{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "# An example showing how to generate bootstrapped error bars." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "from __future__ import print_function" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "import os\n", "import sys\n", "import time\n", "import json\n", "\n", "import pygsti\n", "from pygsti.construction import std1Q_XYI\n", "\n", "%pylab inline" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-- Std Practice: Iter 1 of 1 (TP) --: \n", " --- Gate Sequence Creation ---\n", " --- LGST ---\n", " --- Iterative MLGST: [##################################################] 100.0% 1282 gate strings ---\n", " Iterative MLGST Total Time: 3.5s\n", " --- Re-optimizing logl after robust data scaling ---\n", " -- Performing 'single' gauge optimization on TP estimate --\n", " -- Conveying 'single' gauge optimization to TP.Robust+ estimate --\n" ] } ], "source": [ "#Get a GST estimate (similar to Tutorial 0)\n", "\n", "# 1) get the target GateSet\n", "gs_target = std1Q_XYI.gs_target\n", "\n", "# 2) get the building blocks needed to specify which gate sequences are needed\n", "prep_fiducials, meas_fiducials = std1Q_XYI.prepStrs, std1Q_XYI.effectStrs\n", "germs = std1Q_XYI.germs\n", "maxLengths = [1,2,4,8,16]\n", "\n", "# 3) generate \"fake\" data from a depolarized version of gs_target\n", "gs_datagen = gs_target.depolarize(gate_noise=0.1, spam_noise=0.001)\n", "listOfExperiments = pygsti.construction.make_lsgst_experiment_list(\n", " gs_target, prep_fiducials, meas_fiducials, germs, maxLengths)\n", "ds = pygsti.construction.generate_fake_data(gs_datagen, listOfExperiments, nSamples=1000,\n", " sampleError=\"binomial\", seed=1234)\n", "\n", "\n", "results = pygsti.do_stdpractice_gst(ds, gs_target, prep_fiducials, meas_fiducials,\n", " germs, maxLengths, modes=\"TP\")\n", "estimated_gateset = results.estimates['TP'].gatesets['single']" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Parametric Bootstrapping\n", "Here we do parametric bootstrapping, as indicated by the 'parametric' argument below.\n", "The output is eventually stored in the \"mean\" and \"std\" GateSets, which hold the mean and standard deviation values of the set of bootstrapped gatesets (after gauge optimization). It is this latter \"standard deviation Gateset\"\n", "which holds the collection of error bars. Note: due to print setting issues, the outputs that are printed here will not necessarily reflect the true accuracy of the estimates made.\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "deletable": true, "editable": true, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Creating DataSets: \n", "0 Generating parametric dataset.\n", "1 Generating parametric dataset.\n", "2 Generating parametric dataset.\n", "3 Generating parametric dataset.\n", "4 Generating parametric dataset.\n", "5 Generating parametric dataset.\n", "6 Generating parametric dataset.\n", "7 Generating parametric dataset.\n", "8 Generating parametric dataset.\n", "9 Generating parametric dataset.\n", "Creating GateSets: \n", "Running MLGST Iteration 0 \n", "--- Gate Sequence Creation ---\n", " 1282 sequences created\n", " Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing\n", "--- LGST ---\n", " Singular values of I_tilde (truncating to first 4 of 6) = \n", " 4.243740981718673\n", " 1.196825270321894\n", " 0.9803977850297132\n", " 0.9189829897008691\n", " 0.04573617221601241\n", " 0.02684031856476036\n", " \n", " Singular values of target I_tilde (truncating to first 4 of 6) = \n", " 4.244076587154778\n", " 1.1775300369229778\n", " 0.9531813852474502\n", " 0.945333971342714\n", " 1.9144356219019607e-16\n", " 1.7151168088551026e-16\n", " \n", "--- Iterative MLGST: Iter 1 of 5 92 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 54.6619 (91 data params - 31 model params = expected mean of 60; p-value = 0.67046)\n", " Completed in 0.2s\n", " 2*Delta(log(L)) = 54.714\n", " Iteration 1 took 0.2s\n", " \n", "--- Iterative MLGST: Iter 2 of 5 168 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 129.189 (167 data params - 31 model params = expected mean of 136; p-value = 0.647824)\n", " Completed in 0.3s\n", " 2*Delta(log(L)) = 129.277\n", " Iteration 2 took 0.3s\n", " \n", "--- Iterative MLGST: Iter 3 of 5 450 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 390.627 (449 data params - 31 model params = expected mean of 418; p-value = 0.827677)\n", " Completed in 0.6s\n", " 2*Delta(log(L)) = 390.768\n", " Iteration 3 took 0.7s\n", " \n", "--- Iterative MLGST: Iter 4 of 5 862 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 834.331 (861 data params - 31 model params = expected mean of 830; p-value = 0.451265)\n", " Completed in 1.1s\n", " 2*Delta(log(L)) = 834.617\n", " Iteration 4 took 1.1s\n", " \n", "--- Iterative MLGST: Iter 5 of 5 1282 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 1249.69 (1281 data params - 31 model params = expected mean of 1250; p-value = 0.497174)\n", " Completed in 1.9s\n", " 2*Delta(log(L)) = 1250.2\n", " Iteration 5 took 1.9s\n", " \n", " Switching to ML objective (last iteration)\n", " --- MLGST ---\n", " Maximum log(L) = 625.055 below upper bound of -2.13561e+06\n", " 2*Delta(log(L)) = 1250.11 (1281 data params - 31 model params = expected mean of 1250; p-value = 0.49381)\n", " Completed in 0.8s\n", " 2*Delta(log(L)) = 1250.11\n", " Final MLGST took 0.9s\n", " \n", "Iterative MLGST Total Time: 5.1s\n", " -- Adding Gauge Optimized (go0) --\n", "Running MLGST Iteration 1 \n", "--- Gate Sequence Creation ---\n", " 1282 sequences created\n", " Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing\n", "--- LGST ---\n", " Singular values of I_tilde (truncating to first 4 of 6) = \n", " 4.244955776409719\n", " 1.1654832900216188\n", " 0.956272084807351\n", " 0.9195971979216845\n", " 0.04819500202308558\n", " 0.019674658291966154\n", " \n", " Singular values of target I_tilde (truncating to first 4 of 6) = \n", " 4.244076587154778\n", " 1.1775300369229778\n", " 0.9531813852474502\n", " 0.945333971342714\n", " 1.9144356219019607e-16\n", " 1.7151168088551026e-16\n", " \n", "--- Iterative MLGST: Iter 1 of 5 92 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 69.4303 (91 data params - 31 model params = expected mean of 60; p-value = 0.189526)\n", " Completed in 0.2s\n", " 2*Delta(log(L)) = 69.5064\n", " Iteration 1 took 0.2s\n", " \n", "--- Iterative MLGST: Iter 2 of 5 168 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 139.522 (167 data params - 31 model params = expected mean of 136; p-value = 0.400496)\n", " Completed in 0.3s\n", " 2*Delta(log(L)) = 139.487\n", " Iteration 2 took 0.3s\n", " \n", "--- Iterative MLGST: Iter 3 of 5 450 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 425.208 (449 data params - 31 model params = expected mean of 418; p-value = 0.393237)\n", " Completed in 0.7s\n", " 2*Delta(log(L)) = 424.889\n", " Iteration 3 took 0.7s\n", " \n", "--- Iterative MLGST: Iter 4 of 5 862 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 860.208 (861 data params - 31 model params = expected mean of 830; p-value = 0.226952)\n", " Completed in 1.2s\n", " 2*Delta(log(L)) = 860.294\n", " Iteration 4 took 1.2s\n", " \n", "--- Iterative MLGST: Iter 5 of 5 1282 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 1236.14 (1281 data params - 31 model params = expected mean of 1250; p-value = 0.604438)\n", " Completed in 2.0s\n", " 2*Delta(log(L)) = 1236.41\n", " Iteration 5 took 2.1s\n", " \n", " Switching to ML objective (last iteration)\n", " --- MLGST ---\n", " Maximum log(L) = 618.162 below upper bound of -2.136e+06\n", " 2*Delta(log(L)) = 1236.32 (1281 data params - 31 model params = expected mean of 1250; p-value = 0.603029)\n", " Completed in 1.0s\n", " 2*Delta(log(L)) = 1236.32\n", " Final MLGST took 1.0s\n", " \n", "Iterative MLGST Total Time: 5.6s\n", " -- Adding Gauge Optimized (go0) --\n", "Running MLGST Iteration 2 \n", "--- Gate Sequence Creation ---\n", " 1282 sequences created\n", " Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing\n", "--- LGST ---\n", " Singular values of I_tilde (truncating to first 4 of 6) = \n", " 4.244105950849598\n", " 1.1579831871684374\n", " 0.9724007421046054\n", " 0.9008232174607133\n", " 0.04747934275633835\n", " 0.02335927755344803\n", " \n", " Singular values of target I_tilde (truncating to first 4 of 6) = \n", " 4.244076587154778\n", " 1.1775300369229778\n", " 0.9531813852474502\n", " 0.945333971342714\n", " 1.9144356219019607e-16\n", " 1.7151168088551026e-16\n", " \n", "--- Iterative MLGST: Iter 1 of 5 92 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 53.7231 (91 data params - 31 model params = expected mean of 60; p-value = 0.702929)\n", " Completed in 0.2s\n", " 2*Delta(log(L)) = 53.767\n", " Iteration 1 took 0.2s\n", " \n", "--- Iterative MLGST: Iter 2 of 5 168 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 118.871 (167 data params - 31 model params = expected mean of 136; p-value = 0.851955)\n", " Completed in 0.3s\n", " 2*Delta(log(L)) = 118.848\n", " Iteration 2 took 0.3s\n", " \n", "--- Iterative MLGST: Iter 3 of 5 450 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 410.566 (449 data params - 31 model params = expected mean of 418; p-value = 0.593117)\n", " Completed in 0.9s\n", " 2*Delta(log(L)) = 411.16\n", " Iteration 3 took 0.9s\n", " \n", "--- Iterative MLGST: Iter 4 of 5 862 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 846.655 (861 data params - 31 model params = expected mean of 830; p-value = 0.336363)\n", " Completed in 1.3s\n", " 2*Delta(log(L)) = 847.325\n", " Iteration 4 took 1.4s\n", " \n", "--- Iterative MLGST: Iter 5 of 5 1282 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 1285.78 (1281 data params - 31 model params = expected mean of 1250; p-value = 0.235103)\n", " Completed in 2.4s\n", " 2*Delta(log(L)) = 1286.8\n", " Iteration 5 took 2.5s\n", " \n", " Switching to ML objective (last iteration)\n", " --- MLGST ---\n", " Maximum log(L) = 643.359 below upper bound of -2.13608e+06\n", " 2*Delta(log(L)) = 1286.72 (1281 data params - 31 model params = expected mean of 1250; p-value = 0.229467)\n", " Completed in 1.0s\n", " 2*Delta(log(L)) = 1286.72\n", " Final MLGST took 1.1s\n", " \n", "Iterative MLGST Total Time: 6.4s\n", " -- Adding Gauge Optimized (go0) --\n", "Running MLGST Iteration 3 \n", "--- Gate Sequence Creation ---\n", " 1282 sequences created\n", " Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing\n", "--- LGST ---\n", " Singular values of I_tilde (truncating to first 4 of 6) = \n", " 4.245026706871426\n", " 1.1581551644431194\n", " 0.9751123814360809\n", " 0.917116445045877\n", " 0.04948557817173936\n", " 0.017700857933000646\n", " \n", " Singular values of target I_tilde (truncating to first 4 of 6) = \n", " 4.244076587154778\n", " 1.1775300369229778\n", " 0.9531813852474502\n", " 0.945333971342714\n", " 1.9144356219019607e-16\n", " 1.7151168088551026e-16\n", " \n", "--- Iterative MLGST: Iter 1 of 5 92 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 54.7477 (91 data params - 31 model params = expected mean of 60; p-value = 0.667441)\n", " Completed in 0.2s\n", " 2*Delta(log(L)) = 54.7464\n", " Iteration 1 took 0.2s\n", " \n", "--- Iterative MLGST: Iter 2 of 5 168 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 123.896 (167 data params - 31 model params = expected mean of 136; p-value = 0.763046)\n", " Completed in 0.5s\n", " 2*Delta(log(L)) = 123.873\n", " Iteration 2 took 0.5s\n", " \n", "--- Iterative MLGST: Iter 3 of 5 450 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 375.888 (449 data params - 31 model params = expected mean of 418; p-value = 0.931259)\n", " Completed in 0.8s\n", " 2*Delta(log(L)) = 376.466\n", " Iteration 3 took 0.9s\n", " \n", "--- Iterative MLGST: Iter 4 of 5 862 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 787.336 (861 data params - 31 model params = expected mean of 830; p-value = 0.85296)\n", " Completed in 1.5s\n", " 2*Delta(log(L)) = 787.672\n", " Iteration 4 took 1.6s\n", " \n", "--- Iterative MLGST: Iter 5 of 5 1282 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 1173.37 (1281 data params - 31 model params = expected mean of 1250; p-value = 0.939642)\n", " Completed in 2.4s\n", " 2*Delta(log(L)) = 1173.91\n", " Iteration 5 took 2.5s\n", " \n", " Switching to ML objective (last iteration)\n", " --- MLGST ---\n", " Maximum log(L) = 586.913 below upper bound of -2.1359e+06\n", " 2*Delta(log(L)) = 1173.83 (1281 data params - 31 model params = expected mean of 1250; p-value = 0.938485)\n", " Completed in 1.2s\n", " 2*Delta(log(L)) = 1173.83\n", " Final MLGST took 1.3s\n", " \n", "Iterative MLGST Total Time: 7.0s\n", " -- Adding Gauge Optimized (go0) --\n", "Running MLGST Iteration 4 \n", "--- Gate Sequence Creation ---\n", " 1282 sequences created\n", " Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing\n", "--- LGST ---\n", " Singular values of I_tilde (truncating to first 4 of 6) = \n", " 4.243957692250352\n", " 1.1690547567407383\n", " 0.965190202696205\n", " 0.9062510088586136\n", " 0.058565422676061636\n", " 0.020128461433915477\n", " \n", " Singular values of target I_tilde (truncating to first 4 of 6) = \n", " 4.244076587154778\n", " 1.1775300369229778\n", " 0.9531813852474502\n", " 0.945333971342714\n", " 1.9144356219019607e-16\n", " 1.7151168088551026e-16\n", " \n", "--- Iterative MLGST: Iter 1 of 5 92 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 73.1954 (91 data params - 31 model params = expected mean of 60; p-value = 0.117816)\n", " Completed in 0.2s\n", " 2*Delta(log(L)) = 73.3169\n", " Iteration 1 took 0.2s\n", " \n", "--- Iterative MLGST: Iter 2 of 5 168 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 145.055 (167 data params - 31 model params = expected mean of 136; p-value = 0.281791)\n", " Completed in 0.4s\n", " 2*Delta(log(L)) = 145.31\n", " Iteration 2 took 0.5s\n", " \n", "--- Iterative MLGST: Iter 3 of 5 450 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 450.681 (449 data params - 31 model params = expected mean of 418; p-value = 0.13029)\n", " Completed in 1.0s\n", " 2*Delta(log(L)) = 451.235\n", " Iteration 3 took 1.0s\n", " \n", "--- Iterative MLGST: Iter 4 of 5 862 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 863.504 (861 data params - 31 model params = expected mean of 830; p-value = 0.203884)\n", " Completed in 2.1s\n", " 2*Delta(log(L)) = 864.535\n", " Iteration 4 took 2.2s\n", " \n", "--- Iterative MLGST: Iter 5 of 5 1282 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 1293.67 (1281 data params - 31 model params = expected mean of 1250; p-value = 0.190342)\n", " Completed in 3.2s\n", " 2*Delta(log(L)) = 1294.9\n", " Iteration 5 took 3.3s\n", " \n", " Switching to ML objective (last iteration)\n", " --- MLGST ---\n", " Maximum log(L) = 647.394 below upper bound of -2.13607e+06\n", " 2*Delta(log(L)) = 1294.79 (1281 data params - 31 model params = expected mean of 1250; p-value = 0.184439)\n", " Completed in 1.3s\n", " 2*Delta(log(L)) = 1294.79\n", " Final MLGST took 1.3s\n", " \n", "Iterative MLGST