Machine-learning-assisted correction of correlated qubit errors in a topological code

Paul Baireuther1, Thomas E. O'Brien1, Brian Tarasinski2, and Carlo W. J. Beenakker1

1Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands
2QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands

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A fault-tolerant quantum computation requires an efficient means to detect and correct errors that accumulate in encoded quantum information. In the context of machine learning, neural networks are a promising new approach to quantum error correction. Here we show that a recurrent neural network can be trained, using only experimentally accessible data, to detect errors in a widely used topological code, the surface code, with a performance above that of the established minimum-weight perfect matching (or blossom) decoder. The performance gain is achieved because the neural network decoder can detect correlations between bit-flip (X) and phase-flip (Z) errors. The machine learning algorithm adapts to the physical system, hence no noise model is needed. The long short-term memory layers of the recurrent neural network maintain their performance over a large number of quantum error correction cycles, making it a practical decoder for forthcoming experimental realizations of the surface code.

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Unlike in modern classical computers, error rates in quantum hardware are many orders of magnitude too high to complete most useful calculations. However, careful repeated measurement of small pieces of a quantum computer provides information to detect and correct errors without disturbing the calculation itself. Decoding the information to optimally detect which errors have occurred is in general a hard classical problem of pattern recognition. As machine learning techniques are well suited to this problem, a neural network is a potential candidate for an efficient decoder. Two key properties are required for such a decoder to be of use in a real quantum computer: it must be able to decode information from repeated measurements (instead of a single round), and it must be trainable from data accessible by measurement. In this work we present a decoder that satisfies both of these properties and achieves performance above the well-established minimum-weight perfect matching decoder on an example error correction scheme (the surface code). This makes the neural network decoder a potential candidate for forthcoming quantum error correction experiments.

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► Cited by (beta)

[1] Andrew S. Darmawan, David Poulin, "Linear-time general decoding algorithm for the surface code", Physical Review E 97, 051302 (2018).

[2] Vedran Dunjko, Hans J Briegel, "Machine learning & artificial intelligence in the quantum domain: a review of recent progress", Reports on Progress in Physics 81, 074001 (2018).

[3] Nikolas P. Breuckmann, Xiaotong Ni, "Scalable Neural Network Decoders for Higher Dimensional Quantum Codes", Quantum 2, 68 (2018).

(The above data is from Crossref's cited-by service. Unfortunately not all publishers provide suitable and complete citation data so that some citing works or bibliographic details may be missing.)