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

Physical Review Research, vol. 7

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, 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 the simulated data, while 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 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.

Authors 9

1. Moritz Lange corresponding

   University of Gothenburg

   Affiliation as printed

   University of Gothenburg

   Department of Physics, University of Gothenburg, Gothenburg, Sweden

2. Pontus Havström

   University of Gothenburg

   Affiliation as printed

   University of Gothenburg

   Department of Physics, University of Gothenburg, Gothenburg, Sweden

3. Basudha Srivastava

   Quantinuum (United Kingdom) · Quantinuum (United States) · University of Gothenburg

   Affiliation as printed

   Quantinuum

   University of Gothenburg

   Department of Physics, University of Gothenburg, Gothenburg, Sweden

   Quantinuum, Terrington House, 13-15 Hills Rd, Cambridge CB2 1NL, United Kingdom

4. Isak Bengtsson

   Chalmers University of Technology

   Affiliation as printed

   Chalmers University of Technology

   Department of Physics, Chalmers University of Technology, Gothenburg, Sweden

5. Valdemar Bergentall

   University of Gothenburg

   Affiliation as printed

   University of Gothenburg

   Department of Physics, University of Gothenburg, Gothenburg, Sweden

6. Karl Hammar

   University of Gothenburg

   Affiliation as printed

   University of Gothenburg

   Department of Physics, University of Gothenburg, Gothenburg, Sweden

7. Olivia Heuts

   University of Gothenburg

   Affiliation as printed

   University of Gothenburg

   Department of Physics, University of Gothenburg, Gothenburg, Sweden

8. Evert van Nieuwenburg Aachen Leiden Institute of Advanced Computer Science

   Leiden University

   Affiliation as printed

   Leiden University

   Leiden Inst. of Advanced Computer Science, Leiden University, Leiden, Netherlands

9. Mats Granath

   University of Gothenburg

   Affiliation as printed

   University of Gothenburg

   Department of Physics, University of Gothenburg, Gothenburg, Sweden