hog_score_xeb_fidelity_from_probabilities(hilbert_space_dimension: int, probabilities: Sequence[float]) → float¶
XEB fidelity estimator based on normalized HOG score.
Estimates fidelity from ideal probabilities of observed bitstrings.See
linear_xeb_fidelity_from_probabilitiesfor the assumptions madeby this estimator.
The mean of this estimator is the true fidelity f and the variance is
(1/log(2)^2 - f^2) / Mwhere f is the fidelity and M the number of observations, equal tolen(probabilities). This is always worse than log XEB (see above).Since this estimator is unbiased, the variance is equal to the meansquared error of the estimator.The estimator is intended for use with xeb_fidelity() below. It isbased on the HOG problem defined in https://arxiv.org/abs/1612.05903.
hilbert_space_dimension – Dimension of the Hilbert space on which the channel whose fidelity is being estimated is defined.
probabilities – Ideal probabilities of bitstrings observed in experiment.
Estimate of fidelity associated with an experimental realization of a quantum circuit.