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

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.

9 pages, 3 figures

References in corpus (5)

• Quantum Error Correction with the Gottesman-Kitaev-Preskill Code
• Building a large-scale quantum computer with continuous-variable optical technologies
• Efficient backcasting search for optical quantum state synthesis
• Streamlined quantum computing with macronode cluster states
• Generating Gottesman-Kitaev-Preskill qubit using a cross-Kerr interaction between a squeezed light and Fock states in optics

Cited by in corpus (7)

• Continuous-variable quantum communication
• Good Gottesman-Kitaev-Preskill codes from the NTRU cryptosystem
• Mixing thermal coherent states for precision and range enhancement in quantum thermometry
• Bosonic quantum error correction using squeezed Fock states
• Logical channel for heralded and pure loss with the Gottesman-Kitaev-Preskill code
• Logical channels in approximate Gottesman-Kitaev-Preskill error correction
• Achievable rates for concatenated square Gottesman-Kitaev-Preskill codes