DEEP QUANTUM

Abstract

In quantum many-body physics, finding a correct representation of a physical system in general, and finding the minimum energy (ground energy) in particular is a challenging problem because information about the system scales exponentially with the size of the system. Recently, there are articles saying that the difficulty of finding the ground energy problem could be reduced by using a neural network to represent the quantum system (Carleo and Troyer, 2017). In this project, we have carefully examined a formulation of finding the ground energy problem in quantum physics as a machine learning optimization problem, in which any kind of probabilistic model can be used. By using Restricted Boltzmann Machine as a specific model, we have designed and implemented an algorithm to run on General-purpose Graphics Processing Unit (GPGPU). From that, we have verified the correctness and gave an evaluation of the efficiency of the algorithm. Furthermore, we have attempted to improve the algorithm’s efficiency by using contrastive divergence algorithm and its correctness by imposing regularization. Besides, we also discuss some ideas to tackle few-body problem, which shares a similar difficulty in finding ground energy as many-body problem.