Learning to Decode Quantum LDPC Codes Via Belief Propagation

2026-03-10

AI Summary

This work addresses the convergence challenges of belief propagation (BP) decoding for quantum low-density parity-check (QLDPC) codes, which arise from quantum degeneracy and short cycles in the Tanner graph. The authors formulate the decoding process as a Markov decision process and propose a novel sequential decoding strategy that integrates reinforcement learning with a local syndrome-driven state representation. To enhance computational efficiency, they introduce a second-order neighborhood incremental update mechanism that eliminates the need for global rescan during inference. Experimental results demonstrate that the proposed method outperforms both flooding and random scheduling strategies on representative QLDPC codes, achieving performance comparable to state-of-the-art BP decoders at similar computational complexity while significantly accelerating convergence.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

Abstract

Belief-propagation (BP) decoding for quantum low-density parity-check (QLDPC) codes is appealing due to its low complexity, yet it often exhibits convergence issues due to quantum degeneracy and short cycles that exist in the Tanner graph. To overcome this challenge, this paper proposes a reinforcement-learning (RL) approach that learns (offline) how to decode QLDPC codes based on sequential decoding trajectories. The decoding is formulated as a Markov decision process with a local, syndrome-driven state representation of the underlying RL agent. To enable fast inference, critical for practical implementation, we incrementally update our RL-based QLDPC decoder using second-order neighborhoods that avoid global rescans. Simulation results on representative QLDPC codes demonstrate the superiority of the proposed RL-based QLDPC decoders in terms of performance and convergence speed when compared to flooding and random sequential schedules, while achieving performance competitive with state-of-the-art BP-based decoders at comparable complexity.

Problem

• quantum LDPC codes
• belief propagation
• convergence issues
• quantum degeneracy
• short cycles

Innovation

• reinforcement learning
• quantum LDPC codes
• belief propagation
• Markov decision process
• syndrome-driven decoding