Variational Preparation of the Sachdev-Ye-Kitaev Thermofield Double
This addresses a specific challenge in quantum simulation for condensed matter physics, but it is incremental as it builds on existing variational methods.
The paper tackled the problem of preparing the thermofield double state for the Sachdev-Ye-Kitaev model without an auxiliary bath by using variational quantum circuits, achieving preparation for the q=4 SYK model up to N=12.
We provide an algorithm for preparing the thermofield double (TFD) state of the Sachdev-Ye-Kitaev 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 quantum circuits that prepare the ground state of $H_{\text{TFD}}$ for the $q=4$ SYK model up to $N=12$.