Learning to Decode Quantum LDPC Codes Via Belief Propagation
This addresses decoding challenges in quantum error correction for quantum computing applications, representing an incremental improvement through hybrid RL-BP methods.
The paper tackles the problem of belief-propagation decoding for quantum LDPC codes, which suffers from convergence issues due to quantum degeneracy and short cycles, by proposing a reinforcement-learning approach that learns offline decoding trajectories; simulation results show it achieves superior performance and convergence speed compared to flooding and random sequential schedules, with performance competitive with state-of-the-art BP-based decoders at comparable complexity.
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.