jupyter_notebooks/Examples/Leakage.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Leakage characterization using GST\n",
    "This tutorial demonstrates how to perform GST on a \"leaky-qubit\" described by a 3-level (instead of the desired 2-level) system. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pygsti\n",
    "import pygsti.construction as pc\n",
    "import pygsti.modelpacks.legacy.std1Q_XYI as std1Q\n",
    "import numpy as np\n",
    "import scipy.linalg as sla\n",
    "#import pickle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def to_3level_unitary(U_2level):\n",
    "    U_3level = np.zeros((3,3),complex)\n",
    "    U_3level[0:2,0:2] = U_2level\n",
    "    U_3level[2,2] = 1.0\n",
    "    return U_3level\n",
    "\n",
    "def unitary_to_gmgate(U):\n",
    "    return pygsti.tools.change_basis( \n",
    "        pygsti.tools.unitary_to_process_mx(U), 'std','gm')\n",
    "\n",
    "def state_to_gmvec(state):\n",
    "    pygsti.tools.stdmx_to_gmvec\n",
    "\n",
    "Us = pygsti.tools.internalgates.get_standard_gatename_unitaries()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "mdl_2level_ideal = std1Q.target_model()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "rho0 = np.array( [[1,0,0],\n",
    "                  [0,0,0],\n",
    "                  [0,0,0]], complex)\n",
    "E0 = rho0\n",
    "E1 = np.array( [[0,0,0],\n",
    "                [0,1,0],\n",
    "                [0,0,1]], complex)\n",
    "\n",
    "sslbls = pygsti.obj.StateSpaceLabels(['Qubit+Leakage'],[9])\n",
    "mdl_3level_ideal = pygsti.obj.ExplicitOpModel(sslbls, 'gm')\n",
    "mdl_3level_ideal['rho0'] = pygsti.tools.stdmx_to_gmvec(rho0)\n",
    "mdl_3level_ideal['Mdefault'] = pygsti.obj.TPPOVM([('0',pygsti.tools.stdmx_to_gmvec(E0)),\n",
    "                                                    ('1',pygsti.tools.stdmx_to_gmvec(E1))])\n",
    "\n",
    "mdl_3level_ideal['Gi'] = unitary_to_gmgate( to_3level_unitary(Us['Gi']))\n",
    "mdl_3level_ideal['Gx'] = unitary_to_gmgate( to_3level_unitary(Us['Gxpi2']))\n",
    "mdl_3level_ideal['Gy'] = unitary_to_gmgate( to_3level_unitary(Us['Gypi2']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "sigmaX = np.array([[0,1],[1,0]],complex)\n",
    "rot = sla.expm(1j * 0.1 * sigmaX)\n",
    "Uleakage = np.identity(3,complex)\n",
    "Uleakage[1:3,1:3] = rot\n",
    "leakageOp = unitary_to_gmgate(Uleakage)\n",
    "#print(Uleakage)\n",
    "\n",
    "#Guess of a model w/just unitary leakage\n",
    "mdl_3level_guess = mdl_3level_ideal.copy()\n",
    "mdl_3level_guess['Gi'] = np.dot(leakageOp, mdl_3level_guess['Gi'])\n",
    "#mdl_3level_guess['Gx'] = np.dot(leakageOp, mdl_3level_guess['Gx'])\n",
    "#mdl_3level_guess['Gy'] = np.dot(leakageOp, mdl_3level_guess['Gy'])\n",
    "\n",
    "#Actual model used for data generation (some depolarization too)\n",
    "mdl_3level_noisy = mdl_3level_ideal.depolarize(op_noise=0.005, spam_noise=0.01)\n",
    "mdl_3level_noisy['Gi'] = np.dot(leakageOp, mdl_3level_noisy['Gi'])\n",
    "#mdl_3level_noisy['Gx'] = np.dot(leakageOp, mdl_3level_noisy['Gx'])\n",
    "#mdl_3level_noisy['Gy'] = np.dot(leakageOp, mdl_3level_noisy['Gy'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "#print(mdl_3level_guess)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# get sequences using expected model\n",
    "generate_fiducials = False\n",
    "\n",
    "if generate_fiducials:\n",
    "    prepfids, measfids = pygsti.algorithms.generate_fiducials(\n",
    "        mdl_3level_guess, omitIdentity=False, maxFidLength=4, verbosity=4)\n",
    "    pygsti.io.write_circuit_list(\"example_files/leakage_prepfids.txt\", prepfids)\n",
    "    pygsti.io.write_circuit_list(\"example_files/leakage_measfids.txt\", measfids)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "prepfids = pygsti.io.load_circuit_list(\"example_files/leakage_prepfids.txt\")\n",
    "measfids = pygsti.io.load_circuit_list(\"example_files/leakage_measfids.txt\")\n",
    "germs = std1Q.germs\n",
    "maxLengths = [1,]\n",
