Sampling from the Thermal Quantum Gibbs State and Evaluating Partition Functions with a Quantum Computer

We present a quantum algorithm to prepare the thermal Gibbs state of interacting quantum systems. This algorithm sets a universal upper bound Dα on the thermalization time of a quantum system, where D is the system's Hilbert space dimension and α≤(1/2) is proportional to the Helmholtz free energy density. We also derive an algorithm to evaluate the partition function of a quantum system in a time proportional to the system's thermalization time and inversely proportional to the targeted accuracy squared.