Exact representations of many-body interactions with restricted-Boltzmann-machine neural networks

Rrapaj, Ermal; Roggero, Alessandro

doi:10.1103/physreve.103.013302

Exact representations of many-body interactions with restricted-Boltzmann-machine neural networks

Journal Article · Fri Jan 08 00:00:00 EST 2021 · Physical Review. E

DOI:https://doi.org/10.1103/physreve.103.013302· OSTI ID:1849340

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Univ. of California, Berkeley, CA (United States); Univ. of Minnesota, Minneapolis, MN (United States); OSTI
Univ. of Washington, Seattle, WA (United States)

Restricted Boltzmann machines (RBMs) are simple statistical models defined on a bipartite graph which have been successfully used in studying more complicated many-body systems, both classical and quantum. In this work, we exploit the representation power of RBMs to provide an exact decomposition of many-body contact interactions into one-body operators coupled to discrete auxiliary fields. This construction generalizes the well known Hirsch's transform used for the Hubbard model to more complicated theories such as pionless effective field theory in nuclear physics, which we analyze in detail. Finally, we also discuss possible applications of our mapping for quantum annealing applications and conclude with some implications for RBM parameter optimization through machine learning.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Washington, Seattle, WA (United States)

Sponsoring Organization:: Heising-Simons Foundation; National Science Foundation (NSF); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: FG02-00ER41132

OSTI ID:: 1849340

Journal Information:: Physical Review. E, Journal Name: Physical Review. E Journal Issue: 1 Vol. 103; ISSN 2470-0045

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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