Quantum Error Correction with the GKP Code and Concatenation with Stabilizer Codes

TL;DR

This paper enhances quantum error correction by utilizing the continuous shift information in GKP codes, improving fault-tolerance through maximum-likelihood decoding and leveraging the code's intrinsic continuous properties.

Contribution

It introduces a method to exploit all continuous shift information in GKP codes, boosting error correction performance beyond traditional approaches.

Findings

Maximum-likelihood decoding improves fault-tolerance.

Continuous shift information enhances error correction.

GKP code's intrinsic properties are advantageous for quantum error correction.

Abstract

Gottesman, Kitaev and Preskill have proposed a scheme to encode a qubit in a harmonic oscillator, which is called the GKP code. It is designed to be resistant to small shift errors contained in momentum and position quadratures. Thus there's some intrinsic fault tolerance of the GKP code. In this thesis,we propose a method to utilize all the information contained in the continuous shifts, not just simply map a GKP-encoded qubit to a normal qubit. This method enables us to do maximum-likelihood decisions and thus increase fault-tolerance of the GKP code. This thesis shows that the continuous nature of the GKP code is quite useful for quantum error correction.