dl7sbslMgO+ztewURTTJRSSilHzsx0Y4ypFZHPAYOtbODF2EoHKqW6omGmu/gQlHUuLaQ1EZ6BrCve26W+7jgtiG/WF/PClz/wlwtHNdlntRqWbclkWlIUQT4dp4uEB3gzMMhHywYqpZRSzXQYdIvIucBVwHRgOfACcKVLR6VUX+flB16BsOJx26ubLAOCyQ8OwjyRSGcXercAqz2A3cATTfe5AV8ad75N+NLp/lKig7SCiVJKKdWMMzPd12HL5f4fY0zHtcWUUs65eiEU7OqRriyFm6jL/ZainzzMAA/fjg9opry6nv/7ejdBvh5YDY1lBIf5lHNz/TtMDzgITHSqr5SYYJbtyqOyph7fZkvTK6WUUv1Vh0G3MebqEzEQpfqdYVNtrx5g2f8V5H5LXtJsBoQmdfp4f8BSn8nTSzOYNCyUqYnhTE20EB/iBvMX4Vno/JeDlOggrAZ2HClh3OABnR6LUkop1Rc5ldOtlDq5RfhFAJBfmU8SnQ+6AW6dFs+t0+Jb7giNg7ztTvfjuBx8bwbdxhiq66z4eOpsu1JKqd6nK0sq1QeE+9oW2HFmKfhOixgJeTudbh4T4kuInyfpvZzX/ezyTEY/9BXzP99BSVVtr45FKaWUciroFhFfEena9JlSyuUsfrZVKbtSNrBDEclwNBNqq5xqLiKkRAe1WcGkqraeXUdKe3KErZ7jpZX7CPb15L/f7mX648t5dfV+auutLj2vUkop1ZYOg24RmQtsAr6wv08TkY9dPTCllPO83b0J9g7u9KqUTokYCcYKBbudPmRUdDC7jpS2GuT+4f2t/OQfK7hj4Y/klToXyHfWx5uzKSyv4R9XpbH411MYHhnAnz9O5ydPrmDJ9lyXnFMppZRqjzMz3Q8Ck4AiAGPMJmCYC8eklOoCi6/FReklybZ/83Y4fUhydBA19Vb25JY12b41q5gPfjzM+CED+GLbEWb+/Vte+34/9VbTY8M1xvDyqv0kRQZyRnwYo2KCWfjz03nhugkgcMtr61mzt2cWJVJKKaWc5UzQXWuMaZ6c2XP/D6mU6hEWXwsFlQU933FoHLh5duphyobl4Lc5rExpjOGRz7YT5u/FKzdO5Is7pzI6Npg/fZTOJc+uYmtWz+SAr9l3lB05Jdx45lBEbFXLRYRzkiP59NdTCfLx4I01B3vkXEoppZSznAm600Xkp4C7iCSKyFPAahePSynVSRY/C3mVLkgvcfeE8OGdmukeFuaPn5c72x3yur/ZkccPe49y5zmJBPp4EmcJYMHNp/HPeWlkF1Vx0TMreW5FJsZ07zv9Syv3McDPk4vHxrTY5+vlziVjY/hi2xGOldd06zxKKaVUZzgTdP8aSAGqgTeBYuBOVw5KKdV5Fl8LBRUFWI0LHhaMGNmpoNvNTUiOOr4yZV29lfmf7yDO4s+8SYMb24kIF6XF8M1d0/hJykD+97Od3Pn2Jipr6rs0zENHK/h6Ry5XTxrcZqnAeZMGU1Nv5f0fD3fpHEoppVRXdBh0G2MqjDH3G2Mm2l9/NMa45umnVojISBH5j4gsEpHbTtR5lTrVWPws1Jk6jlUd6/nOI0ZC8UGodr7qSEp0ENtzSrBaDW+tO0Rmfjn3zRmBp3vL/9kJ9vXk2Z+N4+6fJPHx5mwu/89qso5VdHqYr67ej7sI104e0mabkVFBjBkUwltrD3Z7Vl0ppZRyljPVS74WkRCH9wNE5EtnOheRl0QkT0S2Nds+R0R2iUiGiNzXXh/GmB3GmFuBK4EznTmvUv1RwwI5LsnrbniYMr8TK1PGBFNRU8+27GL+sWQ3k4aFMis5ss32IsKvzk7gxesncLCwggufXsX3mc4/8FheXcfb6w9xbmoUUcG+7ba9euIg9uSVsfGgC76gKKWUUq1wZkXKcGNMUcMbY8wxEYlwsv9XgKeB1xo2iIg78AwwC8gC1tlLELoD85sdf5MxJk9ELgRuA1538rxK9TsWX1ut7g8zPiQuJK5nO68sgEB/2LkQKvY5dUiOtRLPkAx++fFmij2qmDwmgUV7stpsH+AZwJyhc5gxIpIPbz+TX7y2nmteXMO8iYO4ecow4iwB7Z7vvY1ZlFbVceOZQzsc29wx0fx18XYWrj3E+CGhTl2PUkop1R3OBN1WERlsjDkIICJDcLJ6iTFmhYgMbbZ5EpBhjNlr7+8t4CJjzHzggjb6+Rj4WEQ+xZZXrpRqZnDQYLzcvFiwY4FrThAeBoe/sr2c5BNlewjExx9ecmKS3OJrYcLACcRbAvjwV2fyv5/t5N31Wby59iDnjIzkF2fFMWHIgMaqJA2sVluZwDGDQpxaet7f24ML06L54MfD/GluMkE+nk5fk1JKKdUVzgTd9wMrReRbQICpwC+6cc4Y4JDD+yzgtLYai8h04FLAG/isnXa/aBjX4MGD22qmVJ8V6hPKt1d9S0Vd53OhnbLgcvAOhCtedvqQ615aw968ct65dTLRIW2nfJTXlnPhhxeyMW8jEwZOACDQx5P5l6by21mJvP79AV7/4QBfb89lzKAQpg23EOrnyQB/L0L9vTh0tJJ9BeX8c16a02ObN3EwC9ce4qNN2Vx7ets54EoppVRP6DDoNsZ8ISLjgNPtm+40xrggabTN8y8HljvR7jngOYAJEybo01GqXwrwCiDAq/00jC6LGAUZS8DP2ewy+H+zT6e0qo606KgO2yaEJLAxb2PL0wb6cNfsJG6bHs97G7J4efV+/vXNnhbtIoO8OS+14/M0GB0bzMioIN5ae1CDbqWUUi7nzEw32GaZj9rbJ4sIxpgVXTznYWCQw/tY+zal1MksYiRsegPKC8E/zKlDzhpucbr7sRFj+WLfF9Rb63F3a1nuz8/Lg2snD+XayUOpq7dSXFnLsYoajpbXcrS8moSIgFYro7RFRLh60iD+9FE6W7OKSY0NdvpYpZRSqrOcqV7yN2AVtjSTu+2v33fjnOuARBEZJiJewDzg4270p5Q6ESJG2v7Nd75ed2eMjRhLaW0pGUUZHbb1cHcjLMCbhIhAJg0LZc6oKBIiAjt9zovSYvDxdGPhOl2hUimllGs5My10MZBkjDnfGDPX/rrQmc5FZCHwPZAkIlkicrMxpg64HfgS2AG8Y4xJ7+oFKKVOkIaygZ1YJKczxkWOA+DHvB9d0n9rgn09OS81io83ZVNeXXfCzquUUqr/cSbo3gt06dF+Y8zVxpgoY4ynMSbWGPOifftnxpjhxph4Y8wjXelbKXWCBUaBT7DLgu5o/2gi/CJazet2pasnDaasuo5PNmef0PMqpZTqX5zJ6a4ANonIN9iWggfAGHOHy0allDr5iNhmu10UdIsIYyPGntCZboAJQwaQFBnIq98f4KqJg1qUI3RUXFnLoaMVhAd4Exbg1akccqWUUv2bM0H3x2jOtVIKbHnd294HY2xBeA8bGzGWL/d/SU5ZDlEBzlci6Q4R4YYzh/KH97eydt9RTotr/SFRYwy3vLqOdfuPr2IZ4udJeIA3A4N8iLf4Ex8RQIIlgISIACyB3u0G8A19llXXEeDt0WFbpZRSpzZnSga+KiK+wGBjjPNrQCul+h7LSKgqgtIjENTzQfG4CFte98a8jZwfcH6P99+Wi9NiePTznbz6/f42g+6VGQWs23/MvjqmPwWlNRSUVVNQVk12USXvbTxMmUNeeIC3BwP8PQnx9SLY15NgX08CfTwoqaolr6Sa3NIq8kqqqa6zcvOUYTxwQfIJulqllFK9ocOgW0TmAk8AXsAwEUkD/uLsw5RKqT6koYJJ3naXBN2JAxLx9/Tnx7wfOT/uxAXdvl7uzJs4iBdW7uNwUSUxzRbyMcbw5Ne7iQ724Z45SXh7tCxpaIwht6SajLwyMvJK2V9YQVFFDcWVtRRV1pJdXElpVR2BPh5EBvowfvAAIoJ8WLE7n+W78jToVkqpPs6Z9JIHsS3dvhzAGLNJROJcOCal1MmqMejeAQkze7x7DzcPxljGnPCHKQGuOX0Iz3+3lwU/HODeOSOa7Fuxp4CNB4t4+OJRrQbcYEtTGRjsw8BgH6Ykhjt93hA/Tx77YhdHy2sI9ffq1jUopZQ6eTnzFFCtMaa42TarKwajlDrJ+YeDf4TLHqYEW153xrEMSmpKXHaO1gwK9WNWciRvrT1IVW194/aGWe6YEF+unDConR66ZsKQUAA2HDjWQUullFKnMmeC7nQR+SngLiKJIvIUsNrF41JKnawiRrpsgRywBd0Gw+a8zSLOjxEAACAASURBVC47R1uuP2Moxypq+XjT8fKBy3fns+lQEb86OwEvj56vVjI6NhhPd2H9gaM93rdSSqmThzP/D/JrIAVbucA3gWLgTlcOSil1EotIhrydYHXNH7xSw1NxF/cTXjoQYHJcGEmRgby8ej/GGIwx/GPJHmJCfLl8fKxLzunj6U5qTDDr9+tMt1JK9WXtBt0i4o7tocn7jTET7a8/GmOqTtD4lFInm4iRUFsOxa5ZOt3P04+RoSN7Ja+7oXzgjpwS1u0/xvJd+Ww+VMT/Z+/O4+Ouq/2Pvz6zZbLvW9t0S5e00FJKWyhrW0BZlQsqCirifkVEvXq9Xq/LXbzqvf7UqwJXENR7ZVEErmwiS1u2AqUblLZJ23RP0yZpmn2f+fz+mJk0bZPJJJmZLPN+Ph7fx3S+8535nmhJT07O53xuXxWbKnfIkuk5bD3UeFJbi4iITCxhF1Jaa33GmAvjFYyIjAOhxZR/+iQkZ8fkFmf7a/ijbaTrf/8GjxlBsps7G674wZBmiofGB/7mtcAkk5KcZG6IUZU7ZMm0bO55eQ/vVjWyZHpOTO8lIiKjI5LpJZuNMU8AjwCtoZPW2sdiFpWIjF1FC2HOFdBaC+2xaYlYbPz8r9uyvbOORdY9vA9pPgq7X4DLvgvu5MGvDwqND/zVy3sA+I8bFsZ858lzpgV+eHlr33El3SIiE1QkSbcXOAas6nPOAkq6RRKR2ws3/SGmt1jUXgd/XMnm8z7JojNvHd6HrL8XnvkadDQNKemGE+MDp2Sn8DeLJw/v/kOQm5bEzLxUNu6vB0pjfj8REYm/SHakHOa/eCIiw5OXnMe0jGlsqtnErQzzW5A3K/DY0QjphUN6a0lOCj+4fgEz89NiXuUOWTI9m+e3H8Xvtzgc2hJeRGSiGfRfE2PMHGPMi8aYd4PPFxpj/in2oYlIIluUv4gtNVuw1g7vA7yZgcfO4c37vnHpVJbGsdVjybQcjrd1s6euJW73FBGR+ImkveRe4OvArwCste8YYx4E/i2WgYlIYltcuJg/V/6Z16tfZ1LqpKF/gL8NXC44vhPSI98hMlpS3ankp+RHfP050wN93Rv2HWdWQXqswhIRkVESSdKdYq1db05e/d8To3hERAA4p/AcAD73/OeG/yElk2DTDyD+0wcBeOK6J5iROSOia2fmpZKT6uGtfcf58LKpMY5MRETiLZKku84YU0pg8STGmA8A1TGNSkQS3rSMadxz+T3Udwxzp8a24/CXr8PZH4OZl0Q3uEFUNlRy79Z7qWuvizjpNsZwzrTs4GJKERGZaCJJum8D7gHKjDFVwF7g5phGJSICLJ+0fPhv7myBP90G3kkw8+roBRWBTUc3ce/We+n2dw/pfUuDiylrmzvJT0+KUXQiIjIaBlxIaYy5I/jHYmvtZUA+UGatvdBauz8u0YmIDJcnFYxz2AspR8LtCMwW7/EPrRPvnGmBhZuRVrs7un1sOjD8WentXT4a24f2g4GIiAxPuOkloTldvwCw1rZaa5tjH5KISBQYA96MwMjAOHM7A0l3l69rSO87c3IGHpeDDfvCJ9I9Pj9/eOsAq368luvvWsdb+4bXkvLPT27jpnvfGNZ7RURkaMK1l+wwxuwCJhlj3ulz3gDWWrswtqGJiIyQNzOwOU6ceRwegCG3lyS5nCyaksWG/f0n3X6/5emt1fz0+Z3sqWvljEkZHG7s4J1DjcMab1hxtJlth5to7ugm3TvMnT9FRCQiAybd1tqPGGOKgL8C74tfSCIiUZI0SpXuYHvJUJNuCIwOvPflPbR3+Uj2OHvPv7yzlh/+pZzt1U3MLUznno+dw+XzC1n6/ReoODK8HyyqGzoA2FHdzLIZ2n5eRCSWwi6ktNYeAc4yxiQDU621FfEJS0QkCryZ46q9BGDJtGzu9lvePtTAeTNz2V3TzL89vYO1FbWU5CTzsxsXce1Zk3AGd62cW5ROxZGhd/51+/wcbQ4k3VurGpV0i4jE2KDTS4wx1wI/BjzADGPMIuBfrLWqfovI2ObNhPo9cb/tiCrd0wKb5Dy//SjPbK3mgTcPkOJ28o9XlXHL+dNJcjlPun5uYQYPrt+Pz297E/FIHGnsILTZ57aq+P9gIiKSaCIZGfg9YBmwFsBau8UYE9ngWRGR0TQOK91ZKR5mF6Rx36t7cToMNy2bypcvm01uWv8jBMuK0+no9nOgvo0ZeakR36e6MVDlTvU4efewkm4RkViLJOnuttY2nrIjpY1RPCIi0ZOUMa4WUoZ84oLprNt9jC9fNpvZheG3hC8rCrxeXt00pKT7cEM7ACvKCvjL1urTeshFRCS6wo0MDNlmjLkJcBpjZhtjfgGsi3FcIiIj582Ermbw++J625G0lwDcfO407rx58aAJN8DsgnQcBsqH2NddFUy63zO/EL+F7dXx/+FERCSRRJJ03w6cAXQCDwKNwJdjGZSISFR4MwOPcd4gx+lw4jAOun2x33gm2eNkem7qkBdTHm5oJyvF3buAcptaTEREYipse4kxxklg0eTXgG/FJyQRkSjxZgQeOxohOTuut/Y4PMOudA/V3KJ0dgyxUl3d2MGkzGSKMrzkpnp4V4spRURiKmyl21rrAy6MUywiItEVqnSP0qzueCXdZUUZ7K9vo60r8m3nDze0MykrGWMMZ0zO5N0qtZeIiMRSJO0lm40xTxhjPmaMuT50xDwyEZGRSgpVuuOfULqd7mFNLxmOuUXpWAs7j7ZE/J6qhnYmZXkBWDA5g51Hm+nojm/vu4hIIokk6fYCx4BVwLXB45pYBiUiEhUJUumeVxxYcBnpzpTNHd00d/QwKSsZgDMnZdLjt+w8OvRNdkREJDKDjgy01t4aj0BERKIu1NMd54WUEEi641XpLslOIcXjjHiCSWhGd2/SPTnww8m7VU0snJIVmyBFRBJcJJVuEZHxyRtMIEeh0u1xxm8hpcNhmF2YTnl1ZEl3aFzg5GB7yZTsZDK8LrZqMaWISMwo6RaRiWs0e7rj2F4CMK8onfIjTVg7+N5loY1xijMDlW5jDGdOztTYQBGRGFLSLSITl9MF7tTRq3THYU53yNyidI63dVPb3DnotdUNHTgdhoL0E1vLL5icSXl1M90+fyzDFBFJWIP2dBtjkoAbgOl9r7fW/kvswhIRiRJv5oRfSAmBpBsCO1MWZHjDXnu4oZ2iDC8u54m6yxmTM+ny+dl1tIX5kzJiGquISCKKpNL9Z+D9QA/Q2ucQERn7vBnQOfGT7rKiQKIcyc6UVQ3tFGeenJifGUy0tUmOiEhsDFrpBqZYa6+IeSQiIrEwWpVup5uW7sjnZo9UTqqHgvQkdkQwNrC6sYNFJSdPKZmem0pakot3DzfyIUpiFaaISMKKpNK9zhizIOaRiIjEQlJGQiykBCgrzhi00u33W6ob23vHBYY4HIb5kzJU6RYRiZFIku4LgY3GmApjzDvGmK3GmHdiHZiISFSMYk93vOZ0h5QVpbOrpoWeMIsh61o66fbZ3nGBfZ05KZPt1U1h3y8iIsMTSXvJlTGPQkQkVryZo7I5TjzndIfMLUynq8fPvmOtzCpI7/eaw8GNcULjAvs6c3IGHd1+9tS1Mqew//eLiMjwDFrpttbuB7I4sQV8VvCciMjY580IVLojmF8dTaPTXnJigslAQjO6T20vgb47U6rFREQk2gZNuo0xdwAPAAXB4/fGmNtjHZiISFR4M8HfA91tcb1tvOd0A8wqSMPpMGF3pjzcuxvl6Ul3aX4aXreDd6vi/5sBEZGJLpL2kk8B51prWwGMMT8CXgd+EcvARESiou+ulJ7UuN12NCrdSS4nM/JSw1a6qxraSfE4yUg+/du/02GYX6zFlCIisRDJQkoD+Po89wXPiYiMfd5Ay0S8F1OORtINgcWU5WHGBlY3dDApKxlj+v82HtoOXjtTiohEVyRJ92+AN40x3zPGfA94A7gvplGJiERLKOmO82JKtzMwvcTGuZe8rCidQ8fbaens6ff1w/2MC+xrZVkBrV0+HnhjbCzd8fkttz2wiTf3HBvtUERERiSShZQ/AW4F6oPHrdban8U6MBGRqBjFSrfF4rO+wS+OosF2pjzc0N7vuMCQFXPyuWh2Hj95fif1rfEdedifQ8fbeHprNc9srR7tUERERmTApNsYkxF8zAH2Ab8PHvuD50RExr5RTLqBuM/qnlsUmGCy7fDpX29Ht4+6lq5+xwWGGGP49jXzae3y8dPnd8Yszkjtrgns6llxdPDt7UVExrJwle4Hg48bgQ19jtBzEZGxr3chZXyTbo/TAxD3vu4p2clMzUnh+e1HT3vtSHBGd7j2EoA5hel87LxpPPDm/rD94fFQWRtMuo80x71VR0QkmgZMuq211wQfZ1hrZ/Y5ZlhrZ8YvRBGRERjlSne8k25jDFcvLGZd5TGOn9IecmJG98DtJSFfvmw2Gclu/uXJ7aOa7IYq3cfbuqlrGf12FxGR4YpkTveLkZwTERmT3MngcMV9IWVvpTvOs7oBrl5QjM9v+eu2Iyedrwol3WHaS0KyUjx89fI5rKs8xnP9VM3jpbK2lSRX4J+qnWoxEZFxLFxPtzfYu51njMk2xuQEj+nA5HgFKCIyIsYEqt0JUukGOGNSBtNyU3j6lMWH1cH2kqLMwSvdADctm8qcwjS+//QOOrrjuyAUwFrL7poWVs4tAAZeHCoiMh6Eq3R/jkD/dhmwKfjnjcCfgV/GPjQRkSjxZgY2x4mj0Uy6jTFcteD0FpPDDe3kpSXhdTsj+hyX08F3rz2DA/Vt3P/a3liFO6BjrV00tnezbEYOuakeVbpFZFwL19P9X9baGcDXgn3coeMsa62SbhEZP5Iy4l/pdo7O9JKQ/lpMqgYZF9ifC2bl8Z75hfxy9W5qmzujHWZYoX7uWQVpzClM1wQTERnXItkcp9EY8/FTj5hHJiISLd7M+G+OM4qVbui/xaS6sSPsuMCBfPU9c2jr8vHijvj2docml5QWpDG3KJ2dmmAiIuNYJEn30j7HRcD3gPfFMCYRkejyxr/SHVpIOVqV7r4tJvWtgZ0xDzeE341yIHML0ynMSOLV3XUxiHRgu2taSPE4Kc7wMqcwndYuX+9iUBGR8SaSHSlv73N8BlgMpMU+NBGRKEmwhZQhoRaT57YdobG9m7YuX0TjAk9ljOGCWXmsqzyG3x+/SnNlbSsz81NxOAxziwL/7KivW0TGq0gq3adqBWZEOxARkZhJSqyFlCF9W0wON0S2Mc5ALpyVR31rFzviuFlOZU0Ls/IDyfbswsBOmxVHWuJ2fxGRaIpkTveTxpgngsdTQAXweOxDExGJEm8mdLdCHGdmj+ac7pC+LSbvBreFH27SfcGsPABei1OLSVtXD1UN7ZQGk+4Mr5tJmV5VukVk3HJFcM2P+/y5B9hvrT0Uo3hERKIvtCtlZzOk5MTllmOh0g2BFpO711by29f2AZHtRtmfwgwvswvSeHX3MT57cWkUI+zfntpWILCIMmROUbpmdYvIuBVJT/dLfY7XlHCLyLjjzQg8djTE7ZahpLvLP7pbl4daTLZXN+FxOshLTRr2Z10wK4+39tbT2TPyjXJ2Hm3m+09vxzdAj3hocsmsPkn33MJ0dte20OPzj/j+IiLxFm5HymZjTFM/R7MxJr7NkSIiIxGqdMexr3sstJdAoMXk6gXFQGAnSofDDPuzLpiVR3u3j80HRv7Dy/2v7uXeV/ay5WD/n1VZ04LDwLTclN5zcwrT6erxs7++bcT3FxGJt3Cb46RbazP6OdKttRnxDFJEZESSQpXu+E0wcTkC3Xuj3V4CcFUw6R5ua0nIuTNzcDrMiPu6rbWsqagBYE15Tb/X7K5tYVpuKkmuE7tnzi0KLaZUi4mIjD8RTS8xxpxljPli8FgY66BERKKqt9Idv6R7tOd093XGpIzgkTmiz8nwujlrSuaI53Vvr27iaFMnLodh9QBJd2VNK6X5qSedm1WQhjFKukVkfIpkeskdwANAQfB4wBhze6wDExGJmlBPdxx3pRwrCykh0GLy+Bcu4FtXzRvxZ104K4+3DzbQ1DH8rytU3b7l/Olsr27iSGPHSa/3+PzsrWs9aRElgNftZHpuqiaYiMi4FEml+1PAudba71hrvwOcB3wmtmGJiETRKFS6x1LSDeBxOUbUzx1ywaw8/BbeqDw27M9YXV7DwimZfGhJCQBrK06udh863k6Xz987LrCvOYVpVCjpFpFxKJKk2wB9l6r7gudERMaH3p7u+FW6XQ4XDuMYE+0l0XT21GyS3U7WDTPprm/tYvPBBlbMLWBOYRqTs5JPazHZXROYXNJf0j23MJ19da10dI98goqISDxFMqf7N8CbxpjHCSTb7wfui2lUIiLR5HCCJ31UtoLv8ffE9Z6x5nE5WDYjZ9h93S/vrMVaWFVWgDGGFXPzeXxzFZ09vt5Fk73jAvurdBel47eBa0baoy4iEk+RzOn+CXArUA8cA2611v4s1oGJiESVNzOuPd0AHodn1Od0x8KFs/LYXdNyWi92JFaX15CX5mHh5EDCvKqsgLYuH+v31vdes7umhby0JDJT3Ke9f25wO3j1dYvIeBPJQspSYJu19ufAVuAiY0xWzCM7cf8VxphXjDH/bYxZEa/7isgE482If6Xb6R71Od2xMNwt4X1+y0s7a7lkTkFvf/n5pXkkuRwntZhU1rYwqyC138+YnpeK22moONIyzOhFREZHJD3djwI+Y8ws4L+BEuDBSD7cGHO/MabGGPPuKeevMMZUGGN2G2P+YZCPsUAL4AW0G6aIDI83M+5Jt8vhGjMLKaOprCid3FTPkJPuzQeO09jezcqy/N5zyR4ny0tzeyeaWGvZXdPSbz83gNvpoDQ/TZVuERl3Ikm6/dbaHuB64JfW2q8DxRF+/m+BK/qeMMY4gTuBK4H5wEeMMfONMQuMMU+dchQAr1hrrwS+AfxzhPcVETlZUvwr3RO1vcThMJw/K49Xd9dhbf/buPdndXkNTofhotn5J51fVVbAvmNt7K1rpa6li6aOnpO2fz/VnMJ0zeoWkXEnkqS72xjzEeDjwFPBc6c32vXDWvsygV7wvpYBu621e6y1XcDDwPuttVuttdecctRYa/3B9x0HkiK5r4jIaUah0j1R20sALijNpaa5s3fSSCRWl9ewZFo2mckn/xOycm5B7+uhRZQDVbohsDNlVUM7zSOYFS4iEm+RJN23AsuB71tr9xpjZgD/O4J7TgYO9nl+KHiuX8aY640xvwre85dhrvusMWaDMWZDbW3tCMITkQlpFBZSuh3uCdleAif6up/fcTSi66sb2yk/0szKsoLTXivJSWFWQRprymtOjAscpNINsGsICb+IyGiLZHrJdmvtl6y1DwWf77XW/ij2ofXe/zFr7eestTdaa9eGue4ea+0Sa+2S/Pz8gS4TkUTlzQjM6R5CO8RITdT2EggkyhfOyuP+V/fR3jX4zOw15YFiyKp+ku7Q+Tf3HuOdQw2keJwUZ3gH/KzeCSZqMRGRcSSSSne0VRFYjBkyJXhORCR2vJlgfdDVGrdbup1uenwTa053X1+6dDZ1LZ08uP7AoNeuLq9hclYysweoYK+cW0C3z/LE24eZmZ8advfMKdnJJLudbDsc399ciIiMxGgk3W8Bs40xM4wxHuDDwBOjEIeIJJLeXSnj19c9kSvdAMtm5LB8Zi7//VJl2B0iO3t8vLa7rndDnP4smZ5NutdFR7e/301x+nI4DBfNzuOBN/fz6EYNtRKR8SGmSbcx5iHgdWCuMeaQMeZTwUkoXwT+CuwA/mit3RbLOERE8AZ3L4xj0u1yuibsQsqQL106m9rmTh4OU+1+c0897d2+k0YFnsrtdHBxcKpJuEWUIT+9cRHLS3P5u0fe5n9e3zfUsEVE4i6SzXGWGGMeN8ZsMsa8Y4zZaox5J5IPt9Z+xFpbbK11W2unWGvvC55/xlo7x1pbaq39/ki/CBGRQXmDle44LqacyAspQ5aX5rJsRg53D1DtttbyyMZDJLkcLJ+ZF/azQosswy2iDElNcnHfLUu5bF4h3/nzNu5cs3tI4wtFROLNFcE1DwBfJ7AbpX+Qa0VExiZvcCNdtZdE3R2XzubmX7/JIxsO8rHl03vPW2v5/tM7ePLtw9y2spRkjzPs51y9oJgjje29IwQH43U7ufuji/naI2/zn3+toKmjm3+4ooxun2V7dROb9h9n88EGWjt7uPOmxYPe/2B9G4UZXjyu0ei8FJGJLpKku9Zaq55rERnfettL4ljpnsBzuvs6vzSXJdOyuWttJR9aWkKSy4m1lh89W8GvX93LJ86fztfeM3fQz0n2OPniqtlDurfb6eCnH1pEWpKLX720hxe2H+Xg8Xa6egI1ooL0JGqaO/njhoPccv70AT/nwLE2LvvJS3x8+TT+6Zr5Q4pBRCQSkfw4/11jzK+NMR8Jzsy+3hhzfcwjExGJpt6FlA1xu2UitJcAGGP40qWzqW7s4JENgYWNP31hF//9UiU3nzuV7147f8AFlNHgcBj+7boz+bvL55CXlsQty6dx982LeeObl/LmP17KOdOyueflPXT7Bv5l7Z1rdtPl8/PAmweob534v50QkfiLpNJ9K1BGYBfK0HcsCzwWq6BERKIuVOmOY0+3x+FJiKQb4KLZeSwqyeLutZXUNnfy8xd38aElU/jX958Z04Q7xBjD7ZfO5vZLT6+Uf2FFKZ/63QaefPsw1y+ectrrB+vbeHTTIS6Zk89LO2v57Wt7+WoElfnh+vOWKpZMz2FyVnLM7iEiY08kle6lwU1nbrHW3ho8PhnzyEREosntBacnrj3didJeAoGk947LZlPV0M5/vbiL68+ezA+uXxh23na8rCoroKwonbvXVuL3n77Y8s41u3EYw49uWMh7zyjkt+v2xWyL+Z1Hm7nj4S38cvWumHy+iIxdkSTd64wxanATkfHPm6mFlDG0Yk4+7z2jkA8vLeE/PrAQ5xhIuCHwA8HfrihlV00LL5yybf3B+jb+tPEQH15WQlGmly+smEVTRw8Pvjn4hj8hNc0dfPWPW7j4P9ZwrKUz7LUPrz8IwNqKWk1bEUkwkSTd5wFbjDEVQx0ZKCIypiRlxHUhpcvhSpj2Eggkt7/62BJ+eMNCXM6xNQHk6gXFlOQkc9faypOS3bvWBqrcf7uiFICzSrK4cFYe976yN+yGPwBdPX7uebmSVT9+iSffPsyB+jYeCJOsd/b4eGzzIdKTXFQ3drDzaEt0vjgRGRci+a54BTAbeA9wLXBN8FFEZHyJc6Xb7XTjt358/vDJm8Sey+ngsxeXsuVgA6/vOQbAoeNtPLLhEDcuLaE480R/9RdWllLX0skjYXa7fHlnLVf818v8+zPlLJ2ezXNfuYRL5uTzP6/vp7On//+/n9t2lIa2br59beCXx2sqaqL4FYrIWDdo0m2t3Q9kEUi0rwWygudERMYXb2bcF1ICCdViMpZ98Jwp5KUlcffaSgDuXFN5UpU7ZPnMXBaVZPGrlyrpOWXiSUNbF198cBMfv389fr/l/k8s4Te3LmNGXiqfunAGdS2dPPl2db/3/8NbB5mclcwHFk+hrCidtUq6RRJKJDtS3kFgg5yC4PF7Y8ztsQ5MRCTqvBnxrXQ73AAJ1WIylnndTj514Qxe2VXHs+8e4U8bD/KhpVOYdMoUEWMMt62cxaHj7Tz5zuHe86/uquOKn73Cs+8e4auXz+GvX7mYVWWFva9fNDuPOYVp3Pfq3tP6tQ/Wt/Hq7jpuXFqCw2FYMbeADfuOx2zBpoiMPZG0l3wKONda+x1r7XcI9Hh/JrZhiYjEgDczrj3dHmeg0p0oE0zGg4+eN5V0r4vbH9oEwBdWzOr3ukvLCphTmMbdaytp7/Lxz09u46P3vUlqkpPHv3ABX7p0Nkmuk3e4NMbwyQtmsKO6qbeFJeQPbx3EYeCDSwIjC1fOzafHb3ltd10MvkoRGYsiSboN0LdBzRc8JyIyviSp0p3o0r1uPr58Gt0+y4eWlJxW5Q5xOAxfWDGLnUdbuOQ/1/Cb1/Zxy/JpPHX7RSyYkjng51939mRyUj3c/+re3nM9Pj+PbDzIirkFvb3ji6dlk57kYm1FbXS/QBEZsyLZHOc3wJvGmMeDz68D7otdSCIiMeLNgp526OkClyfmt3M7g0m3Kt1jyqcvnMmxli7u6Gcjnb6uWVjMz1/cRUtnD7/75DIumZM/6Gd73U4+et40frF6F3vrWpmRl8pLO2s52tTJv7y/pPc6t9PBRXPyekcHxmMDIREZXZEspPwJgV0p64PHrdban8U6MBGRqPMGt4KP02JKLaQcm7JTPfzwhoUUZHjDXudyOnj8tgtY+/UVESXcIR87bxpuh4PfvBaodj/81kHy0pJYVVZw0nUr5hRwpKmD8iPNQ/8iRGTcCVvpNsY4gW3W2jJgU3xCEhGJkdBW8Ic2QObkmN/O3RRYhNddsx062ob25qypJ+KVUZOZ7B7ye/LTk3jfokk8suEQHztvGqvLa/jMRTNxnzK7/JK5gUR+bUUt84ozIvrsv2yt5qcv7OTXH1/K1NyUIcc2Egfr2/ibu9Zx78fP4eyp2XG9t8hEEDbpttb6gpviTLXWRr49l4jIWJQarFY+dGNcbudO9kJRAd1/+iR0DbHaPWUpfPqF2AQmMffJC2bwp42H+PT/bMDnt9y4tOS0awozvMwvzmBNRc1pYwv7U9fSyTcf30pDWzdffGgTf/r8+XhcA//C2ue3Ud0V9Jmt1dS1dPLsu0eUdIsMQyQ93dnANmPMeqA1dNJa+76YRSUiEgszV8BHH4Xu9rjczt24Gyrup+uyb0P6jMjfuPG3cHhLzOKS2Js/KYPzS3NZV3mMc2fkMCMvtd/rVszN51cv76Gpo5sMb/iq+vee2EZbp49vXFHGj54t50fPlvPta+b3e+2Wgw186rdvcdvKWXzyhrWo6wAAIABJREFUwiH83Qvj+e1HAU6bzCIikRkw6TbGJFlrO4FvxzEeEZHYcThh1mVxu537yAaouJ/ukmVQfF7kb6x+B3a/CH5fIGYZlz5z0UzWVR7jpnOnDnjNyrIC7lpbyau76rhqQfGA1z2//ShPvVPN310+h79dUcrRpg7ue3Uvy2fmctn8wpOu3XTgOLfct57mzh5+u24ft14wfcQLNetaOtl44DiZyW7erWqksb17WK03Ioks3ELK14OPn7bWvnTqEY/gRETGs2HP6U7NByy01Uc/KImblWUFPPOli3jfWZMGvObskiwyvK6wu1M2dXTzT/+3lbKidD53SaAN5ZtXlXHm5Ay+9qe3Odxw4jc3G/fX8/H71pOT5uHr753Lgfo23tp3fMRfy+odNVgLd1w6G7+F9Xv1d1NkqMIl3R5jzE3A+caY60894hWgiMh4FZrTPeTpJal5gcdWbRM+3s2flBG2yuxyOrhoTn7v6MD+/OCZcmqbO/nRDQt7e7iTXE5+8ZHFdPf4+dJDm+nx+XlrXyDhzk9P4g+fXc4nzp9OisfJY5sOjfjreG77ESZnJXPTuVNJcjlYV6lNfUSGKlzS/XngIiALuPaU45rYhyYiMr4Ne3Oc0ILPVm2ckghWzMmnprmT7dWnj7J8vfIYD60/wKcvmslZJVknvTYjL5V/v34BG/Yf544/bOGW+9dTmOnl4c+eR1Gml9QkF1eeWczT71TT0e077bMj1dbVwyu76rh8fiFet5NzpmXzeqX6ukWGasCebmvtq8CrxpgN1lpthiMiMkTDbi9JC85zblU1MRGERgf+7+v7ue7syeSlechNTSLJ7eCbj73DtNwUvnLZnH7f+/5Fk1m3+xh/2HCQ0vxUHvrMeSfNH7/hnMk8uukQf912hPcvGt6YzFd21dHZ4+fyYO/4+aW5/Pi5ndS3dpGTGvtNpkQmikGnlyjhFhEZHlW6JRIF6V6WTMvm4bcO8vBbB097/cHPnEuyZ+AFtd973xnMLkzj/Ysmk5+edNJr583IZXJWMo9uqhp20v389qNkeF0sm5EDwPLSXADe2HMs7OJPETlZJCMDRURkGIa9Dbw3C4xTSXcC+f2nz2XfsVaOtXRR19LJsZYujrV2Mrcog/NL88K+N9nj5NMXzez3NYfDcP3iydy5ZjdHmzoo7GcXzl+/sof1e+v55U2LT5v77fNbVpfXsLKsoHdzn4VTskjxOHm9Ukm3yFAo6RYRiZFhL6R0OAKLKVu0kDJReN1Oyooi25VyqK5fPIVfrN7N45ur+PwlJ2/Cs7aihn97egcAv1yzm69efnIby8b9x6lv7eI984t6z7mdDpZOz9G8bpEhCreQEgAT8FFjzHeCz6caY5bFPjQRkfFt2O0lAKkF6umWqJiRl8o507J5dOOhkyakHG5o5yt/2EJZUTrXLCzmzjW72Xqo8aT3Pr/9CB6no7fvPGR5aS67a1qoaeqIy9cgMhEMmnQDdwHLgY8EnzcDd8YsIhGRCWLYCykhUOlWe4lEyQ2Lp7CrpoWtVYGkutvn54sPbqKrx8+dNy/m+9ctIC/Nw989soXOnsCkE2stz20/yvLSXNKSTv7F+PKZgb5uVbtFIhdJ0n2utfY2oAPAWnsc0HJlEZFBOI0Tgxl6ewkEFlMq6ZYouXphMR6Xg8c2VQHww7+Us+lAAz+8YSGl+Wlkprj54Q0L2Xm0hZ8+vwuAXTUt7D/W1ju1pK8zJmWQ7nXxhpJukYhF0tPdbYxxAhbAGJMP+GMalYjIBGCMwe1wD7O9REm3RE9mspvL5xfy5y1VnDMtm/te3cvHl0/j2j67Za6cW8CNS0q45+VK3nNGYe8s7v6SbpfTwbkzclined0iEYuk0v1z4HGgwBjzfeBV4N9jGpWIyAThcXqG116Slg/dbdDVGv2gJCF9YPEUjrd1c8fDm1k4JZNvXT3vtGv+6Zp5FGcm87U/vs3T71Rz1pTMfieeAJw3M5f9x9pO2oZeRAY2aNJtrX0A+HvgB0A1cJ219pFYByYiMhGMqNINqnZL1Fw0O4/89CTSklzcedNiklynz/5O97r5jw8sZE9dK9urm3jPGUX9fFJAaJShdqcUiUwk00vOA6qstXdaa38JVBljzo19aCIi45/bOdKkWxNMJDpcTge/u3UZj33hfEpyUga87oJZeXzsvGkAvKef1pKQsqJ0slPcajERiVAkPd13A4v7PG/p55yIiPTD7XDT5RvOQsrghiia1S1RNH9SZLPAv3PtfD60pITZhekDXuNwGM6dkcsbe45hrcUYE60wRSakSHq6je0z2NNa60eb6oiIRGT47SUFgUe1l8gocDsdLJiSOeh158/KpaqhnYP16usWGUwkSfceY8yXjDHu4HEHsCfWgYmITAQep2dklW4l3TKGheZ1r6scvA3q3apG/vjWwViHJDJmRZJ0fx44H6gCDgHnAp+NZVAiIhPFsCvd7mTwpKunW8a0WQVpFGYk8fKuwX84/M+/VvDNx7fS3uWLQ2QiY8+gbSLW2hrgw3GIRURkwhl20g3alVLGPGMMq8oKePLtarp6/Hhc/dfy2rp6eH3PMXx+y7uHG1k6PScq9w/tntnfJBaRsSaS6SX5xph/NMbcY4y5P3TEIzgRkfFu2HO6AdIKoFULKWVsWzm3gJbOHt7aVz/gNa/tPkZXT2BfvS0HGqJ270/+9i3+9vebovZ5IrEUyYLIPwOvAC8A+p2QiMgQuB1u2nuGucgsNR/qtYRGxrYLZuXhcTl4cUcNF8zK6/ea1eVHSU9ykeZ1seVgdJLuPbUtvLb7GA4DdS2d5KUlReVzRWIlkp7uFGvtN6y1f7TWPho6Yh6ZiMgEMOw53aD2EhkXUpNcLJ+Zy+ryo/2+bq3lxR01XDwnn8XTsqOWdD+2qQoAv4XntvV/b5GxJJKk+yljzFUxj0REZAIa9pxuCFS6246BX79klLHt0nkF7DvWxp7altNe23a4iZrmTlaVFXB2SRZVDe3UNneO6H5+v+XxzVVcPCef6bkp/OXd6hF9nkg8RJJ030Eg8e4wxjQZY5qNMU2xDkxEZCIY2ULKArB+aBu4V1ZkLFg5NzBXfnX56WsQXtxRgzGwYm4+i0qyAEZc7X5j7zGqGtq5YfFkrlxQzLrKYxxvHeYPtyJxMmjSba1Nt9Y6rLVea21G8HlkW1qJiCS4Yc/pBs3qlnGjJCeFuYXpvLjj9KR7dflRzi7JIjctiTMnZ+J0GLYcPD6i+z26sYr0JBfvPaOIq84sxue3PL9DLSYytkUyvcQYYz5qjPl28HmJMWZZ7EMTERn/Rlbpzg88KumWcWDVvALe2ldPY/uJv+81zR28faiRS+cVAuB1OykrSh9Rpbu1s4e/vFvN1QuL8bqdnDk5gynZyfxlq1pMZGyLpL3kLmA5cFPweQtwZ8wiEhGZQDxOj5JuSQirygro8Vte6bNRztry2t7XQhaVZPHOwUb8fjus+zz77hHaunzccM4UIDAr/KoFxby6u+6khF9krIkk6T7XWnsb0AFgrT0OeGIalYjIBOF2uEc2pxuUdMu4cHZJFlkpblb3aTF5sfwokzK9lBWl955bVJJFc2cPlf0suozEo5sOMTUnhSXTsnvPXXlmEd0+y4tqMZExLJKku9sY4wQsBDbLAfwxjUpEZIIYUXuJNwuMU0m3jAsup4MVc/JZU1GDz2/p7PHxyq46Vs0rwBjTe93ZUwOLKTcPo8WkqqGd1/cc4/rFk0/6zEUlWUzK9PLM1iMj/0JEYiSSpPvnwONAgTHm+8CrwL/HNCoRkQnC7XTjsz58wxn753BoVreMK6vmFXK8rZstB4/z5p562rp8XFpWeNI1M/PSSB/mJjn/t7kKa+GGxVNOOm+M4Yozi3l5Vy3NHWoxkbEpkuklDwB/D/wAqAaus9Y+EuvAREQmArfDDTCyvu7WuihGJBI7l8zOx+kwrC6vYXV5DV63g+WluSdd43AYzpqSNeTt4K21PLrxEMtm5FCSk3La61ctKKKrx9/v2EKRsSBs0m2McRpjyq215dbaO621v7TW7ohXcCIi4110km5VumV8yExxs2RaNi/uqOHF8qNcOCsPr9t52nWLSrKoONpMe1fkvwHafLCBPXWtfOCUKnfI4qnZFKQn8Re1mMgYFTbpttb6gApjzNQ4xSMiMqF4nIF15yPalbJFlTsZPy6dV0D5kWYO1rez6pTWkpBFJVn4/JZ3DzdG/LmPbjyE1+3gygVF/b7ucBiuPLOINRU1tHb2DCt2kViKpKc7G9hmjHnRGPNE6Ih1YCIiE4HaSyTR9E20V5bl93vNouBiykhaTEJtJY9tquK9ZxSR7nUPeO2VC4rp7PGztkK/HZKxxxXBNd+OeRQiIhNUqNI9/KQ7D7pboasVPKlRjEwkNkrzU5mem0JqkovizOR+r8lLS2JKdvKgiynrW7v4x8e28uy2Iyydns03r5wX9vql03PIS/Pw6KZDLJySSXGmF5czkvqiSOwNmnRba18yxkwDZltrXzDGpACnN2iJiMhpeivdI57VXaekW8YFYwz//bFzcDnCJ7uLSrLYHKbSvaa8hq//6R0a27v4hyvL+MxFM3E6zIDXAzgdhqsXFPO71/ezurwGh4HizGQmZyUztyidb18zH49LSbiMjkGTbmPMZ4DPAjlAKTAZ+G/g0tiGJiIy/kWlvQQCiymzp0UpKpHYKivKGPSaRSVZPPVONTXNHRSke3vPd3T7+NentvPAmwcoK0rnfz65jPmTBv+8kG9eNY/L5xdx6HgbVQ3tVB1vZ3dtC//7xn7ee0YRF87OG9bXJDJSkbSX3AYsA94EsNbuMsYUhH+LiIhAlNpLQBNMZMI5u09f93vOCCyOPHS8jc//fiPvVjXx2Ytn8nfvmUOSa2i/XPe6nacl1i2dPZz1z8/xxp5jSrpl1ESSdHdaa7tCOz8ZY1wEd6cUEZHwXI7At9kRTS8BJd0y4ZwxKROXw7DlYCDpXldZxxcf3Ex3j5/7blnCpfP6n3wyHGlJLhZMzuSNPcei9pkiQxVJY9NLxph/BJKNMZcDjwBPxjYsEZGJweMYaaVbSbdMTF63k3nFGWw52MCvX9nDx+5bT26qhz9/8YKoJtwh583M5e1DDbR1aZygjI5Iku5/AGqBrcDngGeAf4plUCIiE4XbGejpHnal250MnnRoUdItE89ZJZmsqzzGvz29g8vnFfL4bRcwMz8tJvdaXppLt8+yaf/Qt58XiYYBk25jzIvBP/7AWnuvtfaD1toPBP+s9hIRkQiMeCElBPq6VemWCeji2fkYA19/71zu/uhi0pIi6XodniXTsnE6DK/v0dx7GR3h/nYXG2POB95njHkYOGlOj7V2U0wjExGZAEbcXgLaCl4mrPecUcTW7703psl2SGqSi4VTMnljT33M7yXSn3B/y79DYGOcKcBPTnnNAqtiFZSIyEQx4vYSCMzqrt8bpYhExpZ4JNwhy2fmcs/Le2jr6iHFE7/7ikD4nu5qa+2VwH9aa1eecijhFhGJQKi9pMc/gsVbai8RiYrzZubS47ds3H98SO/z+S1+vzprZWTCJd0/Dz5eF49AREQmohHP6YZAe0lbHfh9UYpKJDGdMy0bl8PweuXQRgd+7n838vnfb4xRVJIowv1updsYcw8w2Rjz81NftNZ+KXZhiYhMDKFK94jaS1Lzwfqh/fiJzXJEZMhO9HVHnnRXNbTzYvlRnMbQ1NFNhtcdwwhlIgtX6b4GWA10ABv7OUREZBDRmV6iWd0i0bK8NJd3DjXS2hlZy9f/ba7CWujxW17eqf8GZfgGTLqttXXW2oeB91lrf3fqEccYRUTGragspFTSLRI1Q+nrttby2KZDLJ6aRVaKm9U7auIQoUxUA7aXGGP+3lr7H8CnjTGnrR5Qe4mIyOBcJvBtNiqV7hb9gy8yUudMy8btNLy+5xgXz8kPe+3WqkYqa1v5wfULWL+3njUVNfj8FqfDhH2fSH/C9XTvCD5uiEcgIiITkTEGj8MTpfYSbeohMlIpHhdnTcmKqK/7sU1VeFwOrlpQTLrXxeObq9h84DhLpufEIVKZaAZMuq21TwYfR7WVxBhzEXAzgVjnW2vPH814RESGyu10j6y9JDkbjFPtJSJRct7MXO5+qZLWzh5SB5gT3u3z88Tbh7l8XiGZyW4unpOPy2F4YUeNkm4ZlnDbwD9pjHlioCOSDzfG3G+MqTHGvHvK+SuMMRXGmN3GmH8I9xnW2lestZ8HngLUSy4i447b4R5Zpdvh0KxukSg6b2YuPr9lQ5i+7pcqaqlv7eL6xZMByPC6WTYjh9XlR+MVpkww4aaX/Bj4f8BeoB24N3i0AJURfv5vgSv6njDGOIE7gSuB+cBHjDHzjTELjDFPnXIU9HnrTcCDEd5XRGTM8Dg8I9scB4Jbwau9RCQaevu6w8zrfmzzIXJTPSf1fa8qK2Dn0RYO1rfFI0yZYMJNL3nJWvsScIG19kZr7ZPB4ybgokg+3Fr7MlB/yullwG5r7R5rbRfwMPB+a+1Wa+01pxw1AMaYqUCjtbZ5OF+kiMhoGnF7CQQr3VpIKRINyR4ni0oG7utubOvmhe01XHvWJNzOE6nSZfMKAXhxh6rdMnThKt0hqcaYmaEnxpgZQOoI7jkZONjn+aHguXA+Bfwm3AXGmM8aYzYYYzbU1upXsCIydoy4vQQgtUDtJSJRdN7MXLZWNdLSz7zup7dW0+Xzc8PiKSedn56Xysz8VF4s1w/AMnThppeEfAVYa4zZAxhgGvDZmEZ1CmvtdyO45h7gHoAlS5acNuJQRGS0RKfSnR8YGVjxl+gEFUtTlkFq7mhHIRLWeTNz+cXq3fzkuZ18/b1zSfY4e197bNMhZhekcebkjNPed9m8Qn7z2l5aOntIG2ARpkh/Bv3bYq191hgzGygLniq31naO4J5VQEmf51OC50REJqSoVLqzp0N3Gzz04ajEFFOLbobr7hrtKETCOndGDtcvnsz9r+3l2Xer+dbV87lqQREH6tvYsP84f3/FXIw5fR73qrIC7nl5D6/srOXKBcWjELmMVxH9iBZMst+O0j3fAmYH21SqgA8TWCQpIjIhjXhON8DST8HU88D6ohNUrDz2OWgbfP6xyGhzOR385EOL