Variational thermal quantum simulation via thermofield double states

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.