    "expList = pc.make_lsgst_experiment_list(mdl_3level_noisy, prepfids, measfids, germs, maxLengths)\n",
    "ds = pc.generate_fake_data(mdl_3level_noisy, expList, 1000, 'binomial', seed=1234)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--- Circuit Creation ---\n",
      "   280 sequences created\n",
      "-- Std Practice:  Iter 1 of 1  (CPTP) --: \n",
      "  --- Iterative MLGST: Iter 1 of 1  280 operation sequences ---: \n",
      "    --- Minimum Chi^2 GST ---\n",
      "    Sum of Chi^2 = 801.665 (280 data params - 31 model params = expected mean of 249; p-value = 0)\n",
      "    Completed in 8.6s\n",
      "    2*Delta(log(L)) = 809.696\n",
      "    Iteration 1 took 8.7s\n",
      "    \n",
      "    Switching to ML objective (last iteration)\n",
      "    --- MLGST ---\n",
      "      Maximum log(L) = 398.424 below upper bound of -421916\n",
      "        2*Delta(log(L)) = 796.848 (280 data params - 31 model params = expected mean of 249; p-value = 0)\n",
      "      Completed in 1.3s\n",
      "    2*Delta(log(L)) = 796.848\n",
      "    Final MLGST took 1.3s\n",
      "    \n",
      "  Iterative MLGST Total Time: 10.0s\n",
      "--- Circuit Creation ---\n",
      "   280 sequences created\n",
      "-- Std Practice:  Iter 1 of 2  (CPTP) --: \n",
      "  --- Iterative MLGST: Iter 1 of 1  280 operation sequences ---: \n",
      "    --- Minimum Chi^2 GST ---\n",
      "      bulk_evaltree: created initial tree (280 strs) in 0s\n",
      "      bulk_evaltree: split tree (1 subtrees) in 0s\n",
      "      Created evaluation tree with 1 subtrees.  Will divide 1 procs into 1 (subtree-processing)\n",
      "       groups of ~1 procs each, to distribute over 360 params (taken as 1 param groups of ~360 params).\n",
      "      --- Outer Iter 0: norm_f = 1.53652e+06, mu=1, |x|=6.32456e-08, |J|=1918.56\n",
      "      --- Outer Iter 1: norm_f = 5099.26, mu=285.685, |x|=0.119235, |J|=2823.13\n",
      "      --- Outer Iter 2: norm_f = 2609.34, mu=2283.99, |x|=0.213143, |J|=2042.32\n",
      "      --- Outer Iter 3: norm_f = 552.948, mu=1173.1, |x|=0.201959, |J|=2169.09\n",
      "      --- Outer Iter 4: norm_f = 304.854, mu=774.594, |x|=0.212428, |J|=2238.79\n",
      "      --- Outer Iter 5: norm_f = 280.095, mu=1549.12, |x|=0.216086, |J|=2252.51\n",
      "      --- Outer Iter 6: norm_f = 265.947, mu=1548.86, |x|=0.223266, |J|=2286.38\n",
      "      --- Outer Iter 7: norm_f = 263.391, mu=2015.59, |x|=0.230447, |J|=2305.34\n",
      "      --- Outer Iter 8: norm_f = 257.986, mu=2037.5, |x|=0.235554, |J|=2314.3\n",
      "      --- Outer Iter 9: norm_f = 254.684, mu=2065.78, |x|=0.240654, |J|=2322.02\n",
      "      --- Outer Iter 10: norm_f = 253.632, mu=2658.14, |x|=0.246082, |J|=2322.53\n",
      "      --- Outer Iter 11: norm_f = 251.262, mu=2659.7, |x|=0.24992, |J|=2326.78\n",
      "      --- Outer Iter 12: norm_f = 249.992, mu=2659.7, |x|=0.253678, |J|=2328.16\n",
      "      Least squares message = Both actual and predicted relative reductions in the sum of squares are at most 0.01\n",
      "    Sum of Chi^2 = 249.992 (280 data params - 161 model params = expected mean of 119; p-value = 2.49065e-11)\n",
      "    Completed in 18.6s\n",
      "    2*Delta(log(L)) = 250.944\n",
      "    Iteration 1 took 18.7s\n",
      "    \n",
      "    Switching to ML objective (last iteration)\n",
      "    --- MLGST ---\n",
      "      --- Outer Iter 0: norm_f = 125.472, mu=1, |x|=0.253678, |J|=1648.25\n",
      "      Least squares message = Both actual and predicted relative reductions in the sum of squares are at most 0.01\n",
      "      Maximum log(L) = 125.472 below upper bound of -421916\n",
      "        2*Delta(log(L)) = 250.944 (280 data params - 161 model params = expected mean of 119; p-value = 1.92685e-11)\n",
      "      Completed in 1.0s\n",
      "    2*Delta(log(L)) = 250.944\n",
      "    Final MLGST took 1.0s\n",
      "    \n",
      "  Iterative MLGST Total Time: 19.6s\n",
