import os
import sys
import time
import json
import pygsti
#The following two lines should be changed to reflect your own paths to GST/src and GSTData/data/Ion_Trap_SNL/2015_03_30/GST_BB1_XX_512_condensed.txt
#sys.path.append('/Users/kmrudin/GST/src/')
#dataFile = '/Users/kmrudin/GSTData/data/Ion_Trap_SNL/2015_03_30/GST_BB1_XX_512_condensed.txt'
#import Bootstrap
%pylab inline
Populating the interactive namespace from numpy and matplotlib
#Load example quantities from files
gs_target = pygsti.io.load_gateset("tutorial_files/Example_Gateset.txt")
gs_mc2gst = pygsti.io.load_gateset("tutorial_files/Example_MC2GST_Gateset.txt")
ds = pygsti.io.load_dataset("tutorial_files/Example_Dataset.txt", cache=True)
fiducials = pygsti.io.load_gatestring_list("tutorial_files/Example_FiducialList.txt")
germs = pygsti.io.load_gatestring_list("tutorial_files/Example_GermsList.txt")
maxLengths = json.load(open("tutorial_files/Example_maxLengths.json","r"))
specs = pygsti.construction.build_spam_specs(fiducials)
Loading from cache file: tutorial_files/Example_Dataset.txt.cache
Here we do parametric bootstrapping, as indicated by the 'parametric' argument below. 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" 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.
#The number of simulated datasets & gatesets made for bootstrapping purposes.
# For good statistics, should probably be greater than 10.
numGatesets=10
param_boot_gatesets = pygsti.drivers.make_bootstrap_gatesets(
numGatesets, ds, 'parametric', fiducials, fiducials, germs, maxLengths,
inputGateSet=gs_mc2gst, startSeed=0, constrainToTP=True, returnData=False,
verbosity=2)
Creating DataSets: 0 Generating parametric dataset. 1 Generating parametric dataset. 2 Generating parametric dataset. 3 Generating parametric dataset. 4 Generating parametric dataset. 5 Generating parametric dataset. 6 Generating parametric dataset. 7 Generating parametric dataset. 8 Generating parametric dataset. 9 Generating parametric dataset. Creating GateSets: Running MLGST Iteration 0 LGST: Singular values of I_tilde (truncating to first 4 of 6) = [ 4.24398536 1.19629118 0.97626973 0.92032344 0.08003613 0.01407496] --- LGST --- --- Gauge Optimization to TP (L-BFGS-B) --- 44s 0.0076147219 44s 0.0040626408 44s 0.0015977696 44s 0.0002658189 44s 0.0000074511 44s 0.0000004158 44s 0.0000000823 44s 0.0000000469 44s 0.0000000468 The resulting TP penalty is: 4.68406e-08 The gauge matrix found (B^-1) is: [[ 1.15008201e+00 -1.48657882e-03 -2.98965618e-03 -2.32610361e-03] [ 1.27907465e-04 9.98963571e-01 8.39537015e-05 1.35119927e-03] [ 2.89883433e-04 7.45000051e-05 9.98964472e-01 -2.00886448e-03] [ -1.29593775e-03 1.47326969e-03 -1.91025957e-03 1.00061072e+00]] The gauge-corrected gates are: rhoVec[0] = 0.7071 0.0186 -0.0529 0.8016 EVec[0] = 0.7220 0.0399 0.0050 -0.6453 Gi = 1.0000 -0.0002 0 0 -0.0024 0.9556 -0.0775 -0.0167 0.0208 0.0083 0.8932 -0.0312 0.0085 -0.0063 0.0030 0.9013 Gx = 1.0000 0 0 0 -0.0066 0.9096 0.0100 0.0918 -0.0311 0.0002 0.0447 0.9359 0.0010 0.0198 -0.8682 -0.0410 Gy = 0.9999 0 0 0 0.1050 -0.0367 0.0313 -0.9988 0.0013 -0.0204 0.8833 0.0472 -0.0370 0.8197 -0.0475 -0.0098 --- Iterative MLEGST: Beginning iter 1 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 65.0876 (92 data params - 31 model params = expected mean of 61; p-value = 0.336443) 2*Delta(log(L)) = 65.3436 --- Iterative MLEGST: Beginning iter 2 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 65.0876 (92 data params - 31 model params = expected mean of 61; p-value = 0.336443) 2*Delta(log(L)) = 65.3436 --- Iterative MLEGST: Beginning iter 3 of 10 : 168 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 146.19 (168 data params - 31 model params = expected mean of 137; p-value = 0.279849) 2*Delta(log(L)) = 146.822 --- Iterative MLEGST: Beginning iter 4 of 10 : 441 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 401.361 (441 data params - 31 model params = expected mean of 410; p-value = 0.610462) 2*Delta(log(L)) = 402.102 --- Iterative MLEGST: Beginning iter 5 of 10 : 817 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 804.557 (817 data params - 31 model params = expected mean of 786; p-value = 0.315188) 2*Delta(log(L)) = 805.62 --- Iterative MLEGST: Beginning iter 6 of 10 : 1201 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1179.88 (1201 data params - 31 model params = expected mean of 1170; p-value = 0.413918) 2*Delta(log(L)) = 1181.23 --- Iterative MLEGST: Beginning iter 7 of 10 : 1585 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1539.83 (1585 data params - 31 model params = expected mean of 1554; p-value = 0.595972) 2*Delta(log(L)) = 1541.35 --- Iterative MLEGST: Beginning iter 8 of 10 : 1969 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1912.56 (1969 data params - 31 model params = expected mean of 1938; p-value = 0.655294) 2*Delta(log(L)) = 1914.3 --- Iterative MLEGST: Beginning iter 9 of 10 : 2353 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2252.41 (2353 data params - 31 model params = expected mean of 2322; p-value = 0.846565) 2*Delta(log(L)) = 2254.24 --- Iterative MLEGST: Beginning iter 10 of 10 : 2737 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2600.32 (2737 data params - 31 model params = expected mean of 2706; p-value = 0.925985) 2*Delta(log(L)) = 2602.31 --- Last Iteration: switching to MLE objective --- --- MLEGST --- Maximum log(L) = 1301.11 below upper bound of -4.60017e+06 2*Delta(log(L)) = 2602.23 (2737 data params - 31 model params = expected mean of 2706; p-value = 0.92219) 2*Delta(log(L)) = 2602.23 Running MLGST Iteration 1 LGST: Singular values of I_tilde (truncating to first 4 of 6) = [ 4.24419327 1.16199565 0.96182325 0.91836467 0.05011952 0.01224851] --- LGST --- --- Gauge Optimization to TP (L-BFGS-B) --- 66s 0.0076289477 66s 0.0040819431 66s 0.0016018022 66s 0.0002661689 66s 0.0000081830 66s 0.0000003287 66s 0.0000000165 66s 0.0000000050 66s 0.0000000049 The resulting TP penalty is: 4.91014e-09 The gauge matrix found (B^-1) is: [[ 1.15005613e+00 -1.50735612e-03 -2.97183483e-03 -2.33238719e-03] [ 1.33078522e-04 9.98895310e-01 1.72583596e-04 1.46583449e-03] [ 3.06082746e-04 1.63598061e-04 9.99086142e-01 -2.03032312e-03] [ -1.32259005e-03 1.55210337e-03 -1.89152328e-03 1.00056816e+00]] The gauge-corrected gates are: rhoVec[0] = 0.7071 0.0132 -0.0675 0.7995 EVec[0] = 0.7089 0.0349 -0.0185 -0.6350 Gi = 1.0000 0 0 0 -0.0078 0.8647 -0.0048 -0.0168 -0.0457 0.0465 0.9435 0.0201 -0.0168 0.0139 -0.0189 0.9123 Gx = 1.0000 0 0 0 0.0002 0.8876 0.0062 0.0902 -0.0321 -0.0025 0.0340 0.9348 -0.0179 0.0744 -0.8527 -0.0361 Gy = 1.0000 0 0 0 0.0731 -0.0023 0.0524 -0.9584 -0.0079 -0.0277 0.8995 0.0438 -0.0359 0.8449 -0.0635 -0.0203 --- Iterative MLEGST: Beginning iter 1 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 54.5064 (92 data params - 31 model params = expected mean of 61; p-value = 0.708568) 2*Delta(log(L)) = 54.5767 --- Iterative MLEGST: Beginning iter 2 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 54.5064 (92 data params - 31 model params = expected mean of 61; p-value = 0.708568) 2*Delta(log(L)) = 54.5767 --- Iterative MLEGST: Beginning iter 3 of 10 : 168 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 125.957 (168 data params - 31 model params = expected mean of 137; p-value = 0.740654) 2*Delta(log(L)) = 125.944 --- Iterative MLEGST: Beginning iter 4 of 10 : 441 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 403.092 (441 data params - 31 model params = expected mean of 410; p-value = 0.586794) 2*Delta(log(L)) = 402.97 --- Iterative MLEGST: Beginning iter 5 of 10 : 817 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 823.88 (817 data params - 31 model params = expected mean of 786; p-value = 0.169231) 2*Delta(log(L)) = 824.046 --- Iterative MLEGST: Beginning iter 6 of 10 : 1201 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1198.08 (1201 data params - 31 model params = expected mean of 1170; p-value = 0.277719) 2*Delta(log(L)) = 1198.32 --- Iterative MLEGST: Beginning iter 7 of 10 : 1585 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1529.88 (1585 data params - 31 model params = expected mean of 1554; p-value = 0.663826) 2*Delta(log(L)) = 1530.26 --- Iterative MLEGST: Beginning iter 8 of 10 : 1969 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1881.6 (1969 data params - 31 model params = expected mean of 1938; p-value = 0.817041) 2*Delta(log(L)) = 1882.18 --- Iterative MLEGST: Beginning iter 9 of 10 : 2353 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2265 (2353 data params - 31 model params = expected mean of 2322; p-value = 0.797741) 2*Delta(log(L)) = 2265.77 --- Iterative MLEGST: Beginning iter 10 of 10 : 2737 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2675.15 (2737 data params - 31 model params = expected mean of 2706; p-value = 0.659773) 2*Delta(log(L)) = 2676.15 --- Last Iteration: switching to MLE objective --- --- MLEGST --- Maximum log(L) = 1338.04 below upper bound of -4.60058e+06 2*Delta(log(L)) = 2676.08 (2737 data params - 31 model params = expected mean of 2706; p-value = 0.655111) 2*Delta(log(L)) = 2676.08 Running MLGST Iteration 2 LGST: Singular values of I_tilde (truncating to first 4 of 6) = [ 4.2444075 1.15325346 0.94183471 0.91961266 0.05815421 0.03512038] --- LGST --- --- Gauge Optimization to TP (L-BFGS-B) --- 86s 0.0075989961 86s 0.0040450959 86s 0.0015757984 87s 0.0002591261 87s 0.0000072972 87s 0.0000003122 87s 0.0000000426 87s 0.0000000224 87s 0.0000000224 The resulting TP penalty is: 2.23798e-08 The gauge matrix found (B^-1) is: [[ 1.15003716e+00 -1.47436225e-03 -2.99185744e-03 -2.36161231e-03] [ 1.43212199e-04 9.98897642e-01 9.76322572e-05 1.38163337e-03] [ 3.09546235e-04 8.96815121e-05 9.99024714e-01 -2.02855775e-03] [ -1.32781030e-03 1.45350676e-03 -1.90146198e-03 1.00063031e+00]] The gauge-corrected gates are: rhoVec[0] = 0.7071 0.0184 -0.0608 0.7981 EVec[0] = 0.7017 0.0207 0.0021 -0.6293 Gi = 1.0000 0 -0.0001 0 0.0178 0.9066 -0.0501 0.0191 0.0191 0.0343 0.9216 -0.0092 -0.0229 -0.0186 -0.0005 0.9285 Gx = 1.0000 0 0 0 0.0041 0.9188 -0.0228 0.0894 -0.0258 -0.0047 0.0341 0.9345 -0.0024 0.0280 -0.8635 -0.0401 Gy = 1.0000 0 0 0 0.0832 0.0241 -0.0001 -0.9391 -0.0025 -0.0406 0.9248 0.0326 -0.0585 0.8461 -0.0468 0.0091 --- Iterative MLEGST: Beginning iter 1 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 58.7927 (92 data params - 31 model params = expected mean of 61; p-value = 0.556349) 2*Delta(log(L)) = 58.788 --- Iterative MLEGST: Beginning iter 2 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 58.7927 (92 data params - 31 model params = expected mean of 61; p-value = 0.556349) 2*Delta(log(L)) = 58.788 --- Iterative MLEGST: Beginning iter 3 of 10 : 168 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 130.995 (168 data params - 31 model params = expected mean of 137; p-value = 0.628466) 2*Delta(log(L)) = 131.476 --- Iterative MLEGST: Beginning iter 4 of 10 : 441 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 458.106 (441 data params - 31 model params = expected mean of 410; p-value = 0.0503503) 2*Delta(log(L)) = 459.27 --- Iterative MLEGST: Beginning iter 5 of 10 : 817 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 850.36 (817 data params - 31 model params = expected mean of 786; p-value = 0.0550576) 2*Delta(log(L)) = 851.606 --- Iterative MLEGST: Beginning iter 6 of 10 : 1201 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1235.25 (1201 data params - 31 model params = expected mean of 1170; p-value = 0.0904073) 2*Delta(log(L)) = 1237.02 --- Iterative MLEGST: Beginning iter 7 of 10 : 1585 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1600.58 (1585 data params - 31 model params = expected mean of 1554; p-value = 0.20067) 2*Delta(log(L)) = 1602.45 --- Iterative MLEGST: Beginning iter 8 of 10 : 1969 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2003.7 (1969 data params - 31 model params = expected mean of 1938; p-value = 0.145871) 2*Delta(log(L)) = 2005.81 --- Iterative MLEGST: Beginning iter 9 of 10 : 2353 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2422.28 (2353 data params - 31 model params = expected mean of 2322; p-value = 0.0720626) 2*Delta(log(L)) = 2424.57 --- Iterative MLEGST: Beginning iter 10 of 10 : 2737 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2753.08 (2737 data params - 31 model params = expected mean of 2706; p-value = 0.259341) 2*Delta(log(L)) = 2755.47 --- Last Iteration: switching to MLE objective --- --- MLEGST --- Maximum log(L) = 1377.68 below upper bound of -4.60062e+06 2*Delta(log(L)) = 2755.36 (2737 data params - 31 model params = expected mean of 2706; p-value = 0.249518) 2*Delta(log(L)) = 2755.36 Running MLGST Iteration 3 LGST: Singular values of I_tilde (truncating to first 4 of 6) = [ 4.24411538 1.21156408 0.97401824 0.93840633 0.04809952 0.0439951 ] --- LGST --- --- Gauge Optimization to TP (L-BFGS-B) --- 107s 0.0076108052 107s 0.0039955032 107s 0.0015456690 107s 0.0002548442 107s 0.0000106835 107s 0.0000006858 107s 0.0000000512 107s 0.0000000438 The resulting TP penalty is: 4.3797e-08 The gauge matrix found (B^-1) is: [[ 1.15011910e+00 -1.47688332e-03 -3.03833652e-03 -2.37473335e-03] [ 1.66930593e-04 9.98957628e-01 1.62745940e-04 1.31167946e-03] [ 3.55071899e-04 1.47331086e-04 9.99103657e-01 -2.11179568e-03] [ -1.28440487e-03 1.48275148e-03 -1.88549663e-03 1.00051624e+00]] The gauge-corrected gates are: rhoVec[0] = 0.7071 0.0041 -0.0747 0.7914 EVec[0] = 0.7196 0.0310 -0.0195 -0.6532 Gi = 1.0000 0.0002 0 0 -0.0075 0.9072 -0.0063 0.0218 -0.0056 0.0074 0.8570 0.0316 0.0018 0.0530 -0.0100 0.8656 Gx = 1.0000 0 0 0 0.0089 0.8961 -0.0250 0.0865 -0.0252 -0.0170 0.0238 0.9316 -0.0078 0.0516 -0.8625 -0.0398 Gy = 1.0000 0 0 0 0.0787 -0.0440 0.0550 -0.9706 -0.0116 -0.0033 0.8906 0.0346 -0.0382 0.8030 -0.0675 -0.0134 --- Iterative MLEGST: Beginning iter 1 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 68.4913 (92 data params - 31 model params = expected mean of 61; p-value = 0.238199) 2*Delta(log(L)) = 69.1311 --- Iterative MLEGST: Beginning iter 2 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 68.4913 (92 data params - 31 model params = expected mean of 61; p-value = 0.238199) 2*Delta(log(L)) = 69.1311 --- Iterative MLEGST: Beginning iter 3 of 10 : 168 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 135.404 (168 data params - 31 model params = expected mean of 137; p-value = 0.522512) 2*Delta(log(L)) = 136.214 --- Iterative MLEGST: Beginning iter 4 of 10 : 441 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 383.843 (441 data params - 31 model params = expected mean of 410; p-value = 0.818643) 2*Delta(log(L)) = 384.846 --- Iterative MLEGST: Beginning iter 5 of 10 : 817 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 754.972 (817 data params - 31 model params = expected mean of 786; p-value = 0.781198) 2*Delta(log(L)) = 756.008 --- Iterative MLEGST: Beginning iter 6 of 10 : 1201 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1099.6 (1201 data params - 31 model params = expected mean of 1170; p-value = 0.929442) 2*Delta(log(L)) = 1100.94 --- Iterative MLEGST: Beginning iter 7 of 10 : 1585 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1492.36 (1585 data params - 31 model params = expected mean of 1554; p-value = 0.866196) 2*Delta(log(L)) = 1493.86 --- Iterative MLEGST: Beginning iter 8 of 10 : 1969 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1895.35 (1969 data params - 31 model params = expected mean of 1938; p-value = 0.751546) 2*Delta(log(L)) = 1897.1 --- Iterative MLEGST: Beginning iter 9 of 10 : 2353 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2269.41 (2353 data params - 31 model params = expected mean of 2322; p-value = 0.778714) 2*Delta(log(L)) = 2271.32 --- Iterative MLEGST: Beginning iter 10 of 10 : 2737 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2653.35 (2737 data params - 31 model params = expected mean of 2706; p-value = 0.761554) 2*Delta(log(L)) = 2655.46 --- Last Iteration: switching to MLE objective --- --- MLEGST --- Maximum log(L) = 1327.69 below upper bound of -4.60043e+06 2*Delta(log(L)) = 2655.37 (2737 data params - 31 model params = expected mean of 2706; p-value = 0.752842) 2*Delta(log(L)) = 2655.37 Running MLGST Iteration 4 LGST: Singular values of I_tilde (truncating to first 4 of 6) = [ 4.24450084 1.16446651 0.99285506 0.87715763 0.03202683 0.01483193] --- LGST --- --- Gauge Optimization to TP (L-BFGS-B) --- 129s 0.0075716681 129s 0.0040035170 129s 0.0015625155 129s 0.0002595522 129s 0.0000104134 129s 0.0000007762 129s 0.0000001600 129s 0.0000001562 The resulting TP penalty is: 1.5615e-07 The gauge matrix found (B^-1) is: [[ 1.15003283e+00 -1.58713241e-03 -2.95906574e-03 -2.31508983e-03] [ 2.21716710e-04 9.98805949e-01 -1.54174270e-05 1.14925579e-03] [ 3.07024577e-04 -3.30432545e-05 9.99085622e-01 -1.97066216e-03] [ -1.30916019e-03 1.37858214e-03 -1.85808238e-03 1.00066356e+00]] The gauge-corrected gates are: rhoVec[0] = 0.7071 -0.0067 -0.0631 0.7963 EVec[0] = 0.7182 -0.0080 -0.0046 -0.6391 Gi = 0.9998 0 0 0.0002 0.0366 0.9052 -0.0924 0.0346 0.0205 -0.0350 0.9127 -0.0254 -0.0081 -0.0326 0.0213 0.8997 Gx = 1.0000 0 0 0 0.0063 0.9088 -0.0588 0.0860 -0.0030 -0.0544 0.0150 0.9277 -0.0006 -0.0320 -0.8436 -0.0418 Gy = 0.9998 0 -0.0002 0 0.0866 0.0215 -0.0116 -0.9554 0.0002 -0.0302 0.9603 0.0544 -0.0424 0.8380 -0.0062 0.0126 --- Iterative MLEGST: Beginning iter 1 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 72.9735 (92 data params - 31 model params = expected mean of 61; p-value = 0.14013) 2*Delta(log(L)) = 73.3874 --- Iterative MLEGST: Beginning iter 2 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 72.9735 (92 data params - 31 model params = expected mean of 61; p-value = 0.14013) 2*Delta(log(L)) = 73.3873 --- Iterative MLEGST: Beginning iter 3 of 10 : 168 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 159.365 (168 data params - 31 model params = expected mean of 137; p-value = 0.0928094) 2*Delta(log(L)) = 159.58 --- Iterative MLEGST: Beginning iter 4 of 10 : 441 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 436.213 (441 data params - 31 model params = expected mean of 410; p-value = 0.178848) 2*Delta(log(L)) = 436.363 --- Iterative MLEGST: Beginning iter 5 of 10 : 817 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 810.394 (817 data params - 31 model params = expected mean of 786; p-value = 0.265734) 2*Delta(log(L)) = 810.946 --- Iterative MLEGST: Beginning iter 6 of 10 : 1201 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1213.83 (1201 data params - 31 model params = expected mean of 1170; p-value = 0.18176) 2*Delta(log(L)) = 1214.33 --- Iterative MLEGST: Beginning iter 7 of 10 : 1585 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1579.23 (1585 data params - 31 model params = expected mean of 1554; p-value = 0.322035) 2*Delta(log(L)) = 1579.96 --- Iterative MLEGST: Beginning iter 8 of 10 : 1969 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1931.8 (1969 data params - 31 model params = expected mean of 1938; p-value = 0.535462) 2*Delta(log(L)) = 1932.67 --- Iterative MLEGST: Beginning iter 9 of 10 : 2353 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2312.24 (2353 data params - 31 model params = expected mean of 2322; p-value = 0.55318) 2*Delta(log(L)) = 2313.28 --- Iterative MLEGST: Beginning iter 10 of 10 : 2737 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2743.89 (2737 data params - 31 model params = expected mean of 2706; p-value = 0.300918) 2*Delta(log(L)) = 2745.16 --- Last Iteration: switching to MLE objective --- --- MLEGST --- Maximum log(L) = 1372.53 below upper bound of -4.60008e+06 2*Delta(log(L)) = 2745.06 (2737 data params - 31 model