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arXiv:2601.09921

Learning to Decode in Parallel: Self-Coordinating Neural Network for Real-Time Quantum Error Correction

Kai Zhang, Zhengzhong Yi, Shaojun Guo, Linghang Kong, Situ Wang, Xiaoyu Zhan, Tan He, Weiping Lin, Tao Jiang, Dongxin Gao, Yiming Zhang, Fangming Liu, Fang Zhang, Zhengfeng Ji, Fusheng Chen, Jianxin Chen

quant-phcs.AISubmitted Jan 14, 2026• Announced Jan 16, 2026• 0 citations
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Abstract

Fast, reliable decoders are pivotal components for enabling fault-tolerant quantum computation (FTQC). Neural network decoders like AlphaQubit have demonstrated potential, achieving higher accuracy than traditional human-designed decoding algorithms. However, existing implementations of neural network decoders lack the parallelism required to decode the syndrome stream generated by a superconducting logical qubit in real time. Moreover, integrating AlphaQubit with sliding window-based parallel decoding schemes presents non-trivial challenges: AlphaQubit is trained solely to output a single bit corresponding to the global logical correction for an entire memory experiment, rather than local physical corrections that can be easily integrated. We address this issue by training a recurrent, transformer-based neural network specifically tailored for parallel window decoding. While it still outputs a single bit, we derive training labels from a consistent set of local corrections and train on various types of decoding windows simultaneously. This approach enables the network to self-coordinate across neighboring windows, facilitating high-accuracy parallel decoding of arbitrarily long memory experiments. As a result, we overcome the throughput bottleneck that previously precluded the use of AlphaQubit-type decoders in FTQC. Our work presents the first scalable, neural-network-based parallel decoding framework that simultaneously achieves SOTA accuracy and the stringent throughput required for real-time quantum error correction. Using an end-to-end experimental workflow, we benchmark our decoder on the Zuchongzhi 3.2 superconducting quantum processor on surface codes with distances up to 7, demonstrating its superior accuracy. Moreover, we demonstrate that, using our approach, a single TPU v6e is capable of decoding surface codes with distances up to 25 within 1us per decoding round.

Comments
The main text consists of 25 pages and 9 figures, extending our prior work (arXiv:2509.03815) with new results on surface code decoding in superconducting qubit systems and real-time performance benchmarks on TPU v6e