+MiyqXz3z9u47cFNnDsjhynZKRgD1y3qv/N1ybRsMrwuXiyvUdItQxLT34sYYx4CVgB5xphDwHettfcZY74I/BVwAvdba7fFMg4RkdEUlfYShxOKF0YnoFhKyYWu1tGOQiRiS6fn8OTtF/LwWwf48V8reHNvPRfMymVSVnK/17ucDlbMLWBNuXanlKGJadJtrf3IAOefAZ6J5b1FRMYKj8NDc0+CDF/ypEKbRhvK+OJ0GG4+dxpXLyjmd+v2s6qsIOz1l84r4Im3D/P2oQYWT82OU5Qy3g06vcQY85gx5mpjTCSTTkRE5BRuh5su/wgr3eOFJxW6NMNYxqesFA93XDabBVMyw163Yk4BTofR6EAZkkgS6bsI9FzvMsb80BgzN8YxiYhMKG6nm27fCHu6xwtPqtpLZMLLTHGzZFo2L2yvwVoNTJPIDJp0W2tfsNbeDCwG9gEvGGPWGWNuNca4Yx2giMh4F5XpJeOFJxW6lXTLxHfNWZOoONocdlfLiaipo5vz/v1F1lWqjWyoImoZMcbkAp8APg1sBv6LQBL+fMwiExGZIBKvvURJt0x8HzxnCoUZSfzshV0JVe3eV9fKkaYOth9uGu1Qxp1IerofB14BUoBrrbXvs9b+wVp7O5AW6wBFRMa7hGovcaeCrwsS5euVhOV1O/nCilms31efUNXuI40dABxvS5BCQhRFUun+ubV2vrX2B9ba6r4vWGuXxCguEZEJIypzuscLT2rgUdVuSQA3Li1JuGr3kaZQ0p0g39OiKJKkO9sYc/0px6XGmPDzdEREBEi0nu6UwKOSbkkAiVjtDlW6G5V0D1kkSfengF8DNwePe4FvAK8ZYz4Ww9hERCYEj9OTOO0lnmDXoZJuSRCJVu1We8nwRZJ0u4F51tobrLU3APMBC5xLIPkWEZEw3A43PbYHv/WPdiixF2ov0QQTSRCDVbuttZQfaaLbNzH++w+1lzSo0j1kkSTdU6y1fae/1wAl1tp6QP+Li4gMwu0MTFdNiBYTt9pLJPEMVO0uP9LER+97kyt+9grX3fnahJj4cSLpVqV7qCJJutcaY54yxtxijLkF+HPwXCrQENvwRETGP7cjmHQnQotJb3uJdqWUxHFqtftYSyffenwrV/3XK2w73MTnLynlaFMH7/vlq/zk+Z109YzPqre1tre9pKE9Ab6fRZkrgmtuA64HLgw+/x/gURv4UW5lrAITEZkoQkl3Qszq7p1e0jK6cYjE2Y1LS7hr7W6++fhW6lu7aOvy8fHl0/nyZbPJSvHwuYtn8i9PbefnL+7iuW1H+M8PnDXodvNjTXNnD21dPjKT3TS2d9PZ4yPJ5RztsMaNsJVuY4wTWG2tfdRa+5Xg8SebCCsFRESixOP0AIlS6VZ7iSQmr9vJF1fNZv+xNhZPzeavX76I773vDLJSAv/9Z6d6+OmNi7jvliUcb+viurte4/89VzGuer1DVe6yonRAE0yGKmyl21rrM8b4jTGZ1trGeAUlIjKR9LaXJEJPd6i9pFvtJZJ4PnruVC6Znc/U3JQBr7l0XiHPTc/hX5/azi9W7+alnbX87MZFzMwf+/sNhpLuecUZvLm3nuNt3RRkeEc5qvEjkp7uFmCrMeY+Y8zPQ0esAxMRmSjUXiKSGIwxYRPukMxkNz/+4FncffNiDtS3cfXPX+XBNw+M+ZGDp1a6NTZwaCLp6X4seIiIyDAkVHuJ0wPGqfYSkQhcuaCYs6dm87VH3uYfH9/K6vKj/PCGheSlJY12aP0KTS6ZG0y6NTZwaAZNuq21vzPGJANTrbUVcYhJRGRCSaj2EmMCLSaaXiISkaJML//zyWX8dt0+fvhsOV9+eAu///S5ox1Wv6obO8hN9VAYbCnR2MChGbS9xBhzLbAFeDb4fJEx5olYByYiMlEkVNINgcWUai8RiZjDYfjkhTP4xPnTWb+3no5uX9xjePbdam79zfqwLS5HmzoozPCSlRL4nqaxgUMTSU/394BlBGdyW2u3ADNjGJOIyITSuzlOIrSXQKCvW+0lIkO2dHoOXT4/bx+M/zYoz2w9wpqKWmpbOge8prqxg+JML8luJx6XQz3dQxRJ0t3dz+SS8TPfRkRklCXUQkoIJN2aXiIyZEumZQOwYf/xuN+74kgzAHtqB/6B+WhTB4WZXowxZCW7NTJwiCJJurcZY24CnMaY2caYXwDrYhyXiMiEkVALKQHcqnSLDEd2qoc5hWms31sf1/t29fiprA20hIUeT9XR7aO+tYviYD93dopHle4hiiTpvh04A+gEHgKagC/HMigRkYkk8Xq6lXSLDNeS6Tls2n8cnz9+4wP31LXQE7xfZU3//+3WNAXaTgozA0l3Zoqb46p0D8mgSbe1ts1a+y1r7VJr7ZLgnzviEZyIyESQkO0lSrpFhmXZ9ByaO3vYUd00pPdZa3ni7cO0dPYM+Z6h1pK0JNeAle7qxnYAinor3WovGapIppfMMcbcY4x5zhizOnTEIzgRkYkg4dpLlHSLDNvSGTkAbNg3tBaTTQca+NJDm/nVS5VDvmf5kWbcTsMlc/IHTLpDM7qLg5XurGS1lwxVJO0ljwCbgX8Cvt7nEBGRCCRke0m3km6R4ZiclczkrGTe2je0xZRrymsAeHTjoSG3ppRXN1Gan8bconSqGtpp7zp9ZGFoN8pQe0lWqpuG9u4xv4vmWBJJ0t1jrb3bWrveWrsxdMQ8MhGRCSLhkm53iirdIiOwZHo26/fVDymhXV1eg9ft4HBjB69XHhvS/SqONDO3KJ2Z+alYC3vrTv/v90hTB6keJ+lJgX0Vs1M8dPX4aR+FmeLjVSRJ95PGmC8YY4qNMTmhI+aRiYhMEInXXpIGvi5IlK9XJMqWTs+htrmT/cciG715pLGD7dVNfP6SUjK8Lh7ZeDDiezW2d3O4sYO5RemU5qcB/U8wOdJ4YlwgQFZycIMc9XVHbNBt4IFbgo99W0os2iBHRCQiCbmQEgLV7uSs0Y1FZBxaFuzrXr+vnul5qYNev6Yi0Fpy5ZnF1LV08siGQzS2d5MZTIzD2Xk0sIiyrCidGXmpGDNA0t3U0dvPDZCVEigmHG/rYlJW8uBflEQ0vWRGP4cSbhGRCLkcgfpGwrSXeFICj2oxERmWWflpZKW4I15Mubq8hslZycwpTOOD55TQ2ePnqXcOR/Te8uDkkrlFGXjdTqZkJ1PZzwY5RxoDW8CHhLaC1wSTyA2YdBtj/r7Pnz94ymv/HsugREQmEmMMboc7sdpLQLtSigyTw2FYMi07osWUnT0+Xttdx8qyfIwxLJySyZzCNB7ZcCiie1UcaSLd62JSsIpdmp9GZc3JlW6f31LT3HlSpTu7t9KdIN/XoiBcpfvDff78zVNeuyIGsYiITFhuhzsB20v6Hz0mIoNbOj2HvXWt1DSH3xrlzT31tHX5WFVWAAR+yP/gOSVsOdjA7prmQe9TcaSZsqL03l7t0vw09ta14u8zAaWupROf3/bO6IYTlW6NDYxcuKTbDPDn/p6LiEgYHqcncSrdbrWXiIzUiXnd4avdq8trSHI5WD4zr/fcdWdPxukwPLIxfLXbWkt5cHJJSGl+Gu3dPqqbTiT7oXGBRZknerdD/eKN7QnyfS0KwiXddoA/9/dcRETCcDvcCdTTHWwv6VJ7ichwnTkpE6/bwVth+rqttaypqOH80lySPc7e8/npSaycm89jm6ro8fkHfP/hxg6aO3qYW5TRe640P/Cbqr4tJqGNcfpWur1uJ8luJ8dbVemOVLik+yxjTJMxphlYGPxz6PmCOMUnIjIheJyeBEq6Q5VutZdGYah2AAAWnUlEQVSIDJfH5WBRSVbYpHtPXSv7j7X1tpb09YFzSqht7uTlXbUDvr/iSGCr+bK+le6C08cGnqh0e+krOyWwQY5EZsCk21rrtNZmWGvTrbWu4J9DzwefQSMiIr0SayFln5GBIjJsy6bnsP1wE80d/X/vCO1CubKfpHtVWQE5qZ6wCypDk0vmFJ5IunNTPWQmu09Oups6cDsNuamek96fleKhQT3dEYtkcxwRERkhl8OVQAspNb1EJBqWzsjBb2HTgYZ+X19dXsOcwjSmZKec9prH5eC6RZN5YcdR6gdoAak40sykTO9J87yNMZTmp1JZc+KH5iONHRSke3E4Tl7Sl5Xi1uY4Q6CkW0QkDhKqvcSt9hKRaDh7ajZOh+l3XndzRzfr99b3W+UO+eCSKXT7LP+3uarf1ytOWUQZUpqfdlp7yamtJRAYG6jpJZFT0i0iEgcJ1V7iSgLj1EJKkRFKS3IxvziD9XtPT7pf3VVHj9+yau7ASfe84gwWT83ivlf30tVz8oLKbp+fytqWkxZRhszMT6OmuZOmYFvLkaaOkxZRhmSq0j0kSrpFROIgoeZ0GxNoMVFPt8iIXTg7jzf31nPrb9az6cCJ8YGry2vI8Lo4Z1p22Pffcdkcqhra+eOGgyed31PbSrfPMq+4v0p3au811towle7AQkprNdQuEkq6RUTiIKHaSyAwwUTtJSIj9qVVs/n6e+ey5WAD19+1jpt//QavVx5jTUUtF8/Jx+UMn8pdPDuPxVOzuHPNbjp7fL3ny4OTS/ptLwlNMKlpoam9h/ZuX7+V7qxkDz6/pbmzZyRfYsJQ0i0iEgcJ1V4CgQkmWkgpMmLJHie3rZzFq99YxbeumkfFkRY+cu8b1LV09jsq8FTGGL5y+RyqGzv441snqt3lR5pxOQwz89JOe8/UnBRcDsOeupYTM7r7qXSHdqVsVItJRJR0i4jEQcJVut0pai8RiaLUJBefuXgmr35jJd+7dj7vPaOQy+YXRvTeC2flsWRaNneuqaSjO1DtrjjSTGl+Gh7X6amg2+lgWm4KlTWtVDe2AwMl3YERglpMGRkl3SIiceByuBIr6VZPt0hMeN1OPnHBDH71sSVkeCPbNiVU7T7S1MEfgtXugSaXhIQmmBztZzfKkOxgpVuLKSOjpFtEJA7cDjddvgSqBnlSlXSLjCHnl+aybHoOd63dTW1zJ1UN7eGT7oI09h1r5dDxQKW7sL+e7jFS6d56qJFthxtHNYZIKOkWEYmDhGsv8ai9RGQsMcbw5ctnc7Spk39+chtw8vbvpyrNT6PbZ3lrXz15aZ5+21CyxkClu7Wzh9sf2sQXH9yMzz+2p6go6RYRiQO3w51gSXeaFlKKjDHnl+Zx7owcnnqnGuh/cklIaGzgpv0N/Va5AbKSRz/p/rend7C/vo0fXr8A5yk7Zo41SrpFROIgMdtLNDJQZKz5yuVzAEhPcjE5K3nA62bmB6aadPn8FPeziBLA5XSQnuQatfaSF3cc5aH1B/jsxTM5d2buqMQwFK7RDkBEJBEkXHuJppeIjEnnzcxl5dx8jDEYM3BlODPZTX56ErXNnQNWugGyUt00tsf/e1tdSyffePQd5hVn8NXgDxJjnZJuEZE4cDvc9Ph78Fs/DpMAv2T0pIGvC3zd4IxswoKIxMe9H18SNuEOKc1Ppba5c8BKN/+/vTsPsqss8zj+fdLdN0l3IB1DhMgieyIiIAMILgioIygDOiCCTAEqKpSWzIxLwTgW5R/MjIXO4sYMKoIru8IwKoNOFBWChD0sAQRCgmACZkECWTrP/HFOk07oTrpjzr23+3w/VV33nnPPPfdt3jqXX95+zvtSLJDT7JHuzOScq+9h+fNr+N7p+zG+s6Opn7+5avDNL0mt1+go7vJfs7YmK7c1inpQR7ul9tPZMW5Y9c/9JSYbHenu7mp6TfflcxZww31/4NNHzthoXXq7MXRLUhN0jStGe2tTYtLoLh4N3dKotVsZugdbGKdfb3eDpU0c6Z7/zHN87r/v45Bdp/KBN+zStM/dEgzdktQEneOKar7a3EzZKJeWdgYTadR6w+5T2W1aD6+avvWQx0zp7mJpk2q6+9Ymn7j8LjrGBV88YV/GtflsJRuypluSmqC/vKQ2I91d/SPdzmAijVYzt9uan3/isI0e09vdYNnzq+lbm5VP2XfJTY8xZ/4SvviefXnFRmZeaVeOdEtSE/SXl9RnpNuabqkOeid2kQnLKx7tfvyZFZx//TwOnzGNv95/+0o/qyqGbklqgsa4mo1095eXrLK8RBrLpvSUC+T8GaF74ZIVnHvNXJ5a9sKgr2cm5/zwbjrGBee9+zXDmnmlHRm6JakJujrqeiOl5SXSWNY7sRhQ2NxpA19Y3cdHvnMbl9w8n+MuuIlHFr/0O+OyWxfwm4ef4Zx3zByVZSX9DN2S1AQvzl7SV5fQXZaXeCOlNKb1dhffbcs2Y9rAzOSzP5rLvb9fztlHzeT51X285z9vZu4Ty1485qllL3De/9zPwbu+jJMO3GmLtbsVDN2S1AT1LS+xplsay3q7N3+k+9JbF3DFbQv5+BG7c8abd+OKMw5hQlcHJ144m5t/9wyZyT/+6B5Wr13L54/bZ9TNVrIhQ7ckNUHtykucvUSqhSnlSPdIF8i5e+FSzr3mXt60xzac9dZiGffdpk3iyjMPYbvJEzj1W7/ls9fM5Wf3L+KTfzmDV07t2eJtbzZDtyQ1Qe1mL+kcD9HhjZTSGLfVhC4iGNECOUueW8WZ372daVuN50snvna9qQanT57IFR85hFdN35rvzn6c/Xbs5f2jbBGcoThPtyQ1Qe1GuiOKum7LS6QxrWNcMHliF0uGOdLdtzY567I7WfzsSq444xCm9DRecsyUngbfP/11/NeNj3D8/jtUPv93sxi6JakJajfSDWXotrxEGuumdDeGPWXg92+Zz40PLuaf3v0a9t2xd8jjesZ38vdv23NLNbEtWF4iSU1QuxspoQjdzl4ijXmTJ3YNu7zkurufZOZ2W3HSQTtW3Kr2Y+iWpCaoXXkJFDdTWl4ijXlTuruGdSPl8hdWM2f+Et7yqpeP2gVu/hyWl0hSE/SXl9y56E4mdEwY9vuS3KzPCzb/f2hDfeZB2x3E1IlTh3+ixiRDt1QDvd0NHlq06VKyXz/0NH1rk8NnvLwJrWo/hm5JaoJJXZMY3zGeqx66iqseuqrVzdksF739ohGG7h5Y8Ux1DZLUFnq7u4a1OM6sBxYxeWIX+22klnssM3RLUhN0d3Vz/XHXs2zlsk0fTDHa/OJo9UgHrQcZqF7vfMMxyKHTe6aPrB2Nblj6+MjeI2nU6Z3Y4NmVa1jdt5aujsErl9euTX7x4GIO3XManUMcM9YZuiWpSaZOnDqykeLRrjHJGymlGpjSs26BnGlbjR/0mHt/v5zFz67k8BnTmtm0tlLPf2pIkqrX1e2UgVINTJ5YhO5lzw89g8mseYuIgEP3NHRLkrRluTiOVAtTuospUTe2QM6seYvYZ4detpk0+Eh4HbR96I6IvSLi8oi4ICKOb3V7JEnD1JgEfaugr0bTJEo11Nu9rrxkMH98bhV3Llha69ISqDh0R8RFEbEoIuZusP/IiJgXEQ9HxNmbOM1RwJcz80zglMoaK0nashrdxaOj3dKYtm6ke/DykhsfXEwmHDGznlMF9qv6RsqLga8A3+7fEREdwFeBtwELgVsj4lqgA/jnDd7/AeA7wLkRcQxQozuQJGmUa/QUj6tXwMR6ThEm1UH/SPdQ0wbOmreIbSY12PsVk5vZrLZTaejOzBsjYucNdh8EPJyZjwBExKXAsZn5z8DRQ5zqo2VYv7qqtkqStrDGpOLRkW5pTJs0vpPOcTHoSHff2uSXDy7mLTO3Zdy4+q1COVArarq3BxYM2F5Y7htUROwcERdSjJafv5HjPhwRcyJizuLFi7dYYyVJm6mrv7zEGUyksSwimN47gZ/OfYrFz65c77U7Fyxl6YrVHD6z3vXcMApupMzMxzLzw5l5cmb+eiPHXZiZB2TmAdOm2bGS1HL95SWrnKtbGuu+cPy+PLnsBd739dk8/ad1wXvWA4voGBe8aXezWStC9xPAjgO2dyj3SZLGkhdDt+Ul0lj3ul2nctFpB7JgyQre9/XZPFMG71nzFvEXO01hcln3XWetCN23AntExC4R0QBOBK5tQTskSVV6MXRbXiLVwSG7TeWiUw9k/jMrOPkbt/DAU8u59/fLOczSEqD6KQN/ANwMzIiIhRHxwcxcA3wMuB64H7g8M++tsh2SpBYYOHuJpFp4/e7b8M1TD+TRp5/j+AtuBuDwGfWeKrBf1bOXnDTE/h8DP67ysyVJLdZleYlUR2/cYxu+fsoBnP7tOWy39QRmbrdVq5vUFqqep1uSVFeWl0i1deie07j6zNezNpOIek8V2M/QLUmqRud4iA5nL5Fqau/t670YzobafspASdIoFVGMdlteIkmGbklShRo9sNrQLUmGbklSdRzpliTA0C1JqlJXt6FbkjB0S5Kq1Jhk6JYkDN2SpCo1HOmWJDB0S5KqZE23JAGGbklSlRqTXAZekjB0S5Kq1NXtipSShKFbklSlRo8rUkoShm5JUpUak6BvJfStbnVLJKmlDN2SpOo0uotHb6aUVHOGbklSdRo9xaM3U0qqOUO3JKk6XWXodqRbUs0ZuiVJ1ekf6XYGE0k1Z+iWJFXnxdBteYmkejN0S5Kq07C8RJLA0C1JqtKLN1IauiXVm6FbklQdR7olCTB0S5Kq5OwlkgQYuiVJVXKkW5IAQ7ckqUqd4yHGGbol1Z6hW5JUnQhoTDJ0S6o9Q7ckqVqNHmcvkVR7hm5JUrW6uh3pllR7hm5JUrUaPa5IKan2DN2SpGo1JsGqP7W6FZLUUoZuSVK1GpaXSFJnqxsgSRrjGj0w/2a45JhyRw7jTVE+RPE8Yv2Xs/8cuYntgacct/75MovjBz7ufwrsc8Lwfi9JGgFDtySpWnsdC88+BWteYP0wPYSBAbo/EA9qw3MNsT3wXLl23fP1An35uLZvJL+ZJA2boVuSVK29jyt+JKnGrOmWJEmSKmboliRJkipm6JYkSZIqZuiWJEmSKmboliRJkipm6JYkSZIqZuiWJEmSKmboliRJkipm6JYkSZIqZuiWJEmSKmboliRJkipm6JYkSZIqZuiWJEmSKmboliRJkipm6JYkSZIqZuiWJEmSKmboliRJkipm6JYkSZIqFpnZ6jZscRGxGJhf8cdsAzxd8Wdo89k/7c3+aW/2T3uzf9qb/dPetnT/vDIzpw3nwDEZupshIuZk5gGtbocGZ/+0N/unvdk/7c3+aW/2T3trZf9YXiJJkiRVzNAtSZIkVczQvfkubHUDtFH2T3uzf9qb/dPe7J/2Zv+0t5b1jzXdkiRJUsUc6ZYkSZIqZujeDBFxZETMi4iHI+LsVren7iJix4iYFRH3RcS9EXFWuf9lEXFDRDxUPk5pdVvrKiI6IuKOiLiu3N4lIm4pr6HLIqLR6jbWWUT0RsSVEfFARNwfEYd4/bSPiPi78rttbkT8ICImeA21TkRcFBGLImLugH2DXi9R+FLZT3dHxP6ta3k9DNE/55ffb3dHxA8jonfAa+eU/TMvIt5eZdsM3SMUER3AV4GjgL2AkyJir9a2qvbWAJ/IzL2Ag4GPln1yNvDzzNwD+Hm5rdY4C7h/wPbngX/LzN2BJcAHW9Iq9fsP4KeZORPYl6KvvH7aQERsD3wcOCAz9wY6gBPxGmqli4EjN9g31PVyFLBH+fNh4IImtbHOLual/XMDsHdm7gM8CJwDUGaFE4FXl+/5WpnzKmHoHrmDgIcz85HMXAVcChzb4jbVWmY+mZm3l8+fpQgM21P0yyXlYZcA72pNC+stInYA3gl8o9wO4AjgyvIQ+6aFImIycCjwTYDMXJWZS/H6aSedwMSI6AS6gSfxGmqZzLwR+OMGu4e6Xo4Fvp2F2UBvRExvTkvrabD+ycz/zcw15eZsYIfy+bHApZm5MjMfBR6myHmVMHSP3PbAggHbC8t9agMRsTPwWuAWYNvMfLJ86Slg2xY1q+7+Hfg0sLbcngosHfAF6DXUWrsAi4FvlSVA34iIHrx+2kJmPgF8AXicImwvA27Da6jdDHW9mBnazweAn5TPm9o/hm6NGRExCbgK+NvMXD7wtSym6XGqniaLiKOBRZl5W6vboiF1AvsDF2Tma4Hn2KCUxOundcra4GMp/nH0CqCHl/7pXG3E66V9RcRnKEpSv9eKzzd0j9wTwI4Dtnco96mFIqKLInB/LzOvLnf/of/PeOXjola1r8beABwTEY9RlGIdQVE/3Fv+qRy8hlptIbAwM28pt6+kCOFeP+3hrcCjmbk4M1cDV1NcV15D7WWo68XM0CYi4jTgaODkXDdfdlP7x9A9crcCe5R3jjcoCvCvbXGbaq2sEf4mcH9m/uuAl64FTi2fnwpc0+y21V1mnpOZO2TmzhTXyv9l5snALOD48jD7poUy8ylgQUTMKHe9BbgPr5928ThwcER0l991/f3jNdRehrpergVOKWcxORhYNqAMRU0SEUdSlDkek5krBrx0LXBiRIyPiF0obnj9bWXtcHGckYuId1DUqXYAF2XmeS1uUq1FxBuBXwH3sK5u+B8o6rovB3YC5gMnZOaGN7+oSSLiMOCTmXl0ROxKMfL9MuAO4G8yc2Ur21dnEbEfxY2uDeAR4P0UgzJeP20gIj4HvJfiz+J3AKdT1J16DbVARPwAOAzYBvgDcC7wIwa5Xsp/KH2FoiRoBfD+zJzTinbXxRD9cw4wHnimPGx2Zp5RHv8ZijrvNRTlqT/Z8JxbrG2GbkmSJKlalpdIkiRJFTN0S5IkSRUzdEuSJEkVM3RLkiRJFTN0S5IkSRUzdEvSKBARfRFx54Cfszf9rkHP84uIOGBLt28Yn/uuiNir2Z8rSe2ic9OHSJLawPOZuV+rG/FneBdwHcXCLpJUO450S9IoFRFHRsQVA7YPi4jryucXRMSciLi3XFxlU+c6MCJuioi7IuK3EbFVREyIiG9FxD0RcUdEHF4ee1pEfGXAe68rFz8iIv4UEeeV55kdEdtGxOuBY4Dzy1H63bbwfwpJanuGbkkaHSZuUF7yXuBnwOsioqc85r0UqxQCfCYzDwD2Ad4cEfsMdeKIaACXAWdl5r7AW4HngY8CmZmvAU4CLomICZtoZw/Fam/7AjcCH8rMmyiWW/5UZu6Xmb/bjN9fkkY1Q7ckjQ7Pl4G1/+eyzFwD/BT4q4joBN4JXFMef0JE3E6xRPirgY3VU88AnszMWwEyc3l57jcC3y33PUCxvPWem2jnKooyEoDbgJ1H+HtK0phkTbckjW6XAh8D/gjMycxnI2IX4JPAgZm5JCIuBjY1Qj0Sa1h/0GbguVdnZpbP+/D/M5IEONItSaPdL4H9gQ+xrrRka+A5YFlEbAsctYlzzAOmR8SBAGU9dyfwK+Dkct+ewE7lsY8B+0XEuIjYEThoGO18FthqBL+XJI0phm5JGh02rOn+F4DM7KMo5ziqfCQz76IoK3kA+D7wm42dODNXUdSDfzki7gJuoBi9/howLiLuoaj5Pi0zV5bne5RiJpIvAbcPo/2XAp8qb8j0RkpJtRPr/gooSZIkqQqOdEuSJEkVM3RLkiRJFTN0S5IkSRUzdEuSJEkVM3RLkiRJFTN0S5IkSRUzdEuSJEkVM3RLkiRJFft/Z+59IAfGzjYAAAAASUVORK5CYII=\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pylab.rcParams['figure.figsize'] = (12, 8)\n", - "for i in range(len(optimizers)):\n", - " pylab.plot(converge_cnts[i], abs(ref - converge_vals[i]), label=optimizers[i].__name__)\n", - "pylab.xlabel('Eval count')\n", - "pylab.ylabel('Energy difference from solution reference value')\n", - "pylab.title('Energy convergence for various optimizers')\n", - "pylab.yscale('log')\n", - "pylab.legend(loc='upper right')" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.1" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} From a9d72318580d78fdf08f5bd399c785e5f70135e9 Mon Sep 17 00:00:00 2001 From: stefan-woerner Date: Wed, 14 Aug 2019 13:40:10 +0200 Subject: [PATCH 116/116] updating references in finance tutorials --- qiskit/aqua/amplitude_estimation.ipynb | 10 +- qiskit/finance/index.ipynb | 6 +- .../portfolio_diversification.ipynb | 14 +- .../optimization/portfolio_optimization.ipynb | 110 +++---- .../asian_barrier_spread_pricing.ipynb | 22 +- .../simulation/basket_option_pricing.ipynb | 22 +- .../simulation/bull_spread_pricing.ipynb | 22 +- .../simulation/credit_risk_analysis.ipynb | 274 +++++++++--------- .../european_call_option_pricing.ipynb | 22 +- .../european_put_option_pricing.ipynb | 22 +- .../simulation/fixed_income_pricing.ipynb | 14 +- .../finance/simulation/option_pricing.ipynb | 17 +- 12 files changed, 287 insertions(+), 268 deletions(-) diff --git a/qiskit/aqua/amplitude_estimation.ipynb b/qiskit/aqua/amplitude_estimation.ipynb index 3cae51447..c18675aec 100644 --- a/qiskit/aqua/amplitude_estimation.ipynb +++ b/qiskit/aqua/amplitude_estimation.ipynb @@ -68,7 +68,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -177,7 +177,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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\n", "text/plain": [ - "
" + "
" ] }, "execution_count": 8, @@ -247,7 +247,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.1" + "version": "3.7.1" } }, "nbformat": 4, diff --git a/qiskit/finance/index.ipynb b/qiskit/finance/index.ipynb index 5ee05e65e..f11cd4a9d 100644 --- a/qiskit/finance/index.ipynb +++ b/qiskit/finance/index.ipynb @@ -55,9 +55,9 @@ ], "metadata": { "kernelspec": { - "display_name": "qiskit_master", + "display_name": "Python 3", "language": "python", - "name": "qiskit_master" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -69,7 +69,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.1" + "version": "3.7.1" } }, "nbformat": 4, diff --git a/qiskit/finance/optimization/portfolio_diversification.ipynb b/qiskit/finance/optimization/portfolio_diversification.ipynb index 1a117ea3b..8a287e782 100644 --- a/qiskit/finance/optimization/portfolio_diversification.ipynb +++ b/qiskit/finance/optimization/portfolio_diversification.ipynb @@ -612,8 +612,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "[0 1 0 1 0 1]\n", - "VQE produces the same solution as the exact eigensolver.\n" + "[1 0 1 0 1 0]\n", + "VQE does not produce the same solution as the exact eigensolver, but that is to be expected.\n" ] } ], @@ -644,7 +644,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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\n", 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\n", 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" ] @@ -683,9 +683,9 @@ ], "metadata": { "kernelspec": { - "display_name": "qiskit_master", + "display_name": "Python 3", "language": "python", - "name": "qiskit_master" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -697,7 +697,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.1" + "version": "3.7.1" } }, "nbformat": 4, diff --git a/qiskit/finance/optimization/portfolio_optimization.ipynb b/qiskit/finance/optimization/portfolio_optimization.ipynb index f63e9521b..caa1c7c51 100644 --- a/qiskit/finance/optimization/portfolio_optimization.ipynb +++ b/qiskit/finance/optimization/portfolio_optimization.ipynb @@ -51,7 +51,11 @@ "\n", "The equality constraint $1^T x = B$ is mapped to a penalty term $(1^T x - B)^2$ which is scaled by a parameter and subtracted from the objective function. \n", "The resulting problem can be mapped to a Hamiltonian whose groundstate corresponds to the optimal solution.\n", - "This notebook shows how to use the Variational Quantum Eigensolver (VQE) or the Quantum Approximate Optimization Algorithm (QAOA) to find the optimal solution for a given set of parameters." + "This notebook shows how to use the Variational Quantum Eigensolver (VQE) or the Quantum Approximate Optimization Algorithm (QAOA) to find the optimal solution for a given set of parameters.\n", + "\n", + "Experiments on real quantum hardware for this problem are reported for instance in the following paper:\n", + "
\n", + "Improving Variational Quantum Optimization using CVaR. Barkoutsos et al. 2019." ] }, { @@ -190,26 +194,26 @@ "name": "stdout", "output_type": "stream", "text": [ - "Optimal: selection [0 0 1 1], value -0.0026\n", + "Optimal: selection [1 1 0 0], value -0.0068\n", "\n", "----------------- Full result ---------------------\n", "selection\tvalue\t\tprobability\n", "---------------------------------------------------\n", - " [0 0 1 1]\t-0.0026\t\t1.0000\n", - " [1 1 1 1]\t15.9996\t\t0.0000\n", - " [0 1 1 1]\t3.9984\t\t0.0000\n", - " [1 0 1 1]\t3.9985\t\t0.0000\n", - " [1 1 0 1]\t4.0000\t\t0.0000\n", - " [0 1 0 1]\t-0.0011\t\t0.0000\n", - " [1 0 0 1]\t-0.0011\t\t0.0000\n", - " [0 0 0 1]\t3.9978\t\t0.0000\n", - " [1 1 1 0]\t4.0017\t\t0.0000\n", - " [0 1 1 0]\t0.0006\t\t0.0000\n", - " [1 0 1 0]\t0.0006\t\t0.0000\n", - " [0 0 1 0]\t3.9995\t\t0.0000\n", - " [1 1 0 0]\t0.0021\t\t0.0000\n", - " [0 1 0 0]\t4.0010\t\t0.0000\n", - " [1 0 0 0]\t4.0011\t\t0.0000\n", + " [1 1 0 0]\t-0.0068\t\t1.0000\n", + " [1 1 1 1]\t15.9945\t\t0.0000\n", + " [0 1 1 1]\t3.9954\t\t0.0000\n", + " [1 0 1 1]\t4.0000\t\t0.0000\n", + " [0 0 1 1]\t0.0010\t\t0.0000\n", + " [1 1 0 1]\t3.9926\t\t0.0000\n", + " [0 1 0 1]\t-0.0065\t\t0.0000\n", + " [1 0 0 1]\t-0.0017\t\t0.0000\n", + " [0 0 0 1]\t3.9993\t\t0.0000\n", + " [1 1 1 0]\t3.9951\t\t0.0000\n", + " [0 1 1 0]\t-0.0039\t\t0.0000\n", + " [1 0 1 0]\t0.0007\t\t0.0000\n", + " [0 0 1 0]\t4.0017\t\t0.0000\n", + " [0 1 0 0]\t3.9942\t\t0.0000\n", + " [1 0 0 0]\t3.9990\t\t0.0000\n", " [0 0 0 0]\t16.0000\t\t0.0000\n" ] } @@ -252,27 +256,27 @@ "name": "stdout", "output_type": "stream", "text": [ - "Optimal: selection [0 1 1 0], value 0.0006\n", + "Optimal: selection [0 1 1 0], value -0.0039\n", "\n", "----------------- Full result ---------------------\n", "selection\tvalue\t\tprobability\n", "---------------------------------------------------\n", - " [0 1 1 0]\t0.0006\t\t0.7038\n", - " [1 0 0 1]\t-0.0011\t\t0.2120\n", - " [1 0 1 0]\t0.0006\t\t0.0272\n", - " [0 1 0 1]\t-0.0011\t\t0.0251\n", - " [1 1 0 0]\t0.0021\t\t0.0167\n", - " [0 0 1 1]\t-0.0026\t\t0.0151\n", - " [1 0 0 0]\t4.0011\t\t0.0000\n", - " [0 1 1 1]\t3.9984\t\t0.0000\n", - " [0 0 0 1]\t3.9978\t\t0.0000\n", - " [1 0 1 1]\t3.9985\t\t0.0000\n", - " [0 1 0 0]\t4.0010\t\t0.0000\n", - " [1 1 1 0]\t4.0017\t\t0.0000\n", - " [1 1 0 1]\t4.0000\t\t0.0000\n", + " [0 1 1 0]\t-0.0039\t\t0.8805\n", + " [0 0 1 1]\t0.0010\t\t0.1186\n", + " [1 1 0 0]\t-0.0068\t\t0.0008\n", + " [1 0 0 1]\t-0.0017\t\t0.0001\n", + " [1 0 1 0]\t0.0007\t\t0.0001\n", + " [0 1 0 1]\t-0.0065\t\t0.0000\n", + " [0 0 0 1]\t3.9993\t\t0.0000\n", + " [1 1 0 1]\t3.9926\t\t0.0000\n", + " [0 1 0 0]\t3.9942\t\t0.0000\n", + " [1 0 1 1]\t4.0000\t\t0.0000\n", + " [1 1 1 1]\t15.9945\t\t0.0000\n", + " [1 0 0 0]\t3.9990\t\t0.0000\n", + " [0 0 1 0]\t4.0017\t\t0.0000\n", + " [0 1 1 1]\t3.9954\t\t0.0000\n", " [0 0 0 0]\t16.0000\t\t0.0000\n", - " [0 0 1 0]\t3.9995\t\t0.0000\n", - " [1 1 1 1]\t15.9996\t\t0.0000\n" + " [1 1 1 0]\t3.9951\t\t0.0000\n" ] } ], @@ -336,27 +340,27 @@ "name": "stdout", "output_type": "stream", "text": [ - "Optimal: selection [1 1 0 0], value 0.0021\n", + "Optimal: selection [0 0 1 1], value 0.0010\n", "\n", "----------------- Full result ---------------------\n", "selection\tvalue\t\tprobability\n", "---------------------------------------------------\n", - " [1 1 0 0]\t0.0021\t\t0.1667\n", - " [1 0 1 0]\t0.0006\t\t0.1667\n", - " [0 1 1 0]\t0.0006\t\t0.1667\n", - " [1 0 0 1]\t-0.0011\t\t0.1666\n", - " [0 1 0 1]\t-0.0011\t\t0.1666\n", - " [0 0 1 1]\t-0.0026\t\t0.1666\n", - " [0 0 0 0]\t16.0000\t\t0.0000\n", - " [1 1 1 1]\t15.9996\t\t0.0000\n", - " [1 1 1 0]\t4.0017\t\t0.0000\n", - " [1 0 0 0]\t4.0011\t\t0.0000\n", - " [0 1 0 0]\t4.0010\t\t0.0000\n", - " [1 1 0 1]\t4.0000\t\t0.0000\n", - " [0 0 1 0]\t3.9995\t\t0.0000\n", - " [1 0 1 1]\t3.9985\t\t0.0000\n", - " [0 1 1 1]\t3.9984\t\t0.0000\n", - " [0 0 0 1]\t3.9978\t\t0.0000\n" + " [0 0 1 1]\t0.0010\t\t0.1668\n", + " [1 0 1 0]\t0.0007\t\t0.1668\n", + " [1 0 0 1]\t-0.0017\t\t0.1667\n", + " [0 1 1 0]\t-0.0039\t\t0.1666\n", + " [0 1 0 1]\t-0.0065\t\t0.1665\n", + " [1 1 0 0]\t-0.0068\t\t0.1665\n", + " [0 0 1 0]\t4.0017\t\t0.0000\n", + " [1 0 1 1]\t4.0000\t\t0.0000\n", + " [1 1 1 1]\t15.9945\t\t0.0000\n", + " [0 0 0 1]\t3.9993\t\t0.0000\n", + " [1 0 0 0]\t3.9990\t\t0.0000\n", + " [0 1 0 0]\t3.9942\t\t0.0000\n", + " [1 1 0 1]\t3.9926\t\t0.0000\n", + " [0 1 1 1]\t3.9954\t\t0.0000\n", + " [1 1 1 0]\t3.9951\t\t0.0000\n", + " [0 0 0 0]\t16.0000\t\t0.0000\n" ] } ], @@ -406,9 +410,9 @@ ], "metadata": { "kernelspec": { - "display_name": "qiskit_master", + "display_name": "Python 3", "language": "python", - "name": "qiskit_master" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -420,7 +424,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.1" + "version": "3.7.1" } }, "nbformat": 4, diff --git a/qiskit/finance/simulation/asian_barrier_spread_pricing.ipynb b/qiskit/finance/simulation/asian_barrier_spread_pricing.ipynb index 0442e31aa..023ab7735 100644 --- a/qiskit/finance/simulation/asian_barrier_spread_pricing.ipynb +++ b/qiskit/finance/simulation/asian_barrier_spread_pricing.ipynb @@ -52,8 +52,10 @@ "
\n", "$$\\mathbb{E}\\left[ P(S_1, S_2) \\right].$$\n", "
\n", - "The approximation of the objective function is explained in detail in the following paper:
