Variational Preparation of the Sachdev-Ye-Kitaev Thermofield Double

TL;DR

This paper introduces a variational quantum algorithm to prepare the thermofield double state of the SYK model, enabling efficient state preparation without auxiliary systems, demonstrated on small quantum devices.

Contribution

It presents a novel variational quantum algorithm for preparing the TFD state of the SYK model, extending quantum state preparation techniques to this complex system.

Findings

Successfully prepared the TFD state for the $q=4$ SYK model up to N=12.

Demonstrated the effectiveness of the variational approach on quantum hardware.

Provided a scalable method for studying thermal states in strongly correlated systems.

Abstract

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 $N=12$.