Z2 Lattice Gauge Theory on Non-trivial Topology and Its Quantum Simulation

Abstract

Wegner duality is essential for Z2 lattice gauge theory, yet the duality on non-trivial topologies has remained implicit. We extend Wegner duality to arbitrary topology and dimension, obtaining a new class of Ising models, in which topology is encoded in non-local domain-wall patterns. Without the overhead of gauge constraints, simulating this model on an L*L torus requires only L*L qubits with two-body couplings, halving the conventional four-body coupled 2L*L qubits, enabling full experimental realization of Z2 lattice gauge theory on near-term devices.