Graph neural network decoders for stabilizer codes

We explore the use of convolutional graph neural networks (GNN) as decoders for error correcting topological stabilizer codes. The syndrome corresponding to stabilizer violations due to qubit errors is mapped to a graph with node and edge features. In contrast to the standard graph decoder algorithms based on minimum weight matching, the decoder find its own graph algorithm through extensive training using randomly generated error configurations. The neural network acts as a graph classifier, mapping the syndrome-graph to the most likely equivalence class of errors. We find that the GNN can outperform MWPM for depolarizing noise, but is also readily adaptable to biased noise and individualized qubit fidelities. Using limited connectivity graphs, the decoder complexity scales favorably with the code distance. This type of decoder can also potentially be trained in a model free context, using experimental stabilizer code data.