Emergence of non-abelian statistics from an abelian model

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It is well known that the toric code model supports abelian anyons. It can be realized on a square lattice of qubits, where the anyons are represented by the endpoints of strings of Pauli operators. We will demonstrate that the non-abelian Ising model can be realized in a similar way, where now the string operators are elements of the Clifford group. The Ising anyons are shown to be essentially superpositions of the abelian toric code ones, 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.