  The phase diagram of strong interactions in nature at finite temperature and
chemical potential remains largely unexplored theoretically due to inadequacy
of Monte-Carlo-based computational techniques in overcoming a sign problem.
Quantum computing offers a sign-problem-free approach but evaluating thermal
expectation values is generally resource intensive on quantum computers. To
facilitate thermodynamic studies of gauge theories, we propose a generalization
of thermal-pure-quantum-state formulation of statistical mechanics applied to
constrained gauge-theory dynamics, and numerically demonstrate that the phase
diagram of a simple low-dimensional gauge theory is robustly determined using
this approach, including mapping a chiral phase transition in the model at
finite temperature and chemical potential. Quantum algorithms, resource
requirements, and algorithmic and hardware error analysis are further discussed
to motivate future implementations. Thermal pure quantum states, therefore, may
present a suitable candidate for efficient thermal-state preparation in gauge
theories in the era of quantum computing.
