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arXiv · 2402.01638

Quantum Codes from Twisted Unitary $t$-groups

Eric Kubischta·Ian Teixeira
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Abstract

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.

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Eric Kubischta, Ian Teixeira. 2024-02-02. Quantum Codes from Twisted Unitary $t$-groups. https://doi.org/10.1103/physrevlett.133.030602

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