jupyter_notebooks/Testing/Model Selection.ipynb

{
 "cells": [
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   "source": [
    "# $\\star\\star$ Currently in development.  This example doesn't work $\\star\\star$\n",
    "Some parts of `pygsti` are works-in-progress. Here, we investigate how to do the task of \"model selection\" within GST, essentially answering the question \"Can we do a better job of modeling the experiment by changing the assumptions within GST?\"."
   ]
  },
  {
   "cell_type": "markdown",
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   },
   "source": [
    "## Testing variable-gateset-dimension GST with model selection"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "editable": true
   },
   "source": [
    "###     Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function"
   ]
  },
  {
   "cell_type": "code",
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   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import pygsti\n",
    "from pygsti.construction import std1Q_XYI"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
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   "source": [
    "#Load gateset and some string lists\n",
    "gs_target = std1Q_XYI.gs_target\n",
    "fiducialList = std1Q_XYI.fiducials\n",
    "germList = std1Q_XYI.germs\n",
    "specs = pygsti.construction.build_spam_specs(fiducialList)\n",
    "expList = [1,2,4]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
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    "deletable": true,
    "editable": true
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   "source": [
    "#Create some testing gate string lists\n",
    "lgstList = pygsti.construction.list_lgst_gatestrings(specs, gs_target.gates.keys())\n",
    "lsgstLists = [ lgstList[:] ]\n",
    "for exp in expList:\n",
    "    gsList = pygsti.construction.create_gatestring_list(\n",
    "                \"f0+germ*exp+f1\", f0=fiducialList, f1=fiducialList,\n",
    "                germ=germList, exp=exp, order=['germ','f0','f1'])\n",
    "    lsgstLists.append( lsgstLists[-1] +  gsList )\n",
    "    \n",
    "dsList = pygsti.remove_duplicates( lsgstLists[-1] )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
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    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "odict_keys(['Gi', 'Gx', 'Gy'])\n"
     ]
    },
    {
     "ename": "AssertionError",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAssertionError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-6-2ba698fe20ff>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     22\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     23\u001b[0m \u001b[0mdsFake4\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpygsti\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconstruction\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgenerate_fake_data\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgs_dataGen4\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdsList\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnSamples\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1000000\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msampleError\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"binomial\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mseed\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1234\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 24\u001b[0;31m \u001b[0mdsFake5\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpygsti\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconstruction\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgenerate_fake_data\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgs_dataGen5\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdsList\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnSamples\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1000000\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msampleError\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"binomial\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mseed\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1234\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m/Users/enielse/research/pyGSTi/packages/pygsti/construction/datasetconstruction.py\u001b[0m in \u001b[0;36mgenerate_fake_data\u001b[0;34m(gatesetOrDataset, gatestring_list, nSamples, sampleError, seed, randState, aliasDict, collisionAction, measurementGates)\u001b[0m\n\u001b[1;32m    152\u001b[0m                     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;32mbreak\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    153\u001b[0m             \u001b[0;31m#TODO: add adjustment if psum < 1?\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 154\u001b[0;31m             \u001b[0;32massert\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1.\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mTOL\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mall_ps\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvalues\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0;36m1.\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mTOL\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    155\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    156\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mnSamples\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mdsGen\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[0m\n",
      "\u001b[0;31mAssertionError\u001b[0m: "
     ]
    }
   ],
   "source": [
    "#Test on fake data by depolarizing target set, increasing its dimension,\n",
    "# and adding leakage to the gates into the new dimension.\n",
    "\n",
    "gs_dataGen4 = gs_target.depolarize(gate_noise=0.1)\n",
    "gs_dataGen5 = gs_dataGen4.increase_dimension(5)\n",
    "leakGate = pygsti.construction.build_gate( [2,1],[('Q0',),('L0',)] , \"LX(pi/4.0,0,2)\",\"gm\") # X(pi,Q0)*LX(pi,0,2)\n",
    "\n",
    "gs_dataGen5['Gx'] = pygsti.objects.compose( gs_dataGen5['Gx'], leakGate, 'gm')\n",
    "gs_dataGen5['Gy'] = pygsti.objects.compose( gs_dataGen5['Gy'], leakGate, 'gm')\n",
    "print(gs_dataGen5.gates.keys())\n",
    "\n",
    "#Some debugging...\n",
    "#NOTE: with LX(pi,0,2) above, dim 5 test will choose a dimension 3 gateset, which may be sensible\n",
    "#       looking at the gate matrices in this case... but maybe LX(pi,...) is faulty?\n",
    "#print(gs_dataGen4)\n",
    "#print(gs_dataGen5)\n",
    "\n",
    "#Jmx = GST.JOps.jamiolkowski_iso(gs_dataGen4['Gx'])\n",
    "#Jmx = GST.JOps.jamiolkowski_iso(gs_dataGen5['Gx'],dimOrStateSpaceDims=[2,1])\n",
    "#print(\"J = \\n\",Jmx)\n",
    "#print(\"evals = \",eigvals(Jmx))\n",
    "\n",
    "dsFake4 = pygsti.construction.generate_fake_data(gs_dataGen4, dsList, nSamples=1000000, sampleError=\"binomial\", seed=1234)\n",
    "dsFake5 = pygsti.construction.generate_fake_data(gs_dataGen5, dsList, nSamples=1000000, sampleError=\"binomial\", seed=1234)"
