Quantum Codes from Twisted Unitary $t$-groups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866910562306228224 |
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| author | Kubischta, Eric Teixeira, Ian |
| author_facet | Kubischta, Eric Teixeira, Ian |
| contents | We introduce twisted unitary $t$-groups, a generalization of unitary $t$-groups under a twisting by an irreducible representation. We then apply representation theoretic methods to the Knill-Laflamme error correction conditions to show that twisted unitary $t$-groups automatically correspond to quantum codes with distance $d=t+1$. By construction these codes have many transversal gates, which naturally do not spread errors and thus are useful for fault tolerance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01638 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum Codes from Twisted Unitary $t$-groups Kubischta, Eric Teixeira, Ian Quantum Physics We introduce twisted unitary $t$-groups, a generalization of unitary $t$-groups under a twisting by an irreducible representation. We then apply representation theoretic methods to the Knill-Laflamme error correction conditions to show that twisted unitary $t$-groups automatically correspond to quantum codes with distance $d=t+1$. By construction these codes have many transversal gates, which naturally do not spread errors and thus are useful for fault tolerance. |
| title | Quantum Codes from Twisted Unitary $t$-groups |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2402.01638 |