2014/12/31 by Claire I. Levaillant, Levaillant, Claire I.
Computer Science · Mathematics · Physics and Astronomy · #20F36 #81P68 #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Group Theory (math.GR) #Information Theory (cs.IT) #Quantum Algebra (math.QA) #Quantum Physics (quant-ph) #Representation Theory (math.RT) #cs.IT #math.GR #math.IT #math.QA #math.RT #msc:20F36 #msc:81P68 #quant-ph
paper · pdf · doi:10.48550/arxiv.1501.01013
21 pages, 33 figures
arxiv created 2014/12/31 · arxiv updated 2015/01/07
We present a way to physically realize a circulant 2-qubit entangling gate in the Kauffman-Jones version of SU(2) Chern-Simons theory at level 4. Our approach uses qubit and qutrit ancillas, braids, fusions and interferometric measurements. Our qubit is formed by four anyons of topological charges 1221. Among other 2-qubit entangling gates we generate in the present paper, we produce in particular the circulant gate CEG = 1/4 I + I sqrt(3)/4 J - 3/4 J2 + I sqrt(3)/4 J3, where J denotes the permutation matrix associated with the cycle (1432) and I denotes the identity matrix.