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