Error correction of the continuous-variable quantum hybrid computation on two-node cluster states: limit of squeezing

TL;DR

This paper analyzes error correction in continuous-variable quantum hybrid computation using two-node cluster states, demonstrating that a hybrid scheme can reduce the squeezing threshold needed for fault-tolerance to -19.25 dB.

Contribution

It introduces a hybrid scheme for universal Gaussian transformations that accounts for realistic imperfections, lowering the squeezing threshold for fault-tolerance.

Findings

Hybrid scheme reduces error in Gaussian transformations

Squeezing threshold for fault-tolerance is lowered to -19.25 dB

Error correction considers imperfect resource states and entanglement

Abstract

In this paper, we investigate the error correction of universal Gaussian transformations obtained in the process of continuous-variable quantum computations. We have tried to bring our theoretical studies closer to the actual picture in the experiment. When investigating the error correction procedure, we have considered that both the resource GKP state itself and the entanglement transformation are imperfect. In reality, the GKP state has a finite width associated with the finite degree of squeezing, and the entanglement transformation is performed with error. We have considered a hybrid scheme to implement the universal Gaussian transformations. In this scheme, the transformations are realized through computations on the cluster state, supplemented by linear optical operation. This scheme gives the smallest error in the implementation of universal Gaussian transformations. The use of such a scheme made it possible to reduce the oscillator squeezing threshold required for the implementing of fault-tolerant quantum computation schemes close to reality to -19.25 dB.