Quantum error correction (QEC) is essential for reliable quantum computing. However, traditional methods like surface codes face significant challenges with complex correlated noise, such as dephasing, charge, and flux noise—often caused by environmental fluctuations. These multi-qubit errors, common in real quantum systems, are difficult to correct using conventional techniques. While Minimum Weight Perfect Matching (MWPM) is a widely used QEC decoder that performs well in correcting isolated errors, it struggles with spatially correlated noise. To address this, we propose a hybrid decoding framework that integrates machine learning—specifically Convolutional Neural Networks (CNNs) and Graph Neural Networks (GNNs)—to extend MWPM’s capabilities and enable effective correction of both localized and correlated errors.

The framework employs a three-stage process. First, CNNs, optimized for local feature detection, process syndrome maps to identify error patterns and estimate error probabilities. These networks leverage convolutional layers to extract spatial features from stabilizer measurements, trained on datasets reflecting noisy environments. Next, GNNs refine CNN predictions by modeling the stabilizer graph as a node-edge system, propagating information across the graph to capture long-range dependencies and inter-qubit correlations. The outputs from CNNs and GNNs are then used to dynamically adjust the edge weights in the MWPM graph, where lower weights indicate higher error probabilities, guiding the decoder toward accurate corrections.

Unlike traditional MWPM methods, which rely on metrics like Manhattan distance, our CNN-GNN-enhanced MWPM decoder adapts to correlated noise, achieving up to a 50% reduction in logical error rates in bosonic bath simulations—a realistic model of correlated noise—compared to conventional MWPM decoders. By preserving the scalable structure of surface codes, this framework provides a robust, machine-learning-enhanced solution to correlated noise, ensuring the fault tolerance of future quantum systems.