params = expected mean of 2706; p-value = 0.295486) 2*Delta(log(L)) = 2745.06 Running MLGST Iteration 5 LGST: Singular values of I_tilde (truncating to first 4 of 6) = [ 4.24466288 1.1587175 0.98838008 0.95598698 0.05932334 0.00855961] --- LGST --- --- Gauge Optimization to TP (L-BFGS-B) --- 149s 0.0076619571 149s 0.0040750172 149s 0.0015782738 149s 0.0002584072 149s 0.0000068199 149s 0.0000004592 149s 0.0000002547 149s 0.0000002033 149s 0.0000002033 The resulting TP penalty is: 2.03295e-07 The gauge matrix found (B^-1) is: [[ 1.14997311e+00 -1.56571270e-03 -3.02255847e-03 -2.30609034e-03] [ 1.64920985e-04 9.98874222e-01 7.87436990e-05 1.28923164e-03] [ 2.97703784e-04 7.50781688e-05 9.98883603e-01 -1.93963940e-03] [ -1.28861729e-03 1.34409398e-03 -1.83638057e-03 1.00082151e+00]] The gauge-corrected gates are: rhoVec[0] = 0.7071 0.0089 -0.0465 0.7926 EVec[0] = 0.7085 0.0098 0.0177 -0.6272 Gi = 0.9999 -0.0002 0.0003 0 0.0008 0.8522 -0.0333 0.0117 0.0406 0.0325 0.8224 -0.0543 -0.0014 0.0008 0.0400 0.9222 Gx = 1.0000 -0.0001 0 0 0.0131 0.8584 -0.0262 0.0859 -0.0288 -0.0068 0.0377 0.9345 0.0100 0.0481 -0.9150 -0.0437 Gy = 0.9999 0 0.0001 0 0.0985 -0.0231 0.0244 -0.9506 0.0335 -0.0999 0.8464 0.0111 -0.0579 0.8523 -0.0032 0.0178 --- Iterative MLEGST: Beginning iter 1 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 64.4812 (92 data params - 31 model params = expected mean of 61; p-value = 0.355882) 2*Delta(log(L)) = 65.424 --- Iterative MLEGST: Beginning iter 2 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 64.4812 (92 data params - 31 model params = expected mean of 61; p-value = 0.355882) 2*Delta(log(L)) = 65.4238 --- Iterative MLEGST: Beginning iter 3 of 10 : 168 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 126.076 (168 data params - 31 model params = expected mean of 137; p-value = 0.738185) 2*Delta(log(L)) = 127.617 --- Iterative MLEGST: Beginning iter 4 of 10 : 441 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 440.095 (441 data params - 31 model params = expected mean of 410; p-value = 0.146991) 2*Delta(log(L)) = 442.059 --- Iterative MLEGST: Beginning iter 5 of 10 : 817 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 777.517 (817 data params - 31 model params = expected mean of 786; p-value = 0.578434) 2*Delta(log(L)) = 779.428 --- Iterative MLEGST: Beginning iter 6 of 10 : 1201 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1165.57 (1201 data params - 31 model params = expected mean of 1170; p-value = 0.531068) 2*Delta(log(L)) = 1167.93 --- Iterative MLEGST: Beginning iter 7 of 10 : 1585 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1531 (1585 data params - 31 model params = expected mean of 1554; p-value = 0.656368) 2*Delta(log(L)) = 1533.47 --- Iterative MLEGST: Beginning iter 8 of 10 : 1969 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1948.55 (1969 data params - 31 model params = expected mean of 1938; p-value = 0.428661) 2*Delta(log(L)) = 1951.24 --- Iterative MLEGST: Beginning iter 9 of 10 : 2353 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2304.7 (2353 data params - 31 model params = expected mean of 2322; p-value = 0.596668) 2*Delta(log(L)) = 2307.61 --- Iterative MLEGST: Beginning iter 10 of 10 : 2737 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2712.85 (2737 data params - 31 model params = expected mean of 2706; p-value = 0.45934) 2*Delta(log(L)) = 2715.92 --- Last Iteration: switching to MLE objective --- --- MLEGST --- Maximum log(L) = 1357.92 below upper bound of -4.60058e+06 2*Delta(log(L)) = 2715.83 (2737 data params - 31 model params = expected mean of 2706; p-value = 0.443309) 2*Delta(log(L)) = 2715.83 Running MLGST Iteration 6 LGST: Singular values of I_tilde (truncating to first 4 of 6) = [ 4.24367211 1.16578283 0.95876107 0.91720068 0.04324467 0.01880064] --- LGST --- --- Gauge Optimization to TP (L-BFGS-B) --- 171s 0.0076061142 171s 0.0040297007 171s 0.0015719451 171s 0.0002600066 171s 0.0000089028 171s 0.0000004473 171s 0.0000000591 171s 0.0000000530 The resulting TP penalty is: 5.29866e-08 The gauge matrix found (B^-1) is: [[ 1.15009388e+00 -1.39187700e-03 -2.97311134e-03 -2.35351700e-03] [ 1.55373131e-04 9.98862563e-01 1.09895388e-04 1.36847520e-03] [ 3.26776773e-04 1.03906850e-04 9.98998020e-01 -1.96428869e-03] [ -1.29447513e-03 1.45698333e-03 -1.78269919e-03 1.00069480e+00]] The gauge-corrected gates are: rhoVec[0] = 0.7071 0.0015 -0.0584 0.7981 EVec[0] = 0.7095 0.0230 0.0032 -0.6301 Gi = 0.9999 0 0 0 -0.0150 0.9045 0.0085 0.0660 0.0226 0.0346 0.8956 0.0208 0.0031 0.0066 -0.0228 0.9138 Gx = 1.0000 0 0 0 -0.0172 0.8951 0.0305 0.0930 -0.0278 0.0301 0.0271 0.9357 0.0024 0.0748 -0.8726 -0.0399 Gy = 1.0000 0 0.0001 0 0.0660 -0.0030 0.0443 -0.9812 0.0203 -0.0228 0.8877 0.0082 -0.0410 0.8331 -0.0041 0.0094 --- Iterative MLEGST: Beginning iter 1 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 77.5392 (92 data params - 31 model params = expected mean of 61; p-value = 0.0750388) 2*Delta(log(L)) = 77.6918 --- Iterative MLEGST: Beginning iter 2 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 77.5392 (92 data params - 31 model params = expected mean of 61; p-value = 0.0750388) 2*Delta(log(L)) = 77.6918 --- Iterative MLEGST: Beginning iter 3 of 10 : 168 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 160.577 (168 data params - 31 model params = expected mean of 137; p-value = 0.0823057) 2*Delta(log(L)) = 160.752 --- Iterative MLEGST: Beginning iter 4 of 10 : 441 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 436.352 (441 data params - 31 model params = expected mean of 410; p-value = 0.17764) 2*Delta(log(L)) = 436.29 --- Iterative MLEGST: Beginning iter 5 of 10 : 817 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 839.619 (817 data params - 31 model params = expected mean of 786; p-value = 0.0902036) 2*Delta(log(L)) = 840.172 --- Iterative MLEGST: Beginning iter 6 of 10 : 1201 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1212.71 (1201 data params - 31 model params = expected mean of 1170; p-value = 0.187754) 2*Delta(log(L)) = 1213.44 --- Iterative MLEGST: Beginning iter 7 of 10 : 1585 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1576.21 (1585 data params - 31 model params = expected mean of 1554; p-value = 0.341467) 2*Delta(log(L)) = 1577.1 --- Iterative MLEGST: Beginning iter 8 of 10 : 1969 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1997.63 (1969 data params - 31 model params = expected mean of 1938; p-value = 0.168824) 2*Delta(log(L)) = 1998.75 --- Iterative MLEGST: Beginning iter 9 of 10 : 2353 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2411.86 (2353 data params - 31 model params = expected mean of 2322; p-value = 0.0948097) 2*Delta(log(L)) = 2413.21 --- Iterative MLEGST: Beginning iter 10 of 10 : 2737 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2792.09 (2737 data params - 31 model params = expected mean of 2706; p-value = 0.121575) 2*Delta(log(L)) = 2793.61 --- Last Iteration: switching to MLE objective --- --- MLEGST --- Maximum log(L) = 1396.77 below upper bound of -4.60039e+06 2*Delta(log(L)) = 2793.54 (2737 data params - 31 model params = expected mean of 2706; p-value = 0.117734) 2*Delta(log(L)) = 2793.54 Running MLGST Iteration 7 LGST: Singular values of I_tilde (truncating to first 4 of 6) = [ 4.24430926 1.1613371 0.93008337 0.90864098 0.03476409 0.01479728] --- LGST --- --- Gauge Optimization to TP (L-BFGS-B) --- 190s 0.0075905098 190s 0.0040467122 190s 0.0015842608 191s 0.0002620310 191s 0.0000076697 191s 0.0000004454 191s 0.0000000992 191s 0.0000000839 191s 0.0000000838 The resulting TP penalty is: 8.38425e-08 The gauge matrix found (B^-1) is: [[ 1.14998810e+00 -1.44900103e-03 -2.93351322e-03 -2.32912149e-03] [ 1.44852389e-04 9.98948512e-01 1.12473839e-04 1.34244447e-03] [ 2.92111289e-04 1.01138533e-04 9.99054309e-01 -2.08688494e-03] [ -1.32657456e-03 1.46588650e-03 -1.98691082e-03 1.00054381e+00]] The gauge-corrected gates are: rhoVec[0] = 0.7071 0.0169 -0.0631 0.7992 EVec[0] = 0.7100 0.0253 -0.0059 -0.6359 Gi = 1.0000 -0.0002 0 0.0001 -0.0244 0.9254 0.0351 -0.0244 -0.0075 -0.0449 0.9444 -0.0142 -0.0015 -0.0013 -0.0386 0.8986 Gx = 1.0000 0 0 0 -0.0039 0.9094 -0.0080 0.0908 -0.0222 -0.0709 0.0307 0.9315 -0.0070 0.0023 -0.8517 -0.0396 Gy = 0.9999 0 -0.0001 0 0.0776 0.0067 0.0657 -0.9570 -0.0003 -0.0530 0.9477 0.0434 -0.0472 0.8199 -0.0850 -0.0120 --- Iterative MLEGST: Beginning iter 1 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 54.4018 (92 data params - 31 model params = expected mean of 61; p-value = 0.71206) 2*Delta(log(L)) = 54.3055 --- Iterative MLEGST: Beginning iter 2 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 54.4018 (92 data params - 31 model params = expected mean of 61; p-value = 0.71206) 2*Delta(log(L)) = 54.3055 --- Iterative MLEGST: Beginning iter 3 of 10 : 168 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 126.768 (168 data params - 31 model params = expected mean of 137; p-value = 0.723635) 2*Delta(log(L)) = 126.815 --- Iterative MLEGST: Beginning iter 4 of 10 : 441 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 386.963 (441 data params - 31 model params = expected mean of 410; p-value = 0.787175) 2*Delta(log(L)) = 386.679 --- Iterative MLEGST: Beginning iter 5 of 10 : 817 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 757.365 (817 data params - 31 model params = expected mean of 786; p-value = 0.762488) 2*Delta(log(L)) = 757.308 --- Iterative MLEGST: Beginning iter 6 of 10 : 1201 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1099.1 (1201 data params - 31 model params = expected mean of 1170; p-value = 0.930891) 2*Delta(log(L)) = 1099.34 --- Iterative MLEGST: Beginning iter 7 of 10 : 1585 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1466.73 (1585 data params - 31 model params = expected mean of 1554; p-value = 0.943376) 2*Delta(log(L)) = 