   ]
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of gates                        =  3\n",
      "Number of fiducials                    = 6\n",
      "Maximum length for a gate string in ds = 30\n",
      "Number of LGST strings                 =  92\n",
      "Number of LSGST strings                =  <map object at 0x10a021ba8>\n"
     ]
    }
   ],
   "source": [
    "print(\"Number of gates                        = \",len(gs_target.gates.keys()))\n",
    "print(\"Number of fiducials                    =\",len(fiducialList))\n",
    "print(\"Maximum length for a gate string in ds =\",max(map(len,dsList)))\n",
    "print(\"Number of LGST strings                 = \",len(lgstList))\n",
    "print(\"Number of LSGST strings                = \",map(len,lsgstLists))"
   ]
  },
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   },
   "source": [
    "### Test using dimension-4 fake data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--- LGST ---\n",
      "  Singular values of I_tilde (truncating to first 4 of 6) = \n",
      "  3.00262981818\n",
      "  0.825857216429\n",
      "  0.671539150077\n",
      "  0.664532662258\n",
      "  0.000838614351546\n",
      "  0.000292355239716\n",
      "  \n",
      "  Singular values of target I_tilde (truncating to first 4 of 6) = \n",
      "  3.0\n",
      "  1.0\n",
      "  1.0\n",
      "  1.0\n",
      "  2.46365884775e-16\n",
      "  9.80956846773e-17\n",
      "  \n",
      "    Resulting gate set:\n",
      "    \n",
      "    rho0 =    0.7072  -0.0214   0.0213   0.7510\n",
      "    \n",
      "    \n",
      "    E0 =    0.6847   0.0028  -0.0026  -0.6446\n",
      "    \n",
      "    \n",
      "    Gi = \n",
      "       1.0002        0   0.0003  -0.0001\n",
      "      -0.0042   0.9000   0.0005  -0.0004\n",
      "       0.0032  -0.0018   0.8995  -0.0009\n",
      "      -0.0030   0.0002   0.0013   0.8999\n",
      "    \n",
      "    \n",
      "    Gx = \n",
      "       1.0001  -0.0002        0        0\n",
      "      -0.0037   0.8982   0.0055   0.0005\n",
      "       0.0006  -0.0014  -0.0052  -1.0001\n",
      "      -0.0624   0.0070   0.8104   0.0065\n",
      "    \n",
      "    \n",
      "    Gy = \n",
      "       1.0003   0.0002        0  -0.0003\n",
      "      -0.0001  -0.0066   0.0002   0.9989\n",
      "       0.0041   0.0069   0.8989        0\n",
      "      -0.0625  -0.8098  -0.0065   0.0067\n",
      "    \n",
      "    \n",
      "    \n",
      "--- LGST ---\n",
      "  Singular values of I_tilde (truncating to first 6 of 6) = \n",
      "  3.00262981818\n",
      "  0.825857216429\n",
      "  0.671539150077\n",
      "  0.664532662258\n",
      "  0.000838614351546\n",
      "  0.000292355239716\n",
      "  \n",
      "  Singular values of target I_tilde (truncating to first 4 of 6) = \n",
      "  3.0\n",
      "  1.0\n",
      "  1.0\n",
      "  1.0\n",
      "  2.46365884775e-16\n",
      "  9.80956846773e-17\n",
      "  \n",
      "  LGST: Padding target B with sqrt of low singular values of I_tilde: \n",
      "  \n",
      "  [ 0.00083861  0.00029236]\n",
      "    Resulting gate set:\n",
      "    \n",
      "    rho0 =    0.7072  -0.0214   0.0213   0.7510   0.0022  -0.0087\n",
      "    \n",
      "    \n",
      "    E0 =    0.6847   0.0028  -0.0026  -0.6446   0.0123   0.0050\n",
      "    \n",
      "    \n",
      "    Gi = \n",
      "       1.0002        0   0.0003  -0.0001  -0.0047   0.0100\n",