Total Time: 8.5s\n", " -- Adding Gauge Optimized (go0) --\n", "Running MLGST Iteration 5 \n", "--- Gate Sequence Creation ---\n", " 1282 sequences created\n", " Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing\n", "--- LGST ---\n", " Singular values of I_tilde (truncating to first 4 of 6) = \n", " 4.244076886752041\n", " 1.1641097446903883\n", " 0.9656589990825546\n", " 0.9256958692572328\n", " 0.05988709636348685\n", " 0.0018089980940076643\n", " \n", " Singular values of target I_tilde (truncating to first 4 of 6) = \n", " 4.244076587154778\n", " 1.1775300369229778\n", " 0.9531813852474502\n", " 0.945333971342714\n", " 1.9144356219019607e-16\n", " 1.7151168088551026e-16\n", " \n", "--- Iterative MLGST: Iter 1 of 5 92 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 46.7157 (91 data params - 31 model params = expected mean of 60; p-value = 0.895039)\n", " Completed in 0.2s\n", " 2*Delta(log(L)) = 46.8907\n", " Iteration 1 took 0.3s\n", " \n", "--- Iterative MLGST: Iter 2 of 5 168 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 110.427 (167 data params - 31 model params = expected mean of 136; p-value = 0.947272)\n", " Completed in 0.8s\n", " 2*Delta(log(L)) = 110.699\n", " Iteration 2 took 0.8s\n", " \n", "--- Iterative MLGST: Iter 3 of 5 450 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 421.079 (449 data params - 31 model params = expected mean of 418; p-value = 0.448567)\n", " Completed in 1.3s\n", " 2*Delta(log(L)) = 421.678\n", " Iteration 3 took 1.4s\n", " \n", "--- Iterative MLGST: Iter 4 of 5 862 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 836.041 (861 data params - 31 model params = expected mean of 830; p-value = 0.43476)\n", " Completed in 2.6s\n", " 2*Delta(log(L)) = 837.086\n", " Iteration 4 took 2.7s\n", " \n", "--- Iterative MLGST: Iter 5 of 5 1282 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 1227.62 (1281 data params - 31 model params = expected mean of 1250; p-value = 0.668945)\n", " Completed in 3.3s\n", " 2*Delta(log(L)) = 1228.84\n", " Iteration 5 took 3.5s\n", " \n", " Switching to ML objective (last iteration)\n", " --- MLGST ---\n", " Maximum log(L) = 614.366 below upper bound of -2.13643e+06\n", " 2*Delta(log(L)) = 1228.73 (1281 data params - 31 model params = expected mean of 1250; p-value = 0.660722)\n", " Completed in 1.8s\n", " 2*Delta(log(L)) = 1228.73\n", " Final MLGST took 1.8s\n", " \n", "Iterative MLGST Total Time: 10.4s\n", " -- Adding Gauge Optimized (go0) --\n", "Running MLGST Iteration 6 \n", "--- Gate Sequence Creation ---\n", " 1282 sequences created\n", " Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing\n", "--- LGST ---\n", " Singular values of I_tilde (truncating to first 4 of 6) = \n", " 4.244075532131559\n", " 1.167915782338968\n", " 0.9557843550642068\n", " 0.9176164826710592\n", " 0.07089776735122219\n", " 0.012139475083936863\n", " \n", " Singular values of target I_tilde (truncating to first 4 of 6) = \n", " 4.244076587154778\n", " 1.1775300369229778\n", " 0.9531813852474502\n", " 0.945333971342714\n", " 1.9144356219019607e-16\n", " 1.7151168088551026e-16\n", " \n", "--- Iterative MLGST: Iter 1 of 5 92 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 63.587 (91 data params - 31 model params = expected mean of 60; p-value = 0.351322)\n", " Completed in 0.3s\n", " 2*Delta(log(L)) = 63.6718\n", " Iteration 1 took 0.3s\n", " \n", "--- Iterative MLGST: Iter 2 of 5 168 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 134.64 (167 data params - 31 model params = expected mean of 136; p-value = 0.516864)\n", " Completed in 0.5s\n", " 2*Delta(log(L)) = 134.834\n", " Iteration 2 took 0.5s\n", " \n", "--- Iterative MLGST: Iter 3 of 5 450 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 422.608 (449 data params - 31 model params = expected mean of 418; p-value = 0.427863)\n", " Completed in 1.2s\n", " 2*Delta(log(L)) = 422.757\n", " Iteration 3 took 1.2s\n", " \n", "--- Iterative MLGST: Iter 4 of 5 862 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 844.495 (861 data params - 31 model params = expected mean of 830; p-value = 0.355667)\n", " Completed in 1.9s\n", " 2*Delta(log(L)) = 844.732\n", " Iteration 4 took 2.0s\n", " \n", "--- Iterative MLGST: Iter 5 of 5 1282 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 1269.48 (1281 data params - 31 model params = expected mean of 1250; p-value = 0.344235)\n", " Completed in 2.9s\n", " 2*Delta(log(L)) = 1269.93\n", " Iteration 5 took 3.0s\n", " \n", " Switching to ML objective (last iteration)\n", " --- MLGST ---\n", " Maximum log(L) = 634.909 below upper bound of -2.13574e+06\n", " 2*Delta(log(L)) = 1269.82 (1281 data params - 31 model params = expected mean of 1250; p-value = 0.341779)\n", " Completed in 1.5s\n", " 2*Delta(log(L)) = 1269.82\n", " Final MLGST took 1.5s\n", " \n", "Iterative MLGST Total Time: 8.6s\n", " -- Adding Gauge Optimized (go0) --\n", "Running MLGST Iteration 7 \n", "--- Gate Sequence Creation ---\n", " 1282 sequences created\n", " Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing\n", "--- LGST ---\n", " Singular values of I_tilde (truncating to first 4 of 6) = \n", " 4.244480338214524\n", " 1.165763527245094\n", " 0.9338843507514768\n", " 0.894817674590485\n", " 0.03560561553467106\n", " 0.011817184934139907\n", " \n", " Singular values of target I_tilde (truncating to first 4 of 6) = \n", " 4.244076587154778\n", " 1.1775300369229778\n", " 0.9531813852474502\n", " 0.945333971342714\n", " 1.9144356219019607e-16\n", " 1.7151168088551026e-16\n", " \n", "--- Iterative MLGST: Iter 1 of 5 92 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 50.8873 (91 data params - 31 model params = expected mean of 60; p-value = 0.792879)\n", " Completed in 0.3s\n", " 2*Delta(log(L)) = 51.09\n", " Iteration 1 took 0.3s\n", " \n", "--- Iterative MLGST: Iter 2 of 5 168 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 118.749 (167 data params - 31 model params = expected mean of 136; p-value = 0.853817)\n", " Completed in 0.5s\n", " 2*Delta(log(L)) = 118.844\n", " Iteration 2 took 0.5s\n", " \n", "--- Iterative MLGST: Iter 3 of 5 450 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 404.585 (449 data params - 31 model params = expected mean of 418; p-value = 0.672167)\n", " Completed in 1.2s\n", " 2*Delta(log(L)) = 404.878\n", " Iteration 3 took 1.2s\n", " \n", "--- Iterative MLGST: Iter 4 of 5 862 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 825.414 (861 data params - 31 model params = expected mean of 830; p-value = 0.538397)\n", " Completed in 1.9s\n", " 2*Delta(log(L)) = 826.085\n", " Iteration 4 took 2.0s\n", " \n", "--- Iterative MLGST: Iter 5 of 5 1282 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 1179.53 (1281 data params - 31 model params = expected mean of 1250; p-value = 0.922688)\n", " Completed in 3.0s\n", " 2*Delta(log(L)) = 1180.31\n", " Iteration 5 took 3.2s\n", " \n", " Switching to ML objective (last iteration)\n", " --- MLGST ---\n", " Maximum log(L) = 590.119 below upper bound of -2.13605e+06\n", " 2*Delta(log(L)) = 1180.24 (1281 data params - 31 model params = expected mean of 1250; p-value = 0.920535)\n", " Completed in 1.5s\n", " 2*Delta(log(L)) = 1180.24\n", " Final MLGST took 1.5s\n", " \n", "Iterative MLGST Total Time: 8.8s\n", " -- Adding Gauge Optimized (go0) --\n", "Running MLGST Iteration 8 \n", "--- Gate Sequence Creation ---\n", " 1282 sequences created\n", " Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing\n", "--- LGST ---\n", " Singular values of I_tilde (truncating to first 4 of 