Enhanced Message-Passing Decoding of Degenerate Quantum Codes Utilizing Trapping Set Dynamics

In this letter, we propose a novel iterative decoding algorithm that exploits the degenerate nature of three different families of quantum low-density parity-check codes, i.e., surface, toric, and row-degree-4 bicycle codes. Such families of codes share harmful trapping sets that constitute symmetric stabilizers, making it impossible for any parallel-scheduled iterative message-passing decoder to converge even for error patterns of weight as low as two. By biasing subsets of nodes in the symmetric stabilizers, the decoder is able to converge to a valid error pattern. Furthermore, the proposed decoder has low decoding complexity - linear in the code’s blocklength - and a fully parallel schedule, making it suitable for low-latency efficient implementation.