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1997
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2007
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S. I. Daitch, J. A. Kelner, and D. A. Spielman, in Proceedings of the 26th Annual International Conference on Machine Learning , ICML ’09 (ACM, New York, NY, USA, 2009) pp. 201–208
2009
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J. E. Avron, M. Fraas, G. M. Graf, and P. Grech, Phys. Rev. A 82
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M. B. Hastings, Quantum Info. Comput. 13
2013
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S. Lloyd, M. Mohseni, and P. Rebentrost, “Quantum algorithms for supervised and unsupervised machine learning,” (2013), arXiv:1307.0411
Original
2013
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A. Perusso, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Asuru-Guzik, and J. O’Brien, Nature Communications 5
2014
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A. W. Cross, G. Smith, and J. A. Smolin, Phys. Rev. A 92
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Then

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2018
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Original
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Later among the works it cites.
M. Schuld, A. Bocharov, K. Svore, and N. Wiebe, “Circuit-centric quantum classifiers,” (2018), arXiv:1804.00633
Original
2018
Later among the works it cites.
C. M. Wilson, J. S. Otterbach, N. Tezak, R. S. Smith, G. E. Crooks, and M. P. da Silva, “Quantum kitchen sinks: An algorithm for machine learning on near-term quantum computers,” (2018), arXiv:1806.08321

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2019

Quantum-Assisted Clustering Algorithms for NISQ-Era Devices

Mendelson, Samuel S., Strand, Robert W., Oldaker IV, Guy B. et al.

Understand

In the NISQ-era of quantum computing, we should not expect to see quantum devices that provide an exponential improvement in runtime for practical problems, due to the lack of error correction and small number of qubits available.

Nevertheless, these devices should be able to provide other performance improvements, particularly when combined with existing classical machines.
In this article, we develop several hybrid quantum-classical clustering algorithms that can be employed as subroutines on small, NISQ-era devices.
These new hybrid algorithms require a number of qubits that is at most logarithmic in the size of the data, provide performance improvement and/or runtime improvement over their classical counterparts, and do not require a black-box oracle.

Built on

S. Lloyd, IEEE Transactions on Information Theory 28
1982
Earlier work this paper cites.
F. R. K. Chung, Spectral Graph Theory (American Mathematical Society, 1997)
1997
Earlier work this paper cites.
D. Arthur and S. Vassilvitskii, in Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms , SODA ’07 (Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2007) pp. 1027–1035
2007
Earlier work this paper cites.
S. I. Daitch, J. A. Kelner, and D. A. Spielman, in Proceedings of the 26th Annual International Conference on Machine Learning , ICML ’09 (ACM, New York, NY, USA, 2009) pp. 201–208
2009
Earlier work this paper cites.
J. E. Avron, M. Fraas, G. M. Graf, and P. Grech, Phys. Rev. A 82
2010
Earlier work this paper cites.
M. B. Hastings, Quantum Info. Comput. 13
2013
Earlier work this paper cites.
S. Lloyd, M. Mohseni, and P. Rebentrost, “Quantum algorithms for supervised and unsupervised machine learning,” (2013), arXiv:1307.0411
Original
2013
Earlier work this paper cites.
A. Perusso, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Asuru-Guzik, and J. O’Brien, Nature Communications 5
2014
Earlier work this paper cites.
A. W. Cross, G. Smith, and J. A. Smolin, Phys. Rev. A 92
2015
Earlier work this paper cites.