Deep Learning of Matrix Product States

Abstract

Machine learning and especially deep learning architectures provide a fresh perspective on the study of many body physics phenomena. In this paper, we employ Restricted Boltzmann machines (RBM) to represent quantum many-body states and find connections that can be made useful to quantum many-body physics research, ultimately leading to a better understanding of the fundamental nature of entanglement entropy in quantum physics. In this work, we establish the conditions for translating RBMs into Matrix Product States (MPS), showing that deep learning algorithms can be exploited as a powerful tool for an efficient representation of quantum states. We present an algorithm for mapping an RBM into an MPS, with a specific proof for Ising model. We discuss the upper entropy bound and entanglement properties resulting from such a connection, together with the consequences of our results in a broader context.