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Journal of High Energy Physics

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

J N Hu, Shu Tian, Xiaopeng Cui, Re-Bing Wu, Man‐Hong Yung, Yu Shi

Published Jul 8, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1007/jhep07(2026)067

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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.
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.
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Abstract We study the quantum simulation of Z2Z_2Z2​ lattice gauge theory in 2+1 dimensions. The dual variable formulation, the so-called Wegner duality, is utilized for reducing redundant gauge degrees of freedom. The problem of artificial charge unconservation is resolved for any charge distribution. As a demonstration, we simulate the real-time evolution of the system with two static electric charges, i.e. with two temporal Wilson lines. Some results obtained by a simulator (with no hardware noise) and a real quantum computing device (with sizable hardware noise) are shown.
Two-dimensional Z2\mathbb{Z}_2Z2​ lattice gauge theory on a near-term quantum simulator: variational quantum optimization, confinement, and topological order
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