Classical Markov Chain Monte Carlo methods have been essentialfor simulating statistical physical systems and have proven well applicable to other systems with complex degrees of freedom. In this talk, I will describe an efficiently implementable discrete-time quantum counterpart to Metropolis sampling that preserves the following desirable features of classical Glauber / Metropolis dynamics: (i) exactly detailed balanced, (ii) efficiently implementable, and (iii) quasi-local for geometrically local systems. This complements the recent results of Chen, Kastoryano, and Gilyén [CKG23] who proposed a smoothed continuous-time variant of the Davies generator featuring the above properties (i)-(iii). Further, I describe a novel highly coherent quantum generalization of detailed balanced dynamics that resembles another physically derived master equation. I will discuss important properties of all constructions, including the uniqueness of the fixed-point and the locality of the resulting operators.
Joint work with Chi-Fang Chen, Joao F. Doriguello, and Michael J.
Kastoryano.