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.
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.
Fault-tolerant quantum computation critically depends on the ability to detect and correct physical qubit errors faster than they accumulate. The surface code (SC) has emerged as the most experimentally promising quantum error correction (QEC) framework due to its high threshold and local stabilizer structure, yet its practical performance is bottlenecked by decoder efficiency. Traditional decoding approaches such as minimum-weight perfect matching (MWPM) achieve near-optimal accuracy under independent noise but struggle with correlated errors, circuit-level noise, and real-time latency constraints. This paper investigates how neural network (NN)-based decoders reduce logical error rates in SC quantum systems by learning complex syndrome-to-correction mappings from data. We propose a hybrid convolutional-recurrent neural architecture that processes stabilizer measurement syndromes across both spatial and temporal dimensions, enabling the decoder to capture correlated error patterns inherent in realistic hardware. Systematic simulations under depolarizing, biased, and circuit-level noise models demonstrate that the proposed neural decoder achieves a logical error rate reduction of up to 41.3% compared to MWPM at a physical error rate of p = 0.008, while maintaining sub-millisecond decoding latency compatible with superconducting qubit cycle times. These results establish that data-driven neural decoders represent a scalable and hardware-compatible pathway toward achieving the logical error rates required for practical fault-tolerant quantum computing.
Quantum error correction is essential to achieve fault-tolerant quantum computation in the presence of noisy qubits. Among the most promising approaches to quantum error correction is the surface code, thanks to a scalable two-dimensional architecture, only nearest-neighbor interactions, and a high error threshold. Decoding the surface code, i.e. finding the most likely error chain given a syndrome measurement outcome is a computationally complex task. Traditional decoders rely on classical algorithms, which, especially for larger systems, can be slow and may not always converge to the optimal solution. This thesis presents a novel approach to decoding the surface code using graph neural networks. By mapping the syndrome measurements to a graph and performing graph classification, we find that the graph neural networks can predict the most likely error configuration with high accuracy. Our results show that the GNN-based decoder outperforms the classic minimum weight perfect matching (MWPM) decoder in terms of accuracy. With a phenomenological noise model with depolarizing noise and perfect syndrome measurements, our networks beat MWPM up to code-size 15 across all relevant error rates. Furthermore, the GNN is capable of surpassing MWPM under circuit-level noise up to code size 7. We also show that training the network on repetition code data from a recent experiment [Google Quantum AI, Nature 614, 676 (2023)] produces per-step error rates comparable to those achieved with a matching decoder specifically adapted to the error rates of the physical qubits. This indicates that graph neural network decoders are capable of learning the underlying error distribution on the qubits. Our findings advance the field of quantum error correction and provide a promising new direction for the development of efficient decoding algorithms.
Abstract One of the critical requirements for fault-tolerant quantum computation is fast and reliable decoding,Minimum-weight perfect matching (MWPM) is a reliable surface-code decoder,but it will face long decoding time when decoding instances grow. Neural-network decoders was used to solve this problem, but large models often require costly retraining when the code distance or noise model changes.In this work, we propose a two-stage decoder that combines pretrained graph neural network (GNN) residual pre-decoding with global MWPM cleanup.The GNN receives a detector graph generated by the established decoding backend and assigns confidence scores to local correction candidates.Two staggered layers of parallel local windows process confidence corrections.The residual syndrome is passed to the NVIDIA-accelerated MWPM backend.On matched batches of 32,768 samples, the complete method reduced the logical failure rate by 6.25% to 18.01% relative to Pure MWPM for code distances d=3,5,7 and 9 at physical error rates p = 0.007 to 0.013. At d=3,it decoded 3.48x – 4.38x faster over p=0.003 to 0.021. We also trained separate GNN residual pre-decoders for four circuit-level noise models over 160 code-distance/error-rate configurations and obtained 2.25x to 5.41x speedups in every case.The logical-failure benefit depended on the noise model,but the pace is all improving. Our work can accelerate surface-code decoding pace and extend to others noise models.
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) 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) 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.
Abstract Artificial neural networks (ANNs) are a promising approach to the decoding problem of quantum error correction (QEC), but have observed consistent difficulty when generalising performance to larger QEC codes. Recent scalability-focused approaches have split the decoding workload by using local ANNs to perform initial syndrome processing and leaving final processing to a global residual decoder. We investigated ANN surface code decoding under a scheme exploiting the spatiotemporal structure of syndrome data. In particular, we present a vectorised method for surface code data simulation and benchmark decoding performance when such data defines a multi-label classification problem and generative modelling problem for rotated surface codes with circuit noise after each gate and idle timestep. Performance was found to generalise to rotated surface codes of sizes up to d = 97, with depolarisation parameter thresholds of up to 0.7% achieved, competitive with minimum weight perfect matching (MWPM). Improved timings, compared with MWPM alone, were found starting at code distances of d = 33 and d = 89 under noise models above and below threshold respectively. These results suggest promising prospects for ANN-based frameworks for surface code decoding with performance sufficient to support the demands expected from fault-tolerant resource estimates.
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 X-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 ZZ-merge lattice-surgery experiment between two distance-3 surface-code patches, improving the decoded correlation between the merge outcome and the final ZZ 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.