Model Violation summary.The aggregate log-likelihood as a function of GST iteration.
%(progressBarPlot)s
Histogram of per-sequence model violation. This histogram shows the distribution of the per-sequence goodness-of-fit values (one count equals one gate sequence).
%(bestEstimateColorHistogram)s
Comparison of GST estimated gates to target gates. This table presents, for each of the gates, three different measures of distance or discrepancy from the GST estimate to the ideal target operation. See text for more detail.
%(bestGatesVsTargetTable_sum)s
Input Summary
Information pertaining to the target gate set and the data set(s).
Target gate set: SPAM (state preparation and measurement). The ideal input state (\rho_0) and `plus' POVM effect E_0 for the device on which we report. SPAM gates are given here as d\times d matrices.
%(targetSpamBriefTable)s
Fiducial sequences. A list of the preparation and measurement fiducial gate sequences. See discussion in text.
%(fiducialListTable)s
Germ sequences. A list of the germ gate sequences. See discussion in text.
%(germList2ColTable)s
General dataset properties. See discussion in text.
%(datasetOverviewTable)s
Target gate set: logic gates. The ideal (generally unitary) logic gates. Each has a name starting with G, and is represented as a d^2\times d^2superoperator that acts by matrix multiplication on vectors in \mathcal{B}(\mathcal{H}). Matrices are displayed using a heat map that ranges between 1.0 (red) and -1.0 (blue).
%(targetGatesBoxTable)s
Model Violation Analysis
Metrics indicating how well the estimated gate set can be trusted -- i.e., how well it fits the data.
Comparison between the computed and expected maximum \log(\mathcal{L}) for different values of L.N_S and N_p are the number of gate strings and parameters, respectively. The quantity 2\Delta\log(\mathcal{L}) measures the goodness of fit of the GST model (small is better) and is expected to lie within [k-\sqrt{2k},k+\sqrt{2k}] where k = N_s-N_p. N_\sigma = (2\Delta\log(\mathcal{L})-k)/\sqrt{2k} is the number of standard deviations from the mean (a p-value can be straightforwardly derived from N_\sigma). The rating from 1 to 5 stars gives a very crude indication of goodness of fit.
%(progressTable)s
Per-sequence model violation. Each point displays the goodness of fit for a single gate sequence.
%(bestEstimateColorScatterPlot)s
%(bestEstimateColorBoxPlotPages)s
%(maxLSwitchboard1)s
2\Delta\log(\mathcal{L}) contributions for every individual experiment in the dataset. Each pixel represents a single experiment (gate sequence), and its color indicates whether GST was able to fit the corresponding frequency well. Shades of white/gray are typical. Red squares represent statistically significant evidence for model violation (non-Markovianity), and should appear with probability at most %(linlg_pcntle)s%% if the data really are Markovian. Square blocks of pixels correspond to base sequences (arranged vertically by germ and horizontally by length); each pixel within a block corresponds to a specific choice of pre- and post-fiducial sequences. See text for further details.
#iftoggle(ShowScaling)
%(dataScalingColorBoxPlot)s
Data scaling factor for every individual experiment in the dataset. Each pixel represents a single experiment (gate sequence), and its color indicates the amount of scaling that was applied to the original data counts when computing the log-likelihood or \chi^2 for this estimate. Values of 1.0 indicate all of the original data was used, whereas numbers between 0 and 1 indicate that the data counts for the experiement were artificially decreased (usually to improve the fit).
#elsetoggle
Note: data-scaling color box figure is not shown because none of the estimates in this report have scaled data.
#endtoggle
Gauge Invariant Outputs
Quantities which are gauge-invariant are the most reliable means of assessing the quality of the gates, as these do not depend on any unphysical gauge degrees of freedom
Eigenvalues of estimated gates and germs. The spectrum (Eigenvalues column) of each estimated gate and estimated germ.
%(bestGatesetEvalTable)s
Gram Matrix Eigenvales.Compares the eigenvalues of the data-derived Gram matrix with those of a Gram matrix computed using the target gates.
%(gramBarPlot)s
Gauge Variant Outputs
The raw estimated gate set, and then some useful derived quantities. These quanties are gauge-dependent, meaning they will depend on unphysical gauge degrees of freedom that are a necessary byproduct of estimating an entire gate set at once (akin to a freedom of reference frame). After finding a best-estimate based on the (physical) data, GST optimizes within the space of all (unphysical) gauge degrees of freedom using the parameters in Table .
Gauge Optimization Details. A list of the parameters used when performing the gauge optimization that produced the final GST results found in subsequent tables and figures.
%(bestGatesetGaugeOptParamsTable)s
The GST estimate of the SPAM operations. Compares the estimated SPAM operations to those desired (repeated from Table for convenience.
