We introduce the domain wall color code, a new variant of the quantum error-correcting color code that exhibits exceptionally high code-capacity error thresholds for qubits subject to biased noise. In the infinite bias regime, a two-dimensional color code decouples into a series of repetition codes, resulting in an error-correcting threshold of 50%. Interestingly, at finite bias, our color code demonstrates thresholds identical to those of the noise-tailored XZZX surface code for all single-qubit Pauli noise channels. The design principle of the code is that it introduces domain walls which permute the code’s excitations upon domain crossing. For practical implementation, we supplement the domain wall code with a scalable restriction decoder based on a matching algorithm. The proposed code is identified as a comparably resource-efficient quantum error-correcting code highly suitable for realistic noise.

中文翻译：

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 域壁颜色代码


我们引入了畴壁颜色代码，这是量子纠错颜色代码的一种新变体，它对于受偏置噪声影响的量子位表现出极高的代码容量错误阈值。在无限偏置状态下，二维颜色代码解耦为一系列重复代码，从而产生 50% 的纠错阈值。有趣的是，在有限偏差下，我们的颜色代码显示的阈值与所有单量子位泡利噪声通道的噪声定制 XZZX 表面代码的阈值相同。该代码的设计原理是引入域壁，在域交叉时对代码的激励进行排列。为了实际实现，我们用基于匹配算法的可扩展限制解码器来补充域墙代码。所提出的代码被认为是一种资源效率较高的量子纠错码，非常适合现实噪声。