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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.19614 |
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| _version_ | 1866915354219905024 |
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| author | Blake, Mike Linden, Noah Thompson, Anthony P. |
| author_facet | Blake, Mike Linden, Noah Thompson, Anthony P. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19614 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fast Scrambling in Classically Simulable Quantum Circuits Blake, Mike Linden, Noah Thompson, Anthony P. Quantum Physics High Energy Physics - Theory 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. |
| title | Fast Scrambling in Classically Simulable Quantum Circuits |
| topic | Quantum Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2410.19614 |