András Gilyén (Rényi Institute): Quantum generalizations of Glauber and Metropolis dynamics

Classical Markov Chain Monte Carlo methods have been essential for simulating statistical physical systems and have proven well applicable to other systems with complex degrees of freedom. I will describe efficiently implementable continuous and discrete-time quantum counterparts to Metropolis sampling and Glauber dynamics that also enjoys the following desirable features: it is (i) exactly detailed balanced, (ii) efficiently implementable, and (iii) quasi-local for geometrically local systems. I will describe generic 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, Michael J. Kastoryano.