\n", - "Quantum Risk Analysis. Woerner, Egger. 2018." + "The approximation of the objective function and a general introduction to option pricing and risk analysis on quantum computers are given in the following papers:\n", + "\n", + "- Quantum Risk Analysis. Woerner, Egger. 2018.\n", + "- Option Pricing using Quantum Computers. Stamatopoulos et al. 2019." ] }, { @@ -140,7 +142,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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CXEUaUGUvYCfSJNXXSPpkF/uNzpr6TJy/aG5nm5mZWf1dDxyWjZq5FTArIl6VNEzSIABJK5L6WHf70K5P1NyZmZm1CknLAzeRauIO6Wbzo4GNgTUi4s2s7HZJGwLfB/Yst1PWZGgcwLIDV/Gw2WZmdSLpcmAksGI2L++pZP2lI+ICUsuL3YDngHeAI7NdPwZcKGkRqULux5W0yHByZ2Zm1iQkLQXcAAwEdo+It7vZZSPg5aLEruAfwHZ1CNHMzKoQEV3OV5qNkvm1MuX3AptVez43yzQzM2sCkgaQmliuD+waEa9XsNvLwHBJw0rKP00aaMXMzPoQ19yZmZk1h/NITXNOBJbP+l4UPBIR8yRNAIiIHbLyy4DvADdKOpPUpOcQYAvgCw2L3MzMmkLDa+4krSfpQkmPSlqYjfxSyX7LSrpY0kxJsyRdKmmFOodrZmbWKKOy17HAfSXLatm6/tkCQES8AmwPvAlcSKr52xDYLyL+0piwzcysWeRRc7cJ6cnk/aQ+BZX6A+mGdQywCPgJcB3w2VoHaGZm1mgRMbyCbUaWKXsY2LUOIZmZWYvJI7n7c0T8CUDS1cCK3e0gaWtgZ2C7iLg7K5sKPCBpx4i4vZ4Bm5mZmZmZNbuGN8uMiOqnfk9PJP9VSOyy4/wdeBE/rTQzMzMzM2uZAVU2Ap4pU/50ts7MOhMBjz8O//pX3pH0yrBHH4X33ss7jN4bOBC22QaWWCLvSMzMzKzNtEpyN4zUWbzUTGCdcjtIGg2MBlhllVXo6OioW3AFc+bMach5Gs3X1VoK17XEjBmscvvtrHrzzSz94ot5h9VrH887gBp6+jvf4V877QS0/9+hmZmZNU6rJHcAUaZMnZQTEeOAcQAjRoyIkSNH1i+yTEdHB404T6P5ulrI/Pk8ceaZbPrgg3DjjbBgAWy5JXzrW7D55nlH1ysPP/wwn/rUp/IOo3dmz4bdduNjq6zCx7K/vbb8O6R9r8vMzKyZtUpyNxNYqUz5cpSv0TPre374Qxgzhk3feANWXRW+8Q04/HDYeOO8I6uJ2e+9B9tum3cYvTNnTnp999184zAzM7O21CrJ3TOUn/JgI9J0CGZ924MPwve+B6NG8dj227P5ySfDgFb5792HDB6cXufNyzcOMzMza0sNHy2zh24CVpX0H4UCSSNI/e1uyi0qs2YxdiwMHQpXXcWMrbZyYtesBgyAfv2c3JmZmVldNPwboKSlSJOYA3wEWEbSftn7GyPiHUnPAXdFxNEAEXGfpFuA30k6mQ8mMf+b57izPm/aNPjDH+C442CZZfKOxrozaJCbZZqZmVld5PF4f2XgqpKywvu1gZdIcfUv2eZA4JfARaQaxxuAE+oWpVmrOP98WLgQjj8+70isEoMHu+bOzMzM6qLhyV1EvEQa5bKrbYaXKXsTODJbzAxg7ly44ALYc09Yp+ysINZsBg1ycmdmZmZ10Sp97sysnMsugzfegJNOyjsSq5SbZZqZmVmdOLkza1URaSCVzTeH7bbLOxqrlJtlmpmZWZ14SD2zVnXnnfD443DRRaAuWzpbM3GzTDMzM6sT19yZtaqxY2GlleCgg/KOxKrhZplmZmZWJ07uzFrRc8/Bn/8Mxx77wcTY1hrcLNPMzMzqxMmdWSs6++w0IfZXvpJ3JFYtN8s0MzOzOnFyZ9ZqZs+Giy+GAw6A1VbLOxqrlptlmpmZWZ04uTNrNRddBG+95ekPWpWbZZqZmVmdOLkzayULF8JZZ8F//Ad8+tN5R2M94WaZZmZmVidO7sxayQ03wIsvwokn5h2J9ZSTOzMzM6sTJ3dmrWTMGFhrLfjiF/OOxHrKfe6sE5L2l3S9pKmS5kh6SFJFc51I+pykuyS9LenN7Oe16h2zmZk1Fyd3Zq3i0UehowOOOy6NlGmtyX3urHPfAOYAXwf2BO4ELpN0fFc7SdoFuB14NNvvEOA+wPOkmJn1Mf6GaNYqxo6FpZaCY47JOxLrDTfLtM7tERFvFL2/Q9LqpKTv7HI7SFoC+BXw04j4btGqG+oXppmZNSvX3Jm1gtdfh0svhSOOgGHD8o7GemPQIJg/HxYtyjsSazIliV3BI8DKXey2E7AGcG5dgjIzs5bi5M6sFVx4YUoITjgh70istwZnLeXmz883DmsV2wBPdbF+S2A6sJWkZyUtkPSEpD0aE56ZmTUTJ3dmzW7ePDjvPNh1V9hww7yjsd4aNCi9ummmdUPSDsBedF0rtyowBBgH/AzYhZQMXitps7oHaWZmXZK0i6RJkp6T9O0y6z8qaYKkxyR1SFqjaN3h2YO7ZyUdXsn5nNyZNbsrr4TXXvP0B+2ikNx5xEzrgqThwGXAnyJifBeb9iMNnPK9iLgwIm4HDgJeBP5fF8cfLWmipInzF82tWdxmZvYBSf1JD+h2BTYGDpK0cclmPwN+FxGbA6cDP8r2XR44ldRCYwvgVEnd9s1xcmfWzCLS9Acf+xiMGpV3NFYLhWaZrrmzTmQ39JuAyaSRL7syI3u9s1AQEQuBu0hfJMqKiHERMSIiRgzst2QvIzYzs05sATwXES9ExHzgClKLjGIbAxOyn+8sWr8zcFtEzIiImcBtpNYZXXJyZ9bM7rkHHn441dpJeUdjteBmmdYFSUuRRrocCOweEW93s8vTnR0K8Kg9Zmb5+gjwStH7KVlZsUeBfbOf9waGSlqhwn0X46kQzJrZmDFpdMxDD807EqsVN8u0TkgaAFwFrA9sGxGvV7DbLcACYAdgUnac/sB2QEd9IjUzaz/TFy7NJTO36cGeV64oaWJRwbiIGJf9XO7JfJS8Pxk4R9IRwN3AVNLneiX7LsbJnVmzevlluPZa+Na30vx21h7cLNM6dx6wG3AisLykrYrWPRIR8yRNAIiIHbLXVyWdC/xYkoDngNGk6RF+1NDozcz6pjciYkQn66YAaxa9XwOYVrxBREwD9gGQtDSwb0TMkjQFGFmyb0d3wTi5M2tW55yTmmJ+7Wt5R2K15GaZ1rlCx9qxZdatDbwE9C+z7lvA28D3gOVJc+PtHBHP1yFGMzOr3IPA+pLWJtXIHQgcXLyBpBWBGRGxCPgf4KJs1S3A/xUNojIqW98lJ3dmzWjOHPjVr2DffWHNNbvf3lqHkzvrREQMr2CbkWXK3gO+my1mZtYkImKBpONIiVp/4KKIeFLS6cDEiLieVDv3I0lBapb5tWzfGZLOICWIAKdHxIzFTlLCyZ1ZM/rtb2HWLDjppLwjsVorNMt0nzszM7O2FxE3AjeWlJ1S9PPVwNWd7HsRH9TkVcSjZZo1m0WL4KyzYIstYKutut/eWotr7szMzKxOXHNn1mxuvhn++U+49FJPf9COnNyZmZlZnbjmzqzZjB0Lq68O++2XdyRWD26WaWZmZnXi5M6smTz5JNx6K3z1qzBwYN7RWD245s7MzMzqxMmdWTM566xUszN6dN6RWL04uTMzM7M6cXJn1iymT4dLLoFDDoGVVso7GquXQnLnZplmZmZWY07uzJrFr34Fc+fCCSfkHYnVU6HPnWvuzMzMrMac3Jk1g/feg3POgR12gM02yzsaq6cBA6BfPyd3ZmZmVnOeCsGsGfzxjzB1KlxwQd6RWCMMGuRmmWZmZlZzTu7MmsGYMbDeerDbbnlHYo0weLBr7sxqaO6mH8k7BLOaWfKJqXmHYC3MyZ1Z3h54AO6/P42U2c8tpfuEQYOc3FnTc8Jklo+5m37ECZ71mJM7s7yNHQvLLANHHJF3JNYobpZpTWTRkks4kTNrMk7wrKcantxJ2hg4G9gaeBP4NfD9iFjYzX4jgP8DPg0IeBj4bkQ8UN+IzepoyhS46io4/ngYOjTvaKxR3CzTrNdmbjgw7xDM6mLYpPmAEzzrmYYmd5KGAbcDTwF7AesCPyeN2vm9LvZbM9vvYeCwrPhbwK2SNo+Il+sZt1ndnHceLFqUkjvrO9ws0/oAJ19mPTNzw4FO8KzHGl1zdyywJLBPRMwGbpO0DHCapDOzsnJ2B4Zm+70JIOle4A1gN+D8+oduVmPvvAPjxsFee8Haa+cdjTWSkztrYn09KXtr3UV5h2B93NDn+znBsx5rdHK3K3BLSRJ3BfATYDvgz53stwSwAJhTVDYnK1Md4jSrv0svhenT4cQT847EGm3wYPe5s6axcLBaLqFzAmbt7K11F72f4EFqpukEzyrV6ORuI+CO4oKImCzpnWxdZ8ndNcDpwM8l/TArOwWYCVxVp1jN6iciDaTyiU/A5z6XdzTWaIMGwdtv5x2FWW6cnJl1rZDgwQfNNAsDHznJs640OrkbRhpEpdTMbF1ZETFN0vbADcAJWfGrwM4R8e+aR2lWbxMmwJNPwvjxIFc+9zmDBsGMGXlHYdZrrZikLb32rLxDMOvSnBeXBconeOBmmta1PKZCiDJl6qQ8rZRWA64GHgKOyYq/BvxF0jYRMbnMPqOB0QCrrLIKHR0dvQy7e3PmzGnIeRrN11V7m/3v/zJ02DDuW201osYx+N+r+W3y1lssNX06D3Z0tNV1FWvX6+oLmj1hc3Jm7W7ptWc5wbMea3RyNxNYrkz5spSv0Sv4FinW/SLiPQBJdwDPAifzQW3e+yJiHDAOYMSIETFy5MheBV6Jjo4OGnGeRvN11dizz6ZJy089le1Gjar54f3v1QLWWAOmTmXkyJHtdV1F2vW62tHCQfkmdK2QrI1aa1LeIVgfcevkDQEneNZzjU7uniH1rXtfNs3BkGxdZzYCniwkdgARMV/Sk6TpFMxax1lnwcCBcOyxeUdiefFomVaGpP2BQ0nzuS4LTAJ+FhGXV3GM60hTDR0fEefUJdAKNEvC5qTMWk3hb/bWyRs6wbMeaXRydxPwLUlDI+KtrOwAYC5wVxf7vQzsJmlgRMwHkDQI2JTOB2Exaz5vvgkXXwwHHgirrpp3NJaXQYM8WqaV8w3gReDrfDDVz2WSVoyIs7vbWdIoYKv6hph/4uaEzfqCUWtNej/Bg9QPzwmeVaLRyd0FpCaUf5T0E2Ad4DTgF8XTI0h6DrgrIo7Oin5N6mt3raTzSH30vgasRtb00qwlXHRRGiXR0x/0bYMHu+bOytkjIt4oen+HpNVJSV+XyZ2kJYCxwHdJ98weyyt5yztpO3TYvbme36zgkpnbAB8kePBBM81CE2rPhWedaWhyFxEzJe0AnEOqcXsT+CUpwSuNq3/Rfg9J2gU4FbgkK34c2CkiHq133GY1sWBBapL5uc/Bpz6VdzSWJzfLtDJKEruCR0jNLLtzIqkVzMVUmdz1H7Sw7gldoxM3J2rWyg4ddm+XCR54LjzrXMNHy4yIp4DPd7PN8DJlE4AJdQrLrP6uvx5efhl+8Yu8I7G8DRoE8+fDouYeldCawjbAU11tIGlV4H9JNX+L1GTTqzixM2scJ3jWL+8AzPqMsWNh+HDYq5KH8NbWBg9Or/Pn5xuHNbWspctewLndbHomcEtE3F3/qKpXqHVolEKNh5lZX+TkzqwRHn4Y7r4bjj8e+vfvfntrb4MGpVc3zbROSBoOXAb8KSLGd7Hd1sB+pCmDqjn+aEkTJU1cMOudXkRaGSd4ZmaN4eTOrBHGjoUhQ+Coo/KOxJqBkzvrgqTlSaNLTwYO6WbzMcCFwCxJy0kqzCW7pKRlO9spIsZFxIiIGDFg2aVqEnd3nOCZmdWfkzuzenvtNbjiCjjySFhuue63t/ZXaJbp6RCshKSlgBuAgcDuEfF2N7tsCJwEzCxaIDXVnF6vOHsqjwTPSZ6Z9SVO7szq7YILUt+qE07IOxJrFq65szIkDQCuAtYHdo2I1yvY7QvA9iULwFnADpWcd+G8xjYVb3SCB67FM7O+w8mdWT3Nmwfnnw+77w7rr593NNYsnNxZeeeRJi4/A1he0lZFyyAASRMkvT9ydET8LSI6ipds1bMRcVelJy4Mr94oTvDMrK+QtIukSZKek/TtMut/Kekf2fJPSW8WrVtYtO76Ss7X8KkQzPqUK66A11+Hk07KOxJrJm6WaeWNyl7Hllm3NvASRXPA1tqcF5dt6ATmt07esOHTJFwycxtPlWBmDSOpP2nE452AKcCDkq7PpoYDICK+XrT98cAniw4xNyI+Uc05XXNnVi8RMGYMbLIJ7FBR6yjrK1yR3JeIAAAgAElEQVRzZ2VExPCIUCfLS9k2IyNiZDfHUUSc05MY8qjB80ArZtbGtgCei4gXImI+cAVpipvOHARc3psTOrkzq5e774Z//ANOPBGabFJhy5mTO2tijU7wwCNpmlnb+gjwStH7KVnZYiR9lNRK446i4sHZtDX3S/piJSd0s0yzehk7FlZYAQ7pbiRz63OKm2Uu1Zhh6M2q0egmmtD4ZppuomlmxWbPH9zTB00rSppY9H5cRIzLfi73dD86Oc6BwNURsbCobK2ImCZpHeAOSY9HxPNdBeOaO7N6ePFF+NOfYPRoWHLJvKOxZuOaO2sBc15ctu0HWnENnpnVwBuFeUOzZVzRuinAmkXv1wCmdXKcAylpkhkR07LXF4AOPtwfrywnd2b1cPbZ0K8ffPWreUdizcjJnbWQvpDgOckzszp5EFhf0tqSBpISuMVGvZS0ITAMuK+obFjRSMkrAtsCT5XuW8rJnVmtvfUW/OY3sP/+sMYaeUdjzcijZVqLafcED1yLZ2a1FxELgOOAW4CngSsj4klJp0vas2jTg4ArIqK4yebHgImSHgXuBH5cPMpmZ9znzqzWxo+H2bPTQCpm5bjmzlqQp0owM6teRNwI3FhSdkrJ+9PK7HcvsFm153PNnVktLVoEZ50FW20FW26ZdzTWrJzcWYtyDZ6ZWXNzcmdWSzfeCM8950nLrWuF5M7NMq0FeS48M7Pm5eTOrJbGjIGPfAT22SfvSKyZFfrcuebOWpTnwjMza05O7sxq5YknYMIEOO44WGKJvKOxZjZgQBpN1cmdtTAneGZmzcfJnVmtjB2b5rT78pfzjsRawaBBTu6s5TnBMzNrLk7uzGrhjTfg97+HQw+FFVbIOxprBYMHu8+dtQVPdm5m1jyc3JnVwrhx6Yu6pz+wSrnmru1I2lvSCdlktMXlx+UVUyP1hQTPSZ6ZNTsnd2a9NX8+nHsujBoFG2+cdzTWKpzctRVJPwZOBNYDbpNUPGTuUflE1XjtnuCBa/HMrLk5uTPrrauvhmnTXGtn1XGzzHazO7BjRJwAfBLYU9JPs3XKL6zGc4JnZpYfJ3dmvRGRpj/YYAPYZZe8o7FW4pq7dtMvIhYARMR0YBdguKTf0AfvtZ4Lz8wsH33uhmNWU/ffDw8+mGrt+vm/k1XByV27eVXSpwpvImI+cAAQwKa5RZUjj6RpZtZ4/jZq1htjx8Kyy8Jhh+UdibUaN8tsN0cA04oLImJRRBwDfDaXiJqAEzwzs8ZycmfWU6+8kvrbffnLsPTSeUdjrcY1d20lIqZExGudrLu30fE0Eyd4ZmaN4+TOrKfOPTf1ufva1/KOxFqRk7uWJGmspL+XKR8g6bOSdpK0TB6xNTPPhWdm1hhO7sx64p130tx2e+8Nw4fnHY21IjfLbFU7AHcWF0gaAkwEOoCbgamSjmh4ZC2gLyR4TvLMLE9O7sx64pJLYOZMOOmk7rc1K8c1d61qTaC0meUJwObAeOBg4M/AryVV1ddO0v6Srpc0VdIcSQ9JOqibfTaUdK6kpyW9I+mFrHZxuWrO3UjtnuCBa/HMLD9O7syqFZEGUvn0p2HbbfOOxlqVk7tWtQQwp6TsYGBKRBwdEX+IiEKC9/+qPPY3smN/HdiTVEN4maTju9hnJ2Bb4HxgN+AHwP7ArZIqusf3z+HP0AmemVl9OLkzq9Ztt8HTT6fpD9Sn5ia2WnJy16qeAbYsvJG0FrAJcH3Jdr8Htq7y2HtExMERcWVE3BERJwOXk5K+zlwOfDIizoqIjoi4iDRy52eoYpTOoc/3Y+jzjf1K4ATPzKz2nNyZVWvMGFh1VfjSl/KOxFqZ+9y1qouAkyWNkrQE8E3SXHbXlWz3OlDVMLoR8UaZ4keAlbvYZ3pERJl96Gq/zvSFBM8DrZhZO3NyZ1aNZ56Bm26Cr3411byY9ZRr7lrVucDtpIFT3gWOBx4HJpRsN5yU4PXWNsBTPdiHHuwHtH+CBx5J08zal5M7s2qcfTYMHAj/9V95R2KtbtAgmD8/9eG0lhHJl4DdgTOBU4Cdy9SefQl4ojfnkrQDsBcpoax0n6WAHwN3RcSTPT23E7zac4JnZo3g5M6sUjNnwvjx8J//CStX3drJ7MMGDwag33vv5RyI9URE3BQR/xMRP4iIfxWvk7QyMBS4sqfHlzQcuAz4U0SMr3AfAb8hNcc8qpttR0uaKGnigrlvl93GCV7tOcEzs3preHInaWNJE7Ihm6dJOl1S/wr33UfSg5LmSpou6eZsfiGz+vv1r9P8dieemHck1g6yZr2aPz/nQKzWIuL1iBhZaVJWStLywE3AZOCQKnb9CbA38MWIeKGbGMdFxIiIGDFgyc5vo3kkeO0+0IrnwjOzemrop7akYaS+CkFqanI6qTP69yvY9xjSU8ybgF2BY4BngQH1itfsfQsWwDnnwMiR8PGP5x2NtYMsuXPNnRXLmlXeAAwEdo+I8tVqi+/3deBk4LCI+GstY2p0ggceSdPMrKca/Yl9LLAksE9E3BYRF5ASu29IWqaznSStCPwSOD4iTsmGe742Io6PiFmNCd36tOuug8mTPWm51U6hWaZr7iwjaQBwFbA+sGtEVDQgi6SDgZ8D34yIHjcF7YoTvPpwgmdmtdboT+tdgVsiYnZR2RWkhG+7LvYrjDn/23oFZtalMWNg7bXhC1/IOxJrF665s8WdR5qI/AxgeUlbFS2DALJuDe+PzClpO2A8cCtwX8k+a9QyOM+FVx9O8Myslhqd3G1EmgD2fRExGXgnW9eZLYFJwNGSpkh6T9IDkvyJaPU3cSLccw+ccAL0r6h7qFn3nNzZ4kZlr2OB+0qW1bJ1/bOlYHtgCWDnMvscU48g+0KC54FWzKxVNTq5Gwa8WaZ8ZrauM6sCGwLfA/4b2AN4G7hZ0iq1DtLsQ8aOhaFD4aguB58zq46bZbaNbKCwQyV9R9KqWdl6koZWc5yIGB4R6mR5KdtmZESMLNrntC72Oa2Gl/kh7Z7ggUfSNLPWlMdgJOUmdVIn5QX9gKWB/SPiZgBJ9wIvA8cB/7vYAaXRwGiAVVZZhY6Ojt5FXYE5c+Y05DyN1peva+D06Wx1xRVM23NPnnv44cYE1kt9+d+rlQx75hk+Drw7a1ZbXVdBu/17lSNpaeAiYF9gAemeejPwGvB/pNEuT84twDob+nw/3lp3UcPON+fFZVl67cZ2s7918oaMWmtSw853ycxtOHTYvQ07n5m1n0YndzOB5cqUL0v5Gr2CGdlrR6EgImZLegjYuNwOETEOGAcwYsSIGDlyZA/CrU5HRweNOE+j9enrOuUUWLiQNX7yE9ZYb72GxNVbffrfq5VIAAwZMIBPtNN1Zdru36u8XwDbADsC9wDvFq27kZTYtW1yB07w6sEJnpn1RqObZT5DSd86SWsCQyjpi1fiaVLNnkrKBTTurmJ9y7vvwgUXwB57QIskdtZC3CyzHewD/HdE3AksLFn3MvDRxofUeJ4Lr/bcRNOsfUjaRdIkSc9J+nYn23xJ0lOSnpR0WVH54ZKezZbDKzlfo5O7m4CdS/ohHADMBe7qYr8bSInc9oUCScsCnwYerUOcZnD55fDvf3vScqsPD6jSDpYEpneybiiLJ3xty1Ml1J4nOzdrfZL6A+eSZgzYGDhI0sYl26wP/A+wbURsApyUlS8PnEoaWHIL4NRszvAudftpLOkwSStUeS2duQCYB/xR0o5Zv7jTgF8UT4+QZba/KbyPiInAn4DfZBns7sD1wHukX5hZbUWk6Q822wy237777c2q5eSuHTwIHNbJuv2APtW2zglefTjBM2tpWwDPRcQLETGfNAXcXiXbfBk4NyJmAhTNcbozcFtEzMjW3Qbs0t0JK/kkvhhYF0DSQklbVHQpZWSB7UAaxvnPpAnMf0nKSosN4MNDPQMcAlxH6uNwNSmx+3zhF2FWUx0d8NhjadJylbYGNquBrFmm3CyzlX0P2EfS7aRpBwLYTdIlwP4sfm9re07w6sMJnlnL+gjwStH7KVlZsQ2ADSTdI+l+SbtUse9iKhlQZSawevZzd6NadisingI+3802w8uUzQG+ki1m9TV2LKy4Ihx8cN6RWLsq1Nw5uWtZEfE3STsAPwbOId0jvw/cD+wYEQ/mGV9eCgleOw+0UkjwPNCKWftYOK9/Tx8WrShpYtH7cdnAjrD4eCGweC41AFgfGAmsAfxV0qYV7ruYSpK724FLJE3KDjhe0tudbRwRPa7ZM2sKzz8P118P3/3u+7UrZjXnZpltISLuAT4raUmyuVwj4p2cw2oKHkmz9pzgmTWlNyJiRCfrpgBrFr1fA5hWZpv7I+I94MUs51o/Kx9Zsm9Hd8FU0n7iKNKTyEdIGeSLwJNdLGat7eyzoX9/+Ioria2OnNy1PEkfl7QbQETMjYhphcRO0m6SNs83wvx5svPacxNNs5byILC+pLUlDQQOJI0bUuw6skEjJa1Iaqb5AnALMErSsGwglVFZWZe6rbnLblQ/y064I/DdiPAIldaeZs+Giy6CAw6A1VfvfnuznvJUCO3gl8BfSXPalfoM8E1SP/M+zTV4tecaPLPWEBELJB1HSsr6AxdFxJOSTgcmRsT1fJDEPUUaZflbETEdQNIZpAQR4PSImLH4WT6sktEyF0r6TPa2A5jdxeZmre3ii+Gtt9JAKmb1NGAA9OvnmrvW9inS5OXl3Ad8soGxNDXPhVd7rsEzaw0RcWNEbBAR60bED7OyU7LEjki+EREbR8RmEXFF0b4XRcR62XJxJeer5NN2PjAo+/kwYKXqLsmsRSxcCGedBdtsAyM6azptVkODBiEnd62sPzCkk3VDgIENjKXpeSTN2vNceGZWqpIBVZ4CTpN0HanP3X6SOvvmGxFxfs2iM2ukv/wFXngBfvzjvCOxvmLwYDfLbG0PAqOBa8usGw1MLFPepzW6iSbkM5JmI5togptpmtkHKknujgcuJPUtCODkLrYNwMmdtaYxY2DNNWHvvfOOxPqKQYOc3LW204DbJT0A/BZ4DViN1Mrl48BO+YVWuf7v9mqGo6o5wasPJ3hmBhU0y4yIe7P2n0uQau62ioh+nSylE4+btYbHHoM774Tjjkt9ocwaYdAg97lrYRFxN2n0skXA2cDVwFhgAbBTRPw1x/CqMmxSYx8yDH2+X9uPpOnJzs0sD9V+sm5PaqZp1l7GjoWlloJjjsk7EutL3Cyz5UVER0RsDQwlzWW0TERs20qJXUGjEzxo/6kSbp28oQdaMbOGqupTNSLuiog5kraU9E1JP8xet6xXgGZ19/rrcOmlcPjhsPzyeUdjfYlr7tpGRLwTEVNbfQJzJ3j14QTPzBqlqvZnkoYAVwE7k+ZhmA6sAPSXdDOwf6vf2KwPuvBCmDcPjj8+70isr/FomS1H0t+BIyLiKUkPkvqadyoitmhMZLUzbNJ8Zm7Y2IE+PRde7bkPnlnfVO3jsjOBrUmzqw+OiNWAwdn7rYGf1DY8szqbPx/OOw922QU+9rG8o7G+ZvBg19y1nieBuUU/d7e0pGGT5ufSD6+RXINnZu2o2pEj9gX+OyKuKhRExCLgKknDgNNJo2uatYYrr4TXXoMTT8w7EuuLBg2i34wZeUdhVYiII4t+PiLHUBqi0bV4edTgAW09kmYhwXMtnlnfUO1jsmWBVzpZ9wqwTO/CMWugiDT9wUYbwahReUdjfZGnQmhZkpaQtK2k1fOOpd7avQYPPJKmmbWPaj9BHwW+IknFhdn7r2TrzVrCMk88AQ89lGrt+jX+y4SZm2W2tIXAHUDN2nNL2l/S9ZKmSpoj6SFJB1Ww3yBJP5f0uqS3Jf1F0vBaxQVO8OrBCZ6Z1UO1n57fIQ2m8oykH0v6uqQfAU+T5vr5Tq0DNKuXNa65BpZbDg49NO9QrK9yzV3LyrokPAusUsPDfgOYA3wd2BO4E7hMUnfdHc4CjgBOBvYDVgRukzS4hrF5Lrw6cIJnZrVW7VQIdwCfBB4B9gd+CHwJeBj4VETcWfMIzerh5ZdZ6a9/hdGjYciQvKOxvsqjZba67wKnSNqsRsfbIyIOjogrI+KOiDgZuJyU9JUlaQ3gaODrEfG7iLgJ2Af4KHBIjeJ6n6dKqD3PhWdmtVT1J2ZEPBURB0bEuhGxVPZ6cER4cnNrHeeem16/9rV847C+zfPctbrvkaYD+oekyZIelPT34qWag0XEG2WKHwFW7mK3QofhPxYdZyrwN2DXas5fKSd49eEEz8xqoapPS0k/k7RxvYIxa4g5c+BXv+Lfn/0srLVW3tFYXzZ4sJtltrYngRuA3wETgCeo/VQI2wBdPTzdCJgSEXNKyp/O1tWFE7z6cIJnZr3Vk6kQvi7pIeAi4PKIaOwsoGa99bvfwZtvMmW//bp8HG5Wd665a2n1ngpB0g7AXsBRXWw2DHizTPnMbF3dFBK8dp8qwZOdm1krqbbP3drAjsAzwE+BVyVdJmnHegRnVnOLFsFZZ8FnPsPsTTbJOxrr6wrJXUTekVgVJC0paV9J35R0sKRaDqpSOMdw4DLgTxExvpvNy/0BqZPywvFHS5ooaeJ789/uaZhA+4+kOefFZdt+oBXX4Jm1j570ubszIg4DViNNWL4GcIuklyV9X9I6tQ7SrGZuuQUmTUrTH3x4Rg+zxhucDWY4b16+cVjFsnvck8BVpIecvwcmSarZZJmSlgduAibT/aAoM4HlypQvR/kaPQAiYlxEjIiIEUsM7P2gUu2e4EH7j6R5ycxtnOSZtYEefzpGxJyI+A1wKnAPsCbwP8A/Jf1J0kdrFKNZ7YwZA6utBvvvn3ckZjBoUHp1ctdKzgQWAZ8FlgI2IQ16cmEtDi5pKVI/voHA7hHRXbXaM8CakkoztI2ydQ3jBK/2PFWCmVWrR5+MkoZLOlXSC8CtpHl59geGkubmGQ5cUasgzWriqafg1lvTCJkDG9dHxKxTTu5a0dbA9yLinoh4NyKeBv4LWEvSar05sKQBpBrB9YFdI+L1Cna7NXvdu+g4q5OSz5t6E09POMGrPSd4ZlaNqgZUkXQocCTwOVJzkYuBiyNiStFmN0p6G7i9ZlGa1cJZZ6Uv06NH5x2JWVJolvnuu/nGYdVYDXihpOx5Uh+3VYFXe3Hs84DdgBOB5SVtVbTukYiYJ2kCQETskL1OkfQbYIwkAf8GTgNeJjUZbbhhk+Y3fJAVoK0HWikkeB5oxcy6U+0jr3HAa8DOEbFORJxRktgV/BP4Qa+jM6uVGTPSKJmHHAIrrZR3NGaJa+5aVb1GwCn02xsL3FeyFGoF+2dLsRNI0zH8ArgGmAGMiojcnhp4qoT68EArZtadaj8JV88mLJ/Q1UYR8WpEfL8XcZnV1q9+BXPnpoFUzJqFk7tWdYuk1wsLH9TWTSguz9ZVLCKGR4Q6WV7KthkZESNL9psXEd+IiJUiYkhE7BYRL9biQnvDCV59OMEzs65U1SwzImbWKxCzunnvPTjnHPj852GzzfKOxuwDHi2zFfnBZRU8F159eC48M+tMtZOYI+kA4MvABsDg0vUR4Xmhrblcey1MmQLnnZd3JGYfVqi5c5+7luFWKT2TRz+8Rid4QMP74TnBM7NSVbVfkHQw8FvgOdL8dteThmzuB8wGzql1gGa9NmYMrLsu7L573pGYfZibZVof4pE0a89z4ZlZqWo/+b4FnAF8LXt/XkQcBawNvAG8U8PYzHrv73+H++6DE06Afo2/0Zt1yc0yrY9xgld7nirBzIpV+6m3PnBPRCwEFgLLAETEW8BPgONqG55ZL40dC8ssA0cemXckZotzs0xrAv3mvtfQ8znBqz0neGZWUO0n3iwg+zbCVOBjResErFCLoMxqYupUuPJKOPpoGDo072jMFudmmdYklnxiakPPl0eC1+4jaTrBMzOoPrmbCGye/Xw9cIqkL0s6HPgp8EAtgzPrlfPOg4UL4ThXKFuTcrPMlibpFEmrd7JuNUmnNDqm3mj3BA/af6qEWydv6KkSzPq4aj/lfgRMzn4+Bfg7cB5wManP3ejahWbWC3PnwoUXwl57wTrr5B2NWXlultnqTiUNLlbO6tn6luIEr/Y8F55Z3yZpF0mTJD0n6dtdbLefpJA0Ins/XNJcSf/IlgsqOV9Fn3CSlpS0L7AtMEDSKhHxZkTsBSwNLBcRW0bEC5Ucz6zuLr0Upk+Hk07KOxKzzrlZZqsTEJ2sWwNoyblhneDVnhM8s75JUn/gXGBXYGPgIEkbl9luKHACi7eCfD4iPpEtx1Zyzm4/3SStAzwJXEVqenkJMEnSKICImBcRsys5mVlDRKSBVD7+cfjc5/KOxqxzTu5ajqTDJd0h6Q5SYnd+4X3Rci/we+CufKPtuTwSvHYfaMUJnlmftAXwXES8EBHzgSuAvcpsdwZwJtDrpjyVfLKdCSwCPgssBWwCPAJc2JMTStpY0gRJ70iaJun0LKutdP9+kh7Kqi2/0JMYrM3dcQc88USqtZPyjsasc4U+d26W2UreAaZni0gDjU0vWV4k3TtbuqtCoxM8aP+RNOe8uGzbD7TiufCsD1pR0sSipfiz/yPAK0Xvp2Rl75P0SWDNiLihzLHXlvSIpLskfbaSYAZUsM3WwDcj4p7s/dOS/it7XS0iXq3kRACShgG3A0+RstZ1gZ+TkszvVXiYYyj5pZh9yJgxsPLKcOCBeUdi1rUBA4h+/ZBr7lpGRFxFasmCpIuBM9q5S8KST0xl7qaNveUOmzSfmRsObNj5hj7fj7fWXdSw80FK8pZee1bDznfr5A0Ztdakhp0PUpJ36LB7G3pOs97oP6/HD3zeiIgRnawrV8vwfnN+Sf2AXwJHlNnuVWCtiJgu6dPAdZI26a7FZCVXsBpQeuN6Pgt21Qr2L3YssCSwT0TcFhEXAN8HviFpme52zpLDHwLfrfK81lc8+yz85S9w7LEf1IqYNbFFSyzhZpktKiKOjIgXJK0uad9s9Oh9OhtBs1Ut+cTUtu+H57nw6sM1eGZMAdYser8GMK3o/VBgU6BD0kvAVsD1kkZkXd+mA0TEQ6T8a4PuTljpp1lnHcartStwS0nGeQUp4duugv3PAO4BJtQoHms3Z58NAwbAV76SdyRmFVk0cKCTuxaVdRM4D3iZVJt3IXA18LKkc7Mnsm2jLyR47d4PzwmeWcM9CKwvaW1JA4EDSdPJARARsyJixYgYHhHDgfuBPSNioqSVCl3XsjFQ1mfxCrfFVPopdouk1wsLqZoQYEJxebauKxsBzxQXRMRkUh+GjbraUdLmwJHAyRXGbH3NrFlw8cVw0EGwarWVymb5WLTEEu5z17pOB44CvgMMJz2oHJ69Pwo4Lae46qbdEzxo/4FWPBeeWeNExALgOOAW4Gngyoh4MhtzZM9udv8c8JikR0kPDo+NiBndnbOSPnffr2CbSg0D3ixTPjNb15WzgXMj4jlJw2sYk7WLiy6COXPgxBPzjsSsYuFmma3sMOB7EfGzorLJwE8lBWlY65aayLwSje6H1+g+eND4fniN7oMHje+H5z541ldFxI3AjSVlZe8NETGy6OdrgGuqPV+3yV1E1DK5g/JNPLuaKwhJBwIbAntUepJspJrRAKussgodHR3VRdkDc+bMach5Gq0lrmvhQrY880zmbbYZ/5g9GyqItyWuqwd8Xa1lxIABvP7KKzzVZtfWrv9eJVYGHutk3WPZ+rbkBK/2nOCZWS1UUnNXSzOB5cqUL0v5Gj0kLUGaX+8nQD9JywGFwVeGSBoaEW+V7hcR44BxACNGjIiRI0f2PvpudHR00IjzNFpLXNe118Jrr7HkOedUHGtLXFcP+Lpay5xBg1h5mWVYuc2urV3/vUr8k9R/4tYy6w4EGjs8YYPlkeABbT2SphM8M+utRnf2foaSvnWS1gSGUNIXr8gQ0sgyvyAlhzOBR7N1V5Dm3LO+buxY+OhHYa9y80KaNS8PqNLSfgAcIel2ScdK2lvSf0m6HTg8W9/WPBde7fWVufDMrD4andzdBOwsaWhR2QHAXOCuTvaZA2xfshyUrfsO8J/1CdVaxiOPwF13wfHHp5EyzVqIk7vWFRFXAruQHkKOJfWNOAtYCtglmxOv7TnBq4++kOA5yTOrvUZ/Wl0AzAP+KGnHrF/cacAviqdHkPScpN9AGmUmIjqKF9IwoQCPR8QDjb0Eazpjx8KQIXD00XlHYlY1j5bZ2iLi1ojYmjRS5qrAkhGxTUTclnNoDeUErz7aPcED1+KZ1VpDP6kiYiawA9Af+DNpJM5fAqeWbDog28asa//6F1x+ORxxBCxXrjunWXPzaJntISIWRcTrEdGrDlqS1pN0oaRHJS2U1FHhfiMk3SppuqQZWVPRLXsTS7U82Xl9OMEzs2o0vA1bRDwFfL6bbYZ3s/4l0gib1tddcAHMnw8nnJB3JGY9smjgQHhrsTGhrEVkk9IeAWwBrEaaB/YB4LcR0ZPMYxNgN1ILlYpGDsn6rt8OPEyangHgW8CtkjaPiJd7EEePtftImoUEr50HWikkeB5oxaz1NP4RlFmtzJsH558Pu+0GG2yQdzRmPeJmma1L0seAZ4FzgU2BhdnrucBzkjbuwWH/HBFrRsT+wJMV7rM7MBTYJyL+EhF/AfYGliYlig3X7jV40P6TnYMHWjFrRU7urHX94Q+pWeZJJ+UdiVmPLXKzzFY2DpgFrBsRW0XEnhGxFbBeVn5BtQfsYbPOJYAFpAHICuZkZbm1cnGCV3tO8MysO07urDVFwJgxsPHGsOOOeUdj1mMeLbOljQBOiYjJxYXZ+1OAzzQojmuAd4CfS1pZ0sqk/uwzgVxH7MwjwWv3fnhO8MysK07urDX97W9pCoQTTwS5+6W1rkUDB7pZZut6CRjcybrBwORO1tVUREwjTRO0L/CvbNkH2Dki/t2IGLrikTRrz3PhmVlnnNxZaxozBpZfHg45JO9IzHrl/7d35+FyVNX6x79vEpIwE2ZEkCciruMAACAASURBVDAIAvLTawQZrgRUZgGRSUUB4SIKiNcJnBHkKiIYAgFkUATEiCgKyAwGZRAhIkKEaJgDqEDCEBIIJOv3x66GptPnnO7T1V3ddd7P89TT3dW7ulad09PqvWsvz5bZ044GvlM7K6Wk9wDHAkd1IghJqwGXAFOBHbNlKvA7SWv2sc0hku6UdOf8hfPaHqMTvPYYCgmekzyz5ji5s97z8MPwm9/Apz4FSyxRdDRmLVm42GJpxteIokOx5n0dWAa4VdKTWfmCJ4FbgGWBr0r6c2VpYxxfIs1+vWdEXB0RV5N68RYAX6y3QUScFRHjImLcyGGLtzG01znBa4+yJ3jgXjyzZnS8FIJZy047LQ3F/Mxnio7ErGULR2ZTuM+fD6NGFRuMNevebCnaBsC0iHilsiIi5kuaBqxTXFiLqiR4ZS+V0MkyCVBMqYROlkkAl0owa5STO+stL7wA55wDe+0Fb35z0dGYtWzhYoulKy+95OSux0TEgUXHkHkE2EnSyEptPUmjSGUZLi80sj64Fl7+nOCZGXhYpvWan/4UnnvO5Q+sNF5L7nzeXU+TtISkIyRNkvQNSW9p4XH2lLQnsDqwUuW2pCWyNjMknVu12TnAm4BLJe0saRfgN6Si6me1dmTt41IJ+StiiKYnWjHrLk7urHcsXAgTJ8Jmm6XFrAReG5bp5K4nSDpJ0j9q1i0N/AWYAOxDKoNwt6S3DmIXK5PKF/wSeA+wYdXtlbM2I4DhlQ0iYiqwA6mQ+QXA+cASwAci4u5BxNAxTvDy51IJZkObkzvrHVddBf/8p3vtrFSikty5HEKv2Aa4sGbdF4G3Av8TESuSetEeBr7R7INHxMMRoT6Wh7M2a0XEATXb3RAR742I5bNl64iY0vTRFcAJXv6c4JkNXU7urHdMmACrrw4f/nDRkZjlxsMye85apDID1T4M/D0ifgyQ1ZY7Cdiys6H1Lhc7z58TPLOhycmd9YZp0+D66+Gww6DyZdisBDwss+eMAF7rZpW0PPA24Maadg8Dq3YurN7nUgn5GyrFzp3kmb3OyZ31hlNOgdGj4ZBDio7ELFdvmC3TesE/gPFVt3fJLq+pabcyMKsTAZWJE7z2KHuCB+7FM6twcmfd7+mn4YIL4OMfhxVWKDoas1x5WGbPOQ04WtJESV8DTgQeAq6tabcd3VEDr+c4wWsPJ3hmQ4OTO+t+Z5+dejWOPLLoSMxy52GZvSUiziPNhrkH8BVgOvCh6gLiklYCdgN+W0SMZbD4vY+XfqKVpR8YVvrz8JzgmXWekzvrbq+8AqedBh/4AGy0UdHRmOXOs2X2noj4bkS8OSKWymaovKfm/qciYtWIOKOoGMui7AkelH+iFdfCM+ssJ3fW3S65BJ54wr12VloelmnWPyd4+fNMmmbl5eTOutspp8B668GOOxYdiVlbeFim2cCc4OXPCZ5ZOTm5s+71pz/B7benXrthfqpaObnnzqwxroWXPyd4ZuXjb8zWvSZMgGWXhf33LzoSs7ZxKQSzxnkmzfwNlVp4ZkOFkzvrTjNnpvPtDj4Yllqq6GjM2iY8LNOsKU7w2mMoJHhO8mwocHJn3WnSJIiAww8vOhKztvI5d2bNc4LXHmVP8MC9eNZ5knaQNF3SDElH17n/UEn3SPqrpJslbVh131ey7aZL2r6R/Tm5s+4zdy786Eew++6w1lpFR2PWVjF8eDqn1MMyzZoyVGrhdZoTPLP8SBoOTAJ2BDYEPlKdvGUuioi3R8Q7gO8DJ2fbbgjsC2wE7ACcnj1ev5zcWfe58EKYPRs+97miIzHrjFGj3HNnNkhDIcEr+0QrTvCsxDYFZkTEgxExH5gM7FbdICKer7q5JBDZ9d2AyRHxckQ8BMzIHq9fTu6su0SkiVTe+U7YaquiozHrjNGjndyZtaDsCR6UfyZNFzu3klodeKzq9sxs3RtIOkzSA6Seu882s20tJ3fWXa67Du67L/XaSUVHY9YZo0Z5WKZZi5zg5c+lEswasqKkO6uWQ6ruq/dlNhZZETEpItYBjgK+3sy2tUY0ErFZx5xyCqyyCuyzT9GRmHWOh2Wa5WLxex9n3sYD/rCdm0qCN3v9kR3b59IPDOOFdRZ2bH9zHlqWpcY+17H9QUrwtltzesf2d8HsLfj4mFs7tj/rTsNfisH+aPN0RIzr476ZwBpVt98MPNHPY00GzhjktoB77qybTJ8OV14Jn/50+rJrNlR4WKZZbjyTZv5cC89s0O4A1pM0VtJI0gQpl1U3kLRe1c2dgX9m1y8D9pU0StJYYD3gzwPt0MmddY+JE2HkSDj00KIjMessD8s0y5UTvPYYCgmekzzLU0S8ChwOXAPcB1wcEdMkHStp16zZ4ZKmSfor8Hlg/2zbacDFwN+Bq4HDImLBQPt0cmfdYfZsOO88+OhH07BMs6HEwzLNcucErz3KnuCBe/EsXxFxZUS8NSLWiYjjs3XfjIjLsutHRsRGEfGOiNgmS+oq2x6fbbd+RFzVyP6c3Fl3OPfcVN/uyCOLjsSs8zws06wtXAuvPZzgmXUvJ3dWvFdfhdNOg623hne8o+hozDrPwzItI2ldST+SdLekBZKmNLHtHpLukDRP0jOSrpa0ZBvD7RlDIcEr+0yaTvDMGuPkzor329/CI4+4aLkNXR6Waa/bCNgJ+Ee2NETSwcBFwFXAjsDBpJPyPSt2puwJHpS/VIJr4ZkNzMmdFW/CBBg7Fj74waIjMSuGh2Xa6y6PiDUiYi9g2oCtAUkrAj8EjsjO45gSEZdGxBER0dk57LucE7z8uRaeWXdxcmfFmjoVbr4ZjjgChg8vOhqzYrjnzjIRMZgCZntnlz/NM5aycoKXPyd4Zt2j48mdpA0l3SBprqQnsqlA+/1WL+ndkn4iaUa23XRJ35I0ulNxW5uccgostRR88pNFR2JWHJ9zZ63ZDJgOHCRppqRXJN0uyd9G+1BEglf2iVac4Jl1h46+8iWNAa4HAtgNOBb4AvDtATbdB1gHOIF0LsIkUh2In7UtWGu/J5+EyZPhwANh2c5/KJh1DffcWWtWBdYHvg4cBXwQeBG4WpJry/TBpRLy52LnZsXrdM/docDiwB4RcV1EnElK7D4vaZl+tjshIt4bEWdn5xJMBL4E7CHpLR2I29rhzDPTTJlHHFF0JGbF8jl31pphwFLAQRHxs4i4GtgdWEAqnrsISYdIulPSnfMXzutgqN3FCV57DIUEz0medatOv+J3BK6JiOer1k0mJXxb97VRRDxVZ/Vd2eXK+YVnHfPSS3DGGbDLLrDeekVHY1YsD8u01szKLqdUVmSfs1OBDettEBFnRcS4iBg3ctji7Y+wiznBa4+yJ3jgXjzrTp1+tW8A3F+9IiIeBeZm9zVjC2Ah6TwD6zU//zk89ZSLlptBSu7mz4eIoiOx3nQf6XQH1awX6XPSBjBUip2X/Tw8J3jF/Fhh3aXTyd0Y4Nk662dn9zVE0qrA14ALanoBrRdEpIlUNt4Ytt226GjMijc6mxtqfudn1bNSuIKUyG1TWSFpWeBdwN1FBdWLyp7gQfknWnEtPBvqiihuWu+nafWxftGG0kjgYmAO8L/9tDsEOARglVVWYcqUKU0H2qw5c+Z0ZD+dlvdxLffXv/KOu+/m/i9+kX/ddFNuj9ss/796S5mPa8Zjj7Eu8MfrrmPBUksVHVIuyvr/ajdJS5AmDgNYHVhG0p7Z7SsjYq6kGcBNEXEQQETcKem3wLmSjgaeBr4MvEKagMyasPi9jzNv49U7tr8x0+cze/2RHdsfpATvhXU616k756FlWWpsZ0suXvvo+my3ZucGd10wews+PubWju3PrC+dTu5mA8vVWb8s9Xv03kCSgPOBjYAtI2J2X20j4izgLIBx48bF+PHjBxNvU6ZMmUIn9tNpuR/XhAmwwgpscOyxbLB4ced6+P/VW8p8XOtutBEA/73pprByOU4jLuv/qwNWBn5Zs65yeyzwMOmzu7aE0H7AicDJwBLALcC2/X1OWt+c4OXPCV77FNEDbN2r08My76fm3DpJawBLUnMuXh9+SCqhsFtENNLeus2DD8Jll8Ghh0KBiZ1ZV6kMy/SMmUNeRDwcEepjeThrs1ZEHFCz3ZyI+HRErBARi0fE+yPiniKOoSxcCy9/roWXnyImybHe0OlnxlXA9pKWrlq3DzAP6Hd8nqSvAEcA+0XEze0L0drq1FNh+HD4zGeKjsSse4walS49Y6ZZV/FMmvlzLbzmtq+OvYjk2HpPp5O7M4GXgV9Len92XtwxwMnVE6NImiHp3KrbHwX+jzQk83FJ76laVursIdigPf88nHsu7L03vOlNRUdj1j0qyZ177sy6jhO89hgKCZ4nWrEidPTVnI39fx/pXIHLSQXMfwh8q6Zp7fkE22WXBwC31Sw7ty9iy9V558ELL7j8gVktD8s062pO8Nqj7AkeeCZN67yOv5Ij4u8RsW12TsBqEfGNiFhQ0+YN5xNExAH9nINwXqePwQZhwQKYOBE23xw23bToaMy6i3vuzLreUKmF12lO8Mzy5bMxrTOuvBIeeAA+97miIzHrPj7nzqxnDIUEr+wTrTjBszJzcmedMWECrLEG7LFH0ZGYdR8PyzTrKWVP8KD8M2m62LmVlZM7a7+//Q1uvBEOOwxGdLq0olkP8LBMs57jBC9/LpVg1jond9Z+Eyemmnb/8z9FR2LWnTws06wnuRZe/pzgmbXGyZ2111NPwYUXwv77w/LLFx2NWXfysEyznuWZNPPnWnhmg+fkztrrRz9KX1g/+9miIzHrXh6WadbTnOC1x1BI8JzkWd6c3Fn7zJ8Pp58O228Pb3tb0dGYdS8PyzTreU7w2qPsCR64F8/y5eTO2ueXv4Qnn3T5A7OBuOfOrBRcC689hlKC50TPWuXkztojAk45BdZfH7bbruhozLqbz7kzK5WhkOCVfaKVbujBKyIG631O7qw9brsN7rgDjjwShvlpZtavESPS68TDMs1Ko+wJHpR/Js0iauGZtcrfuq09JkyA5ZaDT3yi6EjMesOoUe65MysZJ3j5GwqlEuop4ritNzm5s/w9+ij8+teprt2SSxYdjVlvGD3ayZ1ZCTnBy99QTfDMGuHkzvI3aVK6PPzwYuMw6yWjRnlYpllJudh5/pzgWa+QtIOk6ZJmSDq6zv3vlfQXSa9K2rPmvgWS/potlzWyPyd3lq8XX4SzzoI99oA11yw6GrPe4WGZZqXmUgn5GwrFzq23SRoOTAJ2BDYEPiJpw5pmjwIHABfVeYh5EfGObNm1kX06ubN8XXABPPtsmkjFzBrnYZlmpecErz2GWoJXxN/YBm1TYEZEPBgR84HJwG7VDSLi4Yj4G7Awjx362WH5WbgwlT8YNw62cJ0Ws6a4585sSHCC1x5DLcGznrE68FjV7ZnZukaNlnSnpD9J2r2RDZzcWX6uvRbuvz8VLZeKjsast/icO7MhY6gUOy/7eXhO8CyzYpaAVZZDqu6r94U4mnjsNSNiHPBRYIKkdQbaYEQTD27Wv1NOgdVWg732KjoSs97jYZkGSFoX+BLwHmBj4I8RMb6J7YcBdwD/BXwwIq5oR5yWj8XvfZx5GzfzI35rxkyfz+z1R3Zsf5CSvBfWyWW0WUPmPLQsS419rmP7qyR42605vS2Pa50zbN4rg/3R5eksAatnJrBG1e03A080+sAR8UR2+aCkKcA7gQf628Y9d5aP++6Dq6+Gz3wGRnb2g8OsFDws05KNgJ2Af2RLsw6muSE/VrCy9+CBZ9K0Ie0OYD1JYyWNBPYFGpr1UtIYSaOy6ysCWwJ/H2g7J3eWj4kT05fTT32q6EjMepOHZVpyeUSsERF7AdOa2VDSGOB44Gtticzaxgle/pzgWTeIiFeBw4FrgPuAiyNimqRjJe0KIOndkmYCewE/klR5738bcKeku4HfA9+LiAGTOw/LtNbNmgXnnw8f+xistFLR0Zj1Jg/LNCAiWhm/dhxwC3BDTuFYBxUxRBPo6DDNsg/RhJTg5T1Esz9FJOrWnIi4EriyZt03q67fQRquWbvdrcDbm92fe+6sdeecA3PnuvyBWSs8LNNaIGkT4EDgi0XHYoPnmTTzV4ZaeEX0QlrvcnJnrXn1VTjtNNh2W9hkk6KjMetdHpZprTkVmBQRM4oOxFrjBK89ej3BM2uUkztrzaWXwmOPudfOrFXuubNBkrQvsD7wnSa2OaQybff8hfPaF5wNihO89nCCZ0OBkztrzYQJsM46sPPORUdi1tt8zp0NgqTFgBOBE4BhkpYDlsnuXlLS0vW2i4izImJcRIwbOWzxDkVrzRgqtfA6zQmelZ2TOxu8O+6AW2+FI46A4cOLjsast3lYpg3OkqQT8U8GZmfL3dl9k4G7CorLcjIUEryyz6TZbILnhNBa4eTOBu+UU2DppeHAA4uOxKz3jRoF8+dDRNGRWG+ZA2xTs3wku++rwMcKistyVPYED8pfKuHaR9d30mYd4eTOBueJJ+AXv4CDDoJllhm4vZn1b/TodDnf01oPZZKWkLSnpD1JxchXqtyWtETWZoakcyHVUIqIKdUL8Kfs4e6JiNsLORDLnRO8/PViLbwihrJab/EzxAbnjDNgwYI0JNPMWjdqVLr0eXdD3crAL7PlPcCGVbdXztqMADwWfghygpe/XkzwzPrj5M6aN28enHkm7LorrL120dGYlUMlufN5d0NaRDwcEepjeThrs1ZEHNDAY1zRqbitc4pI8Mo+0UoZauGZVTi5s+ZddBE8/TR87nNFR2JWHpVhme65M7MBuFRCe3RjgucC5tYsJ3fWnIg0kcomm8DWWxcdjVl5eFimmTXBCV57dGOCZ9YMJ3fWnN//Hu65J/XaSUVHY1YeHpZpZk1yLbz2cIJnvWxE0QFYj5kwAVZaCT7ykYHbmlnjPCzTzAZp8XsfZ97Gq3dsf2Omz2f2+iM7tr9KgvfCOgs7ts85Dy3LUmOf69j+nOBZXtxzZ42bMQOuuAIOPfT1L6Jmlg8PyzSzFpS9Bw+GxkyaZq1ycmeNO/VUGDECPv3poiMxKx8PyzSzFjnBy58TPOs1Tu6sMc8/Dz/5CeyzD6y2WtHRmJWPh2WaWQ6c4OWvVxK8IibZse7T8eRO0oaSbpA0V9ITko6VNGAxVknLSvqJpNmSnpP0M0krdCJmA378Y3jhBZc/MGsXD8s0s5y4Fl7+eiXBM+voK0PSGOB6IIDdgGOBLwDfbmDzXwDjgYOBA4B3A79pR5xWY8ECmDgRttoK3vWuoqMxKycPyzSzHLlUQv6KKHbenyJ6Ta37dbrn7lBgcWCPiLguIs4kJXafl7RMXxtJ2hzYHtg/In4VEZcC+wFbSXp/JwIfyla47TZ46CE48siiQzErLw/LNLOcOcFrj04leLX7KeJYrfd0+lmyI3BNRDxftW4yKeHrryL2jsC/I+IPlRUR8Wfgoew+y9usWXD55XDUUax32mmw5pqw++5FR2VWXh6WaWZt4ASvPbqpB8+sWqfr3G0A3Fi9IiIelTQ3u+/yfra7v876+7L72mvWLJg5c8BmSz7wACy/fNvDaYuFC+Hee+Hmm9MybVpav9hivPzWtzL65JPTTJlm1h6V5O7BB+Fvfys2lhwM+v1wk03yD8ZsiKskeK6Fl69O18Iza0Snv62PAZ6ts352dt9gtls7h7j695vfwEEHDdjs3W0PpAOWWQa23BI++tF0jt27381dt9/O+PHji47MrNyWXDL9gHLCCWnpcYN6Pxw+HF59Ne9QzCxT9mLnkJI8J3g2lBXRFRN11qmP9YPeTtIhwCEAq6yyClOmTGkixDcavcQSLPXtged8eemllxjdw8W9X3rTm5gzdmz6ggWpN+/225kzZ05Lf79u5ePqLUPhuJaeOJFRTz1VbEA5GdT7ocTTJfwfm3UTJ3j5c4Jn3aTTyd1sYLk665elfs9c9XYr1Vm/XF/bRcRZwFkA48aNi070PE2ZMoVxJezhmjJlSil77nxcvWVIHFeJjq+s74dmZeAEL39O8KxbdPoM1PupOUdO0hrAktQ/p67P7TJ9nYtnZmZmZn1wLbz85TnJiidsscHqdHJ3FbC9pKWr1u0DzANuGmC7VSVtVVkhaRzpfLur2hGomZmZWZl5Js38dVstPBt6Op3cnQm8DPxa0vuz8+KOAU6uLo8gaYakcyu3I+I24BrgfEl7SNod+Blwc0Rc39EjMDMzMysJJ3jtkXeC5xp31qiOPlMiYjbwPmA4qezBt4EfAt+qaToia1NtX1Lv3o+B84GpwIfaGa+ZmZlZ2TnBaw/34FkROj5bZkT8Hdh2gDZr1Vn3LHBgtpiZmZlZToZKLbxOTrICnmjFOs99vGZmZmYGFDPRSict/cCwnp5oxWwgTu7MzMzM7DVlT/Cgt2fShGL+ZjY4knaQND2bU+ToOvePkvSL7P7bJa1Vdd9XsvXTJW3fyP6c3JmZmZnZGzjBy1+jCZ57+spD0nBgErAjsCHwEUkb1jQ7CJgdEeuS5iI5Idt2Q9KcIxsBOwCnZ4/XLyd3ZmZmZrYIJ3j5c+I25GwKzIiIByNiPjAZ2K2mzW7AT7PrlwDvk6Rs/eSIeDkiHgJmZI/XLyd3ZmZmZlaXi53nz7XwhpTVgceqbs/M1tVtExGvAs8BKzS47SI6PltmEaZOnfq0pEc6sKsVgac7sJ9O83H1Fh9Xb/Fx5e8tBe23Jz3/yn+evvrxUzvxGdmobn1NDN24BpfftRbXNYPeciBD9/84ON0YV3VMub3fP//Kf665+vFTVxzEpqMl3Vl1+6yIOCu7rjrto+Z2X20a2XYRQyK5i4iVOrEfSXdGxLhO7KuTfFy9xcfVW3xcVrROfUY2qlufO46rOY6rOY6rce2KKSJ2yPsxSb1ta1TdfjPwRB9tZkoaASwLzGpw20V4WKaZmZmZmVn+7gDWkzRW0kjSBCmX1bS5DNg/u74ncGNERLZ+32w2zbHAesCfB9rhkOi5MzMzMzMz66SIeFXS4aSBxsOBH0fENEnHAndGxGXAucAFkmaQeuz2zbadJuli4O/Aq8BhEbFgoH06ucvXWQM36Uk+rt7i4+otPi6zN+rW547jao7jao7jalw3xtSniLgSuLJm3Terrr8E7NXHtscDxzezP6VePzMzMzMzM+tlPufOzMzMzMysBJzcmZmZWdtJWlfSjyTdLWmBpClNbj9M0lRJIWmXbohL0h6S7pA0T9Izkq6WtGSRcUkaJ+naLJ5Zkq6XtFlOMe0l6TJJj0uak/0/PtLAdqMknSTpP5JelPQ7SWvlEdNg45K0vqRJku6TNFfSg5JOkbRckXHVeYzfZM/5w7shLknvlXRT9n98Nru+ZpFxSVpP0q8k/VvS85JuldSOmS97gpM7MzMz64SNgJ2Af2RLsw6mgQK+gzCouCQdDFwEXAXsmMX3T/Kbz6DpuCStAVyfxfAJ4OPZ9Wsl5VEP7PPAHOB/gV2B3wMXSTpigO0mAgcAXyTNBrgicJ2k0TnENNi4PgBsCZxB+jt/h3Te07WS8vp+PNi/FwCStgPek1MsLceVJUzXA3dn2+0H3AYU9n+UtDRwHbA28GnS8+sJ4HJJm+YUV0/xOXdmZmbWdpKGRcTC7PolwIoRMb7BbceQEpyjgXOAD0bEFUXFJWlF4CHg8xFxdh5x5BTXocAkYIWIeDZbN4ZU8PnwiDijxZhWjIina9ZdBGweEWP72ObNwMPAJyPi/Gzd6qS/32ci4pxWYmohrhWAWVH1RThLpq4BxkfETUXEVdVuMeBvwA9Iz/kjIuK0VmMabFxZPA8C50fE1/KII6e4diD9wLJJRNyTrRsBPA6cFxFHtSPWbuaeO7MeJWlbSSdKulzSzZL+mF0/UdI2RceXF0mbSDpA0v6SNi46HjMbnEqiMkjHAbcAN+QUzmsGGdfe2eVP84yl2iDjWow0ZfqcqnVzsnXKIaan66y+C1i5n822yy5/XfU4jwM3k3o8WzaYuCLimerErmob+tuu3XFVORKYB/wkj1iqDTKuD5CKaE/KO56KQca1WHb5XNXjvAq8SA7P+V7kUgg5kCTgg8B/AQHcCVxZ502j60nalvRmuwEwhnQ8zwL3k47p9wWGlxtJm/D6/2tqRNxbcEgNk7Q8cCnw36RfPu/LLgUsB3wI+IKkPwB7RMSsomJtRvbr3Ncj4sHs9mjg56ShGZU36JD0K+BjEfFKMZEOjl9bZoOTPacOBP5f0bFU2QyYDhwk6WvAKsBfgP+NiFsLjOtXwLHASZIq06d/E5gN/LJN+9yCVIerLxsAMyNiTs36+4DxbYoJBo6rr20YxHbN7qPfx5e0KvANUg/1wvQ1s+0Gimsz4BngPZJOAMaSPr++EhGXFxjXDaSe4R9I+gIpqTuUlBCe18a4upZ77pqUnaT5tqrbY0jV4n9DGiv8BeBy4JZsHHBPkLS8pJtIY6n3IH2Zfgh4JLv+IeAGSVOy5KInSLpI0tpVt0dLupT0S9CPSb+I3S3p4mzIQS+YCKwKbBYR60TELhHx8YjYL7u+LrBp1uaUQiNtzr6k8zAqjge2Bw4jvUmvlF3fBfhqx6MbJL+2euq1Zd3pVGBSRMwoOpAqqwLrA18HjiL9wPsicLWkVYoKKiKeALYBPgz8O1v2ALaPiKfy3p+k9wG70X9vzhjSD1m1Zmf35a7BuGq3WQL4HnBTREwrOK7vA9dExB/aEUetBuNaFViSVGPuB8AOpKTrUklvLyquiJhL+pFgI+BRUgJ6FLBbRLQzSe9eEeGliQVYCGxadftcUjX5HarW7UB60/ph0fE2cVwXkn6FfHc/bcaRfqW5oOh4W/h/nQTMJf2qsyKwQnZ9LvCtouNt8JieJb1pDdRud+DZouNt4X/1BPDNOu2OBf5RdLxNHJdfWz3y2vLSuQW4BJjSQLt9gX8By2S31yL1Cu9ScFzXZXFUf/Yvk332H1dgXKsBM4DfZt9FApnCYAAAFDtJREFUdiD94DwTWDPnmNYiJY+XDtDubOCuOuuPBx5vw9+qobhqthFppMgzwNptem41+vfaPHvffEvVuiCdM1lkXGdncRxatW44aRKh3D+7mohrSVIny82kkT7vJ/24+Czwznb8zbp9cc9d63YFjo2IqysrsuvHk34t6xW7AF+OiDv6ahARd5JOZv9gx6LK30eA70XEmRHxdKQx92eSfoX6WMGxNWohjY0jV9a2V60MTKmz/iYgl2mXO8Svrd55bVkXyXp8TwROAIYpTVG/THb3kgWPjqkMd59SWRERzwNTgQ2LCCjzJdIpN3tGxNXZ95EPAwtIM1XmIhtlcBWpp2S/AZrPJp0yUGs56vfodSquaieQRlHsHtmpAQXGNQH4EfCcpOX0emmGxSUtW2Bclef8a6cQRMQC0mdyrs/5JuM6KNv/LhFxWURcHxEHknoVv51nXL3CyV3rliOdY1drKqkLu1c4YeidhOG3pPMptuyrgaQtSF+KLu1YVPnYQtJOknYi/YK6TJ02y5BOMu8Vfm31zmvLusuSpAkcTiYlCLNJU7ADTOb1yS+KcB+pF6P2tV3063gDYFpUnZMcEfOBacA6eewgG754BTAS2DkiXhxgk/uBNbRo/b8NsvtyMYi4Ktv9Lynx/URE/DGveFqIa33gc7z+nJ+drf8+6XOxqLju6+uhyPE5P4i4NgAeiWx22Cp/JafnfK/xhCqD82FJ47Lrs0nnAtVaEXi+cyG1rJIwPBURt9Rr0OMJQ+VcrjIkDEcCFwN/lPQv0ofjs6QvGsuR3uhWBa4l1YrpJSfX3N6O9CZfbUvSMJBe4ddW77y2rLvMIZ0/Vm1V0vC5rwI3djyi110BfIsU35UAWa/Ku0i91UV5BNhJ0sgsqUPSKGBj0vDMlmRTzP8SWA/YMiL+08Bm12aXHyINU0fSm0iTgn2m1ZhaiAtJHyUNKf9CRFycRyw5xLULi34//z3pfPtfL9q8Y3FdQ5p19X2kUw2QNBzYmvo/7HUqrkeAtSSNiYjZVevfRZpoZchxcjc4X6q5/UEW/VL2fnL8RaoDnDD0SMKQDf3ZQdLmpPMpKrMvQqpldA5wVUT8qaAQB6teDZuX66x7gfRh3Cv82uqR15a1V/aL/E7ZzdWBZSTtmd2+MiLmSppBmtDioEjTmU+peYy1sqv3RMTtRcQFaSi1pN8C50o6mvTe+2XgFXKaKn4wcZHe/w8mTXJxOqlX5TDSuXhn5RDW6VlMRwLLS6ousH1XRLws6QaAiHhfdjlT0rnAhGx28aeAY0hfyi/MIaZBxSVpa9JsitcCt9VsMzMiZhYRV0TcXPsg2WyZ/4wcau+1ENeTkiYB38v+jzOAQ0i9698tKi7gItKPPVdK+j7pfMX9SBPL7ZJTXD3FyV2TIqLRoax3Ar9oZyx5csLQcwkDEXEbcFvRceQlIh5psF1PjaH3a6v3XlvWNiuz6HT8ldtjSb+yjyBN0tBJg41rP1KP+8nAEqQ6fNvW9B50NK6ImKpU1PlbwAXZ6nuAD0TE3bSuUrOu3kzMlZjq/f8+S5pNtPK3ugn4SES8lENMg41rG1KNtO2zpdq3SQloEXF1wmDj+hLp//h1YHnS0OjtI+KBouKKiMeUavseTzpXcTTpR9Q9I+J3OcXVUxTRc6XYzMzMzMzMrIYnVDErKUlnZ0NhSqWsx2VmZmbWKg/LbBNJ15N6Rt83YOMeIulsYFjV+P5SKOlxbUM5f8Ap5XGV9DlY2uMyMzPrRk7u2keU8AsoJf1iTQmPKyLWLTqGdijrcVHC52CmrMdlZmbWdXzOnVmJSBpNmi75xIgozQyFZT0uMzMzszw5uWsTSYsBq0XEo0XH0ipJY0mzFD0UEQ8VHU9eevW4sumx+7Ic8BiwI3AzQETM7URcrSrrcfUnm9Y9Gp0ptFeU9bjMzMy6nYfKDIKkwyQ9IOkFSbdL+nidZv8F9FLCsJikiZJmSZqT1Qohq2kyA7gemCHpZ1nRyp5Q0uN6oZ/lMdKQ4Kuq1vWKUh6XpEOqCn1X1h0p6SngAeBBSf+WlEsx304p63GZmZn1Mp9z1yRJ+wKnAj8n1ffYEjhP0m7AxyNiXpHxteDLpMKnJwOzgCMkrQTsDhwA/AXYCvgB8ClSocleUMbjmgc8T4r5mZr7lgROA75PqvPSS8p6XGcAfyXVtEPSIcAPSYXNL8na7AmcKunZiLiokCibV9bjMjMz61keltkkSXcCN0bEl6vWvQ/4Gam44s4R8YykzYBbI6IneoMk3Q+cGxEnZre3Av4AfD4iJlS1+zbpGMcVE2lzynhckt5ESoC2IxVaPT0iFmT3LQvMBsZHxB+Ki7J5JT6uhcB7IuLP2e37gT9FxAE17S4ANoiId3c+yuaV9bjMzMx6mYdlNm994MrqFRFxA/AeYFngNknrFBFYi94C/Lnq9tTs8s817W4G1u5IRPko3XFFxBMR8VHgQ8AngXskbV9wWC0r63HVsQ6p57/WZGDDDseSp7Iel1lXkHSApKnZKSGzJd0l6eQ27WtvSQc00O4YSVG1PCHpV41+D5J0XvajedtJGibp8OzvNk/S85KmZaduqBMxmHWCk7vmPQesWLsyIh4GtiANUboV6LVfqV8kTVpR8XK21E5aMZzeGs5b1uMiIv4IvAuYBFwk6QrSjw89raTHNVrSEtmkMc8AC+q0WQD02lCKsh6XWVeR9BXgHOAaYA/gE8BvgV3btMu9SacuNOI5YPNs+SLwDuAGSUs2sO1xTeynVZOB7wC/Jv3d9if9WL9FeBiblUhPfZntElNJ52tdUntHRMzOhmheQpq2vZfeLKYD40gfFkTEQmDxOu02Ig0/7RVlPS7gteOZJGkycDzwR3rreVdXCY/r91XXBWxKmsyn2iakiWN6SVmPy6zbHA78KCK+WrXu8uyUgqK9GhF/yq7/SdKjpPfsnYBf1jbOJi8bHhHzI+KBTgQoaUdgL2CniLiq6q5L3WtnZeOeu+ZdCKwtafl6d2YTquxK+oWtl8ognExjX8DeD1za5ljyVNbjeoOIeCYiDgXeSfpV996CQ8pFSY7rQNIw08pyIFBvGNKmwK86GFerynpcZt1oOeBftSure5wqQxwl7S7pfkkvSbpZ0iLDorNhl/dIelnSY5KOlzSi8jjAh4Gtq4ZbHtNErJXTH9aqE9c04CVgs+r7amJ7r6TfZzNcPydpiqR3Vt2/laSbJM2V9IyksyUtPUBMW2eXN9be4V47Kxv33DUpIn5JnV+iatosAA7pTET5iIiGvnxFxI7tjiVPZT2uvkTE34G/Fx1H3nr5uCLipw2227PdseSprMdl1qX+Qprt+VHgioionVG44i2kHzW/QZqB+NvANZLWi4iXACRtB/wCOB/4Eql3/ThgBeDQ7PqapISyUspkZhOxrpVd/qtm3feBY4F/00epKEnjgetIowL2J51asSWwOnCXpC2BG4DfkGbjXQH4HjAmu92XF7PLEyWd5BqcVmZO7szMzMy622GkhOY8ICTdR+oR/0FEPF/VbkVgt4i4FUDSVFLdyQOAM7M2xwJTImL/7PbV2cjE70r6TkQ8IGkWMKxquGW/Kr1+pInJTifVIq0eor0C8P6I+OsAD/Vd4G5g+6oetaur7v8eaSbyfar2/TjpHL+NI6Kv0R1nk4ZlHkFKkqcBFwETI2LOgAdo1kM8LNPMzMysi0XE34C3kU77OJ10jus3gDslLVXV9D+VxC7b7hHSMMlN4bXz3f6LRUcg/YL0nXDzQYS3AvBKtkwnJXj7RMSTVW0eHyixyyZg2Qz4ab2hktnETZsDF0saUVlIs12/QpqIq66I+BdpeP/2pBqdy5HO575V0siqfZwh6XFJHqppPcvJnZmZmVmXi4iXI+LyiDg8IjYEDgbWAw6qavafOpv+B1gtu74isBhpaGS1yu268wkM4DnSDOHjgDcDa9VMWlL9+P0ZQ0pan+zn/uGk5PaVquVl0jGt0d+DR8SCiLg2Ij5DGnb6E+DtvDGh/Tkp+TXrWR6WaWZmZtZjIuJcSd8HNqhavXKdpisD07LrT5MSotp2q2SXswYRyqsRMVCtukZ6wmYDC3k9Ea31bPY4x1BTbzjzRAP7SMFELJR0LWkiqNFV6/8A4Ak0rZe5585a1snCqnmT9M1sCMbCbIawvtp1XfHYrO2gC8h2snjsQJTcLWn/mvVdU3S21VgkTZJ0bidiNbNykbRI0iZpJWBZ3tgrtrKkLararEnqifozvDbh21TS+WfV9iYlVrdlt+dTlfR0QkS8CNwOfKLee2p2/5+A9SPizjpL3eRO0ir11pOGuM7N9mlWGu65s5YoFVY9jjQL1tGkD4N3AfsBny8wtAFJGkeaSeyrwBTqD2cp4hj3Jg2dOa/B9s8BO2TX1ybFeoOkjbIPw74cR/2af0XYmzTk5qKa9ZOB7YCTSB/qSwFbANsUMH11q7GcCNwv6bsRMaN9YZpZCd0j6bfAtaTPqreQCobPBapnrn0auEBSZbbMY7P251W1+RZpBs2fkN7X3k76PDg7IiqzYt4P7CZpd9JMmU/0lTzl7GjSRCxXSTqLNMvl5sCdEXEF8GXS59tCUk3hF0hDLHcGvhYR/6jzmBdLegG4mFTPdmXgY8BuwP9ExLPtPSSzDosIL14GvQCPA5PqrFfRsTUQ+36kIR7LdNMxkj6wpjTY9hjg6Zp1W2XHtVcf2wwHRhb996+J6Rbg+Jp1O2bHsWM7/vbAeLISRw20zSUW0peWk4r+e3vx4qW3FtJsmdeShh6+REpSLgI2qGpzHqnW5B7AP0jnot0CbFzn8fYB7iH10M0kTS4your+FUm1X2dl733H9BHXIp9BddqcR0rOGrqPVJPuD6TE9VlSWYR3VN2/GWkGzedJyd/fSeUflu1jH5/M2s/MjncW8DtgfD8xR9H/cy9eBrsUHoCX3l6yN9ZvDNBmCnBJzbrx2QfGxlXrKh9MO2dv1nOzN+DlgXWzN/gXszabNBDb3tmH18ukQuavfXhl+4qaZfxgj7Em/t1Jv3q+RJrFa8MW4zqmn30u8sFK6o0L4Et14ppGOt/iv/v4UH1v9neeQ+oRnAK8s6bNVsBN2f/nGdIU00tX3b9R9kE6K/vb3Qcc1s8xrJvFW7uf72XrR7XpuTu+0Q/wvGIBPk2q/TSsHcfkxYuXobvUe0/3Mui/ZRQdgxcvg118zp21qlJYdX9JK+TweGuShpF8nVQIfgvgLNLQkcmkIqUjgMn9nedUVaT1L6ShF6eShrCcljU5DvhOdn1b0rCPv/TxcM0cY6WA7HHAR0nnQ1wjaXQTcf0euCuLaXPgnAH2WWut7LJeAdnvAjtRp4BsVjz2BlLytz/pl90/korHVtpUCsj+i/S/+Fz2eD+peqjLgAWkntFds2Ncup9430dKAu+uWV9ddPYt/WzfCXnFcitp4oK3tx6SmZnlSdI5kmZm12dKavbz16xwPufOWtVoYdVGLQ9sHhEPAEjaBPgSsH9EnJ+tE6lHbwNSr1A9jRRpfSC7747ov4hpM8c4UAHZ3IvHZvtpuoBsndx4oOKxMEABWVLStzawe0TckzW5YYDw3wXcFxELa9bnWnQ2e94Mr1o1PFv/hvfBiHi1zuZ5xTKNlPhuyqLJrJmZFSgiDi46BrNWuefOWhKNF1Zt1MOVxC5TmXjixjrrVqeOvIu0NnmMfRaQbVPxWMihgOxAxWOzNo0UkJ1FGmp6pqR96s3wVseqpEkA3iDyLzq7P2+sjVRJfl+pWRbRSCyS1pB0g6T7slk0v1/bu5wljs9mx2xmlpuIOCAixhUdh5kVy8mdtSwaK6zaqNpZq+bXWV9Z19c0zbkXaW3iGPsrINuO4rGQTwHZgYrHVtr0W0A2633bjtSD92PgX5L+KOmd/Tzu6OwxFhH5Fp29nPR3qiyHZuvfXbPU1UAsrwJHRcTbSIngZqSJDWq9TIenGDczM7OhwcMyLXexaGHVl4CRNc0Gm8g0oh1FWt+gzjFW9FdAtl1x5VFAdqDisdBgAdmIuB/4sKTFSBO3nAD8TtKb6wy9hHTcA/ZkRYtFZyPiGdIEMGTtl8rWN13rr14sWU/pk9n1+ZL+BqxRZ/PlyOE5aGZmZlbLPXfWkgYLq85k0SToA+2KKRov0tqQJorHQj8FZJuIq+uKx1a1abiAbES8EhE3kiaYWY2U1NQzHRhbvaKbis4OJpZs4p3dgWtq1q8ELEGaptzMzMwsV+65s1Y1Ulj1UuAgST8kTYSyDencpXZqpEhroxotHgsDF5Dt5eKxMEABWVJS+gPSeYQPkoZyHgXcHRF99VbdAnxT0koR8VS2rpuKzjYVi6RRpL/NhIionfBnHKn381bMzMzMcuaeO2vVsaRp9ieSkp/jSEMQN42IhwAi4nfAV0lT519KSo4+186gIuJaYF/Sl+nLs/2dBBw+iIcb8BirPEKa3fMYUvL2PGn2yZeaiOv0bD8/Bu4glYRou2x44wdIPUsXkhK0rUkJZqXNzaRaeCsBF5CO4cukSVT+TTrX7t+kRO+q7FjuI/Vy9WUKaZjiDlXrfkr68en/SAnnWaShvdtGxLktHWjzGo4lmzTnZ8BdEXFSncfaAbgpGyJqZmZmliv1MTGemTVJ0nmkouyeraxJkk4B1o2InVt4jIiI/k+8a7OsJtJw4JO1s45mid8jwNERcWER8ZmZmVm5uefOzLrBicB4SW9tdsNuKTqbFXg/iNQre5ekv0r6bFWTvUhDdScXEZ+ZmZmVn8+5M7PCRcRMSQeRJl5parKRbik6GxG3kMpJ9EXAQX0USTczMzNrmYdlmpmZmZmZlYCHZZqZmZmZmZWAkzszMzMzM7MScHJnZmZmZmZWAk7uzMzMzMzMSsDJnZmZmZmZWQk4uTMzMzMzMysBJ3dmZmZmZmYl4OTOzMzMzMysBP4/mfLGt2UT228AAAAASUVORK5CYII=\n", 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\n", 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" ] @@ -387,7 +389,7 @@ "text": [ "state qubits: 5\n", "circuit width: 15\n", - "circuit depth: 1441\n" + "circuit depth: 1068\n" ] } ], @@ -507,7 +509,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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\n", 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" ] @@ -564,9 +566,9 @@ ], "metadata": { "kernelspec": { - "display_name": "qiskit_master", + "display_name": "Python 3", "language": "python", - "name": "qiskit_master" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -578,7 +580,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.1" + "version": "3.7.1" } }, "nbformat": 4, diff --git a/qiskit/finance/simulation/basket_option_pricing.ipynb b/qiskit/finance/simulation/basket_option_pricing.ipynb index c3c05cb3a..243d19887 100644 --- a/qiskit/finance/simulation/basket_option_pricing.ipynb +++ b/qiskit/finance/simulation/basket_option_pricing.ipynb @@ -39,8 +39,10 @@ "
\n", "$$\\mathbb{E}\\left[ \\max\\{S_T^1 + S_T^2 - K, 0\\} \\right].$$\n", "
\n", - "The approximation of the objective function is explained in detail in the following paper:
\n", - "Quantum Risk Analysis. Woerner, Egger. 2018." + "The approximation of the objective function and a general introduction to option pricing and risk analysis on quantum computers are given in the following papers:\n", + "\n", + "- Quantum Risk Analysis. Woerner, Egger. 2018.\n", + "- Option Pricing using Quantum Computers. Stamatopoulos et al. 2019." ] }, { @@ -127,7 +129,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -252,7 +254,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -317,7 +319,7 @@ "text": [ "state qubits: 5\n", "circuit width: 11\n", - "circuit depth: 184\n" + "circuit depth: 398\n" ] } ], @@ -435,7 +437,7 @@ "outputs": [ { "data": { - "image/png": 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xvcQdP2utxaZR0jeU+RzwuVzSkKTnge9IendELKlTvkZJ31D2VcBVAAMDAzE4OFi/9iUNDQ3RrrL6WS+00/Szb6m7feVHBzteh15op02B26mcbrVTsxM/JeksSSuAV4Df13jUMwzsWCN9PLXPfOq5Lnt+T65sapS/4X2z5ZuZWRs1Ow/ndOBs4HukM4d/AC4EHgdWkl2aqmM5qa/mdZL2BrZlZN9LI1F4foIUBCcV8k0C1md1NDOzLmk24HwSOB+4OHt/Y0RcABxAChhva7D/POAYSdvn0qaSbn/QbF/RKdnzQwARsY40T+jDhXxTgQc8Qs3MrLua7cN5C7AkIl6T9ArZ5aqIWC/pO8B3SWdAo7mCdJZ0g6RZwL7ATOCS/FDp7JLdwog4LXs/E9ieNOlzNfB+4IvADRHx01z5XyX171xGmic0JXsc2+RxmplZmzV7hvM7YLvs9VPAf8tt24k0qXNUETEMHEGaq3MTcAFwKemsKW8LNp7Ps5w0T2c2cCtwKvCN7Dlf/iLSmc+RwHzgg8CpXmXAzKz7mj3DuQ94L+lH/wekFQJ2Bv4IfBa4s1EBEbEU+ECDPBML7+eSJnA2FBE3ks5uzMxsE9JswJkJ7JW9voh0SW066cxmAfD5dlXMzMz6S1MBJyIeAx7LXq8j3QvnjA7Uy8zM+sxYJn6+GdgTeDYinmlflczMrB+1covpz0j6FfAk8EPgKUlPS/rfba+dmZn1jWZXGjgPuJw0n+Z4YCB7ngd8O9tuZmY2QrOX1D4LXBQRXymk35atbfZZ0soDZmZmG2n2kto4Rr+r50JqLOZpZmYGzQecG4GTR9n2IeDmsVXHzMz6VZlbTE/JvZ0HXCxpIiNvMX0A8Pftr6KZmfWDMn04NzPyVtJ7AcfUyPsvpDtxmpmZbaRMwHlLx2thZmZ9r8wtpp+soiJmZtbfml5pQNIWpAEChwE7A/8F3Eu6VUD9m7+bmdkbVlMBR9LuwO3AgaQ7fD4PHEqaf/OIpKMj4rftrqSZmfW+ZodFXwLsArwvIvaNiEMjYl/gfVn6Je2uoJmZ9YdmA84U4KyI+HE+MXv/JdIyN2ZmZiM0G3C2An4/yrbfA28aW3XMzKxfNRtwHgTOkrRtPjF7f1a23czMbIRmR6mdCdwN/ErS7aRBA7uTJoEKGGxr7czMrG80dYYTEUuAtwFXAbsBR5ECzhXA2yLikbbX0MzM+kLpMxxJWwIHA7+MiLM7VyUzM+tHzZzhvAbcBbyzQ3UxM7M+VjrgRMR64OfAhM5Vx8zM+lWzo9S+DJwn6V2dqIyZmfWvZkepnUtaUWCJpGdIo9QinyEiDm5T3czMrI80G3B+lj3MzMyaUirgSBpHWtbmZ8CvgTsi4vlOVszMzPpLmVtM7wvcAUzMJa+W9JGIuL1TFTMzs/5SZtDAxcB64K+AbYADgIeBKztYLzMz6zNlAs6hwLkRcV9EvBwRy4BPAX8uac/OVs/MzPpFmYCzJ/CLQtoTpLXT9mh7jczMrC+VnYcTjbOYmZmNruyw6PmSXq2RfmcxPSJ2H3u1zMys35QJOBd0vBZmZtb3GgaciHDAMTOzMWt2LTUzM7OWOOCYmVklHHDMzKwSDjhmZlYJBxwzM6uEA46ZmVWi8oAjaX9Jd0paK+lZSRdK2rzBPu+VNFvSimy/xySdL2nrQr6ZkqLG49jOHpWZmTXS7A3YxkTSTqRbHSwFTgD2A75JCnzn1tl1apZ3FvBz4EDgq9nzhwp5VwHFALNsrHU3M7OxqTTgAJ8GxgEnR8RqYIGkHYCZki7O0mqZFRG/zb0fkvQycKWkfSLiydy2VyPiwc5U38zMWlX1JbXjgPmFwDKXFIQOH22nQrDZ4OHs2Wu3mZn1gKoDziRgeT4hIp4C1mbbmvGXpBvDPVZI31HSC5JekfSwpJNbrq2ZmbWNIqq784CkV4AvRsRlhfSngWsi4pyS5ewB/BS4NSKm59I/RjrjWQJsR7pR3BTgQxFxwyhlzQBmAEyYMOGguXPnNntYNa1Zs4btttuuLWX1s15op0efWVV3+7v2Gt/xOvRCO20K3E7ltLOdJk+e/FBEDJTJ242A84WI+FYh/Rng6oj4coky3kQaePBm4KCIGK6TV8D9wLiIeHejsgcGBmLx4sWNspUyNDTE4OBgW8rqZ73QThPPvqXu9pVfP77jdeiFdtoUuJ3KaWc7SSodcKq+pDYM7FgjfTzwYqOdswByDXAAMKVesAGIFE1vAA5sNPTazMw6q+pRassp9NVI2hvYlkLfziguJQ2nPioiyuTfwHcsNTPrsqrPcOYBx0jaPpc2FXgJWFhvR0lfAj4PfCwiFpX5sOyM6CTgkYh4rbUqm5lZO1R9hnMFcDpwg6RZwL7ATOCS/FBpSSuAhRFxWvb+VOAi4GrgGUmH5Mp8YsOwaUkLgetJZ0vbAp8EDgFO7OxhmZlZI5UGnIgYlnQEcDlwE6nf5lJS0CnWK9/ncnT2PD175H2cFIgAVgB/C+xJGjL9E+D4iJjXjvqbmVnrqj7DISKWAh9okGdi4f10RgaaWvudNoaqmZlZB3m1aDMzq4QDjpmZVcIBx8zMKuGAY2ZmlXDAMTOzSjjgmJlZJRxwzMysEg44ZmZWCQccMzOrhAOOmZlVwgHHzMwq4YBjZmaVcMAxM7NKOOCYmVklHHDMzKwSDjhmZlYJBxwzM6uEA46ZmVXCAcfMzCrhgGNmZpVwwDEzs0o44JiZWSUccMzMrBIOOGZmVgkHHDMzq4QDjpmZVcIBx8zMKuGAY2ZmlXDAMTOzSjjgmJlZJRxwzMysEg44ZmZWCQccMzOrhAOOmZlVwgHHzMwq4YBjZmaVcMAxM7NKOOCYmVklHHDMzKwSDjhmZlYJBxwzM6uEA46ZmVWi8oAjaX9Jd0paK+lZSRdK2rzEfuMlzZY0LGmVpO9L2qVGvhMkPSrpZUlLJU3tzJGYmVkzKg04knYC7gACOAG4EDgTuKDE7tcCg8AngOnAe4EbC+UfBlwP3A0cB9wCzJF0dFsOwMzMWrZFxZ/3aWAccHJErAYWSNoBmCnp4ixtBEmHAscAh0fEPVnaM8APJR0ZEXdkWb8C3BMRp2fv75Z0AHAecHvnDsvMzBqpOuAcB8wvBJa5wCzgcOCmOvs9vyHYAETEjyT9Mtt2h6StgMnA6YV95wKzJY2PiFVtOg7rooln39Iwz8qvH19BTcysGVUHnEnAXfmEiHhK0tps22gBZxKwvEb6smwbwH7AljXyLSNdOnw78OPWqm1lOBC0T7Etz3zXq0zPpbkdrRdVHXB2Al6skT6cbWtlv31zeaiRb7iwfSOSZgAzsrdrJD1Wpx7N2BV4oU1l9Q3NGpHUkXaq8TkdU8VnnV5opyqPr8f4/1057WynfcpmrDrgQBowUKRR0lvZr/hedfYnIq4Crmrw2U2TtDgiBtpdbr9xO5XjdirH7VROt9qp6mHRw8CONdLHU/sMptF+O+b2G86lFfPQoHwzM+uwqgPOcv7U5wKApL2BbandRzPqfpl8384TwCs18k0C1gOPt1BfMzNrk6oDzjzgGEnb59KmAi8BCxvst0c2zwYASQOk/pt5ABGxjjT/5sOFfacCD3RhhFrbL9P1KbdTOW6nctxO5XSlnRTRqOukjR+WJn4uBX5GGgq9L3AJcFlEnJvLtwJYGBGn5dJuI400+wLpjGUW8JuI+KtcnsOAIeBy0qTQKVn+YyPC83DMzLqo0jOciBgGjgA2Jw2BvgC4FDi/kHWLLE/eNNJZ0D8D1wAPAScVyl8EnAIcCcwHPgic6mBjZtZ9lZ7hmJnZG5dXi27Ai4021kobSXpv1j4rsv0ek3S+pK0L+WZKihqPYzt7VO3XYjtNHOX459bI2/PfJWi5nUb7noSkL+XyXT1KnlqDkjZpkt4q6UpJj0h6TdJQyf269tvUjXk4PSO32OhS0mKj+wHfJAXqc+vsCmmx0XeQFhvd0Od0I1Dsc7oe+A5pSZ4ppMVGh3vlMuAY2mhqlncW8HPgQOCr2fOHCnlXAcUAs2ysda/SGL9LkPoi78u932jSXj98l2BM7fRd4LZC2onAWWQDi3KWAx8vpK1srcZddQDp3/lB4E1N7Ne936aI8GOUB/Al0vyeHXJpfw+szafV2O9Q0kTT9+fSDs7SjsylzQfuKux7K7Co28deQRvtViNtRtZG++TSZgIvdPs4u9hOE7M2+R8Nyu/579JY2mmUsm4BlhXSrgYWd/s429RWm+VeXwcMldinq79NvqRW32iLjY4jLTZab78Ri40CGxYbJbfY6L8W9p0LHCpp/NirX4mW2igiflsj+eHseff2VW+T0ep3qaE++i5Bm9pJ0s7AUcCc9lZv0xER61vYrau/TQ449Y1YNDQiniL9tVXvmm+7FhvtBa22US1/STrFL65nt6OkFyS9IulhSSe3XNvuGWs7zc6u0z8n6RJJ43Lb+uW7BO37Pp1CapMRfV3A/pJWS1onaZGkMQX8HtPV3yYHnPo6sdjoTrk81MhXd7HRTVCrbbQRSXsAXwb+b+Gv2xWkSyofIfXtPAtc34NBp9V2Wgf8E3AaaUrBlcBn2PiHtF++S9Cm7xNpGsVPIqK4wsjDpJs+/k/go6TpFwskHdxCXXtRV3+bPGigsU1qsdFNVKttlDJKbyKdvq8B/m6jgiP+pZD3JuB+0k31bmilsl3UdDtFxHPA53JJQ5KeB74j6d0RsaRO+b34XYKxf5/2JF1+O2tEwRHfKuS9hTRA4RzSIIM3gq79NvkMpz4vNtpYq20EgCSRJvIeAEyJNDl4VJF6L28ADiwzPH0TMqZ2Krgue35PrmxqlN9r3yVoTzt9hPTjeG2jjBHxEqkz/D2N8vaJrv42OeDU58VGG2u1jTa4lDT89YSIKJN/g177q32s7ZQXhed++S5Be9ppGmk01a+a+Nxe+z61qqu/TQ449b2RFhttVattRDYh7/PAxyItS9RQdkZ0EvBIRLzWWpW7ouV2quGU7Pkh6KvvEoyxnSRNBA6h5Oi0bPDFcWRt+QbQ3d+mbo8l35QfpM6x54AFpPXZZpD6Gb5WyLcC+F4h7TbgF8DJpGvDjwH3FvIcBrwKXAYMAheT/oI4utvH3uk2Ak4l/VU5m/QDkX/slsu3kDTx7GhSoLk1a6MPdvvYK2qnmaSJjydn+11I+vG9vt++S2Npp1z62aS/zmvN8xoP3At8ijQAYypp0uQ6YKDbx95CW21D+uPjFOAB4D9z77cZrZ26+dvU9Ubb1B/A/sBd2X/y50iz4Tcv5FkJXF1I2zH7MX0RWA38ANi1RvknklbPXkc6pZ3W7WOuoo1IE/BilMf0XL7vZf85XgL+kP1gHNftY66wnaYBi0mrLfwx+wG5ENiqH79LrbZTLn0JcNso5W5N6v/7VdZGq7If30O6fcwtttPEOv+HJo7WTt38bfLinWZmVgn34ZiZWSUccMzMrBIOOGZmVgkHHDMzq4QDjpmZVcIBx8zMKuGAY2ZmlXDAMTOzSvx/kIORc9agYsAAAAAASUVORK5CYII=\n", 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\n", 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\n", 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\n", 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" ] @@ -492,9 +494,9 @@ ], "metadata": { "kernelspec": { - "display_name": "qiskit_master", + "display_name": "Python 3", "language": "python", - "name": "qiskit_master" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -506,7 +508,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.1" + "version": "3.7.1" } }, "nbformat": 4, diff --git a/qiskit/finance/simulation/bull_spread_pricing.ipynb b/qiskit/finance/simulation/bull_spread_pricing.ipynb index 5a0969519..ec90b93b5 100644 --- a/qiskit/finance/simulation/bull_spread_pricing.ipynb +++ b/qiskit/finance/simulation/bull_spread_pricing.ipynb @@ -46,8 +46,10 @@ "\\Delta = \\mathbb{P}\\left[K_1 \\leq S \\leq K_2\\right]\n", "$$\n", "
\n", - "The approximation of the objective function is explained in detail in the following paper:
