Sparse Mamba Decoder for Quantum Error Correction: Efficient Defect-Centric Processing of Surface Code Syndromes

Quantum error correction (QEC) is essential for enabling quantum advantages, with decoding as a central algorithmic primitive. Owing to its importance and intrinsic difficulty, substantial effort has been made to QEC decoder design, among which neural decoders have recently emerged as a promising data-driven paradigm. Despite this progress, practical deployment remains hindered by a fundamental accuracy-latency tradeoff, often on the microsecond timescale. To address this challenge, here we revisit neural decoders for surface-code decoding under explicit accuracy-latency constraints, considering code distances up to d=9 (161 physical qubits). We unify and redesign representative neural decoders into five architectural paradigms and develop an end-to-end compression pipeline to evaluate their deployability and performance on FPGA hardware. Through systematic experiments, we reveal several previously underexplored insights: (i) near-term decoding performance is driven more by data scale than architectural complexity; (ii) appropriate inductive bias is essential for achieving high decoding accuracy; and (iii) INT4 quantization is a prerequisite for meeting microsecond-scale latency requirements on FPGAs. Together, these findings provide concrete guidance toward scalable and real-time neural QEC decoding.

Real-time decoding is a major bottleneck in scaling quantum error correction (QEC) from noisy intermediate-scale quantum (NISQ) devices to fault-tolerant quantum computing. We present an adaptive confidence-gated decoding framework for the rotated surface code that treats decoding as a two-stage inference problem. A lightweight feed-forward neural network performs fast-path decoding for the majority of syndrome measurements, while only low-confidence predictions are escalated to a minimum-weight perfect matching (MWPM) refinement stage. We benchmark the framework on rotated surface codes with distances $d \in \{3,5,7,9,11\}$ under circuit-level depolarising noise using the Stim stabiliser simulator. The evaluation characterises logical accuracy, confidence-controlled accuracy-latency trade-offs, decoding throughput, per-shot latency, and decoding-graph resource scaling. Routing only 3.3%-6.2% of syndromes to the refinement stage improves logical accuracy from 99.21% for the neural-only baseline to 99.81% at a confidence threshold of 0.95 while incurring only a bounded increase in average decoding cost. Neural-decoder throughput saturates near $4.6 \times 10^{5}$ samples s$^{-1}$ at batch size 512 on commodity CPU hardware, indicating that the neural fast path is not the dominant throughput bottleneck beyond code distance $d=7$. We release the complete benchmarking pipeline, trained models, raw benchmark data, and source code, and explicitly distinguish the experimentally validated contributions from the broader hardware-aware QEC co-design roadmap, including hardware-constrained code discovery, GPU-accelerated inference, and multi-noise optimisation, which remain directions for future work.

Forward error correction is essential for reliable communication over noisy channels. Attention-based model-free neural decoders have shown strong performance for short codes, but their scalability to longer codes is limited by the quadratic memory and computational cost of attention. In this paper, we introduce the Mamba message-passing decoder (MMPD), an attention-free syndrome-based neural decoder for binary linear codes. MMPD retains the Tanner-graph structure of a message-passing decoder by performing local pairwise aggregation along variable-check edges. To enable efficient long-range information propagation, these local updates are combined with bidirectional Mamba state-space blocks. By avoiding dense attention matrices, MMPD scales more favorably for long codes in both memory and computation. Experiments on the (1056, 880) LDPC code show that MMPD achieves a 0.45 dB gain over the state-of-the-art CrossMPT decoder at a specified target bit error rate, while reducing memory consumption by a factor of 1.5. This reduction factor increases substantially for longer codes, demonstrating the applicability of MMPD to scalable neural decoding of practical long codes.