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Gauge symmetries play a key role in physics appearing in areas such asquantum field theories of the fundamental particles and emergent degrees offreedom in quantum materials. Motivated by the desire to efficiently simulatemany-body quantum systems with exact local gauge invariance, gauge equivariantneural-network quantum states are introduced, which exactly satisfy the localHilbert space constraints necessary for the description of quantum latticegauge theory with Zd gauge group on different geometries. Focusing on thespecial case of Z2 gauge group on a periodically identified square lattice, theequivariant architecture is analytically shown to contain the loop-gas solutionas a special case. Gauge equivariant neural-network quantum states are used incombination with variational quantum Monte Carlo to obtain compact descriptionsof the ground state wavefunction for the Z2 theory away from the exactlysolvable limit, and to demonstrate the confining/deconfining phase transitionof the Wilson loop order parameter.

Gauge equivariant neural networks for quantum lattice gauge theories