Fault-tolerant quantum computing critically relies on quantum error correction. We study surface-code decoding with diagonally correlated two-qubit $\mathbf{Z}$ errors, a structured noise model that breaks assumptions leveraged by MinimumWeight Perfect Matching (MWPM). We develop a graph neural network (GNN) decoder based on learned message passing and benchmark it against a tuned MWPM baseline informed by the same noise statistics. In code-capacity simulations at code distances 3, 5, and 7, the GNN achieves consistently lower logical error rates than MWPM across the tested range of pair-error probabilities. The GNN correction threshold is about 2.5%, surpassing the 2.4% achieved by the MWPM baseline. These results indicate that data-driven message passing can adapt to complex, geometry-dependent noise without hand-crafted correlation models, thereby reducing reliance on manual model specification for quantum error correction.
Fault-tolerant quantum computing critically relies on quantum error correction. We study surface-code decoding with diagonally correlated two-qubit Z errors, a structured noise model that breaks assumptions leveraged by MinimumWeight Perfect Matching (MWPM). We develop a graph neural network (GNN) decoder based on learned message passing and benchmark it against a tuned MWPM baseline informed by the same noise statistics. In code-capacity simulations at code distances 3, 5, and 7, the GNN achieves consistently lower logical error rates than MWPM across the tested range of pair-error probabilities. The GNN correction threshold is about 2.5%, surpassing the 2.4% achieved by the MWPM baseline. These results indicate that data-driven message passing can adapt to complex, geometry-dependent noise without hand-crafted correlation models, thereby reducing reliance on manual model specification for quantum error correction.
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.
Quantum error correction (QEC) is crucial for achieving fault-tolerant quantum computing by addressing errors in noisy qubits. The surface code, a leading QEC framework, traditionally employs the Minimum Weight Perfect Matching (MWPM) decoder. We present a step-by-step methodology that formulates surface code decoding as a supervised machine learning classification problem within a two-level framework, where low-level modules address physical qubit errors and highlevel modules correct logical errors. We implement Feedforward Neural Networks (FFNN) and Graph Neural Networks (GNN), which are individually employed to perform low-level physical qubit error correction and high-level logical error correction for rotated surface codes of distancesd=3,d=5, andd=7. Under depolarizing noise, both FFNN and GNN achieve lower logical error rates than MWPM, with GNN yielding up to 28% improvement atd=7. GNN achieves pseudothresholds of 0.1084, 0.1311, and 0.1441 ford=3,d=5, andd=7, surpassing MWPM's 0.0914, 0.1024, and 0.1126. Crossover points further indicate GNN's robustness at higher noise levels (e.g., 0.1632 vs. 0.1291 for MWPM). By learning error distributions in a two-level setting, both FFNN and GNN outperform MWPM, demonstrating their potential as scalable, high-performance decoders for near-term quantum devices.
We present POLYMECHANON, a graph neural network (GNN) decoder for quantum error correction whose only input is the detection error model (DEM) of a quantum code under a given noise model. We represent the DEM as a tripartite graph of detectors, error mechanisms and logical observables, where every input feature is computed by using the quantum code as data rather than design choice. In this way, the same architecture decodes in principle any stabiliser code, under any noise model that can be expressed as a detection error model, once trained on the DEM. We test this approach along four directions. Firstly, on the rotated surface code the decoder outperforms correlated MWPM under both phenomenological and circuit-level noise, with up to 25% fewer logical failures. Secondly, on a family of high-rate qLDPC codes it matches BP+OSD on the smaller codes and surpasses it on the larger ones, with up to 16% fewer logical failures on [[130,4,6]]. Thirdly, its decoding time does not depend on the physical error rate, whereas that of BP+OSD grows with it: on [[130,4,6]] its effective cost per shot is of the order of a few ms on a single GPU against a few tens of milliseconds for BP+OSD on a single CPU core, and its fixed computational graph makes it a candidate for real-time decoding on neutral-atom processors. Finally, a single model trained across codes of different families outperforms uncorrelated MWPM on the graph-like codes seen during training and stays within 10% of BP+OSD on the others, while it tends to fail to generalize to unseen codes, particularly larger ones. Its probabilistic output enables confidence-based post-selection, lowering the logical error rate by more than an order of magnitude on the surface code while keeping more than 90% of the shots. Since only the DEM changes, new codes and noise models can be decoded without redesigning the decoder.
Quantum computers can solve selected problems more efficiently than classical computers, but current devices are limited by high physical error rates. Quantum Error Correction (QEC) mitigates this by encoding many physical qubits into a logical qubit, with the surface code among the most widely studied approaches. Since syndrome measurements are produced continuously, the decoder must process them fast enough to avoid becoming a system bottleneck, making real-time decoding essential for fault-tolerant quantum computing. While most state-of-the-art real-time decoders rely on Minimum-Weight Perfect Matching (MWPM), we instead use a high-accuracy Graph Neural Network (GNN) that trades higher computational cost for lower logical error rates. To make this GNN practical for real-time decoding, we apply algorithm-hardware co-design. We reduce complexity through hardware-guided pruning and retraining, producing two hardware-friendly models that reduce parameter count by 3.1× and 6.5×. These target, respectively, an average decoding latency of one syndrome cycle and a worst-case latency within one syndrome cycle. We further reduce hardware cost using input-graph filtering and post-training quantization. Based on these optimized models, we propose an FPGA-based architecture for low-latency inference and real-time decoding. Evaluated on surface codes up to distance 7 under circuit-level noise at physical error rate p=10−3, our decoder outperforms MWPM in decoding accuracy for both average-latency and max-latency settings. It reduces logical error rate by 40% at 1μs average latency, and by 13% under a strict 1μs deadline.
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.
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.