Could the Hilbert Space Be a Smaller Place? A Neural Network Perspective

In quantum many-body problems, one of the main difficulties comes from the description of non-negligible interactions which require, at least in principle, an exponential amount of information. Recently, in the context of spin glasses and Boltzmann machines, it has been demonstrated that systematic machine learning of the wave function can reduce these issues to a tractable computational problem. In this work, we apply this approach to a different situation, i.e. the problem of finding the ground state of a given quantum system made of electrons, entirely described by its Hamiltonian operator, and by utilizing feedforward neural networks. Although still in the shape of a proof of concept, one can already observe that this seminal idea is able to substantially simplify the complexity of this peculiar, and important, problem.