  Boltzmann machine is a powerful machine learning model with many real-world
applications, for example by constructing deep belief networks. Statistical
inference on a Boltzmann machine can be carried out by sampling from its
posterior distribution. However, uniform sampling from such a model is not
trivial due to an extremely multi-modal distribution. Quantum computers have
the promise of solving some non-trivial problems in an efficient manner. We
explored the application of a D-Wave quantum annealer to generate samples from
a restricted Boltzmann machine. The samples are further improved by Markov
chains in a hybrid quantum-classical setup. We demonstrated that quantum
annealer samples can improve the performance of Gibbs sampling compared to
random initialization. The hybrid setup is considerably more efficient than a
pure classical sampling. We also investigated the impact of annealing
parameters (temperature) to improve the quality of samples. By increasing the
amount of classical processing (Gibbs updates) the benefit of quantum annealing
vanishes, which may be justified by the limited performance of today's quantum
computers compared to classical.
