Constructing exact representations of quantum many-body systems with deep neural networks

Giuseppe Carleo, Yusuke Nomura, Masatoshi Imada

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

Obtaining accurate properties of many-body interacting quantum matter is a long-standing challenge in theoretical physics and chemistry, rooting into the complexity of the many-body wave-function. Classical representations of many-body states constitute a key tool for both analytical and numerical approaches to interacting quantum problems. Here, we introduce a technique to construct classical representations of many-body quantum systems based on artificial neural networks. Our constructions are based on the deep Boltzmann machine architecture, in which two layers of hidden neurons mediate quantum correlations. The approach reproduces the exact imaginary-time evolution for many-body lattice Hamiltonians, is completely deterministic, and yields networks with a polynomially-scaling number of neurons. We provide examples where physical properties of spin Hamiltonians can be efficiently obtained. Also, we show how systematic improvements upon existing restricted Boltzmann machines ansatze can be obtained. Our method is an alternative to the standard path integral and opens new routes in representing quantum many-body states.

Original languageEnglish
Article number5322
JournalNature communications
Volume9
Issue number1
DOIs
Publication statusPublished - 2018 Dec 1
Externally publishedYes

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Hamiltonians
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Neurons
Physics
Wave functions
Physical properties
Neural networks
neurons
theoretical physics
Deep neural networks
physical properties
routes
wave functions
chemistry
scaling

ASJC Scopus subject areas

  • Chemistry(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Physics and Astronomy(all)

Cite this

Constructing exact representations of quantum many-body systems with deep neural networks. / Carleo, Giuseppe; Nomura, Yusuke; Imada, Masatoshi.

In: Nature communications, Vol. 9, No. 1, 5322, 01.12.2018.

Research output: Contribution to journalArticle

Carleo, Giuseppe ; Nomura, Yusuke ; Imada, Masatoshi. / Constructing exact representations of quantum many-body systems with deep neural networks. In: Nature communications. 2018 ; Vol. 9, No. 1.
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