Universality in the Anticoncentration of Noisy Quantum Circuits at Finite Depths

• URL: http://arxiv.org/abs/2508.14975v2
• Date: Fri, 10 Oct 2025 15:41:47 GMT
• Title: Universality in the Anticoncentration of Noisy Quantum Circuits at Finite Depths
• Authors: Arman Sauliere, Guglielmo Lami, Corentin Boyer, Jacopo De Nardis, Andrea De Luca,
• Abstract summary: We present universal properties of the anticoncentration of noisy quantum circuits at finite depth.<n>In the weak-noise regime different types of noise act in a similar fashion, leading to a universal distribution of bit-string probabilities.<n>We show that, contrary to previous belief, the late-time XEB does give access to the global circuit fidelity, even for large noise strengths.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present universal properties of the anticoncentration of noisy quantum circuits at finite depth. By employing an effective model of random matrix product operators, we show that in the weak-noise regime different types of noise act in a similar fashion, leading to a universal distribution of bit-string probabilities, largely independent of the specific noise channel or circuit architecture. We identify three distinct depth-dependent regimes, each signaled by a different scaling of cross-entropy benchmarking (XEB) over rescaled depth. In the shallow-depth regime, noise effects are perturbatively small; in the intermediate regime, circuit-induced fluctuations and noise compete on equal footing; and in the deep-depth regime, the output distribution becomes effectively classical, up to corrections that are exponentially small in the noise strength. We provide quantitative predictions for the anticoncentration of generic circuits at finite depth, which we benchmark with numerical simulations displaying perfect agreement even for shallow circuits. Moreover, we show that, contrary to previous belief, the late-time XEB does give access to the global circuit fidelity, even for large noise strengths. Our findings are directly applicable to current quantum processors and demonstrate universal behavior beyond pure random-matrix-theory regimes which are only applicable at large depths.

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