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

Abstract

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, ${H}_{\text{TFD}}$. 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 ${H}_{\text{TFD}}$ 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.

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