Correcting finite squeezing errors in continuous-variable cluster states

We introduce an efficient scheme to correct errors due to the finite squeezing effects in continuous-variable cluster states. Specifically, we consider the typical situation where the class of algorithms consists of input states that are known. By using the knowledge of the input states, we correct the errors and significantly improve the fidelity in the context of continuous-variable cluster states. We illustrate the error correction scheme for single- and two-mode unitaries implemented by spatial continuous-variable cluster states. We show that there is no resource advantage to error correcting multimode unitaries implemented by spatial cluster states. However, the generalization to multimode unitaries implemented by temporal continuous-variable cluster states shows significant practical advantages since it costs only a small fixed number of optical elements (squeezer, beam splitter, etc.) for an arbitrary number of modes.