      "      -- Performing 'stdgaugeopt' gauge optimization on CPTP estimate --\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      "WARNING: MLGST failed to improve logl: retaining chi2-objective estimate\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-- Std Practice:  Iter 2 of 2  (True) --: \n",
      "      -- Performing 'stdgaugeopt' gauge optimization on True estimate --\n"
     ]
    }
   ],
   "source": [
    "results_2level = pygsti.do_stdpractice_gst(ds, mdl_2level_ideal, prepfids, measfids,\n",
    "                                           germs, maxLengths, modes=\"CPTP\", verbosity=3)\n",
    "results_3level = pygsti.do_stdpractice_gst(ds, mdl_3level_ideal, prepfids, measfids,\n",
    "                                           germs, maxLengths, modes=\"CPTP,True\",\n",
    "                                           modelsToTest={'True': mdl_3level_noisy}, \n",
    "                                           verbosity=4, advancedOptions={'all': {'tolerance': 1e-2}})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running idle tomography\n",
      "Computing switchable properties\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/enielse/pyGSTi/pygsti/report/factory.py:1236: UserWarning:\n",
      "\n",
      "Idle tomography failed:\n",
      "operands could not be broadcast together with shapes (9,) (16,) \n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found standard clifford compilation from std1Q_XYI\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/enielse/pyGSTi/pygsti/report/factory.py:1303: UserWarning:\n",
      "\n",
      "PDF output is not available for reports with multiple datasets\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statistical hypothesis tests did NOT find inconsistency between the datasets at 5.00% significance.\n",
      "Statistical hypothesis tests did NOT find inconsistency between the datasets at 5.00% significance.\n",
      "Statistical hypothesis tests did NOT find inconsistency between the datasets at 5.00% significance.\n",
      "Statistical hypothesis tests did NOT find inconsistency between the datasets at 5.00% significance.\n"
     ]
    }
   ],
   "source": [
    "pygsti.report.construct_standard_report(\n",
    "    {'two-level': results_2level, 'three-level': results_3level},\n",
    "    \"Leakage Example Report\"\n",
    ").write_html('example_files/leakage_report')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "#try a different basis:\n",
    "gm_basis = pygsti.obj.Basis.cast('gm',9)\n",
    "   \n",
    "leakage_basis_mxs = [ np.sqrt(2)/3*(np.sqrt(3)*gm_basis[0] + 0.5*np.sqrt(6)*gm_basis[8]),\n",
    "                      gm_basis[1], gm_basis[4], gm_basis[7],\n",
    "                     gm_basis[2], gm_basis[3], gm_basis[5], gm_basis[6],\n",
    "                     1/3*(np.sqrt(3)*gm_basis[0] - np.sqrt(6)*gm_basis[8]) ]\n",
    "#for mx in leakage_basis_mxs:\n",
    "#    pygsti.tools.print_mx(mx)\n",
    "\n",
    "check = np.zeros( (9,9), complex)\n",
    "for i,m1 in enumerate(leakage_basis_mxs):\n",
    "    for j,m2 in enumerate(leakage_basis_mxs):\n",
    "        check[i,j] = np.trace(np.dot(m1,m2))\n",
    "assert(np.allclose(check, np.identity(9,complex)))\n",
    "\n",
    "leakage_basis = pygsti.obj.ExplicitBasis(leakage_basis_mxs, name=\"LeakageBasis\",  \n",
    "                                        longname=\"2+1 level leakage basis\", real=True,\n",
    "                                        labels=['I','X','Y','Z','LX0','LX1','LY0','LY1','L'])\n",
    "\n",
    "def changebasis_3level_model(mdl):\n",
    "    new_mdl = mdl.copy()\n",
    "    new_mdl.preps['rho0'] = pygsti.obj.FullSPAMVec(\n",
    "        pygsti.tools.change_basis(mdl.preps['rho0'].todense(), gm_basis, leakage_basis))\n",
    "    new_mdl.povms['Mdefault'] = pygsti.obj.UnconstrainedPOVM(\n",
    "        [('0', pygsti.tools.change_basis(mdl.povms['Mdefault']['0'].todense(), gm_basis, leakage_basis)),\n",
    "         ('1', pygsti.tools.change_basis(mdl.povms['Mdefault']['1'].todense(), gm_basis, leakage_basis))])\n",
    "    \n",
    "    for lbl,op in mdl.operations.items():\n",
    "        new_mdl.operations[lbl] = pygsti.obj.FullDenseOp(\n",
