Sequential BP-based Decoding of QLDPC Codes

2026-02-13

AI Summary

This work addresses the convergence difficulties and performance limitations of conventional belief propagation (BP) decoders for quantum low-density parity-check (QLDPC) codes, which arise from short cycles and degeneracy induced by stabilizer constraints. To mitigate these issues, the authors propose sequential check-node scheduling (SCNS) and sequential variable-node scheduling (SVNS), which enhance BP stability through fixed-order message updates. By integrating a guided elimination strategy, they further develop the SBPGD decoder. Notably, this approach improves decoding performance without altering the code structure—requiring only a reordering of message scheduling. Under Pauli-X noise, the method demonstrates significantly enhanced error-correction capability and convergence efficiency. Experimental results show that SVNS-BP outperforms BP-OSD-0 at comparable complexity, while SBPGD achieves substantially lower block error rates and reduced computational overhead compared to BPGD.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

Quantum low-density parity-check (QLDPC) codes are a leading approach to quantum error correction, yet conventional belief propagation (BP) decoders often perform poorly, primarily due to non-convergence exacerbated by stabilizer constraints, which induce short cycles and degeneracy. We propose two scheduling variants, sequential check node scheduling (SCNS) and sequential variable node scheduling (SVNS), that improve BP's error-correction ability by processing check nodes (CNs) or variable nodes (VNs), respectively, in a fixed order, stabilizing message updates and reducing stalls. We also employ this technique to an improved BP-variant called BP guided decimation (BPGD), where symbols are progressively fixed during decoding iterations. Here, we demonstrate that the sequential BPGD (SBPGD) decoder can further improve the convergence properties and performance of the decoder. On standard QLDPC benchmarks under a Pauli-X noise model, our sequential schedules are shown to lower the block error rate relative to conventional BP, and SBPGD outperforms BPGD while using significantly fewer decimation rounds, translating to lower computational cost. These results demonstrate that changing the update schedule, without altering the code, can improve both the reliability and efficiency of BP-based decoding for QLDPC codes. For the [[1922,50,16]] C2 hypergraph-product code with independent X errors, SVNS-BP surpasses BP-OSD-0 in error correction at roughly the same complexity as standard BP.

Problem

• QLDPC codes
• belief propagation
• quantum error correction
• decoder convergence
• stabilizer constraints

Innovation

• sequential scheduling
• QLDPC decoding
• belief propagation
• BP guided decimation
• quantum error correction