Hardware-Efficient Reinforcement-Learned Scheduling for Quantum LDPC Decoders

Quantum low-density parity-check (QLDPC) codes are promising for fault-tolerant quantum computing, but their decoding algorithms present significant hardware implementation challenges. Reinforcement-learned sequential belief propagation (RL-S) improves the error-correction performance of conventional belief propagation (BP) through adaptive variable-node scheduling. However, its heap-based priority management introduces substantial hardware overhead. This paper presents hardware implementations of BP, RL-S, and bucket-based reinforcement-learned BP (BRL-S) for the [[288,12,18]] bivariate bicycle QLDPC code. The BRL-S architectures employ quantized priorities and first-in, first-out (FIFO) buckets to simplify scheduling. Three configurations with two, four, and eight priority levels are evaluated. FPGA synthesis results demonstrate that BRL-S reduces lookup-table utilization by approximately 68--72% compared with RL-S. ASIC synthesis further shows reductions of 63--67% in area and 64--69% in estimated power consumption. These results demonstrate that bucket-based scheduling substantially improves the hardware efficiency of reinforcement-learned QLDPC decoders.