Precision-Pyramid: Towards real-time neural decoding for fault-tolerant quantum computing

Real-time quantum error correction (QEC) is a critical bottleneck for fault-tolerant quantum computing due to strict hardware latency constraints. While neural decoders achieve state-of-the-art logical accuracy, their reliance on high-precision, compute-intensive inference precludes real-time deployment. Conversely, uniformly quantizing these models to extreme low-bit regimes for FPGAs triggers a catastrophic collapse in decoding accuracy. To overcome this precision-accuracy bottleneck, we propose Precision Pyramid ($\mathsf{PP}$), a hardware-algorithm co-designed neural decoder applicable to both surface and BB codes. $\mathsf{PP}$ features a monotonically escalating activation precision hierarchy built upon a globally weight-binarized (W1) foundation. By scaling intermediate activations down to INT2 for the massive perception stages and reserving higher precision strictly for the lightweight final logical decision, this hierarchy effectively shifts over $99\%$ of the computational workload to abundant FPGA look-up tables. Comprehensive evaluations on both simulated and hardware-calibrated noise data demonstrate that $\mathsf{PP}$ consistently suppresses logical errors below highly optimized classical baselines (e.g., MWPM and Relay-BP) while seamlessly satisfying stringent sub-microsecond latency budgets.