Universality in the Anticoncentration of Chaotic Quantum Circuits
Abstract
We identify a \emph{universal functional form} that governs anticoncentration in random quantum circuits-one that holds across diverse circuit architectures and depths, and crucially remains valid even at finite system sizes and shallow depth. We support this claim through analytical results for ensembles of random tensor-network states and random-phase models. This compact, universal expression for the output bitstring probability distribution is fully characterized by just two fitting parameters, as validated through extensive numerical simulations. Our findings underscore the pivotal role of finite-size and finite-depth effects in shaping anticoncentration and introduce a practical framework for benchmarking quantum devices using shallow circuits, thereby enabling validation of systems significantly larger than previously accessible.
Cite
@article{arxiv.2503.00119,
title = {Universality in the Anticoncentration of Chaotic Quantum Circuits},
author = {Arman Sauliere and Beatrice Magni and Guglielmo Lami and Xhek Turkeshi and Jacopo De Nardis},
journal= {arXiv preprint arXiv:2503.00119},
year = {2025}
}