Variational preparation of the thermofield double state of the Sachdev-Ye-Kitaev model

Journal Article · 29 July 2021 · Physical Review A

DOI: https://doi.org/10.1103/physreva.104.012427 · OSTI ID:1853150

Su, Vincent Paul ^[1]

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1. Univ. of California, Berkeley, CA (United States); OSTI

Here, we provide an algorithm for preparing the thermofield double (TFD) state of the Sachdev-Ye-Kitaev (SYK) model without the need for an auxiliary bath. Following previous work, the TFD can be cast as the approximate ground state of a Hamiltonian, H_TFD. Using variational quantum circuits, we propose and implement a gradient-based algorithm for learning parameters that find this ground state, an application of the variational quantum eigensolver. Concretely, we find shallow quantum circuits that prepare the ground state of H_TFD for the q = 4 SYK model for N = 8 Majoranas per side. For N = 12, we achieve a variational energy within 1% of the true ground-state energy.

• Research Organization: Univ. of California, Oakland, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• Grant/Contract Number: AC02-05CH11231; SC0019380
• OSTI ID: 1853150
• Journal Information: Physical Review A, Journal Name: Physical Review A Journal Issue: 1 Vol. 104; ISSN 2469-9926
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English