论文标题

有偏见的Gottesman-Kitaev-Preskill重复代码

Biased Gottesman-Kitaev-Preskill repetition code

论文作者

Stafford, Matthew P., Menicucci, Nicolas C.

论文摘要

基于Gottesmann-Kitaev-Preskill(GKP)编码的连续变量量子计算体系结构已成为有前途的候选人,因为人们可以通过GKP状态和高斯操作的概率供应实现耐受性的耐受性。此外,通过将矩形晶格GKP状态推广,可以通过串联与量子代码的串联引入和利用偏差,从而在偏见下显示出改善的性能。但是,这些代码(例如XZZX表面代码)仍然需要重量四面稳定器测量,并且具有复杂的解码要求以克服。在这项工作中,我们研究了在各向同性高斯流离失所通道下与重复代码相连的矩形晶格GKP的代码容量行为。对于噪声的标准偏差,我们发现$σ= 0.599 $的数值阈值,它的表现优于偏见的GKP平面表面代码,而在GKP级别上的偏见增加了。这一切都是仅通过重量测试稳定器运算符和量子级的简单解码而实现的。此外,对于$σ\ leq 0.3 $,仍然可以实现中等水平的偏差(长宽比$ \ leq 2.4 $)和九个或更少的数据模式,逻辑错误率仍然可以显着降低,开放了将GKP偏置的重复代码作为简单的低级静态测试代码的可能性,以进一步交汇。

Continuous-variable quantum computing architectures based upon the Gottesmann-Kitaev-Preskill (GKP) encoding have emerged as a promising candidate because one can achieve fault-tolerance with a probabilistic supply of GKP states and Gaussian operations. Furthermore, by generalising to rectangular-lattice GKP states, a bias can be introduced and exploited through concatenation with qubit codes that show improved performance under biasing. However, these codes (such as the XZZX surface code) still require weight-four stabiliser measurements and have complex decoding requirements to overcome. In this work, we study the code-capacity behaviour of a rectangular-lattice GKP encoding concatenated with a repetition code under an isotropic Gaussian displacement channel. We find a numerical threshold of $σ= 0.599$ for the noise's standard deviation, which outperforms the biased GKP planar surface code with a trade-off of increased biasing at the GKP level. This is all achieved with only weight-two stabiliser operators and simple decoding at the qubit level. Furthermore, with moderate levels of bias (aspect ratio $\leq 2.4$) and nine or fewer data modes, significant reductions in logical error rates can still be achieved for $σ\leq 0.3$, opening the possibility of using GKP-biased repetition codes as a simple low-level qubit encoding for further concatenation.

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