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More global randomness from less-random local gates

Ryotaro Suzuki1,*, Hosho Katsura2,3,4, Yosuke Mitsuhashi5, Tomohiro Soejima6, Jens Eisert1, and Nobuyuki Yoshioka7

  • *Contact author: ryotaro.suzuki.2139@gmail.com
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Phys. Rev. A 114, 022424 – Published 12 August, 2026

DOI: https://doi.org/10.1103/9tnv-2559

Abstract

Random circuits giving rise to unitary designs are key tools in quantum information science and many-body physics. In this work, we investigate a class of random quantum circuits with a specific gate structure. Within this framework, we prove that one-dimensional structured random circuits with non-Haar-random local gates can exhibit substantially more global randomness compared to Haar-random circuits with the same underlying circuit architecture. In particular, under a solvability condition, we exactly diagonalize the second-moment operators for these structured random circuits by establishing a link to free-fermionic models, and we show that their spectral gaps can exceed those of Haar-random circuits. While solvable structured random circuits exhibit free-fermionic behavior, the underlying fixed gate need not be a matchgate. Our findings have applications in improving circuit depth bounds for randomized benchmarking, in generating approximate unitary 2-designs from shallow random circuits, and in enabling exact analyses of quantum many-body dynamics.

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Phys. Rev. A 114, 022424– Published 12 August, 2026
  • Received 10 April 2025
  • Accepted 30 June 2026
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