通过设计偏置增强表面GKP码的抗噪声能力
Enhanced noise resilience of the surface-GKP code via designed bias
摘要：
我们研究了标准的单模Gottesman-Kitaev-Preskill（GKP）码与表面码级联得到的码。我们表明，这种表面GKP代码相对于（高斯）位移误差的噪声容限提高时，单模压缩酉适用于每个模式，假设与逻辑泡利算子的正交识别适当修改。当不使用GKP综合征信息解码表面码时，我们观察到高达$σ\approx 0.58$移位误差标准差的噪声容限阈值。相反，Fukui等人和Vuillot等人的先前结果报告了标准（分别为复曲面）表面GKP代码的$σ\approx 0.54$和$σ\approx 0.55$之间的阈值。修改后的表面GKP码有效地呈现模式级物理噪声不对称，使GKP量子位上的逻辑级噪声偏置。因此，代码可以受益于表面码对偏置噪声的弹性。我们使用Bravyi等人的近似极大似然解码算法来获得我们的阈值估计。在整个过程中，我们考虑一个理想化的情况下，测量是无噪声和GKP状态是理想的。我们的工作表明，高斯编码的个别模式可以增强级联码。
英文摘要：
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.
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