Quantum Codes and Irreducible Products of Characters

Abstract

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.

References in corpus (6)

• Restrictions on Transversal Encoded Quantum Gate Sets
• Evenly distributed unitaries: on the structure of unitary designs
• Optimizing quantum process tomography with unitary 2-designs
• Unitary designs and codes
• Quantum circuits for exact unitary $t$-designs and applications to higher-order randomized benchmarking
• Quantum Codes from Twisted Unitary $t$-groups

Cited by in corpus (1)

• Quantum error correction beyond $SU(2)$: spin, bosonic, and permutation-invariant codes from convex geometry