\n", - "Quantum Risk Analysis. Woerner, Egger. 2018." + "The approximation of the objective function and a general introduction to option pricing and risk analysis on quantum computers are given in the following papers:\n", + "\n", + "- Quantum Risk Analysis. Woerner, Egger. 2018.\n", + "- Option Pricing using Quantum Computers. Stamatopoulos et al. 2019." ] }, { @@ -118,7 +120,7 @@ "outputs": [ { "data": { - "image/png": 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lbRoRj2Tlx2TxfjQilgA3SHodcKKkH0ZENBGjmZn1g1Yvwb0f2DQivtZL8iEi/h4RzXRI2BO4ppBoJpKS0s697P/fNYr/lP3coLD/S7Pkk9//a0mXDc3MrCStJqCRpGkYViBpI0kntLi/rYHp+YKIeBSYn61rxbuAZaQ2KSStCWxS3D9pLqOeY5uZWUlaTUAnks4eanlNtr4VQ4E5NcpnZ+uaImlD4CvAT3JnU+tkP4v7n507tpmZlaTVNiAB9dpNXstLH+6tqLW/3o6zfEVpNeBXwFzgC03uv265pMNIHSsYNmwYkydPbiaMfjF37txSj19PVeOC/ovtqO2WNK7UwLBB7e+n+NyqGlenDMT3WruqGlctDROQpJ5eb5A+tL8nqdg5YA1gO+DaFo8/m5fOVPKGUPvMqBibSN293wTsGBH5BNizfXH/QwvrlxMR40mjPTBy5MgYPXp0ozD6zeTJkynz+PVUNS7ov9gOPu7Ktvdx1HZLOHNqe7fHzTxo9HLLVY2rUwbie61dVY2rlmbedfOBp7PfBTwLPFOo8wJwNXB+i8efTqEtRtImpKm+i203tZxN6r793ogotiXNk/SP4v5zy83s38zM+knDBBQRvybdXIqki4CTeusB16KrgWMkrRURz2dlY4EFwE29bSjpy8DngAMj4pZe9v8BSV+NiKW5/f8D+Fvb0ZuZWZ+1OhbcIR1MPgAXAIuASyXtlrW/jAPOynfNzkY8+GFu+SPAN0mX32ZJ2iH3WD+3/zNIbVM/kTRG0rHAp0lJ1PcAmZmVqNTx2iJitqRdgfOAy0ntMmeTklDeqkB+eJ7ds58HZ4+8Q0g3yhIRMyS9DziLdDb0L+Aoj4JgZla+Zjoh3AUcHBHTJN1Ng95pEfGOVgKIiGnALg3qDC8sH8yKiafetreQhuAxM7MKaeYM6F5Sm0zP7750ZWZmbWumE8Ihud8P7tdozMxswOjzdAxmZmbtaKYNqGG7T16rbUBmZjYwNdsG5HYfMzPrqGbagA7uQhxmZjbAuA3IzMxKUfp9QGZmNjD5PiAzMyuF7wMyM7NStDwWXDYB3MGk4W02Av4J3An8OCJe6Gh0Zma20mqpE4KkNwIPAN8FtgWWZj+/C8yQtE3HIzQzs5VSq2dA40kT0r07Ih7tKZT0OuBK0vQK7+lceGZmtrJqNQGNBD6cTz4AEfGopBOAn3csMhtwhndoeul2p6meeerebcdhZo21eh/QTGCNOuvWAB6ts87MzGw5rSag44BvSHpnvlDSDsBJwJc6FZiZma3c+jIY6drAbZKeBJ4ENsgeTwPHA5f1Q5xmZraS6ctgpPf2UyxmZjaAlD4YadZ1+1xgFDAHuBD4ekQs7WWb1YBTgB1IHSPWiAjVqDcB+HiNXbwxIqa3H72ZmfVVyzeidpKkocB1wDRgH2AL4ExS29RXe9n0VcAngbuA24Bdeqk7HTikUDazbxGbmVmnlJqAgMOBQcB+EfEcMEnS2sA4SadnZSuIiDmSXh0RIekIek9A8yLijs6HbmZm7Wh5OgZJYyVdJ+lRSU8WHy3ubk/gmkKimUhKSjv3tmFEeFBUM7OXsVaH4vkI8GNgBvBa4HfAFdl+ngPOa/H4W5Mukb0ou8l1frauE7aR9JykRZJukdRrYjMzs+5QKycSkv4E/AY4FVgMjIyIP0paC5gE/CYivt3C/hYDx0TEdwrljwEXR8TxTezjCODcOp0QPg+8QGpjWh84ChgB7BQRd9XZ32HAYQDDhg0bMXHixGafTsfNnTuXwYMHl3b8evorrqmznm17H8MGwRMLGtfrzXYbD1mhrKqxVTWuTqnq/wBUN7ay4xozZsyUiBjZTN1W24C2BG6NiKWSlpLuCSIinpd0GnA20HQCytTKgKpT3tqOI85ZbqfSlaRkdDywb51txpPGvGPkyJExevTodsPos8mTJ1Pm8evpr7jaHUIH0lA8Z05tr2lz5kGjVyiramxVjatTqvo/ANWNrapx1dJqG9CzwOrZ77OAN+bWCVi3xf3NBtapUT6E1CW7oyJiAXAV8LZO79vMzFrT6teee4A3A9eQ2n9OkLSEdJnrBNK8QK2YTqGtR9ImwJoU2oY6zB0YzMxK1moC+hawafb7Cdnv5wOrAHeTtZ204GrgGElrRcTzWdlY0hTgN7W4r4YkDSL1vJvS6X2bmVlrWkpA2f00d2S/zwH2kbQ6sHq9e3YauAA4Erg0a0PaHBgHnJXfn6QZwE0RcWiubE/SmdL22fIHs1V3R8QjkoaQeuj9lNRrbz3gC8DGwIF9iNXMzDqoY1NyS2p5Su6ImC1pV1L37ctJ7T5nk5JQMc5VCmXf46WzMYBfZz8PASYAi4B/k0ZU2ABYCNwO7BwR97QSp5mZdV5LCSibkvv3wGtIl7GeJE3J/V/A1yS9LyKmtbLPrH5vIxkQEcObKSusXwjs10osZmbWPZ6S28zMStFqN+yRwAm1puQmdUp4e6cCMzOzlZun5DYzs1K0egnuOOBMSQ9HxIv3/OSm5D6mk8GZ2cvX8A6N0tDuaA8zT9277Tisf3hKbjMzK4Wn5DYzs1KUPiW3mZkNTH0aAlfSa4BRwKtJl97uiIjHOxmYmZmt3Fq9EXUV4FzgUyw/MsFSSeOBz0XEsg7GZ2ZmK6lWu2F/HfgEqbPBcNLU2cOz5U+w4hA6ZmZmNbV6Ce6/gK8WZj19FDhDUpAGFj2hU8GZmdnKq9UzoA2Av9ZZ99dsvZmZWUOtJqC/Ax+qs+5DwP3thWNmZgNFq5fgvgFMzAYf/Q3wBOms5wBgDPWTk5mZ2XJanZDuV5LmkDojnAO8ElhMmprhfRExqfMhmpnZyqjpBCTplaRJ6P4WEaMkvYI0y+hT7nptZmataqUNaClwA/BGgIhYFhFPOvmYmVlfNJ2AskTzADCskwFI2kbS9ZLmS3pc0knZDa+9bbOapDMk/UHSgqwLeL26+0iaKmmhpGmSxnYyfjMz65tWe8F9BThB0nadOLikocB1pMFO9yFN6XAUqY2pN68CPgnMB27rZf87AZcANwJ7kmZt/YWk3dsO3szM2tJqL7ivAusCf5Y0i9QLbrmzj4h4Rwv7O5w0msJ+EfEcMEnS2sA4SadnZSuIiDmSXh0RIekIYJc6+/8acHNEHJkt3yjpTaSbZa9tIU4zM+uwVhPQvcDfOnj8PYFrColmInAasDNweb0NI6LuZTcASauTuoYfWVg1EbhI0pCIeLZPUZuZWdta7YZ9cIePvzWpY0P+GI9Kmp+tq5uAmrAFqZv49EL5faRLj28A7m5j/2Zm1oamEpCkQcBepIFH/wlcHxFPdOD4Q4E5NcpnZ+va3Tc19j+7sN7MzEqgBleykLQ5qaPA8Fzxc8CBEdFWO4qkxcDREXFOoXwWMCEivtLEPo4Azo0IFcp3BG4Bto+Iv+TKtyQNKbR7rRtnJR0GHAYwbNiwERMnTmz9iXXI3LlzGTx4cGnHr6e/4po6q/0rosMGwRML2tvHdhsPWaGsqrFVNS6odmydMND+P5s1ZsyYKRExspm6zZwBnQ4sA95NGvFgM+B84PvZ7+2YDaxTo3wItc+MWt03Nfbfs1xz/xExHhgPMHLkyBg9enSbYfTd5MmTKfP49fRXXAcfd2Xb+zhquyWcObVP8yy+aOZBo1coq2psVY0Lqh1bJwy0/8/+0Ew37FGkKRhujYiFEXEf8GngdZI2avP400ltPS+StAmwJiu23bTqQdIwQVsXyrcmJdS/t7l/MzNrQzMJaCPgoULZg4CADds8/tXAHpLWypWNBRYAN7Wz44hYRLr/54DCqrHA7e4BZ2ZWrmbPbXtvKOq7C0jdpC+VdBqwOWlW1bPyXbMlzQBuiohDc2V7ks6Uts+WP5itujsiHsl+PxmYLOk7wGWkjhR7Ae/rp+djZmZNajYBXSNpSY3y64vlEdH0pHQRMVvSrsB5pC7Xc4CzWXFq71WB4vA83wM2zS3/Ovt5CDAh2/8tWWL6BvAZ4GHgI+12njAzs/Y1k4AaDYvTloiYRv2RDHrqDG+mrM62l5HOfszMrEIaJqCI6NcEZGZmA1Org5GamZl1hBOQmZmVwgnIzMxK4QRkZmalcAIyM7NSOAGZmVkpnIDMzKwUTkBmZlYKJyAzMyuFE5CZmZXCCcjMzErhBGRmZqVwAjIzs1I4AZmZWSmcgMzMrBROQGZmVgonIDMzK0XpCUjSNpKulzRf0uOSTpK0ShPbDZF0kaTZkp6V9DNJ6xbqTJAUNR5b998zMjOzZjSckrs/SRoKXAdMA/YBtgDOJCXGrzbY/JfAVsAngWXAacBlwLsL9aYDhxTKZrYTt5mZta/UBAQcDgwC9ouI54BJktYGxkk6PStbgaRRwB7AzhFxc1Y2C7hT0m4RcV2u+ryIuKN/n4aZmbWq7EtwewLXFBLNRFJS2rnBdk/0JB+AiLgLeDhbZ2ZmFVd2AtqadInsRRHxKDA/W9f0dpn7amy3jaTnJC2SdIuk3hKbmZl1iSKivINLi4FjIuI7hfLHgIsj4vg6200iXVrbt1D+U2DziHhXtvx54AVSG9P6wFHACGCn7Iyp1r4PAw4DGDZs2IiJEye28QzbM3fuXAYPHlza8evpr7imznq27X0MGwRPLGhvH9ttPGSFsqrGVtW4oNqxdcJA+/9s1pgxY6ZExMhm6pbdBgRQKwOqTnlL20XEOcutlK4kJaPjgX2pISLGA+MBRo4cGaNHj24QRv+ZPHkyZR6/nv6K6+Djrmx7H0dtt4Qzp7b3tp550OgVyqoaW1XjgmrH1gkD7f+zP5R9CW42sE6N8iHAnD5st05v20XEAuAq4G0txGhmZv2g7AQ0nUKbjaRNgDWp3cZTd7tMvbahovKuO5qZGVB+Aroa2EPSWrmyscAC4KYG220oaaeeAkkjgc2zdTVJGkTqJTelnaDNzKx9ZSegC4BFwKWSdss6AIwDzsp3zZY0Q9IPe5Yj4nbgGuBiSftJ2hf4GXBLzz1A2UgJf5D0aUm7ShoL3AhsDHyzW0/QzMxqK7UTQkTMlrQrcB5wOan95mxSEspbFSgOz/OhrO6PSIn0CuDI3PpFwL9JIypsACwEbifdvHpPR5+ImZm1rPRecBExDdilQZ3hNcrmkIbYKQ6z07N+IbBfB0I0s5XM8A710Gunp9/MU/duO4aXu7IvwZmZ2QDlBGRmZqVwAjIzs1I4AZmZWSmcgMzMrBROQGZmVgonIDMzK4UTkJmZlcIJyMzMSlH6SAjWXVW4Axx8F7iZ+QzIzMxK4gRkZmalcAIyM7NSOAGZmVkpnIDMzKwUTkBmZlYKJyAzMytF6QlI0jaSrpc0X9Ljkk6SVJx+u9Z2QyRdJGm2pGcl/UzSujXq7SNpqqSFkqZJGts/z8TMzFpR6o2okoYC1wHTgH2ALYAzSYnxqw02/yWwFfBJYBlwGnAZ8O7c/ncCLgHOB44E9gJ+IWl2RFzb0SdjZtamgXajeNkjIRwODAL2i4jngEmS1gbGSTo9K1uBpFHAHsDOEXFzVjYLuFPSbhFxXVb1a8DNEXFktnyjpDcBJwBOQGZmJSr7EtyewDWFRDORlJR2brDdEz3JByAi7gIeztYhaXVgDPCrwrYTgVGShrQfvpmZ9VXZCWhrYHq+ICIeBeZn65reLnNfbrstgFfWqHcf6Xm/oQ/xmplZh5SdgIYCc2qUz87WtbNdz89ivdmF9WZmVgJFRHkHlxYDR0fEOYXyWcCEiPhKne0mAXMj4gOF8p8BwyNiR0k7ArcA20fEX3J1tgT+DuweEZNq7Psw4LBscSvg/j4/wfatBzxV4vHrqWpc4Nj6oqpxgWPri7Lj2jQi1m+mYtmdEGYD69QoH0LtM5z8drWe4Dq57Wbnyop1qLf/iBgPjO/l2F0j6Z6IGFl2HEVVjQscW19UNS5wbH1R1bhqKfsS3HQKbT2SNgHWpHYbT93tMvm2oQeBxTXqbU3qtv33PsRrZmYdUnYCuhrYQ9JaubKxwALgpgbbbZjd5wOApJHA5tk6ImIRcCNwQGHbscDtEfFs++GbmVlflZ2ALgAWAZdK2i1rfxkHnJXvmi1phqQf9ixHxO3ANcDFkvaTtC/wM+CW3D1AACcDoyV9R9JoSaeTbkY9qd+fWWdU4lI65KO6AAAYxUlEQVRgDVWNCxxbX1Q1LnBsfVHVuFZQaicESEPxAOcBo0jtMhcC4yJiaa7OTGByRBycK1sHOBv4ACmRXgEcGRHLNb5lyekbwJak+4TGRcTEfnxKZmbWhNITkJmZDUxlX4IzM7MBygnIzMxK4QRkZmalcAIyM7NSlD0SggGSROrNtzfwRuDVwFLgCeAO0rBEpdw4m90YvBcg4NcR8bSk1wJHkwZ8nQmMj4ipXYzpS8BV3TxmsyQNAlaNiOdzZesDRwDbkG6C/jNwfjfvRZP0VmBQRNyWK3sf8OVcXH8h9RK9rfZeuif7n3g/8DYggHtIf/NK9JrKpo15CtglIm4pMYZdgNWAKyNiXvZe+yzpnsiHSP+bj5cRXzPcC65k2RvmKmAEKeEsAjYm/dNdTXojbQWcHBEndzm2d5DmTRoMLAGeIc3DdBUpQd4LbAtsCOwWEX/oUlzLSK/PdODnwC8jYkY3jt2IpKuAByLi89nyKNLfcRkwhZTIRwAvkD687u1SXHcAl0fEKdnyJ0i3PNwI3JDFtStpQsf9I+K33Ygri+U24NCIuC9bHkp6340A5mbVBpO+jO2RT+79HNd/97J6EHAGcA7wAEBEnN+NuAAkvR64HtgkK3oY2B2YRBpu7EHS58YCYEREPNat2FoSEX6U+AB+QXoDb5crew3we+CSbHln0j/iJ7oc2yTSB9Q6pKktzgMeA34LvDKrszrpA/bGLsa1DPgW6d6vRaRkeDfwBWDjkv+eTwH75JbvIH1QrJUrG0Ia6eOaLsb1HGkA3p7lGcC5NepdAPyly6/ZMuAdueUfkr7svC9X9j7S+I5ndzmupdnPWo/8uqVdfs1+RTpjfT3pislPss+R23rea6RBSf8CfL+bsbX0PMoOYKA/SDff7l+jfHj2Bt8oWz6+hA+Gp4E9c8sbZP9suxfq7Q081cW4XvzAIk2rcVj2Ib8ke0zOytYt4e85H3hPbvmF4uuVe83mdfl9lk9Ai0kzChfr7QYs7PJrVkxA/wb+p0a9o4FHuhjXZcA/gUPIrhbl1q2Txf2ebsVTOP7jwIG55U2zePYr1DsE+HsZMTbzcCeE8omUaIqWZut6Zm69k+5PohfZI79MoazWctdExOyIGB8RuwKvBY4iXRO/AHhc0pVdDulvpJl4ezxB+oZatC4pWXXLH4CDcsv3ArVGTH47MKsrEdW3DqnNp2gK6XJvV0TEvsDHgWOAu7MpXl5c3a046hgK/Cu33PM3e6RQ7yHS/0UluRNC+a4DviHprxHxELx4Dfx/SW+wns4Hg4FuD6A6BTha0q3APNJZ2CzgM5JuiIilklYF/pv0wVuqiPgX6Zr8OZI2BT5MGny2m04FfibpH8DFwCnAGZKeJl12EylBfYsVp4vvT8cDt0p6BXAuqfPBjyW9mnTGCKkN6H+A47oYV4/9swGFof50K+uRLiV2TURcK+nNpNflSkm/J52JdaUdqhdPks56eiwFvk/6wpO3AeXHWl/Zp2AD/UH6dvI30iWRGcA0UsPhHJa//HU6qbG9m7GNJH0YLM5iehp4C+la80PA5aTGz0XAmC7Gtdwlm6o9gE+SPiifBe7Kfl+aPZZkP/8PeFWX49oeuJ0a7RfZz6eBz5fwetVqX/lRjXrfB/5Q4t91Q9KXirnAmdnrVtYluMtqvUY16p0LXFfWa9bo4V5wFSBpFeBA0of7GqRE9POIeKbUwICsy/V/kM6WL4mIf0raEDiW1MvmEeDCiPhjF2M6EfhBVLl7qbQu6ezrHaQPrleQGtbvA66IiCklxvZG4J014rotIhaXFVcjkj4FPBgRN5QcxyjSQMhbAXtHCd3WJQ0jfYF5uEG9L5Lajq/vTmStcQIyM7NSuA2oQiS9iTRj61BSI+ccYHp06V6RVklaJXLTZpRN0hqkm2OXATPK/jaftY9tTu7G4oh4tMyYXm6yG1KJEr8pZzcXKyLm58q2J7sRu8yz2Ze9sq8B+hEAnyBdyqp1z8FS0mgDh5QU236k681XAe/PysZmMS3N4v5Ul2P6KLl7okhfpE4l9SrraWt5HjiupNdsBPA7UrvZ0sJjFmlCxK62/2Rx/Qepu/pU4JfUaL8gXZrr9j0tu5O7Tyor2xf4I6nNbDGpV9zeXY5rCKmtbnEWxw+AVYAfF/4/bwXWK+O91sRz2L/bf89WHu6GXTJJnyM1rl4BjCb1Wnll9tiAdBPqFcAFkj7b5dgOBH5D6n20GPhldh3+J6QPsiNJN75dIGmPLoZ2POkG2B6nZbF8C3gP6TU7EzhR0vFdjAtJu5Nek9cA3yHNynst6YNqHHAW6UPhtqy3Y7fiei/pBuI1SL3xXg/cKOnMnrOMEl1NGoIKAEkfAC4FFpJ65H2ZdD/Vb7PXt1tOJo0M8UXSl8R3kXou7kK6MXYYKakPz+pai9wGVDJJDwEXRMTpDeodCxweEZt3JzKQdDcwJSIOz5YPAn4EnBcRR+XqXQRsEhG7dSmu+aQegjdly08Cp0TEOYV6RwOfi4hNa+ymv2KbAvwtIj5eKP8c6R6lzUn3Kd0G3BERvQ330sm4biENEXRIruwTpO7+k4APR8RCSe8kdUZYpRtxZXEsA3aIiLuy5T8CsyLi/YV6VwFrRsTOXYrrYeCbEfGDbPmtpFsTDomIH+fqfQo4PiI260Zc2TF/1GTVTYHR3fx7tsJnQOXbkNRVt5G76OJNeJmtSGdAPa4gnZkVb+68lDSgZbc8Szor6zGENORI0V9IZ5HdtA3w0xrlPwVeB2wVEQtJZ0cf6GJc2xbjiogfkc4WdwBuyO4JqoJtSVcFisaTBiftlg146T48yMZ8I42zljeD2vct9aePky5dbtfg0bUvX33hBFS+vwKfym4QrCm7RPKprG43Bemad4+egSHnFOrNJd293i2/I90gu1q2fB3pptOiD5Pu+O+mJ0nd6YveQno9e24mfoSXRrnohoXAmsXCSA3oO5I+QG8DuvYtvhhK7vdneem9ljeP7n5mPUxK0D3eTWr3eVeh3o5AtzuXPADcEBFv7+1BOTcVN8294Mp3FGng0WmSLiWN8DyH9A+5DqlX3AdIN6y+r8uxPUL6Rn8NQKSRD0aR7hnJ25zlhwXpb18mDS3zN0kXkm6IPU3Strx0V/8uwFtJQ/p303jgZElrktrJXiANb/MV0oCtPfcubU53P7T+CuxJSt7LiYiHsmFmrgImdDGmvGskLcl+H0K6aXZyoc7WpLHZuuUC0qga25GS4oGk994JkgaTzrDfRhoEt9ttQHewYiKsJUijb1SSE1DJIuLWrEvnsaSxujYpVPkHqZH2jIgonvr3t0spjCMVEXfWqPcRoGtzokTEM5J2IH2of5GXLrONyh4vkNo13h0Rd3crriy2U7I2jeOAE3uKSaOe/0+u6mLgm10M7RLgeEmvjho3OEfEk5J2JvX66kpbXs7Xa5Q9WaNsf9Lo7F0REedlVyY+TDozPDYiLpD0GKntrGc8vwuAb3crrsy5pF6CjdzE8mMTVoo7IVSMpFfx0uWsOZG796CqJL2OFGtXx+nKHX84y9/V/2CUfw/QK0n3iawBPFTWa2P9I7ssvl5E/LvsWF7OnIDMzKwUvgRXEdnU1xsA90fECg2wktYD9oqIi7seXA3ZNfA/Agd1+zJXVae9zsVSuWnMm5WNE3dARJzU5eO+LKaXrjFV+BRSvF3/Jp+NHr4/6X02ISKmS3oL6ZJmz/vsuxHx+27H1iyfAZVM0uqk7rH7ZUXLSCPufjH/4VnS/Rl79bJ6TdLd9MeRTcUQEVd1Ka5KTnudxVLJacybJWl/4Fddfp9Vcnrpqk4VnsWyB6nzzTOk3oHrA/uQ2m2nkb6AjSB1gNk/Ii7rVmwtKXsohoH+AE4g9Xr7FGn6g8+T5vR4ANgyV6+MIVIqOSUxFZ32OjtuVacxf12Tj8NLeJ9VcnppKjpVeHbcW4FfA6tky8dncfywUO8npBueuxZbS8+j7AAG+oPU7fqIQtmGwM2kqYlHZWVlJKApvDQl8aaFx5uzf9ADe8q6GFclp73OjlnlacyL49LVenT1y0QWWyWnl66RgCoxVXh2zGdJZ9A9y0OzeHcp1Nud1EGoa7G18nAbUPk2oXCDaUT8S9KupG8v12VD4HTz/oceI0lnZqeR7rs5OrL5RyT13ET5r4goTgPc33qmvb45W67KtNdQ3WnMnwduAC5sUG8n0i0B3fRymV66ElOFZxaw/I3FPb8PKtR7Fekm5EpyAirf48CWvPRhCkCkbsQfkvQd0ql21zsfRPoKNV7Sr4BvAH+VdF72e5mqOu01VHca87uAIRFRHEZpOdmUFt1W5emlKzlVOOkS3AmSHsiO/W1S28+XJN0cEc9nXxKPJb0nq6nsU7CB/iAN7jm5QZ0vU8KlkRpxvJl0d/rjpLaqMqckruq011WdxvxrwD+aqPceutg2lR2zktNLU+GpwkntZTNz7/kHSW14Pf8LU0nJejawfTdja+XhXnAly75djQVOjYine6n3EeC9kRvNuCySPgScTrocMjoibm6wSX/FUclpr6s4jXmVvdynly5rqvDsVogdSZ1dro+IBdmN7J/kpffZz6NLvQb7wgnI+iS7jLQmMDcqNCuqmb18OAGZmVkpPB3Dy4SkH0j6Ydlx1FLV2KoaF1Q3NknXSarUJa4eVY2tqnFBtWMD94J7ORlDdb8wVDW2qsYF1Y1NVDMuqG5sVY0Lqh2bL8GZmVk5KpsZbXmS1simPaicqsZW1bigurFJemUV44LqxlbVuKDasYET0MvJ3qT7R6qoqrFVNS4oITZJn5X0oKTnJd0p6WM1qr2t23FVObaqxlX12JrlBGQ2AGT3bp1LGrj166SbiSdI+k02vYVje5nEVfXYWuE2oJJJavbmtfWBbaK7w+RXMraqxgXVjU3SPcANEXFsrmxX4GekO+r3jjRvURnTflQytqrGVfXYWuEzoPK9BxhGGrKlt0e3x8CqcmxVjavKsW1FmpPoRdmIAjuQpq64XdIWXY6pR1Vjq2pcUO3YmuZu2OX7G2kW1LG9VZL0QdIEcN1U1diqGhdUN7ZnSYNmLiciZkp6F3Alaf6dk7sYU4+qxlbVuKDasTXNZ0Dlu5P0raWRIPXp76aqxlbVuKC6sU0B9q0ZSMRsYFfSVAP/28WYelQ1tqrGBdWOrWlOQOU7HfhcE/WuAjbr51iKqhpbVeOC6sb2U2BzSbXmTSIiFgD/SZov6NEuxgXVja2qcUG1Y2uaOyGYmVkpfAZkZmalcAIyM7NSOAGZmVkpnIDMzKwUTkDWK0kHS5qSjTc1W9KfJJ3VT8c6UNLBTdQbJylyj8clXdLsjXeSJmR3kpeu2eec1e153g/UWT8jWz+uv2Jocb/Lvc6dPo6kV0g6IntPLpD0nKR7Jf2vpD51cVfyF0kfr7N+gqThddZ9VxWc46nKnICsLklfJnXjvAbYD/gv4Lek7p394UDg4CbrPguMyh5HA9sD10tas4ltT27hOP2tlecMsBDYTNLIfKGktwObZuv7O4ZmFV/nTh9nIvAN4FLSe/LjpO7t74q+d+89EBgK/LwP254BHCTp9X089oDjkRCsN0cA34+I43Nll0v6elkB5SyJiDuy3++Q9CjwB2Av4NfFypJWAVaJiBci4sEuxtlp84A/Ah8i3WjY40PADcCIMoLq0a3XWdKewAHAXhFxdW7V//X17CdzJPCTiFicO9aqpGT6MeA1wIclPQh8PSJeHM0iG4XgFuAzwFFtxDBg+AzIerMO8K9iYf7bZc9lFkn7SpouaaGkWyRtU9wuuwQzVdIiSf+QdEr2z42kCcD+wM65S2vjWoh1SvZzeI247iWdGbwzv64Q23sk3ShprqRnJU2W9Nbc+p0k3SRpvqSnlabUXqu3gCSNkvS77BLhPEl/lnRQ/rXr43OeCBzY80Gb/TwwK+9YDNlr8JvC/kZndbbNv5aNXud6x5G0t6RlkjYrHGezrLze2fbO2c8VBn/t69lPdubyLuA3hVWfB44ljSpwFfAJ4EfAujV2cwnpLMifrU3wGZD15o/A57Kziysi4uk69TYFzgK+BiwgDQ9/jaQtI2IhgKTdSWOfXQwcA7yZ9K1yXeDw7PfXkZLef2f7fayFWIdnP/9VKDsdOAl4gjrzokgaDUwCbiRdxpkH7AhsDPxJ0o7A9cBlwAezmE8lXar5YC8xbQrcClxA+mDeEbhI0rKI+AV9f86XAt8DdiKd9b2bNLr2/5EuA3UjhrzhNH6d6x3nn6SpBD4OjMvVPxj4N4UBN3PmZT/PkHRmRDzSYsy17Jrt9y+F8p1JI0+fnn2xujUiZtbZx22kwWi3q7EfK4oIP/yo+SAliYdI45YtA+4lfcisnaszIVv/rlzZpsAS4PBc2R3AjYX9HwssBV6bLf8GmNxEXOOAp0hfoFYF3kBKHs8BGxXi2r7G9hOAe3LLt5MuZ6nO8f5QI/Zdsv1v2+RrqSzW75M+zHrKm3rO+eed/f5b4LvZ7+cDl2W/PwWM60QMwGTgN4Wy0fnn3eLrXO843yAlLeXinAl8u5fXYkPgr9mxgzQI7PHA4Dbe7+OBu2uUfx/4R3bMCcDwXvaxavbe/1Rf4xhID58mWl0R8VfgjaQG3vNJHwxfA+6RNDhX9cmIuC233SOkS2LvgBfbBd7Gim0zvyRdBh7Vh/DWBRZnj/uBzYGxEfHPXJ1ZEfHn3naSdVp4J/DjyD5BCutflcX3K0mr9jyAW7Jj121zkTRUqUfWI7lYDyMlzHZNBD4oaXXSWdgKl9+6EEOPhq9zAz8ifWkZnS2PyZYvqrdBRPwLeCuwB+lscB3gFOA2SavBiz04/5w9FmWXiP+s1KvzlTV2uyEpgRedQjozepj0v3B0dlZcK64lwJxsX9aAE5D1KiIWRcTlEXFERGwDfBLYEjg0V+3JGps+CWyU/b4e8ErS5Zm8nuWaAyo28CzwdmAk8FrSt9KrC3WKx6tlKCmx/rOX9auQEvDi3GMR6Tlt0su+JwBjSZfFds/i/RGwRhNxNfI7YDDpw3FN4PISYujRzOtcV0Q8RDrbOiQrOgS4KyLubbDd0oi4NiL+m3R57yLSpa9R2foJEbE96cvPEmDHiNg+IkZErpNBzhqkv2vxOI9m+/0A6YrATsAtqn87wiI6+/qutNwGZC2JiB9KOh3YOle8QY2qG5Au2UH6Vrm4Rr1h2c9n+hDKkohodC9PM43Rs0mXFzeqs35Otp9x1G6PeLzWRpLWAPYGjoiIC3LlHfnSFxHzJF0BfAH4dUTMK9bpQAwLgdUKZbW+LHRiROMLgR8odf3fjxZ7kUXEMknXkpJX8cN/S2B21G/D7PEMdc5csoT1e6WpsMeRpkI4W9J3sgSVtw59e08POD4DsrokrZBYJK1PmnEx/613A6VJsHrqvI70rfMuSN9USZfkDijs7kDSh//t2fILdPmbY/bBfSfwXz29ymqsvwPYKiLuqfGomYCA1UlnTi9+o856zRV7dbXznL9HOvO5oM76dmN4jOW/aAC8t0+R9n4cSB0rXiBdSnwFdS4pAkgaVmfVfwLzSX/PvLfQXIeA+6kxRUat9wVwd/bz1YW66wOvAv7exPEGPJ8BWW+mSvotcC3pktqmpJs+5wM/ztV7CviJpJ5ecCdl9Sfk6pxI6hl3EenDZTtSz6gfRERPr6vpwD6S9iV9+D3eywd8Jx0HXAdcLWk86Xr/KFID+hWkzhLXS1pGakh/nnTJZ2/gKxGxwodNRDwr6W7gBEnPkRLtcaRLh2vnqvb5OUfEZNKlq3rr243h/4BDJZ1NmmFzDKnNpa/qPteIWCjpZ8BngV9ExJxe9vMrSc8DvyJ1VtgAOAjYh9T4X9z2LaQOC43cSnqt1o+If+fKfy7pT8DNpMudI0hnnrOA+wr7GEk6I7wNa6zsXhB+VPdB+jC4lnSZaSHpn/3nwNa5OhNIPcj2I33rW0T6R16hdxipLWIq6ZvuY6T2i1Vz69cjfeg9Q3bZq05c48h6g/US+wRyPbAarSN1tb2ZlFznkHrVbZ9b/07g96SedvOAaaSu50N6ieH1pPtU5pEmBTu2GHuzz7mF571cL7h2YwC+TOoB9jxpErT/ZMVecE29zo2eK7BbVr5bg+f4iexv8Vj2XnqGlCBH16l/OfChJt7vqwFPAx8rlH8gO96/SEn8OVLif2uNfZxDocekH/UfnpDO2pLdYLhtRIxsVNesN1nb4lhgs4hY1sH9PgrsERHFs5Vadc8BXh8Re9dZP4GUOGfWWLcK8AhwXET8tK2gBwhfgjOzUknaCtiGNITN1zucfIaSbtJttk3mDOB+SW+IGpdWGziAdAm6bvuVLc+dEMysbN8nXdq9ijTcTcdExOyIGBSpI0wz9R8j3WJQr1fkZaRLtLUIODTSvUDWBF+CMzOzUvgMyMzMSuEEZGZmpXACMjOzUjgBmZlZKZyAzMysFE5AZmZWCicgMzMrhROQmZmV4v8Bzzme+z7FdgYAAAAASUVORK5CYII=\n", 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\n", 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\n", + "image/png": 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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" ] @@ -494,9 +496,9 @@ ], "metadata": { "kernelspec": { - "display_name": "qiskit_master", + "display_name": "Python 3", "language": "python", - "name": "qiskit_master" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -508,7 +510,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.1" + "version": "3.7.1" } }, "nbformat": 4, diff --git a/qiskit/finance/simulation/credit_risk_analysis.ipynb b/qiskit/finance/simulation/credit_risk_analysis.ipynb index 7a842f4cb..a90318cee 100644 --- a/qiskit/finance/simulation/credit_risk_analysis.ipynb +++ b/qiskit/finance/simulation/credit_risk_analysis.ipynb @@ -30,8 +30,9 @@ "### Introduction\n", "This tutorial shows how quantum algorithms can be used for credit risk analysis.\n", "More precisecly, how Quantum Amplitude Estimation (QAE) can be used to estimate risk measures with a quadratic speed-up over classical Monte Carlo simulation.\n", - "The tutorial is based on the following paper:\n", - "Quantum Risk Analysis. Stefan Woerner, Daniel J. Egger. [Woerner2019]\n", + "The tutorial is based on the following papers:\n", + "- Quantum Risk Analysis. Stefan Woerner, Daniel J. Egger. [Woerner2019]\n", + "- Credit Risk Analysis using Quantum Computers. Egger et al. (2019) [Egger2019]\n", "\n", "A general introduction to QAE can be found in the following paper and tutorial:\n", "- Quantum Amplitude Amplification and Estimation. Gilles Brassard et al.\n", @@ -101,7 +102,8 @@ "$$ \\text{CVaR}_{\\alpha}(L) = \\mathbb{E}[ L \\mid L \\geq \\text{VaR}_{\\alpha}(L) ].$$\n", "\n", "For more details on the considered model, see, e.g.,
\n", - "Regulatory Capital Modelling for Credit Risk. Marek Rutkowski, Silvio Tarca.\n", + "Regulatory Capital Modelling for Credit Risk. Marek Rutkowski, Silvio Tarca\n", + "\n", "\n", "\n", "The problem is defined by the following parameters:\n", @@ -141,7 +143,7 @@ "$$ |\\Psi\\rangle = \\sum_{i=0}^{2^{n_z}-1} \\sqrt{p_z^i} |z_i \\rangle \\bigotimes_{k=1}^K \n", "\\left( \\sqrt{1 - p_k(z_i)}|0\\rangle + \\sqrt{p_k(z_i)}|1\\rangle\\right),$$\n", "\n", - "where we denote by $z_i$ the $i$-th value of the discretized and trucated $Z$." + "where we denote by $z_i$ the $i$-th value of the discretized and trucated $Z$ [Egger2019]." ] }, { @@ -255,7 +257,7 @@ }, { "data": { - "image/png": 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\n", 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\n", 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\n", + "image/png": 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\n", 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\n", 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\n", 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                                                ┌───┐┌────────────────┐┌───┐»\n",
-       "  q_0: |0>──────────────────────────────────────┤ X ├┤ U3(0.7907,0,0) ├┤ X ├»\n",
-       "          ┌────────────────┐     ┌───────┐      └─┬─┘└────────────────┘└─┬─┘»\n",
-       "  q_1: |0>┤ U3(1.5708,0,0) ├─────┤ U1(0) ├────────■──────────────────────■──»\n",
-       "          └─┬────────────┬─┘┌────┴───────┴─────┐                            »\n",
-       "  q_2: |0>──┤ Ry(1.1847) ├──┤ U3(-0.14182,0,0) ├────────────────────────────»\n",
-       "            ├────────────┤  ├──────────────────┤                            »\n",
-       "  q_3: |0>──┤ Ry(1.3696) ├──┤ U3(-0.11174,0,0) ├────────────────────────────»\n",
-       "            └────────────┘  └──────────────────┘                            »\n",
-       "  q_4: |0>──────────────────────────────────────────────────────────────────»\n",
-       "                                                                            »\n",
-       "q_a_0: |0>──────────────────────────────────────────────────────────────────»\n",
-       "                                                                            »\n",
-       "q_a_1: |0>──────────────────────────────────────────────────────────────────»\n",
-       "                                                                            »\n",
-       "q_a_2: |0>──────────────────────────────────────────────────────────────────»\n",
-       "                                                                            »\n",
-       "«       ┌────────────────┐┌───┐┌───────┐┌───┐┌───────┐                        »\n",
-       "«  q_0: ┤ U3(1.5708,0,0) ├┤ X ├┤ U1(0) ├┤ X ├┤ U1(0) ├──■─────────────────────»\n",
-       "«       └────────────────┘└─┬─┘└───────┘└─┬─┘└───────┘  │                     »\n",
-       "«  q_1: ────────────────────■─────────────■─────────────┼─────────────────────»\n",
-       "«                                                     ┌─┴─┐┌─────────────────┐»\n",
-       "«  q_2: ──────────────────────────────────────────────┤ X ├┤ U3(0.14182,0,0) ├»\n",
-       "«                                                     └───┘└─────────────────┘»\n",
-       "«  q_3: ──────────────────────────────────────────────────────────────────────»\n",
-       "«                                                                             »\n",
-       "«  q_4: ──────────────────────────────────────────────────────────────────────»\n",
-       "«                                                                             »\n",
-       "«q_a_0: ──────────────────────────────────────────────────────────────────────»\n",
-       "«                                                                             »\n",
-       "«q_a_1: ──────────────────────────────────────────────────────────────────────»\n",
-       "«                                                                             »\n",
-       "«q_a_2: ──────────────────────────────────────────────────────────────────────»\n",
-       "«                                                                             »\n",
+       "
                                              ┌───┐┌────────────────┐┌───┐»\n",
+       "  q_0: |0>────────────────────────────────────┤ X ├┤ U3(0.7907,0,0) ├┤ X ├»\n",
+       "          ┌──────────────┐     ┌───────┐      └─┬─┘└────────────────┘└─┬─┘»\n",
+       "  q_1: |0>┤ U3(pi/2,0,0) ├─────┤ U1(0) ├────────■──────────────────────■──»\n",
+       "          └┬────────────┬┘┌────┴───────┴─────┐                            »\n",
+       "  q_2: |0>─┤ Ry(1.1847) ├─┤ U3(-0.14182,0,0) ├────────────────────────────»\n",
+       "           ├────────────┤ ├──────────────────┤                            »\n",
+       "  q_3: |0>─┤ Ry(1.3696) ├─┤ U3(-0.11174,0,0) ├────────────────────────────»\n",
+       "           └────────────┘ └──────────────────┘                            »\n",
+       "  q_4: |0>────────────────────────────────────────────────────────────────»\n",
+       "                                                                          »\n",
+       "q_a_0: |0>────────────────────────────────────────────────────────────────»\n",
+       "                                                                          »\n",
+       "q_a_1: |0>────────────────────────────────────────────────────────────────»\n",
+       "                                                                          »\n",
+       "q_a_2: |0>────────────────────────────────────────────────────────────────»\n",
+       "                                                                          »\n",
+       "«       ┌──────────────┐┌───┐┌───────┐┌───┐┌───────┐                        »\n",
+       "«  q_0: ┤ U3(pi/2,0,0) ├┤ X ├┤ U1(0) ├┤ X ├┤ U1(0) ├──■─────────────────────»\n",
+       "«       └──────────────┘└─┬─┘└───────┘└─┬─┘└───────┘  │                     »\n",
+       "«  q_1: ──────────────────■─────────────■─────────────┼─────────────────────»\n",
+       "«                                                   ┌─┴─┐┌─────────────────┐»\n",
+       "«  q_2: ────────────────────────────────────────────┤ X ├┤ U3(0.14182,0,0) ├»\n",
+       "«                                                   └───┘└─────────────────┘»\n",
+       "«  q_3: ────────────────────────────────────────────────────────────────────»\n",
+       "«                                                                           »\n",
+       "«  q_4: ────────────────────────────────────────────────────────────────────»\n",
+       "«                                                                           »\n",
