Quantum machine learning with adaptive linear optics

Ulysse Chabaud1,2,3, Damian Markham3,4, 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

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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.

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.

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[3] Rawad Mezher and Shane Mansfield, "Assessing the quality of near-term photonic quantum devices", arXiv:2202.04735.

[4] Wentao Chen, Yao Lu, Shuaining Zhang, Kuan Zhang, Guanhao Huang, Mu Qiao, Xiaolu Su, Jialiang Zhang, Jingning Zhang, Leonardo Banchi, M. S. Kim, and Kihwan Kim, "Scalable and Programmable Phononic Network with Trapped Ions", arXiv:2207.06115.

[5] Ulysse Chabaud, "Continuous Variable Quantum Advantages and Applications in Quantum Optics", arXiv:2102.05227.

[6] Kamil Bradler and Hugo Wallner, "Certain properties and applications of shallow bosonic circuits", arXiv:2112.09766.

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