论文标题
跨量子LDPC代码景观进行解码
Decoding Across the Quantum LDPC Code Landscape
论文作者
论文摘要
我们表明,信仰传播与有序的统计后处理相结合,是量子低密度平等校准代码从HyperGraph产品构建的一般解码器。为此,我们运行了应用于三个系列HyperGraph产品代码的解码器的数值仿真:拓扑代码,固定速率随机代码和我们称为半知名代码的新一类代码。我们的新代码家族共享拓扑和随机超图产品代码的属性,其结构允许在代码阈值和稳定器区域之间进行精心控制的权衡。我们的结果表明,所有三个HyperGraph产品代码家族的阈值,并提供了低误差制度中指数抑制的证据。对于曲折代码,我们观察到$ 9.9 \ pm0.2 \%$的范围内的阈值。基于信念传播的先前量子解码器改善了这一结果,并处理最小重量完美匹配算法的性能。我们预计,半主体代码的阈值与感谢您在大量中相同的阈值相同,并且我们提供了支持这一观察结果的数值证据。
We show that belief propagation combined with ordered statistics post-processing is a general decoder for quantum low density parity check codes constructed from the hypergraph product. To this end, we run numerical simulations of the decoder applied to three families of hypergraph product code: topological codes, fixed-rate random codes and a new class of codes that we call semi-topological codes. Our new code families share properties of both topological and random hypergraph product codes, with a construction that allows for a finely-controlled trade-off between code threshold and stabilizer locality. Our results indicate thresholds across all three families of hypergraph product code, and provide evidence of exponential suppression in the low error regime. For the Toric code, we observe a threshold in the range $9.9\pm0.2\%$. This result improves upon previous quantum decoders based on belief propagation, and approaches the performance of the minimum weight perfect matching algorithm. We expect semi-topological codes to have the same threshold as Toric codes, as they are identical in the bulk, and we present numerical evidence supporting this observation.