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PreprintCC BY 4.0arXiv

Exact Recovery for Non-Abelian Surface Codes

  • Alison Warman
  • Nathanan Tantivasadakarn
  • Sakura Schafer-Nameki
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Abstract

We study exact recovery for non-Abelian topological surface codes based on the quantum double D(G) of any finite group G. We determine an orthogonal error basis, that is comprised of group multiplication and irreducible representation operators. Whenever the errors are supported on closed loops on the lattice or dual lattice, there is a redundancy in the basis, due to stabilizers. To remedy this, we introduce a gauge-fixing that results in a complete and orthogonal error basis on the code space. Assuming as input predetermined, neutral correctable error clusters, we construct charge and flux transfer circuits that move the errors onto ancillas that then get projected out. This is an exact and deterministic recovery protocol, applicable to surface codes for any finite, in particular non-Abelian, group G.

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Cite

BibTeXRIS
BibTeX
@misc{warman2026exact,
  title = {{Exact Recovery for Non-Abelian Surface Codes}},
  author = {Alison Warman and Nathanan Tantivasadakarn and Sakura Schafer-Nameki},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.03677},
  eprint = {2610.03677},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.03677},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Exact Recovery for Non-Abelian Surface Codes
AU  - Alison Warman
AU  - Nathanan Tantivasadakarn
AU  - Sakura Schafer-Nameki
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.03677
UR  - https://arxiv.org/abs/2610.03677
AB  - We study exact recovery for non-Abelian topological surface codes based on the quantum double D(G) of any finite group G. We determine an orthogonal error basis, that is comprised of group multiplication and irreducible representation operators. Whenever the errors are supported on closed loops on the lattice or dual lattice, there is a redundancy in the basis, due to stabilizers. To remedy this, we introduce a gauge-fixing that results in a complete and orthogonal error basis on the code space. Assuming as input predetermined, neutral correctable error clusters, we construct charge and flux transfer circuits that move the errors onto ancillas that then get projected out. This is an exact and deterministic recovery protocol, applicable to surface codes for any finite, in particular non-Abelian, group G.
ER  -