  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.