    "            pygsti.tools.change_basis(op.todense(), gm_basis, leakage_basis))\n",
    "    new_mdl.basis = leakage_basis\n",
    "    return new_mdl\n",
    "\n",
    "def changebasis_3level_results(results):\n",
    "    new_results = results.copy()\n",
    "    for estlbl,est in results.estimates.items():\n",
    "        for mlbl,mdl in est.models.items():\n",
    "            if isinstance(mdl,(list,tuple)): #assume a list/tuple of models\n",
    "                new_results.estimates[estlbl].models[mlbl] = \\\n",
    "                    [ changebasis_3level_model(m) for m in mdl ]\n",
    "            else:\n",
    "                new_results.estimates[estlbl].models[mlbl] = changebasis_3level_model(mdl)\n",
    "    return new_results\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "results_3level_leakage_basis = changebasis_3level_results( results_3level )    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running idle tomography\n",
      "Computing switchable properties\n",
      "Found standard clifford compilation from std1Q_XYI\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/enielse/pyGSTi/pygsti/report/factory.py:1236: UserWarning:\n",
      "\n",
      "Idle tomography failed:\n",
      "operands could not be broadcast together with shapes (9,) (16,) \n",
      "\n",
      "/Users/enielse/pyGSTi/pygsti/report/factory.py:1303: UserWarning:\n",
      "\n",
      "PDF output is not available for reports with multiple datasets\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statistical hypothesis tests did NOT find inconsistency between the datasets at 5.00% significance.\n",
      "Statistical hypothesis tests did NOT find inconsistency between the datasets at 5.00% significance.\n",
      "Statistical hypothesis tests did NOT find inconsistency between the datasets at 5.00% significance.\n",
      "Statistical hypothesis tests did NOT find inconsistency between the datasets at 5.00% significance.\n"
     ]
    }
   ],
   "source": [
    "pygsti.report.construct_standard_report(\n",
    "    {'two-level': results_2level, 'three-level': results_3level_leakage_basis},\n",
    "    \"Leakage Example Report\"\n",
    ").write_html('example_files/leakage_report')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Open the report [here](example_files/leakage_report/main.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# use \"kite\" density-matrix structure\n",
    "def to_2plus1_superop(superop_2level):\n",
    "    ret = np.zeros((5,5),'d')\n",
    "    ret[0:4,0:4] = superop_2level\n",
    "    ret[4,4] = 1.0 #leave leakage population where it is\n",
    "    return ret\n",
    "\n",
    "#Tack on a single extra \"0\" for the 5-th dimension corresponding\n",
    "# to the classical leakage level population.\n",
    "rho0 = np.concatenate( (mdl_2level_ideal.preps['rho0'],[[0]]), axis=0)\n",
    "E0 = np.concatenate( (mdl_2level_ideal.povms['Mdefault']['0'],[[0]]), axis=0)\n",
    "E1 = np.concatenate( (mdl_2level_ideal.povms['Mdefault']['1'],[[0]]), axis=0)\n",
    "\n",
    "\n",
    "sslbls = pygsti.obj.StateSpaceLabels([('Qubit',),('Leakage',)],[(4,),(1,)])\n",
    "mdl_2plus1_ideal = pygsti.obj.ExplicitOpModel(sslbls, 'gm')\n",
    "mdl_2plus1_ideal['rho0'] = rho0\n",
    "mdl_2plus1_ideal['Mdefault'] = pygsti.obj.UnconstrainedPOVM([('0',E0),('1',E1)])\n",
    "\n",
    "mdl_2plus1_ideal['Gi'] = to_2plus1_superop(mdl_2level_ideal['Gi'])\n",
    "mdl_2plus1_ideal['Gx'] = to_2plus1_superop(mdl_2level_ideal['Gi'])\n",
    "mdl_2plus1_ideal['Gy'] = to_2plus1_superop(mdl_2level_ideal['Gi'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--- Circuit Creation ---\n",
      "   280 sequences created\n",
      "--- Iterative MLGST: Iter 1 of 1  280 operation sequences ---: \n",
      "  --- Minimum Chi^2 GST ---\n",
      "    bulk_evaltree: created initial tree (280 strs) in 0s\n",
      "    bulk_evaltree: split tree (1 subtrees) in 0s\n",
      "    Created evaluation tree with 1 subtrees.  Will divide 1 procs into 1 (subtree-processing)\n",
