Random circuits satisfy an ergodicity condition for positive-coefficient polynomials, and its deviation can benchmark quantum chip fidelity, recovering and generalizing linear cross-entropy benchmarking.
Therefore, typically (with high probability) we have C f (PU,χ U) = EU[C f (PU,χ U)]± O 1√ N ! = 1 + O 1√ N ! , (40) for any U
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Generalized Cross-Entropy Benchmarking for Random Circuits with Ergodicity
Random circuits satisfy an ergodicity condition for positive-coefficient polynomials, and its deviation can benchmark quantum chip fidelity, recovering and generalizing linear cross-entropy benchmarking.