Learning-Based List Sequential Belief Propagation Decoding of Quantum LDPC Codes

2026-06-18

AI Summary

This work addresses key limitations of belief propagation (BP) decoding for quantum low-density parity-check (QLDPC) codes—namely, performance degradation due to short cycles, degeneracy, and convergence difficulties. The authors propose a reinforcement learning–based list-sequential BP decoder (RL-LS), which uniquely integrates reinforcement learning–driven scheduling of variable-node update order with list-based search. A policy network dynamically selects the update sequence at each step, while soft-biased branches corresponding to suboptimal symbol choices enable effective exploration. Efficient path pruning is achieved through accumulated path metrics. Experimental results demonstrate that, under depolarizing noise and across representative QLDPC codes, the proposed method substantially outperforms existing BP-based decoders, yielding marked improvements in both convergence behavior and error-correction performance.

Abstract

Quantum low-density parity-check (QLDPC) codes are strong candidates for fault-tolerant quantum computation, but efficient decoding remains a major challenge due to short cycles, degeneracy, and the poor convergence of standard belief-propagation (BP) decoders. We propose a reinforcement learning-based list sequential (RL-LS) BP decoder for QLDPC codes by extending the reinforcement-learning-based sequential variable-node scheduling (RL-S) framework with list-based search. At each step, the learned policy selects the next variable node to update; the decoder then retains the ordinary RL-S trajectory while also exploring a competing branch obtained by softly biasing the post-update LLR pair toward the second-most likely Pauli symbol, recomputing the incident local BP messages, and setting the visited variable node to that second-best symbol. Candidate trajectories are ranked and pruned using our proposed cumulative path metric. The resulting decoder extends the learned decoder by combining the improved convergence of learned sequential scheduling with list exploration. Numerical results on representative QLDPC benchmark codes over the depolarizing channel show that our proposed method improves the decoding performance of the underlying decoder and compares favorably with existing BP-based decoding methods.

Problem

• quantum LDPC codes
• decoding
• belief propagation
• degeneracy
• short cycles

Innovation

• reinforcement learning
• list decoding
• sequential scheduling
• belief propagation
• quantum LDPC codes