Sampling problems on a Quantum Computer

Due to the advances in the manufacturing of quantum hardware in the recent years, significant research efforts have been directed towards employing quantum methods to solving problems in various areas of interest. Thus a plethora of novel quantum methods have been developed in recent years. In this paper, we provide a survey of quantum sampling methods along-side needed theory and applications of those sampling methods as a starting point for research in this area. This work focuses in particular on Gaussian Boson sampling, quantum Monte Carlo methods, quantum variational Monte Carlo, quantum Boltzmann Machines and quantum Bayesian networks. We strive to provide a self-contained overview over the mathematical background, technical feasibility, applicability for other problems and point out potential areas of future research.