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Universality in the Anticoncentration of Noisy Quantum Circuits at Finite Depths

Arman Sauliere1,*, Guglielmo Lami1, Corentin Boyer1, Jacopo De Nardis1, and Andrea De Luca1,2

  • *Contact author: armansauliere@gmail.com
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PRX Quantum 7, 020365 – Published 22 June, 2026

DOI: https://doi.org/10.1103/xl16-cdy9

Abstract

We present universal properties of anticoncentration in weakly noisy quantum circuits at finite depth. We develop a generic framework for single- and multi-qubit noise channels in the weak-noise limit and introduce an effective description in terms of a random matrix product operator. Within this weak-noise regime, we show that distinct noise mechanisms act in a quantitatively similar way, yielding a universal distribution of bit-string probabilities that is largely independent of the microscopic noise channel and of the circuit architecture. We identify three depth-dependent regimes, each characterized by a distinct scaling of cross-entropy benchmarking (XEB) with 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 anticoncentration in generic finite-depth circuits and benchmark them against numerical simulations, finding excellent agreement even at shallow depths. Moreover, we show that, contrary to previous expectations, the late-time value of XEB provides direct access to the global circuit fidelity, even at large noise strengths. Our results are directly applicable to current quantum processors and demonstrate universal behavior beyond the pure random-matrix-theory regime, which only emerges at asymptotically large depths.

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Popular Summary

Understanding how quantum computers behave under noise is key to evaluating their performance. We uncover universal features in how noisy quantum circuits spread their output probabilities—a property known as anticoncentration. Using an effective model based on random matrix product operators, we show that different types of noise lead to similar statistical behavior, largely independent of the circuit design.

We identify three depth-dependent regimes: a perturbative regime where noise is weak, an intermediate regime where noise and circuit dynamics compete, and a deep regime where the output becomes effectively classical. The transitions between these regimes are captured by how cross-entropy benchmarking (XEB) scales with circuit depth.

Our results provide quantitative predictions for noisy circuits at finite depth and demonstrate that XEB remains informative about the global circuit fidelity even under strong noise. This establishes a unified, universal framework relevant to today’s quantum processors.

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PRX Quantum 7, 020365– Published 22 June, 2026
  • Received 11 October 2025
  • Revised 3 February 2026
  • Accepted 17 March 2026
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