论文标题
在平面图表代码中，错误的校正和噪声确定性阈值
Error-correction and noise-decoherence thresholds for coherent errors in planar-graph surface codes
论文作者
论文摘要
我们在平面图上的表面代码中数字研究相干错误，重点是$ z $ - 或$ x $ - 单个Qubits的噪声。我们发现，与不连贯的位和相卷曲的情况类似，可以通过图表的连接性进行相对于连贯的$ x $ - 与$ z $ - 旋转之间的韧性之间的权衡。但是，我们的结果表明，与不一致的情况不同，各个图的误差校正阈值不会接近通用界限。我们还研究了错误校正后最终状态的分布。我们表明，图属于三个不同的类，每个类别导致定性不同的最终状态分布。特别是，我们表明存在图类类别，其中逻辑级别的噪声表现出略高于误差校正阈值略高的脱谐度阈值。因此，在这些类别中，即使对于大距离代码，误差校正阈值上方的逻辑级噪声也可以保留大量的连贯性。为了进行我们的分析，我们开发了平面形式表面代码的主要植物特性表示，并使用基于费米尼 - 线性 - 镜头的模拟来描述逻辑状态存储的表征。因此，我们概括了Bravyi \ textit {et al}为方格引入的方法。 [NPJ量子Inf。 4，55（2018）]到一般平面图上的表面代码。
We numerically study coherent errors in surface codes on planar graphs, focusing on noise of the form of $Z$- or $X$-rotations of individual qubits. We find that, similarly to the case of incoherent bit- and phase-flips, a trade-off between resilience against coherent $X$- and $Z$-rotations can be made via the connectivity of the graph. However, our results indicate that, unlike in the incoherent case, the error-correction thresholds for the various graphs do not approach a universal bound. We also study the distribution of final states after error correction. We show that graphs fall into three distinct classes, each resulting in qualitatively distinct final-state distributions. In particular, we show that a graph class exists where the logical-level noise exhibits a decoherence threshold slightly above the error-correction threshold. In these classes, therefore, the logical level noise above the error-correction threshold can retain significant amount of coherence even for large-distance codes. To perform our analysis, we develop a Majorana-fermion representation of planar-graph surface codes and describe the characterization of logical-state storage using fermion-linear-optics-based simulations. We thereby generalize the approach introduced for the square lattice by Bravyi \textit{et al}. [npj Quantum Inf. 4, 55 (2018)] to surface codes on general planar graphs.
