Built on

N. J. Higham, Computing a nearest symmetric positive semidefinite matrix, Linear Algebra and its Applications 103
1988
Earlier work this paper cites.
V. N. Vapnik, The Nature of Statistical Learning (Springer, 1996)
1996
Earlier work this paper cites.
P. W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM Review 41
1999
Earlier work this paper cites.
B. Schölkopf, A. J. Smola, F. Bach, et al. , Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond (MIT Press, 2002)
2002
Earlier work this paper cites.
J. Shawe-Taylor and N. Cristianini, Kernel Methods for Pattern Analysis (Cambridge University Press, 2004)
2004
Earlier work this paper cites.
Y. Bengio, O. Delalleau, and N. L. Roux, The curse of highly variable functions for local kernel machines, in Proceedings of the 18th International Conference on Neural Information Processing Systems , NeurIPS’05 (MIT Press, Cambridge, MA, USA, 2005) pp. 107–114
2005
Earlier work this paper cites.
T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning , 2nd ed. (Springer, 2009)
2009
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 Édouard Duchesnay, Scikit-learn: Machine learning in Python, Journal of Machine Learning Research 12
2011
Earlier work this paper cites.
N. Wiebe and V. Kliuchnikov, Floating point representations in quantum circuit synthesis, New Journal of Physics 15
2013
Earlier work this paper cites.
S. Y. Kung, Kernel Methods and Machine Learning (Cambridge University Press, 2014)
2014
Earlier work this paper cites.

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Y. Liu, S. Arunachalam, and K. Temme, A rigorous and robust quantum speed-up in supervised machine learning, Nature Physics 17
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J. R. Glick, T. P. Gujarati, A. D. Corcoles, Y. Kim, A. Kandala, J. M. Gambetta, and K. Temme, Covariant quantum kernels for data with group structure, arXiv:2105.03406 10.48550/arXiv.2105.03406 (2021)
Original

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2021

Importance of Kernel Bandwidth in Quantum Machine Learning

Shaydulin, Ruslan, Wild, Stefan M.

Understand

Quantum kernel methods are considered a promising avenue for applying quantum computers to machine learning problems.

Identifying hyperparameters controlling the inductive bias of quantum machine learning models is expected to be crucial given the central role hyperparameters play in determining the performance of classical machine learning methods.
In this work we introduce the hyperparameter controlling the bandwidth of a quantum kernel and show that it controls the expressivity of the resulting model.
We use extensive numerical experiments with multiple quantum kernels and classical datasets to show consistent change in the model behavior from underfitting (bandwidth too large) to overfitting (bandwidth too small), with optimal generalization in between.

Built on

N. J. Higham, Computing a nearest symmetric positive semidefinite matrix, Linear Algebra and its Applications 103
1988
Earlier work this paper cites.
V. N. Vapnik, The Nature of Statistical Learning (Springer, 1996)
1996
Earlier work this paper cites.
P. W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM Review 41
1999
Earlier work this paper cites.
B. Schölkopf, A. J. Smola, F. Bach, et al. , Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond (MIT Press, 2002)
2002
Earlier work this paper cites.
J. Shawe-Taylor and N. Cristianini, Kernel Methods for Pattern Analysis (Cambridge University Press, 2004)
2004
Earlier work this paper cites.
Y. Bengio, O. Delalleau, and N. L. Roux, The curse of highly variable functions for local kernel machines, in Proceedings of the 18th International Conference on Neural Information Processing Systems , NeurIPS’05 (MIT Press, Cambridge, MA, USA, 2005) pp. 107–114
2005
Earlier work this paper cites.
T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning , 2nd ed. (Springer, 2009)
2009
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 Édouard Duchesnay, Scikit-learn: Machine learning in Python, Journal of Machine Learning Research 12
2011
Earlier work this paper cites.
N. Wiebe and V. Kliuchnikov, Floating point representations in quantum circuit synthesis, New Journal of Physics 15
2013
Earlier work this paper cites.
S. Y. Kung, Kernel Methods and Machine Learning (Cambridge University Press, 2014)
2014
Earlier work this paper cites.