+       "«q_a_0: ────────────────────────────────────────────────────────────────────»\n",
+       "«                                                                           »\n",
+       "«q_a_1: ────────────────────────────────────────────────────────────────────»\n",
+       "«                                                                           »\n",
+       "«q_a_2: ────────────────────────────────────────────────────────────────────»\n",
+       "«                                                                           »\n",
        "«                                                             »\n",
        "«  q_0: ──■────■───────────────────────────────────────────■──»\n",
        "«         │    │                                           │  »\n",
@@ -496,60 +498,60 @@
        "«                                                                            ░ »\n",
        "«q_a_2: ─────────────────────────────────────────────────────────────────────░─»\n",
        "«                                                                            ░ »\n",
-       "«                                                ░               »\n",
-       "«  q_0: ─────────────────────────────────────────░───────────────»\n",
-       "«                                                ░               »\n",
-       "«  q_1: ─────────────────────────────────────────░───────────────»\n",
-       "«                                                ░               »\n",
-       "«  q_2: ──■────■────■─────────■──────────────────░───────────────»\n",
-       "«         │    │    │         │                  ░               »\n",
-       "«  q_3: ──┼────┼────┼─────────┼────■────■────────░───────────────»\n",
-       "«         │    │    │         │    │    │        ░ ┌────────────┐»\n",
-       "«  q_4: ──┼────┼────┼─────────┼────┼────┼────────░─┤ Ry(1.1781) ├»\n",
-       "«         │  ┌─┴─┐  │  ┌───┐  │    │    │  ┌───┐ ░ └────────────┘»\n",
-       "«q_a_0: ──■──┤ X ├──┼──┤ X ├──■────┼────┼──┤ X ├─░───────────────»\n",
-       "«         │  └───┘┌─┴─┐└───┘  │  ┌─┴─┐┌─┴─┐└───┘ ░               »\n",
-       "«q_a_1: ──┼───────┤ X ├───────┼──┤ X ├┤ X ├──────░───────────────»\n",
-       "«       ┌─┴─┐     └─┬─┘     ┌─┴─┐└───┘└─┬─┘      ░               »\n",
-       "«q_a_2: ┤ X ├───────■───────┤ X ├───────■────────░───────────────»\n",
-       "«       └───┘               └───┘                ░               »\n",
-       "«                                                                             »\n",
-       "«  q_0: ──────────────────────────────────────────────────────────────────────»\n",
-       "«                                                                             »\n",
-       "«  q_1: ──────────────────────────────────────────────────────────────────────»\n",
-       "«                                                                             »\n",
-       "«  q_2: ──────────────────────────────────────────────────────────────────────»\n",
-       "«                                                                             »\n",
-       "«  q_3: ──────────────────────────────────────────────────────────────────────»\n",
-       "«       ┌────────────────┐┌───┐┌─────────────────┐┌───┐┌────────────────┐┌───┐»\n",
-       "«  q_4: ┤ U3(0.1309,0,0) ├┤ X ├┤ U3(-0.1309,0,0) ├┤ X ├┤ U3(0.2618,0,0) ├┤ X ├»\n",
-       "«       └────────────────┘└─┬─┘└─────────────────┘└─┬─┘└────────────────┘└─┬─┘»\n",
-       "«q_a_0: ────────────────────■───────────────────────■──────────────────────┼──»\n",
-       "«                                                                          │  »\n",
-       "«q_a_1: ───────────────────────────────────────────────────────────────────■──»\n",
-       "«                                                                             »\n",
-       "«q_a_2: ──────────────────────────────────────────────────────────────────────»\n",
-       "«                                                                             »\n",
-       "«                                ░                                          ░ \n",
-       "«  q_0: ─────────────────────────░──────────────────────────────────────────░─\n",
-       "«                                ░                                          ░ \n",
-       "«  q_1: ─────────────────────────░──────────────────────────────────────────░─\n",
-       "«                                ░                                          ░ \n",
-       "«  q_2: ─────────────────────────░──────────────────■────■─────────■────■───░─\n",
-       "«                                ░                  │    │         │    │   ░ \n",
-       "«  q_3: ─────────────────────────░───■─────────■────┼────┼─────────┼────┼───░─\n",
-       "«       ┌─────────────────┐┌───┐ ░   │         │    │    │         │    │   ░ \n",
-       "«  q_4: ┤ U3(-0.2618,0,0) ├┤ X ├─░───┼─────────┼────┼────┼─────────┼────┼───░─\n",
-       "«       └─────────────────┘└─┬─┘ ░   │  ┌───┐  │    │    │  ┌───┐┌─┴─┐  │   ░ \n",
-       "«q_a_0: ─────────────────────┼───░───┼──┤ X ├──┼────■────┼──┤ X ├┤ X ├──■───░─\n",
-       "«                            │   ░ ┌─┴─┐└───┘┌─┴─┐  │  ┌─┴─┐└───┘└───┘  │   ░ \n",
-       "«q_a_1: ─────────────────────■───░─┤ X ├─────┤ X ├──┼──┤ X ├────────────┼───░─\n",
-       "«                                ░ └─┬─┘     └───┘┌─┴─┐└─┬─┘          ┌─┴─┐ ░ \n",
-       "«q_a_2: ─────────────────────────░───■────────────┤ X ├──■────────────┤ X ├─░─\n",
-       "«                                ░                └───┘               └───┘ ░ 
"
+       "«                                                ░              »\n",
+       "«  q_0: ─────────────────────────────────────────░──────────────»\n",
+       "«                                                ░              »\n",
+       "«  q_1: ─────────────────────────────────────────░──────────────»\n",
+       "«                                                ░              »\n",
+       "«  q_2: ──■────■────■─────────■──────────────────░──────────────»\n",
+       "«         │    │    │         │                  ░              »\n",
+       "«  q_3: ──┼────┼────┼─────────┼────■────■────────░──────────────»\n",
+       "«         │    │    │         │    │    │        ░ ┌───────────┐»\n",
+       "«  q_4: ──┼────┼────┼─────────┼────┼────┼────────░─┤ Ry(3pi/8) ├»\n",
+       "«         │  ┌─┴─┐  │  ┌───┐  │    │    │  ┌───┐ ░ └───────────┘»\n",
+       "«q_a_0: ──■──┤ X ├──┼──┤ X ├──■────┼────┼──┤ X ├─░──────────────»\n",
+       "«         │  └───┘┌─┴─┐└───┘  │  ┌─┴─┐┌─┴─┐└───┘ ░              »\n",
+       "«q_a_1: ──┼───────┤ X ├───────┼──┤ X ├┤ X ├──────░──────────────»\n",
+       "«       ┌─┴─┐     └─┬─┘     ┌─┴─┐└───┘└─┬─┘      ░              »\n",
+       "«q_a_2: ┤ X ├───────■───────┤ X ├───────■────────░──────────────»\n",
+       "«       └───┘               └───┘                ░              »\n",
+       "«                                                                          »\n",
+       "«  q_0: ───────────────────────────────────────────────────────────────────»\n",
+       "«                                                                          »\n",
+       "«  q_1: ───────────────────────────────────────────────────────────────────»\n",
+       "«                                                                          »\n",
+       "«  q_2: ───────────────────────────────────────────────────────────────────»\n",
+       "«                                                                          »\n",
+       "«  q_3: ───────────────────────────────────────────────────────────────────»\n",
+       "«       ┌───────────────┐┌───┐┌────────────────┐┌───┐┌───────────────┐┌───┐»\n",
+       "«  q_4: ┤ U3(pi/24,0,0) ├┤ X ├┤ U3(-pi/24,0,0) ├┤ X ├┤ U3(pi/12,0,0) ├┤ X ├»\n",
+       "«       └───────────────┘└─┬─┘└────────────────┘└─┬─┘└───────────────┘└─┬─┘»\n",
+       "«q_a_0: ───────────────────■──────────────────────■─────────────────────┼──»\n",
+       "«                                                                       │  »\n",
+       "«q_a_1: ────────────────────────────────────────────────────────────────■──»\n",
+       "«                                                                          »\n",
+       "«q_a_2: ───────────────────────────────────────────────────────────────────»\n",
+       "«                                                                          »\n",
+       "«                               ░                                          ░ \n",
+       "«  q_0: ────────────────────────░──────────────────────────────────────────░─\n",
+       "«                               ░                                          ░ \n",
+       "«  q_1: ────────────────────────░──────────────────────────────────────────░─\n",
+       "«                               ░                                          ░ \n",
+       "«  q_2: ────────────────────────░──────────────────■────■─────────■────■───░─\n",
+       "«                               ░                  │    │         │    │   ░ \n",
+       "«  q_3: ────────────────────────░───■─────────■────┼────┼─────────┼────┼───░─\n",
+       "«       ┌────────────────┐┌───┐ ░   │         │    │    │         │    │   ░ \n",
+       "«  q_4: ┤ U3(-pi/12,0,0) ├┤ X ├─░───┼─────────┼────┼────┼─────────┼────┼───░─\n",
+       "«       └────────────────┘└─┬─┘ ░   │  ┌───┐  │    │    │  ┌───┐┌─┴─┐  │   ░ \n",
+       "«q_a_0: ────────────────────┼───░───┼──┤ X ├──┼────■────┼──┤ X ├┤ X ├──■───░─\n",
+       "«                           │   ░ ┌─┴─┐└───┘┌─┴─┐  │  ┌─┴─┐└───┘└───┘  │   ░ \n",
+       "«q_a_1: ────────────────────■───░─┤ X ├─────┤ X ├──┼──┤ X ├────────────┼───░─\n",
+       "«                               ░ └─┬─┘     └───┘┌─┴─┐└─┬─┘          ┌─┴─┐ ░ \n",
+       "«q_a_2: ────────────────────────░───■────────────┤ X ├──■────────────┤ X ├─░─\n",
+       "«                               ░                └───┘               └───┘ ░
" ], "text/plain": [ - "" + "" ] }, "execution_count": 12, @@ -643,7 +645,7 @@ "outputs": [ { "data": { - "image/png": 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WWotNY6SvK/M54PO5pGFJzwPflfSeiFhUp3yNkb6u7CuAKwCGhoZi8uTJ9Wtf0vDwMJ0qa5D1QzvNOOPmutuXf2xy1+vQD+20IXA7ldOrdmp24qcknS5pGfAK8Icaj3pGgO1rpI+n9plPPddmz+/NlU2N8te9b7Z8MzProGbn4ZwCnAF8n3Tm8A/AecDjwHKyS1N1LCX11bxO0h7A1ozue2kkCs9PkILgpEK+ScDarI5mZtYjzQacTwHnABdm72+IiHOBfUkB4+0N9p8LHCVp21zaNNLtD5rtKzoxe34IICLWkOYJfaSQbxrwgEeomZn1VrN9OG8FFkXEa5JeIbtcFRFrJX0X+B7pDGgsl5HOkq6XdAGwFzALuCg/VDq7ZLcgIk7O3s8CtiVN+lwJfAD4EnB9RPwsV/7XSP07l5DmCU3NHkc3eZxmZtZhzZ7h/B7YJnv9FPDfctt2IE3qHFNEjACHkebq3AicC1xMOmvK24z15/MsJc3TuRK4BTgJ+Gb2nC//XtKZz+HAPOCDwEleZcDMrPeaPcO5D3gf6Uf/h6QVAnYE/gR8DrijUQERsRg4tEGeiYX3c0gTOBuKiBtIZzdmZrYBaTbgzAJ2z16fT7qkNoN0ZjMf+EKnKmZmZoOlqYATEY8Bj2Wv15DuhXNqF+plZmYDpp2Jn28BdgOejYhnOlclMzMbRK3cYvqzkn4NPAn8CHhK0tOS/nfHa2dmZgOj2ZUGzgYuJc2nORYYyp7nAt/JtpuZmY3S7CW1zwHnR8RXC+m3ZmubfY608oCZmdl6mr2kNo6x7+q5gBqLeZqZmUHzAecG4IQxtn0YuKm96piZ2aAqc4vpqbm3c4ELJU1k9C2m9wX+vvNVNDOzQVCmD+cmRt9KenfgqBp5/4V0J04zM7P1lAk4b+16LczMbOCVucX0k1VUxMzMBlvTKw1I2ow0QOBgYEfgv4B7SLcKqH/zdzMz22g1FXAk7QLcBuxHusPn88BBpPk3j0g6MiJ+1+lKmplZ/2t2WPRFwJuB90fEXhFxUETsBbw/S7+o0xU0M7PB0GzAmQqcHhE/ySdm779MWubGzMxslGYDzhbAH8bY9gfgTe1Vx8zMBlWzAedB4HRJW+cTs/enZ9vNzMxGaXaU2mnAXcCvJd1GGjSwC2kSqIDJHa2dmZkNjKbOcCJiEfB24ApgZ+AIUsC5DHh7RDzS8RqamdlAKH2GI2lz4ADgVxFxRveqZGZmg6iZM5zXgDuBd3WpLmZmNsBKB5yIWAv8ApjQveqYmdmganaU2leAsyW9uxuVMTOzwdXsKLWzSCsKLJL0DGmUWuQzRMQBHaqbmZkNkGYDzs+zh5mZWVNKBRxJ40jL2vwc+A1we0Q8382KmZnZYClzi+m9gNuBibnklZI+GhG3datiZmY2WMoMGrgQWAv8FbAVsC/wMHB5F+tlZmYDpkzAOQg4KyLui4iXI2IJ8GngzyXt1t3qmZnZoCgTcHYDfllIe4K0dtquHa+RmZkNpLLzcKJxFjMzs7GVHRY9T9KrNdLvKKZHxC7tV8vMzAZNmYBzbtdrYWZmA69hwIkIBxwzM2tbs2upmZmZtcQBx8zMKuGAY2ZmlXDAMTOzSjjgmJlZJRxwzMysEpUHHEn7SLpD0mpJz0o6T9KmDfZ5n6QrJS3L9ntM0jmStizkmyUpajyO7u5RmZlZI83egK0tknYg3epgMXAcsDfwLVLgO6vOrtOyvBcAvwD2A76WPX+4kHcFUAwwS9qtu5mZtafSgAN8BhgHnBARK4H5krYDZkm6MEur5YKI+F3u/bCkl4HLJe0ZEU/mtr0aEQ92p/pmZtaqqi+pHQPMKwSWOaQgdMhYOxWCzToPZ89eu83MrA9UHXAmAUvzCRHxFLA629aMvyTdGO6xQvr2kl6Q9IqkhyWd0HJtzcysYxRR3Z0HJL0CfCkiLimkPw1cHRFnlixnV+BnwC0RMSOX/nHSGc8iYBvSjeKmAh+OiOvHKGsmMBNgwoQJ+8+ZM6fZw6pp1apVbLPNNh0pa5D1Qzs9+syKutvfvfv4rtehH9ppQ+B2KqeT7TRlypSHImKoTN5eBJwvRsS3C+nPAFdFxFdKlPEm0sCDtwD7R8RInbwC7gfGRcR7GpU9NDQUCxcubJStlOHhYSZPntyRsgZZP7TTxDNurrt9+TeO7Xod+qGdNgRup3I62U6SSgecqi+pjQDb10gfD7zYaOcsgFwN7AtMrRdsACJF0+uB/RoNvTYzs+6qepTaUgp9NZL2ALam0LczhotJw6mPiIgy+dfxHUvNzHqs6jOcucBRkrbNpU0DXgIW1NtR0peBLwAfj4h7y3xYdkZ0PPBIRLzWWpXNzKwTqj7DuQw4Bbhe0gXAXsAs4KL8UGlJy4AFEXFy9v4k4HzgKuAZSQfmynxi3bBpSQuA60hnS1sDnwIOBD7U3cMyM7NGKg04ETEi6TDgUuBGUr/NxaSgU6xXvs/lyOx5RvbI+wQpEAEsA/4W2I00ZPqnwLERMbcT9Tczs9ZVfYZDRCwGDm2QZ2Lh/QxGB5pa+53cRtXMzKyLvFq0mZlVwgHHzMwq4YBjZmaVcMAxM7NKOOCYmVklHHDMzKwSDjhmZlYJBxwzM6uEA46ZmVXCAcfMzCrhgGNmZpVwwDEzs0o44JiZWSUccMzMrBIOOGZmVgkHHDMzq4QDjpmZVcIBx8zMKuGAY2ZmlXDAMTOzSjjgmJlZJRxwzMysEg44ZmZWCQccMzOrhAOOmZlVwgHHzMwq4YBjZmaVcMAxM7NKOOCYmVklHHDMzKwSDjhmZlYJBxwzM6uEA46ZmVXCAcfMzCrhgGNmZpVwwDEzs0o44JiZWSUccMzMrBIOOGZmVgkHHDMzq4QDjpmZVcIBx8zMKlF5wJG0j6Q7JK2W9Kyk8yRtWmK/8ZKulDQiaYWkH0h6c418x0l6VNLLkhZLmtadIzEzs2ZsVuWHSdoBuB1YDBwH7A18ixT4zmqw+zXAO4FPAmuBC4AbgL/KlX8wcB3wXeAUYCowW9JIRNzW0YOxnpl4xs0N8yz/xrEV1MTMmlFpwAE+A4wDToiIlcB8SdsBsyRdmKWNIukg4CjgkIi4O0t7BviRpMMj4vYs61eBuyPilOz9XZL2Bc4GHHCsbxSD6mnvfpUZuTQHVOtHVV9SOwaYVwgsc0hB6JAG+z2/LtgARMSPgV9l25C0BTAF+NfCvnOAgySNb7/6ZmbWqqrPcCYBd+YTIuIpSauzbTfW2W9pjfQl2TZIl+c2r5FvCSmwvgP4SWvVHizduiTlS139q+p/O39XNk5VB5wdgBdrpI9k21rZb69cHmrkGylsX4+kmcDM7O0qSY/VqUczdgJe6FBZldMFlZXblXbqVv179VmnFNqpyuPr1We2+Hl9/f+uQp1spz3LZqw64ABEjTSNkd7KfsX3qrM/EXEFcEWDz26apIURMdTpcgeN26kct1M5bqdyetVOVffhjADb10gfT+0zmEb7bZ/bbySXVsxDg/LNzKzLqg44S3mjzwUASXsAW1O7j2bM/TL5vp0ngFdq5JtEGkb9eAv1NTOzDqk64MwFjpK0bS5tGvASsKDBfrtm82wAkDRE6r+ZCxARa4C7gI8U9p0GPBARK9qvflM6fpluQLmdynE7leN2Kqcn7aSIRl0nHfywNPFzMfBz0sTNvYCLgEsi4qxcvmXAgog4OZd2K2mk2Rd5Y+LnbyOiOPFzGLiUNCl0apb/aE/8NDPrrUrPcCJiBDgM2JQ0BPpc4GLgnELWzbI8edNJZ0H/DFwNPAQcXyj/XuBE4HBgHvBB4CQHGzOz3qv0DMfMzDZeXi26AS822lgrbSTpfVn7LMv2e0zSOZK2LOSbJSlqPI7u7lF1XovtNHGM459TI2/ff5eg5XYa63sSkr6cy3fVGHlqDUraoEl6m6TLJT0i6TVJwyX369lvUy/m4fQNLzbaWBttNC3LewHwC2A/4GvZ84cLeVcAxQCzpN26V6nN7xKkvsj7cu/Xm7Q3CN8laKudvgfcWkj7EHA62cCinKXAJwppy1urcU/tS/p3fhB4UxP79e63KSL8GOMBfJk0v2e7XNrfA6vzaTX2O4g00fQDubQDsrTDc2nzgDsL+94C3NvrY6+gjXaukTYza6M9c2mzgBd6fZw9bKeJWZv8jwbl9/13qZ12GqOsm4ElhbSrgIW9Ps4OtdUmudfXAsMl9unpb5MvqdXnxUYba6mNIuJ3NZIfzp536Vz1NhitfpcaGqDvEnSonSTtCBwBzO5s9TYcEbG2hd16+tvkgFPfqEVDI+Ip0l9b9a75dmqx0X7QahvV8pekU/zienbbS3pB0iuSHpZ0Qsu17Z122+nK7Dr9c5IukjQut21QvkvQue/TiaQ2GdXXBewjaaWkNZLuldRWwO8zPf1tcsCprxuLje6Qy0ONfHUXG90AtdpG65G0K/AV4P8W/rpdRrqk8lFS386zwHV9GHRabac1wD8BJ5OmFFwOfJb1f0gH5bsEHfo+kaZR/DQiiiuMPAycBvxP4GOk6RfzJR3QQl37UU9/mzxooLENarHRDVSrbZQySm8inb6vAv5uvYIj/qWQ90bgftJN9a5vpbI91HQ7RcRzwOdzScOSnge+K+k9EbGoTvn9+F2C9r9Pu5Euv50+quCIbxfy3kwaoHAmaZDBxqBnv00+w6nPi4021mobASBJpIm8+wJTI00OHlOk3svrgf3KDE/fgLTVTgXXZs/vzZVNjfL77bsEnWmnj5J+HK9plDEiXiJ1hr+3Ud4B0dPfJgec+rzYaGOtttE6F5OGvx4XEWXyr9Nvf7W32055UXgelO8SdKadppNGU/26ic/tt+9Tq3r62+SAU9/GtNhoq1ptI7IJeV8APh5pWaKGsjOi44FHIuK11qrcEy23Uw0nZs8PwUB9l6DNdpI0ETiQkqPTssEXx5C15Uagt79NvR5LviE/SJ1jzwHzSeuzzST1M3y9kG8Z8P1C2q3AL4ETSNeGHwPuKeQ5GHgVuAS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5XNKQpOeB70p6T0QsbFK+RkhfW/YVwBUAAwMDMTg42Lz2JQ0NDdGrssayfmin6Wfc3HT7so8NVl6HfminDYHbqZy62qndiZaSdLqkpcArwB8aPJoZBrZvkD6exmc2zVybPb83VzYNyl/7vt3yzcysC+3OgzkFOAP4PunM4B+A84DHgWVkl5qaWELqa3mdpD2ArVm/76SVKDw/QQp6kwr5JgFrsjqamVlN2g0wnwLOAS7M3t8QEecC+5ICxNtb7D8HOErStrm0qaTbAbTb13Ni9vwQQESsJs3T+Ugh31TgAY8gMzOrV7t9MG8FFkbEa5JeIbv8FBFrJH0X+B7pDGckl5HOgq6XdAGwFzATuCg/dDm7BDc/Ik7O3s8EtiVNslwBfAD4EnB9RPwsV/7XSP0zl5Dm6UzJHke3eZxmZtalds9gfg9sk71+CvhvuW07kCZRjigihoHDSHNlbgTOBS4mnRXlbca682mWkObJXAncApwEfDN7zpd/L+nM5nBgLvBB4CTP4jczq1+7ZzD3Ae8j/cj/kDQDf0fgT8DngDtaFRARi4BDW+SZWHg/mzRhsqWIuIF09mJmZqOo3QAzE9g9e30+6RLZdNKZyzzgC72qmJmZ9be2AkxEPAY8lr1eTboXzKkV1MvMzPpcNxMt3wLsBjwbEc/0rkpmZjYWdHLL5M9K+jXwJPAj4ClJT0v63z2vnZmZ9a12Z/KfDVxKms9yLDCQPc8BvpNtNzMza/sS2eeA8yPiq4X0W7O1wT5HmtlvZmYbuXYvkY1j5LtWzqfB4pdmZrZxajfA3ACcMMK2DwM3dVcdMzMbK8rcMnlK7u0c4EJJE1n/lsn7An/f+yqamVk/KtMHcxPr3xp5d+CoBnn/hXSnSTMz28iVCTBvrbwWZmY25pS5ZfKTdVTEzMzGlrZn8kvajNShfzCwI/BfwD2kpfOb37zczMw2Gm0FGEm7ALcB+5HuYPk8cBBp/ssjko6MiN/1upJmZtZ/2h2mfBHwZuD9EbFXRBwUEXsB78/SL+p1Bc3MrD+1G2CmAKdHxE/yidn7L5OWjTEzM2s7wGwB/GGEbX8A3tRddczMbKxoN8A8CJwuaet8Yvb+9Gy7mZlZ26PITgPuAn4t6TZSJ/8upEmXAgZ7WjszM+tbbZ3BRMRC4O3AFcDOwBGkAHMZ8PaIeKTnNTQzs75U+gxG0ubAAcCvIuKM6qpkZmZjQTtnMK8BdwLvqqguZmY2hpQOMBGxBvgFMKG66piZ2VjR7iiyrwBnS3p3FZUxM7Oxo91RZGeRZuwvlPQMaRRZ5DNExAE9qpuZmfWxdgPMz7OHmZlZU6UCjKRxpGVifg78Brg9Ip6vsmJmZtbfytwyeS/gdmBiLnmFpI9GxG1VVczMzPpbmU7+C4E1wF8BWwH7Ag8Dl1dYLzMz63NlAsxBwFkRcV9EvBwRi4FPA38uabdqq2dmZv2qTIDZDfhlIe0J0tpju/a8RmZmNiaUnQcTrbOYmZm9oeww5bmSXm2QfkcxPSJ26b5aZmbW78oEmHMrr4WZmY05LQNMRDjAmJlZ29pdi8zMzKwUBxgzM6uEA4yZmVXCAcbMzCrhAGNmZpVwgDEzs0rUHmAk7SPpDkmrJD0r6TxJm7bY532SrpS0NNvvMUnnSNqykG+mpGjwOLraozIzs6J2bzjWFUk7kJb+XwQcB+wNfIsU6M5qsuvULO8FwC+A/YCvZc8fLuRdDhQDyuJu625mZu2pNcAAnwHGASdExApgnqTtgJmSLszSGrkgIn6Xez8k6WXgckl7RsSTuW2vRsSD1VTfzMzKqvsS2THA3EIgmU0KOoeMtFMhuKz1cPbstc/MzDZAdQeYScCSfEJEPAWsyra14y9JN0J7rJC+vaQXJL0i6WFJJ3RcWzMz65gi6luJX9IrwJci4pJC+tPA1RFxZslydgV+BtwSEdNz6R8nndEsBLYh3RhtCvDhiLh+hLJmADMAJkyYsP/s2bPbPayGVq5cyTbbbNOTssayfminR59Z3nT7u3cfX3kd+qGdNgRup3J62U6TJ09+KCIGGm0bjQDzxYj4diH9GeCqiPhKiTLeRBoo8BZg/4gYbpJXwP3AuIh4T6uyBwYGYsGCBa2ylTI0NMTg4GBPyhrL+qGdJp5xc9Pty75xbOV16Id22hC4ncrpZTtJGjHA1H2JbBjYvkH6eODFVjtnAeNqYF9gSrPgAhApel4P7NdqKLSZmfVW3aPIllDoa5G0B7A1hb6ZEVxMGt58RESUyb+W78hpZlazus9g5gBHSdo2lzYVeAmY32xHSV8GvgB8PCLuLfNh2RnP8cAjEfFaZ1U2M7NO1H0GcxlwCnC9pAuAvYCZwEX5ocuSlgLzI+Lk7P1JwPnAVcAzkg7MlfnE2mHMkuYD15HOhrYGPgUcCHyo2sMyM7OiWgNMRAxLOgy4FLiR1O9yMSnIFOuV7zM5Mnuenj3yPkEKPABLgb8FdiMNYf4pcGxEzOlF/c3MrLy6z2CIiEXAoS3yTCy8n876gaXRfid3UTUzM+shr6ZsZmaVcIAxM7NKOMCYmVklHGDMzKwSDjBmZlYJBxgzM6uEA4yZmVXCAcbMzCrhAGNmZpVwgDEzs0o4wJiZWSUcYMzMrBIOMGZmVgkHGDMzq4QDjJmZVcIBxszMKuEAY2ZmlXCAMTOzSjjAmJlZJRxgzMysEg4wZmZWCQcYMzOrhAOMmZlVwgHGzMwq4QBjZmaVcIAxM7NKOMCYmVklHGDMzKwSDjBmZlYJBxgzM6uEA4yZmVXCAcbMzCrhAGNmZpVwgDEzs0o4wJiZWSUcYMzMrBIOMGZmVgkHGDMzq4QDjJmZVcIBxszMKuEAY2ZmlXCAMTOzStQeYCTtI+kOSaskPSvpPEmblthvvKQrJQ1LWi7pB5Le3CDfcZIelfSypEWSplZzJGZm1sxmdX6YpB2A24FFwHHA3sC3SIHurBa7XwO8E/gksAa4ALgB+Ktc+QcD1wHfBU4BpgCzJA1HxG09PRgbNRPPuLllnmXfOLaGmphZM7UGGOAzwDjghIhYAcyTtB0wU9KFWdp6JB0EHAUcEhF3Z2nPAD+SdHhE3J5l/Spwd0Sckr2/S9K+wNmAA4z1jWIQPe3drzI9l+YAav2g7ktkxwBzC4FkNinoHNJiv+fXBheAiPgx8KtsG5K2ACYD/1rYdzZwkKTx3VffzMzKqvsMZhJwZz4hIp6StCrbdmOT/ZY0SF+cbYN0uW3zBvkWkwLpO4CfdFbtsaWqS0y+dNW/6v6383dl41B3gNkBeLFB+nC2rZP99srloUG+4cL2dUiaAczI3q6U9FiTerRjJ+CFHpVVO11QW7mVtFNV9R+tzzql0E51Ht9ofWaHn9fX/+9q1Mt22nOkDXUHGIBokKYR0jvZr/heTfYnIq4Armjx2W2TtCAiBnpd7ljjdirH7VSO26mcutqp7j6YYWD7BunjaXyG0mq/7XP7DefSinloUb6ZmfVY3QFmCW/0mQAgaQ9gaxr3sYy4XybfN/ME8EqDfJNIw5of76C+ZmbWoboDzBzgKEnb5tKmAi8B81vst2s2zwUASQOk/pc5ABGxGrgL+Ehh36nAAxGxvPvqt6Xnl93GKLdTOW6nctxO5dTSTopo1fXRww9LEy0XAT8nTZTcC7gIuCQizsrlWwrMj4iTc2m3kkaCfZE3Jlr+NiKKEy2HgEtJkzCnZPmP9kRLM7N61XoGExHDwGHApqQhyecCFwPnFLJuluXJm0Y6y/ln4GrgIeD4Qvn3AicChwNzgQ8CJzm4mJnVr9YzGDMz23h4NeUWvDhna520kaT3Ze2zNNvvMUnnSNqykG+mpGjwOLrao+q9Dttp4gjHP7tB3r7/LkHH7TTS9yQkfTmX76oR8jQaRLRBk/Q2SZdLekTSa5KGSu5X22/TaMyD6RtenLO1Ltpoapb3AuAXwH7A17LnDxfyLgeKAWVxt3WvU5ffJUh9iffl3q8zSW4sfJegq3b6HnBrIe1DwOlkA4FylgCfKKQt66zGo2pf0r/zg8Cb2tivvt+miPBjhAfwZdL8mu1yaX8PrMqnNdjvINLEzg/k0g7I0g7Ppc0F7izsewtw72gfew1ttHODtBlZG+2ZS5sJvDDaxzmK7TQxa5P/0aL8vv8uddNOI5R1M7C4kHYVsGC0j7NHbbVJ7vW1wFCJfWr9bfIlsua8OGdrHbVRRPyuQfLD2fMuvaveBqPT71JLY+i7BD1qJ0k7AkcAs3pbvQ1HRKzpYLdaf5scYJpbb5HNiHiK9NdUs2u2vVqcsx902kaN/CXplL24Htz2kl6Q9IqkhyWd0HFtR0+37XRldp39OUkXSRqX2zZWvkvQu+/TiaQ2Wa+vCthH0gpJqyXdK6mrAN9nav1tcoBprorFOXfI5aFBvqaLc26AOm2jdUjaFfgK8H8Lf70uJV0i+Sipb+ZZ4Lo+DDKdttNq4J+Ak0lD/C8HPsu6P5xj5bsEPfo+kaY1/DQiiit4PAycBvxP4GOk6RDzJB3QQV37Ua2/Te7kb22DWpxzA9VpG6WM0ptIp+Mrgb9bp+CIfynkvRG4n3QTues7qewoarudIuI54PO5pCFJzwPflfSeiFjYpPx+/C5B99+n3UiX005fr+CIbxfy3kwaUHAmaVDAxqC23yafwTTnxTlb67SNAJAk0sTZfYEpkSbjjihSb+P1wH5lhotvQLpqp4Jrs+f35sqmQfn99l2C3rTTR0k/hte0yhgRL5E6r9/bKu8YUetvkwNMc16cs7VO22iti0nDUY+LiDL51+q3v8q7bae8KDyPle8S9KadppFGO/26jc/tt+9Tp2r9bXKAaW5jWpyzU522EdkEuC8AH4+0zE9L2RnP8cAjEfFaZ1UeFR23UwMnZs8PwZj6LkGX7SRpInAgJUePZYMljiFry41Avb9Noz2We0N+kDqzngPmkdY3m0HqJ/h6Id9S4PuFtFuBXwInkK7tPgbcU8hzMPAqcAkwCFxI+gvhyNE+9qrbCDiJ9FfjlaQfhPxj51y++aSJXkeSAsstWRt9cLSPvaZ2mkmaaHhCtt95pB/b68bad6mbdsqln0H667vRPKvxwD3Ap0kDJqaSJimuBgZG+9g7aKutSH9snAg8APxn7v1WI7VTnb9No95IG/oD2Ae4M/tP/RxptvmmhTzLgKsKadtnP54vAiuAHwI7NSj/Q6TVpVeTTlGnjfYx19FGpAlvMcJjei7f97P/DC8Bf8x+II4Z7WOusZ2mAQtIqxn8KfvBOA/YYix+lzptp1z6QuDWEcrdktR/9+usjZZnP7YHjvYxd9hOE5v8H5o4UjvV+dvkxS7NzKwS7oMxM7NKOMCYmVklHGDMzKwSDjBmZlYJBxgzM6uEA4yZmVXCAcbMzCrhAGNmZpX4/7B6cf+/ofCKAAAAAElFTkSuQmCC\n", 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\n", + "image/png": 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" ] @@ -791,40 +793,40 @@ { "data": { "text/html": [ - "
                                                ┌───┐┌────────────────┐┌───┐»\n",
-       "  q_0: |0>──────────────────────────────────────┤ X ├┤ U3(0.7907,0,0) ├┤ X ├»\n",
-       "          ┌────────────────┐     ┌───────┐      └─┬─┘└────────────────┘└─┬─┘»\n",
-       "  q_1: |0>┤ U3(1.5708,0,0) ├─────┤ U1(0) ├────────■──────────────────────■──»\n",
-       "          └─┬────────────┬─┘┌────┴───────┴─────┐                            »\n",
-       "  q_2: |0>──┤ Ry(1.1847) ├──┤ U3(-0.14182,0,0) ├────────────────────────────»\n",
-       "            ├────────────┤  ├──────────────────┤                            »\n",
-       "  q_3: |0>──┤ Ry(1.3696) ├──┤ U3(-0.11174,0,0) ├────────────────────────────»\n",
-       "            └────────────┘  └──────────────────┘                            »\n",
-       "  q_4: |0>──────────────────────────────────────────────────────────────────»\n",
-       "                                                                            »\n",
-       "q_a_0: |0>──────────────────────────────────────────────────────────────────»\n",
-       "                                                                            »\n",
-       "q_a_1: |0>──────────────────────────────────────────────────────────────────»\n",
-       "                                                                            »\n",
-       "q_a_2: |0>──────────────────────────────────────────────────────────────────»\n",
