Neural Network Representation of Tensor Network and Chiral States

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Neural Network Representation of Tensor Network and Chiral States

Yichen Huang (黄溢辰) and Joel E. Moore

Phys. Rev. Lett. 127, 170601 – Published 18 October 2021

Abstract

We study the representational power of Boltzmann machines (a type of neural network) in quantum many-body systems. We prove that any (local) tensor network state has a (local) neural network representation. The construction is almost optimal in the sense that the number of parameters in the neural network representation is almost linear in the number of nonzero parameters in the tensor network representation. Despite the difficulty of representing (gapped) chiral topological states with local tensor networks, we construct a quasilocal neural network representation for a chiral $p$ -wave superconductor. These results demonstrate the power of Boltzmann machines.

Received 20 July 2021
Accepted 20 September 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.170601

Physics Subject Headings (PhySH)

Topological superconductors

Machine learning Many-body techniques Tensor network methods

Condensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Yichen Huang (黄溢辰)^*,†

Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA

Joel E. Moore^‡

Department of Physics, University of California, Berkeley, Berkeley, California 94720, USA and Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

^*yichuang@mit.edu
^†Present address: Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
^‡jemoore@berkeley.edu