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A hybrid classical-quantum approach for multi-class classification

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Abstract

Quantum machine learning recently gained prominence due to the computational ability of quantum computers in solving machine learning problems that are intractable on a classical computer. However, achieving a quantum advantage on present-day quantum computers remains an open challenge. In this work, we primarily focus on solving machine learning problems using a hybrid model based on both quantum and classical computers together for the classification task. We propose the quantum multi-class classifier (QMCC) as a variational circuit with a hybrid classical-quantum approach using quantum mechanical properties such as superposition and entanglement. A unitary operation on a single qubit for the state preparation is designed and also demonstrated using a real quantum computer on the IBMQX platform. The entire variational circuit for the classification task is implemented on a quantum simulator. We performed our quantum simulations on three benchmark datasets: Iris dataset, Banknote Authentication (BNA) dataset, and Wireless Indoor Localization (WIL) dataset for machine learning algorithms. Our simulation results show that the proposed QMCC model classified Iris dataset with an accuracy of 92.10%, BNA dataset with an accuracy of 89.50%, and WIL dataset with an accuracy of 91.73%. The proposed model can also be extended to multiple class classifiers.

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References

  1. Zidan, M., Abdel-Aty, A.H., Nguyen, D.M., Mohamed, A.S., Al-Sbou, Y., Eleuch, H., Abdel-Aty, M.: A quantum algorithm based on entanglement measure for classifying boolean multivariate function into novel hidden classes. Res. Phys. 15, 102549 (2019)

    Google Scholar 

  2. Feynman, R.P.: Simulating physics with computers. Int. J. Theor. Phys. 21(6), 467–488 (1982)

    MathSciNet  Google Scholar 

  3. Mooij, J., Orlando, T., Levitov, L., Tian, L., Van der Wal, C.H., Lloyd, S.: Josephson persistent-current qubit. Science 285(5430), 1036–1039 (1999)

    Google Scholar 

  4. Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79(2), 325 (1997)

    ADS  Google Scholar 

  5. Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303–332 (1999)

    ADS  MathSciNet  MATH  Google Scholar 

  6. Harrow, A.W., Hassidim, A., Lloyd, S.: Quantum algorithm for linear systems of equations. Phys. Rev. Lett. 103(15), 150502 (2009)

    ADS  MathSciNet  Google Scholar 

  7. Chuang, I.L., Vandersypen, L.M., Zhou, X., Leung, D.W., Lloyd, S.: Experimental realization of a quantum algorithm. Nature 393(6681), 143 (1998)

    ADS  Google Scholar 

  8. Jones, J.A., Mosca, M., Hansen, R.H.: Implementation of a quantum search algorithm on a quantum computer. Nature 393(6683), 344 (1998)

    ADS  Google Scholar 

  9. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition, 10th edn. Cambridge University Press, New York (2011)

    MATH  Google Scholar 

  10. Zidan, M., Abdel-Aty, A., Younes, A., Zanaty, E., El-khayat, I., Abdel-Aty, M.: A novel algorithm based on entanglement measurement for improving speed of quantum algorithms. Appl. Math. Inf. Sci 12(1), 265–269 (2018)

    MathSciNet  Google Scholar 

  11. Abdel-Aty, A.H., Kadry, H., Zidan, M., Al-Sbou, Y., Zanaty, E., Abdel-Aty, M.: A quantum classification algorithm for classification incomplete patterns based on entanglement measure. J. Intell. Fuzzy Syst. (Preprint) pp. 1–8, (2020)

  12. Zidan, M., Abdel-Aty, A.H., El-shafei, M., Feraig, M., Al-Sbou, Y., Eleuch, H., Abdel-Aty, M.: Quantum classification algorithm based on competitive learning neural network and entanglement measure. Appl. Sci. 9(7), 1277 (2019)

    Google Scholar 

  13. Zidan, M., Sagheer, A., Metwally, N.: An autonomous competitive learning algorithm using quantum hamming neural networks. In: 2015 International Joint Conference on Neural Networks (IJCNN), pp. 1–7. IEEE (2015)

  14. Sagheer, A., Zidan, M., Abdelsamea, M.M.: A novel autonomous perceptron model for pattern classification applications. Entropy 21(8), 763 (2019)

    ADS  MathSciNet  Google Scholar 

  15. Zidan, M., Abdel-Aty, A.H., El-Sadek, A., Zanaty, E., Abdel-Aty, M.: Low-cost autonomous perceptron neural network inspired by quantum computation. In: AIP Conference Proceedings, vol. 1905, p. 020005. AIP Publishing LLC (2017)

