论文标题
改进了更高维超图产品代码的单发解码
Improved single-shot decoding of higher dimensional hypergraph product codes
论文作者
论文摘要
在这项工作中，我们研究了使用信念传播和有序统计量解码解码的较高维度超图产品代码的单发性能[Panteleev and Kalachev，2021]。我们发现，在单个阶段中解码数据量子量和综合征测量误差会导致单发阈值，这些阈值大大超过了这些代码的所有先前观察到的单次单次阈值。对于3D复曲面代码和现象学噪声模型，我们的结果与$ z $错误的可持续阈值7.1％一致，而先前使用两阶段解码器〜[Quintavalle等人，2021年）的阈值2.90％。对于4D复合代码，$ x $和$ z $错误校正都是单发的，我们的结果与可持续的单发阈值4.3％是一致的，甚至高于相同噪声模型的2D感谢您的阈值2.93％，但使用$ L $ l $ $ $ $ $ $ $ l $ $。我们还探讨了平衡产品和4D超盖产品代码的性能，我们显示的导致量子额外的降低，比较了现象学误差率高达1％的表面代码。
In this work we study the single-shot performance of higher dimensional hypergraph product codes decoded using belief-propagation and ordered-statistics decoding [Panteleev and Kalachev, 2021]. We find that decoding data qubit and syndrome measurement errors together in a single stage leads to single-shot thresholds that greatly exceed all previously observed single-shot thresholds for these codes. For the 3D toric code and a phenomenological noise model, our results are consistent with a sustainable threshold of 7.1% for $Z$ errors, compared to the threshold of 2.90% previously found using a two-stage decoder~[Quintavalle et al., 2021]. For the 4D toric code, for which both $X$ and $Z$ error correction is single-shot, our results are consistent with a sustainable single-shot threshold of 4.3% which is even higher than the threshold of 2.93% for the 2D toric code for the same noise model but using $L$ rounds of stabiliser measurement. We also explore the performance of balanced product and 4D hypergraph product codes which we show lead to a reduction in qubit overhead compared the surface code for phenomenological error rates as high as 1%.
