  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. Motivated by the statistical physics origins,
Chen, Kastoryano, and Gily\'en [CKG23] proposed a continuous-time quantum
thermodynamic analog to Glauber dynamic that is (i) exactly detailed balanced,
(ii) efficiently implementable, and (iii) quasi-local for geometrically local
systems. Physically, their construction gives a smooth variant of the Davies'
generator derived from weak system-bath interaction. In this work, we give an
efficiently implementable discrete-time quantum counterpart to Metropolis
sampling that also enjoys the desirable features (i)-(iii). Also, we give an
alternative highly coherent quantum generalization of detailed balanced
dynamics that resembles another physically derived master equation, and propose
a smooth interpolation between this and earlier constructions. We study generic
properties of all constructions, including the uniqueness of the fixed-point
and the locality of the resulting operators. We hope our results provide a
systematic approach to the possible quantum generalizations of classical
Glauber and Metropolis dynamics.