      "      -0.0042   0.9000   0.0005  -0.0004   0.0027   0.0341\n",
      "       0.0032  -0.0018   0.8995  -0.0009   0.0164  -0.0220\n",
      "      -0.0030   0.0002   0.0013   0.8999   0.0359   0.0568\n",
      "       0.0012  -0.0156   0.0249  -0.0288   0.4451  -0.8206\n",
      "       0.0168  -0.0497   0.0435   0.0986  -0.8074  -2.7233\n",
      "    \n",
      "    \n",
      "    Gx = \n",
      "       1.0001  -0.0002        0        0   0.0034   0.0250\n",
      "      -0.0037   0.8982   0.0055   0.0005  -0.0199   0.0606\n",
      "       0.0006  -0.0014  -0.0052  -1.0001  -0.0254   0.0212\n",
      "      -0.0624   0.0070   0.8104   0.0065   0.0003   0.0024\n",
      "      -0.0076  -0.0219  -0.0256   0.0008  -0.0984  -1.9243\n",
      "       0.0070   0.0435   0.0193  -0.0007   0.0558  -0.1647\n",
      "    \n",
      "    \n",
      "    Gy = \n",
      "       1.0003   0.0002        0  -0.0003   0.0115  -0.0010\n",
      "      -0.0001  -0.0066   0.0002   0.9989   0.0597  -0.0196\n",
      "       0.0041   0.0069   0.8989        0  -0.0091  -0.0682\n",
      "      -0.0625  -0.8098  -0.0065   0.0067   0.0225  -0.0122\n",
      "       0.0132   0.0329   0.0020  -0.0336  -0.7649  -0.4999\n",
      "       0.0009  -0.0169   0.0394   0.0067   0.4817   0.5269\n",
      "    \n",
      "    \n",
      "    \n",
      "LGST dim=4 chiSq =  377.497001528\n",
      "LGST dim=6 chiSq =  974.596182221\n",
      "--- Iterative MC2GST: Iter 1 of 4 92 gate strings ---: \n",
      "  --- Minimum Chi^2 GST with model selection (starting dim = 4) ---\n",
      "  Dim 4: chi^2 = 61.7228, nGateStrings=92, nParams=56 (so expected mean = 36)\n",
      "  Rejected dim 3: chi^2 = 5.51525e+06 (+5.51519e+06 w.r.t. expected mean of 92 strings - 33 params = 59) (dChi^2=5515185, 2*dParams=-46)\n",
      "  Rejected dim 5: chi^2 = 38.326 (+31.326 w.r.t. expected mean of 92 strings - 85 params = 7) (dChi^2=-23, 2*dParams=58)\n",
      "--- Iterative MC2GST: Iter 2 of 4 488 gate strings ---: \n",
      "  --- Minimum Chi^2 GST with model selection (starting dim = 4) ---\n",
      "  Dim 4: chi^2 = 438.344, nGateStrings=488, nParams=56 (so expected mean = 432)\n",
      "  Rejected dim 3: chi^2 = 4.86648e+07 (+4.86644e+07 w.r.t. expected mean of 488 strings - 33 params = 455) (dChi^2=48664372, 2*dParams=-46)\n",
      "  Rejected dim 5: chi^2 = 393.935 (-9.06498 w.r.t. expected mean of 488 strings - 85 params = 403) (dChi^2=-44, 2*dParams=58)\n",
      "--- Iterative MC2GST: Iter 3 of 4 884 gate strings ---: \n",
      "  --- Minimum Chi^2 GST with model selection (starting dim = 4) ---\n",
      "  Dim 4: chi^2 = 866.447, nGateStrings=884, nParams=56 (so expected mean = 828)\n",
      "  Rejected dim 3: chi^2 = 7.23237e+07 (+7.23228e+07 w.r.t. expected mean of 884 strings - 33 params = 851) (dChi^2=72322819, 2*dParams=-46)\n",
      "  Rejected dim 5: chi^2 = 828.008 (+29.0078 w.r.t. expected mean of 884 strings - 85 params = 799) (dChi^2=-38, 2*dParams=58)\n",
      "--- Iterative MC2GST: Iter 4 of 4 1280 gate strings ---: \n",
      "  --- Minimum Chi^2 GST with model selection (starting dim = 4) ---\n",
      "  Dim 4: chi^2 = 1258.19, nGateStrings=1280, nParams=56 (so expected mean = 1224)\n",
      "  Rejected dim 3: chi^2 = 8.374e+07 (+8.37388e+07 w.r.t. expected mean of 1280 strings - 33 params = 1247) (dChi^2=83738775, 2*dParams=-46)\n",
      "  Rejected dim 5: chi^2 = 1213.69 (+18.6931 w.r.t. expected mean of 1280 strings - 85 params = 1195) (dChi^2=-44, 2*dParams=58)\n"
     ]
    }
   ],
