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2021

Subtleties in the trainability of quantum machine learning models

Thanasilp, Supanut, Wang, Samson, Nghiem, Nhat A. et al.

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A new paradigm for data science has emerged, with quantum data, quantum models, and quantum computational devices.

This field, called Quantum Machine Learning (QML), aims to achieve a speedup over traditional machine learning for data analysis.
However, its success usually hinges on efficiently training the parameters in quantum neural networks, and the field of QML is still lacking theoretical scaling results for their trainability.
Some trainability results have been proven for a closely related field called Variational Quantum Algorithms (VQAs).

Subtleties in the trainability of quantum machine learning models · Around

Built on

Shun-Ichi Amari, “Natural gradient works efficiently in learning,” Neural computation 10
1998
Earlier work this paper cites.
Yann LeCun, “The mnist database of handwritten digits,” http://yann. lecun. com/exdb/mnist/ (1998)
1998
Earlier work this paper cites.
Michel Ledoux, The concentration of measure phenomenon , 89 (American Mathematical Soc., 2001)
2001
Earlier work this paper cites.
Kunal Sharma, M. Cerezo, Lukasz Cincio, and Patrick J Coles, “Trainability of dissipative perceptron-based quantum neural networks,” arXiv preprint arXiv:2005.12458 (2020b)
Original
2005
Earlier work this paper cites.
Ian Jolliffe, “Principal component analysis,” Encyclopedia of statistics in behavioral science (2005)
2005
Earlier work this paper cites.
Fernando GSL Brandao and Michał Horodecki, “On hastings’ counterexamples to the minimum output entropy additivity conjecture,” Open Systems & Information Dynamics 17
2010
Earlier work this paper cites.
F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, “Scikit-learn: Machine learning in Python,” Journal of Machine Learning Research 12
2011
Earlier work this paper cites.
Michael J Bremner, Richard Jozsa, and Dan J Shepherd, “Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467
2011
Earlier work this paper cites.
Maria Schuld, Ilya Sinayskiy, and Francesco Petruccione, “The quest for a quantum neural network,” Quantum Information Processing 13
2014
Earlier work this paper cites.
Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Peter J Love, Alán Aspuru-Guzik, and Jeremy L O’brien, “A variational eigenvalue solver on a photonic quantum processor,” Nature communications 5
2014
Earlier work this paper cites.
Maria Schuld, Ilya Sinayskiy, and Francesco Petruccione, “An introduction to quantum machine learning,” Contemporary Physics 56
2015
Earlier work this paper cites.
Diederik P Kingma and Jimmy Ba, “Adam: A method for stochastic optimization,” in Proceedings of the 3rd International Conference on Learning Representations (ICLR) (2015)
Original
2015
Earlier work this paper cites.
Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe, and Seth Lloyd, “Quantum machine learning,” Nature 549
2017
Earlier work this paper cites.
Y. Li and S. C. Benjamin, “Efficient variational quantum simulator incorporating active error minimization,” Phys. Rev. X 7
2017
Earlier work this paper cites.
John Preskill, “Quantum computing in the nisq era and beyond,” Quantum 2
2018
Earlier work this paper cites.
Edward Farhi and Hartmut Neven, “Classification with quantum neural networks on near term processors,” arXiv preprint arXiv:1802.06002 (2018)
Original
2018
Earlier work this paper cites.
Jarrod R McClean, Sergio Boixo, Vadim N Smelyanskiy, Ryan Babbush, and Hartmut Neven, “Barren plateaus in quantum neural network training landscapes,” Nature communications 9
2018
Earlier work this paper cites.
Kosuke Mitarai, Makoto Negoro, Masahiro Kitagawa, and Keisuke Fujii, “Quantum circuit learning,” Physical Review A 98
2018
Earlier work this paper cites.
Iris Cong, Soonwon Choi, and Mikhail D Lukin, “Quantum convolutional neural networks,” Nature Physics 15
2019
Earlier work this paper cites.
Guillaume Verdon, Jacob Marks, Sasha Nanda, Stefan Leichenauer, and Jack Hidary, “Quantum hamiltonian-based models and the variational quantum thermalizer algorithm,” arXiv preprint arXiv:1910.02071 (2019)
Original
2019
Earlier work this paper cites.

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