# cirq.experiments.log_xeb_fidelity_from_probabilities

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.

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