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Implementing Quantum-Kernel-Based Classifiers in the NISQ Era

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Artificial Intelligence Research (SACAIR 2021)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1551))

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Abstract

There is an intrinsic link between operations that can be performed on a quantum computer and kernel methods. This has inspired the development of quantum-kernel-based classifiers that exploit the ability of quantum computers to efficiently perform operations in large Hilbert spaces. This work performs a proof of principle demonstration of a quantum-kernel-based classifier applied to the binary classification of various non-linearly separable datasets. For each classification task, a quantum device provided by the IBM Quantum (IBMQ) platform is used to estimate a kernel matrix. A number of novel strategies comprised of combinations of existing post-processing methods are then applied to the matrix to mitigate the effects of noise from the quantum device, readout error and account for the effects of finite sampling. The application of certain strategies is shown to improve the quality of the kernel matrices estimated by the quantum device. The raw and post-processed kernel matrices are fed into a classical support vector machines (SVM) that learns a model to perform the classification. For each classification task, the classifiers exhibits high accuracies that are comparable to the classifiers that use ideal, simulated kernel matrices. The classifiers that use certain post-processed kernel matrices exhibit higher accuracies than the classifiers that use the raw kernel matrices. This demonstrates the effectiveness of quantum-kernel-based classifiers in the Noisy Intermediate Scale Quantum (NISQ) computing era as well as the power of certain of post-processing strategies.

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Notes

  1. 1.

    A brief introduction to quantum computing and kernels can be found in Sections A and B, respectively, of the Supplementary Material [29].

  2. 2.

    R-TIK and R-THR were originally applied to quantum kernel estimation in [25]. R-TIK, R-THR and R-FLP were originally applied quantum kernel estimation in [26].

References

  1. Li, W., Deng, D.-L.: Recent advances for quantum classifiers. arXiv preprint arXiv:2108.13421 (2021)

  2. Schuld, M., Petruccione, F.: Supervised Learning with Quantum Computers, vol. 17. Springer (2018)

    Google Scholar 

  3. Zoufal, C., Lucchi, A., Woerner, S.: Quantum generative adversarial networks for learning and loading random distributions. NPJ Quant. Inf. 5(1), 1–9 (2019)

    Google Scholar 

  4. Romero, J., Olson, J.P., Aspuru-Guzik, A.: Quantum autoencoders for efficient compression of quantum data. Quant. Sci. Technol. 2(4), 045001 (2017)

    Google Scholar 

  5. Dunjko, V., Briegel, H.J.: Machine learning & artificial intelligence in the quantum domain: a review of recent progress. Rep. Prog. Phys. 81(7), 074001 (2018)

    Google Scholar 

  6. Ciliberto, C.: Quantum machine learning: a classical perspective. Proc. R. Soci. Math. Phys. Eng. Sci. 474(2209), 20170551 (2018)

    Google Scholar 

  7. Killoran, N., Bromley, T.R., Miguel Arrazola, J., Schuld, M., Quesada, N., Lloyd, S.: Continuous-variable quantum neural networks. Phys. Rev. Res. 1(3), 033063 (2019)

    Google Scholar 

  8. Schuld, M., Sinayskiy, I., Petruccione, F.: The quest for a quantum neural network. Quant. Inf. Process. 13(11), 2567–2586 (2014)

    Article  MathSciNet  Google Scholar 

  9. Farhi, E., Neven, H.: Classification with quantum neural networks on near term processors. arXiv preprint arXiv:1802.06002 (2018)

  10. Lu, S., Braunstein, S.L.: Quantum decision tree classifier. Quant. Inf. Process. 13(3), 757–770 (2013). https://doi.org/10.1007/s11128-013-0687-5

    Article  MathSciNet  MATH  Google Scholar 

  11. Lloyd, S., Mohseni, M., Rebentrost, P.: Quantum algorithms for supervised and unsupervised machine learning. arXiv preprint arXiv:1307.0411 (2013)

  12. Wiebe, N., Kapoor, A., Svore, K.: Quantum algorithms for nearest-neighbor methods for supervised and unsupervised learning. arXiv preprint arXiv:1401.2142 (2014)

  13. Rebentrost, P., Mohseni, M., Lloyd, S.: Quantum support vector machine for big data classification. Phys. Rev. Lett. 113(13), 130503 (2014)

    Google Scholar 

  14. Chatterjee, R., Yu, T.: Generalized coherent states, reproducing kernels, and quantum support vector machines. arXiv preprint arXiv:1612.03713 (2016)

  15. Schuld, M., Fingerhuth, M., Petruccione, F.: Implementing a distance-based classifier with a quantum interference circuit. EPL (Europhys. Lett.) 119(6), 60002 (2017)

    Article  Google Scholar 

  16. Schuld, M., Killoran, N.: Quantum machine learning in feature Hilbert spaces. Phys. Rev. Lett.122(4), 040504 (2019)

    Google Scholar 

  17. Havlíček, V., et al.: Supervised learning with quantum-enhanced feature spaces. Nature 567(7747), 209–212 (2019)

    Google Scholar 

  18. Blank, C., Park, D.K., Kevin Rhee, J.-K., Petruccione, F.: Quantum classifier with tailored quantum kernel. NPJ Quant. Inf. 6(1), 1–7 (2020)

    Google Scholar 

  19. Liu, Y., Arunachalam, S., Temme, K.: A rigorous and robust quantum speed-up in supervised machine learning. Nat. Phys. 1–5 (2021)

