Correcting finite squeezing errors in continuous-variable cluster states

Abstract

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 can diagnose exactly what errors have occurred and correct them in the context of temporal continuous-variable cluster states. We illustrate the error correction scheme for single-mode 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 finite number of optical elements (squeezer, beam splitter, etc).

17 pages, 4 figures

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• CZ vs Beam Splitter: errors of entangled operations
• Error of an arbitrary single-mode Gaussian transformation on a weighted cluster state using a cubic phase gate
• Quantum computations on the ensemble of two-node cluster states, obtained by sub-Poissonian lasers
• Estimation of the set of states obtained in particle number measurement schemes