Variational Thermal Quantum Simulation via Thermofield Double States

Abstract: We present a variational approach for quantum simulators to realize finite temperature Gibbs states by preparing thermofield double (TFD) states. Our protocol is motivated by the quantum approximate optimization algorithm (QAOA) and involves alternating time evolution between the Hamiltonian of interest and interactions which entangle the system and its auxiliary counterpart. As a simple example, we demonstrate that thermal states of the 1d classical Ising model at any temperature can be prepared with perfect fidelity using L/2 iterations, where L is system size. We also show that a free fermion TFD can be prepared with nearly optimal efficiency. Given the simplicity and efficiency of the protocol, our approach enables near-term quantum platforms to access finite temperature phenomena via preparation of thermofield double states.