论文标题
线性速率LDPC量子代码高性能的单发解码
Single-Shot Decoding of Linear Rate LDPC Quantum Codes with High Performance
论文作者
论文摘要
我们使用线性编码速率，多项式缩放距离和有效的解码方案来构建和分析低密度均衡检查（LDPC）量子代码的家族。该代码家族基于Guth和Lubotzky首先提出的封闭，四维，双曲线歧管的镶嵌。这项工作的主要贡献是通过Coxeter组的有限表现，对Galois领域的线性表示和拓扑覆盖物来构建合适的歧管。我们在〜13/72 = 0.180的编码率〜k/n上建立了一个下限，并且我们证明，对于我们构建的示例，界限很紧。数值模拟提供了证据表明，低计算复杂性的可行解码方案足以获得高性能。这些解码方案可以处理综合征噪声，因此不必重复均等检查测量值即可解码。我们的数据与单摄制方案中综合征噪声的现象学噪声模型中约为4％的阈值一致。
We construct and analyze a family of low-density parity check (LDPC) quantum codes with a linear encoding rate, polynomial scaling distance and efficient decoding schemes. The code family is based on tessellations of closed, four-dimensional, hyperbolic manifolds, as first suggested by Guth and Lubotzky. The main contribution of this work is the construction of suitable manifolds via finite presentations of Coxeter groups, their linear representations over Galois fields and topological coverings. We establish a lower bound on the encoding rate~k/n of~13/72 = 0.180... and we show that the bound is tight for the examples that we construct. Numerical simulations give evidence that parallelizable decoding schemes of low computational complexity suffice to obtain high performance. These decoding schemes can deal with syndrome noise, so that parity check measurements do not have to be repeated to decode. Our data is consistent with a threshold of around 4% in the phenomenological noise model with syndrome noise in the single-shot regime.