   "source": [
    "#Run LGST to get an initial estimate for the gates in gs_target based on the data in ds\n",
    "# NOTE: with nSamples less than 1M (100K, 10K, 1K) this routine will choose a higher-than-4 dimensional gateset\n",
    "ds = dsFake4\n",
    "gs_lgst4 = pygsti.do_lgst(ds, specs, targetGateset=gs_target, svdTruncateTo=4, verbosity=3)\n",
    "gs_lgst6 = pygsti.do_lgst(ds, specs, targetGateset=gs_target, svdTruncateTo=6, verbosity=3)\n",
    "\n",
    "#Print chi^2 of 4-dim and 6-dim estimates\n",
    "chiSq4 = pygsti.chi2(ds, gs_lgst4, lgstList, minProbClipForWeighting=1e-4)\n",
    "chiSq6 = pygsti.chi2(ds, gs_lgst6, lgstList, minProbClipForWeighting=1e-4)\n",
    "print(\"LGST dim=4 chiSq = \", chiSq4)\n",
    "print(\"LGST dim=6 chiSq = \", chiSq6)\n",
    "\n",
    "# Least squares GST with model selection\n",
    "gs_lsgst = pygsti.do_iterative_mc2gst_with_model_selection(ds, gs_lgst4, 1, lsgstLists, verbosity=2,\n",
    "                                                           minProbClipForWeighting=1e-3, probClipInterval=(-1e5,1e5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rho0 =    0.7072  -0.0217   0.0216   0.7511\n",
      "\n",
      "\n",
      "E0 =    0.6849   0.0022  -0.0021  -0.6447\n",
      "\n",
      "\n",
      "Gi = \n",
      "   1.0000        0        0        0\n",
      "  -0.0035   0.9001   0.0001   0.0003\n",
      "   0.0035        0   0.8998   0.0002\n",
      "  -0.0034  -0.0001   0.0002   0.9000\n",
      "\n",
      "\n",
      "Gx = \n",
      "   1.0000        0        0        0\n",
      "  -0.0037   0.8998   0.0060   0.0004\n",
      "   0.0004  -0.0004  -0.0063  -0.9999\n",
      "  -0.0625   0.0067   0.8101   0.0064\n",
      "\n",
      "\n",
      "Gy = \n",
      "   1.0000        0        0        0\n",
      "  -0.0002  -0.0065        0   0.9994\n",
      "   0.0038   0.0072   0.9000  -0.0009\n",
      "  -0.0624  -0.8105  -0.0059   0.0066\n",
      "\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(gs_lsgst)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Test using dimension-5 fake data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--- LGST ---\n",
      "  Singular values of I_tilde (truncating to first 4 of 6) = \n",
      "  3.56525557364\n",
      "  0.755465956932\n",
      "  0.496239591347\n",
      "  0.487203220172\n",
      "  0.00691003018424\n",
      "  0.000321987001111\n",
      "  \n",
      "  Singular values of target I_tilde (truncating to first 4 of 6) = \n",
      "  3.0\n",
      "  1.0\n",
      "  1.0\n",
      "  1.0\n",
      "  2.46365884775e-16\n",
      "  9.80956846773e-17\n",
      "  \n",
      "    Resulting gate set:\n",
      "    \n",
      "    rho0 =    0.6961  -0.0307   0.0425   0.7832\n",
      "    \n",
      "    \n",
      "    E0 =    0.7554   0.0111  -0.0141  -0.6685\n",
      "    \n",
      "    \n",
      "    Gi = \n",
      "       0.9997  -0.0005   0.0007  -0.0063\n",
      "      -0.0064   0.8998   0.0007  -0.0020\n",
      "       0.0037  -0.0023   0.8991  -0.0002\n",
      "      -0.0080   0.0006   0.0017   0.9024\n",
      "    \n",
      "    \n",
      "    Gx = \n",
      "       1.0223   0.0007   0.0476  -0.0050\n",
      "      -0.0039   0.8292   0.0241  -0.0040\n",
      "       0.0070   0.0263  -0.0403  -1.0042\n",
      "      -0.1197   0.0279   0.6526   0.0271\n",
      "    \n",
      "    \n",
      "    Gy = \n",
      "       1.0221  -0.0478  -0.0009  -0.0034\n",
      "      -0.0182  -0.0538   0.0319   1.0079\n",