      "     groups of ~1 procs each, to distribute over 90 params (taken as 1 param groups of ~90 params).\n",
      "    --- Outer Iter 0: norm_f = 1.10463e+09, mu=1, |x|=4.24264, |J|=246913\n",
      "    --- Outer Iter 1: norm_f = 106758, mu=2.30523e+06, |x|=4.23094, |J|=4045.54\n",
      "    --- Outer Iter 2: norm_f = 76699.5, mu=768410, |x|=4.21158, |J|=3590.63\n",
      "    --- Outer Iter 3: norm_f = 69764.7, mu=256137, |x|=4.2006, |J|=3504.09\n",
      "    --- Outer Iter 4: norm_f = 68704, mu=85378.9, |x|=4.19376, |J|=3476.38\n",
      "    --- Outer Iter 5: norm_f = 67412.7, mu=28459.6, |x|=4.17968, |J|=3422.34\n",
      "    --- Outer Iter 6: norm_f = 66403.8, mu=11408.7, |x|=4.166, |J|=3376.7\n",
      "    --- Outer Iter 7: norm_f = 66147.1, mu=6650.94, |x|=4.16608, |J|=3369.15\n",
      "    --- Outer Iter 8: norm_f = 66093.8, mu=2216.98, |x|=4.1746, |J|=3379.62\n",
      "    --- Outer Iter 9: norm_f = 66019, mu=738.994, |x|=4.19649, |J|=3445.39\n",
      "    --- Outer Iter 10: norm_f = 65902.5, mu=246.331, |x|=4.23102, |J|=3579.46\n",
      "    --- Outer Iter 11: norm_f = 65735.9, mu=82.1104, |x|=4.27791, |J|=3821.13\n",
      "    --- Outer Iter 12: norm_f = 64623.4, mu=27.3701, |x|=4.33488, |J|=4241.65\n",
      "    --- Outer Iter 13: norm_f = 64142, mu=2009.45, |x|=4.39261, |J|=5860.49\n",
      "    --- Outer Iter 14: norm_f = 61597.7, mu=1620.53, |x|=4.358, |J|=4917.3\n",
      "    --- Outer Iter 15: norm_f = 60952.1, mu=1631.1, |x|=4.41398, |J|=5481.58\n",
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    {
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     "text": [
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      "    --- Outer Iter 196: norm_f = 603.743, mu=0.75105, |x|=7.66257, |J|=30248.4\n",
      "    --- Outer Iter 197: norm_f = 603.737, mu=0.728965, |x|=7.71374, |J|=30801.7\n",
      "    --- Outer Iter 198: norm_f = 603.731, mu=0.707414, |x|=7.76503, |J|=31362.9\n",
      "    --- Outer Iter 199: norm_f = 603.725, mu=0.686389, |x|=7.81641, |J|=31932\n",
      "    --- Outer Iter 200: norm_f = 603.719, mu=0.665883, |x|=7.86787, |J|=32508.7\n",
      "    --- Outer Iter 201: norm_f = 603.713, mu=0.645885, |x|=7.91941, |J|=33092.9\n",
      "    --- Outer Iter 202: norm_f = 603.707, mu=0.626386, |x|=7.971, |J|=33684.6\n",
      "    --- Outer Iter 203: norm_f = 603.702, mu=0.607378, |x|=8.02265, |J|=34283.6\n",
      "    --- Outer Iter 204: norm_f = 603.697, mu=0.58885, |x|=8.07433, |J|=34889.7\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    --- Outer Iter 205: norm_f = 603.692, mu=0.570793, |x|=8.12603, |J|=35502.8\n",
      "    --- Outer Iter 206: norm_f = 603.687, mu=0.553197, |x|=8.17775, |J|=36122.7\n",
      "    --- Outer Iter 207: norm_f = 603.683, mu=0.536052, |x|=8.22946, |J|=36749.3\n",
      "    --- Outer Iter 208: norm_f = 603.678, mu=0.519349, |x|=8.28117, |J|=37382.4\n",
      "    --- Outer Iter 209: norm_f = 603.674, mu=0.503077, |x|=8.33284, |J|=38021.7\n",
      "    --- Outer Iter 210: norm_f = 603.67, mu=0.487227, |x|=8.38448, |J|=38667.2\n",
      "    --- Outer Iter 211: norm_f = 603.666, mu=0.471789, |x|=8.43607, |J|=39318.6\n",
      "    --- Outer Iter 212: norm_f = 603.662, mu=0.456753, |x|=8.48759, |J|=39975.8\n",
      "    --- Outer Iter 213: norm_f = 603.658, mu=0.44211, |x|=8.53903, |J|=40638.4\n",
      "    --- Outer Iter 214: norm_f = 603.655, mu=0.427849, |x|=8.59039, |J|=41306.4\n",
      "    --- Outer Iter 215: norm_f = 603.651, mu=0.413962, |x|=8.64164, |J|=41979.5\n",
      "    --- Outer Iter 216: norm_f = 603.648, mu=0.400438, |x|=8.69277, |J|=42657.5\n",
      "    --- Outer Iter 217: norm_f = 603.645, mu=0.387269, |x|=8.74378, |J|=43340.1\n",
      "    --- Outer Iter 218: norm_f = 603.642, mu=0.374445, |x|=8.79464, |J|=44027.2\n",
      "    --- Outer Iter 219: norm_f = 603.639, mu=0.361957, |x|=8.84534, |J|=44718.3\n",
      "    --- Outer Iter 220: norm_f = 603.636, mu=0.349796, |x|=8.89588, |J|=45413.5\n",
      "    --- Outer Iter 221: norm_f = 603.634, mu=0.337954, |x|=8.94623, |J|=46112.2\n",
