Abstract
The ground state and thermal state are among the most important problems in condensed matter physics and quantum chemistry. Recently, a series of quantum algorithms based on simulating open system evolution has been proposed to prepare these states. Although these algorithms provably converge to the steady state, their mixing times remain widely open. In this work, we present the first numerical study of the mixing time of various 1D local Hamiltonian models in condensed matter physics. For the first time, we provide evidence of fast mixing or even rapid mixing in general (non-commuting) quantum systems. Our results show that we can prepare the ground state of many quantum systems by simulating the open system evolution up to a very short time.