Non-Abelian statistics from an Abelian model

Abstract

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 end points of stringlike 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 nontrivial chirality of this model.