Developing Quantum Algorithms for Preparing Thermal States of the Hubbard Model

Thermal state preparation of the Hubbard model is known to be a difficult problem to solve. Here, we approach the problem approximately, using physical principles to create the approximate thermal state. Starting from an efficient preparation of the ground state, we drive the system by turning on an electric field, which adds energy while keeping the system in a pure state. To study relaxation, we couple the excited system to an external reservoir and evolve it in time, incorporating mid-circuit measurements to remove energy from the system. Because the driving and coupling protocols are designed to preserve the model's fundamental symmetries, the system is expected to evolve toward an approximate symmetry-projected thermal distribution. This framework can be mapped onto quantum circuits suitable for execution on quantum hardware, providing insight into how symmetry constraints influence how we can create approximate thermal states for strongly correlated systems.