We devise a new realization of the surface code on a rectangular lattice of qubits utilizing single-qubit and nearest-neighbor two-qubit Pauli measurements and three auxiliary qubits per plaquette. This realization gains substantial advantages over prior pairwise measurement-based realizations of the surface code. It has a short operation period of 4 steps and our performance analysis for a standard circuit noise model yields a high fault-tolerance threshold of approximately $0.66\% $. The syndrome extraction circuits avoid bidirectional hook errors, so we can achieve full code distance by choosing appropriate boundary conditions. We also construct variants of the syndrome extraction circuits that entirely prevent hook errors, at the cost of larger circuit depth. This achieves full distance regardless of boundary conditions, with only a modest decrease in the threshold. Furthermore, we propose an efficient strategy for dealing with dead components (qubits and measurements) in our surface code realization, which can be adopted more generally for other surface code realizations. This new surface code realization is highly optimized for Majorana-based hardware, accounting for constraints imposed by layouts and the implementation of measurements, making it competitive with the recently proposed Floquet codes.

中文翻译：

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改进的基于成对测量的表面代码


我们利用单量子位和最近邻的两个量子位泡利测量以及每个斑块的三个辅助量子位，在量子位的矩形晶格上设计了表面代码的新实现。与表面代码的先前基于成对测量的实现相比，这种实现获得了显着的优势。它的操作周期很短，只有 4 个步骤，我们对标准电路噪声模型的性能分析产生了大约 0.66%$ 的高容错阈值。校正子提取电路避免了双向钩子错误，因此我们可以通过选择适当的边界条件来实现全码距。我们还构建了校正子提取电路的变体，以完全防止钩子错误，但代价是更大的电路深度。无论边界条件如何，这都实现了全距离，并且阈值仅略有下降。此外，我们提出了一种有效的策略来处理表面代码实现中的死组件（量子位和测量），该策略可以更普遍地用于其他表面代码实现。这种新的表面代码实现针对基于 Majorana 的硬件进行了高度优化，考虑了布局和测量实施所施加的限制，使其与最近提出的 Floquet 代码具有竞争力。