      "    --- Outer Iter 222: norm_f = 603.631, mu=0.326421, |x|=8.99638, |J|=46814.4\n",
      "    --- Outer Iter 223: norm_f = 603.629, mu=0.315189, |x|=9.04632, |J|=47519.7\n",
      "    --- Outer Iter 224: norm_f = 603.626, mu=0.30425, |x|=9.09604, |J|=48227.8\n",
      "    --- Outer Iter 225: norm_f = 603.624, mu=0.293595, |x|=9.14552, |J|=48938.4\n",
      "    --- Outer Iter 226: norm_f = 603.622, mu=0.283216, |x|=9.19474, |J|=49651.4\n",
      "    --- Outer Iter 227: norm_f = 603.62, mu=0.273106, |x|=9.24369, |J|=50366.2\n",
      "    --- Outer Iter 228: norm_f = 603.618, mu=0.263256, |x|=9.29237, |J|=51082.7\n",
      "    --- Outer Iter 229: norm_f = 603.616, mu=0.253659, |x|=9.34075, |J|=51800.6\n",
      "    --- Outer Iter 230: norm_f = 603.614, mu=0.244307, |x|=9.38881, |J|=52519.4\n",
      "    --- Outer Iter 231: norm_f = 603.613, mu=0.235194, |x|=9.43655, |J|=53238.9\n",
      "    --- Outer Iter 232: norm_f = 603.611, mu=0.226311, |x|=9.48395, |J|=53958.7\n",
      "    --- Outer Iter 233: norm_f = 603.61, mu=0.217652, |x|=9.53099, |J|=54678.5\n",
      "    --- Outer Iter 234: norm_f = 603.608, mu=0.209209, |x|=9.57766, |J|=55397.9\n",
      "    --- Outer Iter 235: norm_f = 603.607, mu=0.200977, |x|=9.62394, |J|=56116.5\n",
      "    --- Outer Iter 236: norm_f = 603.606, mu=0.192948, |x|=9.66982, |J|=56834\n",
      "    --- Outer Iter 237: norm_f = 603.605, mu=0.185116, |x|=9.71528, |J|=57549.9\n",
      "    --- Outer Iter 238: norm_f = 603.603, mu=0.177474, |x|=9.76031, |J|=58263.9\n",
      "    --- Outer Iter 239: norm_f = 603.602, mu=0.170017, |x|=9.80488, |J|=58975.6\n",
      "    --- Outer Iter 240: norm_f = 603.601, mu=0.162738, |x|=9.84899, |J|=59684.5\n",
      "    --- Outer Iter 241: norm_f = 603.6, mu=0.155631, |x|=9.89261, |J|=60390.3\n",
      "    --- Outer Iter 242: norm_f = 603.6, mu=0.14869, |x|=9.93573, |J|=61092.4\n",
      "    --- Outer Iter 243: norm_f = 603.599, mu=0.14191, |x|=9.97832, |J|=61790.5\n",
      "    --- Outer Iter 244: norm_f = 603.598, mu=0.135285, |x|=10.0204, |J|=62484\n",
      "    --- Outer Iter 245: norm_f = 603.597, mu=0.128809, |x|=10.0619, |J|=63172.5\n",
      "    --- Outer Iter 246: norm_f = 603.597, mu=0.122477, |x|=10.1028, |J|=63855.5\n",
      "    --- Outer Iter 247: norm_f = 603.596, mu=0.116283, |x|=10.1431, |J|=64532.6\n",
      "    --- Outer Iter 248: norm_f = 603.595, mu=0.110222, |x|=10.1829, |J|=65203.1\n",
      "    --- Outer Iter 249: norm_f = 603.595, mu=0.104289, |x|=10.2219, |J|=65866.5\n",
      "    --- Outer Iter 250: norm_f = 603.594, mu=0.0984776, |x|=10.2604, |J|=66522.4\n",
      "    --- Outer Iter 251: norm_f = 603.594, mu=0.0927839, |x|=10.2981, |J|=67170.1\n",
      "    Least squares message = Both actual and predicted relative reductions in the sum of squares are at most 1e-06\n",
      "  Sum of Chi^2 = 603.594 (280 data params - 65 model params = expected mean of 215; p-value = 0)\n",
      "  Completed in 23.5s\n",
      "  2*Delta(log(L)) = 613.182\n",
      "  Iteration 1 took 23.6s\n",
      "  \n",
      "  Switching to ML objective (last iteration)\n",
      "  --- MLGST ---\n",
      "    --- Outer Iter 0: norm_f = 306.591, mu=1, |x|=10.2981, |J|=47563.3\n",
      "    --- Outer Iter 1: norm_f = 302.819, mu=193418, |x|=10.2982, |J|=47623\n",
      "    --- Outer Iter 2: norm_f = 301.967, mu=64472.5, |x|=10.2982, |J|=47611.6\n",
      "    --- Outer Iter 3: norm_f = 301.659, mu=21490.8, |x|=10.2983, |J|=47635.2\n",
      "    --- Outer Iter 4: norm_f = 301.541, mu=7163.61, |x|=10.2983, |J|=47682.2\n",
      "    --- Outer Iter 5: norm_f = 301.465, mu=2387.87, |x|=10.2983, |J|=47747.8\n",
      "    --- Outer Iter 6: norm_f = 301.407, mu=795.957, |x|=10.2983, |J|=47826\n",
      "    --- Outer Iter 7: norm_f = 301.374, mu=265.319, |x|=10.2983, |J|=47885.2\n",
      "    --- Outer Iter 8: norm_f = 301.344, mu=88.4396, |x|=10.2983, |J|=47898.7\n",
      "    --- Outer Iter 9: norm_f = 301.293, mu=29.4799, |x|=10.2986, |J|=47914.9\n",
      "    --- Outer Iter 10: norm_f = 301.241, mu=15.7421, |x|=10.2992, |J|=48107.2\n",
