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

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 gradientbased 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.