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Quantum machine learning

Quantum neural networks can be normal

As many classical neural networks get larger, they can be described as Gaussian processes, the generalization of the normal distribution to infinite dimensions. A similar connection has now been proven for quantum neural networks.

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Fig. 1: The emergence of a Gaussian process from a neural network.

References

  1. Feller, W. An Introduction to Probability Theory and Its Applications 3rd edn, Vol. 1 (Wiley, 1968).

  2. García-Martín, D., Larocca, M. & Cerezo, M. Nat. Phys. https://doi.org/10.1038/s41567-025-02883-z (2025).

  3. van der Vaart, A. W. Asymptotic Statistics (Cambridge Univ. Press, 1998).

  4. McClean, J. R., Boixo, S., Smelyanskiy, V. N., Babbush, R. & Neven, H. Nat. Commun. 9, 4812 (2018).

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Correspondence to Jayne Thompson.

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Thompson, J. Quantum neural networks can be normal. Nat. Phys. 21, 1042–1043 (2025). https://doi.org/10.1038/s41567-025-02941-6

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