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arXiv · 2602.20661

Qudit stabiliser codes for $\mathbb{Z}_N$ lattice gauge theories with matter

Luca Spagnoli·Alessandro Roggero·Nathan Wiebe
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Abstract

In this work we extend the connection between Quantum Error Correction (QEC) and Lattice Gauge Theories (LGTs) by showing that a $\mathbb{Z}_N$ gauge theory with prime dimension $N$ coupled to dynamical matter can be expressed as a qudit stabilizer code. Using the stabilizer formalism we show how to formulate an exact mapping of the encoded $\mathbb{Z}_N$ gauge theory onto two different bosonic models, uncovering a logical duality generated by error correction itself. From this perspective, quantum error correction provides a unifying language to expose dual descriptions of lattice gauge theories. In addition, we generalize earlier $\mathbb{Z}_2$ constructions on qubits to $\mathbb{Z}_N$ on $N$-level qudits and demonstrate how universal fault-tolerant gates can be implemented via state injection between compatible qudit codes.

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Luca Spagnoli, Alessandro Roggero, Nathan Wiebe. 2026-02-24. Qudit stabiliser codes for $\mathbb{Z}_N$ lattice gauge theories with matter. https://arxiv.org/abs/2602.20661

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