A generalization of the cluster-state model of quantum computation to continuous-variable systems is described, along with a proposal for an optical implementation using squeezed-light sources, linear optics, and homodyne detection.
For universal quantum computation, a truly nonlinear element is required. This requirement can be satisfied by adding to the toolbox any single-mode non-Gaussian measurement, while the initial cluster state itself remains Gaussian.
We propose a systematic way on how to build any Gaussian cluster state most efficiently via a network of beam splitters.
Various methods for suppressing finite-squeezing induced errors in cluster computation are discussed.