Classical computability of linear cross-entropy (F_XEB) for 56-qubit random-geometry circuits

Develop classical methods to compute the linear cross-entropy benchmarking value F_XEB for 56‑qubit random‑geometry circuits at depths ≥ 12 without prohibitive resource requirements, enabling verification beyond shallow depths.

Background

For circuits at N = 56 and depths where exact tensor-network contraction becomes infeasible, the authors rely on mirror benchmarking rather than directly computing F_XEB to estimate fidelity. They emphasize that, given present classical tools, computing F_XEB for their deeper 56‑qubit circuits appears out of reach.

They explicitly state that they do not know how to compute F_XEB for these circuits except possibly at the lowest depths with significant effort, underscoring the need for improved classical verification methods.

References

this data supports our expectation that F_{\rm XEB} of the data taken from 56-qubit circuits (and available at ) should agree well with the mirror benchmarking return probabilities for those circuits, despite the fact that we have not computed the cross-entropy of that data ourselves (and we do not know how it could be computed except possibly at the lowest depths with significant effort).

— The computational power of random quantum circuits in arbitrary geometries  (2406.02501 - DeCross et al., 2024) in Appendix: Comparison of various fidelity estimators