import os
import sys
import time
import json
import pygsti
from pygsti.modelpacks.legacy import std1Q_XYI
%pylab inline
Populating the interactive namespace from numpy and matplotlib
#Get a GST estimate (similar to Tutorial 0)
# 1) get the target Model
target_model = std1Q_XYI.target_model()
# 2) get the building blocks needed to specify which operation sequences are needed
prep_fiducials, meas_fiducials = std1Q_XYI.prepStrs, std1Q_XYI.effectStrs
germs = std1Q_XYI.germs
maxLengths = [1,2,4,8,16]
# 3) generate "fake" data from a depolarized version of target_model
mdl_datagen = target_model.depolarize(op_noise=0.1, spam_noise=0.001)
listOfExperiments = pygsti.construction.make_lsgst_experiment_list(
target_model, prep_fiducials, meas_fiducials, germs, maxLengths)
ds = pygsti.construction.generate_fake_data(mdl_datagen, listOfExperiments, nSamples=1000,
sampleError="binomial", seed=1234)
results = pygsti.do_stdpractice_gst(ds, target_model, prep_fiducials, meas_fiducials,
germs, maxLengths, modes="TP")
estimated_model = results.estimates['TP'].models['stdgaugeopt']
--- Circuit Creation --- 1282 sequences created Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing -- Std Practice: Iter 1 of 1 (TP) --: --- Iterative MLGST: [##################################################] 100.0% 1282 operation sequences --- Iterative MLGST Total Time: 7.2s
Here we do parametric bootstrapping, as indicated by the 'parametric' argument below. The output is eventually stored in the "mean" and "std" Models, which hold the mean and standard deviation values of the set of bootstrapped models (after gauge optimization). It is this latter "standard deviation Model" 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 & models made for bootstrapping purposes.
# For good statistics, should probably be greater than 10.
numGatesets=10
param_boot_models = pygsti.drivers.make_bootstrap_models(
numGatesets, ds, 'parametric', prep_fiducials, meas_fiducials, germs, maxLengths,
inputModel=estimated_model, startSeed=0, 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 Models: Running MLGST Iteration 0 --- Circuit Creation --- 1282 sequences created Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing --- LGST --- Singular values of I_tilde (truncating to first 4 of 6) = 4.244653976670047 1.192830953128653 0.9689326363609111 0.9189157715091224 0.07422658287182586 0.011606078537692615 Singular values of target I_tilde (truncating to first 4 of 6) = 4.244164062089174 1.169453419312999 0.9475116980891475 0.9403516426340927 2.709096598579531e-16 1.7684881472925075e-16 --- Iterative MLGST: Iter 1 of 5 92 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 54.3315 (92 data params - 31 model params = expected mean of 61; p-value = 0.7144) Completed in 0.3s 2*Delta(log(L)) = 54.4952 Iteration 1 took 0.4s --- Iterative MLGST: Iter 2 of 5 168 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 139.054 (168 data params - 31 model params = expected mean of 137; p-value = 0.434979) Completed in 0.3s 2*Delta(log(L)) = 139.281 Iteration 2 took 0.4s --- Iterative MLGST: Iter 3 of 5 450 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 433.775 (450 data params - 31 model params = expected mean of 419; p-value = 0.298928) Completed in 0.6s 2*Delta(log(L)) = 434.566 Iteration 3 took 0.8s --- Iterative MLGST: Iter 4 of 5 862 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 871.047 (862 data params - 31 model params = expected mean of 831; p-value = 0.16274) Completed in 1.2s 2*Delta(log(L)) = 872.842 Iteration 4 took 1.4s --- Iterative MLGST: Iter 5 of 5 1282 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 1273.04 (1282 data params - 31 model params = expected mean of 1251; p-value = 0.325873) Completed in 1.8s 2*Delta(log(L)) = 1274.82 Iteration 5 took 2.1s Switching to ML objective (last iteration) --- MLGST --- Maximum log(L) = 637.362 below upper bound of -2.136e+06 2*Delta(log(L)) = 1274.72 (1282 data params - 31 model params = expected mean of 1251; p-value = 0.313964) Completed in 2.1s 2*Delta(log(L)) = 1274.72 Final MLGST took 2.1s Iterative MLGST Total Time: 7.2s Running MLGST Iteration 1 --- Circuit Creation --- 1282 sequences created Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing --- LGST --- Singular values of I_tilde (truncating to first 4 of 6) = 4.243869714012627 1.16340135495376 0.9505771532444359 0.9192169139457478 0.03669226197655027 0.007493766406182375 Singular values of target I_tilde (truncating to first 4 of 6) = 4.244164062089174 1.169453419312999 0.9475116980891475 0.9403516426340927 2.709096598579531e-16 1.7684881472925075e-16 --- Iterative MLGST: Iter 1 of 5 92 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 62.8464 (92 data params - 31 model params = expected mean of 61; p-value = 0.410693) Completed in 0.4s 2*Delta(log(L)) = 62.9639 Iteration 1 took 0.4s --- Iterative MLGST: Iter 2 of 5 168 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 141.38 (168 data params - 31 model params = expected mean of 137; p-value = 0.38131) Completed in 0.3s 2*Delta(log(L)) = 141.59 Iteration 2 took 0.4s --- Iterative MLGST: Iter 3 of 5 450 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 417.084 (450 data params - 31 model params = expected mean of 419; p-value = 0.517254) Completed in 0.9s 2*Delta(log(L)) = 417.095 Iteration 3 took 1.0s --- Iterative MLGST: Iter 4 of 5 862 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 870.4 (862 data params - 31 model params = expected mean of 831; p-value = 0.166552) Completed in 1.2s 2*Delta(log(L)) = 870.82 Iteration 4 took 1.4s --- Iterative MLGST: Iter 5 of 5 1282 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 1245.19 (1282 data params - 31 model params = expected mean of 1251; p-value = 0.540991) Completed in 2.1s 2*Delta(log(L)) = 1245.74 Iteration 5 took 2.5s Switching to ML objective (last iteration) --- MLGST --- Maximum log(L) = 622.828 below upper bound of -2.13648e+06 2*Delta(log(L)) = 1245.66 (1282 data params - 31 model params = expected mean of 1251; p-value = 0.537301) Completed in 6.6s 2*Delta(log(L)) = 1245.66 Final MLGST took 6.6s Iterative MLGST Total Time: 12.3s Running MLGST Iteration 2 --- Circuit Creation --- 1282 sequences created Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing --- LGST --- Singular values of I_tilde (truncating to first 4 of 6) = 4.244707863399396 1.1537403437788096 0.9521888844551547 0.9084465475528515 0.03371022411959681 0.02563577347463864 Singular values of target I_tilde (truncating to first 4 of 6) = 4.244164062089174 1.169453419312999 0.9475116980891475 0.9403516426340927 2.709096598579531e-16 1.7684881472925075e-16 --- Iterative MLGST: Iter 1 of 5 92 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 48.434 (92 data params - 31 model params = expected mean of 61; p-value = 0.878044) Completed in 0.4s 2*Delta(log(L)) = 48.3704 Iteration 1 took 0.4s --- Iterative MLGST: Iter 2 of 5 168 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 122.032 (168 data params - 31 model params = expected mean of 137; p-value = 0.815624) Completed in 0.4s 2*Delta(log(L)) = 122.378 Iteration 2 took 0.5s --- Iterative MLGST: Iter 3 of 5 450 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 419.72 (450 data params - 31 model params = expected mean of 419; p-value = 0.480909) Completed in 0.8s 2*Delta(log(L)) = 420.806 Iteration 3 took 1.0s --- Iterative MLGST: Iter 4 of 5 862 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 845.378 (862 data params - 31 model params = expected mean of 831; p-value = 0.356808) Completed in 1.3s 2*Delta(log(L)) = 847.099 Iteration 4 took 1.5s --- Iterative MLGST: Iter 5 of 5 1282 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 1301.32 (1282 data params - 31 model params = expected mean of 1251; p-value = 0.157176) Completed in 2.0s 2*Delta(log(L)) = 1303.25 Iteration 5 took 2.4s Switching to ML objective (last iteration) --- MLGST --- Maximum log(L) = 651.59 below upper bound of -2.13642e+06 2*Delta(log(L)) = 1303.18 (1282 data params - 31 model params = expected mean of 1251; p-value = 0.148633) Completed in 5.5s 2*Delta(log(L)) = 1303.18 Final MLGST took 5.5s Iterative MLGST Total Time: 11.3s Running MLGST Iteration 3 --- Circuit Creation --- 1282 sequences created Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing --- LGST --- Singular values of I_tilde (truncating to first 4 of 6) = 4.244050277155162 1.2124619829658454 0.9762089809043478 0.9203172425509635 0.03313244495774025 0.02235228395337996 Singular values of target I_tilde (truncating to first 4 of 6) = 4.244164062089174 1.169453419312999 0.9475116980891475 0.9403516426340927 2.709096598579531e-16 1.7684881472925075e-16 --- Iterative MLGST: Iter 1 of 5 92 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 63.0797 (92 data params - 31 model params = expected mean of 61; p-value = 0.402678) Completed in 0.3s 2*Delta(log(L)) = 63.7862 Iteration 1 took 0.4s --- Iterative MLGST: Iter 2 of 5 168 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 135.696 (168 data params - 31 model params = expected mean of 137; p-value = 0.515429) Completed in 0.3s 2*Delta(log(L)) = 136.6 Iteration 2 took 0.4s --- Iterative MLGST: Iter 3 of 5 450 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 417.539 (450 data params - 31 model params = expected mean of 419; p-value = 0.510963) Completed in 0.7s 2*Delta(log(L)) = 418.44 Iteration 3 took 0.9s --- Iterative MLGST: Iter 4 of 5 862 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 805.317 (862 data params - 31 model params = expected mean of 831; p-value = 0.732436) Completed in 1.0s 2*Delta(log(L)) = 806.567 Iteration 4 took 1.3s --- Iterative MLGST: Iter 5 of 5 1282 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 1185.16 (1282 data params - 31 model params = expected mean of 1251; p-value = 0.907703) Completed in 1.7s 2*Delta(log(L)) = 1186.39 Iteration 5 took 2.1s Switching to ML objective (last iteration) --- MLGST --- Maximum log(L) = 593.158 below upper bound of -2.1362e+06 2*Delta(log(L)) = 1186.32 (1282 data params - 31 model params = expected mean of 1251; p-value = 0.90367) Completed in 1.4s 2*Delta(log(L)) = 1186.32 Final MLGST took 1.4s Iterative MLGST Total Time: 6.4s Running MLGST Iteration 4 --- Circuit Creation --- 1282 sequences created Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing --- LGST --- Singular values of I_tilde (truncating to first 4 of 6) = 4.24484375709879 1.1649382938018655 0.9568638742519098 0.9031869835559561 0.033200958666622024 0.017284232230193083 Singular values of target I_tilde (truncating to first 4 of 6) = 4.244164062089174 1.169453419312999 0.9475116980891475 0.9403516426340927 2.709096598579531e-16 1.7684881472925075e-16 --- Iterative MLGST: Iter 1 of 5 92 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 56.7701 (92 data params - 31 model params = expected mean of 61; p-value = 0.629839) Completed in 0.3s 2*Delta(log(L)) = 56.8667 Iteration 1 took 0.4s --- Iterative MLGST: Iter 2 of 5 168 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 130.755 (168 data params - 31 model params = expected mean of 137; p-value = 0.634092) Completed in 0.3s 2*Delta(log(L)) = 131.182 Iteration 2 took 0.4s --- Iterative MLGST: Iter 3 of 5 450 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 442.102 (450 data params - 31 model params = expected mean of 419; p-value = 0.209906) Completed in 0.7s 2*Delta(log(L)) = 442.695 Iteration 3 took 0.8s --- Iterative MLGST: Iter 4 of 5 862 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 888.55 (862 data params - 31 model params = expected mean of 831; p-value = 0.0812685) Completed in 1.3s 2*Delta(log(L)) = 889.66 Iteration 4 took 1.6s --- Iterative MLGST: Iter 5 of 5 1282 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 1313.66 (1282 data params - 31 model params = expected mean of 1251; p-value = 0.106446) Completed in 1.7s 2*Delta(log(L)) = 1314.88 Iteration 5 took 2.1s Switching to ML objective (last iteration) --- MLGST --- Maximum log(L) = 657.405 below upper bound of -2.1359e+06 2*Delta(log(L)) = 