Non-abelian statistics from an abelian model

Details Non-abelian statistics from an abelian model Non-abelian statistics from an abelian model

2008-04-06

arxiv.org/abs/0804.0931v4

Phys. Rev. B 78, 161102(R) (2008)

Physics

Condensed Matter

Statistical Mechanics

5 pages, 3 figures

Scientific paper

10.1103/PhysRevB.78.161102

It is well known that the abelian $Z_2$ anyonic model (toric code) can be realized on a highly entangled two-dimensional spin lattice, where the anyons are quasiparticles located at the endpoints of string-like concatenations of Pauli operators. Here we show that the same entangled states of the same lattice are capable of supporting the non-abelian Ising model, where the concatenated operators are elements of the Clifford group. The Ising anyons are shown to be essentially superpositions of the abelian toric code anyons, reproducing the required fusion, braiding and statistical properties. We propose a string framing and ancillary qubits to implement the non-trivial chirality of this model.

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