This paper presents quantum generalizations of classical Glauber and Metropolis dynamics, focusing on efficient and physically motivated constructions for detailed balanced quantum dynamics. The authors propose a discrete-time quantum counterpart to Metropolis sampling that satisfies detailed balance, quasi-locality, and efficient implementation. They also introduce an alternative coherent reweighing scheme that achieves exact detailed balance, inspired by physically derived master equations. The constructions are analyzed for their properties, including uniqueness of fixed points, locality, and ergodicity. The paper also discusses the physical origins of the continuous-time construction and its relationship to existing quantum MCMC methods. The authors show that their discrete-time construction can be implemented efficiently on a quantum computer, and that it inherits the quasi-local nature of the continuous-time construction. The paper also compares different quantum detailed balance constructions and highlights the importance of understanding the mixing time and efficiency of these methods. The authors conclude that while quantum MCMC methods are still in their early stages, they offer promising avenues for simulating complex quantum systems and improving the efficiency of quantum algorithms.This paper presents quantum generalizations of classical Glauber and Metropolis dynamics, focusing on efficient and physically motivated constructions for detailed balanced quantum dynamics. The authors propose a discrete-time quantum counterpart to Metropolis sampling that satisfies detailed balance, quasi-locality, and efficient implementation. They also introduce an alternative coherent reweighing scheme that achieves exact detailed balance, inspired by physically derived master equations. The constructions are analyzed for their properties, including uniqueness of fixed points, locality, and ergodicity. The paper also discusses the physical origins of the continuous-time construction and its relationship to existing quantum MCMC methods. The authors show that their discrete-time construction can be implemented efficiently on a quantum computer, and that it inherits the quasi-local nature of the continuous-time construction. The paper also compares different quantum detailed balance constructions and highlights the importance of understanding the mixing time and efficiency of these methods. The authors conclude that while quantum MCMC methods are still in their early stages, they offer promising avenues for simulating complex quantum systems and improving the efficiency of quantum algorithms.