-       "                                                                            »\n",
-       "«       ┌────────────────┐┌───┐┌───────┐┌───┐┌───────┐                        »\n",
-       "«  q_0: ┤ U3(1.5708,0,0) ├┤ X ├┤ U1(0) ├┤ X ├┤ U1(0) ├──■─────────────────────»\n",
-       "«       └────────────────┘└─┬─┘└───────┘└─┬─┘└───────┘  │                     »\n",
-       "«  q_1: ────────────────────■─────────────■─────────────┼─────────────────────»\n",
-       "«                                                     ┌─┴─┐┌─────────────────┐»\n",
-       "«  q_2: ──────────────────────────────────────────────┤ X ├┤ U3(0.14182,0,0) ├»\n",
-       "«                                                     └───┘└─────────────────┘»\n",
-       "«  q_3: ──────────────────────────────────────────────────────────────────────»\n",
-       "«                                                                             »\n",
-       "«  q_4: ──────────────────────────────────────────────────────────────────────»\n",
-       "«                                                                             »\n",
-       "«q_a_0: ──────────────────────────────────────────────────────────────────────»\n",
-       "«                                                                             »\n",
-       "«q_a_1: ──────────────────────────────────────────────────────────────────────»\n",
-       "«                                                                             »\n",
-       "«q_a_2: ──────────────────────────────────────────────────────────────────────»\n",
-       "«                                                                             »\n",
+       "
                                              ┌───┐┌────────────────┐┌───┐»\n",
+       "  q_0: |0>────────────────────────────────────┤ X ├┤ U3(0.7907,0,0) ├┤ X ├»\n",
+       "          ┌──────────────┐     ┌───────┐      └─┬─┘└────────────────┘└─┬─┘»\n",
+       "  q_1: |0>┤ U3(pi/2,0,0) ├─────┤ U1(0) ├────────■──────────────────────■──»\n",
+       "          └┬────────────┬┘┌────┴───────┴─────┐                            »\n",
+       "  q_2: |0>─┤ Ry(1.1847) ├─┤ U3(-0.14182,0,0) ├────────────────────────────»\n",
+       "           ├────────────┤ ├──────────────────┤                            »\n",
+       "  q_3: |0>─┤ Ry(1.3696) ├─┤ U3(-0.11174,0,0) ├────────────────────────────»\n",
+       "           └────────────┘ └──────────────────┘                            »\n",
+       "  q_4: |0>────────────────────────────────────────────────────────────────»\n",
+       "                                                                          »\n",
+       "q_a_0: |0>────────────────────────────────────────────────────────────────»\n",
+       "                                                                          »\n",
+       "q_a_1: |0>────────────────────────────────────────────────────────────────»\n",
+       "                                                                          »\n",
+       "q_a_2: |0>────────────────────────────────────────────────────────────────»\n",
+       "                                                                          »\n",
+       "«       ┌──────────────┐┌───┐┌───────┐┌───┐┌───────┐                        »\n",
+       "«  q_0: ┤ U3(pi/2,0,0) ├┤ X ├┤ U1(0) ├┤ X ├┤ U1(0) ├──■─────────────────────»\n",
+       "«       └──────────────┘└─┬─┘└───────┘└─┬─┘└───────┘  │                     »\n",
+       "«  q_1: ──────────────────■─────────────■─────────────┼─────────────────────»\n",
+       "«                                                   ┌─┴─┐┌─────────────────┐»\n",
+       "«  q_2: ────────────────────────────────────────────┤ X ├┤ U3(0.14182,0,0) ├»\n",
+       "«                                                   └───┘└─────────────────┘»\n",
+       "«  q_3: ────────────────────────────────────────────────────────────────────»\n",
+       "«                                                                           »\n",
+       "«  q_4: ────────────────────────────────────────────────────────────────────»\n",
+       "«                                                                           »\n",
+       "«q_a_0: ────────────────────────────────────────────────────────────────────»\n",
+       "«                                                                           »\n",
+       "«q_a_1: ────────────────────────────────────────────────────────────────────»\n",
+       "«                                                                           »\n",
+       "«q_a_2: ────────────────────────────────────────────────────────────────────»\n",
+       "«                                                                           »\n",
        "«                                                             »\n",
        "«  q_0: ──■────■───────────────────────────────────────────■──»\n",
        "«         │    │                                           │  »\n",
@@ -895,7 +897,7 @@
        "«            └───┘               └───┘ ░ 
"
       ],
       "text/plain": [
-       ""
+       ""
       ]
      },
      "execution_count": 21,
@@ -969,7 +971,7 @@
     },
     {
      "data": {
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\n",
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\n",
       "text/plain": [
        "
"
       ]
@@ -1317,7 +1319,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "
"
       ]
@@ -1329,7 +1331,7 @@
     },
     {
      "data": {
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\n",
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YA7D55ptPWbBgjXEDr7Fy5UrGjx/f0ueti7EQ87Tp6e+gxX19APzu0VcvVt+x5cTOBjeIsfA914FjrkarMU+fPn1ZRExtuDMihrWRrgrWL25NjlkNHNmg/FHSRM123v9wUhPdu7LX78te/89Cve2y8g80O+eUKVOimb6+vqZ16mZMxJzuBPPKy62PueyVrSpj4nuuAcdcjVZjBpbGIL9T2xqmnC0Pc4yk+7Jk8bcG21D6gY0alE8EnmwnFuCS7HHH3LlpcP6B1+2e38zMRqDdeTBHAMcC3yN17p8GnArcAzxI1tQ0hBWkvpZXSNoK2IA1+06aicLj/aSkN7lQbzLwchaj9aqBaxgzq412E8xs4GTgjOz1pRFxCrADKUFs1+T4RcDekjbMlc0k3Q7ghjZjOTB7XAYQEc+T5ukcVKg3E7g5PILMzKxS7U603Aa4PSJeyjrsNwKIiJclfQf4LukKZzDnka6CFko6HdgWmAecFbmhy1kT3A0RcUj2eh6wIWmS5dPA7sDRwMKI+G3u/F8FFks6hzRPZ0a27dPm5zQzsxFq9wrmCWBgWMHDwLtz+zYmTaIcVET0A3uS5sr8HDgFOJt0VZS3Dq+dT7OCNE/mQuAK4GDgm9lj/vxLSFc2ewFXAR8BDg7P4u99U6akzcxqo90rmF8AO5F+yf+INAN/E+AF4J9JqywPKSLuBN7fpM6kwusFpAmTTUXEpaSrFxtLli/vdgRmVtBugpkHbJk9/zqpiWwW6crlGuDznQrMzMxGt7YSTETcDdydPX+edE+YI0uIy8zMRrm272g5QNLfA1sAf4yIRzsXkpmZ9YJ2O/mRdLikPwAPAbcAD0t6RNLnOh6dmZmNWu3O5D8JOJc0n+VDwNTscRHwrWy/mZlZ201k/wx8PSJOLJRfKenP2f5TOxKZWTtmz+52BGZW0G6CGcfgd628AY8is27x7ZLNaqfdPphLgQMG2fcx4LKRhWNmZr2ilVsmz8i9XAScIWkSa94yeQfgy50P0awFy5alR8/mN6uNVprILmPNWyNvCezdoO4PSXeaNKvW1Ox+R15R2aw2Wkkw25QehZmZ9ZymCSYiHqoiEDMz6y1tz+SXtA6pQ383YBPgr8BNpKXzX+xseGZmNlq1lWAkbQZcDbyTdAfLPwO7kOa//EbSByPisU4HaWZmo0+7w5TPAt4AvCcito2IXSJiW+A9WflZnQ7QzMxGp3YTzAzgmIj4db4we/0V0rIxZmZmbffBvA742yD7/gasN7JwzIZp6dJuR2BmBe0mmF8Bx0i6PiKeGSiUtAFwTLbfrHqeYGlWO+0mmKOAPuAPkq4mdfJvRpp0KWBaR6MzM7NRq60+mIi4HdgOmA9sCnyAlGDOA7aLiN90PEKzVsyZkzYzq42Wr2AkrQvsDDwQEceWF5LZMFxwQXr0qspmtdHOFcxLwPXA/ygpFjMz6yEtJ5iIeBm4F9i8vHDMzKxXtDsP5njgJEnvKCMYMzPrHe2OIjuBNGP/dkmPkkaRvWZ99IjYuUOxmZnZKNZugrkj28zMzIbUUoKRNI60TMwdwH8D10bEn8sMzKwtO+7Y7QjMrKCVWyZvC1wLTMoVPy3p4xFxdVmBmbVl4JbJZlYbrXTynwG8DPwjsD6wA3AbcH6JcZmZ2SjXSoLZBTghIn4REc9FxF3AXODNkrYoNzwzMxutWkkwWwC/L5TdT1p77E0dj8hsOKS0mVlttDoPJppXMTMze1Wrw5SvkvRig/LriuURsdnIwzIzs9GulQRzSulRmJlZz2maYCLCCcbMzNrW7lpkZmZmLXGCMTOzUrS7FplZPZ3veb9mdeMEY73Bt0s2qx03kZmZWSmcYKw3zJ+fNjOrjcoTjKTtJV0naZWkP0o6VdLaTY7ZSdKFku7Ljrtb0smSXl+oN09SNNj2KfdTWdfNnZs2M6uNSvtgJG1MWvr/TmA/4C3AmaREd8IQh87M6p4O3Au8E/hq9vixQt2ngGJCuWuksZuZWXuq7uQ/DBgHHBARTwPXSJoAzJN0RlbWyOkR8Vju9WJJzwHnS9o6Ih7K7XsxIn5VTvhmZtaqqpvI9gWuKiSSBaSks8dgBxWSy4DbskevfWZmVkNVJ5jJwIp8QUQ8DKzK9rVjV9KN0O4ulG8k6XFJqyXdJumAYUdrZmbDpojqVuKXtBo4OiLOKZQ/AlwUEce1eJ43Ab8FroiIWbnyT5GuaG4HxpNujDYD+FhELBzkXHOAOQCbb775lAULFgz53itXrmT8+PGthFkbYyHmadOnA7C4rw+A3z361Cv73rHlxM4GN4ix8D3XgWOuRqsxT58+fVlETG24MyIq24DVwJENyh8FTmvxHOsBN5JugrZxk7oCbgZub+XcU6ZMiWb6+vqa1qmbMREzpC2z9TGXvbJVZUx8zzXgmKvRaszA0hjkd2rVTWT9wEYNyicCTzY7WJKAi4AdgBkR0T9U/ezDLwTe2WwotI1yAynGzGqj6lFkKyj0tUjaCtiAQt/MIM4mDW/+QES0Un+Af/OYmVWs6iuYRcDekjbMlc0EngVuGOpASV8BPg98KiKWtPJm2RXP/sBvIuKl4YVsZmbDUfUVzHnAEcBCSacD2wLzgLMiN3RZ0n3ADRFxSPb6YODrwA+ARyW9N3fO+yMbxizpBuCnpKuhDYDZwHuBj5b7sazrpkxJj8uWdTcOM3tFpQkmIvol7QmcC/yc1O9yNinJFOPK95l8MHuclW15nyElHoD7gP8DbEEawrwc+FBELOpE/FZjy5d3OwIzK6h8uf6IuBN4f5M6kwqvZ7FmYml03CEjCM3MzDrIqymbmVkpnGDMzKwUTjBmZlYKJxgzMytF5Z38ZqWYPbvbEZhZgROM9QbfLtmsdtxEZmZmpXCCsd6wbJln8ZvVjJvIrDdMzW5H4RWVzWrDVzBmZlYKJxgzMyuFE4yZmZXCCcbMzErhBGNmZqXwKDIbtSYde/krzx/sXhhmNggnGOsNS5d2OwIzK3CCsd4wcMtkM6sN98GYmVkpnGCsN8yZkzYzqw0nGOsNF1yQNjOrDScYMzMrhROMmZmVwgnGzMxK4QRjZmalcIIxM7NSeKKl9YYdd+x2BGZW4ARjvcG3SzarHTeRmZlZKZxgzMysFE4w1huktJlZbTjBmJlZKZxgzMysFE4wZmZWCicYMzMrhROMmZmVwgnGzMxK4Zn81hvOP7/bEZhZgROM9QbfLtmsdpxgbMyZdOzlrzx/8Bsf6mIkZr3NfTDWG+bPT5uZ1YavYKw3zJ2bHt1UZlYbTjBWa27OMhu9Km8ik7S9pOskrZL0R0mnSlq7heMmSrpQUr+kpyT9m6Q3NKi3n6TfSXpO0p2SZpbzSczMbCiVJhhJGwPXAgHsB5wKHAWc0sLhFwPTgEOBWcBOwKWF8+8G/BToA/YFLgd+LOmDHfkAZmbWsqqbyA4DxgEHRMTTwDWSJgDzJJ2Rla1B0i7A3sAeEXFjVvYocIukvSLi2qzqicCNEXFE9rpP0g7AScDV5X0s6xVukjPrnKoTzL7AVYVEsgA4HdgD+PkQx/15ILkARMStkh7I9l0r6XXAdOCIwrELgAslTYyIpzr0OayD8r/Uob6/2J18zNpTdYKZDFyfL4iIhyWtyvYNlmAmAysalN+V7QN4C7Bug3p3kZoC3wb8enhhj22D/WLtVHkvmHTs5Rz1jheZlX3GwT53cV9xf699Lza2KSKqezNpNXB0RJxTKH8EuCgijhvkuGuAZyLio4XyHwLbRsSukt4HLAHeHRG35+q8FbgX2Dsi1mgmkzQHGBjb+nbg7iYf443A403q1I1jroZjroZjrkarMW8dEZs22tGNYcqNMpoGKR/OccXXGqQ8FUbMB1qeoSdpaURMbbV+HTjmajjmajjmanQi5qqHKfcDGzUonwg8OYzjNsod158rK9ahyfnNzKzDqk4wK3i1zwQASVsBG9C4j2XQ4zL5vpn7gdUN6k0GXgbuGUa8ZmY2TFUnmEXA3pI2zJXNBJ4Fbmhy3JuyeS4ASJoKbJvtIyKeJ81/Oahw7Ezg5g6OIBuNC1455mo45mo45mqMOOaqO/k3Bu4E7iANTd4WOAs4JyJOyNW7D7ghIg7JlV1JGgn2JdIVyenAXyLiH3N1dgMWA+eSJmHOyOrv06iD38zMylPpFUxE9AN7AmuThiSfApwNnFyouk5WJ+8TpKuc7wMXAcuA/QvnXwIcCOwFXAV8BDjYycXMrHqVXsGYmdnY4fvBtEDSBEmnSLo1W2jzvyX9h6S3Najb0qKcFcU9U9JCSX+SFJJmDVJvy+zzrJT0uKRzJa1fcbjDXgi1KpLeKul8Sb+R9JKkxQ3qSNJxkv4g6VlJN0p6VxfCRdJBkn4m6dHs33aZpE82qDdb0r3ZArHLJO3ZjXizWA6U9EtJT2Tx3C3pBEnr5erU5jtuJPv/tDL7Pzc+V16buCXNyuIrbod1Ml4nmNa8GZhNanY7EJgLbEFaC22rQt2mi3JW6EBgEnDZYBUkrUP6XFuTBkQcSRooUWmnpEa2EGpVdiD1693D4KMSjyWtiXc68GFgJWkpozdVEuFrfTF7/y+Qmov7gB9J+vxABUmfAM4jNTvvC/wXcJmkf6g+XADeQIrz0Cye7wPHk/pqB9TpO27km6SYiuoY9/uBXXLbwty+kccbEd6abKRh1OMKZZtkX/jJubJdSL8gd8+V7ZyV7dWFuNfKHsdnMcxqUOeTwEvANrmyj5MGUmxXYaxfIc1lmpAr+zKwKl/W5Z+DtXLPLwEWF/a/HngKOKnws/MY8LUuxPvGBmU/Ah7Ivb4b+H7+MwK/A37Y7e87F9NppHlsqtt33CDWfwT+ShpcFMD4mv5szMrH12B/R+L1FUwLIuKZiHi2UPZX4CFgs1xxw0U5gYFFOSsVES+3UG1f4NcR8UCu7FLgBWCfUgIbPI5GC6GOIy2E2nUtfJ+7AhOAf88d8wxpQEs3/v0bLfNxG9nPrKRtSSMz8/G+DPyELsQ7hCeAgSayWn3HeVlz7r+Srr6L331t4x5ER+J1ghkmSZsCbyUNux7QyqKcdbNGzBHxAmniapUxN4rjYdIVTF2/u6LJpKvBewvldfr335VXf2YHYmq0QOwm2c94V0haW9L62dSDI4D/G+nP6Dp/x4eR/vL/doN9dY37fkkvZn1dc3PlHYnXt0wevjNJTWQLcmUb03hJmn7SnJ86GirmjcdgHCOxMbAyIl4qlPcD60taL0veXZF13u8HfDYrGvhei997f27/YxWE1sgzwOuy5xcBR2fPa/kdZwN5vgp8KiJWSypWqVvcfyL1r9xKmhLySeA8SetHxNmdinfMJhhJE0kd9UOKiDWuSCQdDnwK+FhEPFE8pNHbDVLelpHE3OyQRm83SHmZ6hLHSAz2GQbbVwlJk0j9L/8ZET8o7G5rgdiK7AqsT+rDPIk0efpz2b46fsenAbdExBVD1KlN3BFxFWlwz4BFSvfUOkHSvwwRU1vxjtkEQxopdUEL9V7zp4ikj5DaWY+JiP8o1O0HGjUr5BflHIlhxdxEKwuJVmG4C6HWST+woaS1C3/5bQSsiojV3QhK0iakJZUeJv1hNCC/QGx+KaWuLxAbEcuzp0skPQ78P0lnUsPvWOmuuZ8Fdpc08N0NDPOfKOklahh3A5eQBvhMokPxjtk+mIj4bkSo2ZY/RtKupCax8yLimw1O28qinJXG3IJGC5CuR2rSG3HMI4yjlYVQ62QFqbnhrYXyjvz7D0c2n+kyUif5h7KO2gEDMTVaIPavEdGt5rGigWSzDTX8joHtSDc7vJn0i7mfV/thHiH9QVrHuAcTdCjeMZtg2pX9lXIZcCVr3pZ5QNNFOWtoEbCTpK1zZR8htX9fWXEcw1kItU5+CTxNbsHV7Bf8h+nCv382x+knpF+A+0bEX/L7I+L3pPk8+XjXyl7X6ef1fdnjA9TsO84sId2uPb+dnu2bQZoXU8e4iz5GGv32EB2Kdyw3kbVM0makX7YrgW8BO+c68Z6OiDsBIuJmSVcBF0nKL8q5JCKu7ULc2wPbk0a2AEyVtBJ4LCIGfmlfQprItlDSiaQmqbOBH0VEcQRJmc4jJe6FkgYWQp0HnFUYutw12X+wGdnLLYEJkg7MXl8REaPLoLoAAAFDSURBVKskfQM4UVI/6S+9L5L+kPvXygOG75DiPZI0Kuy9uX23RVqBfB7wQ0kPAr8A/omUkA6uNtREaVHba0kTPl8iJZejgIsj4v6sTp2+44Hh4IvzZVmfF8BNEbEyK6tN3JJ+Surg/y3pSmVmth2RDVV/riPxVj3BZzRupJn5Mci2uFB3I+BCUvv106SO1TUmvFUU97wWY/570tyXlaQ5B98G1u9CvNsD15OuWv5EGpWzdrf//XPxTRri52BSVkekhP1I9jluIt3GuxvxPtgs3qzebOA+4HlSc9SeXfyOv0pabX1l9n9oOfB5YN1cndp8x0N8jlkUJjLWKW7g66RJtquyWJYBny7UGXG8XuzSzMxK4T4YMzMrhROMmZmVwgnGzMxK4QRjZmalcIIxM7NSOMGYmVkpnGDMzKwUTjBmZlaK/w9NMWzBUWOSxgAAAABJRU5ErkJggg==\n",
       "text/plain": [
        "
"
       ]
@@ -1374,9 +1376,9 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "qiskit_master",
+   "display_name": "Python 3",
    "language": "python",
-   "name": "qiskit_master"
+   "name": "python3"
   },
   "language_info": {
    "codemirror_mode": {
@@ -1388,7 +1390,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.1"
+   "version": "3.7.1"
   }
  },
  "nbformat": 4,
diff --git a/qiskit/finance/simulation/european_call_option_pricing.ipynb b/qiskit/finance/simulation/european_call_option_pricing.ipynb
index e402d2a93..f472c217c 100644
--- a/qiskit/finance/simulation/european_call_option_pricing.ipynb
+++ b/qiskit/finance/simulation/european_call_option_pricing.ipynb
@@ -46,8 +46,10 @@
     "\\Delta = \\mathbb{P}\\left[S_T \\geq K\\right]\n",
     "$$\n",
     "
\n",
-    "The approximation of the objective function is explained in detail in the following paper:
\n",
-    "Quantum Risk Analysis. Woerner, Egger. 2018."
+    "The approximation of the objective function and a general introduction to option pricing and risk analysis on quantum computers are given in the following papers:\n",
+    "\n",
+    "- Quantum Risk Analysis. Woerner, Egger. 2018.\n",
+    "- Option Pricing using Quantum Computers. Stamatopoulos et al. 2019."
    ]
   },
   {
@@ -118,7 +120,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "
"
       ]
@@ -214,7 +216,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
+      "image/png": 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\n",
       "text/plain": [
        "
"
       ]
@@ -319,7 +321,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "
"
       ]
@@ -331,7 +333,7 @@
     },
     {
      "data": {
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\n",
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1wMOkGQG2B54Cfg3sExELS6mAmZm1rOOTXUbE7cBbhsgzoUH665vs8xRwyIgKZ+u3yZPT6yK3qJqVwbMpm9UsXtztEpj1FT9wzMzMKuEAY2ZmlXCAMTOzSjjAmJlZJRxgzMysEr6LzKxmxoxul8CsrzjAmNXUHplsZqVwE5mZmVWirQAjqd70LWb9YdEij+I3K1G7TWT3SzoXODsi7qiiQGZdM2VKevWMymalaLeJbA5wKPB7Sb+RNFPSlhWUy8zMelxbASYivhgRE4G3AkuB04EHJf1I0v5VFNDMzHrTsDr5I+LaiPgAsAPwceDVwJWSlkuaLeklZRbSzMx6z0jvIpsCvJn0GORB4HrgaGCZpPeP8NhmZtbD2g4wknaW9EVJdwHXADsCHwJeEhH/CuxM6qv5WqklNTOzntLWXWSSriVdsdwHnEO6m+zufJ6IeEbSj4FPlFVIMzPrPe3epvwIMA24KqLpvZy3AC8fdqnMumGhn6xtVqZ2A8y3gcX1goukzYHdI+K6iHgauHudvc1Gs9ojk82sFO32wcwHdm2w7dXZdjMzs7YDjJps2xxYNYKymHXXzJlpMbNSDNlEJunNwNRc0tGSDixk2xQ4GLitvKKZddhZZ6VXz6psVopW+mDeRBpMCRDAYcDaQp6/A0uAT5VXNDMz62VDBpiI+BrZmBZJfwbeFRG3VF0wMzPrbW3dRRYRvvXYzMxa0kofzDTghohYkf3cVERcVkrJzMysp7VyBfNzYE/gt9nPQeO7yQLwQ8nMzKylAPNy4MHcz2b9affdu10Cs77SSif/3fV+Nus7flyyWala6YN5cTsHjAgPtjQzs5aayFaS+lZa5T4YMzNrKcB8iPYCjFlvUnbvStOJws2sVa30wZzTgXKYmVmfGekjk83MzOpqpZP/t8CREXG7pJsYorksIvYoq3BmZta7WumD+QOwOvezG6jNzGxIrfTBfDD385GVlsbMzPrGsPtglGwnqdlDyMzMbD3V1mzK8NzklycAk7P910paBHw5Ii4tuXxmnTNnTrdLYNZX2gowkmYB3wGuAT4B/BXYHjgE+F9JH40I/5Zab/Ljks1K1e4VzGeBuRHxkUL6mZLOBD4HOMCYmVnbfTDbABc12HYhsPVQB5C0q6RrJK2S9ICkkyQ1nV5G0gRJUWeZVyfvdEm3SXpK0u2SDm+pZmZz56bFzErR7hXMfGAf4Ko62/YBrmu2s6RxwNXA7cB04BXAaaRAd0IL738s8Mvc+iOF4+9NCnTfAY4BpgHnSRqMiF+0cHxbn82alV7dVGZWilYGWu6aW/0m8F1J2wAX83wfzLuAg4Cjhzjch4ExwCERsQK4StKWwGxJp2ZpzSyNiBubbP88cF1EHJOtz5e0G/AFwAHGzKyDWrmC+T0vHFwpYFa2FJ9ueQXNZ1M+CLiyEEjmAaeQroAuaaE8dUnaBNiXdOWSNw84W9LYiHh8uMc3M7P2tBJg9i3x/SYB1+YTIuIeSauybUMFmLMlbU26cjoP+FxE1GYZeAWwMbCksM8dpCa4XYCbRlZ8MzNrVSsj+ReU+H7jgMfqpA9m2xpZA/w3qZlrBTAVOI4UVKbnjk2d4w8Wtr+ApJnATIDx48czMDDQrPyjysqVK3uqvGUru/5Ts9deOafr++cPPgejvf5tD7SskbQBsGkxvYUnWtaby0wN0mvHfBD4t1zSgKSHgO9Ien1E3NLk+GqQXjv2XGAuwJQpU2Lq1KnNSz+KDAwM0EvlLdtw6j/h+BeOBV7+1YPXydMr53R9//zB52C017+t25Sz6WGOk7QMeBp4os7SzCCwVZ30sdS/smnmgux199yxqXP82nq7xzczsxFodxzMMcDxwPdIVwZfBk4C7gSWkzU1NbGE1NfyHEk7AZuxbt/JUKLwehcp6E0q5JsEPJuV0ayxCD/N0qxE7QaYGcAXgVOz9Ysj4kRgN1KAeNUQ+18OHCBpi1za4aTHAbTb13No9roIICLWkMbpHFbIdzjwa99BZmbWWe32wbwcuCUinpH0NFnzU0Q8K+k7wHdJVziNnEm6CrpI0inARGA2cHr+1uWsCW5BRByVrc8GtiANslwBvBn4FHBRRPwud/yTSf0z3yCN05mWLQe2WU8zMxuhdq9gHgU2z36+B3hDbts40iDKhiJiENiPNFbmEuBE4AzSVVHeRrxwPM0S0jiZs4HLgPcCX8te88e/gXRlsz9wJfAO4L0exW8tmTw5LWZWinavYH4JvJH0R/7HpBH4WwN/Bz5GmmW5qYi4HXjLEHkmFNbnkQZMDikiLiZdvZi1Z/HibpfArK+0G2BmAy/Nfv4KqYnsSNKVy1XAx8sqmJmZ9ba2AkxELAWWZj+vIT0T5hMVlMvMzHrcSAZa/gOwI/BARNxfXpHMzKwftNvJj6SPSLoXuBv4DXCPpPskfbT00pmZWc9qdyT/F4Bvk8azHAxMyV4vB76ZbTczM2u7iexjwFci4vOF9CuyucE+RhrZb9Z7ZszodgnM+kq7AWYMjZ9auQDfRWa9zI9LNitVu30wFwOHNNj2buDnIyuOmZn1i1YemTwtt3o5cKqkCaz7yOTdgE+XX0SzDlm0KL16NL9ZKVppIvs56z4a+aXAAXXy/pD0pEmz3jNlSnr1jMpmpWglwLy88lKYmVnfaeWRyXd3oiBmZtZf2h7JL2kjUof+3sDWwN+A60lT568tt3hmZtar2gowkrYHfgG8jvQEy4eAvUjjX26V9LaIeLjsQpqZWe9p9zbl04FtgDdFxMSI2CsiJgJvytJPL7uAZmbWm9oNMNOA4yLipnxitv4Z0rQxZmZmbffBbAI80WDbE8CLRlYcsy5auLDbJTDrK+0GmBuB4yRdGxFP1hIlbQYcl203600eYGlWqnYDzCeB+cC9kn5B6uTfnjToUsDUUktnZmY9q60+mIi4BXgVMBfYDngrKcCcCbwqIm4tvYRmnTJzZlrMrBQtX8FI2hjYA/hzRBxfXZHMuuSss9KrZ1U2K0U7VzDPANcC/1hRWczMrI+0HGAi4lngj8D46opjZmb9ot1xMJ8DviDptVUUxszM+ke7d5GdQBqxf4uk+0l3kb1gbvOI2KOkspmZWQ9rN8D8PlvMzMyaainASBpDmibm98BfgKsj4qEqC2bWcbvv3u0SmPWVVh6ZPBG4GpiQS14h6T0R8YuqCmbWcbVHJptZKVrp5D8VeBb4Z+DFwG7AzcCcCstlZmY9rpUAsxdwQkT8MiKeiog7gFnAyyTtWG3xzMysV7USYHYE/lRIu4s099gOpZfIrFuktJhZKVq9iyyGzmLW3yYcf+kL1pd/1Y8/Mmum1QBzpaS1ddKvKaZHxPYjL5aZmfW6VgLMiZWXwszM+s6QASYiHGDMzKxt7c5FZmZm1hIHGDMzq0S7c5GZ9a85HjtsViYHGLMaPy7ZrFRuIjMzs0o4wJjVzJ2bFjMrRccDjKRdJV0jaZWkBySdJGnDIfZ5o6SzJS3L9lsq6YuSNi3kmy0p6iwHVlsr6wuzZqXFzErR0T4YSeNIU//fDkwHXgGcRgp0JzTZ9fAs7ynAH4HXASdnr+8u5H0cKAaUO0ZadjMza0+nO/k/DIwBDomIFcBVkrYEZks6NUur55SIeDi3PiDpKWCOpJ0j4u7ctrURcWM1xTczs1Z1uonsIODKQiCZRwo6+zTaqRBcam7OXj33mZnZKNTpADMJWJJPiIh7gFXZtnb8E+lBaEsL6VtJekTS05JulnTIsEtrZmbDpojOzcQv6WngUxHxjUL6fcC5EfHZFo+zA/A74LKIODKX/n7SFc0twOakB6NNA94dERc1ONZMYCbA+PHjJ8+bN6/danXNypUr2XzzzbtdjK4ZTv1vu//xF6y/9qVjn/t56r77AjAwf37b+3bD+v75g8/BaKj/vvvuuygiptTb1o0Ac2xE/Fch/X7gnIj4XAvHeBHpRoF/ACZHxGCTvAJ+BYyJiNcPdewpU6bEwoULh8o2agwMDDB16tRuF6NrhlP/ps90qT1srMHvxGh7Hsz6/vmDz8FoqL+khgGm001kg8BWddLHAo8NtXMWMM4FdgOmNQsuAJGi50XA64a6FdqMiIbBxcza1+m7yJZQ6GuRtBOwGYW+mQbOIN3e/NaIaCV/jf9qmJl1WKevYC4HDpC0RS7tcGA1sKDZjpI+A3wceH9E3NDKm2VXPO8Cbo2IZ4ZXZDMzG45OX8GcCRwDXCTpFGAiMBs4PX/rsqRlwIKIOCpbfy/wFeAc4H5Je+aOeVftNmZJC4ALSVdDmwEzgD2Bd1ZbLesLkyen10WLulsOsz7R0QATEYOS9gO+DVxC6nc5gxRkiuXK95m8LXs9MlvyPkgKPADLgH8HdiTdwrwYODgiLi+j/NbnFi/udgnM+krHp+uPiNuBtwyRZ0Jh/UjWDSz19jtqBEUzM7MSeTZlMzOrhAOMmZlVwgHGzMwq4QBjZmaV6Hgnv9moNWNGt0tg1lccYMxq/Lhks1K5iczMzCrhAGNWs2iRR/GblchNZGY1U7IZxz2jslkpfAVjZmaVcIAxM7NKOMCYmVklHGDMzKwSDjBmZlYJBxgzM6uEb1M2q1m4sNslMOsrDjBmNbVHJptZKdxEZmZmlXCAMauZOTMtZlYKBxizmrPOSouZlcIBxszMKuEAY2ZmlXCAMTOzSjjAmJlZJRxgzMysEh5oaVaz++7dLoFZX3GAMavx45LNSuUmMjMzq4QDjJmZVcIBxqxGSouZlcIBxszMKuEAY2ZmlXCAMTOzSjjAmJlZJRxgzMysEg4wZmZWCY/kt5512/2Pc+TxlwKw/KsHj/yAc+aM/Bhm9hwHGLMaPy7ZrFQOMGYVm5BdZdWUcrVl1gPcB2NWM3duWsysFL6CMauZNSu9uqnMrBS+gjEzs0p0PMBI2lXSNZJWSXpA0kmSNmxhv7GSzpY0KOlxST+StE2dfNMl3SbpKUm3Szq8mpqYmVkzHW0ikzQOuBq4HZgOvAI4jRToThhi9/OBVwNHA88CpwAXA/+cO/7ewIXAd4BjgGnAeZIGI+IXpVbGSuNO8MZ8bqyXdboP5sPAGOCQiFgBXCVpS2C2pFOztHVI2gs4ANgnIq7L0u4HfiNp/4i4Osv6eeC6iDgmW58vaTfgC4ADjJlZB3U6wBwEXFkIJPNIVyP7AJc02e+hWnABiIjfSvpztu1qSZsA+5KuXPLmAWdLGhsRj5dUD2si/1+3/+PuHl/9WLd1OsBMAq7NJ0TEPZJWZdsaBZhJwJI66Xdk2yA1t21cJ98dpCa4XYCbhlfs4av3S97sF7/ZH+fifuccuFlL79dquRrxH6r1y0g+7+HuO5x/SiYcfymffO3almdzaLds/t6PnCKic28mPQ18KiK+UUi/Dzg3Ij7bYL+rgCcj4p2F9B8CEyPinyT9H+AG4A0RcUsuzyuBPwIH1OuHkTQTqN2X+mpg6bAr2HnbAo90uxBd5Pqv3/UHn4PRUP+dI2K7ehu6MQ6mXkRTg/Th7FdcV4P0lBgxF+jJ0XWSFkbElG6Xo1tc//W7/uBzMNrr3+nblAeBreqkjwUeG8Z+W+X2G8ylFfMwxPHNzKxknQ4wS3i+zwQASTsBm1G/j6Xhfpl838xdwNN18k0i3dZ85zDKa2Zmw9TpAHM5cICkLXJphwOrgQVD7LdDNs4FAElTgInZNiJiDTAfOKyw7+HAr/v0DrKebNorketv6/s5GNX173Qn/zjSIMvfk25NngicDnwjIk7I5VsGLIiIo3JpV5DuBDuW5wda/jUiigMtB4BvkwZhTsvyH+iBlmZmndXRK5iIGAT2AzYk3ZJ8InAG8MVC1o2yPHlHkK5yvg+cCywC3lU4/g3AocD+wJXAO4D3OriYmXVeR69gzMxs/eHZlHuIpBmS/phN5LlI0n4t7DNbUtRZDuxEmYej6glRR7vh1F/ShAaf87xOlbsskl4paY6kWyU9I2mgxf364vOH4Z2D0fgd8PNgeoSkI4AzgdmkAaUfBH4u6Y0R8fshdn8cKAaUO0ovZAmqnhB1tBth/SH1Of4yt97tQXjDsRup//RG4EVt7Nfzn3/OcM8BjKbvQER46YGFNMPA93PrGwC3AT8cYr/ZwCPdLn8b9fwMaUzTlrm0TwOr8o5CEaoAAAMmSURBVGl19tuLNJj2zbm0PbK0/btdrw7Uf0JW17d3uw4lnIMNcj9fAAy0sE9ffP4jPAej7jvgJrIeIGki6Q66n9TSIuJZ4KekyT77SaMJUceQJkRttt86E6ICtQlRe8Vw6983su92u/rl8weGfQ5GHQeY3lAbPFpvIs+tJdWdByhnK0mPSHpa0s2SDim/iKVZZ2LTiLiH9B98vcG2DffL5CdE7QXDrX/N2Vmb/YOSTpc0popCjkL98vmXYdR8B9wH0xvGZa/F6W4Gc9sfbrDvMlITyy3A5sAs4EJJ746Ii8ouaAnGUX9an0GePw/t7jexhHJ1ynDrvwb4b9Jzj1YAU4HjSH0408st4qjUL5//SIy674ADTJdIGgvsOFS+iMj/V9bWRJ7Z/j8svO8lwK9ID2EbjQEGqp8QdbRrux4R8SDwb7mkAUkPAd+R9PrIzTDex/rl8x+W0fgdcBNZ9xxGunwfaoESJ/KM1Bt4EfC6Vm797YIqJ0TtBcOtfz0XZK+7j6hEvaFfPv+ydfU74ADTJRHx3YjQUEuWvXYVU28iz79FRKPmsaZFGHbhq1XlhKi9YLj1rycKr/2sXz7/snX1O+AA0wMi4k+k2aCfm8hT0gbZ+uXtHEuSSFPs3BoRz5RZzpJUNiFqjxhu/es5NHtdVEbBRrl++fzL1t3vQLfvk/bS2gL8C/AMabDdvsA5pD86r8nl2QdYC+yTS1sAHAO8jRRYLiMNQntHt+vUoJ7jgAeBq0hzys0EVgJfKuRbBnyvkHYF8CfgEOCdpLFD13e7Tp2oP2m802lZ3fcHTsq+Hxd2u07DOAcvJv1hPBT4NfCH3PqL+/nzH8k5GI3fga6fSC9tfFgwI/tSrQEWA/sVtk8lXQpPzaV9L/ulWw08CVwPHNTtugxRz12Ba7MyPwicDGxYyLMcOKeQthVwNqnNfQXwY2DbbtenE/UnTQa7kDRrw9+z78lJwCbdrs8w6j8h+x7XWyb0++c/3HMwGr8DnuzSzMwq4T4YMzOrhAOMmZlVwgHGzMwq4QBjZmaVcIAxM7NKOMCYmVklHGDMzKwSDjBmZlaJ/w9ViDFb48S6iQAAAABJRU5ErkJggg==\n",
       "text/plain": [
        "
"
       ]
@@ -459,7 +461,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "
"
       ]
@@ -493,9 +495,9 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "qiskit_master",
+   "display_name": "Python 3",
    "language": "python",
-   "name": "qiskit_master"
+   "name": "python3"
   },
   "language_info": {
    "codemirror_mode": {
@@ -507,7 +509,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.1"
+   "version": "3.7.1"
   }
  },
  "nbformat": 4,
diff --git a/qiskit/finance/simulation/european_put_option_pricing.ipynb b/qiskit/finance/simulation/european_put_option_pricing.ipynb
index d9897256a..dfa2901c2 100644
--- a/qiskit/finance/simulation/european_put_option_pricing.ipynb
+++ b/qiskit/finance/simulation/european_put_option_pricing.ipynb
@@ -46,8 +46,10 @@
     "\\Delta = -\\mathbb{P}\\left[S_T \\leq K\\right]\n",
     "$$\n",
     "
\n",
-    "The approximation of the objective function is explained in detail in the following paper:
\n",
-    "Quantum Risk Analysis. Woerner, Egger. 2018."
