Exact representations of many body interactions with RBM neural networks

Understand

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 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 EFT in nuclear physics, which we analyze in detail.
• We also discuss possible applications of our mapping for quantum annealing applications and conclude with some implications for RBM parameter optimization through machine learning.