Fast Scrambling in Classically Simulable Quantum Circuits

• URL: http://arxiv.org/abs/2410.19614v1
• Date: Fri, 25 Oct 2024 15:05:35 GMT
• Title: Fast Scrambling in Classically Simulable Quantum Circuits
• Abstract summary: We study operator scrambling in quantum circuits built from super-Clifford' gates. In addition to operator entanglement, certain out-of-time ordered correlation functions (OTOCs) can be classically simulated within the same formalism.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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