      "    --- Outer Iter 11: norm_f = 301.217, mu=10.5499, |x|=10.3, |J|=48492.9\n",
      "    --- Outer Iter 12: norm_f = 301.208, mu=5.33888, |x|=10.3003, |J|=48828.2\n",
      "    --- Outer Iter 13: norm_f = 301.206, mu=4.69523, |x|=10.2998, |J|=49119.2\n",
      "    --- Outer Iter 14: norm_f = 301.204, mu=1.56508, |x|=10.2988, |J|=49274.6\n",
      "    --- Outer Iter 15: norm_f = 301.203, mu=0.521692, |x|=10.2946, |J|=49371.3\n",
      "    --- Outer Iter 16: norm_f = 301.202, mu=0.173897, |x|=10.2809, |J|=49291\n",
      "    --- Outer Iter 17: norm_f = 301.202, mu=0.129846, |x|=10.2385, |J|=48801.5\n",
      "    --- Outer Iter 18: norm_f = 301.201, mu=0.129846, |x|=10.1819, |J|=48116.9\n",
      "    --- Outer Iter 19: norm_f = 301.2, mu=0.12793, |x|=10.1256, |J|=47426.7\n",
      "    --- Outer Iter 20: norm_f = 301.199, mu=0.126963, |x|=10.0689, |J|=46731.8\n",
      "    --- Outer Iter 21: norm_f = 301.198, mu=0.126124, |x|=10.0125, |J|=46041.1\n",
      "    --- Outer Iter 22: norm_f = 301.196, mu=0.125355, |x|=9.9567, |J|=45359.9\n",
      "    --- Outer Iter 23: norm_f = 301.195, mu=0.124608, |x|=9.90153, |J|=44690.5\n",
      "    --- Outer Iter 24: norm_f = 301.194, mu=0.123843, |x|=9.84716, |J|=44034.9\n",
      "    --- Outer Iter 25: norm_f = 301.193, mu=0.123041, |x|=9.79365, |J|=43394.2\n",
      "    --- Outer Iter 26: norm_f = 301.192, mu=0.122186, |x|=9.74104, |J|=42768.8\n",
      "    --- Outer Iter 27: norm_f = 301.192, mu=0.121266, |x|=9.68936, |J|=42159.1\n",
      "    --- Outer Iter 28: norm_f = 301.191, mu=0.120272, |x|=9.63863, |J|=41565.1\n",
      "    --- Outer Iter 29: norm_f = 301.19, mu=0.119198, |x|=9.58883, |J|=40986.5\n",
      "    --- Outer Iter 30: norm_f = 301.189, mu=0.118037, |x|=9.53998, |J|=40423.3\n",
      "    --- Outer Iter 31: norm_f = 301.188, mu=0.116786, |x|=9.49206, |J|=39875\n",
      "    --- Outer Iter 32: norm_f = 301.187, mu=0.115443, |x|=9.44507, |J|=39341.4\n",
      "    --- Outer Iter 33: norm_f = 301.187, mu=0.114005, |x|=9.39899, |J|=38822.1\n",
      "    --- Outer Iter 34: norm_f = 301.186, mu=0.112471, |x|=9.35382, |J|=38316.8\n",
      "    --- Outer Iter 35: norm_f = 301.185, mu=0.110842, |x|=9.30953, |J|=37825.1\n",
      "    --- Outer Iter 36: norm_f = 301.185, mu=0.109116, |x|=9.26613, |J|=37346.7\n",
      "    --- Outer Iter 37: norm_f = 301.184, mu=0.107295, |x|=9.2236, |J|=36881.3\n",
      "    --- Outer Iter 38: norm_f = 301.184, mu=0.105378, |x|=9.18193, |J|=36428.5\n",
      "    --- Outer Iter 39: norm_f = 301.183, mu=0.103367, |x|=9.14111, |J|=35988.1\n",
      "    --- Outer Iter 40: norm_f = 301.183, mu=0.101263, |x|=9.10113, |J|=35559.7\n",
      "    --- Outer Iter 41: norm_f = 301.182, mu=0.099066, |x|=9.06198, |J|=35143.1\n",
      "    --- Outer Iter 42: norm_f = 301.182, mu=0.0967775, |x|=9.02366, |J|=34738.1\n",
      "    --- Outer Iter 43: norm_f = 301.181, mu=0.0943984, |x|=8.98616, |J|=34344.4\n",
      "    --- Outer Iter 44: norm_f = 301.181, mu=0.0919296, |x|=8.94947, |J|=33961.7\n",
      "    --- Outer Iter 45: norm_f = 301.18, mu=0.0893721, |x|=8.91359, |J|=33589.9\n",
      "    --- Outer Iter 46: norm_f = 301.18, mu=0.0867267, |x|=8.87852, |J|=33228.8\n",
      "    --- Outer Iter 47: norm_f = 301.18, mu=0.0839945, |x|=8.84424, |J|=32878\n",
      "    --- Outer Iter 48: norm_f = 301.179, mu=0.0811763, |x|=8.81076, |J|=32537.6\n",
      "    --- Outer Iter 49: norm_f = 301.179, mu=0.0782729, |x|=8.77807, |J|=32207.2\n",
      "    --- Outer Iter 50: norm_f = 301.179, mu=0.0752852, |x|=8.74618, |J|=31886.8\n",
      "    --- Outer Iter 51: norm_f = 301.179, mu=0.0722142, |x|=8.71507, |J|=31576.2\n",
      "    --- Outer Iter 52: norm_f = 301.178, mu=0.0690606, |x|=8.68476, |J|=31275.2\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    --- Outer Iter 53: norm_f = 301.178, mu=0.0658253, |x|=8.65523, |J|=30983.7\n",
      "    Least squares message = Both actual and predicted relative reductions in the sum of squares are at most 1e-06\n",
      "    Maximum log(L) = 301.178 below upper bound of -421916\n",
