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

2025-07-15

AI Summary

This study addresses the error floor phenomenon observed in quantum quasi-cyclic low-density parity-check (QC-LDPC) codes under joint belief propagation (BP) decoding. Through Tanner graph substructure analysis, we systematically characterize a sharp error-rate phase transition—reminiscent of a threshold behavior—for the first time in non-zero-rate quantum LDPC codes. We identify small-scale trapping sets as the primary source of residual errors causing the floor. Our method precisely pinpoints the local graph structures responsible for dominant error events, thereby establishing a causal link between trapping sets and the error floor. The results provide a theoretical foundation for understanding BP decoding failure mechanisms in quantum codes and reveal a critical pathway—graph-structural optimization targeting trapping-set suppression—to break through the error floor. This work offers essential guidance for designing high-performance quantum error-correcting codes with improved iterative decoding performance.

Technology Category

• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Other Foundations of Search & Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

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 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.

Problem

• Analyzing steep error-rate transitions in quantum QC-LDPC codes
• Investigating error floor causes via trapping sets in Tanner graphs
• Exploring joint BP decoding for quantum codes with non-zero rates

Innovation

• Joint BP decoding for quantum QC-LDPC codes
• Threshold-like behavior with non-vanishing rate
• Trapping sets cause error floor in codes