Built on

A. W. Harrow, A. Hassidim, and S. Lloyd, Physical review letters 103
2009
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N. Wiebe, D. Braun, and S. Lloyd, Physical review letters 109
2012
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S. Lloyd, M. Mohseni, and P. Rebentrost, Nature Physics 10
2014
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P. Wittek, Quantum machine learning: what quantum computing means to data mining (Academic Press, 2014)
2014
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N. Wiebe, A. Kapoor, and K. M. Svore, arXiv preprint arXiv:1412.3489 (2014)
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2014
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P. Rebentrost, M. Mohseni, and S. Lloyd, Physical review letters 113
2014
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2014
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2014
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J. R. McClean, J. Romero, R. Babbush, and A. Aspuru-Guzik, New Journal of Physics 18
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J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, Nature 549
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J. Lee, Y. Bahri, R. Novak, S. S. Schoenholz, J. Pennington, and J. Sohl-Dickstein, arXiv preprint arXiv:1711.00165 (2017)
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2017
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2017
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2017
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Similar

J. R. McClean, S. Boixo, V. N. Smelyanskiy, R. Babbush, and H. Neven, Nature communications 9
2018
Cited alongside, same era.
A. Jacot, F. Gabriel, and C. Hongler, arXiv preprint arXiv:1806.07572 (2018)
Original
2018
Cited alongside, same era.
L. Chizat, E. Oyallon, and F. Bach, arXiv preprint arXiv:1812.07956 (2018)
Original
2018
Cited alongside, same era.
E. Farhi and H. Neven, arXiv preprint arXiv:1802.06002 (2018)
Original
2018
Cited alongside, same era.
M. Schuld and N. Killoran, Physical review letters 122
2019
Cited alongside, same era.

Then

S. McArdle, S. Endo, A. Aspuru-Guzik, S. C. Benjamin, and X. Yuan, Reviews of Modern Physics 92
2020
Later among the works it cites.
A. Lewkowycz, Y. Bahri, E. Dyer, J. Sohl-Dickstein, and G. Gur-Ari, arXiv preprint arXiv:2003.02218 (2020)
Original
2020
Later among the works it cites.
Y. Liu, S. Arunachalam, and K. Temme, Nature Physics , 1 (2021)
2021
Closest in time.
J. Halverson, A. Maiti, and K. Stoner, Machine Learning: Science and Technology 2
2021
Closest in time.
D. A. Roberts, arXiv preprint arXiv:2104.00008 (2021)
Original
2021
Closest in time.
D. A. Roberts, S. Yaida, and B. Hanin, arXiv preprint arXiv:2106.10165 (2021)

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2021

Representation Learning via Quantum Neural Tangent Kernels

Liu, Junyu, Tacchino, Francesco, Glick, Jennifer R. et al.

Understand

Variational quantum circuits are used in quantum machine learning and variational quantum simulation tasks.

Designing good variational circuits or predicting how well they perform for given learning or optimization tasks is still unclear.
Here we discuss these problems, analyzing variational quantum circuits using the theory of neural tangent kernels.
We define quantum neural tangent kernels, and derive dynamical equations for their associated loss function in optimization and learning tasks.

Built on

A. W. Harrow, A. Hassidim, and S. Lloyd, Physical review letters 103
2009
Earlier work this paper cites.
N. Wiebe, D. Braun, and S. Lloyd, Physical review letters 109
2012
Earlier work this paper cites.
S. Lloyd, M. Mohseni, and P. Rebentrost, Nature Physics 10
2014
Earlier work this paper cites.
P. Wittek, Quantum machine learning: what quantum computing means to data mining (Academic Press, 2014)
2014
Earlier work this paper cites.
N. Wiebe, A. Kapoor, and K. M. Svore, arXiv preprint arXiv:1412.3489 (2014)
Original
2014
Earlier work this paper cites.
P. Rebentrost, M. Mohseni, and S. Lloyd, Physical review letters 113
2014
Earlier work this paper cites.
A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O’brien, Nature communications 5
2014
Earlier work this paper cites.
E. Farhi, J. Goldstone, and S. Gutmann, arXiv preprint arXiv:1411.4028 (2014)
Original
2014
Earlier work this paper cites.
J. R. McClean, J. Romero, R. Babbush, and A. Aspuru-Guzik, New Journal of Physics 18
2016
Earlier work this paper cites.
J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, Nature 549
2017
Earlier work this paper cites.
J. Lee, Y. Bahri, R. Novak, S. S. Schoenholz, J. Pennington, and J. Sohl-Dickstein, arXiv preprint arXiv:1711.00165 (2017)
Original
2017
Earlier work this paper cites.
A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta, Nature 549
2017
Earlier work this paper cites.
J. Otterbach, R. Manenti, N. Alidoust, A. Bestwick, M. Block, B. Bloom, S. Caldwell, N. Didier, E. S. Fried, S. Hong, et al. , arXiv preprint arXiv:1712.05771 (2017)
Original
2017
Earlier work this paper cites.
D. A. Roberts and B. Yoshida, JHEP 04
Original
2017
Earlier work this paper cites.

