Quantum machine learning with adaptive linear optics

Ulysse Chabaud; Damian Markham; Adel Sohbi

doi:10.22331/q-2021-07-05-496

Quantum machine learning with adaptive linear optics

Ulysse Chabaud^1,2,3, Damian Markham^3,4, and Adel Sohbi⁵

¹Department of Computing and Mathematical Sciences, California Institute of Technology
²Université de Paris, IRIF, CNRS, France
³Laboratoire d'Informatique de Paris 6, CNRS, Sorbonne Université, 4 place Jussieu, 75005 Paris, France
⁴JFLI, CNRS, National Institute of Informatics, University of Tokyo, Tokyo, Japan
⁵School of Computational Sciences, Korea Institute for Advanced Study, Seoul 02455, Korea

Published:	2021-07-05, volume 5, page 496
Eprint:	arXiv:2102.04579v2
Doi:	https://doi.org/10.22331/q-2021-07-05-496
Citation:	Quantum 5, 496 (2021).

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Abstract

We study supervised learning algorithms in which a quantum device is used to perform a computational subroutine – either for prediction via probability estimation, or to compute a kernel via estimation of quantum states overlap. We design implementations of these quantum subroutines using Boson Sampling architectures in linear optics, supplemented by adaptive measurements. We then challenge these quantum algorithms by deriving classical simulation algorithms for the tasks of output probability estimation and overlap estimation. We obtain different classical simulability regimes for these two computational tasks in terms of the number of adaptive measurements and input photons. In both cases, our results set explicit limits to the range of parameters for which a quantum advantage can be envisaged with adaptive linear optics compared to classical machine learning algorithms: we show that the number of input photons and the number of adaptive measurements cannot be simultaneously small compared to the number of modes. Interestingly, our analysis leaves open the possibility of a near-term quantum advantage with a single adaptive measurement.

Popular summary

Quantum information processing promises various technological applications for cryptography, communication and computing. In particular, classical machine learning algorithms assisted with quantum computers may provide speedups for computational tasks such as supervised learning. However, it is not yet clear how complicated these quantum computers must be to reach interesting advantages compared to existing classical machine learning algorithms, and whether these may be built in the near future. In this work, we consider the use of linear optical quantum interferometers for machine learning and we derive minimal requirements to obtain useful algorithms compared to classical algorithms.

► BibTeX data

@article{Chabaud2021quantummachine,
  doi = {10.22331/q-2021-07-05-496},
  url = {https://doi.org/10.22331/q-2021-07-05-496},
  title = {Quantum machine learning with adaptive linear optics},
  author = {Chabaud, Ulysse and Markham, Damian and Sohbi, Adel},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {496},
  month = jul,
  year = {2021}
}

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[5] Beng Yee Gan, Daniel Leykam, and Dimitris G. Angelakis, "Fock state-enhanced expressivity of quantum machine learning models", EPJ Quantum Technology 9 1, 16 (2022).

[6] C Bowie, S Shrapnel, and M J Kewming, "Quantum kernel evaluation via Hong–Ou–Mandel interference", Quantum Science and Technology 9 1, 015001 (2024).

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[9] Ulysse Chabaud, "Continuous Variable Quantum Advantages and Applications in Quantum Optics", arXiv:2102.05227, (2021).

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