Quantum Codes and Irreducible Products of Characters
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909162921787392 |
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| author | Kubischta, Eric Teixeira, Ian |
| author_facet | Kubischta, Eric Teixeira, Ian |
| contents | In a recent paper, we defined twisted unitary $1$-groups and showed that they automatically induced error-detecting quantum codes. We also showed that twisted unitary $1$-groups correspond to irreducible products of characters thereby reducing the problem of code-finding to a computation in the character theory of finite groups. Using a combination of GAP computations and results from the mathematics literature on irreducible products of characters, we identify many new non-trivial quantum codes with unusual transversal gates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08999 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum Codes and Irreducible Products of Characters Kubischta, Eric Teixeira, Ian Quantum Physics Representation Theory In a recent paper, we defined twisted unitary $1$-groups and showed that they automatically induced error-detecting quantum codes. We also showed that twisted unitary $1$-groups correspond to irreducible products of characters thereby reducing the problem of code-finding to a computation in the character theory of finite groups. Using a combination of GAP computations and results from the mathematics literature on irreducible products of characters, we identify many new non-trivial quantum codes with unusual transversal gates. |
| title | Quantum Codes and Irreducible Products of Characters |
| topic | Quantum Physics Representation Theory |
| url | https://arxiv.org/abs/2403.08999 |