Qudit stabiliser codes for $\mathbb{Z}_N$ lattice gauge theories with matter
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866912923063943168 |
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| author | Spagnoli, Luca Roggero, Alessandro Wiebe, Nathan |
| author_facet | Spagnoli, Luca Roggero, Alessandro Wiebe, Nathan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20661 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Qudit stabiliser codes for $\mathbb{Z}_N$ lattice gauge theories with matter Spagnoli, Luca Roggero, Alessandro Wiebe, Nathan Quantum Physics 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. |
| title | Qudit stabiliser codes for $\mathbb{Z}_N$ lattice gauge theories with matter |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2602.20661 |