2013/12/23 by Claire Levaillant, Claire I. Levaillant, Levaillant, Claire I.
Computer Science · Mathematics · Physics and Astronomy · #81P68 #FOS: Mathematics #FOS: Physical sciences #Group Theory (math.GR) #Quantum Algebra (math.QA) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata #Representation Theory (math.RT) #math.GR #math.QA #math.RT #msc:81P68 #quant-ph
paper · pdf · doi:10.48550/arxiv.1401.0506
17 pages, 18 figures
arxiv created 2013/12/23 · openalex publication_date 2013/12/23 · arxiv updated 2014/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
As part of a protocol, we braid in a certain way six anyons of topological charges 222211 in the Kauffman-Jones version of SU(2) Chern-Simons theory at level 4. The gate we obtain is a braid for the usual qutrit 2222 but with respect to a different basis. With respect to that basis, the Freedman group of \citeLEV is identical to the D-group D(18,1,1;2,1,1). We give a physical interpretation for each Blichfeld generator of the group D(18,1,1;2,1,1). Inspired by these new techniques for the qutrit, we are able to make new ancillas, namely (1)/(√(2))(|1> +|3>) and (1)/(√(2))(|1> -|3>), for the qubit 1221.