Correcting finite squeezing errors in continuous-variable cluster states

TL;DR

This paper presents an efficient error correction scheme for finite squeezing effects in continuous-variable cluster states, leveraging known input states to diagnose and correct errors, especially in temporal cluster states, with practical resource benefits.

Contribution

The paper introduces a novel error correction method tailored for continuous-variable cluster states that exploits known input states for precise error diagnosis and correction.

Findings

Error correction scheme effectively mitigates finite squeezing errors.

No resource advantage for spatial cluster states in multimode unitaries.

Significant practical benefits for temporal cluster states with finite optical elements.

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).