%(bestGatesetSpamBriefTable)s
GST estimate of SPAM probabilities. Computed by taking the dot products of vectors in Table . The symbol E_C, when it appears, refers to the complement effect given by subtracting each of the other effects from the identity.
%(bestGatesetSpamParametersTable)s
Decomposition of estimated gates. A rotation axis and angle are extracted from each gate by considering the projection of its logarithm onto a the Pauli Hamiltonian projectors. The direction and magnitude (up to a conventional constant) give the axis and angle respectively.
%(bestGatesetDecompTable)s
Comparison of GST estimated gate set to target gate set. This table displays the values of metrics which measure the aggregated distance between entire gate sets. In this case, the two gate sets under consideration are the GST estimate and the target.
%(bestGatesetVsTargetTable)s
Comparison of GST estimated gates to target gates. This table presents, for each of the gates, different measures of distance or discrepancy from the GST estimate to the ideal target operation.
%(bestGatesVsTargetTable)s
Comparison of GST estimated SPAM to target SPAM. This table presents, for each state preparation and POVM effect, two different measures of distance or discrepancy from the GST estimate to the ideal target operation. See text for more detail.
%(bestGatesetSpamVsTargetTable)s
The GST estimate of the logic gate operations. Compares the ideal (generally unitary) logic gates (second column, also in Table ) with those estimated by GST (third column). Each gate is represented as a d^2\times d^2superoperator that acts by matrix multiplication on vectors in \mathcal{B}(\mathcal{H}). Matrices are displayed using a heat map that ranges between 1.0 (red) and -1.0 (blue). Note that it is impossible to discern even order-1%% deviations from the ideal using this color scale, and one should rely on other analysis for more a precise comparison.
%(bestGatesetGatesBoxTable)s
The GST estimate of the logic gate operation generators. A heat map of the Error Generator for each gate, which is the Lindbladian \mathbb{L} that describes how the gate is failing to match the target. This error generator is defined by the equation %(errorgenformula)s. When all elements of these matrices is zero, the estimated gates match the target gates (Table ). Note that the range of the color scale is variable, being determined by the data. In the third column, each generator is projected onto each of the Hamiltonian generators given by the action of commutation with each Pauli-product basis element. In the forth column, each generator is projected onto each of the Stochastic generators given by the action of conjugation with each Pauli-product basis element. Columns and rows correspond to Pauli operators on the first and second (if present) qubit.
%(bestGatesetErrGenBoxTable)s
Choi matrix spectrum of the GST estimated gate set. The eigenvalues of the Choi representation of each estimated gate. In the third column, magnitudes of negative values are plotted using red bars. Unitary gates have a spectrum (1,0,0\ldots), just like pure quantum states. Negative eigenvalues are non-physical, and may represent either statistical fluctuations or violations of the CPTP model used by GST.
%(bestGatesetChoiEvalTable)s
#iftoggle(CompareDatasets)
Dataset comparisons
This report contains information for more than one data set. This page shows comparisons between different data sets.
%(dsComparisonSummary)s
For every pair of data sets, the likelihood is computed for two different models: 1) the model in which a single set of probabilities (one per gate sequence, obtained by the combined outcome frequencies) generates both data sets, and 2) the model in which each data is generated from different sets of probabilities. Twice the ratio of these log-likelihoods can be compared to the value that is expected when model 1) is valid. This plot shows the difference between the expected and actual twice-log-likelihood ratio in units of standard deviations. Zero or negative values indicate the data sets appear to be generated by the same underlying probabilities. Large positive values indicate the data sets appear to be generated by different underlying probabilities.
%(dsComparisonHistogram)s
%(dscmpSwitchboard)s
Histogram of p-values comparing two data sets. Each gate sequence is assigned a p-value based on how consistent that sequence's counts are between the two selected data sets. The line shows what would be expected for perfectly consistent data.
%(dsComparisonBoxPlot)s
Per-sequence 2\Delta\log(\mathcal{L}) values comparing two data sets. In a similar fashion to other color box plots, this plot shows two times the log-likelihood-ratio for each gate sequence corresponding to how consistent that sequences' counts are between the two selected data sets. The likelihood ratio is between a models that supposes there is either one or two separate probability distributions from which the data counts are drawn.
#endtoggle
System and pyGSTi parameters
This section contains a raw dump of system information and various pyGSTi parameters. It's purpose is to stamp this report with parameters indicating how exactly GST was run to create it, as well as to record the software environment in within which the report creation was run. Note that if the core GST computation was done on a machine different from the one that created this report, the software information contained here will be of less value.
Listing of GST parameters and meta-data. These parameters and related metadata describe how the GST computation was performed which led to this report.
%(metadataTable)s
Listing of the software environment. Note that this describes the software environment of the machine used to generate this report, and not necessarily the machine used to perform the core GST gate set estimation.
%(softwareEnvTable)s