1314.81 (1282 data params - 31 model params = expected mean of 1251; p-value = 0.102417) Completed in 4.8s 2*Delta(log(L)) = 1314.81 Final MLGST took 4.9s Iterative MLGST Total Time: 10.1s Running MLGST Iteration 5 --- Circuit Creation --- 1282 sequences created Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing --- LGST --- Singular values of I_tilde (truncating to first 4 of 6) = 4.244643403566763 1.1562039604688137 0.9496844028666662 0.9318264748631984 0.07270157916508631 0.008013391048464916 Singular values of target I_tilde (truncating to first 4 of 6) = 4.244164062089174 1.169453419312999 0.9475116980891475 0.9403516426340927 2.709096598579531e-16 1.7684881472925075e-16 --- Iterative MLGST: Iter 1 of 5 92 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 46.2692 (92 data params - 31 model params = expected mean of 61; p-value = 0.918875) Completed in 0.4s 2*Delta(log(L)) = 46.4106 Iteration 1 took 0.5s --- Iterative MLGST: Iter 2 of 5 168 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 98.0874 (168 data params - 31 model params = expected mean of 137; p-value = 0.995035) Completed in 0.3s 2*Delta(log(L)) = 98.0483 Iteration 2 took 0.4s --- Iterative MLGST: Iter 3 of 5 450 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 414.136 (450 data params - 31 model params = expected mean of 419; p-value = 0.557892) Completed in 0.8s 2*Delta(log(L)) = 414.601 Iteration 3 took 1.0s --- Iterative MLGST: Iter 4 of 5 862 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 807.782 (862 data params - 31 model params = expected mean of 831; p-value = 0.711756) Completed in 1.3s 2*Delta(log(L)) = 808.505 Iteration 4 took 1.6s --- Iterative MLGST: Iter 5 of 5 1282 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 1206.65 (1282 data params - 31 model params = expected mean of 1251; p-value = 0.811649) Completed in 1.9s 2*Delta(log(L)) = 1207.53 Iteration 5 took 2.2s Switching to ML objective (last iteration) --- MLGST --- Maximum log(L) = 603.738 below upper bound of -2.13676e+06 2*Delta(log(L)) = 1207.48 (1282 data params - 31 model params = expected mean of 1251; p-value = 0.80705) Completed in 4.7s 2*Delta(log(L)) = 1207.48 Final MLGST took 4.8s Iterative MLGST Total Time: 10.4s Running MLGST Iteration 6 --- Circuit Creation --- 1282 sequences created Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing --- LGST --- Singular values of I_tilde (truncating to first 4 of 6) = 4.243488108495374 1.165012987691403 0.9474366699518069 0.9203189657954223 0.04090095083314043 0.0070200724732477505 Singular values of target I_tilde (truncating to first 4 of 6) = 4.244164062089174 1.169453419312999 0.9475116980891475 0.9403516426340927 2.709096598579531e-16 1.7684881472925075e-16 --- Iterative MLGST: Iter 1 of 5 92 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 72.5965 (92 data params - 31 model params = expected mean of 61; p-value = 0.146998) Completed in 0.4s 2*Delta(log(L)) = 72.4835 Iteration 1 took 0.4s --- Iterative MLGST: Iter 2 of 5 168 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 148.693 (168 data params - 31 model params = expected mean of 137; p-value = 0.23353) Completed in 0.5s 2*Delta(log(L)) = 148.773 Iteration 2 took 0.6s --- Iterative MLGST: Iter 3 of 5 450 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 435.476 (450 data params - 31 model params = expected mean of 419; p-value = 0.279334) Completed in 0.7s 2*Delta(log(L)) = 435.899 Iteration 3 took 0.8s --- Iterative MLGST: Iter 4 of 5 862 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 867.184 (862 data params - 31 model params = expected mean of 831; p-value = 0.186384) Completed in 1.1s 2*Delta(log(L)) = 868.062 Iteration 4 took 1.3s --- Iterative MLGST: Iter 5 of 5 1282 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 1278.84 (1282 data params - 31 model params = expected mean of 1251; p-value = 0.285778) Completed in 1.8s 2*Delta(log(L)) = 1279.9 Iteration 5 took 2.1s Switching to ML objective (last iteration) --- MLGST --- Maximum log(L) = 639.908 below upper bound of -2.13566e+06 2*Delta(log(L)) = 1279.82 (1282 data params - 31 model params = expected mean of 1251; p-value = 0.27927) Completed in 5.8s 2*Delta(log(L)) = 1279.82 Final MLGST took 5.8s Iterative MLGST Total Time: 11.0s Running MLGST Iteration 7 --- Circuit Creation --- 1282 sequences created Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing --- LGST --- Singular values of I_tilde (truncating to first 4 of 6) = 4.244825840755222 1.1607854217596698 0.9292803921438999 0.8958478552912302 0.03648710217525403 0.005481843557321346 Singular values of target I_tilde (truncating to first 4 of 6) = 4.244164062089174 1.169453419312999 0.9475116980891475 0.9403516426340927 2.709096598579531e-16 1.7684881472925075e-16 --- Iterative MLGST: Iter 1 of 5 92 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 61.4652 (92 data params - 31 model params = expected mean of 61; p-value = 0.45923) Completed in 0.4s 2*Delta(log(L)) = 61.3186 Iteration 1 took 0.4s --- Iterative MLGST: Iter 2 of 5 168 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 126.314 (168 data params - 31 model params = expected mean of 137; p-value = 0.733237) Completed in 0.3s 2*Delta(log(L)) = 126.31 Iteration 2 took 0.4s --- Iterative MLGST: Iter 3 of 5 450 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 408.23 (450 data params - 31 model params = expected mean of 419; p-value = 0.637659) Completed in 0.7s 2*Delta(log(L)) = 408.489 Iteration 3 took 0.9s --- Iterative MLGST: Iter 4 of 5 862 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 846.207 (862 data params - 31 model params = expected mean of 831; p-value = 0.349347) Completed in 1.2s 2*Delta(log(L)) = 846.906 Iteration 4 took 1.4s --- Iterative MLGST: Iter 5 of 5 1282 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 1204.55 (1282 data params - 31 model params = expected mean of 1251; p-value = 0.823037) Completed in 1.8s 2*Delta(log(L)) = 1205.22 Iteration 5 took 2.1s Switching to ML objective (last iteration) --- MLGST --- Maximum log(L) = 602.585 below upper bound of -2.13604e+06 2*Delta(log(L)) = 1205.17 (1282 data params - 31 model params = expected mean of 1251; p-value = 0.819723) Completed in 4.0s 2*Delta(log(L)) = 1205.17 Final MLGST took 4.0s Iterative MLGST Total Time: 9.3s Running MLGST Iteration 8 --- Circuit Creation --- 1282 sequences created Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing --- LGST --- Singular values of I_tilde (truncating to first 4 of 6) = 4.244918327291839 1.1497175414386247 0.9499958939687557 0.8863416645506449 0.03990669419647161 0.028278621122238244 Singular values of target I_tilde (truncating to first 4 of 6) = 4.244164062089174 1.169453419312999 0.9475116980891475 0.9403516426340927 2.709096598579531e-16 1.7684881472925075e-16 --- Iterative MLGST: Iter 1 of 5 92 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 38.1221 (92 data params - 31 model params = expected mean of 61; p-value = 0.99049) Completed in 0.5s 2*Delta(log(L)) = 38.2328 Iteration 1 took 0.5s --- Iterative MLGST: Iter 2 of 5 168 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 117.187 (168 data params - 31 model params = expected mean of 137; p-value = 0.888629) Completed in 0.3s 2*Delta(log(L)) = 117.364 Iteration 2 took 0.4s --- Iterative MLGST: Iter 3 of 5 450 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 397.889 (450 data params - 31 model params = expected mean of 419; p-value = 0.763857) Completed in 0.7s 2*Delta(log(L)) = 398.011 Iteration 3 took 0.8s --- Iterative MLGST: Iter 4 of 5 862 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 771.555 (862 data params - 31 model params = expected mean of 831; p-value = 0.930295) Completed in 1.1s 2*Delta(log(L)) = 772.308 Iteration 4 took 1.3s --- Iterative MLGST: Iter 5 of 5 1282 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 1147.5 (1282 data params - 31 model params = expected mean of 1251; p-value = 0.982818) Completed in 1.8s 2*Delta(log(L)) = 1148.41 Iteration 5 took 2.2s Switching to ML objective (last iteration) --- MLGST --- Maximum log(L) = 574.173 below upper bound of -2.13653e+06 2*Delta(log(L)) = 1148.35 (1282 data params - 31 model params = expected mean of 1251; p-value = 0.982039) Completed in 1.4s 2*Delta(log(L)) = 1148.35 Final MLGST took 1.4s Iterative MLGST Total Time: 6.6s Running MLGST Iteration 9 --- Circuit Creation --- 1282 sequences created Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing --- LGST --- Singular values of I_tilde (truncating to first 4 of 6) = 4.244329086925476 1.170786859388005 0.9552770215877492 0.9397649029334779 0.030389543292175643 0.017057158675289986 Singular values of target I_tilde (truncating to first 4 of 6) = 4.244164062089174 1.169453419312999 0.9475116980891475 0.9403516426340927 2.709096598579531e-16 1.7684881472925075e-16 --- Iterative MLGST: Iter 1 of 5 92 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 45.9565 (92 data params - 31 model params = expected mean of 61; p-value = 0.923886) Completed in 0.4s 2*Delta(log(L)) = 46.0754 Iteration 1 took 0.5s --- Iterative MLGST: Iter 2 of 5 168 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 112.293 (168 data params - 31 model params = expected mean of 137; p-value = 0.939692) Completed in 0.3s 2*Delta(log(L)) = 112.386 Iteration 2 took 0.4s --- Iterative MLGST: Iter 3 of 5 450 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 400.962 (450 data params - 31 model params = expected mean of 419; p-value = 0.728788) Completed in 0.6s 2*Delta(log(L)) = 400.815 Iteration 3 took 0.8s --- Iterative MLGST: Iter 4 of 5 862 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 835.78 (862 data params - 31 model params = expected mean of 831; p-value = 0.446954) Completed in 1.3s 2*Delta(log(L)) = 836.156 Iteration 4 took 1.5s --- Iterative MLGST: Iter 5 of 5 1282 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 1205.73 (1282 data params - 31 model params = expected mean of 1251; p-value = 0.816695) Completed in 1.7s 2*Delta(log(L)) = 1205.95 Iteration 5 took 2.1s Switching to ML objective (last iteration) --- MLGST --- Maximum log(L) = 602.944 below upper bound of -2.13618e+06 2*Delta(log(L)) = 1205.89 (1282 data params - 31 model params = expected mean of 1251; p-value = 0.815828) Completed in 4.8s 2*Delta(log(L)) = 1205.89 Final MLGST took 4.8s Iterative MLGST Total Time: 10.0s
gauge_opt_pboot_models = pygsti.drivers.gauge_optimize_model_list(param_boot_models, estimated_model,
plot=False) #plotting support removed w/matplotlib
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_model(gauge_opt_pboot_models, estimated_model)
pboot_std = pygsti.drivers.to_std_model(gauge_opt_pboot_models, estimated_model)
#Summary of the error bars
print("Parametric bootstrapped error bars, with", numGatesets, "resamples\n")
print("Error in rho vec:")
print(pboot_std['rho0'], end='\n\n')
print("Error in effect vecs:")
print(pboot_std['Mdefault'], end='\n\n')
print("Error in Gi:")
print(pboot_std['Gi'], end='\n\n')
print("Error in Gx:")
print(pboot_std['Gx'], end='\n\n')
print("Error in Gy:")
print(pboot_std['Gy'])
Parametric bootstrapped error bars, with 10 resamples Error in rho vec: TPSPAMVec with dimension 4 0.71 0 0 0 Error in effect vecs: TPPOVM with effect vectors: 0: FullSPAMVec with dimension 4 0 0 0 0 1: ComplementSPAMVec with dimension 4 1.41 0 0 0 Error in Gi: TPDenseOp with shape (4, 4) 1.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Error in Gx: TPDenseOp with shape (4, 4) 1.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Error in Gy: TPDenseOp with shape (4, 4) 1.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Here we do non-parametric bootstrapping, as indicated by the 'nonparametric' argument below. The output is again eventually stored in the "mean" and "std" Models, which hold the mean and standard deviation values of the set of bootstrapped models (after gauge optimization). It is this latter "standard deviation Model" 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 & models made for bootstrapping purposes.
