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arXiv:2601.16776

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

Jiaqi Hu, Shu Tian, Xiaopeng Cui, Rebing Wu, Man-Hong Yung, Yu Shi

hep-latcond-mat.otherquant-phSubmitted Jan 23, 2026• Announced Jan 26, 2026• 0 citations
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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.

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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 LL torus requires only LL 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.
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.
Non-invertible topological defects in 4-dimensional Z2\mathbb {Z}_2Z2​ pure lattice gauge theory
Abstract We explore topological defects in the 4D pure Z2\mathbb {Z}_2Z2​ lattice gauge theory. This theory has 1-form Z2\mathbb {Z}_{2}Z2​ center symmetry as well as Kramers–Wannier–Wegner (KWW) duality. We construct the KWW duality topological defects in a similar way to those constructed by Aasen et al. [J. Phys. A 49, 354001 (2016)] for the 2D Ising model. These duality defects turn out to be non-invertible. We also construct 1-form Z2\mathbb {Z}_{2}Z2​ symmetry defects as well as the junctions between the KWW duality defects and 1-form Z2\mathbb {Z}_{2}Z2​ center symmetry defects. The crossing relations between these defects are derived. The expectation values of some configurations of these topological defects are calculated by using these crossing relations.
We relate two classical dualities in low-dimensional quantum field theory: Kramers-Wannier duality of the Ising and related lattice models in 222 dimensions, with electromagnetic duality for finite gauge theories in 333 dimensions. The relation is mediated by the notion of boundary field theory: Ising models are boundary theories for pure gauge theory in one dimension higher. Thus the Ising order/disorder operators are endpoints of Wilson/'t Hooft defects of gauge theory. Symmetry breaking on low-energy states reflects the multiplicity of topological boundary states. In the process we describe lattice theories as (extended) topological field theories with boundaries and domain walls. This allows us to generalize the duality to non-abelian groups; finite, semi-simple Hopf algebras; and, in a different direction, to finite homotopy theories in arbitrary dimension.
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
We propose an implementation of a two-dimensional Z2\mathbb{Z}_2Z2​ lattice gauge theory model on a shallow quantum circuit, involving a number of single and two-qubits gates comparable to what can be achieved with present-day and near-future technologies. The ground state preparation is numerically analyzed on a small lattice with a variational quantum algorithm, which requires a small number of parameters to reach high fidelities and can be efficiently scaled up on larger systems. Despite the reduced size of the lattice we consider, a transition between confined and deconfined regimes can be detected by measuring expectation values of Wilson loop operators or the topological entropy. Moreover, if periodic boundary conditions are implemented, the same optimal solution is transferable among all four different topological sectors, without any need for further optimization on the variational parameters. Our work shows that variational quantum algorithms provide a useful technique to be added in the growing toolbox for digital simulations of lattice gauge theories.
Kitaev's toric code is an exactly solvable model with Z2{\mathbb{Z}}_{2}Z2​-topological order, which has potential applications in quantum computation and error correction. However, a direct experimental realization remains an open challenge. Here, we propose a building block for Z2{\mathbb{Z}}_{2}Z2​ lattice gauge theories coupled to dynamical matter and demonstrate how it allows for an implementation of the toric-code ground state and its topological excitations. This is achieved by introducing separate matter excitations on individual plaquettes, whose motion induce the required plaquette terms. The proposed building block is realized in the second-order coupling regime and is well suited for implementations with superconducting qubits. Furthermore, we propose a pathway to prepare topologically nontrivial initial states during which a large gap on the order of the underlying coupling strength is present. This is verified by both analytical arguments and numerical studies. Moreover, we outline experimental signatures of the ground-state wave function and introduce a minimal braiding protocol. Detecting a $\ensuremath{\pi}$-phase shift between Ramsey fringes in this protocol reveals the anyonic excitations of the toric-code Hamiltonian in a system with only three triangular plaquettes. Our work paves the way for realizing non-Abelian anyons in analog quantum simulators.