      "      2*Delta(log(L)) = 602.356 (280 data params - 65 model params = expected mean of 215; p-value = 0)\n",
      "    Completed in 5.1s\n",
      "  2*Delta(log(L)) = 602.356\n",
      "  Final MLGST took 5.1s\n",
      "  \n",
      "Iterative MLGST Total Time: 28.7s\n",
      "    -- Performing 'go0' gauge optimization on default estimate --\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/enielse/pyGSTi/pygsti/algorithms/gaugeopt.py:242: UserWarning:\n",
      "\n",
      "No gauge group specified, so no gauge optimization performed.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "results_2plus1 = pygsti.do_long_sequence_gst(ds, mdl_2plus1_ideal, prepfids, measfids,\n",
    "                                             germs, maxLengths, verbosity=3,\n",
    "                                             advancedOptions={\"starting point\": \"target\"})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running idle tomography\n",
      "Computing switchable properties\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/enielse/pyGSTi/pygsti/report/factory.py:1236: UserWarning:\n",
      "\n",
      "Idle tomography failed:\n",
      "operands could not be broadcast together with shapes (9,) (16,) \n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found standard clifford compilation from std1Q_XYI\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/enielse/pyGSTi/pygsti/report/factory.py:1303: UserWarning:\n",
      "\n",
      "PDF output is not available for reports with multiple datasets\n",
      "\n",
      "/Users/enielse/pyGSTi/pygsti/tools/matrixtools.py:613: UserWarning:\n",
      "\n",
      "Cannot construct a real log: unpaired negative real eigenvalues: [(-1.0084172062338246+0j)]\n",
      "\n",
      "/Users/enielse/pyGSTi/pygsti/report/reportables.py:1090: UserWarning:\n",
      "\n",
      "Truncating imaginary logarithm!\n",
      "\n",
      "/Users/enielse/pyGSTi/pygsti/tools/optools.py:1239: UserWarning:\n",
      "\n",
      "Near-identity matrix log failed; falling back to approximate log for logGTi error generator:\n",
      "Failed to construct a real logarithm! This is probably because M is not near the identity.\n",
      "Its eigenvalues are: [-1.00841721+0.j          0.01252335+0.97927003j  0.01252335-0.97927003j\n",
      "  1.00037875+0.j          1.00405493+0.j        ]\n",
      "\n",
      "/Users/enielse/pyGSTi/pygsti/tools/optools.py:1243: UserWarning:\n",
      "\n",
      "Falling back to approximate log for logGTi error generator\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statistical hypothesis tests did NOT find inconsistency between the datasets at 5.00% significance.\n",
      "Statistical hypothesis tests did NOT find inconsistency between the datasets at 5.00% significance.\n",
      "Statistical hypothesis tests did NOT find inconsistency between the datasets at 5.00% significance.\n",
      "Statistical hypothesis tests did NOT find inconsistency between the datasets at 5.00% significance.\n",
      "Statistical hypothesis tests did NOT find inconsistency between the datasets at 5.00% significance.\n",
      "Statistical hypothesis tests did NOT find inconsistency between the datasets at 5.00% significance.\n",
      "Statistical hypothesis tests did NOT find inconsistency between the datasets at 5.00% significance.\n",
      "Statistical hypothesis tests did NOT find inconsistency between the datasets at 5.00% significance.\n",
      "Statistical hypothesis tests did NOT find inconsistency between the datasets at 5.00% significance.\n"
     ]
    }
   ],
   "source": [
    "pygsti.report.construct_standard_report(\n",
    "    {'two-level': results_2level, 'three-level': results_3level_leakage_basis,\n",
    "     'two+one level': results_2plus1},\n",
    "    \"Leakage Example Report\"\n",
    ").write_html('example_files/leakage_report', autosize='none')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Open the report [here](example_files/leakage_report/main.html)"
   ]
  }
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