2024/03/13 by Kubischta, Eric, Teixeira, Ian · 2 citations
#FOS: Mathematics #FOS: Physical sciences #Quantum Physics (quant-ph) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2403.08999
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.