论文标题
比较2D拓扑代码及其解码性能
Comparison of 2D topological codes and their decoding performances
论文作者
论文摘要
拓扑量子代码受到青睐，因为它们允许适合实际实施的量子布局。如果是CSS-type，则可以通过具有复杂性$ o（\ text {poly}（n））$的最小重量匹配（MWPM）来解码$ n $ qubit的拓扑代码。最近表明，包括非CSS代码在内的各种量子代码可以通过适应性的信念传播和内存效应（表示为MBP）进行解码，其复杂性几乎是$ n $的线性。在本文中，我们表明，无论布局如何，各种二维拓扑代码，CSS或非CSS都可以通过MBP解码，包括颜色代码和扭曲的XZZX代码。假设完美的错误综合症，我们将在代码效率和解码性能方面进行全面比较这些代码。
Topological quantum codes are favored because they allow qubit layouts that are suitable for practical implementation. An $N$-qubit topological code can be decoded by minimum-weight perfect matching (MWPM) with complexity $O(\text{poly}(N))$ if it is of CSS-type. Recently it is shown that various quantum codes, including non-CSS codes, can be decoded by an adapted belief propagation with memory effects (denoted MBP) with complexity almost linear in $N$. In this paper, we show that various two-dimensional topological codes, CSS or non-CSS, regardless of the layout, can be decoded by MBP, including color codes and twisted XZZX codes. We will comprehensively compare these codes in terms of code efficiency and decoding performance, assuming perfect error syndromes.