# For good statistics, should probably be greater than 10.
numModels=10
nonparam_boot_models = pygsti.drivers.make_bootstrap_models(
numModels, ds, 'nonparametric', prep_fiducials, meas_fiducials, germs, maxLengths,
targetModel=estimated_model, startSeed=0, 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 Models: Running MLGST Iteration 0 --- Circuit Creation --- 1282 sequences created Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing --- LGST --- Singular values of I_tilde (truncating to first 4 of 6) = 4.244845695931912 1.180285364189147 0.9862995636431281 0.902101822920102 0.09233562824970798 0.06946279872379223 Singular values of target I_tilde (truncating to first 4 of 6) = 4.244164062089174 1.169453419312999 0.9475116980891475 0.9403516426340927 2.709096598579531e-16 1.7684881472925075e-16 --- Iterative MLGST: Iter 1 of 5 92 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 163.213 (92 data params - 31 model params = expected mean of 61; p-value = 2.89595e-11) Completed in 0.4s 2*Delta(log(L)) = 163.979 Iteration 1 took 0.5s --- Iterative MLGST: Iter 2 of 5 168 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 366.335 (168 data params - 31 model params = expected mean of 137; p-value = 0) Completed in 0.6s 2*Delta(log(L)) = 367.229 Iteration 2 took 0.7s --- Iterative MLGST: Iter 3 of 5 450 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 1002.45 (450 data params - 31 model params = expected mean of 419; p-value = 0) Completed in 0.7s 2*Delta(log(L)) = 1004.83 Iteration 3 took 0.9s --- Iterative MLGST: Iter 4 of 5 862 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 1811.85 (862 data params - 31 model params = expected mean of 831; p-value = 0) Completed in 1.3s 2*Delta(log(L)) = 1815.26 Iteration 4 took 1.5s --- Iterative MLGST: Iter 5 of 5 1282 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 2698.48 (1282 data params - 31 model params = expected mean of 1251; p-value = 0) Completed in 1.8s 2*Delta(log(L)) = 2701.78 Iteration 5 took 2.2s Switching to ML objective (last iteration) --- MLGST --- Maximum log(L) = 1350.7 below upper bound of -2.13485e+06 2*Delta(log(L)) = 2701.4 (1282 data params - 31 model params = expected mean of 1251; p-value = 0) Completed in 1.4s 2*Delta(log(L)) = 2701.4 Final MLGST took 1.4s Iterative MLGST Total Time: 7.0s Running MLGST Iteration 1 --- Circuit Creation --- 1282 sequences created Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing --- LGST --- Singular values of I_tilde (truncating to first 4 of 6) = 4.244188636580856 1.1517827075400349 0.9655135770562866 0.9082976321749557 0.04860263960205439 0.02186639107735652 Singular values of target I_tilde (truncating to first 4 of 6) = 4.244164062089174 1.169453419312999 0.9475116980891475 0.9403516426340927 2.709096598579531e-16 1.7684881472925075e-16 --- Iterative MLGST: Iter 1 of 5 92 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 146.601 (92 data params - 31 model params = expected mean of 61; p-value = 5.25726e-09) Completed in 0.3s 2*Delta(log(L)) = 147.869 Iteration 1 took 0.4s --- Iterative MLGST: Iter 2 of 5 168 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 274.874 (168 data params - 31 model params = expected mean of 137; p-value = 2.78093e-11) Completed in 0.3s 2*Delta(log(L)) = 276.479 Iteration 2 took 0.4s --- Iterative MLGST: Iter 3 of 5 450 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 861.635 (450 data params - 31 model params = expected mean of 419; p-value = 0) Completed in 0.8s 2*Delta(log(L)) = 864.309 Iteration 3 took 0.9s --- Iterative MLGST: Iter 4 of 5 862 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 1662.57 (862 data params - 31 model params = expected mean of 831; p-value = 0) Completed in 1.1s 2*Delta(log(L)) = 1664.8 Iteration 4 took 1.4s --- Iterative MLGST: Iter 5 of 5 1282 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 2456.71 (1282 data params - 31 model params = expected mean of 1251; p-value = 0) Completed in 2.8s 2*Delta(log(L)) = 2459.77 Iteration 5 took 3.1s Switching to ML objective (last iteration) --- MLGST --- Maximum log(L) = 1229.73 below upper bound of -2.13563e+06 2*Delta(log(L)) = 2459.47 (1282 data params - 31 model params = expected mean of 1251; p-value = 0) Completed in 1.7s 2*Delta(log(L)) = 2459.47 Final MLGST took 1.7s Iterative MLGST Total Time: 7.8s Running MLGST Iteration 2 --- Circuit Creation --- 1282 sequences created Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing --- LGST --- Singular values of I_tilde (truncating to first 4 of 6) = 4.2448073300699045 1.141572198045367 0.9828516150265091 0.8821924040403455 0.03264139759550893 0.018800305608607182 Singular values of target I_tilde (truncating to first 4 of 6) = 4.244164062089174 1.169453419312999 0.9475116980891475 0.9403516426340927 2.709096598579531e-16 1.7684881472925075e-16 --- Iterative MLGST: Iter 1 of 5 92 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 152.32 (92 data params - 31 model params = expected mean of 61; p-value = 9.10147e-10) Completed in 0.4s 2*Delta(log(L)) = 152.971 Iteration 1 took 0.4s --- Iterative MLGST: Iter 2 of 5 168 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 298.087 (168 data params - 31 model params = expected mean of 137; p-value = 5.62883e-14) Completed in 0.3s 2*Delta(log(L)) = 299.453 Iteration 2 took 0.5s --- Iterative MLGST: Iter 3 of 5 450 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 937.718 (450 data params - 31 model params = expected mean