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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2511.03920 |
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| _version_ | 1866914140201680896 |
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| author | Maimon, Itai |
| author_facet | Maimon, Itai |
| contents | 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 $S^2$ is constructed explicitly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03920 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Novel Encodings of Homology, Cohomology, and Characteristic Classes Maimon, Itai Quantum Physics Mathematical Physics 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 $S^2$ is constructed explicitly. |
| title | Novel Encodings of Homology, Cohomology, and Characteristic Classes |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2511.03920 |