      "       0.0003   0.0110   0.8295  -0.0148\n",
      "      -0.1260  -0.6490  -0.0304   0.0388\n",
      "    \n",
      "    \n",
      "    \n",
      "--- LGST ---\n",
      "  Singular values of I_tilde (truncating to first 6 of 6) = \n",
      "  3.56525557364\n",
      "  0.755465956932\n",
      "  0.496239591347\n",
      "  0.487203220172\n",
      "  0.00691003018424\n",
      "  0.000321987001111\n",
      "  \n",
      "  Singular values of target I_tilde (truncating to first 4 of 6) = \n",
      "  3.0\n",
      "  1.0\n",
      "  1.0\n",
      "  1.0\n",
      "  2.46365884775e-16\n",
      "  9.80956846773e-17\n",
      "  \n",
      "  LGST: Padding target B with sqrt of low singular values of I_tilde: \n",
      "  \n",
      "  [ 0.00691003  0.00032199]\n",
      "    Resulting gate set:\n",
      "    \n",
      "    rho0 =    0.6961  -0.0307   0.0425   0.7832   0.0374  -0.0007\n",
      "    \n",
      "    \n",
      "    E0 =    0.7554   0.0111  -0.0141  -0.6685  -0.0376  -0.0002\n",
      "    \n",
      "    \n",
      "    Gi = \n",
      "       0.9997  -0.0005   0.0007  -0.0063  -0.0015  -0.0020\n",
      "      -0.0064   0.8998   0.0007  -0.0020  -0.0171  -0.0049\n",
      "       0.0037  -0.0023   0.8991  -0.0002   0.0107  -0.0284\n",
      "      -0.0080   0.0006   0.0017   0.9024  -0.0006  -0.0612\n",
      "      -0.0013   0.0107  -0.0129   0.0197   0.9113  -0.3506\n",
      "       0.0073  -0.0197   0.0143   0.0980   0.2630   1.7004\n",
      "    \n",
      "    \n",
      "    Gx = \n",
      "       1.0223   0.0007   0.0476  -0.0050   0.0615  -0.0337\n",
      "      -0.0039   0.8292   0.0241  -0.0040  -0.0141   0.0412\n",
      "       0.0070   0.0263  -0.0403  -1.0042   0.3136  -0.0878\n",
      "      -0.1197   0.0279   0.6526   0.0271  -0.0017  -0.0003\n",
      "      -0.0748  -0.0036  -0.1573   0.0164   0.6755  -0.4246\n",
      "       0.0038   0.0568   0.0102  -0.0015  -0.2004  -0.2516\n",
      "    \n",
      "    \n",
      "    Gy = \n",
      "       1.0221  -0.0478  -0.0009  -0.0034   0.0676  -0.0495\n",
      "      -0.0182  -0.0538   0.0319   1.0079  -0.3170   0.0147\n",
      "       0.0003   0.0110   0.8295  -0.0148   0.0105   0.0349\n",
      "      -0.1260  -0.6490  -0.0304   0.0388  -0.0006  -0.0394\n",
      "      -0.0798   0.1549  -0.0002   0.0193   0.7669  -0.5002\n",
      "      -0.0245  -0.0182   0.0293   0.0340  -0.1267  -1.7344\n",
      "    \n",
      "    \n",
      "    \n",
      "LGST dim=4 chiSq =  1236262.37706\n",
      "LGST dim=6 chiSq =  704616.980106\n",
      "--- Iterative MC2GST: Iter 1 of 4 92 gate strings ---: \n",
      "  --- Minimum Chi^2 GST with model selection (starting dim = 4) ---\n",
      "  Dim 4: chi^2 = 278034, nGateStrings=92, nParams=56 (so expected mean = 36)\n",
      "  Rejected dim 3: chi^2 = 3.17675e+06 (+3.17669e+06 w.r.t. expected mean of 92 strings - 33 params = 59) (dChi^2=2898715, 2*dParams=-46)\n",
      "  Selected dim 5: chi^2 = 44.5421 (+37.5421 w.r.t. expected mean of 92 strings - 85 params = 7) (dChi^2=-277989, 2*dParams=58)\n",
      "--- Iterative MC2GST: Iter 2 of 4 488 gate strings ---: \n",
      "  --- Minimum Chi^2 GST with model selection (starting dim = 5) ---\n",
      "  Dim 5: chi^2 = 397.086, nGateStrings=488, nParams=85 (so expected mean = 403)\n",
      "  Rejected dim 4: chi^2 = 1.39997e+06 (+1.39953e+06 w.r.t. expected mean of 488 strings - 56 params = 432) (dChi^2=1399568, 2*dParams=-58)\n",