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Fast, reliable decoders are pivotal components for enabling fault-tolerant quantum computation (FTQC). Neural network decoders like AlphaQubit have demonstrated potential, achieving higher accuracy than traditional human-designed decoding algorithms. However, existing implementations of neural network decoders lack the parallelism required to decode the syndrome stream generated by a superconducting logical qubit in real time. Moreover, integrating AlphaQubit with sliding window-based parallel decoding schemes presents non-trivial challenges: AlphaQubit is trained solely to output a single bit corresponding to the global logical correction for an entire memory experiment, rather than local physical corrections that can be easily integrated. We address this issue by training a recurrent, transformer-based neural network specifically tailored for parallel window decoding. While it still outputs a single bit, we derive training labels from a consistent set of local corrections and train on various types of decoding windows simultaneously. This approach enables the network to self-coordinate across neighboring windows, facilitating high-accuracy parallel decoding of arbitrarily long memory experiments.
As a result, we overcome the throughput bottleneck that previously precluded the use of AlphaQubit-type decoders in FTQC. Our work presents the first scalable, neural-network-based parallel decoding framework that simultaneously achieves SOTA accuracy and the stringent throughput required for real-time quantum error correction. Using an end-to-end experimental workflow, we benchmark our decoder on the Zuchongzhi 3.2 superconducting quantum processor on surface codes with distances up to 7, demonstrating its superior accuracy. Moreover, we demonstrate that, using our approach, a single TPU v6e is capable of decoding surface codes with distances up to 25 within 1us per decoding round.
Fault-tolerant quantum computing will require error rates far below those achievable with physical qubits. Quantum error correction (QEC) bridges this gap, but depends on decoders being simultaneously fast, accurate, and scalable. This combination of requirements remains unmet by a machine-learning decoder, nor by any decoder for promising resource-efficient codes such as the color code. Here we introduce AlphaQubit 2, a neural-network decoder that achieves near-optimal logical error rates for both surface and color codes at scale under realistic noise. For the color code, it is orders of magnitude faster than other high-accuracy decoders. We demonstrate real-time decoding faster than 1μs per cycle on commercial accelerators: for the surface code to distance 11, with better accuracy than leading real-time decoders; and the first real-time decoding of the color code to distance 9. These results support the practical application of a wider class of promising QEC codes, and establish a credible path towards high-accuracy, real-time neural decoding at the scales required for fault-tolerant quantum computation.
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.
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.
Quantum error-correcting codes (QECCs) can eliminate the negative effects of quantum noise, the major obstacle to the execution of quantum algorithms. However, realizing practical quantum error correction (QEC) requires resolving many challenges to implement a high-performance real-time decoding system. Many decoding algorithms have been proposed and optimized in the past few decades, of which neural network (NNs) based solutions have drawn an increasing amount of attention due to their high efficiency. Unfortunately, previous works on neural decoders are still at an early stage and have only relatively simple architectures, which makes them unsuitable for practical QEC. In this work, we propose a scalable, fast, and programmable neural decoding system to meet the requirements of FTQEC for rotated surface codes (RSC). Firstly, we propose a hardware-efficient NN decoding algorithm with relatively low complexity and high accuracy. Secondly, we develop a customized hardware decoder with architectural optimizations to reduce latency. Thirdly, our proposed programmable architecture boosts the scalability and flexibility of the decoder by maximizing parallelism. Fourthly, we build an FPGA-based decoding system with integrated control hardware for evaluation. Our L=5L=5L=5 (LLL is the code distance) decoder achieves an extremely low decoding latency of 197 ns, and the L=7L=7L=7 configuration also requires only 1.136 μμμs, both taking 2L2L2L rounds of syndrome measurements. The accuracy results of our system are close to minimum weight perfect matching (MWPM). Furthermore, our programmable architecture reduces hardware resource consumption by up to 3.0×3.0\times3.0× with only a small latency loss. We validated our approach in real-world scenarios by conducting a proof-of-concept benchmark with practical noise models, including one derived from experimental data gathered from physical hardware.
Quantum error correction (QEC) is essential for achieving low error rates required for fault-tolerant quantum computation. In stabilizer-based codes such as the surface code, errors are inferred from repeated syndrome measurements and corrected by a classical decoder. To prevent error accumulation, decoding must be performed with both high throughput and low latency to keep pace with the QEC cycle and enable real-time feedback for universal logical operations. Here we report a hardware-integrated control architecture featuring an FPGA-based neural-network (NN) decoder and experimentally demonstrate real-time surface-code (distance-3) QEC on a superconducting quantum processor. The system achieves a deterministic closed-loop latency of 550 ns, including 124 ns for NN decoding, enabling feedback corrections within a 1.25 us QEC cycle. We show that real-time decoding and feedback correction achieve logical performance comparable to offline decoding while maintaining robustness against varying error conditions. We further demonstrate mid-circuit feedback correction in non-Clifford logical circuits, where Pauli-frame updating alone becomes insufficient. Our results establish a low-latency hardware architecture for embedded QEC control and provide a pathway towards scalable fault-tolerant quantum computing systems.
Decoding is an essential component of quantum error correction (QEC), translating stabilizer measurement outcomes into corrective actions that suppress logical errors and preserve logical quantum information. Building fault-tolerant architectures requires increasing the code distance, which in turn places growing demands on decoding accuracy, scalability, and practical deployability. While a wide range of decoding algorithms have been proposed and demonstrated, achieving reliable, scalable, and real-time decoding remains a significant challenge. Machine-learning (ML) approaches are particularly well suited to this setting, as quantum error decoding is fundamentally a problem of processing large volumes of classical data with complex spatiotemporal correlations. This chapter surveys ML-based methods for quantum error decoding, with a focus on topological codes and an emphasis on architectural principles, practical performance, and real-time considerations. We first frame decoding as a learning problem and outline key paradigms, including discriminative, generative, and reinforcement-learning formulations. We then introduce the neural network building blocks that underpin most contemporary neural decoders and discuss how these components can be integrated to balance expressivity, scalability, and latency. Building on this architectural perspective, we review recent progress and benchmarks in neural decoding for memory experiments, and discuss real-time decoding, open challenges, and future directions toward scalable fault-tolerant quantum computing.