论文标题
Gottesman-Kitaev-Preskill代码与XZZX表面代码的串联
Concatenation of the Gottesman-Kitaev-Preskill code with the XZZX surface code
论文作者
论文摘要
玻感代码为量子误差校正提供了替代选项。最近，一个重要的类别的骨气代码，称为Gottesman-Kitaev-Preskill（GKP）代码，最近引起了极大的兴趣。从理论上讲，GKP代码的误差校正能力受到限制，因为它只能纠正位置和动量四倍的小移位错误。一种自然的方法来促进大规模，耐故障量子计算的GKP误差校正，这是用稳定器代码串联编码的GKP状态。 XZZX Surface-GKP代码的性能，即，在两个不同的噪声模型下，研究了与XZZX表面代码相连的单模GKP代码。首先，在代码容量噪声模型中，引入了带有参数$λ$的非对称矩形GKP代码。使用最小重量的完美匹配解码器与连续变量的GKP信息相结合，与阈值$σ\ c $σ\σ\大约0.60 $的标准表面GKP代码相比，XZZX-SURFACE GKP代码的最佳阈值达到$σ\大约0.67 $。其次，我们在实际实现中分析了两倍门的偏移误差，并构建了完整的电路级噪声模型。通过设置适当的偏差参数，在某些情况下，逻辑错误率会降低多次。这些结果表明XZZX Surface-GKP代码更适合在一般噪声模型下的不对称串联。我们还估计了XZZX-Surface GKP代码的开销，该代码使用噪声参数约为291 GKP状态18.5 dB（$κ/g \ \ \ \ \ \ \ \％$ 0.71 \％$），用错误率$ 2.53 \ times10^{-7} $与使用QUBIT基于Qubit Surface Codial的逻辑率进行编码，并使用3041 QUITS，将其编码为$ 2.53 \ times10^{-7} $。
Bosonic codes provide an alternative option for quantum error correction. An important category of bosonic codes called the Gottesman-Kitaev-Preskill (GKP) code has aroused much interest recently. Theoretically, the error correction ability of GKP code is limited since it can only correct small shift errors in position and momentum quadratures. A natural approach to promote the GKP error correction for large-scale, fault-tolerant quantum computation is concatenating encoded GKP states with a stabilizer code. The performance of the XZZX surface-GKP code, i.e., the single-mode GKP code concatenated with the XZZX surface code is investigated in this paper under two different noise models. Firstly, in the code-capacity noise model, the asymmetric rectangular GKP code with parameter $λ$ is introduced. Using the minimum weight perfect matching decoder combined with the continuous-variable GKP information, the optimal threshold of the XZZX-surface GKP code reaches $σ\approx0.67$ when $λ=2.1$, compared with the threshold $σ\approx0.60$ of the standard surface-GKP code. Secondly, we analyze the shift errors of two-qubit gates in the actual implementation and build the full circuit-level noise model. By setting the appropriate bias parameters, the logical error rate is reduced by several times in some cases. These results indicate the XZZX surface-GKP codes are more suitable for asymmetric concatenation under the general noise models. We also estimate the overhead of the XZZX-surface GKP code which uses about 291 GKP states with the noise parameter 18.5 dB ($κ/g \approx 0.71\%$) to encode a logical qubit with the error rate $2.53\times10^{-7}$, compared with the qubit-based surface code using 3041 qubits to achieve almost the same logical error rate.