      "  Rejected dim 6: chi^2 = 338.432 (-29.5677 w.r.t. expected mean of 488 strings - 120 params = 368) (dChi^2=-58, 2*dParams=70)\n",
      "--- Iterative MC2GST: Iter 3 of 4 884 gate strings ---: \n",
      "  --- Minimum Chi^2 GST with model selection (starting dim = 5) ---\n",
      "  Dim 5: chi^2 = 802.805, nGateStrings=884, nParams=85 (so expected mean = 799)\n",
      "  Rejected dim 4: chi^2 = 2.69456e+06 (+2.69373e+06 w.r.t. expected mean of 884 strings - 56 params = 828) (dChi^2=2693755, 2*dParams=-58)\n",
      "  Rejected dim 6: chi^2 = 757.678 (-6.32234 w.r.t. expected mean of 884 strings - 120 params = 764) (dChi^2=-45, 2*dParams=70)\n",
      "--- Iterative MC2GST: Iter 4 of 4 1280 gate strings ---: \n",
      "  --- Minimum Chi^2 GST with model selection (starting dim = 5) ---\n",
      "  Dim 5: chi^2 = 1197.51, nGateStrings=1280, nParams=85 (so expected mean = 1195)\n",
      "  Rejected dim 4: chi^2 = 4.21903e+06 (+4.2178e+06 w.r.t. expected mean of 1280 strings - 56 params = 1224) (dChi^2=4217830, 2*dParams=-58)\n",
      "  Rejected dim 6: chi^2 = 1146.27 (-13.7322 w.r.t. expected mean of 1280 strings - 120 params = 1160) (dChi^2=-51, 2*dParams=70)\n"
     ]
    }
   ],
   "source": [
    "#Run LGST to get an initial estimate for the gates in gs_target based on the data in ds\n",
    "ds = dsFake5\n",
    "gs_lgst4 = pygsti.do_lgst(ds, specs, targetGateset=gs_target, svdTruncateTo=4, verbosity=3)\n",
    "gs_lgst6 = pygsti.do_lgst(ds, specs, targetGateset=gs_target, svdTruncateTo=6, verbosity=3)\n",
    "\n",
    "#Print chi^2 of 4-dim and 6-dim estimates\n",
    "chiSq4 = pygsti.chi2(ds, gs_lgst4, lgstList, minProbClipForWeighting=1e-2)\n",
    "chiSq6 = pygsti.chi2(ds, gs_lgst6, lgstList, minProbClipForWeighting=1e-2)\n",
    "print(\"LGST dim=4 chiSq = \", chiSq4)\n",
    "print(\"LGST dim=6 chiSq = \", chiSq6)\n",
    "\n",
    "# Least squares GST with model selection\n",
    "gs_lsgst = pygsti.do_iterative_mc2gst_with_model_selection(ds, gs_lgst4, 1, lsgstLists, verbosity=2, minProbClipForWeighting=1e-3, probClipInterval=(-1e5,1e5), useFreqWeightedChiSq=False, regularizeFactor=1.0, check=False, check_jacobian=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rho0 =    0.7072  -0.0141   0.0218   0.7481  -0.0373\n",
      "\n",
      "\n",
      "E0 =    0.7007   0.0431  -0.0421  -0.6482   0.2446\n",
      "\n",
      "\n",
      "Gi = \n",
      "   1.0000        0        0        0        0\n",
      "  -0.0042   0.8991   0.0007   0.0014  -0.0073\n",
      "   0.0023   0.0004   0.8992  -0.0011   0.0078\n",
      "  -0.0091  -0.0002   0.0004   0.9002  -0.0006\n",
      "  -0.0002   0.0092  -0.0090  -0.0138   1.0004\n",
      "\n",
      "\n",
      "Gx = \n",
      "   1.0000        0   0.0001  -0.0001        0\n",
      "  -0.0210   0.8322   0.0094  -0.0114   0.0043\n",
      "   0.0199   0.0222  -0.0175  -1.0220  -0.0412\n",
      "  -0.1081   0.0314   0.6711   0.0272  -0.0476\n",
      "   0.1734  -0.0049   0.0221  -0.0089   0.7705\n",
      "\n",
      "\n",
      "Gy = \n",
      "   1.0000  -0.0001        0  -0.0002        0\n",
      "  -0.0364  -0.0359   0.0230   1.0195   0.0415\n",
      "   0.0164  -0.0023   0.8315  -0.0122  -0.0053\n",
      "  -0.1186  -0.6737  -0.0266   0.0465  -0.0455\n",
      "   0.1732  -0.0227   0.0049  -0.0071   0.7705\n",
      "\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(gs_lsgst)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": []
  }
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