6) = \n", " 4.244787150940367\n", " 1.1501560865775227\n", " 0.9566739054733346\n", " 0.9046650260494242\n", " 0.030204804282964466\n", " 0.005737486195909679\n", " \n", " Singular values of target I_tilde (truncating to first 4 of 6) = \n", " 4.244076587154778\n", " 1.1775300369229778\n", " 0.9531813852474502\n", " 0.945333971342714\n", " 1.9144356219019607e-16\n", " 1.7151168088551026e-16\n", " \n", "--- Iterative MLGST: Iter 1 of 5 92 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 60.9529 (91 data params - 31 model params = expected mean of 60; p-value = 0.441424)\n", " Completed in 0.3s\n", " 2*Delta(log(L)) = 60.9843\n", " Iteration 1 took 0.3s\n", " \n", "--- Iterative MLGST: Iter 2 of 5 168 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 131.827 (167 data params - 31 model params = expected mean of 136; p-value = 0.585153)\n", " Completed in 0.4s\n", " 2*Delta(log(L)) = 131.864\n", " Iteration 2 took 0.5s\n", " \n", "--- Iterative MLGST: Iter 3 of 5 450 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 400.15 (449 data params - 31 model params = expected mean of 418; p-value = 0.726826)\n", " Completed in 1.0s\n", " 2*Delta(log(L)) = 400.548\n", " Iteration 3 took 1.1s\n", " \n", "--- Iterative MLGST: Iter 4 of 5 862 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 785.227 (861 data params - 31 model params = expected mean of 830; p-value = 0.864959)\n", " Completed in 2.3s\n", " 2*Delta(log(L)) = 786.042\n", " Iteration 4 took 2.4s\n", " \n", "--- Iterative MLGST: Iter 5 of 5 1282 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 1167.95 (1281 data params - 31 model params = expected mean of 1250; p-value = 0.952028)\n", " Completed in 3.2s\n", " 2*Delta(log(L)) = 1168.9\n", " Iteration 5 took 3.3s\n", " \n", " Switching to ML objective (last iteration)\n", " --- MLGST ---\n", " Maximum log(L) = 584.416 below upper bound of -2.13586e+06\n", " 2*Delta(log(L)) = 1168.83 (1281 data params - 31 model params = expected mean of 1250; p-value = 0.950166)\n", " Completed in 1.4s\n", " 2*Delta(log(L)) = 1168.83\n", " Final MLGST took 1.4s\n", " \n", "Iterative MLGST Total Time: 8.9s\n", " -- Adding Gauge Optimized (go0) --\n", "Running MLGST Iteration 9 \n", "--- Gate Sequence Creation ---\n", " 1282 sequences created\n", " Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing\n", "--- LGST ---\n", " Singular values of I_tilde (truncating to first 4 of 6) = \n", " 4.244086871227867\n", " 1.1742535252889312\n", " 0.9742543570194043\n", " 0.9330064213489485\n", " 0.048119822313218055\n", " 0.014464994594877137\n", " \n", " Singular values of target I_tilde (truncating to first 4 of 6) = \n", " 4.244076587154778\n", " 1.1775300369229778\n", " 0.9531813852474502\n", " 0.945333971342714\n", " 1.9144356219019607e-16\n", " 1.7151168088551026e-16\n", " \n", "--- Iterative MLGST: Iter 1 of 5 92 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 47.5036 (91 data params - 31 model params = expected mean of 60; p-value = 0.878839)\n", " Completed in 0.3s\n", " 2*Delta(log(L)) = 47.5543\n", " Iteration 1 took 0.3s\n", " \n", "--- Iterative MLGST: Iter 2 of 5 168 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 115.65 (167 data params - 31 model params = expected mean of 136; p-value = 0.896252)\n", " Completed in 0.5s\n", " 2*Delta(log(L)) = 115.791\n", " Iteration 2 took 0.6s\n", " \n", "--- Iterative MLGST: Iter 3 of 5 450 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 398.455 (449 data params - 31 model params = expected mean of 418; p-value = 0.746548)\n", " Completed in 0.9s\n", " 2*Delta(log(L)) = 398.689\n", " Iteration 3 took 0.9s\n", " \n", "--- Iterative MLGST: Iter 4 of 5 862 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 806.048 (861 data params - 31 model params = expected mean of 830; p-value = 0.718111)\n", " Completed in 2.1s\n", " 2*Delta(log(L)) = 806.647\n", " Iteration 4 took 2.2s\n", " \n", "--- Iterative MLGST: Iter 5 of 5 1282 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 1182.69 (1281 data params - 31 model params = expected mean of 1250; p-value = 0.912722)\n", " Completed in 3.0s\n", " 2*Delta(log(L)) = 1183.65\n", " Iteration 5 took 3.1s\n", " \n", " Switching to ML objective (last iteration)\n", " --- MLGST ---\n", " Maximum log(L) = 591.796 below upper bound of -2.13645e+06\n", " 2*Delta(log(L)) = 1183.59 (1281 data params - 31 model params = expected mean of 1250; p-value = 0.909723)\n", " Completed in 1.3s\n", " 2*Delta(log(L)) = 1183.59\n", " Final MLGST took 1.4s\n", " \n", "Iterative MLGST Total Time: 8.5s\n", " -- Adding Gauge Optimized (go0) --\n" ] } ], "source": [ "#The number of simulated datasets & gatesets made for bootstrapping purposes. \n", "# For good statistics, should probably be greater than 10.\n", "numGatesets=10\n", "\n", "param_boot_gatesets = pygsti.drivers.make_bootstrap_gatesets(\n", " numGatesets, ds, 'parametric', prep_fiducials, meas_fiducials, germs, maxLengths,\n", " inputGateSet=estimated_gateset, startSeed=0, returnData=False,\n", " verbosity=2)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "deletable": true, "editable": true, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Spam weight 0\n", "Spam weight 1\n", "Spam weight 2\n", "Spam weight 3\n", "Spam weight 4\n", "Spam weight 5\n", "Spam weight 6\n", "Spam weight 7\n", "Spam weight 8\n", "Spam weight 9\n", "Spam weight 10\n", "Spam weight 11\n", "Spam weight 12\n", "Best SPAM weight is 1.0\n" ] } ], "source": [ "gauge_opt_pboot_gatesets = pygsti.drivers.gauge_optimize_gs_list(param_boot_gatesets, estimated_gateset,\n", " plot=False) #plotting support removed w/matplotlib" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "deletable": true, "editable": true, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Parametric bootstrapped error bars, with 10 resamples\n", "\n", "Error in rho vec:\n", "TPParameterizedSPAMVec with dimension 4\n", " 0.71 0 0 0\n", "\n", "\n", "Error in effect vecs:\n", "TPPOVM with effect vectors:\n", "0: FullyParameterizedSPAMVec with dimension 4\n", " 0 0 0 0\n", "\n", "1: ComplementSPAMVec with dimension 4\n", " 1.41 0 0 0\n", "\n", "\n", "\n", "Error in Gi:\n", "TPParameterizedGate with shape (4, 4)\n", " 1.00 0 0 0\n", " 0 0 0 0\n", " 0 0 0 0\n", " 0 0 0 0\n", "\n", "\n", "Error in Gx:\n", "TPParameterizedGate with shape (4, 4)\n", " 1.00 0 0 0\n", " 0 0 0 0\n", " 0 0 0 0\n", " 0 0 0 0\n", "\n", "\n", "Error in Gy:\n", "TPParameterizedGate with shape (4, 4)\n", " 1.00 0 0 0\n", " 0 0 0 0\n", " 0 0 0 0\n", " 0 0 0 0\n", "\n" ] } ], "source": [ "pboot_mean = pygsti.drivers.to_mean_gateset(gauge_opt_pboot_gatesets, estimated_gateset)\n", "pboot_std = pygsti.drivers.to_std_gateset(gauge_opt_pboot_gatesets, estimated_gateset)\n", "\n", "#Summary of the error bars\n", "print(\"Parametric bootstrapped error bars, with\", numGatesets, \"resamples\\n\")\n", "print(\"Error in rho vec:\") \n", "print(pboot_std['rho0'], end='\\n\\n')\n", "print(\"Error in effect vecs:\")\n", "print(pboot_std['Mdefault'], end='\\n\\n')\n", "print(\"Error in Gi:\")\n", "print(pboot_std['Gi'], end='\\n\\n')\n", "print(\"Error in Gx:\")\n", "print(pboot_std['Gx'], end='\\n\\n')\n", "print(\"Error in Gy:\")\n", "print(pboot_std['Gy'])" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Non-parametric Bootstrapping\n", "Here we do non-parametric bootstrapping, as indicated by the 'nonparametric' argument below.