# cirq.hog_score_xeb_fidelity_from_probabilities¶

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

XEB fidelity estimator based on normalized HOG score.

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

(1/log(2)^2 - f^2) / M

where f is the fidelity and M the number of observations, equal to
len(probabilities). This is always worse than log XEB (see above).
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. It is
based on the HOG problem defined in https://arxiv.org/abs/1612.05903.
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.