  16. Abubakar, M.Y., Jung, L.T., Zakaria, N., Younes, A., Abdel-Aty, A.H.: Reversible circuit synthesis by genetic programming using dynamic gate libraries. Quant. Inf. Process. 16(6), 160 (2017)

    ADS  MathSciNet  MATH  Google Scholar 

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

    ADS  Google Scholar 

  18. Schuld, M., Sinayskiy, I., Petruccione, F.: An introduction to quantum machine learning. Contemp. Phys. 56(2), 172–185 (2015)

    ADS  MATH  Google Scholar 

  19. Biamonte, J., Wittek, P., Pancotti, N., Rebentrost, P., Wiebe, N., Lloyd, S.: Quantum machine learning. Nature 549(7671), 195 (2017)

    ADS  Google Scholar 

  20. Fingerhuth, M., Babej, T., Wittek, P.: Open source software in quantum computing. PloS ONE 13(12), e0208561 (2018)

    Google Scholar 

  21. Liu, D., Ran, S.J., Wittek, P., Peng, C., García, R.B., Su, G., Lewenstein, M.: Machine learning by unitary tensor network of hierarchical tree structure. N. J. Phys. 21(7), 073059 (2019)

    MathSciNet  Google Scholar 

  22. Arute, F., Arya, K., Babbush, R., Bacon, D., Bardin, J.C., Barends, R., Biswas, R., Boixo, S., Brandao, F.G., Buell, D.A., et al.: Quantum supremacy using a programmable superconducting processor. Nature 574(7779), 505–510 (2019)

    ADS  Google Scholar 

  23. 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(7747), 209 (2019)

    ADS  Google Scholar 

  24. Preskill, J.: Quantum computing in the NISQ era and beyond. Quantum 2, 79 (2018)

    Google Scholar 

  25. IBM Quantum Experience (2016). https://quantum-computing.ibm.com. [Online; accessed 28. Aug. 2020]

  26. Bergholm, V., Izaac, J., Schuld, M., Gogolin, C., Killoran, N.: Pennylane: Automatic differentiation of hybrid quantum-classical computations. (2018). arXiv preprint arXiv:1811.04968

  27. Michie, D., Spiegelhalter, D.J., Taylor, C., et al.: Machine learning. Neural Stat. Classif. 13(1994), 1–298 (1994)

    ADS  MATH  Google Scholar 

  28. LeCun, Y., Bengio, Y., Hinton, G.: Deep learning. Nature 521(7553), 436–444 (2015)

    ADS  Google Scholar 

  29. Goodfellow, I., Bengio, Y., Courville, A.: Deep Learning. MIT press, Cambridge (2016)

    MATH  Google Scholar 

  30. Wittek, P.: Quantum Machine Learning: What Quantum Computing Means to Data Mining. Academic Press, London (2014)

    MATH  Google Scholar 

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

  32. Dunjko, V., Taylor, J.M., Briegel, H.J.: Quantum-enhanced machine learning. Phys. Rev. Lett. 117(13), 130501 (2016)

    ADS  MathSciNet  Google Scholar 

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

    ADS  Google Scholar 

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

    MATH  Google Scholar 

  35. Grant, E., Benedetti, M., Cao, S., Hallam, A., Lockhart, J., Stojevic, V., Green, A.G., Severini, S.: Hierarchical quantum classifiers. NPJ Quant. Inf. 4(1), 65 (2018)

    ADS  Google Scholar 

  36. Tacchino, F., Macchiavello, C., Gerace, D., Bajoni, D.: An artificial neuron implemented on an actual quantum processor. NPJ Quant. Inf. 5(1), 26 (2019)

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  38. Mengoni, R., Di Pierro, A.: Kernel methods in quantum machine learning. Quant. Mach. Intell. 1(3), 65–71 (2019). https://doi.org/10.1007/s42484-019-00007-4

    Article  Google Scholar 

  39. Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nat. Phys. 15(12), 1273–1278 (2019)

    Google Scholar 

  40. Amin, M.H., Andriyash, E., Rolfe, J., Kulchytskyy, B., Melko, R.: Quantum boltzmann machine. Phys. Rev. X 8(2), 021050 (2018)

