论文标题
通用的信念传播算法用于解码表面代码
Generalized Belief Propagation Algorithms for Decoding of Surface Codes
论文作者
论文摘要
信念传播（BP）众所周知，是一种低复杂性解码算法，对于重要类别的量子误差校正代码，例如值得注意的是，对于量子低密度奇偶校验检查（LDPC）代码的随机扩展器代码类。但是，众所周知，当面对诸如表面代码之类的拓扑代码时，BP的性能会破裂，因为幼稚的BP完全无法达到阈值低于阈值的制度，即误差校正变得有用的政权。先前的作品表明，可以通过诉诸BP框架之外的后处理解码器来进行修复。在这项工作中，我们提出了一种具有外部重新定位循环的广义信念传播方法，该方法成功解码了表面代码，即与天真的BP相对，它恢复了从量身定制的地表代码和统计机械映射的解码器中恢复的子阈值。我们报告在独立的位和相纤维数据噪声下（与理想阈值20.6％相比），在去极化数据噪声下（与理想阈值为18.9％）的阈值为14％$，这与非BP后处理方法所达到的阈值相当。
Belief propagation (BP) is well-known as a low complexity decoding algorithm with a strong performance for important classes of quantum error correcting codes, e.g. notably for the quantum low-density parity check (LDPC) code class of random expander codes. However, it is also well-known that the performance of BP breaks down when facing topological codes such as the surface code, where naive BP fails entirely to reach a below-threshold regime, i.e. the regime where error correction becomes useful. Previous works have shown, that this can be remedied by resorting to post-processing decoders outside the framework of BP. In this work, we present a generalized belief propagation method with an outer re-initialization loop that successfully decodes surface codes, i.e. opposed to naive BP it recovers the sub-threshold regime known from decoders tailored to the surface code and from statistical-mechanical mappings. We report a threshold of 17% under independent bit-and phase-flip data noise (to be compared to the ideal threshold of 20.6%) and a threshold value of 14%$under depolarizing data noise (compared to the ideal threshold of 18.9%), which are on par with thresholds achieved by non-BP post-processing methods.
