  Understanding superfluidity remains a major goal of condensed matter physics.
Here we tackle this challenge utilizing the recently developed Fermionic neural
network (FermiNet) wave function Ansatz [D. Pfau et al., Phys. Rev. Res. 2,
033429 (2020).] for variational Monte Carlo calculations. We study the unitary
Fermi gas, a system with strong, short-range, two-body interactions known to
possess a superfluid ground state but difficult to describe quantitatively. We
demonstrate key limitations of the FermiNet Ansatz in studying the unitary
Fermi gas and propose a simple modification based on the idea of an
antisymmetric geminal power singlet (AGPs) wave function. The new AGPs FermiNet
outperforms the original FermiNet significantly in paired systems, giving
results which are more accurate than fixed-node diffusion Monte Carlo and are
consistent with experiment. We prove mathematically that the new Ansatz, which
only differs from the original Ansatz by the method of antisymmetrization, is a
strict generalization of the original FermiNet architecture, despite the use of
fewer parameters. Our approach shares several advantages with the original
FermiNet: the use of a neural network removes the need for an underlying basis
set; and the flexibility of the network yields extremely accurate results
within a variational quantum Monte Carlo framework that provides access to
unbiased estimates of arbitrary ground-state expectation values. We discuss how
the method can be extended to study other superfluids.
