log_xeb_fidelity_from_probabilities(hilbert_space_dimension: int, probabilities: Sequence[float]) → float¶
Logarithmic XEB fidelity estimator.
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
(pi^2/6 - f^2) / Mwhere f is the fidelity and M the number of observations, equal tolen(probabilities). This is better than linear XEB (see above) whenfidelity is f > 0.32. Since this estimator is unbiased, the varianceis equal to the mean squared error of the estimator.
The estimator is intended for use with xeb_fidelity() below.
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.