Examples of Gaussian cluster computation

We give simple examples that illustrate the principles of one-way quantum computation using Gaussian continuous-variable cluster states. In these examples, we only consider single-mode evolutions, realizable via linear clusters. In particular, we focus on Gaussian single-mode transformations performed through the cluster state. Our examples highlight the differences between cluster-based schemes and protocols in which special quantum states are prepared off-line and then used as a resource for the on-line computation.