Tiurev Konstantin, Pesah Arthur, Derks Peter-Jan H S, Roffe Joschka, Eisert Jens, Kesselring Markus S, Reiner Jan-Michael
HQS Quantum Simulations GmbH, Rintheimer Strasse 23, 76131 Karlsruhe, Germany.
Department of Physics and Astronomy, <a href="https://ror.org/02jx3x895">University College London</a>, London WC1E 6BT, United Kingdom.
Phys Rev Lett. 2024 Sep 13;133(11):110601. doi: 10.1103/PhysRevLett.133.110601.
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.
我们引入了畴壁色码，这是量子纠错色码的一种新变体，对于受偏置噪声影响的量子比特，它展现出极高的码容量错误阈值。在无限偏置 regime 中，二维色码解耦为一系列重复码，从而产生 50% 的纠错阈值。有趣的是，在有限偏置下，对于所有单比特泡利噪声通道，我们的色码展示出与噪声定制的 XZZX 表面码相同的阈值。该码的设计原理是引入畴壁，这些畴壁在畴穿越时会置换码的激发。为了实际实现，我们用基于匹配算法的可扩展限制解码器对畴壁码进行补充。所提出的码被认为是一种资源效率相当高的量子纠错码，非常适合实际噪声情况。
