We propose a novel fault-tolerant scheme for quantum computation based on the topological phase of a spin lattice model. Abelian anyons are used to simulate non-Abelian properties relevant to topological quantum computation. Universality is realized by using anyon transport and single spin measurements. Along with the topological nature of the encoding, logical states are protected from thermal excitations by a finite energy gap. A proof of principle scheme is proposed that can be realized in Josephson junctions with state of the art technology.