ℤ2 lattice gauge theory on non-trivial topology and its quantum simulation

A bstract Wegner duality is essential for ℤ 2 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 2 qubits with two-body couplings, halving the conventional four-body coupled 2 L 2 qubits, enabling full experimental realization of ℤ 2 lattice gauge theory on near-term devices.