1467.07 --- Iterative MLEGST: Beginning iter 8 of 10 : 1969 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1828.69 (1969 data params - 31 model params = expected mean of 1938; p-value = 0.962394) 2*Delta(log(L)) = 1829.16 --- Iterative MLEGST: Beginning iter 9 of 10 : 2353 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2193.69 (2353 data params - 31 model params = expected mean of 2322; p-value = 0.971857) 2*Delta(log(L)) = 2194.35 --- Iterative MLEGST: Beginning iter 10 of 10 : 2737 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2612.96 (2737 data params - 31 model params = expected mean of 2706; p-value = 0.898039) 2*Delta(log(L)) = 2613.85 --- Last Iteration: switching to MLE objective --- --- MLEGST --- Maximum log(L) = 1306.9 below upper bound of -4.60019e+06 2*Delta(log(L)) = 2613.79 (2737 data params - 31 model params = expected mean of 2706; p-value = 0.895952) 2*Delta(log(L)) = 2613.79 Running MLGST Iteration 8 LGST: Singular values of I_tilde (truncating to first 4 of 6) = [ 4.24524022 1.14935918 0.96390213 0.89029095 0.03684335 0.01637745] --- LGST --- --- Gauge Optimization to TP (L-BFGS-B) --- 210s 0.0075497790 210s 0.0040501462 211s 0.0015867755 211s 0.0002616685 211s 0.0000067830 211s 0.0000003863 211s 0.0000002067 211s 0.0000001537 211s 0.0000001537 The resulting TP penalty is: 1.53717e-07 The gauge matrix found (B^-1) is: [[ 1.15013292e+00 -1.67160152e-03 -2.97684138e-03 -2.40714061e-03] [ 1.98007516e-04 9.98715590e-01 6.41529914e-05 1.27337845e-03] [ 3.07227691e-04 6.14912502e-05 9.99142553e-01 -2.01501343e-03] [ -1.39002448e-03 1.31242932e-03 -1.90891151e-03 1.00066431e+00]] The gauge-corrected gates are: rhoVec[0] = 0.7071 -0.0037 -0.0740 0.8019 EVec[0] = 0.7211 0.0125 0.0190 -0.6325 Gi = 0.9998 -0.0002 0 0.0002 -0.0050 0.8807 -0.0167 -0.0049 -0.0036 -0.0348 0.9415 -0.0259 -0.0101 -0.0206 0.0353 0.9074 Gx = 0.9999 0 0 0 0.0020 0.8795 -0.0282 0.0868 -0.0241 -0.0650 0.0150 0.9299 -0.0280 0.0123 -0.8344 -0.0358 Gy = 0.9998 0 0 0 0.0738 -0.0196 0.0655 -0.9349 -0.0096 -0.0659 0.9622 0.0381 -0.0635 0.8694 -0.0165 0.0348 --- Iterative MLEGST: Beginning iter 1 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 62.7955 (92 data params - 31 model params = expected mean of 61; p-value = 0.41245) 2*Delta(log(L)) = 62.9674 --- Iterative MLEGST: Beginning iter 2 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 62.7955 (92 data params - 31 model params = expected mean of 61; p-value = 0.41245) 2*Delta(log(L)) = 62.9674 --- Iterative MLEGST: Beginning iter 3 of 10 : 168 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 131.864 (168 data params - 31 model params = expected mean of 137; p-value = 0.607899) 2*Delta(log(L)) = 131.936 --- Iterative MLEGST: Beginning iter 4 of 10 : 441 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 393.648 (441 data params - 31 model params = expected mean of 410; p-value = 0.7107) 2*Delta(log(L)) = 393.815 --- Iterative MLEGST: Beginning iter 5 of 10 : 817 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 766.648 (817 data params - 31 model params = expected mean of 786; p-value = 0.682719) 2*Delta(log(L)) = 767.649 --- Iterative MLEGST: Beginning iter 6 of 10 : 1201 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1117.12 (1201 data params - 31 model params = expected mean of 1170; p-value = 0.863503) 2*Delta(log(L)) = 1118.27 --- Iterative MLEGST: Beginning iter 7 of 10 : 1585 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1490.19 (1585 data params - 31 model params = expected mean of 1554; p-value = 0.874639) 2*Delta(log(L)) = 1491.46 --- Iterative MLEGST: Beginning iter 8 of 10 : 1969 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1885.6 (1969 data params - 31 model params = expected mean of 1938; p-value = 0.799177) 2*Delta(log(L)) = 1887.07 --- Iterative MLEGST: Beginning iter 9 of 10 : 2353 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2247.33 (2353 data params - 31 model params = expected mean of 2322; p-value = 0.863881) 2*Delta(log(L)) = 2248.96 --- Iterative MLEGST: Beginning iter 10 of 10 : 2737 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2617.55 (2737 data params - 31 model params = expected mean of 2706; p-value = 0.886194) 2*Delta(log(L)) = 2619.33 --- Last Iteration: switching to MLE objective --- --- MLEGST --- Maximum log(L) = 1309.64 below upper bound of -4.60065e+06 2*Delta(log(L)) = 2619.28 (2737 data params - 31 model params = expected mean of 2706; p-value = 0.881513) 2*Delta(log(L)) = 2619.28 Running MLGST Iteration 9 LGST: Singular values of I_tilde (truncating to first 4 of 6) = [ 4.24384488 1.17311576 0.97627543 0.92925124 0.02526008 0.00961336] --- LGST --- --- Gauge Optimization to TP (L-BFGS-B) --- 233s 0.0076564256 233s 0.0041049633 233s 0.0016179435 233s 0.0002695705 233s 0.0000064359 233s 0.0000002138 233s 0.0000000196 233s 0.0000000095 233s 0.0000000095 The resulting TP penalty is: 9.46113e-09 The gauge matrix found (B^-1) is: [[ 1.15005087e+00 -1.49766174e-03 -2.98015213e-03 -2.36177720e-03] [ 1.43630471e-04 9.98840585e-01 4.51599688e-05 1.22223907e-03] [ 2.85285934e-04 4.35043464e-05 9.98971553e-01 -1.99352541e-03] [ -1.28278630e-03 1.24694300e-03 -1.94252900e-03 1.00073182e+00]] The gauge-corrected gates are: rhoVec[0] = 0.7071 0.0054 -0.0510 0.8006 EVec[0] = 0.7169 0.0306 0.0130 -0.6343 Gi = 1.0000 0 0 0 -0.0023 0.8549 0.0182 0.0219 0.0138 -0.0676 0.8847 -0.0222 0.0100 -0.0339 -0.0211 0.9105 Gx = 1.0000 0 0 0 0.0041 0.8921 0.0063 0.0898 -0.0327 -0.0674 0.0536 0.9344 0.0123 -0.0302 -0.8702 -0.0441 Gy = 1.0000 0 0 0 0.0785 -0.0464 0.1089 -0.9510 -0.0081 -0.0506 0.9019 0.0562 -0.0433 0.8572 -0.0567 -0.0023 --- Iterative MLEGST: Beginning iter 1 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 48.9845 (92 data params - 31 model params = expected mean of 61; p-value = 0.865925) 2*Delta(log(L)) = 48.9268 --- Iterative MLEGST: Beginning iter 2 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 48.9845 (92 data params - 31 model params = expected mean of 61; p-value = 0.865926) 2*Delta(log(L)) = 48.9269 --- Iterative MLEGST: Beginning iter 3 of 10 : 168 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 129.975 (168 data params - 31 model params = expected mean of 137; p-value = 0.652248) 2*Delta(log(L)) = 129.959 --- Iterative MLEGST: Beginning iter 4 of 10 : 441 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 401.466 (441 data params - 31 model params = expected mean of 410; p-value = 0.609034) 2*Delta(log(L)) = 402.426 --- Iterative MLEGST: Beginning iter 5 of 10 : 817 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 793.036 (817 data params - 31 model params = expected mean of 786; p-value = 0.423195) 2*Delta(log(L)) = 793.942 --- Iterative MLEGST: Beginning iter 6 of 10 : 1201 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1131.25 (1201 data params - 31 model params = expected mean of 1170; p-value = 0.787041) 2*Delta(log(L)) = 1132.32 --- Iterative MLEGST: Beginning iter 7 of 10 : 1585 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1499.06 (1585 data params - 31 model params = expected mean of 1554; p-value = 0.837768) 2*Delta(log(L)) = 1500.38 --- Iterative MLEGST: Beginning iter 8 of 10 : 1969 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1901.7 (1969 data params - 31 model params = expected mean of 1938; p-value = 0.717697) 2*Delta(log(L)) = 1903.27 --- Iterative MLEGST: Beginning iter 9 of 10 : 2353 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2318.65 (2353 data params - 31 model params = expected mean of 2322; p-value = 0.515714) 2*Delta(log(L)) = 2320.43 --- Iterative MLEGST: Beginning iter 10 of 10 : 2737 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2700.35 (2737 data params - 31 model params = expected mean of 2706; p-value = 0.527045) 2*Delta(log(L)) = 2702.33 --- Last Iteration: switching to MLE objective --- --- MLEGST --- Maximum log(L) = 1351.14 below upper bound of -4.60045e+06 2*Delta(log(L)) = 2702.28 (2737 data params - 31 model params = expected mean of 2706; p-value = 0.516583) 2*Delta(log(L)) = 2702.28
gauge_opt_pboot_gatesets = pygsti.drivers.gauge_optimize_gs_list(param_boot_gatesets, gs_mc2gst,
constrainToTP=True, plot=True)
Spam weight 0 Spam weight 1 Spam weight 2 Spam weight 3 Spam weight 4 Spam weight 5 Spam weight 6 Spam weight 7 Spam weight 8 Spam weight 9 Spam weight 10 Spam weight 11 Spam weight 12 Best SPAM weight is 1.0
pboot_mean = pygsti.drivers.to_mean_gateset(gauge_opt_pboot_gatesets, gs_mc2gst)
pboot_std = pygsti.drivers.to_std_gateset(gauge_opt_pboot_gatesets, gs_mc2gst)
#Summary of the error bars
print "Parametric bootstrapped error bars, with",numGatesets,"resamples\n"
print "Error in rho vec:"
print pboot_std.rhoVecs[0]
print
print "Error in E vec:"
print pboot_std.EVecs[0]
print
print "Error in Gi:"
print pboot_std['Gi']
print
print "Error in Gx:"
print pboot_std['Gx']
print
print "Error in Gy:"
print pboot_std['Gy']
Parametric bootstrapped error bars, with 10 resamples Error in rho vec: [[ 1.17027782e-16] [ 3.89810443e-03] [ 2.76108647e-03] [ 2.86059502e-04]] Error in E vec: [[ 0.0003536 ] [ 0.00298662] [ 0.00389878] [ 0.00030908]] Error in Gi: [[ 0. 0. 0. 0. ] [ 0.00056446 0.00299186 0.00346371 0.00397397] [ 0.00055001 0.0031167 0.00215489 0.00390212] [ 0.00043662 0.00252196 0.00207141 0.00263584]] Error in Gx: [[ 0. 0. 0. 0. ] [ 0.00055667 0.00273887 0.00351836 0.00230334] [ 0.00111585 0.00300194 0.00335682 0.00147985] [ 0.00085498 0.00240279 0.00151616 0.00190966]] Error in Gy: [[ 0. 0. 0. 0. ] [ 0.00159497 0.00477895 0.0030408 0.00152758] [ 0.00049893 0.00183629 0.00332884 0.00339016] [ 0.00125118 0.00155437 0.0030288 0.00193707]]
Here we do non-parametric bootstrapping, as indicated by the 'nonparametric' argument below. 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" 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.
