Logarithmic XEB fidelity estimator.

Estimates fidelity from ideal probabilities of observed bitstrings.

See linear_xeb_fidelity_from_probabilities for the assumptions made by this estimator.

The mean of this estimator is the true fidelity f and the variance is

(pi^2/6 - f^2) / M

where f is the fidelity and M the number of observations, equal to len(probabilities). This is better than linear XEB (see above) when fidelity is f > 0.32. Since this estimator is unbiased, the variance is 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.