Comparison of 2D topological codes and their decoding performances
Kao-Yueh Kuo, Ching–Yi Lai
Topological quantum codes are favored because they allow suitable qubit layouts for practical implementation. An N-qubit topological code can be decoded by minimum-weight perfect matching (MWPM) with complexity O(poly(N)). Recently it is shown that various quantum codes, including topological 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 a family of twisted XZZX codes. We will comprehensively compare these codes in terms of code efficiency and decoding performance, assuming perfect error syndromes.
arXiv:2202.06612•IEEE International Symposium on Information Theory (ISIT)•Jun 26, 2022•9 citations