Sharp Error-Rate Transitions in Quantum QC-LDPC Codes under Joint BP Decoding

In this study, we report that quantum quasi-cyclic low-density parity-check codes decoded via joint belief propagation (BP) exhibit steep error-rate curves, despite the presence of error floors. To the best of our knowledge, this is the first observation of such threshold-like behavior for quantum LDPC codes with non-vanishing coding rate, excluding those decoded with non-binary BP decoders. Moreover, we find that dominant error events contributing to the error floor typically involve only a small number of bits. These findings suggest that the error floor is caused by trapping sets–specific subgraph structures in the Tanner graph–and indicate that identifying and avoiding such structures may lead to further reduction of the error floor.