  Due to its unique scalability potential, continuous variable quantum optics
is a promising platform for large scale quantum computing. In particular, very
large cluster states with a two-dimensional topology that are suitable for
universal quantum computing and quantum simulation can be readily generated in
a deterministic manner, and routes towards fault-tolerance via bosonic quantum
error-correction are known. In this article we propose a complete
measurement-based quantum computing architecture for the implementation of a
universal set of gates on the recently generated two-dimensional cluster states
[1,2]. We analyze the performance of the various quantum gates that are
executed in these cluster states as well as in other two-dimensional cluster
states (the bilayer-square lattice and quad-rail lattice cluster states [3,4])
by estimating and minimizing the associated stochastic noise addition as well
as the resulting gate error probability. We compare the four different states
and find that, although they all allow for universal computation, the quad-rail
lattice cluster state performs better than the other three states which all
exhibit similar performance.