    Google Scholar 

  41. Lloyd, S., Weedbrook, C.: Quantum generative adversarial learning. Phys. Rev. Lett. 121(4), 040502 (2018)

    ADS  MathSciNet  Google Scholar 

  42. Ciliberto, C., Herbster, M., Ialongo, A.D., Pontil, M., Rocchetto, A., Severini, S., Wossnig, L.: Quantum machine learning: a classical perspective. Proc. R. Soc. A Math. Phys. Eng. Sci. 474(2209), 20170551 (2018)

    ADS  MathSciNet  MATH  Google Scholar 

  43. Von Lilienfeld, O.A.: Quantum machine learning in chemical compound space. Angew. Chem. Int. Ed. 57(16), 4164–4169 (2018)

    Google Scholar 

  44. McClean, J.R., Romero, J., Babbush, R., Aspuru-Guzik, A.: The theory of variational hybrid quantum-classical algorithms. N. J. Phys. 18(2), 023023 (2016)

    MATH  Google Scholar 

  45. Peruzzo, A., McClean, J., Shadbolt, P., Yung, M.H., Zhou, X.Q., Love, P.J., Aspuru-Guzik, A., O’brien, J.L.: A variational eigenvalue solver on a photonic quantum processor. Nat. Commun. 5, 4213 (2014)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  47. Benedetti, M., Lloyd, E., Sack, S., Fiorentini, M.: Parameterized quantum circuits as machine learning models. Quant. Sci. Technol. 4(4), 043001 (2019)

    ADS  Google Scholar 

  48. Draper, T., Kutin, S.: Qpic: Quantum circuit diagrams in latex (2016). https://github.com/qpic/qpic

  49. Stoudenmire, E., Schwab, D.J.: Supervised learning with tensor networks. In: Advances in Neural Information Processing Systems, pp. 4799–4807 (2016)

  50. Bridle, J.S.: Probabilistic Interpretation of Feedforward Classification Network outputs, with relationships to statistical pattern recognition. Springer, Berlin (1990)

    Google Scholar 

  51. Schuld, M., Bergholm, V., Gogolin, C., Izaac, J., Killoran, N.: Evaluating analytic gradients on quantum hardware. Phys. Rev. A 99(3), 032331 (2019)

    ADS  Google Scholar 

  52. IBM Research, Q.c.: Qiskit (2017). https://github.com/Qiskit. [Online; accessed 28. Aug. 2020]

  53. PennyLaneAI: pennylane-qiskit (2018). https://github.com/PennyLaneAI/pennylane-qiskit. [Online; accessed 28. Aug. 2020]

  54. UCI Machine Learning Repository: Iris Data Set (1988). https://archive.ics.uci.edu/ml/datasets/Iris

  55. UCI Machine Learning Repository: Banknote Authentication Data Set (2013). https://archive.ics.uci.edu/ml/datasets/banknote+authentication

  56. UCI Machine Learning Repository: Wireless Indoor Localization Data Set (2017). https://archive.ics.uci.edu/ml/datasets/Wireless+Indoor+Localization

  57. IBM Q 16 Melbourne. ibmq-device-information (2019). https://github.com/Qiskit/ibmq-device-information/blob/master/backends/melbourne/V1/version_log.md

  58. Schuld, M., Petruccione, F.: Information Encoding, pp. 139–171. Springer International Publishing, Berlin (2018). https://doi.org/10.1007/978-3-319-96424-9_5

    Book  Google Scholar 

  59. Kingma, D.P., Ba, J.: Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980 (2014)

  60. Prechelt, L.: Early Stopping-but When? In: Neural Networks: Tricks of the Trade, pp. 55–69. Springer (1998)

  61. Schuld, M., Petruccione, F.: Quantum Information, pp. 75–125. Springer International Publishing, Berlin (2018). https://doi.org/10.1007/978-3-319-96424-9_3

    Book  MATH  Google Scholar 

  62. Möttönen, M., Vartiainen, J.J., Bergholm, V., Salomaa, M.M.: Transformation of quantum states using uniformly controlled rotations. Quant. Inf. Comput. 5(6), 467–473 (2005)

    MathSciNet  MATH  Google Scholar 

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Acknowledgements

We thank Maria Schuld and PennyLane team of Xanadu Inc., Kaushik Mukherjee of Indian Institute of Space Science and Technology and Indranil Ghosh from Jadavpur University for the useful discussions.

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Correspondence to B. S. Manoj.

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Chalumuri, A., Kune, R. & Manoj, B.S. A hybrid classical-quantum approach for multi-class classification. Quantum Inf Process 20, 119 (2021). https://doi.org/10.1007/s11128-021-03029-9

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