# cirq.log_xeb_fidelity_from_probabilities¶

cirq.log_xeb_fidelity_from_probabilities(hilbert_space_dimension: int, probabilities: Sequence[float]) → float[source]

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.

Parameters
• 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.

Returns

Estimate of fidelity associated with an experimental realization of a quantum circuit.