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.

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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