Similar

H. Xiao, K. Rasul, and R. Vollgraf, Fashion-MNIST: a novel image dataset for benchmarking machine learning algorithms, arXiv:1708.07747 10.48550/arXiv.1708.07747 (2017)
Original
2017
Cited alongside, same era.
M. Belkin, S. Ma, and S. Mandal, To understand deep learning we need to understand kernel learning, in Proceedings of the 35th International Conference on Machine Learning , Proceedings of Machine Learning Research, Vol. 80, edited by J. Dy and A. Krause (PMLR, 2018) pp. 541–549
2018
Cited alongside, same era.
T. Clanuwat, M. Bober-Irizar, A. Kitamoto, A. Lamb, K. Yamamoto, and D. Ha, Deep learning for classical Japanese literature, arXiv:1812.01718 10.20676/00000341 (2018)
Original
2018
Cited alongside, same era.
The PLAsTiCC team, T. A. Jr., A. Bahmanyar, R. Biswas, M. Dai, L. Galbany, R. Hložek, E. E. O. Ishida, S. W. Jha, D. O. Jones, R. Kessler, M. Lochner, A. A. Mahabal, A. I. Malz, K. S. Mandel, J. R. Martínez-Galarza, J. D. McEwen, D. Muthukrishna, G. Narayan, H. Peiris, C. M. Peters, K. Ponder, C. N. Setzer, T. L. D. E. S. Collaboration, T. L. Transients, and V. S. S. Collaboration, The photometric LSST astronomical time-series classification challenge (PLAsTiCC): Data set, arXiv:1810.00001 10.48550/arXiv.1810.00001 (2018)

Then

Y. Liu, S. Arunachalam, and K. Temme, A rigorous and robust quantum speed-up in supervised machine learning, Nature Physics 17
2021
Closest in time.
H.-Y. Huang, M. Broughton, M. Mohseni, R. Babbush, S. Boixo, H. Neven, and J. R. McClean, Power of data in quantum machine learning, Nature Communications 12
2021
Closest in time.
L. Banchi, J. Pereira, and S. Pirandola, Generalization in quantum machine learning: A quantum information standpoint, PRX Quantum 2
2021
Closest in time.
J. Kübler, S. Buchholz, and B. Schölkopf, The inductive bias of quantum kernels, Advances in Neural Information Processing Systems 34
2021
Closest in time.
J. R. Glick, T. P. Gujarati, A. D. Corcoles, Y. Kim, A. Kandala, J. M. Gambetta, and K. Temme, Covariant quantum kernels for data with group structure, arXiv:2105.03406 10.48550/arXiv.2105.03406 (2021)
Original

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Original

2018

Cited alongside, same era.

M. Schuld and N. Killoran, Quantum machine learning in feature Hilbert spaces, Physical Review Letters 122

2019

Cited alongside, same era.

V. Havlíček, A. D. Córcoles, K. Temme, A. W. Harrow, A. Kandala, J. M. Chow, and J. M. Gambetta, Supervised learning with quantum-enhanced feature spaces, Nature 567

2019

Cited alongside, same era.

F. Arute et al. , Quantum supremacy using a programmable superconducting processor, Nature 574

2019

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S. Lloyd, M. Schuld, A. Ijaz, J. Izaac, and N. Killoran, Quantum embeddings for machine learning, arXiv:2001.03622 (2020)

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2020

Cited alongside, same era.

M. Otten, I. R. Goumiri, B. W. Priest, G. F. Chapline, and M. D. Schneider, Quantum machine learning using Gaussian processes with performant quantum kernels (2020)

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2020

Cited alongside, same era.

M. Schuld, Supervised quantum machine learning models are kernel methods (2021), arXiv:2101.11020

Original

2021

Cited alongside, same era.

[Online] https://github.com/rsln-s/Importance-of-Kernel-Bandwidth-in-Quantum-Machine-Learning/blob/c402b6ab2d761842e6ca198b9c577120e2af2e90/code/variance_depends_on_state.py

Cited in the paper.

2021

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M. Schuld, R. Sweke, and J. J. Meyer, Effect of data encoding on the expressive power of variational quantum-machine-learning models, Physical Review A 103

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[Online] Retrieved 11/03/2021. https://www.tensorflow.org/quantum/tutorials/quantum_data

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E. Peters, J. Caldeira, A. Ho, S. Leichenauer, M. Mohseni, H. Neven, P. Spentzouris, D. Strain, and G. N. Perdue, Machine learning of high dimensional data on a noisy quantum processor, npj Quantum Information 7

2021

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[Online] Retrieved 11/03/2021. https://ionq.com/best-practices

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H. Abraham et al. , Qiskit: An open-source framework for quantum computing (2021)

2021

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