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  • Open Access

Fast scrambling in classically simulable quantum circuits

Mike Blake1, Noah Linden1, and Anthony P. Thompson1,2

  • 1School of Mathematics, University of Bristol, Fry Building, Woodland Road, Bristol BS8 1UG, United Kingdom
  • 2Quantum Engineering Center for Doctoral Training, University of Bristol, Tyndall Avenue, Bristol BS8 1FD, United Kingdom

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Phys. Rev. A 112, 022406 – Published 1 August, 2025

DOI: https://doi.org/10.1103/yx7v-m2zz

Abstract

We study operator scrambling in quantum circuits built from “super-Clifford” gates. For such circuits it was established by Blake and Linden [Phys. Rev. Lett. 125, 030502 (2020)] that the time evolution of operator entanglement for a large class of many-body operators can be efficiently simulated on a classical computer, including for operators with volume-law entanglement. Here we extend the scope of this formalism in two key ways. First we provide evidence that these classically simulable circuits include examples of fast scramblers, by constructing a circuit for which operator entanglement is numerically found to saturate in a time t*∼ln(N) (with N the number of qubits). Second we demonstrate that, in addition to operator entanglement, certain out-of-time-ordered correlation functions (OTOCs) can be classically simulated within the same formalism. As a consequence such OTOCs can be computed numerically in super-Clifford circuits with thousands of qubits and we study several explicit examples in the aforementioned fast scrambling circuits.

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Information

Phys. Rev. A 112, 022406– Published 1 August, 2025
  • Received 25 November 2024
  • Revised 9 June 2025
  • Accepted 12 June 2025
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