Quantum computation of Restricted Boltzmann Machines by Monte Carlo Methods

Abstract

In recent years, the diversification of problems that require computers to solve has attracted attention to the construction of meta-heuristics that can be applied to a wide range of problems, and to specialized computers that implement these meta-heuristics in their devices. The representative meta-heuristics are Simulated Annealing (SA) and its extension to quantum computation, Quantum Annealing (QA), and its path-integral Monte Carlo method for classical simulation Crosson and Harrow showed that for certain problems where QA outperformed SA, SQA achieved performance close to that of QA, and SQA sometimes outperformed SA by an exponential time factor. On the other hand, it remains unclear whether SQA can work efficiently on a wide range of other problems. In this study, we experimentally compared SA and SQA on instances of the restricted Boltzmann machine RBM, known as a fundamental building block in deep learning, and 3SAT, a fundamental combinatorial optimization problem. The results show that SQA gives slightly better solutions than SA as the problem size increases for RBM in terms of both accuracy and computation time in our setting, but the opposite trend is observed for 3SAT, indicating that there is no significant difference between the two methods. From the viewpoint of artificial intelligence research, it is necessary to further examine whether deep learning can be made more efficient by applying QA and SQA to RBM.