Optimized Gottesman-Kitaev-Preskill Error Correction via Tunable Preprocessing

TL;DR

This paper introduces a tunable preprocessing step in GKP error correction that optimizes noise reduction, outperforming existing schemes in certain regimes by actively reshaping noise propagation.

Contribution

It proposes a flexible, parameterized framework for GKP error correction that generalizes and improves upon existing methods through active noise shaping.

Findings

P-Steane scheme reproduces performance of ME-Steane and teleportation-based schemes.

Optimal noise reduction occurs when 2a = b in the small-noise regime.

P-Steane outperforms ME-Steane within specific squeezing parameter ranges.

Abstract

The Gottesman-Kitaev-Preskill (GKP) code is a promising bosonic candidate for realizing fault-tolerant quantum computation. Among existing error-correction protocols for GKP code, the Steane-type scheme is a canonical and widely adopted paradigm, yet its intrinsic noise propagation pattern limits further performance improvement. In this work, we propose a preprocessing-based Steane-type (P-Steane) scheme, which introduces a tunable preprocessing stage with squeezing parameters $a$ and $b$ to actively reshape noise propagation, thereby constituting a parameter framework. This framework spans a spectrum of protocols beyond existing methods, reproducing the performance of both the ME-Steane scheme ($a=1$, $b=1$) and the teleportation-based scheme ($a=1/\sqrt{2}$, $b=\sqrt{2}$) as special cases. Crucially, in the small-noise regime and when the data qubit is noisier than the ancilla qubits, P-Steane scheme achieves the minimum product of position- and momentum-quadrature output noise variances when $2a = b$, and consistently outperforms the ME-Steane scheme within a specific squeezing-parameter range under this condition.