Quantum Entanglement in Deep Learning Architectures

Yoav Levine, Or Sharir, Nadav Cohen, and Amnon Shashua
Phys. Rev. Lett. 122, 065301 – Published 12 February 2019
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Abstract

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.

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  • Received 3 May 2018
  • Revised 31 October 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.065301

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsNetworks

Authors & Affiliations

Yoav Levine1,*, Or Sharir1,†, Nadav Cohen2,‡, and Amnon Shashua1,§

  • 1The Hebrew University of Jerusalem, 9190401 Israel
  • 2School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540, USA

  • *yoavlevine@cs.huji.ac.il
  • or.sharir@cs.huji.ac.il
  • cohennadav@ias.edu
  • §shashua@cs.huji.ac.il

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Issue

Vol. 122, Iss. 6 — 15 February 2019

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