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arXiv:1710.04045 · Physical Review X

Neural-Network Quantum States, String-Bond States, and Chiral Topological States

Ivan Glasser, Nicola Pancotti, Moritz August, Ivan D. Rodriguez, J. I. Cirac

Published Jan 11, 2018• 215 citations
arXivHTMLPDF

Abstract

Two tools show great promise in approximating low-temperature, condensed-matter systems: Tensor-network states and artificial neural networks. A new analysis builds a bridge between these techniques, opening the way to a host of powerful approaches to understanding complex quantum systems.
DOI
10.1103/physrevx.8.011006

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Much attention has been devoted to the use of machine learning to approximate physical concepts. Yet, due to challenges in interpretability of machine learning techniques, the question of what physics machine learning models are able to learn remains open. Here, we bridge the concept of a physical quantity and its machine learning approximation in the context of the original application of neural networks in physics: topological phase classification. We construct a hybrid tensor-neural network object that exactly expresses the real-space topological invariant and rigorously assess its trainability and generalization. Specifically, we benchmark the accuracy and trainability of a tensor-neural network to multiple types of neural networks, thus exemplifying the differences in trainability and representational power. Our work highlights the challenges in learning topological invariants and constitutes a stepping stone toward more accurate and better generalizable machine learning representations in condensed matter physics.