(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.)
#The number of simulated datasets & gatesets made for bootstrapping purposes.
# For good statistics, should probably be greater than 10.
numGatesets=10
nonparam_boot_gatesets = pygsti.drivers.make_bootstrap_gatesets(
numGatesets, ds, 'nonparametric', fiducials, fiducials, germs, maxLengths,
targetGateSet=gs_mc2gst, startSeed=0, constrainToTP=True, returnData=False,
verbosity=2)
Creating DataSets: 0 Generating non-parametric dataset. 1 Generating non-parametric dataset. 2 Generating non-parametric dataset. 3 Generating non-parametric dataset. 4 Generating non-parametric dataset. 5 Generating non-parametric dataset. 6 Generating non-parametric dataset. 7 Generating non-parametric dataset. 8 Generating non-parametric dataset. 9 Generating non-parametric dataset. Creating GateSets: Running MLGST Iteration 0 LGST: Singular values of I_tilde (truncating to first 4 of 6) = [ 4.24456639 1.20003951 0.98516344 0.91779559 0.03726084 0.01213483] --- LGST --- --- Gauge Optimization to TP (L-BFGS-B) --- 939s 0.0076712320 939s 0.0040413435 939s 0.0015620716 939s 0.0002570980 939s 0.0000098219 939s 0.0000007384 939s 0.0000002003 939s 0.0000001976 The resulting TP penalty is: 1.97603e-07 The gauge matrix found (B^-1) is: [[ 1.15001433e+00 -1.55670238e-03 -2.96397033e-03 -2.24745357e-03] [ 1.29098445e-04 9.98921753e-01 1.59896007e-04 1.39162129e-03] [ 3.06475673e-04 1.48314271e-04 9.99015607e-01 -1.97162945e-03] [ -1.25129320e-03 1.53452623e-03 -1.78706335e-03 1.00065920e+00]] The gauge-corrected gates are: rhoVec[0] = 0.7071 0.0133 -0.0539 0.7896 EVec[0] = 0.7243 0.0365 0.0052 -0.6484 Gi = 0.9998 0 0.0003 0 0.0185 0.9975 -0.1446 -0.0485 0.0367 0.0050 0.8895 0.0143 -0.0154 0.0172 -0.0071 0.9117 Gx = 1.0000 0 0 0 0.0124 0.8985 -0.0222 0.0849 -0.0098 -0.0796 0.0425 0.9299 -0.0025 0.0631 -0.8724 -0.0389 Gy = 0.9998 0 -0.0002 0 0.0374 0.0028 -0.0122 -0.9445 0.0057 -0.0247 0.8454 0.0013 -0.0238 0.8429 -0.0661 -0.0267 --- Iterative MLEGST: Beginning iter 1 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 98.7299 (92 data params - 31 model params = expected mean of 61; p-value = 0.00159549) 2*Delta(log(L)) = 99.1962 --- Iterative MLEGST: Beginning iter 2 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 98.7299 (92 data params - 31 model params = expected mean of 61; p-value = 0.00159549) 2*Delta(log(L)) = 99.1967 --- Iterative MLEGST: Beginning iter 3 of 10 : 168 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 301.881 (168 data params - 31 model params = expected mean of 137; p-value = 1.96509e-14) 2*Delta(log(L)) = 303.041 --- Iterative MLEGST: Beginning iter 4 of 10 : 441 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 907.187 (441 data params - 31 model params = expected mean of 410; p-value = 0) 2*Delta(log(L)) = 910.808 --- Iterative MLEGST: Beginning iter 5 of 10 : 817 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1715.43 (817 data params - 31 model params = expected mean of 786; p-value = 0) 2*Delta(log(L)) = 1721.88 --- Iterative MLEGST: Beginning iter 6 of 10 : 1201 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2469.91 (1201 data params - 31 model params = expected mean of 1170; p-value = 0) 2*Delta(log(L)) = 2477.52 --- Iterative MLEGST: Beginning iter 7 of 10 : 1585 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 3279.9 (1585 data params - 31 model params = expected mean of 1554; p-value = 0) 2*Delta(log(L)) = 3288.27 --- Iterative MLEGST: Beginning iter 8 of 10 : 1969 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 4055.4 (1969 data params - 31 model params = expected mean of 1938; p-value = 0) 2*Delta(log(L)) = 4064.52 --- Iterative MLEGST: Beginning iter 9 of 10 : 2353 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 4752.46 (2353 data params - 31 model params = expected mean of 2322; p-value = 0) 2*Delta(log(L)) = 4762.28 --- Iterative MLEGST: Beginning iter 10 of 10 : 2737 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 5453.98 (2737 data params - 31 model params = expected mean of 2706; p-value = 0) 2*Delta(log(L)) = 5464.47 --- Last Iteration: switching to MLE objective --- --- MLEGST --- Maximum log(L) = 2732.09 below upper bound of -4.59866e+06 2*Delta(log(L)) = 5464.17 (2737 data params - 31 model params = expected mean of 2706; p-value = 0) 2*Delta(log(L)) = 5464.17 Running MLGST Iteration 1 LGST: Singular values of I_tilde (truncating to first 4 of 6) = [ 4.24411165 1.1694558 0.9619148 0.92361444 0.04372413 0.0078674 ] --- LGST --- --- Gauge Optimization to TP (L-BFGS-B) --- 960s 0.0076015997 960s 0.0040247163 960s 0.0015655316 960s 0.0002595018 960s 0.0000107308 960s 0.0000006540 960s 0.0000000584 960s 0.0000000481 960s 0.0000000476 The resulting TP penalty is: 4.75534e-08 The gauge matrix found (B^-1) is: [[ 1.15003563e+00 -1.51480062e-03 -2.95268188e-03 -2.32521168e-03] [ 1.66079106e-04 9.98850091e-01 1.57456091e-04 1.36768332e-03] [ 3.71217850e-04 1.47816213e-04 9.99169715e-01 -2.07051922e-03] [ -1.31651556e-03 1.46864335e-03 -1.81486840e-03 1.00055119e+00]] The gauge-corrected gates are: rhoVec[0] = 0.7071 0.0059 -0.0802 0.7937 EVec[0] = 0.7116 0.0307 -0.0192 -0.6391 Gi = 0.9999 0.0001 0 0 -0.0253 0.8869 -0.0420 -0.0085 0.0088 0.0260 0.9267 0.0833 -0.0054 0.0160 0.0393 0.9232 Gx = 1.0000 0 0 0 0.0159 0.8954 -0.0486 0.0852 -0.0187 -0.0253 -0.0037 0.9287 -0.0087 0.0623 -0.8529 -0.0393 Gy = 0.9999 0 0 0 0.0268 -0.0319 0.1173 -0.9440 0.0216 -0.0423 0.8888 -0.0059 -0.0492 0.8441 -0.0545 -0.0053 --- Iterative MLEGST: Beginning iter 1 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 108.043 (92 data params - 31 model params = expected mean of 61; p-value = 0.000195529) 2*Delta(log(L)) = 108.402 --- Iterative MLEGST: Beginning iter 2 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 108.043 (92 data params - 31 model params = expected mean of 61; p-value = 0.000195529) 2*Delta(log(L)) = 108.402 --- Iterative MLEGST: Beginning iter 3 of 10 : 168 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 259.376 (168 data params - 31 model params = expected mean of 137; p-value = 1.3572e-09) 2*Delta(log(L)) = 260.02 --- Iterative MLEGST: Beginning iter 4 of 10 : 441 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 809.938 (441 data params - 31 model params = expected mean of 410; p-value = 0) 2*Delta(log(L)) = 811.513 --- Iterative MLEGST: Beginning iter 5 of 10 : 817 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1548.51 (817 data params - 31 model params = expected mean of 786; p-value = 0) 2*Delta(log(L)) = 1550.87 --- Iterative MLEGST: Beginning iter 6 of 10 : 1201 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2209.29 (1201 data params - 31 model params = expected mean of 1170; p-value = 0) 2*Delta(log(L)) = 2212.4 --- Iterative MLEGST: Beginning iter 7 of 10 : 1585 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 3036.81 (1585 data params - 31 model params = expected mean of 1554; p-value = 0) 2*Delta(log(L)) = 3040.8 --- Iterative MLEGST: Beginning iter 8 of 10 : 1969 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 3826.57 (1969 data params - 31 model params = expected mean of 1938; p-value = 0) 2*Delta(log(L)) = 3831.26 --- Iterative MLEGST: Beginning iter 9 of 10 : 2353 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 4517.72 (2353 data params - 31 model params = expected mean of 2322; p-value = 0) 2*Delta(log(L)) = 4523.03 --- Iterative MLEGST: Beginning iter 10 of 10 : 2737 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 5248.32 (2737 data params - 31 model params = expected mean of 2706; p-value = 0) 2*Delta(log(L)) = 5254.36 --- Last Iteration: switching to MLE objective --- --- MLEGST --- Maximum log(L) = 2627.06 below upper bound of -4.59916e+06 2*Delta(log(L)) = 5254.13 (2737 data params - 31 model params = expected mean of 2706; p-value = 0) 2*Delta(log(L)) = 5254.13 Running MLGST Iteration 2 LGST: Singular values of I_tilde (truncating to first 4 of 6) = [ 4.24427705 1.16035247 0.96396723 0.91801576 0.02234415 0.00845476] --- LGST --- --- Gauge Optimization to TP (L-BFGS-B) --- 981s 0.0076212404 981s 0.0040105501 981s 0.0015429112 981s 0.0002525477 981s 0.0000099986 981s 0.0000006993 981s 0.0000000489 981s 0.0000000457 The resulting TP penalty is: 4.5718e-08 The gauge matrix found (B^-1) is: [[ 1.15008192e+00 -1.47929368e-03 -3.00440491e-03 -2.37474779e-03] [ 1.97010409e-04 9.98819300e-01 1.08895818e-04 1.31374370e-03] [ 3.44869008e-04 9.30303340e-05 9.99148552e-01 -2.02923423e-03] [ -1.31227073e-03 1.48021344e-03 -1.81965967e-03 1.00062069e+00]] The gauge-corrected gates are: rhoVec[0] = 0.7071 0.0052 -0.0727 0.7896 EVec[0] = 0.7044 0.0159 0.0012 -0.6332 Gi = 1.0000 0 0.0001 0 -0.0186 0.9053 -0.0899 -0.0248 0.0184 0.0247 0.9247 0.0403 -0.0198 -0.0099 0.0439 0.9408 Gx = 1.0000 0 0 0 0.0138 0.8997 -0.0568 0.0828 -0.0057 -0.0218 0.0064 0.9273 -0.0056 0.0267 -0.8519 -0.0413 Gy = 1.0000 0 0.0001 0 0.0275 0.0396 0.0516 -0.9422 0.0041 -0.0550 0.9423 0.0019 -0.0582 0.8610 -0.0429 0.0015 --- Iterative MLEGST: Beginning iter 1 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 98.0755 (92 data params - 31 model params = expected mean of 61; p-value = 0.00183385) 2*Delta(log(L)) = 98.2102 --- Iterative MLEGST: Beginning iter 2 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 98.0755 (92 data params - 31 model params = expected mean of 61; p-value = 0.00183385) 2*Delta(log(L)) = 98.2102 --- Iterative MLEGST: Beginning iter 3 of 10 : 168 