Universality in the Anticoncentration of Noisy Quantum Circuits at Finite Depths
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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BibTeX
@article{sauliere2026universality,
title = {{Universality in the Anticoncentration of Noisy Quantum Circuits at Finite Depths}},
author = {Arman Sauliere and Guglielmo Lami and Corentin Boyer and Jacopo de Nardis and Andrea De Luca},
journal = {PRX Quantum},
year = {2026},
month = jun,
doi = {10.1103/xl16-cdy9},
eprint = {2508.14975},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05768910v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Universality in the Anticoncentration of Noisy Quantum Circuits at Finite Depths
AU - Arman Sauliere
AU - Guglielmo Lami
AU - Corentin Boyer
AU - Jacopo de Nardis
AU - Andrea De Luca
PY - 2026
DA - 2026/06/22
JO - PRX Quantum
DO - 10.1103/xl16-cdy9
UR - https://hal.science/hal-05768910v1
AB - 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.
SN - 2691-3399
ER -