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PreprintarXiv licencearXiv

Topological Quantum Error-Correcting Thresholds of a Symmetry-Enriched Toric Code

  • Jiasheng He
  • Ryan Thorngren
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Abstract

We study the error thresholds of a new topological quantum error-correcting code under the independent bit-flip and phase-flip noisy channel. By mapping to classical spin-glass models, we find that if Pauli X and Z errors are equally probable, the threshold of vertex syndromes is improved by 30% compared to that of the toric code, while the threshold of plaquette syndromes is lowered. Both thresholds increase when the Z component is less likely than the X component, reaching 0.5 if the Z component is absent. An analytical proof justifies this special case of perfect correctability, and a disordered version of Peierls's argument establishes a lower bound for the vertex-syndrome threshold.

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Cite

BibTeXRIS
BibTeX
@misc{he2026topological,
  title = {{Topological Quantum Error-Correcting Thresholds of a Symmetry-Enriched Toric Code}},
  author = {Jiasheng He and Ryan Thorngren},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37791},
  eprint = {2610.37791},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37791},
}
RIS
TY  - UNPB
TI  - Topological Quantum Error-Correcting Thresholds of a Symmetry-Enriched Toric Code
AU  - Jiasheng He
AU  - Ryan Thorngren
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.37791
UR  - https://arxiv.org/abs/2610.37791
AB  - We study the error thresholds of a new topological quantum error-correcting code under the independent bit-flip and phase-flip noisy channel. By mapping to classical spin-glass models, we find that if Pauli X and Z errors are equally probable, the threshold of vertex syndromes is improved by 30% compared to that of the toric code, while the threshold of plaquette syndromes is lowered. Both thresholds increase when the Z component is less likely than the X component, reaching 0.5 if the Z component is absent. An analytical proof justifies this special case of perfect correctability, and a disordered version of Peierls's argument establishes a lower bound for the vertex-syndrome threshold.
ER  -