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 266.597 (168 data params - 31 model params = expected mean of 137; p-value = 2.27918e-10) 2*Delta(log(L)) = 266.586 --- Iterative MLEGST: Beginning iter 4 of 10 : 441 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 819.651 (441 data params - 31 model params = expected mean of 410; p-value = 0) 2*Delta(log(L)) = 821.396 --- Iterative MLEGST: Beginning iter 5 of 10 : 817 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1582.45 (817 data params - 31 model params = expected mean of 786; p-value = 0) 2*Delta(log(L)) = 1586.1 --- Iterative MLEGST: Beginning iter 6 of 10 : 1201 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2390.47 (1201 data params - 31 model params = expected mean of 1170; p-value = 0) 2*Delta(log(L)) = 2395.27 --- Iterative MLEGST: Beginning iter 7 of 10 : 1585 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 3156.48 (1585 data params - 31 model params = expected mean of 1554; p-value = 0) 2*Delta(log(L)) = 3161.98 --- Iterative MLEGST: Beginning iter 8 of 10 : 1969 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 4008.17 (1969 data params - 31 model params = expected mean of 1938; p-value = 0) 2*Delta(log(L)) = 4014.51 --- Iterative MLEGST: Beginning iter 9 of 10 : 2353 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 4799.38 (2353 data params - 31 model params = expected mean of 2322; p-value = 0) 2*Delta(log(L)) = 4806.72 --- Iterative MLEGST: Beginning iter 10 of 10 : 2737 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 5488.18 (2737 data params - 31 model params = expected mean of 2706; p-value = 0) 2*Delta(log(L)) = 5496.11 --- Last Iteration: switching to MLE objective --- --- MLEGST --- Maximum log(L) = 2747.9 below upper bound of -4.59897e+06 2*Delta(log(L)) = 5495.81 (2737 data params - 31 model params = expected mean of 2706; p-value = 0) 2*Delta(log(L)) = 5495.81 Running MLGST Iteration 3 LGST: Singular values of I_tilde (truncating to first 4 of 6) = [ 4.24378174 1.21996329 0.97803729 0.93844487 0.04306628 0.02239944] --- LGST --- --- Gauge Optimization to TP (L-BFGS-B) --- 1000s 0.0076403998 1000s 0.0040200451 1000s 0.0015645621 1000s 0.0002607634 1000s 0.0000122074 1000s 0.0000008477 1000s 0.0000001449 1000s 0.0000001384 The resulting TP penalty is: 1.38357e-07 The gauge matrix found (B^-1) is: [[ 1.15006757e+00 -1.53798773e-03 -3.02124408e-03 -2.34934106e-03] [ 1.52087211e-04 9.99008922e-01 1.23402611e-04 1.29372604e-03] [ 3.71743395e-04 1.00788651e-04 9.99156130e-01 -2.11713829e-03] [ -1.25116692e-03 1.49021465e-03 -1.89490672e-03 1.00041617e+00]] The gauge-corrected gates are: rhoVec[0] = 0.7071 0.0128 -0.0809 0.7910 EVec[0] = 0.7222 0.0271 -0.0202 -0.6574 Gi = 1.0001 0 0 0 -0.0153 0.9370 -0.0322 -0.0400 -0.0021 -0.0077 0.8507 0.0161 0.0273 0.0034 0.0334 0.8532 Gx = 1.0000 -0.0001 0 0 0.0146 0.9075 -0.0467 0.0871 -0.0280 -0.0066 0.0125 0.9303 0.0011 0.0132 -0.8570 -0.0432 Gy = 0.9998 0 0.0003 0 0.0300 -0.0199 0.1280 -0.9489 -0.0145 -0.0025 0.8813 0.0533 -0.0345 0.8061 -0.0736 -0.0290 --- Iterative MLEGST: Beginning iter 1 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 126.605 (92 data params - 31 model params = expected mean of 61; p-value = 1.69489e-06) 2*Delta(log(L)) = 127.672 --- Iterative MLEGST: Beginning iter 2 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 126.605 (92 data params - 31 model params = expected mean of 61; p-value = 1.69489e-06) 2*Delta(log(L)) = 127.673 --- Iterative MLEGST: Beginning iter 3 of 10 : 168 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 268.601 (168 data params - 31 model params = expected mean of 137; p-value = 1.37708e-10) 2*Delta(log(L)) = 269.617 --- Iterative MLEGST: Beginning iter 4 of 10 : 441 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 830.416 (441 data params - 31 model params = expected mean of 410; p-value = 0) 2*Delta(log(L)) = 832.644 --- Iterative MLEGST: Beginning iter 5 of 10 : 817 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1535.86 (817 data params - 31 model params = expected mean of 786; p-value = 0) 2*Delta(log(L)) = 1540 --- Iterative MLEGST: Beginning iter 6 of 10 : 1201 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2244.84 (1201 data params - 31 model params = expected mean of 1170; p-value = 0) 2*Delta(log(L)) = 2249.67 --- Iterative MLEGST: Beginning iter 7 of 10 : 1585 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 3090.48 (1585 data params - 31 model params = expected mean of 1554; p-value = 0) 2*Delta(log(L)) = 3096.14 --- Iterative MLEGST: Beginning iter 8 of 10 : 1969 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 3919.57 (1969 data params - 31 model params = expected mean of 1938; p-value = 0) 2*Delta(log(L)) = 3926.32 --- Iterative MLEGST: Beginning iter 9 of 10 : 2353 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 4636.48 (2353 data params - 31 model params = expected mean of 2322; p-value = 0) 2*Delta(log(L)) = 4643.85 --- Iterative MLEGST: Beginning iter 10 of 10 : 2737 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 5305.75 (2737 data params - 31 model params = expected mean of 2706; p-value = 0) 2*Delta(log(L)) = 5313.62 --- Last Iteration: switching to MLE objective --- --- MLEGST --- Maximum log(L) = 2656.67 below upper bound of -4.59909e+06 2*Delta(log(L)) = 5313.34 (2737 data params - 31 model params = expected mean of 2706; p-value = 0) 2*Delta(log(L)) = 5313.34 Running MLGST Iteration 4 LGST: Singular values of I_tilde (truncating to first 4 of 6) = [ 4.24379659 1.17392033 0.9948911 0.87843068 0.04711465 0.02007583] --- LGST --- --- Gauge Optimization to TP (L-BFGS-B) --- 1022s 0.0076057750 1022s 0.0040394666 1022s 0.0015986437 1022s 0.0002723128 1022s 0.0000141310 1022s 0.0000006542 1022s 0.0000001497 1022s 0.0000001422 The resulting TP penalty is: 1.42157e-07 The gauge matrix found (B^-1) is: [[ 1.15003729e+00 -1.45510385e-03 -2.97819405e-03 -2.41253445e-03] [ 1.99478704e-04 9.98833444e-01 3.19373899e-05 1.19016202e-03] [ 2.72655428e-04 1.54715840e-05 9.99013645e-01 -1.99061651e-03] [ -1.25800834e-03 1.44781016e-03 -1.93191917e-03 1.00068055e+00]] The gauge-corrected gates are: rhoVec[0] = 0.7071 -0.0018 -0.0494 0.8033 EVec[0] = 0.7208 -0.0117 -0.0046 -0.6426 Gi = 0.9998 0.0002 -0.0002 0 0.0201 0.9304 -0.1277 -0.0103 0.0285 -0.0181 0.9130 0.0455 -0.0070 -0.0438 0.0110 0.9088 Gx = 1.0000 0 0 0 0.0021 0.9034 -0.0573 0.0858 -0.0218 -0.0893 0.0665 0.9296 0.0107 -0.0519 -0.8396 -0.0433 Gy = 0.9999 0 0 0 0.0470 0.0607 -0.0099 -0.9342 0.0007 -0.0263 0.9231 0.0257 -0.0240 0.8349 -0.0598 -0.0084 --- Iterative MLEGST: Beginning iter 1 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 139.106 (92 data params - 31 model params = expected mean of 61; p-value = 4.90802e-08) 2*Delta(log(L)) = 140.144 --- Iterative MLEGST: Beginning iter 2 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 139.106 (92 data params - 31 model params = expected mean of 61; p-value = 4.90802e-08) 2*Delta(log(L)) = 140.144 --- Iterative MLEGST: Beginning iter 3 of 10 : 168 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 297.331 (168 data params - 31 model params = expected mean of 137; p-value = 6.92779e-14) 2*Delta(log(L)) = 298.2 --- Iterative MLEGST: Beginning iter 4 of 10 : 441 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 812.901 (441 data params - 31 model params = expected mean of 410; p-value = 0) 2*Delta(log(L)) = 813.838 --- Iterative MLEGST: Beginning iter 5 of 10 : 817 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1461.81 (817 data params - 31 model params = expected mean of 786; p-value = 0) 2*Delta(log(L)) = 1464.45 --- Iterative MLEGST: Beginning iter 6 of 10 : 1201 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2335.92 (1201 data params - 31 model params = expected mean of 1170; p-value = 0) 2*Delta(log(L)) = 2339.93 --- Iterative MLEGST: Beginning iter 7 of 10 : 1585 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 3257.88 (1585 data params - 31 model params = expected mean of 1554; p-value = 0) 2*Delta(log(L)) = 3263.06 --- Iterative MLEGST: Beginning iter 8 of 10 : 1969 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 4011.91 (1969 data params - 31 model params = expected mean of 1938; p-value = 0) 2*Delta(log(L)) = 4017.83 --- Iterative MLEGST: Beginning iter 9 of 10 : 2353 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 4829.36 (2353 data params - 31 model params = expected mean of 2322; p-value = 0) 2*Delta(log(L)) = 4836.21 --- Iterative MLEGST: Beginning iter 10 of 10 : 2737 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 5592.65 (2737 data params - 31 model params = expected mean of 2706; p-value = 0) 2*Delta(log(L)) = 5600.26 --- Last Iteration: switching to MLE objective --- --- MLEGST --- Maximum log(L) = 2800.03 below upper bound of -4.59866e+06 2*Delta(log(L)) = 5600.06 (2737 data params - 31 model params = expected mean of 2706; p-value = 0) 2*Delta(log(L)) = 5600.06 Running MLGST Iteration 5 LGST: Singular values of I_tilde (truncating to first 4 of 6) = [ 4.24427826 1.1671019 0.96738801 0.92230681 0.06939313 0.02182648] --- LGST --- --- Gauge Optimization to TP (L-BFGS-B) --- 1044s 0.0076324668 1044s 0.0040520315 1044s 0.0015722243 1044s 0.0002575094 1044s 0.0000067335 1044s 0.0000003967 1044s 0.0000002012 1044s 0.0000001684 1044s 0.0000001683 The resulting TP penalty is: 1.68349e-07 The gauge matrix found (B^-1) is: [[ 1.15007305e+00 -1.59347321e-03 -3.01831647e-03 -2.42142562e-03] [ 1.36517457e-04 9.98886074e-01 