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Trapped Ion Quantum Computing

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

arXiv

Authors: Luca Spagnoli, Alessandro Roggero, Nathan Wiebe

Year

2026

Paper ID

15480

Status

Preprint

Abstract Read

~2 min

Abstract Words

128

Citations

N/A

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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This paper contributes to the Trapped-Ion Quantum Computing research area in the Quantum Articles archive.
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In this work we extend the connection between Quantum Error Correction (QEC) and Lattice Gauge Theories (LGTs) by showing that a mathbbZN gauge theory with prime dimension N...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2602.20661 [2] arXiv https://arxiv.org/abs/2602.20661 [3] Publisher https://arxiv.org/abs/2602.20661

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