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arXiv:2607.05814

Latency-Constrained Hardware-Aware Quantum Error Correction Co-Design with Adaptive Confidence-Gated Neural Decoding for the Rotated Surface Code

Sumit Chongder

quant-phcs.ETcs.LGSubmitted Jul 7, 2026• Announced Jul 8, 2026• 0 citations• Revised Jul 8, 2026 (v2)
v1 · Jul 7, 2026v2 · Jul 8, 2026
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Abstract

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.

Comments
29 pages, 18 figures, 12 tables. Source code, trained models, and benchmark data: https://github.com/Sumitchongder/adaptive-qec-decoder

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Neural decoders for quantum error correction have achieved high accuracy on surface code memory experiments, but practical fault-tolerant computation requires decoders that transfer across devices, noise conditions, and logical operations. We introduce a modular graph-recurrent decoder designed for this setting. Built from reusable local syndrome encoders, it is pretrained in simulation and fine-tuned to hardware using a common pipeline, with only lightweight spatial aggregation adapted between experiments. The decoder performs competitively on conventional memory benchmarks, outperforming minimum-weight perfect matching (MWPM) at distances 3 and 5 on an IBM Nighthawk-generation processor and closely approaching AlphaQubit on Google's below-threshold hardware data. We then test the framework in two settings beyond memory decoding on the same IBM device. First, in an XXX-type stability experiment, we continuously tune the effective measurement error rate using a variable pre-readout rotation and train a single decoder jointly across the resulting noise range. It matches or outperforms MWPM across the sweep without requiring a separately calibrated decoder for each setting. Second, we decode a ZZZZZZ-merge lattice-surgery experiment between two distance-3 surface-code patches, improving the decoded correlation between the merge outcome and the final ZZZZZZ parity relative to MWPM on real hardware. Together, these experiments demonstrate neural decoding that is portable not only across hardware, but also across qualitatively different surface code observables and logical operations, using models trainable on single-GPU academic resources.
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Abstract. Suppressing qubit errors is one of the main challenges in building fault-tolerant quantum computers, requiring quantum error correction to protect fragile quantum information during computation cycles. The surface code is a leading approach because of its high error tolerance and compatibility with realistic hardware, but it requires a decoder that can accurately and quickly use the syndrome measurements to discern whether a logical error has occurred. This study investigates whether a feedforward neural-network can serve as a practical decoder for the surface code under circuit-level noise. Using the Stim software package, this study generates surface code circuits at multiple code distances and physical error rates and compiles them into detector samplers, then trains a PyTorch neural-network to predict whether a logical observable flip occurred from the syndrome data. The neural-network decoder is compared against Minimum-Weight Perfect Matching (MWPM), focusing on metrics including logical error rate and inference speed. The results show that the neural-network decoder performs competitively with MWPM for code distances 3 and 5 and provides inference time advantages at higher physical error rates as its inference time remains relatively constant over increasing physical error rates. However, MWPM outperforms the neural-network at distance 7, suggesting that scalability remains a major limitation for neural-network decoders. These results show that neural-networks are a promising approach for tackling quantum error correction, although future work is still needed to improve these models for real systems at larger code distances.
Fast, scalable decoding architectures that operate in a block-wise parallel fashion across space and time are essential for real-time fault-tolerant quantum computing. We introduce a scalable AI-based pre-decoder for the surface code that performs local, parallel error correction with low decoding runtimes, removing the majority of physical errors before passing residual syndromes to a downstream global decoder. This modular architecture is backend-agnostic and composes with arbitrary global decoding algorithms designed for surface codes, and our implementation is completely open source. Integrated with uncorrelated PyMatching, the pipeline achieves end-to-end decoding runtimes of order O(1μs)\mathcal{O}(1 μ\text{s})O(1μs) per round at large code distances on NVIDIA GB300 GPUs while reducing logical error rates (LERs) relative to global decoding alone. In a block-wise parallel decoding scheme with access to multiple GPUs, the decoding runtime can be reduced to well below O(1μs)\mathcal{O}(1 μ\text{s})O(1μs) per round. We observe further LER improvements by training a larger model, outperforming correlated PyMatching up to distance-13. We additionally introduce a noise-learning architecture that infers decoding weights directly from experimentally accessible syndrome statistics without requiring an explicit circuit-level noise model. We show that purely data-driven graph weight estimation can nearly match uncorrelated PyMatching and exceed correlated PyMatching in certain regimes, enabling highly-optimized decoding when hardware noise models are unknown or time-varying, as well as training pre-decoders with realistic noise models. Together, these results establish a practical, modular, and high-throughput decoding framework suitable for large-distance surface-code implementations.