\n", "The output is again eventually stored in the \"mean\" and \"std\" GateSets, which hold the mean and standard deviation values of the set of bootstrapped gatesets (after gauge optimization). It is this latter \"standard deviation Gateset\"\n", "which holds the collection of error bars. Note: due to print setting issues, the outputs that are printed here will not necessarily reflect the true accuracy of the estimates made.\n", "\n", "(Technical note: ddof = 1 is by default used when computing the standard deviation -- see numpy.std -- meaning that we are computing a standard deviation of the sample, not of the population.)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Creating DataSets: \n", "0 Generating non-parametric dataset.\n", "1 Generating non-parametric dataset.\n", "2 Generating non-parametric dataset.\n", "3 Generating non-parametric dataset.\n", "4 Generating non-parametric dataset.\n", "5 Generating non-parametric dataset.\n", "6 Generating non-parametric dataset.\n", "7 Generating non-parametric dataset.\n", "8 Generating non-parametric dataset.\n", "9 Generating non-parametric dataset.\n", "Creating GateSets: \n", "Running MLGST Iteration 0 \n", "--- Gate Sequence Creation ---\n", " 1282 sequences created\n", " Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing\n", "--- LGST ---\n", " Singular values of I_tilde (truncating to first 4 of 6) = \n", " 4.244212085138186\n", " 1.1843719301091324\n", " 0.9857947532159174\n", " 0.9013030041875327\n", " 0.09547108379285918\n", " 0.04886490428154151\n", " \n", " Singular values of target I_tilde (truncating to first 4 of 6) = \n", " 4.244076587154778\n", " 1.1775300369229778\n", " 0.9531813852474502\n", " 0.945333971342714\n", " 1.9144356219019607e-16\n", " 1.7151168088551026e-16\n", " \n", "--- Iterative MLGST: Iter 1 of 5 92 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 170.59 (91 data params - 31 model params = expected mean of 60; p-value = 1.52711e-12)\n", " Completed in 0.2s\n", " 2*Delta(log(L)) = 171.166\n", " Iteration 1 took 0.3s\n", " \n", "--- Iterative MLGST: Iter 2 of 5 168 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 344.819 (167 data params - 31 model params = expected mean of 136; p-value = 0)\n", " Completed in 0.4s\n", " 2*Delta(log(L)) = 345.262\n", " Iteration 2 took 0.5s\n", " \n", "--- Iterative MLGST: Iter 3 of 5 450 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 991.904 (449 data params - 31 model params = expected mean of 418; p-value = 0)\n", " Completed in 0.8s\n", " 2*Delta(log(L)) = 993.352\n", " Iteration 3 took 0.8s\n", " \n", "--- Iterative MLGST: Iter 4 of 5 862 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 1815.39 (861 data params - 31 model params = expected mean of 830; p-value = 0)\n", " Completed in 1.5s\n", " 2*Delta(log(L)) = 1817.16\n", " Iteration 4 took 1.6s\n", " \n", "--- Iterative MLGST: Iter 5 of 5 1282 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 2701.38 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 2.0s\n", " 2*Delta(log(L)) = 2703.31\n", " Iteration 5 took 2.1s\n", " \n", " Switching to ML objective (last iteration)\n", " --- MLGST ---\n", " Maximum log(L) = 1351.47 below upper bound of -2.13485e+06\n", " 2*Delta(log(L)) = 2702.94 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 0.9s\n", " 2*Delta(log(L)) = 2702.94\n", " Final MLGST took 0.9s\n", " \n", "Iterative MLGST Total Time: 6.1s\n", " -- Adding Gauge Optimized (go0) --\n", "--- Re-optimizing logl after robust data scaling ---\n", " --- MLGST ---\n", " Maximum log(L) = 1351.47 below upper bound of -2.13485e+06\n", " 2*Delta(log(L)) = 2702.94 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 0.5s\n", " -- Adding Gauge Optimized (go0) --\n", "Running MLGST Iteration 1 \n", "--- Gate Sequence Creation ---\n", " 1282 sequences created\n", " Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing\n", "--- LGST ---\n", " Singular values of I_tilde (truncating to first 4 of 6) = \n", " 4.244167171173532\n", " 1.153514315008981\n", " 0.9636315553213499\n", " 0.908474545441188\n", " 0.046056950903486917\n", " 0.014789568961852528\n", " \n", " Singular values of target I_tilde (truncating to first 4 of 6) = \n", " 4.244076587154778\n", " 1.1775300369229778\n", " 0.9531813852474502\n", " 0.945333971342714\n", " 1.9144356219019607e-16\n", " 1.7151168088551026e-16\n", " \n", "--- Iterative MLGST: Iter 1 of 5 92 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 147.684 (91 data params - 31 model params = expected mean of 60; p-value = 2.37591e-09)\n", " Completed in 0.2s\n", " 2*Delta(log(L)) = 148.749\n", " Iteration 1 took 0.2s\n", " \n", "--- Iterative MLGST: Iter 2 of 5 168 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 274.913 (167 data params - 31 model params = expected mean of 136; p-value = 1.91974e-11)\n", " Completed in 0.3s\n", " 2*Delta(log(L)) = 276.308\n", " Iteration 2 took 0.3s\n", " \n", "--- Iterative MLGST: Iter 3 of 5 450 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 866.238 (449 data params - 31 model params = expected mean of 418; p-value = 0)\n", " Completed in 0.8s\n", " 2*Delta(log(L)) = 868.748\n", " Iteration 3 took 0.9s\n", " \n", "--- Iterative MLGST: Iter 4 of 5 862 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 1658.63 (861 data params - 31 model params = expected mean of 830; p-value = 0)\n", " Completed in 1.3s\n", " 2*Delta(log(L)) = 1661.19\n", " Iteration 4 took 1.3s\n", " \n", "--- Iterative MLGST: Iter 5 of 5 1282 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 2467.46 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 2.2s\n", " 2*Delta(log(L)) = 2470.98\n", " Iteration 5 took 2.2s\n", " \n", " Switching to ML objective (last iteration)\n", " --- MLGST ---\n", " Maximum log(L) = 1235.33 below upper bound of -2.13563e+06\n", " 2*Delta(log(L)) = 2470.66 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 0.9s\n", " 2*Delta(log(L)) = 2470.66\n", " Final MLGST took 0.9s\n", " \n", "Iterative MLGST Total Time: 5.9s\n", " -- Adding Gauge Optimized (go0) --\n", "--- Re-optimizing logl after robust data scaling ---\n", " --- MLGST ---\n", " Maximum log(L) = 1235.33 below upper bound of -2.13563e+06\n", " 2*Delta(log(L)) = 2470.66 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 0.6s\n", " -- Adding Gauge Optimized (go0) --\n", "Running MLGST Iteration 2 \n", "--- Gate Sequence Creation ---\n", " 1282 sequences created\n", " Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing\n", "--- LGST ---\n", " Singular values of I_tilde (truncating to first 4 of 6) = \n", " 4.244617505701195\n", " 1.1425181984723756\n", " 0.9821383251044142\n", " 0.8825511904531211\n", " 0.03538596563546793\n", " 0.019645266130539504\n", " \n", " Singular values of target I_tilde (truncating to first 4 of 6) = \n", " 4.244076587154778\n", " 1.1775300369229778\n", " 0.9531813852474502\n", " 0.945333971342714\n", " 1.9144356219019607e-16\n", " 1.7151168088551026e-16\n", " \n", "--- Iterative MLGST: Iter 1 of 5 92 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 152.339 (91 data params - 31 model params = expected mean of 60; p-value = 5.59761e-10)\n", " Completed in 0.2s\n", " 2*Delta(log(L)) = 152.658\n", " Iteration 1 took 0.2s\n", " \n", "--- Iterative MLGST: Iter 2 of 5 168 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 287.202 (167 data params - 31 model params = expected mean of 136; p-value = 7.42517e-13)\n", " Completed in 0.3s\n", " 2*Delta(log(L)) = 287.882\n", " Iteration 2 took 0.3s\n", " \n", "--- Iterative MLGST: Iter 3 of 5 450 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 932.984 (449 data params - 31 model params = expected mean of 418; p-value = 0)\n", " Completed