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

Open access
Date
2018-12-14Type
- Journal Article
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Cited 80 times in
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Cited 81 times in
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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. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000313237Publication status
publishedExternal links
Journal / series
Nature CommunicationsVolume
Pages / Article No.
Publisher
Nature Publishing GroupMore
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Citations
Cited 80 times in
Web of Science
Cited 81 times in
Scopus
ETH Bibliography
yes
Altmetrics