Free Quantum Codes from Twisted Unitary $t$-groups

TitleFree Quantum Codes from Twisted Unitary $t$-groups
Publication TypeJournal Article
Year of Publication2024
AuthorsKubischta, E, Teixeira, I
Date Published2/2/2024

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 are naturally fault tolerant.