in 0.7s\n", " 2*Delta(log(L)) = 934.913\n", " Iteration 3 took 0.8s\n", " \n", "--- Iterative MLGST: Iter 4 of 5 862 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 1720.38 (861 data params - 31 model params = expected mean of 830; p-value = 0)\n", " Completed in 1.1s\n", " 2*Delta(log(L)) = 1723.17\n", " Iteration 4 took 1.1s\n", " \n", "--- Iterative MLGST: Iter 5 of 5 1282 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 2634.67 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 1.7s\n", " 2*Delta(log(L)) = 2638.42\n", " Iteration 5 took 1.7s\n", " \n", " Switching to ML objective (last iteration)\n", " --- MLGST ---\n", " Maximum log(L) = 1318.98 below upper bound of -2.13523e+06\n", " 2*Delta(log(L)) = 2637.96 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 0.9s\n", " 2*Delta(log(L)) = 2637.96\n", " Final MLGST took 0.9s\n", " \n", "Iterative MLGST Total Time: 5.0s\n", " -- Adding Gauge Optimized (go0) --\n", "--- Re-optimizing logl after robust data scaling ---\n", " --- MLGST ---\n", " Maximum log(L) = 1318.98 below upper bound of -2.13523e+06\n", " 2*Delta(log(L)) = 2637.96 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 0.5s\n", " -- Adding Gauge Optimized (go0) --\n", "Running MLGST Iteration 3 \n", "--- Gate Sequence Creation ---\n", " 1282 sequences created\n", " Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing\n", "--- LGST ---\n", " Singular values of I_tilde (truncating to first 4 of 6) = \n", " 4.243988002748227\n", " 1.2013993194238075\n", " 0.9736701526820217\n", " 0.9363076178129426\n", " 0.027172808326342654\n", " 0.005255940106641545\n", " \n", " Singular values of target I_tilde (truncating to first 4 of 6) = \n", " 4.244076587154778\n", " 1.1775300369229778\n", " 0.9531813852474502\n", " 0.945333971342714\n", " 1.9144356219019607e-16\n", " 1.7151168088551026e-16\n", " \n", "--- Iterative MLGST: Iter 1 of 5 92 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 159.939 (91 data params - 31 model params = expected mean of 60; p-value = 5.00061e-11)\n", " Completed in 0.2s\n", " 2*Delta(log(L)) = 160.22\n", " Iteration 1 took 0.2s\n", " \n", "--- Iterative MLGST: Iter 2 of 5 168 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 289.265 (167 data params - 31 model params = expected mean of 136; p-value = 4.25104e-13)\n", " Completed in 0.3s\n", " 2*Delta(log(L)) = 289.212\n", " Iteration 2 took 0.3s\n", " \n", "--- Iterative MLGST: Iter 3 of 5 450 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 849.321 (449 data params - 31 model params = expected mean of 418; p-value = 0)\n", " Completed in 0.7s\n", " 2*Delta(log(L)) = 849.302\n", " Iteration 3 took 0.7s\n", " \n", "--- Iterative MLGST: Iter 4 of 5 862 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 1686.29 (861 data params - 31 model params = expected mean of 830; p-value = 0)\n", " Completed in 1.2s\n", " 2*Delta(log(L)) = 1687.79\n", " Iteration 4 took 1.2s\n", " \n", "--- Iterative MLGST: Iter 5 of 5 1282 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 2496.17 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 1.8s\n", " 2*Delta(log(L)) = 2498.46\n", " Iteration 5 took 1.8s\n", " \n", " Switching to ML objective (last iteration)\n", " --- MLGST ---\n", " Maximum log(L) = 1249.03 below upper bound of -2.13547e+06\n", " 2*Delta(log(L)) = 2498.05 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 0.8s\n", " 2*Delta(log(L)) = 2498.05\n", " Final MLGST took 0.8s\n", " \n", "Iterative MLGST Total Time: 5.1s\n", " -- Adding Gauge Optimized (go0) --\n", "--- Re-optimizing logl after robust data scaling ---\n", " --- MLGST ---\n", " Maximum log(L) = 1249.03 below upper bound of -2.13547e+06\n", " 2*Delta(log(L)) = 2498.05 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 0.5s\n", " -- Adding Gauge Optimized (go0) --\n", "Running MLGST Iteration 4 \n", "--- Gate Sequence Creation ---\n", " 1282 sequences created\n", " Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing\n", "--- LGST ---\n", " Singular values of I_tilde (truncating to first 4 of 6) = \n", " 4.246180502104294\n", " 1.1521822289971684\n", " 0.9764404175045424\n", " 0.906610245735585\n", " 0.07369893163659891\n", " 0.020240938685679086\n", " \n", " Singular values of target I_tilde (truncating to first 4 of 6) = \n", " 4.244076587154778\n", " 1.1775300369229778\n", " 0.9531813852474502\n", " 0.945333971342714\n", " 1.9144356219019607e-16\n", " 1.7151168088551026e-16\n", " \n", "--- Iterative MLGST: Iter 1 of 5 92 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 160.269 (91 data params - 31 model params = expected mean of 60; p-value = 4.49542e-11)\n", " Completed in 0.2s\n", " 2*Delta(log(L)) = 161.452\n", " Iteration 1 took 0.2s\n", " \n", "--- Iterative MLGST: Iter 2 of 5 168 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 268.207 (167 data params - 31 model params = expected mean of 136; p-value = 1.07333e-10)\n", " Completed in 0.3s\n", " 2*Delta(log(L)) = 269.635\n", " Iteration 2 took 0.3s\n", " \n", "--- Iterative MLGST: Iter 3 of 5 450 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 906.473 (449 data params - 31 model params = expected mean of 418; p-value = 0)\n", " Completed in 0.7s\n", " 2*Delta(log(L)) = 908.592\n", " Iteration 3 took 0.8s\n", " \n", "--- Iterative MLGST: Iter 4 of 5 862 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 1752.98 (861 data params - 31 model params = expected mean of 830; p-value = 0)\n", " Completed in 1.1s\n", " 2*Delta(log(L)) = 1756.15\n", " Iteration 4 took 1.1s\n", " \n", "--- Iterative MLGST: Iter 5 of 5 1282 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 2618.09 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 1.8s\n", " 2*Delta(log(L)) = 2621.8\n", " Iteration 5 took 1.9s\n", " \n", " Switching to ML objective (last iteration)\n", " --- MLGST ---\n", " Maximum log(L) = 1310.73 below upper bound of -2.13509e+06\n", " 2*Delta(log(L)) = 2621.45 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 0.8s\n", " 2*Delta(log(L)) = 2621.45\n", " Final MLGST took 0.8s\n", " \n", "Iterative MLGST Total Time: 5.1s\n", " -- Adding Gauge Optimized (go0) --\n", "--- Re-optimizing logl after robust data scaling ---\n", " --- MLGST ---\n", " Maximum log(L) = 1310.73 below upper bound of -2.13509e+06\n", " 2*Delta(log(L)) = 2621.45 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 0.5s\n", " -- Adding Gauge Optimized (go0) --\n", "Running MLGST Iteration 5 \n", "--- Gate Sequence Creation ---\n", " 1282 sequences created\n", " Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing\n", "--- LGST ---\n", " Singular values of I_tilde (truncating to first 4 of 6) = \n", " 4.244326073733323\n", " 1.1441327581502785\n", " 0.9622582316708493\n", " 0.9502766969909989\n", " 0.04152115972837583\n", " 0.029558409756115962\n", " \n", " Singular values of target I_tilde (truncating to first 4 of 6) = \n", " 4.244076587154778\n", " 1.1775300369229778\n", " 0.9531813852474502\n", " 0.945333971342714\n", " 1.9144356219019607e-16\n", " 1.7151168088551026e-16\n", " \n", "--- Iterative MLGST: Iter 1 of 5 92 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 123.979 (91 data params - 31 model params = expected mean of 60; p-value = 2.358e-06)\n", " Completed in 0.2s\n", " 2*Delta(log(L)) = 125.106\n", " Iteration 1 took 0.2s\n", " \n", "--- Iterative MLGST: Iter 2 of 5 168 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 247.859 (167 data params - 31 model params = expected mean of 136; p-value = 1.54293e-08)\n", " Completed in 0.2s\n", " 2*Delta(log(L)) = 