Fast Scrambling in Classically Simulable Quantum Circuits

TL;DR

This paper demonstrates that certain classically simulable quantum circuits built from super-Clifford gates can exhibit fast scrambling, with operator entanglement saturating in logarithmic time and out-of-time ordered correlators being efficiently computable.

Contribution

It extends the formalism for classically simulating super-Clifford circuits to include fast scramblers and the computation of out-of-time ordered correlators.

Findings

Operator entanglement saturates in logarithmic time in a constructed circuit.

Out-of-time ordered correlators can be efficiently simulated in these circuits.

Super-Clifford circuits can exhibit fast scrambling behavior.

Abstract

We study operator scrambling in quantum circuits built from `super-Clifford' gates. For such circuits it was established in arXiv:2002.12824 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. Firstly 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 $t_* \sim \mathrm{ln}(N)$ (with $N$ the number of qubits). Secondly 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.