Modern deep learning has enabled unprecedented achievements in various domains. Nonetheless, employment of machine learning for wave function representations is focused on more traditional architectures such as restricted Boltzmann machines (RBMs) and fully connected neural networks. In this Letter, we establish that contemporary deep learning architectures, in the form of deep convolutional and recurrent networks, can efficiently represent highly entangled quantum systems. By constructing tensor network equivalents of these architectures, we identify an inherent reuse of information in the network operation as a key trait which distinguishes them from standard tensor network-based representations, and which enhances their entanglement capacity. Our results show that such architectures can support volume-law entanglement scaling, polynomially more efficiently than presently employed RBMs. Thus, beyond a quantification of the entanglement capacity of leading deep learning architectures, our analysis formally motivates a shift of trending neural-network-based wave function representations closer to the state-of-the-art in machine learning.
Bibliographical noteFunding Information:
We thank Guifre Vidal, Thomas Spencer, John Imbrie, Bartlomiej Czech, Eyal Bairey, Eyal Leviatan, Miles Stoudenmire, Giuseppe Carleo, Ivan Glasser, and Lei Wang for useful discussions. This work is supported by ISF Center Grant No. 1790/12 and by the European Research Council (TheoryDL project). Nadav Cohen is a member of the Zuckerman Israeli Postdoctoral Scholars Program, and is supported by the Schmidt Foundation. Yoav Levine is supported by the Adams Fellowship Program of the Israel Academy of Sciences and Humanities.
© 2019 American Physical Society.