In this talk I’ll present recent results relating the time of preparation of thermal states by quantum Gibbs samplers, the analogue of classical metropolis sampling. In particular I will connect the efficiency of quantum Gibbs samplers to the static properties of the thermal state, in particular whether it has a finite correlation length. The goal is to generalize to the quantum case a sequence of beautiful works—by Stroock, Zergalinski, Martinelli and others—in mathematical physics and statistical mechanics showing the equivalence of mixing in time (fast convergence of the Glauber dynamics) to mixing in space (finite correlation length in the Gibbs state) for classical models. (The talk will be based on joint work with Michael Kastoryano.)