+    "The approximation of the objective function and a general introduction to option pricing and risk analysis on quantum computers are given in the following papers:\n",
+    "\n",
+    "- Quantum Risk Analysis. Woerner, Egger. 2018.\n",
+    "- Option Pricing using Quantum Computers. Stamatopoulos et al. 2019."
    ]
   },
   {
@@ -118,7 +120,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "
"
       ]
@@ -214,7 +216,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
+      "image/png": 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\n",
       "text/plain": [
        "
"
       ]
@@ -319,7 +321,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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zm8HclD1/Ilc2Ncpf9b7Z8s3MrA3NzoM5DTgb+CHpzOCfgIuBZ4DFZJeaBrGQ1NfyHkk7ABszsO+kkSg8P0sKemML+cYCK7M6mplZlzQbYL4EXAhclr2/NSIuAnYnBYgPN9h/BnCYpE1zaRNJtwNotq/nuOz5MYCIWEGap/O5Qr6JwCMeQWZm1l3N9sHsBMyLiHclvU12+SkiVkq6GvgB6QynnmtIZ0G3SLoU2BmYAlyeH7qcXYKbHREnZ++nAJuSJlkuAfYDzgRuiYhf5sr/Jql/5krSPJ0J2ePwJo/TzMza1OwZzO+BTbLXLwB/mds2ijSJsq6I6AcOIs2VuQ24CLiCdFaUtx6rz6dZSJonMxW4EzgB+E72nC9/DunM5mBgJvAZ4ATP4jcz675mz2AeAvYk/cj/hDQDfwvgT8BXgHsbFRAR84EDG+QZU3g/nTRhsqGIuJV09mJmZkOo2QAzBdg+e30J6RLZiaQzl1nA1zpVMTMz621NBZiIeBp4Onu9gnQvmNMrqJeZmfW4diZafhDYDnglIl7uXJXMzGxt0Motk78s6UXgeeCnwAuSXpL0fzpeOzMz61nNzuS/ALiKNJ/lSGBc9jwD+H623czMrOlLZF8BLomIbxTS78rWBvsKaWa/mZkNc80GmBHUv2vlbDyKzNZSY86+Y0Da4m8fOQQ1MesdzfbB3AocW2fbZ4Hb26uOmZmtLcrcMnlC7u0M4DJJYxh4y+TdgX/sfBXNzKwXlblEdjsDb428PXBYjbw/It1p0szMhrkyAWanymthZmZrnTK3TH6+GxUxM7O1S9Mz+SWtR+rQ3xfYAvgf4EHS0vnvdLZ6ZmbWq5oKMJK2Ae4G9iDdwfI1YB/S/JcnJB0aEb/rdCXNzKz3NDtM+XJgS+BTEbFzROwTETsDn8rSL+90Bc3MrDc1G2AmAGdFxM/zidn7c0jLxpiZmTUdYDYA/lBn2x+AD7RXHTMzW1s0G2AeBc6StHE+MXt/VrbdzMys6VFkZwD3Ay9KupvUyb8NadKlgPEdrZ2ZmfWsZu9oOU/Sh4GvA3uSRpO9ClwDXB4Rr3e+imad40UrzbqndICRtD6wF/BcRJxdXZXMzGxt0EwfzLvAfcBHK6qLmZmtRUoHmIhYCfwKGF1ddczMbG3R7Ciy84ALJH2sisqYmdnao9lRZOeTZuzPk/QyaRRZ5DNExF4dqpuZmfWwZgPMU9nDzMxsUKUCjKQRpGVingJ+A9wTEa9VWTEzM+ttZW6ZvDNwDzAml7xE0vERcXdVFTMzs95WppP/MmAl8NfARsDuwOPAtRXWy8zMelyZALMPcH5EPBQRb0XEAuAU4M8lbVdt9czMrFeVCTDbAb8upD1LWnts247XyMzM1gpl58FE4yxmZmbvKztMeaakd2qk31tMj4ht2q+WmZn1ujIB5qLKa2FmZmudhgEmIhxgzMysac2uRWZmZlaKA4yZmVXCAcbMzCrhAGNmZpVwgDEzs0o4wJiZWSW6HmAk7SbpXknLJL0i6WJJ6zbYZ09JUyUtyvZ7WtKFkjYs5JsiKWo8Dq/2qMzMrKjZG461RdIo0tL/84GjgF2A75IC3fmD7Doxy3sp8CtgD+Cb2fNnC3nfBIoBZUG7dTczs+Z0NcAApwIjgGMjYgkwS9JmwBRJl2VptVwaEb/Lve+T9BZwraQdI+L53LZ3IuLRaqpvZmZldfsS2RHAzEIgmU4KOvvX26kQXFZ5PHv22mdmZmugbgeYscDCfEJEvAAsy7Y149OkG6E9XUjfXNLrkt6W9LikY1uurZmZtUwR3VuJX9LbwJkRcWUh/SXghog4t2Q52wK/BO6MiBNz6V8gndHMAzYh3RhtAvDZiLilTlmTgckAo0eP/uT06dObPazVLF26lE022aStMoaLoWirJ19+c0Dax7YfWdl+neLvVXluq/I60VYHHHDAYxExrta2oQgwX4+I7xXSXwauj4jzSpTxAdJAgQ8Cn4yI/kHyCngYGBERH29U9rhx42Lu3LmNsg2qr6+P8ePHt1XGcDEUbTXm7DsGpC3+9pGV7dcp/l6V57YqrxNtJalugOn2JbJ+YPMa6SOBNxrtnAWMG4DdgQmDBReASNHzFmCPRkOhzcyss7o9imwhhb4WSTsAG1Pom6njCtLw5kMiokz+VXxHTjOzLuv2GcwM4DBJm+bSJgLLgdmD7SjpHOBrwBciYk6ZD8vOeI4BnoiId1urspmZtaLbZzDXAKcBt0i6FNgZmAJcnh+6LGkRMDsiTs7enwBcAlwPvCxp71yZz64axixpNnAz6WxoY+BLwN7A0dUelpmZFXU1wEREv6SDgKuA20j9LleQgkyxXvk+k0Oz5xOzR95JpMADsAj4e2A70hDmXwBHRsSMTtTfzMzK6/YZDBExHziwQZ4xhfcnMjCw1Nrv5DaqZmZmHeTVlM3MrBIOMGZmVgkHGDMzq4QDjJmZVcIBxszMKuEAY2ZmlXCAMTOzSjjAmJlZJRxgzMysEg4wZmZWCQcYMzOrhAOMmZlVwgHGzMwq4QBjZmaVcIAxM7NKOMCYmVklHGDMzKwSDjBmZlYJBxgzM6uEA4yZmVXCAcbMzCrhAGNmZpVwgDEzs0o4wJiZWSUcYMzMrBIOMGZmVgkHGDMzq4QDjJmZVcIBxszMKuEAY2ZmlXCAMTOzSjjAmJlZJRxgzMysEg4wZmZWCQcYMzOrhAOMmZlVwgHGzMwqsd5QV8CsFWPOvmNA2uJvHzkENWmsl+pq1kk+gzEzs0o4wJiZWSUcYMzMrBIOMGZmVomuBxhJu0m6V9IySa9IuljSuiX2GylpqqR+SW9K+rGkLWvkO0rSk5LekjRf0sRqjsTMzAbT1VFkkkYB9wDzgaOAXYDvkgLd+Q12vxHYFfgisBK4FLgV+Otc+fsCNwNXA6cBE4Bpkvoj4u6OHox1jEdZ1beqbc742DucePYdbhfrKd0epnwqMAI4NiKWALMkbQZMkXRZljaApH2Aw4D9I+KBLO1l4KeSDo6Ie7Ks3wAeiIjTsvf3S9oduABwgDEz66JuB5gjgJmFQDKddDayP3DbIPu9tiq4AETEzyQ9l227R9IGwAGkM5e86cBUSSMj4s0OHYfV4bORNYP/HWxN0O0AMxa4L58QES9IWpZtqxdgxgILa6QvyLZButy2fo18C0iX4D4C/Ly1areu1n/0WhZ/+8iGPwplfjSKeer9qJTN12xe632t/nu3GtRa2a8b+/h73z5FRPc+THobODMiriykvwTcEBHn1tlvFvDHiDi6kP4jYOeI+LSkvwLmAH8ZEfNyeT4E/Ao4rFY/jKTJwOTs7a7A0y0fYLIV8HqbZQwXbqvy3Fblua3K60Rb7RgRW9faMBRLxdSKaKqT3sp+xfcaZH8i4jrgugafXZqkuRExrlPlrc3cVuW5rcpzW5VXdVt1e5hyP7B5jfSRwBst7Ld5br/+XFoxDw3KNzOzDut2gFnI+30mAEjaAdiY2n0sdffL5PtmngXerpFvLGlY8zMt1NfMzFrU7QAzAzhM0qa5tInAcmB2g/22zea5ACBpHLBzto2IWAHcD3yusO9E4JEujiDr2OW2YcBtVZ7bqjy3VXmVtlW3O/lHkSZZPkUamrwzcDlwZUScn8u3CJgdESfn0u4ijQT7Ou9PtPxtRBQnWvYBV5EmYU7I8h/uiZZmZt3V1TOYiOgHDgLWJQ1Jvgi4AriwkHW9LE/eJNJZzr8CNwCPAccUyp8DHAccDMwEPgOc4OBiZtZ9XT2DMTOz4cOrKdfgBTnLa6WtJO2ZtdOibL+nJV0oacNCvimSosbj8GqPqhotttWYOm0wvUbe4f69qvd9CUnn5PJdXydPrYFEazxJH5J0raQnJL0rqa/kfpX/XvmWyQVekLO8NtpqYpb3UtIk2D2Ab2bPny3kfRMoBpQF7da929r8XkHqS3wo9361yXH+XgHwA+CuQtrRwFlkg4FyFgInFdIWt1bjIbc76d/7UeADTexX/e9VRPiRewDnkObUbJZL+0dgWT6txn77kCZz7pdL2ytLOziXNhO4r7DvncCcoT72LrbV1jXSJmdttWMubQrw+lAf5xC31ZisXf5Xg/KH/feqTll3AAsKadcDc4f6ODvYXuvkXt8E9JXYpyu/V75ENlC9BTlHkBbkHGy/AQtyAqsW5CS3IOe/F/adDuwjaWT71e+qltoqIn5XI/nx7HmbzlVvjdLq96ohf69qk7QFcAgwrbPVW7NExMoWduvK75UDzEADFtaMiBdIfz0Ndo22Uwty9pJW26qWT5NO04trwW0u6XVJb0t6XNKxLdd2aLXbVlOz6+uvSrpc0ojcNn+vajuO1C4D+quA3SQtkbRC0hxJbQX5HtSV3ysHmIFGUXtZmf5sWzv7rXou5usvbO8VrbbVaiRtC5wH/Fvhr9ZFpEsjx5P6Zl4Bbu7RINNqW60A/gU4mTTE/1rgy6z+o+nvVW2TgF9ERHEVj8eBM4C/AT5PmhIxS9JeLdS1V3Xl98qd/LWtUQtyruFabauUUfoA6RR8KfAPqxUc8aNC3tuAh0k3kLullcoOsabbKiJeBb6aS+qT9BpwtaSPR27l8BrlDOfv1Xaky2lnDSg44nuFvHeQBhScSxoUMFxU/nvlM5iBvCBnea22FQCSRJo0uzswIdJE3Loi9TDeAuxRZtj4Gqattiq4KXv+RK5sapQ/LL9XmeNJP4Q3NsoYEctJHdefaJR3LdKV3ysHmIG8IGd5rbbVKleQhqEeFRFl8q/Si3+Rt9tWeVF49vdqoEmkkU4vNvG5vfi9alVXfq8cYAYaDgtydkqrbUU28e1rwBciLfHTUHbGcwzwRES821qVh0zLbVXDcdnzY+DvVZGkMcDelBw9lg2YOIKsPYeJ7vxeDfUY7jXtQeq4ehWYRVrTbDKpf+BbhXyLgB8W0u4Cfg0cS7qW+zTwYCHPvsA7wJXAeOAy0l8Dhw71sXerrYATSH8tTiX9EOQfW+fyzSZN7jqUFFjuzNrqM0N97F1sqymkSYbHZvtdTPqhvdnfq4H/B7P0s0l/edeabzUSeBA4hTRoYiJpguIKYNxQH3uL7bUR6Y+O44BHgP/Ovd+oXlt14/dqyBtnTXwAuwH3Zf+RXyXNMl+3kGcxcH0hbfPsR/MNYAnwE2CrGuUfTVpRegXpdHTSUB9zN9uKNNEt6jxOzOX7YfYfYDnwx+yH4YihPuYut9UkYC5pRYM/ZT8UFwMb+Hs18P9glj4PuKtOuRuS+vFezNrpzeyHdu+hPuY22mrMIP+fxtRrq278XnmxSzMzq4T7YMzMrBIOMGZmVgkHGDMzq4QDjJmZVcIBxszMKuEAY2ZmlXCAMTOzSjjAmJlZJf4/jMGuUp1I/cgAAAAASUVORK5CYII=\n",
       "text/plain": [
        "
"
       ]
@@ -331,7 +333,7 @@
     },
     {
      "data": {
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vsW018DhpxoLtgWeBXwP7RsT8UhpgZmZDVvnknRFxN/D2QfKMq5P+5gZlngUOHVblzCZOTK8L3AtrVjbPFm2Wt3Bhp2tg1rP8ADYzM6uEA46ZmVXCAcfMzCrhgGNmZpVwwDEzs0p4lJpZ3rRpna6BWc9ywDHLG3jEtJmVzl1qZmZWiZYCjqRa082Y9Y4FCzzLgFmbtNql9rCkC4HzI+KedlTIrKMmTUqvnjHarHStdqnNAg4D7pL0G0nTJW3ZhnqZmVmPaSngRMSXImI88A5gMXAm8KikH0k6oB0VNDOz3jCkQQMRcWNEfAjYAfgE8HrgWklLJc2U9IoyK2lmZt1vuKPUJgFvIz02uh+4GTgWWCLpg8Pct5mZ9ZCWA46knSV9SdJ9wA3AjsBHgFdExL8CO5Ou9Xyj1JqamVlXa2mUmqQbSWc0DwEXkEar3Z/PExHPS/ox8MmyKmlmZt2v1WHRy4ApwHURDceN3gG8esi1MuuU+X4auVm7tBpwzgYW1go2kjYHdo+ImyLiOeD+dUqbjXQDj5g2s9K1eg1nLrBrnW2vz7abmZmto9WAowbbNgdWDqMuZp03fXpazKx0g3apSXobMDmXdKykgwrZNgUOAe4sr2pmHXDeeenVs0abla6ZazhvJd3cCRDA4cCaQp6/A4uAT5dXNTMz6yWDBpyI+AbZPTWS/gy8NyLuaHfFzMyst7Q0Si0iPNTZzMyGpJlrOFOAWyJiefZzQxFxVSk1MzOzntLMGc7Pgb2A32Y/B/VHqwXgh7SZmdk6mgk4rwYezf1s1rt2373TNTDrWc0MGri/1s9mPcmPlzZrm2au4by8lR1GhG/+NDOzdTTTpbaCdG2mWb6GY2Zm62gm4HyE1gKOWfdSNh6m4WToZjYUzVzDuaCCepiZWY8b7iOmzczMmtLMoIHfAkdHxN2SbmOQ7rWI2LOsypmZWe9o5hrOH4BVuZ/duW1mZi1r5hrOh3M/H93W2piZWc8a8jUcJdtJavRQNjMzM6DF2aLhxck8TwYmZuXXSFoAfDUiriy5fmbVmjWr0zUw61ktBRxJM4BzgBuATwJ/BbYHDgX+V9LHI8K/sda9/Hhps7Zp9Qznc8DsiPhYIf1cSecCnwcccMzMbB2tXsPZBriszrZLga0H24GkXSXdIGmlpEcknSqp4XQ4ksZJihrLnBp5p0q6U9Kzku6WdERTLTMDmD07LWZWulbPcOYC+wLX1di2L3BTo8KSxgDXA3cDU4HXAGeQAt/JTbz/CcAvc+vLCvvfhxT4zgGOB6YAF0nqj4hfNLF/W9/NmJFe3bVmVrpmbvzcNbf6beC7krYBLuelazjvBQ4Gjh1kdx8FRgGHRsRy4DpJWwIzJZ2epTWyOCJubbD9C8BNEXF8tj5X0m7AFwEHHDOzDmrmDOcu1r7ZU8CMbCk+/fMaGs8WfTBwbSGwzAFOI50hXdFEfWqStAmwH+nMJm8OcL6k0RHx1FD3b2Zmw9NMwNmvxPebANyYT4iIByStzLYNFnDOl7Q16czqIuDzETEwC8JrgI2BRYUy95C67HYBbhte9c3MbKiamWlgXonvNwZ4skZ6f7atntXAf5O6xZYDk4ETSUFmam7f1Nh/f2H7WiRNB6YDjB07lr6+vkb1H1FWrFjRVfUtWzvaPzl77Ybjur5//uBj0G3tb/nGzwGSNgA2LaY38cTPWnOxqU76wD4fBf4tl9Qn6THgHElvjog7GuxfddIH9j0bmA0wadKkmDx5cuPajyB9fX10U33L1s72d8NxXd8/f/Ax6Lb2tzQsOpvO5kRJS4DngKdrLI30A1vVSB9N7TOfRi7JXnfP7Zsa+x9Yb3X/ZmZWolbvwzkeOAn4HunM4avAqcC9wFKyrqkGFpGu1bxI0k7AZqx77WUwUXi9jxQEJxTyTQBeyOpo1liEn/Zp1iatBpxpwJeA07P1yyPiFGA3UsB43SDlrwYOlLRFLu0I0uMPWr1WdFj2ugAgIlaT7hM6vJDvCODXHqFmZtZZrV7DeTVwR0Q8L+k5su6qiHhB0jnAd0lnQPWcSzpLukzSacB4YCZwZn6odNZlNy8ijsnWZwJbkG76XA68Dfg0cFlE/D63/y+Tru98i3Sf0JRsOajFdpqZWclaPcN5Atg8+/kB4C25bWNIN3XWFRH9wP6ke3WuAE4BziKdNeVtxNr38ywi3adzPnAVcBTwjew1v/9bSGc+BwDXAu8GjvIsA9a0iRPTYmala/UM55fAHqQ/+j8mzRCwNfB34DjSLNINRcTdwNsHyTOusD6HdAPnoCLictLZjVnrFi7sdA3MelarAWcm8Mrs56+RutSOJp3ZXAd8oqyKmZlZb2kp4ETEYmBx9vNq0jNxPtmGepmZWY8Zzo2f/wDsCDwSEQ+XVyUzM+tFrQ4aQNLHJD0I3A/8BnhA0kOSPl567czMrGe0OtPAF4GzSffTHAJMyl6vBr6dbTczM1tHq11qxwFfi4gvFNKvyeY2O44084BZd5o2rdM1MOtZrQacUdR/quc8PErNul2Dx0uPO+nKtdaXfv2QdtfGrKe0eg3ncuDQOtveB/x8eNUxM7Ne1cwjpqfkVq8GTpc0jnUfMb0b8Jnyq2hWoQUL0qtnGzArXTNdaj9n3UdJvxI4sEbeH5KexGnWnSZNSq+eMdqsdM0EnFe3vRZmZtbzmnnE9P1VVMTMzHpbyzMNSNqINEBgH2Br4G/AzaRHBawpt3pmZtYrWgo4krYHfgG8ifSEz8eAvUn33/xO0jsj4vGyK2lmZt2v1WHRZwLbAG+NiPERsXdEjAfemqWfWXYFzcysN7QacKYAJ0bEbfnEbP2zpGluzMzM1tHqNZxNgKfrbHsaeNnwqmPWYfPnd7oGZj2r1YBzK3CipBsj4pmBREmbASdm2826l2/4NGubVgPOp4C5wIOSfkEaNLA96SZQAZNLrZ2ZmfWMVp/4eYek1wEnAHuQRqs9CpwLnBkRy8qvoll5Bp2Ac/r09NpgEk8zG5qmA46kjYE9gT9HxEntq5JZB513Xnp1wDErXSuj1J4HbgT+sU11MTOzHtZ0wImIF4A/AmPbVx0zM+tVrd6H83ngi5Le2I7KmJlZ72p1lNrJpBkF7pD0MGmU2lrzuEfEniXVzczMekirAeeubDEzM2tJUwFH0ijStDZ3AX8Bro+Ix9pZMbOO2H33TtfArGc184jp8cD1wLhc8nJJ74+IX7SrYmYdMfCIaTMrXTODBk4HXgD+GXg5sBtwOzCrjfUyM7Me00zA2Rs4OSJ+GRHPRsQ9wAzgVZJ2bG/1zMysVzQTcHYE/lRIu480d9oOpdfIrJOktJhZ6Zq9DycGz2JmZlZfs8Oir5W0pkb6DcX0iNh++NUyM7Ne00zAOaXttTAzs543aMCJCAccMzMbtlbnUjMzMxsSBxwzM6tEq3OpmfW2Wb6f2axdHHDM8gYeMW1mpXOXmpmZVcIBxyxv9uy0mFnpKg84knaVdIOklZIekXSqpA0HKbOHpPMlLcnKLZb0JUmbFvLNlBQ1loPa2yrrGTNmpMXMSlfpNRxJY0iPOrgbmAq8BjiDFPhOblD0iCzvacAfgTcBX85e31fI+xRQDDD3DLfuZmY2PFUPGvgoMAo4NCKWA9dJ2hKYKen0LK2W0yLi8dx6n6RngVmSdo6I+3Pb1kTEre2pvpmZDVXVXWoHA9cWAsscUhDat16hQrAZcHv26rnbzMy6QNUBZwKwKJ8QEQ8AK7Ntrfgn0oPhFhfSt5K0TNJzkm6XdOiQa2tmZqVRRHVPHpD0HPDpiPhWIf0h4MKI+FyT+9kB+D1wVUQcnUv/IOmM5w5gc9KD4qYA74uIy+rsazowHWDs2LET58yZ02qzOmbFihVsvvnmna5Gxwyl/Xc+/NRa62985ei11ifvtx8AfXPntly2auv75w8+BiOh/fvtt9+CiJjUTN5OBJwTIuK/CukPAxdExOeb2MfLSAMP/gGYGBH9DfIK+BUwKiLePNi+J02aFPPnzx8s24jR19fH5MmTO12NjhlK+8eddOVa60u/fsjaGQYevlbj92LQshVb3z9/8DEYCe2X1HTAqbpLrR/Yqkb6aODJwQpnAeRCYDdgSqNgAxApml4GvGmwoddmQAo0Ff4TZrY+qXqU2iIK12ok7QRsRuHaTh1nkYZTvyMimsk/wH9BzMw6rOoznKuBAyVtkUs7AlgFzGtUUNJngU8AH4yIW5p5s+yM6L3A7yLi+aFV2czMylD1Gc65wPHAZZJOA8YDM4Ez80OlJS0B5kXEMdn6UcDXgAuAhyXtldvnfQPDpiXNAy4lnS1tBkwD9gLe095mWc+YODG9LljQ2XqY9aBKA05E9EvaHzgbuIJ03eYsUtAp1it/zeWd2evR2ZL3YVIgAlgC/DuwI2nI9ELgkIi4uoz623pg4cJO18CsZ1X+eIKIuBt4+yB5xhXWj2bdQFOr3DHDqJqZmbWRZ4s2M7NKOOCYmVklHHDMzKwSDjhmZlaJygcNmI1o06Z1ugZmPcsBxyzPj5c2axt3qZmZWSUccMzyFizwLANmbeIuNbO8Sdks654x2qx0PsMxM7NKOOCYmVklHHDMzKwSDjhmZlYJBxwzM6uEA46ZmVXCw6LN8ubP73QNzHqWA45Z3sAjps2sdO5SMzOzSjjgmOVNn54WMyudA45Z3nnnpcXMSueAY2ZmlXDAMTOzSjjgmJlZJRxwzMysEg44ZmZWCd/4aZa3++6droFZz3LAMcvz46XN2sZdamZmVgkHHDMzq4QDjlmelBYzK50DjpmZVcIBx8zMKuGAY2ZmlXDAMTOzSjjgmJlZJRxwzMysEp5pwCxv1qxO18CsZzngWNe68+GnOPqkKwFY+vVDytlpGx4vPS6r44DS6mrWZdylZmZmlXDAMcubPTstZlY6d6mZ5c2YkV7b0LVmtr7zGY6ZmVWi8oAjaVdJN0haKekRSadK2rCJcqMlnS+pX9JTkn4kaZsa+aZKulPSs5LulnREe1piZmatqLRLTdIY4HrgbmAq8BrgDFLgO3mQ4hcDrweOBV4ATgMuB/45t/99gEuBc4DjgSnARZL6I+IXpTbGSuNRXPX52FgvqfoazkeBUcChEbEcuE7SlsBMSadnaeuQtDdwILBvRNyUpT0M/EbSARFxfZb1C8BNEXF8tj5X0m7AFwEHHDOzDqo64BwMXFsILHNIZyv7Alc0KPfYQLABiIjfSvpztu16SZsA+5HObPLmAOdLGh0RT5XUDmsg/1+5/yPvHJ8d2UhTdcCZANyYT4iIByStzLbVCzgTgEU10u/JtkHqntu4Rr57SF12uwC3Da3aQ1frl77RH4JGf6yL5S44aLOm3q/ZetXjP1zrl+F83kMtO5R/UsaddCWfeuOapm/+bbVu/t6XTxFR3ZtJzwGfjohvFdIfAi6MiM/VKXcd8ExEvKeQ/kNgfET8k6T/A9wCvCUi7sjleS3wR+DAWtdxJE0HBsbAvh5YPOQGVm9bYFmnK9FBbv/63X7wMRgJ7d85IrZrJmMn7sOpFeFUJ30o5YrrqpOeEiNmA115p5+k+RExqdP16BS3f/1uP/gYdFv7qx4W3Q9sVSN9NPDkEMptlSvXn0sr5mGQ/ZuZWZtVHXAW8dI1FwAk7QRsRu1rNHXLZfLXdu4DnquRbwJpGPW9Q6ivmZmVpOqAczVwoKQtcmlHAKuAeYOU2yG7zwYASZOA8dk2ImI1MBc4vFD2CODXPTpCrSu7Akvk9tv6fgy6qv1VDxoYQ7rp8y7SUOjxwJnAtyLi5Fy+JcC8iDgml3YNaaTZCbx04+dfI6J442cfcDbpptApWf6DfOOnmVlnVXqGExH9wP7AhqQh0KcAZwFfKmTdKMuTdyTpLOj7wIXAAuC9hf3fAhwGHABcC7wbOMrBxsys8yo9wzEzs/WXZ4vuIpKmSfpjNjHpAkn7N1FmpqSosRxURZ2Hot0TvI50Q2m/pHF1Puc5VdW7LJJeK2mWpN9Jel5SX5PleuLzh6Edg274Dvh5OF1C0pHAucBM0g2uHwZ+LmmPiLhrkOJPAcUAc0/plSxBuyd4HemG2X5I1yx/mVvv9E2BQ7Eb6frrrcDLWijX9Z9/zlCPAYzk70BEeOmChTQDwvdz6xsAdwI/HKQ6XxvsAAADO0lEQVTcTGBZp+vfQjs/S7qnastc2meAlfm0GuX2Jt3c+7Zc2p5Z2gGdblcF7R+XtfVdnW5DCcdgg9zPlwB9TZTpic9/mMdgxH8H3KXWBSSNJ43Q+8lAWkS8APyUNHlpL6k3weso0gSvjcqtM8ErMDDBa7cYavt7RvbdblWvfP7AkI/BiOeA0x0GbmatNTHp1pIGm8doK0nLJD0n6XZJh5ZfxdKsM1FrRDxA+g+/1s2/dctl8hO8doOhtn/A+Vmf/6OSzpQ0qh2VHIF65fMvw4j9DvgaTncYk70Wp+fpz21/vE7ZJaQumTuAzYEZwKWS3hcRl5Vd0RKMofY0RP28dBxaLTe+hHpVZajtXw38N+m5T8uBycCJpGtAU8ut4ojUK5//cIz474ADTodIGg3sOFi+iMj/19bSxKRZ+R8W3vcK4Fekh9KNxIAD7Z/gdaRruR0R8Sjwb7mkPkmPAedIenPkZlDvYb3y+Q9JN3wH3KXWOYeTTvcHW6DEiUkjXV28DHhTM0ONO6CdE7x2g6G2v5ZLstfdh1Wj7tArn3/ZRtR3wAGnQyLiuxGhwZYs+8BZTq2JSf8WEfW60xpWYciVb692TvDaDYba/lqi8NrLeuXzL9uI+g444HSBiPgTabbrFycmlbRBtn51K/uSJNKUQL+LiOfLrGdJ2jbBa5cYavtrOSx7XVBGxUa4Xvn8yzayvgOdHpftpbkF+BfgedLNf/sBF5D+CL0hl2dfYA2wby5tHnA88E5SoLmKdFPcuzvdpjrtHAM8ClxHmhNvOrAC+Eoh3xLge4W0a4A/AYcC7yHdu3Rzp9tURftJ91udkbX9AODU7PtxaafbNIRj8HLSH8rDgF8Df8itv7yXP//hHINu+A50vAJeWviwYFr2JVsNLAT2L2yfTDp1npxL+172S7gKeAa4GTi4020ZpJ27AjdmdX4U+DKwYSHPUuCCQtpWwPmkPvvlwI+BbTvdniraT5rcdj5pVom/Z9+TU4FNOt2eIbR/XPY9rrWM6/XPf6jHoBu+A56808zMKuFrOGZmVgkHHDMzq4QDjpmZVcIBx8zMKuGAY2ZmlXDAMTOzSjjgmJlZJRxwzMysEv8fqlZ6tMgSuLcAAAAASUVORK5CYII=\n",
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\n",
       "text/plain": [
        "
"
       ]
@@ -459,7 +461,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "
"
       ]
@@ -493,9 +495,9 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "qiskit_master",
+   "display_name": "Python 3",
    "language": "python",
-   "name": "qiskit_master"
+   "name": "python3"
   },
   "language_info": {
    "codemirror_mode": {
@@ -507,7 +509,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.1"
+   "version": "3.7.1"
   }
  },
  "nbformat": 4,
diff --git a/qiskit/finance/simulation/fixed_income_pricing.ipynb b/qiskit/finance/simulation/fixed_income_pricing.ipynb
index 3eed08902..28e7d03bf 100644
--- a/qiskit/finance/simulation/fixed_income_pricing.ipynb
+++ b/qiskit/finance/simulation/fixed_income_pricing.ipynb
@@ -111,7 +111,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "
"
       ]
@@ -155,7 +155,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "
"
       ]
@@ -272,7 +272,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "
"
       ]
@@ -284,7 +284,7 @@
     },
     {
      "data": {
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\n",
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\n",
       "text/plain": [
        "
"
       ]
@@ -329,9 +329,9 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "qiskit_master",
+   "display_name": "Python 3",
    "language": "python",
-   "name": "qiskit_master"
+   "name": "python3"
   },
   "language_info": {
    "codemirror_mode": {
@@ -343,7 +343,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.1"
+   "version": "3.7.1"
   }
  },
  "nbformat": 4,
diff --git a/qiskit/finance/simulation/option_pricing.ipynb b/qiskit/finance/simulation/option_pricing.ipynb
index f02bd60f4..de1324e8d 100644
--- a/qiskit/finance/simulation/option_pricing.ipynb
+++ b/qiskit/finance/simulation/option_pricing.ipynb
@@ -33,10 +33,11 @@
     "- path-dependency (sum/average, barrier, etc.).\n",
     "\n",
     "The basic ideas on using QAE for option pricing and risk analysis are provided here:
\n",
-    "Quantum Risk Analysis. Stefan Woerner, Daniel J. Egger (2019).\n",
+    "- Quantum Risk Analysis. Stefan Woerner, Daniel J. Egger (2019)\n",
+    "- Option Pricing using Quantum Computers. Stamatopoulos et al. (2019)\n",
     "\n",
     "A Qiskit Aqua tutorial on QAE can be found here:
\n",
-    "Qiskit Tutorial on QAE\n",
+    "Qiskit Tutorial on QAE\n",
     "\n",
     "We provide tutorials for the following types simple options:\n",
     "\n",
@@ -50,10 +51,12 @@
     "- Basket Option (multivariate, payoff with 2 segments)\n",
     "- Asian Barrier Spread (multivariate, path-dependent, payoff with 3 segments)\n",
     "\n",
-    "More examples on option pricing with a quantum computer can be found in the [Qiskit Finance Community](https://github.com/Qiskit/qiskit-tutorials-community/tree/master/finance) section of the Qiskit Tutorials.\n",
+    "More examples on option pricing with a quantum computer can be found in the [Qiskit Finance Community](https://github.com/Qiskit/qiskit-tutorials-community/tree/master/finance) section of the Qiskit Community Tutorials.\n",
     "\n",
     "All examples illustrate how to use the genereric Qiskit Finance framework to construct QAE-operators (uncertainty problems). The same framework can be easily adjusted to estimate risk as well, for instance, the Value at Risk (VaR) or the Conditional Value at Risk (CVaR, also known as Expected Shortfall). How to use Qiskit Finance for risk analysis is illustrated in the following tutorial:\n",
-    "Credit Risk Analysis.\n",
+    "Credit Risk Analysis\n",
+    "based on the paper\n",
+    "Credit Risk Analysis using Quantum Computers. Egger et al. (2019).\n",
     "\n",
     "An example of how quantum Generative Adversarial Networks (qGANs) can be used to learn and efficiently load generic random distributions for option pricing can be found here:\n",
     "QGANs to learn and load random distributions for option pricing"
@@ -69,9 +72,9 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "qiskit_master",
+   "display_name": "Python 3",
    "language": "python",
-   "name": "qiskit_master"
+   "name": "python3"
   },
   "language_info": {
    "codemirror_mode": {
@@ -83,7 +86,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.1"
+   "version": "3.7.1"
   }
  },
  "nbformat": 4,