Gauge equivariant neural networks for quantum lattice gauge theories

Gauge symmetry plays a fundamental role in physics. We propose a family of neural-network quantum states with gauge equivariant architecture which exactly satisfy the local Hilbertspace constraints of quantum lattice gauge theories. It is shown that the gauge equivariant neural network has exact represention of the ground state solutions for Zn Toric code model corresponding to the loop-gas solution. For Z2 Toric code model with transverse field away from the exactly solvable limit, we apply the gauge equivariant neural-network quantum states as trial wavefunctions within variational quantum Monte Carlo to obtain compact descriptions of the ground state and understand the phase transition.