6.02594062e-05 1.37307317e-03] [ 2.69850390e-04 5.36676438e-05 9.99020753e-01 -1.95764644e-03] [ -1.29767558e-03 1.45432234e-03 -1.89957434e-03 1.00064902e+00]] The gauge-corrected gates are: rhoVec[0] = 0.7071 0.0207 -0.0544 0.7953 EVec[0] = 0.7112 0.0066 0.0185 -0.6307 Gi = 0.9999 -0.0002 0 0.0002 0.0198 0.8799 -0.0855 -0.0057 0.0144 0.0047 0.8817 0.0086 0.0116 -0.0095 0.0258 0.9309 Gx = 0.9999 0 0 0 0.0091 0.8874 -0.0226 0.0867 -0.0399 -0.0333 0.0748 0.9371 -0.0091 0.0109 -0.8563 -0.0388 Gy = 0.9999 0 0.0003 0 0.0516 0.0411 0.0541 -0.9298 0.0064 -0.0619 0.8971 0.0150 -0.0450 0.8577 -0.0341 -0.0036 --- Iterative MLEGST: Beginning iter 1 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 120.204 (92 data params - 31 model params = expected mean of 61; p-value = 9.39776e-06) 2*Delta(log(L)) = 120.767 --- Iterative MLEGST: Beginning iter 2 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 120.204 (92 data params - 31 model params = expected mean of 61; p-value = 9.39785e-06) 2*Delta(log(L)) = 120.767 --- Iterative MLEGST: Beginning iter 3 of 10 : 168 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 260.388 (168 data params - 31 model params = expected mean of 137; p-value = 1.06006e-09) 2*Delta(log(L)) = 261.55 --- Iterative MLEGST: Beginning iter 4 of 10 : 441 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 866.769 (441 data params - 31 model params = expected mean of 410; p-value = 0) 2*Delta(log(L)) = 870.238 --- Iterative MLEGST: Beginning iter 5 of 10 : 817 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1542.46 (817 data params - 31 model params = expected mean of 786; p-value = 0) 2*Delta(log(L)) = 1548.23 --- Iterative MLEGST: Beginning iter 6 of 10 : 1201 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2252.29 (1201 data params - 31 model params = expected mean of 1170; p-value = 0) 2*Delta(log(L)) = 2259.42 --- Iterative MLEGST: Beginning iter 7 of 10 : 1585 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 3103.51 (1585 data params - 31 model params = expected mean of 1554; p-value = 0) 2*Delta(log(L)) = 3111.78 --- Iterative MLEGST: Beginning iter 8 of 10 : 1969 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 4006.2 (1969 data params - 31 model params = expected mean of 1938; p-value = 0) 2*Delta(log(L)) = 4015.53 --- Iterative MLEGST: Beginning iter 9 of 10 : 2353 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 4790.55 (2353 data params - 31 model params = expected mean of 2322; p-value = 0) 2*Delta(log(L)) = 4800.59 --- Iterative MLEGST: Beginning iter 10 of 10 : 2737 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 5598.25 (2737 data params - 31 model params = expected mean of 2706; p-value = 0) 2*Delta(log(L)) = 5609.35 --- Last Iteration: switching to MLE objective --- --- MLEGST --- Maximum log(L) = 2804.54 below upper bound of -4.59901e+06 2*Delta(log(L)) = 5609.07 (2737 data params - 31 model params = expected mean of 2706; p-value = 0) 2*Delta(log(L)) = 5609.07 Running MLGST Iteration 6 LGST: Singular values of I_tilde (truncating to first 4 of 6) = [ 4.24411097 1.19781472 0.96382721 0.92811765 0.05292843 0.01809055] --- LGST --- --- Gauge Optimization to TP (L-BFGS-B) --- 1062s 0.0076381535 1062s 0.0039975744 1062s 0.0015405771 1062s 0.0002547658 1062s 0.0000129347 1062s 0.0000009167 1062s 0.0000001658 1062s 0.0000001581 The resulting TP penalty is: 1.58087e-07 The gauge matrix found (B^-1) is: [[ 1.15014094e+00 -1.54690514e-03 -3.07326463e-03 -2.46417758e-03] [ 1.75971116e-04 9.98971423e-01 1.27182054e-04 1.37512843e-03] [ 3.49388982e-04 9.95667707e-05 9.99127038e-01 -2.06258100e-03] [ -1.25641151e-03 1.62026363e-03 -1.86399886e-03 1.00048413e+00]] The gauge-corrected gates are: rhoVec[0] = 0.7071 0.0131 -0.0758 0.7891 EVec[0] = 0.7201 0.0259 -0.0024 -0.6454 Gi = 0.9999 0 0 0.0001 -0.0371 0.9483 -0.0275 -0.0416 0.0076 -0.0138 0.8832 -0.0262 0.0172 0.0004 0.0388 0.9031 Gx = 0.9999 -0.0002 0 0 0.0194 0.9067 -0.0595 0.0858 -0.0133 -0.0839 0.0085 0.9274 -0.0076 0.0447 -0.8674 -0.0407 Gy = 0.9998 0 0 0 0.0285 0.0391 0.0353 -0.9483 0.0125 -0.0446 0.9056 0.0503 -0.0371 0.8135 -0.0369 -0.0200 --- Iterative MLEGST: Beginning iter 1 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 90.9393 (92 data params - 31 model params = expected mean of 61; p-value = 0.00774664) 2*Delta(log(L)) = 91.0163 --- Iterative MLEGST: Beginning iter 2 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 90.9392 (92 data params - 31 model params = expected mean of 61; p-value = 0.00774672) 2*Delta(log(L)) = 91.016 --- Iterative MLEGST: Beginning iter 3 of 10 : 168 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 258.243 (168 data params - 31 model params = expected mean of 137; p-value = 1.7879e-09) 2*Delta(log(L)) = 258.471 --- Iterative MLEGST: Beginning iter 4 of 10 : 441 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 813.918 (441 data params - 31 model params = expected mean of 410; p-value = 0) 2*Delta(log(L)) = 814.846 --- Iterative MLEGST: Beginning iter 5 of 10 : 817 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1529.73 (817 data params - 31 model params = expected mean of 786; p-value = 0) 2*Delta(log(L)) = 1531.93 --- Iterative MLEGST: Beginning iter 6 of 10 : 1201 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2294.1 (1201 data params - 31 model params = expected mean of 1170; p-value = 0) 2*Delta(log(L)) = 2297.15 --- Iterative MLEGST: Beginning iter 7 of 10 : 1585 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 3066.22 (1585 data params - 31 model params = expected mean of 1554; p-value = 0) 2*Delta(log(L)) = 3070.28 --- Iterative MLEGST: Beginning iter 8 of 10 : 1969 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 3948.92 (1969 data params - 31 model params = expected mean of 1938; p-value = 0) 2*Delta(log(L)) = 3953.97 --- Iterative MLEGST: Beginning iter 9 of 10 : 2353 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 4824.27 (2353 data params - 31 model params = expected mean of 2322; p-value = 0) 2*Delta(log(L)) = 4830.33 --- Iterative MLEGST: Beginning iter 10 of 10 : 2737 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 5657.07 (2737 data params - 31 model params = expected mean of 2706; p-value = 0) 2*Delta(log(L)) = 5664.04 --- Last Iteration: switching to MLE objective --- --- MLEGST --- Maximum log(L) = 2831.87 below upper bound of -4.5984e+06 2*Delta(log(L)) = 5663.75 (2737 data params - 31 model params = expected mean of 2706; p-value = 0) 2*Delta(log(L)) = 5663.75 Running MLGST Iteration 7 LGST: Singular values of I_tilde (truncating to first 4 of 6) = [ 4.24416701 1.1687148 0.95543029 0.88774402 0.03874886 0.02387817] --- LGST --- --- Gauge Optimization to TP (L-BFGS-B) --- 1082s 0.0075759229 1082s 0.0040217319 1082s 0.0015697392 1082s 0.0002589775 1082s 0.0000083096 1082s 0.0000004112 1082s 0.0000000365 1082s 0.0000000327 The resulting TP penalty is: 3.2732e-08 The gauge matrix found (B^-1) is: [[ 1.14997377e+00 -1.51014048e-03 -2.91410724e-03 -2.25350869e-03] [ 1.67833160e-04 9.98947441e-01 8.28906243e-05 1.27721475e-03] [ 2.95137603e-04 7.01432618e-05 9.99058473e-01 -2.06791453e-03] [ -1.33505628e-03 1.42519096e-03 -1.96128226e-03 1.00055359e+00]] The gauge-corrected gates are: rhoVec[0] = 0.7071 0.0090 -0.0642 0.7964 EVec[0] = 0.7126 0.0215 -0.0061 -0.6394 Gi = 1.0000 -0.0002 0 0 -0.0219 0.9656 -0.0319 -0.0032 0.0137 -0.0437 0.9065 0.0312 -0.0105 0.0248 0.0352 0.9192 Gx = 1.0000 0 0 0 -0.0017 0.9337 -0.0249 0.0891 -0.0127 -0.1067 0.0374 0.9291 -0.0064 -0.0142 -0.8486 -0.0403 Gy = 1.0000 0 0 0 0.0145 0.0090 0.0979 -0.9323 -0.0055 -0.0134 0.9410 0.0526 -0.0449 0.8138 -0.0692 -0.0099 --- Iterative MLEGST: Beginning iter 1 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 106.624 (92 data params - 31 model params = expected mean of 61; p-value = 0.000272868) 2*Delta(log(L)) = 106.668 --- Iterative MLEGST: Beginning iter 2 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 106.624 (92 data params - 31 model params = expected mean of 61; p-value = 0.000272869) 2*Delta(log(L)) = 106.669 --- Iterative MLEGST: Beginning iter 3 of 10 : 168 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 267.873 (168 data params - 31 model params = expected mean of 137; p-value = 1.65455e-10) 2*Delta(log(L)) = 268.005 --- Iterative MLEGST: Beginning iter 4 of 10 : 441 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 737.673 (441 data params - 31 model params = expected mean of 410; p-value = 0) 2*Delta(log(L)) = 738.63 --- Iterative MLEGST: Beginning iter 5 of 10 : 817 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1412.14 (817 data params - 31 model params = expected mean of 786; p-value = 0) 2*Delta(log(L)) = 1414.15 --- Iterative MLEGST: Beginning iter 6 of 10 : 1201 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2111.25 (1201 data params - 31 model params = expected mean of 1170; p-value = 0) 2*Delta(log(L)) = 2113.94 --- Iterative MLEGST: Beginning iter 7 of 10 : 1585 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2955.25 (1585 data params - 31 model params = expected mean of 1554; p-value = 0) 2*Delta(log(L)) = 2958.51 --- Iterative MLEGST: Beginning iter 8 of 10 : 1969 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 3802.54 (1969 data params - 31 model params = expected mean of 1938; p-value = 0) 2*Delta(log(L)) = 3806.88 --- Iterative MLEGST: Beginning iter 9 of 10 : 2353 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 4536.4 (2353 data params - 31 model params = expected