Adaptive variational quantum minimally entangled typical thermal states for finite temperature simulations

Scalable quantum algorithms to simulate quantum many-body systems in thermal equilibrium are under active research. Here we develop a quantum version of the minimally entangled typical thermal states algorithm to compute finite temperature properties of quantum systems. We adopt a recently developed adaptive variational approach to realize high-fidelity state propagation along the imaginary time axis at each thermal step. The algorithm leverages highly compact, dynamically generated, problem-specific quantum circuits, which are suitable for current and near-term quantum hardware. Through thermal energy calculations of integrable and nonintegrable spin models in one and two dimensions, we demonstrate approximately linear system-size scaling of the circuit complexity for our benchmark systems. Finally, we showcase the approach by mapping out representative points on a two-phase critical line of a 2D quantum spin model.