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The properties of strongly-coupled lattice gauge theories at finite densityas well as in real time have largely eluded first-principles studies on thelattice. This is due to the failure of importance sampling for systems with acomplex action. An alternative to evade the sign problem is quantum simulation.Although still in its infancy, a lot of progress has been made in devisingalgorithms to address these problems. In particular, recent efforts haveaddressed the question of how to produce thermal Gibbs states on a quantumcomputer. In this study, we apply a variational quantum algorithm to alow-dimensional model which has a local abelian gauge symmetry. We demonstratehow this approach can be applied to obtain information regarding the phasediagram as well as unequal-time correlation functions at non-zero temperature.

Simulating $\mathbb{Z}_2$ Lattice Gauge Theory with the Variational Quantum Thermalizer