Quantum Codes from Twisted Unitary $t$-groups
| Autor: | Kubischta, Eric, Teixeira, Ian |
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| Rok vydání: | 2024 |
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| Zdroj: | Phys. Rev. Lett. 133, 030602 (2024) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevLett.133.030602 |
| Popis: | 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. Comment: Updated to PRL version: changed the title, removed the word "free", added a non-additive codes disclaimer, reorganized the supplemental material |
| Databáze: | arXiv |
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