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

Restricted Boltzmann Machines (RBM) 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 contact interactions into one-body operators coupled discrete auxiliary fields. This construction generalizes well known Hirsch's transform for Hubbard model theories such as Pionless EFT nuclear physics, analyze detail. We also discuss possible applications our mapping quantum annealing conclude with some implications RBM parameter optimization through machine learning.