  We describe how continuous-variable abelian anyons, created on the surface of
a continuous-variable analogue of Kitaev's lattice model can be utilized for
quantum computation. In particular, we derive protocols for the implementation
of quantum gates using topological operations. We find that the topological
operations alone are insufficient for universal quantum computation which leads
us to study additional non-topological operations such as offline squeezing and
single-mode measurements. It is shown that these in conjunction with a
non-Gaussian element allow for universal quantum computation using
continuous-variable abelian anyons.
