论文标题
克利福德（Clifford）形成的表面代码
Clifford-deformed Surface Codes
论文作者
论文摘要
Kitaev表面代码的各种认识对于有偏见的Pauli噪音表现出色。在这些潜在的收益中，我们研究了通过应用单Qubit Clifford操作员从表面代码获得的Clifford呈现的表面代码（CDSC）的性能。我们首先在$ 3 \ times 3 $方格上分析CDSC，并发现，根据噪声偏差，它们的逻辑错误率可能会因数量级而有所不同。为了解释观察到的行为，我们介绍了有效距离$ d'$，这将减少到无偏噪声的标准距离。为了研究热力学极限的CDSC性能，我们关注随机CDSC。使用量子代码的统计机械映射，我们发现了一个相图，该相图描述了无限偏见的$ 50 \％$阈值的随机CDSC家族。在高阈值区域，我们进一步证明，典型的代码实现优于最著名的翻译不变代码的阈值和子阈值逻辑错误率。我们通过构建属于高性能随机CDSC家族的翻译不变的CDSC来证明这些随机CDSC家族的实际相关性。我们还表明，我们的翻译不变的CDSC优于众所周知的翻译不变的CDSC，例如XZZX和XY代码。
Various realizations of Kitaev's surface code perform surprisingly well for biased Pauli noise. Attracted by these potential gains, we study the performance of Clifford-deformed surface codes (CDSCs) obtained from the surface code by applying single-qubit Clifford operators. We first analyze CDSCs on the $3\times 3$ square lattice and find that, depending on the noise bias, their logical error rates can differ by orders of magnitude. To explain the observed behavior, we introduce the effective distance $d'$, which reduces to the standard distance for unbiased noise. To study CDSC performance in the thermodynamic limit, we focus on random CDSCs. Using the statistical mechanical mapping for quantum codes, we uncover a phase diagram that describes random CDSC families with $50\%$ threshold at infinite bias. In the high-threshold region, we further demonstrate that typical code realizations outperform the thresholds and subthreshold logical error rates, at finite bias, of the best-known translationally invariant codes. We demonstrate the practical relevance of these random CDSC families by constructing a translation-invariant CDSC belonging to a high-performance random CDSC family. We also show that our translation-invariant CDSC outperforms well-known translation-invariant CDSCs such as the XZZX and XY codes.
