High-Performance Reinforcement-Learned BP Decoding of Quantum LDPC Codes

2026-07-27

AI Summary

This work addresses the limitations of conventional belief propagation (BP) decoding for quantum low-density parity-check (LDPC) codes, which often suffers from stagnation due to stabilizer degeneracy and short cycles in the Tanner graph, thereby compromising error-correction performance. To overcome this, the authors propose a reinforcement learning–based second-order locally updated BP decoder (RL-S2LU) that employs offline learning to derive adaptive scheduling policies for variable nodes, intelligently optimizing the message-passing order. By preserving locality and maintaining low computational complexity, RL-S2LU significantly enhances decoding convergence and outperforms both standard BP and the BP-OSD-10 baseline in error-correction capability, effectively circumventing the performance bottleneck inherent in fixed scheduling strategies.

Abstract

Belief-propagation (BP) decoding is attractive for quantum low-density parity-check (QLDPC) codes because it uses local message passing on sparse Tanner graphs. However, conventional flooding BP often stalls due to stabilizer degeneracy and short cycles. Reinforcement-learning-based sequential variable-node scheduling (RL-S), which learns the update order offline, has shown that adaptive scheduling can improve BP convergence. In this paper, we extend this idea with a second-order local update decoder, RL-S2LU. The proposed decoder preserves BP locality and low complexity, while numerical results show significant error-correction gains over conventional BP and the considered BP-OSD-10 baseline.

Problem

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

Innovation

• reinforcement learning
• quantum LDPC codes
• belief propagation
• adaptive scheduling
• second-order local update