of 419; p-value = 0) Completed in 0.7s 2*Delta(log(L)) = 941.677 Iteration 3 took 0.8s --- Iterative MLGST: Iter 4 of 5 862 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 1719.38 (862 data params - 31 model params = expected mean of 831; p-value = 0) Completed in 1.3s 2*Delta(log(L)) = 1724.64 Iteration 4 took 1.6s --- Iterative MLGST: Iter 5 of 5 1282 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 2633.13 (1282 data params - 31 model params = expected mean of 1251; p-value = 0) Completed in 1.7s 2*Delta(log(L)) = 2639.19 Iteration 5 took 2.0s Switching to ML objective (last iteration) --- MLGST --- Maximum log(L) = 1319.4 below upper bound of -2.13523e+06 2*Delta(log(L)) = 2638.8 (1282 data params - 31 model params = expected mean of 1251; p-value = 0) Completed in 1.4s 2*Delta(log(L)) = 2638.8 Final MLGST took 1.4s Iterative MLGST Total Time: 6.7s Running MLGST Iteration 3 --- Circuit Creation --- 1282 sequences created Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing --- LGST --- Singular values of I_tilde (truncating to first 4 of 6) = 4.243897328409793 1.2017515643930934 0.9736351960551161 0.9362239850082709 0.029479066656238114 0.006692004333867255 Singular values of target I_tilde (truncating to first 4 of 6) = 4.244164062089174 1.169453419312999 0.9475116980891475 0.9403516426340927 2.709096598579531e-16 1.7684881472925075e-16 --- Iterative MLGST: Iter 1 of 5 92 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 174.837 (92 data params - 31 model params = expected mean of 61; p-value = 6.36491e-13) Completed in 0.3s 2*Delta(log(L)) = 175.493 Iteration 1 took 0.4s --- Iterative MLGST: Iter 2 of 5 168 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 325.315 (168 data params - 31 model params = expected mean of 137; p-value = 0) Completed in 0.4s 2*Delta(log(L)) = 326.067 Iteration 2 took 0.4s --- Iterative MLGST: Iter 3 of 5 450 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 858.545 (450 data params - 31 model params = expected mean of 419; p-value = 0) Completed in 0.7s 2*Delta(log(L)) = 859.868 Iteration 3 took 0.8s --- Iterative MLGST: Iter 4 of 5 862 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 1692.02 (862 data params - 31 model params = expected mean of 831; p-value = 0) Completed in 1.3s 2*Delta(log(L)) = 1694.63 Iteration 4 took 1.8s --- Iterative MLGST: Iter 5 of 5 1282 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 2494.42 (1282 data params - 31 model params = expected mean of 1251; p-value = 0) Completed in 2.2s 2*Delta(log(L)) = 2497.55 Iteration 5 took 2.6s Switching to ML objective (last iteration) --- MLGST --- Maximum log(L) = 1248.61 below upper bound of -2.13547e+06 2*Delta(log(L)) = 2497.23 (1282 data params - 31 model params = expected mean of 1251; p-value = 0) Completed in 1.5s 2*Delta(log(L)) = 2497.23 Final MLGST took 1.5s Iterative MLGST Total Time: 7.5s Running MLGST Iteration 4 --- Circuit Creation --- 1282 sequences created Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing --- LGST --- Singular values of I_tilde (truncating to first 4 of 6) = 4.246202328766042 1.1520853452470667 0.9764545650798362 0.9066489771225429 0.07354357830082349 0.019302775885633176 Singular values of target I_tilde (truncating to first 4 of 6) = 4.244164062089174 1.169453419312999 0.9475116980891475 0.9403516426340927 2.709096598579531e-16 1.7684881472925075e-16 --- Iterative MLGST: Iter 1 of 5 92 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 176.392 (92 data params - 31 model params = expected mean of 61; p-value = 3.78142e-13) Completed in 0.3s 2*Delta(log(L)) = 177.609 Iteration 1 took 0.4s --- Iterative MLGST: Iter 2 of 5 168 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 316.436 (168 data params - 31 model params = expected mean of 137; p-value = 3.33067e-16) Completed in 0.3s 2*Delta(log(L)) = 318.349 Iteration 2 took 0.4s --- Iterative MLGST: Iter 3 of 5 450 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 913.377 (450 data params - 31 model params = expected mean of 419; p-value = 0) Completed in 0.7s 2*Delta(log(L)) = 915.855 Iteration 3 took 0.8s --- Iterative MLGST: Iter 4 of 5 862 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 1743.39 (862 data params - 31 model params = expected mean of 831; p-value = 0) Completed in 1.3s 2*Delta(log(L)) = 1746.68 Iteration 4 took 1.5s --- Iterative MLGST: Iter 5 of 5 1282 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 2606.38 (1282 data params - 31 model params = expected mean of 1251; p-value = 0) Completed in 1.7s 2*Delta(log(L)) = 2610.2 Iteration 5 took 2.0s Switching to ML objective (last iteration) --- MLGST --- Maximum log(L) = 1304.96 below upper bound of -2.13509e+06 2*Delta(log(L)) = 2609.92 (1282 data params - 31 model params = expected mean of 1251; p-value = 0) Completed in 3.5s 2*Delta(log(L)) = 2609.92 Final MLGST took 3.5s Iterative MLGST Total Time: 8.6s Running MLGST Iteration 5 --- Circuit Creation --- 1282 sequences created Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing --- LGST --- Singular values of I_tilde (truncating to first 4 of 6) = 4.244598260247877 1.1437330330943303 0.9616678165967568 0.9507864730743012 0.032108008334019424 0.01837190929970882 Singular values of target I_tilde (truncating to first 4 of 6) = 4.244164062089174 1.169453419312999 0.9475116980891475 0.9403516426340927 2.709096598579531e-16 1.7684881472925075e-16 --- Iterative MLGST: Iter 1 of 5 92 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 