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Supervised learning with a quantum classifier using multi-level systems

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Abstract

We propose a quantum classifier, which can classify data under the supervised learning scheme using a quantum feature space. The input feature vectors are encoded in a single quNit (a N-level quantum system), as opposed to more commonly used entangled multi-qubit systems. For training, we use the much used quantum variational algorithm—a hybrid quantum–classical algorithm, in which the forward part of the computation is performed on a quantum hardware, whereas the feedback part is carried out on a classical computer. We introduce “single-shot training”, where all input samples belonging to the same class are used to train the classifier simultaneously. This significantly speeds up the training procedure and provides an advantage over classical machine learning classifiers. We demonstrate successful classification of popular benchmark datasets with our quantum classifier and compare its performance with respect to classical machine learning classifiers. We also show that the number of training parameters in our classifier is significantly less than the classical classifiers.

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References

  1. Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70(13), 1895–1899 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  2. Bennett, C., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. In: Proceedings IEEE International Conference on Computers, Systems and Signal Processing (ICCSSP) 175 (1984)

  3. Ren, J.G., Xu, P., Yong, H.L., Zhang, L., Liao, S.K., Yin, J., Liu, W.Y., Cai, W.Q., Yang, M., Li, L., et al.: Ground-to-satellite quantum teleportation. Nature 549, 70 (2017)

    Article  ADS  Google Scholar 

  4. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press (2010). https://doi.org/10.1017/CBO9780511976667

  5. Grover, L.K.: A fast quantum mechanical algorithm for database search. Preprint ar**v:quant-ph/9605043) (1996)

  6. Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67(6), 661–663 (1991). https://doi.org/10.1103/PhysRevLett.67.661

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Biamonte, J., Wittek, P., Pancotti, N., Rebentrost, P., Wiebe, N., Lloyd, S.: Quantum machine learning. Nature 549, 195 (2017)

    Article  ADS  Google Scholar 

  8. LeCun, Y., Bengio, Y., Hinton, G.: Deep learning. Nature 521, 436–444 (2015)

    Article  ADS  Google Scholar 

  9. Bishop, C.M.: Pattern Recognition and Machine Learning. Springer, Berlin (2006)

    MATH  Google Scholar 

  10. Havlíček, V., Córcoles, A.D., Temme, K., Harrow, A.W., Kandala, A., Chow, J.M., Gambetta, J.M.: Supervised learning with quantum-enhanced feature spaces. Nature 567, 209 (2019)

    Article  ADS  Google Scholar 

  11. Schuld, M., Killoran, N.: Quantum machine learning in feature Hilbert spaces. Phys. Rev. Lett. 122(4), 040504 (2019). https://doi.org/10.1103/PhysRevLett.122.040504

    Article  ADS  Google Scholar 

  12. Wan, K.H., Dahlsten, O., Kristjánsson, H., Gardner, R., Kim, M.: Quantum generalisation of feedforward neural networks. npj Quantum Inf. 3, 36 (2017)

    Article  ADS  Google Scholar 

  13. Farhi, E., Neven, H.: Classification with quantum neural networks on near term processors. ar**v preprint ar**v:1802.06002 (2018)

  14. Rebentrost, P., Bromley, T.R., Weedbrook, C., Lloyd, S.: Quantum Hopfield neural network. Phys. Rev. A 98(4), 042308 (2018)

    Article  ADS  Google Scholar 

  15. McClean, J.R., Romero, J., Babbush, R., Aspuru-Guzik, A.: The theory of variational hybrid quantum-classical algorithms. New J. Phys. 18, 023023 (2016). https://doi.org/10.1088/1367-2630/18/2/023023

    Article  ADS  Google Scholar 

  16. Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Phys. Rev. A 98(3), 032309 (2018)

    Article  ADS  Google Scholar 

  17. Russell, S.J., Norvig, P.: Artificial Intelligence: A Modern Approach. Pearson Education Limited, Kuala Lumpur (2016)

    MATH  Google Scholar 

  18. Schuld, M., Bocharov, A., Svore, K., Wiebe, N.: Circuit-centric quantum classifiers. ar**v preprint ar**v:1804.00633 (2018)

  19. Preskill, J.: Quantum computing in the NISQ era and beyond. Quantum 2, 79 (2018). https://doi.org/10.22331/q-2018-08-06-79. ISSN 2521-327X

    Article  Google Scholar 

  20. Malik, M., Mirhosseini, M., Lavery, M.P., Leach, J., Padgett, M.J., Boyd, R.W.: Direct measurement of a 27-dimensional orbital-angular-momentum state vector. Nat. Commun. 5, 3115 (2014)

    Article  ADS  Google Scholar 

  21. Department of Information and Computer Science, University of California Irvine: UCI repository of machine learning databases. https://archive.ics.uci.edu/ml/datasets/Iris (1998). Accessed 12 June 2019

  22. Department of Information and Computer Science, University of California Irvine: UCI repository of machine learning databases. https://archive.ics.uci.edu/ml/datasets/connectionist+bench+(sonar,+mines+vs.+rocks) (1998). Accessed 12 June 2019

  23. Department of Information and Computer Science, University of California Irvine: UCI repository of machine learning databases. http://archive.ics.uci.edu/ml/datasets/Breast+Cancer+Wisconsin+%28Diagnostic%29 (1998). Accessed 12 June 2019

  24. Tilma, T., Sudarshan, E.C.G.: Generalized Euler angle parametrization for SU(N). J. Phys. A: Math. General 35, 10467–10501 (2002). https://doi.org/10.1088/0305-4470/35/48/316

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Netw. 2, 359–366 (1989). ISSN 0893-6080

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Acknowledgements

SA thanks CSIR (Grant No. - 09/086(1203)/2014-EMR-I), and DB thanks the Department of Science and Technology INSPIRE Faculty Award and Science and Engineering Research Board Early Career Research (ECR) award for funding the research.

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Correspondence to Soumik Adhikary.

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Adhikary, S., Dangwal, S. & Bhowmik, D. Supervised learning with a quantum classifier using multi-level systems. Quantum Inf Process 19, 89 (2020). https://doi.org/10.1007/s11128-020-2587-9

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