Quantum annealing is a metaheuristic that is used to find the global optimum of a given an objective function. Real world implementations of quantum annealers do not provide optimal solution directly, but in fact sample from a Boltzmann distribution which minimum energy state corresponds to the optimal solution.

Sampling has become the most important application of current quantum information processing systems in machine learning over the last two years [1]. The focus has been on Boltzmann machines as a precursor to deep learning architectures, but more generic probabilistic graphical methods are worthy of attention. The general inference problem is #P-complete, hence an efficient approximate method such as quantum-enhanced sampling can give a major boost in these models. In this work, the student will investigate usage of quantum annealers (such as D-Wave 2000Q) as samplers for probabilistic graphical models, with focus on pairwise, nearest-neighbor interacting, binary Markov random field in particular and compare the efficiency of classical and quantum-enhanced sampling methods [2].

• Problems related to classical Markov chain Monte Carlo methods, and Gibbs sampling in particular.
• Benchmarking MCMC Gibbs sampling against hardware-based sampling.
• Robustness of spurious graph embeddings in the quality of sampling.