116.694 (92 data params - 31 model params = expected mean of 61; p-value = 2.32753e-05) Completed in 0.3s 2*Delta(log(L)) = 117.694 Iteration 1 took 0.4s --- Iterative MLGST: Iter 2 of 5 168 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 249.287 (168 data params - 31 model params = expected mean of 137; p-value = 1.50925e-08) Completed in 0.4s 2*Delta(log(L)) = 250.142 Iteration 2 took 0.5s --- Iterative MLGST: Iter 3 of 5 450 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 884.985 (450 data params - 31 model params = expected mean of 419; p-value = 0) Completed in 0.9s 2*Delta(log(L)) = 888.74 Iteration 3 took 1.0s --- Iterative MLGST: Iter 4 of 5 862 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 1681.69 (862 data params - 31 model params = expected mean of 831; p-value = 0) Completed in 1.3s 2*Delta(log(L)) = 1685.49 Iteration 4 took 1.5s --- Iterative MLGST: Iter 5 of 5 1282 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 2479.15 (1282 data params - 31 model params = expected mean of 1251; p-value = 0) Completed in 2.1s 2*Delta(log(L)) = 2483.66 Iteration 5 took 2.5s Switching to ML objective (last iteration) --- MLGST --- Maximum log(L) = 1241.68 below upper bound of -2.13534e+06 2*Delta(log(L)) = 2483.36 (1282 data params - 31 model params = expected mean of 1251; p-value = 0) Completed in 2.1s 2*Delta(log(L)) = 2483.36 Final MLGST took 2.1s Iterative MLGST Total Time: 8.0s Running MLGST Iteration 6 --- Circuit Creation --- 1282 sequences created Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing --- LGST --- Singular values of I_tilde (truncating to first 4 of 6) = 4.244215220611 1.1794071130858117 0.9621288682814436 0.9237222775504998 0.03227630273126832 0.017188885795577733 Singular values of target I_tilde (truncating to first 4 of 6) = 4.244164062089174 1.169453419312999 0.9475116980891475 0.9403516426340927 2.709096598579531e-16 1.7684881472925075e-16 --- Iterative MLGST: Iter 1 of 5 92 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 160.089 (92 data params - 31 model params = expected mean of 61; p-value = 7.8896e-11) Completed in 0.3s 2*Delta(log(L)) = 160.35 Iteration 1 took 0.3s --- Iterative MLGST: Iter 2 of 5 168 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 321.056 (168 data params - 31 model params = expected mean of 137; p-value = 1.11022e-16) Completed in 0.4s 2*Delta(log(L)) = 321.985 Iteration 2 took 0.5s --- Iterative MLGST: Iter 3 of 5 450 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 907.37 (450 data params - 31 model params = expected mean of 419; p-value = 0) Completed in 0.7s 2*Delta(log(L)) = 908.307 Iteration 3 took 0.9s --- Iterative MLGST: Iter 4 of 5 862 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 1832.64 (862 data params - 31 model params = expected mean of 831; p-value = 0) Completed in 1.4s 2*Delta(log(L)) = 1836.11 Iteration 4 took 1.7s --- Iterative MLGST: Iter 5 of 5 1282 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 2766.72 (1282 data params - 31 model params = expected mean of 1251; p-value = 0) Completed in 1.9s 2*Delta(log(L)) = 2771.52 Iteration 5 took 2.3s Switching to ML objective (last iteration) --- MLGST --- Maximum log(L) = 1385.58 below upper bound of -2.13458e+06 2*Delta(log(L)) = 2771.16 (1282 data params - 31 model params = expected mean of 1251; p-value = 0) Completed in 1.3s 2*Delta(log(L)) = 2771.16 Final MLGST took 1.3s Iterative MLGST Total Time: 7.0s Running MLGST Iteration 7 --- Circuit Creation --- 1282 sequences created Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing --- LGST --- Singular values of I_tilde (truncating to first 4 of 6) = 4.244815425123308 1.149149730793523 0.9449066135785853 0.8893549404955351 0.05783633057230394 0.03235959131326644 Singular values of target I_tilde (truncating to first 4 of 6) = 4.244164062089174 1.169453419312999 0.9475116980891475 0.9403516426340927 2.709096598579531e-16 1.7684881472925075e-16 --- Iterative MLGST: Iter 1 of 5 92 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 186.944 (92 data params - 31 model params = expected mean of 61; p-value = 1.04361e-14) Completed in 0.3s 2*Delta(log(L)) = 187.248 Iteration 1 took 0.4s --- Iterative MLGST: Iter 2 of 5 168 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 361.082 (168 data params - 31 model params = expected mean of 137; p-value = 0) Completed in 0.4s 2*Delta(log(L)) = 361.613 Iteration 2 took 0.5s --- Iterative MLGST: Iter 3 of 5 450 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 916.064 (450 data params - 31 model params = expected mean of 419; p-value = 0) Completed in 0.8s 2*Delta(log(L)) = 918.454 Iteration 3 took 0.9s --- Iterative MLGST: Iter 4 of 5 862 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 1693.04 (862 data params - 31 model params = expected mean of 831; p-value = 0) Completed in 1.4s 2*Delta(log(L)) = 1696.61 Iteration 4 took 1.6s --- Iterative MLGST: Iter 5 of 5 1282 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 2570.75 (1282 data params - 31 model params = expected mean of 1251; p-value = 0) Completed in 1.8s 2*Delta(log(L)) = 2575.11 Iteration 5 took 2.2s Switching to ML objective (last iteration) --- MLGST --- Maximum log(L) = 1287.42 below upper bound of -2.13547e+06 2*Delta(log(L)) = 2574.84 (1282 data params - 31 model params = expected mean of 1251; p-value = 0) Completed in 5.7s 2*Delta(log(L)) = 2574.84 Final MLGST took 5.7s Iterative MLGST Total Time: 11.4s Running