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.

• Received 20 January 2021
• Accepted 13 July 2021

DOI:https://doi.org/10.1103/PhysRevA.104.012427