Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2008-12-12
J. Stat. Mech. (2009) P12013
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
9 pages, 2 figures, published version
Scientific paper
10.1088/1742-5468/2009/12/P12013
We demonstrate that the two inequivalent spinor representations of the braid group \B_{2n+2}, describing the exchanges of 2n+2 non-Abelian Ising anyons in the Pfaffian topological quantum computer, are equivalent from computational point of view, i.e., the sets of topologically protected quantum gates that could be implemented in both cases by braiding exactly coincide. We give the explicit matrices generating almost all braidings in the spinor representations of the 2n+2 Ising anyons, as well as important recurrence relations. Our detailed analysis allows us to understand better the physical difference between the two inequivalent representations and to propose a process that could determine the type of representation for any concrete physical realization of the Pfaffian quantum computer.
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