  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.
