Degenerate Quantum LDPC Codes With Good Finite Length Performance

We study the performance of medium-length quantum LDPC (QLDPC) codes in depolarizing channel. Only degenerate with maximal stabilizer weight much smaller than their minimum distance are considered. It is shown that help OSD-like post-processing standard belief propagation (BP) decoder on many QLDPC can be improved by several orders magnitude. Using this new BP-OSD we known classes including hypergraph product codes, hyperbicycle homological and Haah's cubic codes. also construct interesting examples short generalized bicycle Some them have an additional property syndromes protected small BCH which may useful for fault-tolerant syndrome measurement. propose a large family contains class where one used parity-check matrices square. some cases such better Finally, demonstrate proposed constructed relatively surface code decoded near-optimal decoder.