The plots and tables on this tab summarize how well the GST estimate actually fits the data. Although they may be less familiar to you than, say, process fidelity, these analyses are essential to understanding the GST estimate, and how much to trust it! Real qubit systems often display behavior that isn't consistent with modeling each gate as a stationary CPTP map. When pyGSTi tries to fit such data to its model (a single gateset), this "non-Markovianity" manifests as model violation. This tab provides several views of the model violation observed for this fit, ranging from the coarse-grained (total violation) to hyper-detailed (per-circuit violation). More observed model violation ⇒ the error metrics on other tabs should be trusted less.
Model violation summary.This plot summarizes how well GST was able to fit the data -- or subsets of it -- to a gateset. Bars indicate the difference between the actual and expected log-likelihood values, and are given in units of standard deviations of the appropriate \chi^2 distribution. Each bar corresponds to a subset of the data including only circuits of length up to \sim L; the rightmost bar corresponds to the full dataset. Low values are better (less model violation), and bars are colored according to the star rating found in a later table detailing the overall model violation.
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Detailed overall model violation. This table provides a detailed look at how the observed model violation -- defined by how badly the GST model fits the data -- evolves as more and more of the data are incorporated into the fit. PyGSTi fits the data iteratively, starting by just fitting data from the shortest circuits (L=1), and then adding longer and longer sequences. Each subset of the data, defined by its maximum sequence length L, yields an independent fit that is analyzed here. The key quantity is the difference between the observed and expected maximum loglikelihood (\log(\mathcal{L})). If the model fits, then 2\Delta\log(\mathcal{L}) should be a \chi^2_k random variable, where k (the degrees of freedom) is the difference between N_S (the number of independent data points) and N_p (the number of model parameters). So 2\Delta\log(\mathcal{L}) should lie in [k-\sqrt{2k},k+\sqrt{2k}], and N_\sigma = (2\Delta\log(\mathcal{L})-k)/\sqrt{2k} quantifies how many standard deviations it falls above 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. Heading tool tips provide descriptions of each column's value.
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Per-circuit model violation vs. circuit lengthThe fit's total 2\Delta\log(\mathcal{L}) is a sum over all N_s circuits used for GST. This plot shows 2\Delta\log(\mathcal{L}) for each individual circuit, plotted against that circuit's length (on the X axis). Certain forms of non-Markovian noise, like slow drift, produce a characteristic linear relationship. Note that the length plotted here is the actual length of the circuit, not its nominal L.
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