  Aiming at evading the notorious sign problem in classical Monte-Carlo
approaches to lattice quantum chromodynamics, we present an approach for
quantum computing finite-temperature lattice gauge theories at non-zero
density. Based on the thermal pure-quantum-state formalism of statistical
mechanics when extended to gauge-theory systems, our approach allows for
sign-problem-free quantum computations of thermal expectation values and
non-equal time correlation functions. By taking a simple lattice gauge theory
for which classical benchmarks are possible, namely $\mathbb{Z}_2$ lattice
gauge theory in 1+1 dimensions at finite chemical potential, we discuss
resource requirements and robustness to algorithmic and hardware imperfections
for near-term quantum-hardware realizations.
