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

TL;DR

This paper extends Wegner duality for Z2 lattice gauge theory to arbitrary topologies, resulting in a new class of Ising models that are more efficient for quantum simulation on near-term devices.

Contribution

It generalizes Wegner duality to non-trivial topologies and introduces a more resource-efficient model for quantum simulation of Z2 gauge theories.

Findings

New class of Ising models encoding topology via non-local domain walls

Reduced qubit requirements for simulating Z2 gauge theory on a torus

Feasibility of experimental realization on near-term quantum devices

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.