mean of 2322; p-value = 0) 2*Delta(log(L)) = 4541.46 --- Iterative MLEGST: Beginning iter 10 of 10 : 2737 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 5284.02 (2737 data params - 31 model params = expected mean of 2706; p-value = 0) 2*Delta(log(L)) = 5289.86 --- Last Iteration: switching to MLE objective --- --- MLEGST --- Maximum log(L) = 2644.83 below upper bound of -4.59896e+06 2*Delta(log(L)) = 5289.65 (2737 data params - 31 model params = expected mean of 2706; p-value = 0) 2*Delta(log(L)) = 5289.65 Running MLGST Iteration 8 LGST: Singular values of I_tilde (truncating to first 4 of 6) = [ 4.24541065 1.15693434 0.94546793 0.91471381 0.01258141 0.00825079] --- LGST --- --- Gauge Optimization to TP (L-BFGS-B) --- 1105s 0.0075794433 1105s 0.0040870194 1105s 0.0016176564 1105s 0.0002720506 1105s 0.0000098808 1105s 0.0000012692 1105s 0.0000007654 1105s 0.0000007596 The resulting TP penalty is: 7.59592e-07 The gauge matrix found (B^-1) is: [[ 1.14972260e+00 -1.77259176e-03 -2.77310331e-03 -2.08281900e-03] [ 2.00664884e-04 9.98788778e-01 1.07377658e-04 1.35344041e-03] [ 2.91424900e-04 9.19262668e-05 9.99125235e-01 -1.99610245e-03] [ -1.36268393e-03 1.52126759e-03 -1.87863134e-03 1.00063891e+00]] The gauge-corrected gates are: rhoVec[0] = 0.7071 0.0020 -0.0710 0.8002 EVec[0] = 0.7235 0.0085 0.0190 -0.6358 Gi = 0.9995 -0.0004 0.0004 0 0.0166 0.9313 -0.0719 -0.0377 -0.0078 0.0593 0.9471 0.0044 0.0015 -0.0206 0.0373 0.9092 Gx = 1.0001 0 0 0 0.0133 0.8994 -0.0594 0.0853 -0.0334 0.0099 0.0211 0.9342 -0.0209 0.0477 -0.8500 -0.0364 Gy = 0.9996 0 0 0 0.0530 0.0268 0.0444 -0.9338 0.0147 -0.0892 0.9202 0.0083 -0.0468 0.8609 -0.0240 -0.0045 --- Iterative MLEGST: Beginning iter 1 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 116.163 (92 data params - 31 model params = expected mean of 61; p-value = 2.66469e-05) 2*Delta(log(L)) = 116.876 --- Iterative MLEGST: Beginning iter 2 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 116.163 (92 data params - 31 model params = expected mean of 61; p-value = 2.66469e-05) 2*Delta(log(L)) = 116.876 --- Iterative MLEGST: Beginning iter 3 of 10 : 168 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 251.379 (168 data params - 31 model params = expected mean of 137; p-value = 9.23554e-09) 2*Delta(log(L)) = 252.048 --- Iterative MLEGST: Beginning iter 4 of 10 : 441 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 713.091 (441 data params - 31 model params = expected mean of 410; p-value = 0) 2*Delta(log(L)) = 713.544 --- Iterative MLEGST: Beginning iter 5 of 10 : 817 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1370.67 (817 data params - 31 model params = expected mean of 786; p-value = 0) 2*Delta(log(L)) = 1371.78 --- Iterative MLEGST: Beginning iter 6 of 10 : 1201 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2157.02 (1201 data params - 31 model params = expected mean of 1170; p-value = 0) 2*Delta(log(L)) = 2159.12 --- Iterative MLEGST: Beginning iter 7 of 10 : 1585 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2970.64 (1585 data params - 31 model params = expected mean of 1554; p-value = 0) 2*Delta(log(L)) = 2973.65 --- Iterative MLEGST: Beginning iter 8 of 10 : 1969 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 3798.7 (1969 data params - 31 model params = expected mean of 1938; p-value = 0) 2*Delta(log(L)) = 3802.65 --- Iterative MLEGST: Beginning iter 9 of 10 : 2353 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 4532.19 (2353 data params - 31 model params = expected mean of 2322; p-value = 0) 2*Delta(log(L)) = 4536.88 --- Iterative MLEGST: Beginning iter 10 of 10 : 2737 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 5247.32 (2737 data params - 31 model params = expected mean of 2706; p-value = 0) 2*Delta(log(L)) = 5252.66 --- Last Iteration: switching to MLE objective --- --- MLEGST --- Maximum log(L) = 2626.23 below upper bound of -4.59911e+06 2*Delta(log(L)) = 5252.46 (2737 data params - 31 model params = expected mean of 2706; p-value = 0) 2*Delta(log(L)) = 5252.46 Running MLGST Iteration 9 LGST: Singular values of I_tilde (truncating to first 4 of 6) = [ 4.2436575 1.18038008 0.97266877 0.94120446 0.04391035 0.01137498] --- LGST --- --- Gauge Optimization to TP (L-BFGS-B) --- 1124s 0.0076769285 1124s 0.0040996794 1124s 0.0016052334 1124s 0.0002662842 1124s 0.0000072470 1124s 0.0000003493 1124s 0.0000000840 1124s 0.0000000496 1124s 0.0000000496 The resulting TP penalty is: 4.95644e-08 The gauge matrix found (B^-1) is: [[ 1.14994121e+00 -1.62182916e-03 -2.90668101e-03 -2.26973722e-03] [ 1.39429934e-04 9.98925776e-01 6.81348351e-05 1.33037896e-03] [ 2.87591565e-04 6.01955455e-05 9.98983439e-01 -1.97711947e-03] [ -1.26366252e-03 1.43378439e-03 -1.91444361e-03 1.00066150e+00]] The gauge-corrected gates are: rhoVec[0] = 0.7071 0.0230 -0.0501 0.7956 EVec[0] = 0.7194 0.0265 0.0127 -0.6378 Gi = 0.9999 0 0 0 -0.0204 0.9354 0.0097 -0.0002 0.0531 -0.0199 0.8469 -0.0324 0.0025 0.0322 0.0433 0.9166 Gx = 1.0000 0 0 0 0.0197 0.8965 -0.0394 0.0838 -0.0033 -0.0942 0.0481 0.9276 0.0213 -0.0139 -0.8742 -0.0455 Gy = 0.9999 0 0 0 0.0491 -0.0077 0.0761 -0.9527 0.0088 -0.0750 0.8918 0.0345 -0.0455 0.8535 -0.0670 -0.0193 --- Iterative MLEGST: Beginning iter 1 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 110.592 (92 data params - 31 model params = expected mean of 61; p-value = 0.00010618) 2*Delta(log(L)) = 110.928 --- Iterative MLEGST: Beginning iter 2 of 10 : 92 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 110.592 (92 data params - 31 model params = expected mean of 61; p-value = 0.00010618) 2*Delta(log(L)) = 110.928 --- Iterative MLEGST: Beginning iter 3 of 10 : 168 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 232.717 (168 data params - 31 model params = expected mean of 137; p-value = 6.24904e-07) 2*Delta(log(L)) = 233.414 --- Iterative MLEGST: Beginning iter 4 of 10 : 441 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 734.231 (441 data params - 31 model params = expected mean of 410; p-value = 0) 2*Delta(log(L)) = 735.603 --- Iterative MLEGST: Beginning iter 5 of 10 : 817 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 1457.84 (817 data params - 31 model params = expected mean of 786; p-value = 0) 2*Delta(log(L)) = 1461.25 --- Iterative MLEGST: Beginning iter 6 of 10 : 1201 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 2219.12 (1201 data params - 31 model params = expected mean of 1170; p-value = 0) 2*Delta(log(L)) = 2223.53 --- Iterative MLEGST: Beginning iter 7 of 10 : 1585 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 3017.78 (1585 data params - 31 model params = expected mean of 1554; p-value = 0) 2*Delta(log(L)) = 3022.95 --- Iterative MLEGST: Beginning iter 8 of 10 : 1969 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 3817.98 (1969 data params - 31 model params = expected mean of 1938; p-value = 0) 2*Delta(log(L)) = 3823.85 --- Iterative MLEGST: Beginning iter 9 of 10 : 2353 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 4593.09 (2353 data params - 31 model params = expected mean of 2322; p-value = 0) 2*Delta(log(L)) = 4599.75 --- Iterative MLEGST: Beginning iter 10 of 10 : 2737 gate strings --- --- Least Squares GST --- Sum of Chi^2 = 5347.24 (2737 data params - 31 model params = expected mean of 2706; p-value = 0) 2*Delta(log(L)) = 5354.67 --- Last Iteration: switching to MLE objective --- --- MLEGST --- Maximum log(L) = 2677.23 below upper bound of -4.59872e+06 2*Delta(log(L)) = 5354.46 (2737 data params - 31 model params = expected mean of 2706; p-value = 0) 2*Delta(log(L)) = 5354.46
gauge_opt_npboot_gatesets = pygsti.drivers.gauge_optimize_gs_list(nonparam_boot_gatesets, gs_mc2gst,
constrainToTP=True, plot=True)
Spam weight 0 Spam weight 1 Spam weight 2 Spam weight 3 Spam weight 4 Spam weight 5 Spam weight 6 Spam weight 7 Spam weight 8 Spam weight 9 Spam weight 10 Spam weight 11 Spam weight 12 Best SPAM weight is 1.0
npboot_mean = pygsti.drivers.to_mean_gateset(gauge_opt_npboot_gatesets, gs_mc2gst)
npboot_std = pygsti.drivers.to_std_gateset(gauge_opt_npboot_gatesets, gs_mc2gst)
#Summary of the error bars
print "Non-parametric bootstrapped error bars, with",numGatesets,"resamples\n"
print "Error in rho vec:"
print npboot_std.rhoVecs[0]
print
print "Error in E vec:"
print npboot_std.EVecs[0]
print
print "Error in Gi:"
print npboot_std['Gi']
print
print "Error in Gx:"
print npboot_std['Gx']
print
print "Error in Gy:"
print npboot_std['Gy']
Non-parametric bootstrapped error bars, with 10 resamples Error in rho vec: [[ 1.17027782e-16] [ 1.99738104e-03] [ 2.79844232e-03] [ 1.90448157e-04]] Error in E vec: [[ 0.00041479] [ 0.00306108] [ 0.00266744] [ 0.0002764 ]] Error in Gi: [[ 0. 0. 0. 0. ] [ 0.00064338 0.00222999 0.00350751 0.00384113] [ 0.00054401 0.00258955 0.0014322 0.00261458] [ 0.00039303 0.00234993 0.00164841 0.00262405]] Error in Gx: [[ 0. 0. 0. 0. ] [ 0.00047712 0.00220532 0.00373996 0.0021974 ] [ 0.00103899 0.0028076 0.00268864 0.00135054] [ 0.00120535 0.00151766 0.00147284 0.00166546]] Error in Gy: [[ 0. 0. 0. 0. ] [ 0.0008808 0.00265367 0.00258749 0.00128926] [ 0.00047863 0.00190443 0.00281074 0.0024489 ] [ 0.00072845 0.00145286 0.00242723 0.00197883]]
loglog(npboot_std.to_vector(),pboot_std.to_vector(),'.')
loglog(np.logspace(-4,-2,10),np.logspace(-4,-2,10),'--')
xlabel('Non-parametric')
ylabel('Parametric')
xlim((1e-4,1e-2)); ylim((1e-4,1e-2))
title('Scatter plot comparing param vs. non-param bootstrapping error bars.')
<matplotlib.text.Text at 0x5956b90>