论文标题
通过设计偏见增强了表面GKP代码的噪声弹性
Enhanced noise resilience of the surface-GKP code via designed bias
论文作者
论文摘要
我们通过将标准的单模Gottesman-Kitaev-Preskill（GKP）代码与表面代码连接来研究代码。我们表明，当将单模挤压统一的单位应用于每种模式时，该表面GKP代码相对于（高斯）位移误差的噪声耐力会改善，假设使用逻辑Pauli操作员识别四足动物的识别。当在不使用GKP综合征信息的情况下解码表面代码时，我们观察到高达$σ\ $σ\的噪声阈值。相比之下，Fukui等人的先前结果。和Vuillot等。报告标准（分别为感谢您的）表面gkp代码的$σ\约0.54 $和$σ\ $σ\ $σ\ $σ\ $ 0.55 $的阈值。修改的表面GKP代码有效地呈现模式级的物理噪声不对称，从而偏向GKP Qubits上的逻辑级别噪声。因此，该代码可以从偏置噪声的表面代码的弹性中受益。我们使用Bravyi等人的近似最大似然解码算法。获得我们的阈值估计。在整个过程中，我们都考虑了一个理想化的场景，其中测量是无噪用的，而GKP状态是理想的。我们的工作表明，单个模式的高斯编码可以增强串联代码。
We study the code obtained by concatenating the standard single-mode Gottesman-Kitaev-Preskill (GKP) code with the surface code. We show that the noise tolerance of this surface-GKP code with respect to (Gaussian) displacement errors improves when a single-mode squeezing unitary is applied to each mode assuming that the identification of quadratures with logical Pauli operators is suitably modified. We observe noise-tolerance thresholds of up to $σ\approx 0.58$ shift-error standard deviation when the surface code is decoded without using GKP syndrome information. In contrast, prior results by Fukui et al. and Vuillot et al. report a threshold between $σ\approx 0.54$ and $σ\approx 0.55$ for the standard (toric-, respectively) surface-GKP code. The modified surface-GKP code effectively renders the mode-level physical noise asymmetric, biasing the logical-level noise on the GKP-qubits. The code can thus benefit from the resilience of the surface code against biased noise. We use the approximate maximum likelihood decoding algorithm of Bravyi et al. to obtain our threshold estimates. Throughout, we consider an idealized scenario where measurements are noiseless and GKP states are ideal. Our work demonstrates that Gaussian encodings of individual modes can enhance concatenated codes.
