Quantum computation with Abelian anyons on the honeycomb lattice

We consider a two-dimensional spin system that exhibits Abelian anyonic excitations. Manipulations of these excitations enable the construction of a quantum computational model. While the one-qubit gates are performed dynamically, the model offers the advantage of having a two-qubit gate that is of topological nature. The transport and braiding of anyons on the lattice can be performed adiabatically enjoying the robust characteristics of geometrical evolutions. The same control procedures can be used when dealing with non-Abelian anyons. A possible implementation of the manipulations with optical lattices is developed.