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Topological Quantum Computing Quantum Error Correction Fault Tolerance

Novel Encodings of Homology, Cohomology, and Characteristic Classes

arXiv
Authors: Itai Maimon

Year

2025

Paper ID

17575

Status

Preprint

Abstract Read

~2 min

Abstract Words

107

Citations

N/A

Abstract

Topological quantum error-correcting codes (QECC) encode a variety of topological invariants in their code space. A classic structure that has not been encoded directly is that of obstruction classes of a fiber bundle, such as the Chern or Euler class. Here, we construct and analyze extensions of toric codes. We then analyze the topological structure of their errors and finally construct a novel code using these errors to encode the obstruction class to a fiber bundle. In so doing, we construct an encoding of characteristic classes such as the Chern and Pontryagin class in topological QECC. An example of the Euler class of S2 is constructed explicitly.

Why This Paper Matters

  • This paper contributes to the Quantum Error Correction & Fault Tolerance research area in the Quantum Articles archive.
  • It adds a 2025 reference point for readers tracking recent quantum research.
  • Topological quantum error-correcting codes (QECC) encode a variety of topological invariants in their code space.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2511.03920 [2] arXiv https://arxiv.org/abs/2511.03920 [3] Publisher https://arxiv.org/abs/2511.03920

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