Similar

J. R. McClean, S. Boixo, V. N. Smelyanskiy, R. Babbush, and H. Neven, Nature communications 9
2018
Cited alongside, same era.
A. Jacot, F. Gabriel, and C. Hongler, arXiv preprint arXiv:1806.07572 (2018)
Original
2018
Cited alongside, same era.
L. Chizat, E. Oyallon, and F. Bach, arXiv preprint arXiv:1812.07956 (2018)
Original
2018
Cited alongside, same era.
E. Farhi and H. Neven, arXiv preprint arXiv:1802.06002 (2018)
Original
2018
Cited alongside, same era.
M. Schuld and N. Killoran, Physical review letters 122
2019
Cited alongside, same era.

Then

S. McArdle, S. Endo, A. Aspuru-Guzik, S. C. Benjamin, and X. Yuan, Reviews of Modern Physics 92
2020
Later among the works it cites.
A. Lewkowycz, Y. Bahri, E. Dyer, J. Sohl-Dickstein, and G. Gur-Ari, arXiv preprint arXiv:2003.02218 (2020)
Original
2020
Later among the works it cites.
Y. Liu, S. Arunachalam, and K. Temme, Nature Physics , 1 (2021)
2021
Closest in time.
J. Halverson, A. Maiti, and K. Stoner, Machine Learning: Science and Technology 2
2021
Closest in time.
D. A. Roberts, arXiv preprint arXiv:2104.00008 (2021)
Original
2021
Closest in time.
D. A. Roberts, S. Yaida, and B. Hanin, arXiv preprint arXiv:2106.10165 (2021)

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E. Tang, in Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing (2019) pp. 217–228

2019

Cited alongside, same era.

V. Havlíček, A. D. Córcoles, K. Temme, A. W. Harrow, A. Kandala, J. M. Chow, and J. M. Gambetta, Nature 567

2019

Cited alongside, same era.

J. Lee, L. Xiao, S. Schoenholz, Y. Bahri, R. Novak, J. Sohl-Dickstein, and J. Pennington, Advances in neural information processing systems 32

2019

Cited alongside, same era.

S. Arora, S. S. Du, W. Hu, Z. Li, R. Salakhutdinov, and R. Wang, arXiv preprint arXiv:1904.11955 (2019)

Original

2019

Cited alongside, same era.

E. Dyer and G. Gur-Ari, arXiv preprint arXiv:1909.11304 (2019)

Original

2019

Cited alongside, same era.

G. Aleksandrowicz et al. , “Qiskit: An open-source framework for quantum computing,” (2019)

2019

Cited alongside, same era.

J. Sohl-Dickstein, R. Novak, S. S. Schoenholz, and J. Lee, arXiv preprint arXiv:2001.07301 (2020)

Original

2020

Cited alongside, same era.

Original

2021

Closest in time.

J. Liu, Does Richard Feynman Dream of Electric Sheep? Topics on Quantum Field Theory, Quantum Computing, and Computer Science , Ph.D. thesis , Caltech (2021)

2021

Closest in time.

K. Nakaji, H. Tezuka, and N. Yamamoto, “Quantum-enhanced neural networks in the neural tangent kernel framework,” (2021), arXiv:2109.03786 [quant-ph]

Original

2021

Closest in time.

D. A. Roberts and S. Yaida, Deep Learning Theory Summer School at Princeton (2021)

2021

Closest in time.

M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincio, et al. , Nature Reviews Physics , 1 (2021)

2021

Closest in time.

“Qiskit machine learning,” https://qiskit.org/documentation/machine-learning/ (2021)

2021

Closest in time.

A. Abbas, D. Sutter, C. Zoufal, A. Lucchi, A. Figalli, and S. Woerner, Nature Computational Science 1

2021

Closest in time.

T. Haug, K. Bharti, and M. Kim, arXiv preprint arXiv:2102.01659 (2021)

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2021

Closest in time.

N. Shirai, K. Kubo, K. Mitarai, and K. Fujii, “Quantum tangent kernel,” (2021), arXiv:2111.02951 [quant-ph]

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Closest in time.