Sample-efficient benchmarking of shallow all-to-all random quantum circuits

• URL: http://arxiv.org/abs/2605.22909v1
• Date: Thu, 21 May 2026 18:00:28 GMT
• Title: Sample-efficient benchmarking of shallow all-to-all random quantum circuits
• Abstract summary: We show that the nonlinear cross-entropy provides a sample-efficient benchmark for shallow-depth random quantum circuits.<n>We also develop a binary classifier based on the notion of heavy output generation that features logarithmic sample complexity at short depth.<n>Our evidence comes from exact analytic expressions for all-to-all Brownian circuit ensembles derived using replica tricks, and numerical simulations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Random circuit sampling (RCS) remains one of the most competitive frameworks for demonstrating quantum advantage in near-term noisy intermediate-scale quantum (NISQ) hardware. Unfortunately, absent error-correction, existing benchmarks to characterize these experiments, like linear cross-entropy, have been classically spoofed due to noise. Because of this, there are interesting regimes, like shallow-depth random quantum circuits, where sampling is plausibly classically intractable, but no existing benchmark can distinguish between a noisy quantum computer and an adversarial classical spoofer. In this paper, we demonstrate that the nonlinear cross-entropy provides a sample-efficient benchmark for shallow-depth all-to-all random quantum circuits whose score cleanly separates noisy quantum computers from state-of-the-art classical spoofers, even in the presence of depolarizing noise. Further, we develop a binary classifier based on the notion of heavy output generation that features logarithmic sample complexity at short depth. Our evidence comes from exact analytic expressions for all-to-all Brownian circuit ensembles derived using replica tricks, and numerical simulations that corroborate these results for discrete Haar-random unitary circuits.

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