Towards Quantum Simulation of Confining Gauge Theories at Finite Temperature and Density

Numerically simulating strongly coupled gauge theories at finite density is a

longstanding challenge in nuclear and high-energy physics that also has fundamental implications for condensed matter physics. Recently it has been suggested that digital and analog quantum hardware could provide pathways to efficiently simulate such systems. In this work, we adapt numerical tools based on imaginary time evolution, originally developed to simulate strongly correlated condensed matter systems, to study this problem. We do so in the simplest model of a confining gauge theory, namely $mathbb{Z}_2$ gauge theory coupled to spinless fermionic matter in 1+1 dimensions, which can be directly mapped to a local, interacting quantum spin chain. We discuss classical numerical results (from both sparse matrix and matrix product state calculations) on the finite-temperature and -density equation of state, as well as the chiral and confinement phase diagrams. We comment on how the relevant observables can be obtained with a recently proposed quantum algorithm, adaptive variational quantum minimally entangled typical thermal states (AVQMETTS), and when this approach is expected to outperform classical methods. Our work sets the stage for new approaches to study strongly coupled gauge theories on quantum hardware that can be generalized to higher dimensions where classical numerics become severely limited.