    Google Scholar 

  20. Huang, H.-Y., et al.: Power of data in quantum machine learning. Nat. Commun. 12(1), 1–9 (2021)

    Google Scholar 

  21. Bittel, L., Kliesch, M.: Training variational quantum algorithms is np-hard. Phy. Rev. Lett.127(12), 120502 (2021)

    Google Scholar 

  22. Bartkiewicz, K., Gneiting, C., Černoch, A., Jiráková, K., Lemr, K., Nori, F.: Experimental kernel-based quantum machine learning in finite feature space. Sci. Rep. 10(1), 1–9 (2020)

    Article  Google Scholar 

  23. Kusumoto, T., Mitarai, K., Fujii, K., Kitagawa, M., Negoro, M.: Experimental quantum kernel machine learning with nuclear spins in a solid. arXiv preprint arXiv:1911.12021 (2019)

  24. Peters, E.: Machine learning of high dimensional data on a noisy quantum processor. arXiv preprint arXiv:2101.09581 (2021)

  25. Hubregtsen, T.: Training quantum embedding kernels on near-term quantum computers. arXiv preprint arXiv:2105.02276 (2021)

  26. Wang, X., Du, Y., Luo, Y., Tao, D.: Towards understanding the power of quantum kernels in the NISQ era. arXiv preprint arXiv:2103.16774 (2021)

  27. Asfaw, A., et al.: Learn quantum computation using Qiskit (2020)

    Google Scholar 

  28. Suzuki, Y., et al.: Analysis and synthesis of feature map for kernel-based quantum classifier. Quant. Mach. Intell. 2(1), 1–9 (2020). https://doi.org/10.1007/s42484-020-00020-y

    Article  Google Scholar 

  29. Mahashakti Pillay, S., Sinayskiy, I., Jembere, E., Petruccione,F.: Implementing-quantum-kernel-based-classifiers-in-the-NISQ-Era-Supp-Material. 11 (2021). https://git.io/JX8cp

  30. Nielsen, M., Chuang, I.: Quantum Computation and Quantum Information, 10th Anniversary edition. Cambridge University Press, Cambridge (2010)

    Google Scholar 

  31. Roth, V., Laub, J., Kawanabe, M., Buhmann, J.M.: Optimal cluster preserving embedding of nonmetric proximity data. IEEE Trans. Patt. Anal. Mach. Intell. 25(12), 1540–1551 (2003)

    Google Scholar 

  32. Wu, G., Chang, E.Y., Zhang, Z.: An analysis of transformation on non-positive semidefinite similarity matrix for kernel machines. In: Proceedings of the 22nd International Conference on Machine Learning, vol. 8. Citeseer (2005)

    Google Scholar 

  33. Graepel, T., Herbrich, R., Bollmann-Sdorra, P., Obermayer, K.: Classification on pairwise proximity data. Adv. Neural Inf. Process. Syst. 11, 438–444 (1999)

    Google Scholar 

  34. Abraham, H., et al.: Qiskit: an open-source framework for quantum computing (2019)

    Google Scholar 

  35. Bergholm, V., et al.: Automatic differentiation of hybrid quantum-classical computations (2020)

    Google Scholar 

  36. Pedregosa, F., et al.: Scikit-learn: machine learning in python. J. Mach. Learn. Res. 12, 2825–2830 (2011)

    MathSciNet  MATH  Google Scholar 

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Acknowlegdements

This work is based upon research supported by the South African Research Chair Initiative, Grant No. 64812 of the Department of Science and Innovation and the National Research Foundation of the Republic of South Africa. Support from the CSIR DSI-Interbursary Support (IBS) Programme is gratefully acknowledged. Support from the Center of Artificial Intelligence Research is appreciated. We would like to thank Mr I. J. David for his assistance in proof reading the manuscript. We acknowledge the use of IBM Quantum services for this work. The views expressed are those of the authors and do not reflect the official policy or position of IBM or the IBM Quantum team.

Author information

Authors and Affiliations

  1. School of Mathematics, Statistics, and Computer Science, University of KwaZulu-Natal, Durban, South Africa

    Shivani Mahashakti Pillay & Edgar Jembere

  2. Quantum Research Group, School of Chemistry and Physics, University of KwaZulu-Natal, Durban, South Africa

    Shivani Mahashakti Pillay, Ilya Sinayskiy & Francesco Petruccione

  3. Centre for Artificial Intelligence Research (CAIR), Cape Town, South Africa

    Shivani Mahashakti Pillay & Edgar Jembere

  4. National Institute for Theoretical and Computational Sciences (NITheCS), Johannesburg, South Africa

    Ilya Sinayskiy & Francesco Petruccione

Authors
  1. Shivani Mahashakti Pillay
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  2. Ilya Sinayskiy
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  3. Edgar Jembere
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  4. Francesco Petruccione
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Correspondence to Shivani Mahashakti Pillay .

Editor information

Editors and Affiliations

  1. University of KwaZulu-Natal, Durban, South Africa

    Edgar Jembere

  2. University of Pretoria, Pretoria, South Africa

    Aurona J. Gerber

  3. University of KwaZulu-Natal, Durban, South Africa

    Serestina Viriri

  4. University of KwaZulu-Natal, Durban, South Africa

    Anban Pillay

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Pillay, S.M., Sinayskiy, I., Jembere, E., Petruccione, F. (2022). Implementing Quantum-Kernel-Based Classifiers in the NISQ Era. In: Jembere, E., Gerber, A.J., Viriri, S., Pillay, A. (eds) Artificial Intelligence Research. SACAIR 2021. Communications in Computer and Information Science, vol 1551. Springer, Cham. https://doi.org/10.1007/978-3-030-95070-5_17

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  • DOI: https://doi.org/10.1007/978-3-030-95070-5_17

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  • Online ISBN: 978-3-030-95070-5

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