248.561\n", " Iteration 2 took 0.3s\n", " \n", "--- Iterative MLGST: Iter 3 of 5 450 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 872.89 (449 data params - 31 model params = expected mean of 418; p-value = 0)\n", " Completed in 0.6s\n", " 2*Delta(log(L)) = 876.046\n", " Iteration 3 took 0.7s\n", " \n", "--- Iterative MLGST: Iter 4 of 5 862 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 1682.54 (861 data params - 31 model params = expected mean of 830; p-value = 0)\n", " Completed in 1.0s\n", " 2*Delta(log(L)) = 1686.15\n", " Iteration 4 took 1.0s\n", " \n", "--- Iterative MLGST: Iter 5 of 5 1282 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 2484.67 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 1.6s\n", " 2*Delta(log(L)) = 2489.05\n", " Iteration 5 took 1.7s\n", " \n", " Switching to ML objective (last iteration)\n", " --- MLGST ---\n", " Maximum log(L) = 1244.35 below upper bound of -2.13534e+06\n", " 2*Delta(log(L)) = 2488.7 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 0.8s\n", " 2*Delta(log(L)) = 2488.7\n", " Final MLGST took 0.8s\n", " \n", "Iterative MLGST Total Time: 4.6s\n", " -- Adding Gauge Optimized (go0) --\n", "--- Re-optimizing logl after robust data scaling ---\n", " --- MLGST ---\n", " Maximum log(L) = 1244.35 below upper bound of -2.13534e+06\n", " 2*Delta(log(L)) = 2488.7 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 0.5s\n", " -- Adding Gauge Optimized (go0) --\n", "Running MLGST Iteration 6 \n", "--- Gate Sequence Creation ---\n", " 1282 sequences created\n", " Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing\n", "--- LGST ---\n", " Singular values of I_tilde (truncating to first 4 of 6) = \n", " 4.243826627679486\n", " 1.181000471428712\n", " 0.9620835176798799\n", " 0.9235835321348868\n", " 0.029932975327267443\n", " 0.01795053898160025\n", " \n", " Singular values of target I_tilde (truncating to first 4 of 6) = \n", " 4.244076587154778\n", " 1.1775300369229778\n", " 0.9531813852474502\n", " 0.945333971342714\n", " 1.9144356219019607e-16\n", " 1.7151168088551026e-16\n", " \n", "--- Iterative MLGST: Iter 1 of 5 92 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 167.863 (91 data params - 31 model params = expected mean of 60; p-value = 3.77098e-12)\n", " Completed in 0.2s\n", " 2*Delta(log(L)) = 168.443\n", " Iteration 1 took 0.2s\n", " \n", "--- Iterative MLGST: Iter 2 of 5 168 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 305.858 (167 data params - 31 model params = expected mean of 136; p-value = 4.21885e-15)\n", " Completed in 0.3s\n", " 2*Delta(log(L)) = 306.043\n", " Iteration 2 took 0.3s\n", " \n", "--- Iterative MLGST: Iter 3 of 5 450 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 897.008 (449 data params - 31 model params = expected mean of 418; p-value = 0)\n", " Completed in 0.7s\n", " 2*Delta(log(L)) = 897.009\n", " Iteration 3 took 0.8s\n", " \n", "--- Iterative MLGST: Iter 4 of 5 862 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 1832.6 (861 data params - 31 model params = expected mean of 830; p-value = 0)\n", " Completed in 1.3s\n", " 2*Delta(log(L)) = 1834.65\n", " Iteration 4 took 1.4s\n", " \n", "--- Iterative MLGST: Iter 5 of 5 1282 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 2774.87 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 1.7s\n", " 2*Delta(log(L)) = 2778.26\n", " Iteration 5 took 1.8s\n", " \n", " Switching to ML objective (last iteration)\n", " --- MLGST ---\n", " Maximum log(L) = 1388.92 below upper bound of -2.13458e+06\n", " 2*Delta(log(L)) = 2777.85 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 0.8s\n", " 2*Delta(log(L)) = 2777.85\n", " Final MLGST took 0.8s\n", " \n", "Iterative MLGST Total Time: 5.2s\n", " -- Adding Gauge Optimized (go0) --\n", "--- Re-optimizing logl after robust data scaling ---\n", " --- MLGST ---\n", " Maximum log(L) = 1388.92 below upper bound of -2.13458e+06\n", " 2*Delta(log(L)) = 2777.85 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 0.5s\n", " -- Adding Gauge Optimized (go0) --\n", "Running MLGST Iteration 7 \n", "--- Gate Sequence Creation ---\n", " 1282 sequences created\n", " Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing\n", "--- LGST ---\n", " Singular values of I_tilde (truncating to first 4 of 6) = \n", " 4.244526056080279\n", " 1.151251520412904\n", " 0.9439701878450454\n", " 0.8888666392207678\n", " 0.06087224198184396\n", " 0.030748143014395605\n", " \n", " Singular values of target I_tilde (truncating to first 4 of 6) = \n", " 4.244076587154778\n", " 1.1775300369229778\n", " 0.9531813852474502\n", " 0.945333971342714\n", " 1.9144356219019607e-16\n", " 1.7151168088551026e-16\n", " \n", "--- Iterative MLGST: Iter 1 of 5 92 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 181.945 (91 data params - 31 model params = expected mean of 60; p-value = 3.28626e-14)\n", " Completed in 0.2s\n", " 2*Delta(log(L)) = 182.096\n", " Iteration 1 took 0.2s\n", " \n", "--- Iterative MLGST: Iter 2 of 5 168 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 329.174 (167 data params - 31 model params = expected mean of 136; p-value = 0)\n", " Completed in 0.3s\n", " 2*Delta(log(L)) = 329.668\n", " Iteration 2 took 0.3s\n", " \n", "--- Iterative MLGST: Iter 3 of 5 450 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 926.384 (449 data params - 31 model params = expected mean of 418; p-value = 0)\n", " Completed in 0.5s\n", " 2*Delta(log(L)) = 928.499\n", " Iteration 3 took 0.6s\n", " \n", "--- Iterative MLGST: Iter 4 of 5 862 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 1717.46 (861 data params - 31 model params = expected mean of 830; p-value = 0)\n", " Completed in 1.0s\n", " 2*Delta(log(L)) = 1720.98\n", " Iteration 4 took 1.0s\n", " \n", "--- Iterative MLGST: Iter 5 of 5 1282 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 2590.11 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 1.5s\n", " 2*Delta(log(L)) = 2594.67\n", " Iteration 5 took 1.5s\n", " \n", " Switching to ML objective (last iteration)\n", " --- MLGST ---\n", " Maximum log(L) = 1297.17 below upper bound of -2.13547e+06\n", " 2*Delta(log(L)) = 2594.34 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 0.8s\n", " 2*Delta(log(L)) = 2594.34\n", " Final MLGST took 0.8s\n", " \n", "Iterative MLGST Total Time: 4.4s\n", " -- Adding Gauge Optimized (go0) --\n", "--- Re-optimizing logl after robust data scaling ---\n", " --- MLGST ---\n", " Maximum log(L) = 1297.17 below upper bound of -2.13547e+06\n", " 2*Delta(log(L)) = 2594.34 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 0.4s\n", " -- Adding Gauge Optimized (go0) --\n", "Running MLGST Iteration 8 \n", "--- Gate Sequence Creation ---\n", " 1282 sequences created\n", " Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing\n", "--- LGST ---\n", " Singular values of I_tilde (truncating to first 4 of 6) = \n", " 4.243854590804392\n", " 1.1359961161784795\n", " 0.9430730695955586\n", " 0.9111704896479723\n", " 0.09720933554376518\n", " 0.03639925023022892\n", " \n", " Singular values of target I_tilde (truncating to first 4 of 6) = \n", " 4.244076587154778\n", " 1.1775300369229778\n", " 0.9531813852474502\n", " 0.945333971342714\n", " 1.9144356219019607e-16\n", " 1.7151168088551026e-16\n", " \n", "--- Iterative MLGST: Iter 1 of 5 92 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 115.208 (91 data params - 31 model params = expected mean of 60; p-value = 2.39894e-05)\n", " Completed in 0.2s\n", " 2*Delta(log(L)) = 115.295\n", " Iteration 1 took 0.2s\n", " \n", "--- Iterative MLGST: