Fermionic wave functions from neural-network constrained hidden states

Significance Large systems of interacting quantum particles present a notorious computational challenge, since they require to solve an eigenvalue problem in an exponentially large dimensional space. The problem can be approached variationally: A trial wave function is proposed, depending on a set of parameters that are determined by an optimization procedure. Neural networks are a great candidate for the task as they provide an extremely flexible family of trial states. We introduce a neural-network-based trial wave function formalism for the study of systems of interacting fermions. This formalism is based on the addition of extra hidden fermions that, aided by neural networks, “mediate” the correlations between the particles in the wave function when projected back on the physical space.