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

TL;DR

This paper introduces a data-driven, graph neural network-based decoder for quantum error correction that outperforms traditional methods in certain scenarios, offering a fast, scalable, and versatile solution using simulated and experimental data.

Contribution

The work presents a novel GNN-based decoding approach for quantum error correction, demonstrating superior performance over traditional decoders with efficient inference and applicability to real experimental data.

Findings

GNN decoder outperforms matching decoder on surface code with circuit noise

Decoding accuracy on par with minimum weight perfect matching using experimental data

Inference scales linearly with code size, enabling practical deployment

Abstract

To leverage the full potential of quantum error-correcting stabilizer codes it is crucial to have an efficient and accurate decoder. Accurate, maximum likelihood, decoders are computationally very expensive whereas decoders based on more efficient algorithms give sub-optimal performance. In addition, the accuracy will depend on the quality of models and estimates of error rates for idling qubits, gates, measurements, and resets, and will typically assume symmetric error channels. In this work, instead, we explore a model-free, data-driven, approach to decoding, using a graph neural network (GNN). The decoding problem is formulated as a graph classification task in which a set of stabilizer measurements is mapped to an annotated detector graph for which the neural network predicts the most likely logical error class. We show that the GNN-based decoder can outperform a matching decoder for circuit level noise on the surface code given only simulated experimental data, even if the matching decoder is given full information of the underlying error model. Although training is computationally demanding, inference is fast and scales approximately linearly with the space-time volume of the code. We also find that 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 perfect matching. The results show that a purely data-driven approach to decoding may be a viable future option for practical quantum error correction, which is competitive in terms of speed, accuracy, and versatility.