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arXiv 2201.07802quant-phcond-mat.dis-nncond-mat.mes-hallcond-mat.stat-mech
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Clifford 变形的表面码

Clifford-deformed Surface Codes

Arpit Dua, Aleksander Kubica, Liang Jiang, Steven T. Flammia, Michael J. Gullans

备注：
6+10 pages, 14 figures, v2 changes: added a section on a translation-invariant code belonging to a high-performance random CDSC family to demonstrate the practical relevance of the random CDSCs. The code used for the simulations in the paper is available at https://github.com/dua-arpit/qecsim. See also https://errorcorrectionzoo.org/c/clifford-deformed_surface, v3 changes: PRX Quantum version
发表信息：
PRX Quantum 5, 010347 (2024)
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AI总结：

本文研究 Clifford 变形表面码在偏置噪声下的性能，引入有效距离并揭示随机 CDSC 的相图，证明其优于已知平移不变码，并构造了高性能平移不变 CDSC。

摘要：

Kitaev 表面码的各种实现在偏置泡利噪声下表现出色。受这些潜在增益的吸引，我们研究了通过对表面码应用单比特 Clifford 算子而获得的 Clifford 变形表面码（CDSC）的性能。我们首先分析了 $3\ imes 3$ 方格上的 CDSC，发现根据噪声偏置的不同，其逻辑错误率可能相差几个数量级。为了解释观察到的行为，我们引入了有效距离 $d'$，它在无偏噪声下退化为标准距离。为了研究热力学极限下的 CDSC 性能，我们专注于随机 CDSC。利用量子码的统计力学映射，我们揭示了一个相图，描述了在无限偏置下具有 50% 阈值的随机 CDSC 族。在高阈值区域，我们进一步证明了典型码实现优于已知最佳平移不变码在有限偏置下的阈值和亚阈值逻辑错误率。我们通过构造一个属于高性能随机 CDSC 族的平移不变 CDSC，证明了这些随机 CDSC 族的实际相关性。我们还表明，我们的平移不变 CDSC 优于众所周知的平移不变 CDSC，如 XZZX 和 XY 码。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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