This project aims at the implementation of quantum enhanced machine learning protocols in a photonics platform. It focuses on the implementation of protocols based on network structures, e.g., quantum reservoir computing, via multimode quantum optics.

The experimental activity concerns the implementation of quantum complex networks by using femtosecond laser sources and parametric processes [1,2]. Such systems can deterministically generate entanglement correlations between quadratures of the electromagnetic field of several spectral-temporal modes that can be exploited in Continuous Variables (CV) quantum information protocols. In most experiments, parametric processes take place in a resonant cavity in order to enhance the non-linear effect [3]. The peculiarity of our approach is the use of non-linear waveguides (in order to reach high enough non-linearity) in a single-pass configuration [4,5], which allows us to preserve the entanglement structure in the laser-pulse basis. This, combined with a fast homodyne detection technique, will allow us to generate very large entangled networks, exploiting both spectral and temporal degrees of freedom. The generated resource will be used for quantum enhanced machine learning.

Machine learning covers a wide range of algorithms and modelling tools with automated data processing capabilities. Here, we consider network-based strategies, like neural networks and reservoir computing. The latter exploits the dynamics of a non-linear system (the reservoir) for information processing of a time dependent input. In the classical case, it has achieved state-of- the-art performance in tasks such as continuous speech recognition and nonlinear time series prediction. The reservoir can have the same architecture as neural networks, but it only needs to train connections leading to the final output layer. In the classical framework it has been implemented in photonics and spintronics hardware.

The quantum implementation of neural networks [6] and, more recently, of reservoir computing [7,8] has been proposed in the CV encoding. In particular it has been proved that Gaussian states provide universal reservoir computing and that quantum Gaussian resources, like squeezed state, provide a larger information capacity than classical states [8]. The proposed PhD project aims at getting the first experimental implementations of quantum reservoir computing. The assessment of the advantage of the quantum setting over the classical one will be studied in collaboration with a theory group based at IFISC (University of Baleares Island).

We will develop tailored protocols based on the experimental resources that, beside the Gaussian large entangled structure, will involve Non-gaussian states derived from single-photon subtraction or addition operations [9,10]. It is in fact known that non-Gaussian probability distributions of quadratures are needed to demonstrate a form of quantum advantage in computation protocols. But it is still unknown the amount of non-Gaussian resources needed for reaching the advantage in different quantum machine learning tasks. The experiment will thus serve as testbed for identifying the resources needed for the Quantum Reservoir Computing to outperform the classical setting.

The project is intended to be inserted in the initiative of the Quantum Information Center Sorbonne (QICS). It in fact covers instances concerning the broad impact of quantum information on machine learning protocols.

The PhD candidate should have a Master diploma in Physics. Familiarity with experimental optics and knowledge of quantum optics and quantum information will be valuable.

Contact to submit your application :
Valentina Parigi, valentina.parigi@lkb.upmc.fr

[1] J. Nokkala, F. Arzani, F. Galve, R. Zambrini, S. Maniscalco, J. Piilo, N. Treps, V. Parigi, “Reconfigurable optical implementation of quantum complex networks”, New J. Phys. 20, 053024 (2018)

[2] F. Sansavini and V. Parigi “Continuous variables graph states shaped as complex networks: optimization and manipulation” Entropy 22, 26 (2020)

[3] Cai, Y. et al. “Multimode entanglement in reconfigurable graph states using optical frequency combs”. Nat. Commun. 8, 15645 (2017).

[4] L. La Volpe, S. De, T. Kouadou, D. Horoshko, M. I. Kolobov, C. Fabre, V. Parigi, and N. Treps, “Multimode single-pass spatio-temporal squeezing” Optics Express Vol. 28, Issue 8, pp. 12385- 12394 (2020)

[5] V. Roman-Rodriguez, B. Brecht, S. Kaali, C. Silberhorn, N. Treps, E. Diamanti, and V. Parigi “Continuous variable multimode quantum states via symmetric group velocity matching”, arXiv:2012.13629

[6] N. Killoran et al. “Continuous-variable quantum neural networks”, Physical Review Research 1, 033063 (2019).

[7] L. C. G. Govia, et al. “Quantum reservoir computing with a single nonlinear oscillator”, Phys. Rev. Research 3, 013077 (2021).

[8] J. Nokkala, R. Martínez-Peña, G. L. Giorgi, V. Parigi, M. C. Soriano, R. Zambrini, “Gaussian states provide universal and versatile quantum reservoir computing” arXiv:2006.04821

[9] M Walschaers, V Parigi, N Treps, “Practical Framework for Conditional Non-Gaussian Quantum State Preparation” PRX Quantum 1 (2), 020305 (2020)

[10] V Parigi, A Zavatta, M Kim, M Bellini “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field” Science 317 (5846), 1890-1893 (2007)