Low-Latency Belief-Propagation Decoding of Quantum LDPC Codes with Reinforcement-Learned Scheduling

Abstract

Belief propagation (BP) is attractive for quantum low-density parity-check (QLDPC) decoding because of its low complexity and low latency, but short cycles and degeneracy can limit its error-correction performance. Reinforcement-learned sequential scheduling (RL-S) substantially improves this performance by adapting the variable node (VN) update order, although Q-table storage and heap-based selection introduce additional overhead. We propose bucket RL-S (B-RL-S), which quantizes learned Q-values into integer priorities and schedules VN updates using dynamically maintained first-in, first-out buckets. Without retraining or changing the BP message updates, B-RL-S reduces policy storage and refreshes only priorities affected by local residual syndrome changes. A fixed number of priority levels enables constant-time VN selection and queue relocation. For the $[[288,12,18]]$ bivariate bicycle code over the depolarizing channel at $p=0.05$, B-RL-S with eight priority levels achieves approximately one fifth the block error rate (BLER) of flooding BP followed by order-10 ordered-statistics decoding. The respective caps are $1000$ sequential iterations for B-RL-S and $1000$ flooding iterations for the BP stage of the reference decoder. These results highlight strong error correction with inexpensive scheduling and no additional post-processing stage.