Iter 2 of 5 168 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 256.019 (167 data params - 31 model params = expected mean of 136; p-value = 2.20819e-09)\n", " Completed in 0.2s\n", " 2*Delta(log(L)) = 255.846\n", " Iteration 2 took 0.2s\n", " \n", "--- Iterative MLGST: Iter 3 of 5 450 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 837.178 (449 data params - 31 model params = expected mean of 418; p-value = 0)\n", " Completed in 0.5s\n", " 2*Delta(log(L)) = 837.916\n", " Iteration 3 took 0.6s\n", " \n", "--- Iterative MLGST: Iter 4 of 5 862 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 1599.73 (861 data params - 31 model params = expected mean of 830; p-value = 0)\n", " Completed in 1.0s\n", " 2*Delta(log(L)) = 1600.86\n", " Iteration 4 took 1.0s\n", " \n", "--- Iterative MLGST: Iter 5 of 5 1282 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 2488.63 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 1.7s\n", " 2*Delta(log(L)) = 2490.51\n", " Iteration 5 took 1.7s\n", " \n", " Switching to ML objective (last iteration)\n", " --- MLGST ---\n", " Maximum log(L) = 1245.07 below upper bound of -2.13539e+06\n", " 2*Delta(log(L)) = 2490.15 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 0.6s\n", " 2*Delta(log(L)) = 2490.15\n", " Final MLGST took 0.6s\n", " \n", "Iterative MLGST Total Time: 4.3s\n", " -- Adding Gauge Optimized (go0) --\n", "--- Re-optimizing logl after robust data scaling ---\n", " --- MLGST ---\n", " Maximum log(L) = 1245.07 below upper bound of -2.13539e+06\n", " 2*Delta(log(L)) = 2490.15 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 0.4s\n", " -- Adding Gauge Optimized (go0) --\n", "Running MLGST Iteration 9 \n", "--- Gate Sequence Creation ---\n", " 1282 sequences created\n", " Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing\n", "--- LGST ---\n", " Singular values of I_tilde (truncating to first 4 of 6) = \n", " 4.244088493382835\n", " 1.158491440342675\n", " 0.9765988971692087\n", " 0.9291379020211377\n", " 0.06900998568202234\n", " 0.015665820756577954\n", " \n", " Singular values of target I_tilde (truncating to first 4 of 6) = \n", " 4.244076587154778\n", " 1.1775300369229778\n", " 0.9531813852474502\n", " 0.945333971342714\n", " 1.9144356219019607e-16\n", " 1.7151168088551026e-16\n", " \n", "--- Iterative MLGST: Iter 1 of 5 92 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 164.287 (91 data params - 31 model params = expected mean of 60; p-value = 1.22036e-11)\n", " Completed in 0.2s\n", " 2*Delta(log(L)) = 165.06\n", " Iteration 1 took 0.2s\n", " \n", "--- Iterative MLGST: Iter 2 of 5 168 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 296.859 (167 data params - 31 model params = expected mean of 136; p-value = 5.30687e-14)\n", " Completed in 0.3s\n", " 2*Delta(log(L)) = 298.794\n", " Iteration 2 took 0.3s\n", " \n", "--- Iterative MLGST: Iter 3 of 5 450 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 869.949 (449 data params - 31 model params = expected mean of 418; p-value = 0)\n", " Completed in 0.6s\n", " 2*Delta(log(L)) = 873.417\n", " Iteration 3 took 0.7s\n", " \n", "--- Iterative MLGST: Iter 4 of 5 862 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 1691.71 (861 data params - 31 model params = expected mean of 830; p-value = 0)\n", " Completed in 0.9s\n", " 2*Delta(log(L)) = 1696.13\n", " Iteration 4 took 0.9s\n", " \n", "--- Iterative MLGST: Iter 5 of 5 1282 gate strings ---: \n", " --- Minimum Chi^2 GST ---\n", " Sum of Chi^2 = 2508.01 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 1.2s\n", " 2*Delta(log(L)) = 2513.11\n", " Iteration 5 took 1.3s\n", " \n", " Switching to ML objective (last iteration)\n", " --- MLGST ---\n", " Maximum log(L) = 1256.4 below upper bound of -2.13552e+06\n", " 2*Delta(log(L)) = 2512.81 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 0.8s\n", " 2*Delta(log(L)) = 2512.81\n", " Final MLGST took 0.8s\n", " \n", "Iterative MLGST Total Time: 4.1s\n", " -- Adding Gauge Optimized (go0) --\n", "--- Re-optimizing logl after robust data scaling ---\n", " --- MLGST ---\n", " Maximum log(L) = 1256.4 below upper bound of -2.13552e+06\n", " 2*Delta(log(L)) = 2512.81 (1281 data params - 31 model params = expected mean of 1250; p-value = 0)\n", " Completed in 0.4s\n", " -- Adding Gauge Optimized (go0) --\n" ] } ], "source": [ "#The number of simulated datasets & gatesets made for bootstrapping purposes. \n", "# For good statistics, should probably be greater than 10.\n", "numGatesets=10\n", "\n", "nonparam_boot_gatesets = pygsti.drivers.make_bootstrap_gatesets(\n", " numGatesets, ds, 'nonparametric', prep_fiducials, meas_fiducials, germs, maxLengths,\n", " targetGateSet=estimated_gateset, startSeed=0, returnData=False, verbosity=2)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Spam weight 0\n", "Spam weight 1\n", "Spam weight 2\n", "Spam weight 3\n", "Spam weight 4\n", "Spam weight 5\n", "Spam weight 6\n", "Spam weight 7\n", "Spam weight 8\n", "Spam weight 9\n", "Spam weight 10\n", "Spam weight 11\n", "Spam weight 12\n", "Best SPAM weight is 1.0\n" ] } ], "source": [ "gauge_opt_npboot_gatesets = pygsti.drivers.gauge_optimize_gs_list(nonparam_boot_gatesets, estimated_gateset,\n", " plot=False) #plotting removed w/matplotlib" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Non-parametric bootstrapped error bars, with 10 resamples\n", "\n", "Error in rho vec:\n", "TPParameterizedSPAMVec with dimension 4\n", " 0.71 0 0 0\n", "\n", "\n", "Error in effect vecs:\n", "TPPOVM with effect vectors:\n", "0: FullyParameterizedSPAMVec with dimension 4\n", " 0 0 0 0\n", "\n", "1: ComplementSPAMVec with dimension 4\n", " 1.41 0 0 0\n", "\n", "\n", "\n", "Error in Gi:\n", "TPParameterizedGate with shape (4, 4)\n", " 1.00 0 0 0\n", " 0 0 0 0\n", " 0 0 0 0\n", " 0 0 0 0\n", "\n", "\n", "Error in Gx:\n", "TPParameterizedGate with shape (4, 4)\n", " 1.00 0 0 0\n", " 0 0 0 0\n", " 0 0 0 0\n", " 0 0 0 0\n", "\n", "\n", "Error in Gy:\n", "TPParameterizedGate with shape (4, 4)\n", " 1.00 0 0 0\n", " 0 0 0 0\n", " 0 0 0 0\n", " 0 0 0 0\n", "\n" ] } ], "source": [ "npboot_mean = pygsti.drivers.to_mean_gateset(gauge_opt_npboot_gatesets, estimated_gateset)\n", "npboot_std = pygsti.drivers.to_std_gateset(gauge_opt_npboot_gatesets, estimated_gateset)\n", "\n", "#Summary of the error bars\n", "print(\"Non-parametric bootstrapped error bars, with\", numGatesets, \"resamples\\n\")\n", "print(\"Error in rho vec:\")\n", "print(npboot_std['rho0'], end='\\n\\n')\n", "print(\"Error in effect vecs:\")\n", "print(npboot_std['Mdefault'], end='\\n\\n')\n", "print(\"Error in Gi:\")\n", "print(npboot_std['Gi'], end='\\n\\n')\n", "print(\"Error in Gx:\")\n", "print(npboot_std['Gx'], end='\\n\\n')\n", "print(\"Error in Gy:\")\n", "print(npboot_std['Gy'])" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "deletable": true, "editable": true, "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "Text(0.5,1,'Scatter plot comparing param vs. non-param bootstrapping error bars.')" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "loglog(npboot_std.to_vector(),pboot_std.to_vector(),'.')\n", "loglog(np.logspace(-4,-2,10),np.logspace(-4,-2,10),'--')\n", "xlabel('Non-parametric')\n", "ylabel('Parametric')\n", "xlim((1e-4,1e-2)); ylim((1e-4,1e-2))\n", "title('Scatter plot comparing param vs. non-param bootstrapping error bars.')" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true, "deletable": true, "editable": 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": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 0 }