MLGST Iteration 8 --- Circuit Creation --- 1282 sequences created Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing --- LGST --- Singular values of I_tilde (truncating to first 4 of 6) = 4.244035041550426 1.1358903361549433 0.9427163127298118 0.9110426801402571 0.09879829799276398 0.02505584386042377 Singular values of target I_tilde (truncating to first 4 of 6) = 4.244164062089174 1.169453419312999 0.9475116980891475 0.9403516426340927 2.709096598579531e-16 1.7684881472925075e-16 --- Iterative MLGST: Iter 1 of 5 92 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 112.981 (92 data params - 31 model params = expected mean of 61; p-value = 5.91678e-05) Completed in 0.3s 2*Delta(log(L)) = 113.15 Iteration 1 took 0.4s --- Iterative MLGST: Iter 2 of 5 168 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 264.276 (168 data params - 31 model params = expected mean of 137; p-value = 4.06604e-10) Completed in 0.4s 2*Delta(log(L)) = 264.144 Iteration 2 took 0.5s --- Iterative MLGST: Iter 3 of 5 450 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 837.798 (450 data params - 31 model params = expected mean of 419; p-value = 0) Completed in 0.8s 2*Delta(log(L)) = 838.614 Iteration 3 took 1.0s --- Iterative MLGST: Iter 4 of 5 862 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 1605.14 (862 data params - 31 model params = expected mean of 831; p-value = 0) Completed in 1.6s 2*Delta(log(L)) = 1606.16 Iteration 4 took 1.8s --- Iterative MLGST: Iter 5 of 5 1282 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 2494.35 (1282 data params - 31 model params = expected mean of 1251; p-value = 0) Completed in 1.8s 2*Delta(log(L)) = 2496.13 Iteration 5 took 2.1s Switching to ML objective (last iteration) --- MLGST --- Maximum log(L) = 1247.91 below upper bound of -2.13539e+06 2*Delta(log(L)) = 2495.82 (1282 data params - 31 model params = expected mean of 1251; p-value = 0) Completed in 3.3s 2*Delta(log(L)) = 2495.82 Final MLGST took 3.3s Iterative MLGST Total Time: 9.1s Running MLGST Iteration 9 --- Circuit Creation --- 1282 sequences created Dataset has 1282 entries: 1282 utilized, 0 requested sequences were missing --- LGST --- Singular values of I_tilde (truncating to first 4 of 6) = 4.244395806039566 1.1575590718440645 0.9761127108175292 0.9288056665120381 0.07242344826070647 0.02966632169440047 Singular values of target I_tilde (truncating to first 4 of 6) = 4.244164062089174 1.169453419312999 0.9475116980891475 0.9403516426340927 2.709096598579531e-16 1.7684881472925075e-16 --- Iterative MLGST: Iter 1 of 5 92 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 144.031 (92 data params - 31 model params = expected mean of 61; p-value = 1.14063e-08) Completed in 0.3s 2*Delta(log(L)) = 144.887 Iteration 1 took 0.3s --- Iterative MLGST: Iter 2 of 5 168 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 311.047 (168 data params - 31 model params = expected mean of 137; p-value = 1.44329e-15) Completed in 0.4s 2*Delta(log(L)) = 313.029 Iteration 2 took 0.4s --- Iterative MLGST: Iter 3 of 5 450 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 885.685 (450 data params - 31 model params = expected mean of 419; p-value = 0) Completed in 0.7s 2*Delta(log(L)) = 889.834 Iteration 3 took 0.9s --- Iterative MLGST: Iter 4 of 5 862 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 1697.91 (862 data params - 31 model params = expected mean of 831; p-value = 0) Completed in 1.2s 2*Delta(log(L)) = 1702.77 Iteration 4 took 1.4s --- Iterative MLGST: Iter 5 of 5 1282 operation sequences ---: --- Minimum Chi^2 GST --- Sum of Chi^2 = 2511.4 (1282 data params - 31 model params = expected mean of 1251; p-value = 0) Completed in 1.9s 2*Delta(log(L)) = 2516.97 Iteration 5 took 2.2s Switching to ML objective (last iteration) --- MLGST --- Maximum log(L) = 1258.34 below upper bound of -2.13552e+06 2*Delta(log(L)) = 2516.69 (1282 data params - 31 model params = expected mean of 1251; p-value = 0) Completed in 1.6s 2*Delta(log(L)) = 2516.69 Final MLGST took 1.6s Iterative MLGST Total Time: 6.8s
gauge_opt_npboot_models = pygsti.drivers.gauge_optimize_model_list(nonparam_boot_models, estimated_model,
plot=False) #plotting removed w/matplotlib
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_model(gauge_opt_npboot_models, estimated_model)
npboot_std = pygsti.drivers.to_std_model(gauge_opt_npboot_models, estimated_model)
#Summary of the error bars
print("Non-parametric bootstrapped error bars, with", numGatesets, "resamples\n")
print("Error in rho vec:")
print(npboot_std['rho0'], end='\n\n')
print("Error in effect vecs:")
print(npboot_std['Mdefault'], end='\n\n')
print("Error in Gi:")
print(npboot_std['Gi'], end='\n\n')
print("Error in Gx:")
print(npboot_std['Gx'], end='\n\n')
print("Error in Gy:")
print(npboot_std['Gy'])
Non-parametric bootstrapped error bars, with 10 resamples Error in rho vec: TPSPAMVec with dimension 4 0.71 0 0 0 Error in effect vecs: TPPOVM with effect vectors: 0: FullSPAMVec with dimension 4 0 0 0 0 1: ComplementSPAMVec with dimension 4 1.41 0 0 0 Error in Gi: TPDenseOp with shape (4, 4) 1.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Error in Gx: TPDenseOp with shape (4, 4) 1.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Error in Gy: TPDenseOp with shape (4, 4) 1.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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.')
Text(0.5,1,'Scatter plot comparing param vs. non-param bootstrapping error bars.')