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To leverage the full potential of quantum error-correcting stabilizer codesit is crucial to have an efficient and accurate decoder. Accurate, maximumlikelihood, decoders are computationally very expensive whereas decoders basedon more efficient algorithms give sub-optimal performance. In addition, theaccuracy will depend on the quality of models and estimates of error rates foridling qubits, gates, measurements, and resets, and will typically assumesymmetric error channels. In this work, instead, we explore a model-free,data-driven, approach to decoding, using a graph neural network (GNN). Thedecoding problem is formulated as a graph classification task in which a set ofstabilizer measurements is mapped to an annotated detector graph for which theneural network predicts the most likely logical error class. We show that theGNN-based decoder can outperform a matching decoder for circuit level noise onthe surface code given only simulated experimental data, even if the matchingdecoder is given full information of the underlying error model. Althoughtraining is computationally demanding, inference is fast and scalesapproximately linearly with the space-time volume of the code. We also findthat we can use large, but more limited, datasets of real experimental data[Google Quantum AI, Nature {\bf 614}, 676 (2023)] for the repetition code,giving decoding accuracies that are on par with minimum weight perfectmatching. The results show that a purely data-driven approach to decoding maybe a viable future option for practical quantum error correction, which iscompetitive in terms of speed, accuracy, and versatility.

Data-driven decoding of quantum error correcting codes using graph neural networks