  We study the possibility of producing and detecting continuous variable
cluster states in an optical set-up in an extremely compact fashion. This
method is based on a multi-pixel homodyne detection system recently
demonstrated experimentally, which includes classical data post-processing. It
allows to incorporate the linear optics network, usually employed in standard
experiments for the production of cluster states, in the stage of the
measurement. After giving an example of cluster state generation by this
method, we further study how this procedure can be generalized to perform
gaussian quantum computation.
