Analysis of loss correction with the Gottesman-Kitaev-Preskill code

TL;DR

This paper demonstrates that for GKP quantum error correction against loss, amplification is unnecessary and can even impair performance, simplifying practical implementations.

Contribution

It shows that teleportation-based GKP error correction can effectively handle loss without amplification, challenging previous assumptions.

Findings

Amplification worsens GKP error correction performance in realistic scenarios.

Teleportation-based GKP correction effectively mitigates loss without additional amplification.

Avoiding amplification reduces implementation complexity and potential noise sources.

Abstract

The Gottesman-Kitaev-Preskill (GKP) code is a promising bosonic quantum error-correcting code, encoding logical qubits into a bosonic mode in such a way that many physically relevant noise types can be corrected effectively. A particularly relevant noise channel is the pure loss channel, which the GKP code is known to protect against. In particular, it is commonly pointed out that losses can be corrected by the GKP code by transforming the losses into random Gaussian displacements through a quantum-limited amplification channel. However, implementing such amplification in practice is not ideal and could easily introduce an additional overhead of noise from associated experimental imperfections. Here, we analyse the performance of teleportation-based GKP error correction against loss in the absence of an amplification channel. We show that amplification is not required to perform GKP error correction, and that performing amplification actually worsens the performance for practically relevant parameter regimes.