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Entanglement assisted training algorithm for supervised quantum classifiers

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Abstract

We propose a new training algorithm for supervised quantum classifiers. Here, we have harnessed the property of quantum entanglement to build a model that can simultaneously manipulate multiple training samples along with their labels. Subsequently, a Bell-inequality-based cost function is constructed, that can encode errors from multiple samples, simultaneously, in a way that is not possible by any classical means. We show that upon minimizing this cost function one can achieve successful classification in benchmark datasets. The results presented in this paper are for binary classification problems. Nevertheless, the analysis can be extended to multi-class classification problems as well.

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References

  1. L. Gondara, in 2016 IEEE 16th International Conference on Data Mining Workshops (ICDMW) (IEEE, 2016) pp. 241-246

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

    Article  ADS  Google Scholar 

  3. Segler, M.H., Kogej, T., Tyrchan, C., Waller, M.P.: Generating focused molecule libraries for drug discovery with recurrent neural networks. ACS Central Sci. 4, 120 (2018)

    Article  Google Scholar 

  4. Sanchez-Lengeling, B., Aspuru-Guzik, A.: Inverse molecular design using machine learning: generative models for matter engineering, Science 361, 360 (2018)

    Article  ADS  Google Scholar 

  5. P. W. Shor, in Algorithms for quantum computation: discrete logarithms and factoring Proceedings 35th annual symposium on foundations of computer science ( organization Ieee, 1994) pp. 124–134

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

    Article  ADS  Google Scholar 

  7. Scarani, V., Bechmann-Pasquinucci, H., Cerf, N.J., Dušek, M., Lütkenhaus, N., Peev, M.: The security of practical quantum key distribution. Rev. Mod. Phys. 81, 1301 (2009)

    Article  ADS  Google Scholar 

  8. Lund, A., Bremner, M.J., Ralph, T.: Quantum sampling problems. BosonSampling Quantum Supremacy npj Quantum Inform. 3, 1–8 (2017)

    Google Scholar 

  9. Spring, J.B., Metcalf, B.J., Humphreys, P.C., Kolthammer, W.S., Jin, X.-M., Barbieri, M., Datta, A., Thomas-Peter, N., Langford, N.K., Kundys, D., et al.: Boson sampling on a photonic chip. Science 339, 798 (2013)

    Article  ADS  Google Scholar 

  10. Obada, A.-S., Hessian, H., Mohamed, A.-B., Homid, A.H.: A proposal for the realization of universal quantum gates via superconducting qubits inside a cavity. Annals Phys. 334, 47 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Obada, A.-S., Hessian, H.A., Mohamed, A.-B., Homid, A.H.: Efficient protocol of \( N \) N-bit discrete quantum Fourier transform via transmon qubits coupled to a resonator. Quantum Inform. Process. 13, 475 (2014)

    Article  ADS  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  13. Schuld, M., Sinayskiy, I., Petruccione, F.: The quest for a quantum neural network. Quantum Inform. Process. 13, 2567 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

  15. Benedetti, M., Garciapintos, D., Perdomo, O., Leytonortega, V., Nam, Y.: A generative modeling approach for benchmarking and training shallow quantum circuits. npj Quantum Inform. 5, 1–9 (2019)

    Article  Google Scholar 

  16. Beer, K., Bondarenko, D., Farrelly, T., Osborne, T.J., Salzmann, R., Scheiermann, D., Wolf, R.: Training deep quantum neural networks. Nature Commun. 11, 1 (2020)

    Article  Google Scholar 

  17. Blank, C., Park, D.K., Rhee, J.K.K., Petruccione, F.: Quantum classifier with tailored quantum kernel. npj Quantum Inform. 6, 1–7 (2020)

    Article  ADS  Google Scholar 

  18. Wossnig, L., Zhao, Z., Prakash, A.: Quantum linear system algorithm for dense matrices. Phys. Rev. Lett. 120, 050502 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  19. 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 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  22. Zhu, D., Linke, N.M., Benedetti, M., Landsman, K.A., Nguyen, N.H., Alderete, C.H., Perdomo-Ortiz, A., Korda, N., Garfoot, A., Brecque, C., et al.: Training of quantum circuits on a hybrid quantum computer. Sci. Adv. 5, eaaw9918 (2019)

    Article  ADS  Google Scholar 

  23. Schuld, M., Bocharov, A., Svore, K.M., Wiebe, N.: Circuit-centric quantum classifiers. Phys. Rev. A 101, 032308 (2020)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  25. A. Harrow and J. Napp, Low-depth gradient measurements can improve convergence in variational hybrid quantum-classical algorithms arXiv preprint arXiv:1901.05374 ( 2019)

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

    Article  ADS  Google Scholar 

  27. Cao, S., Wossnig, L., Vlastakis, B., Leek, P., Grant, E.: Cost-function embedding and dataset encoding for machine learning with parametrized quantum circuits. Phys. Rev. A 101, 052309 (2020)

    Article  ADS  Google Scholar 

  28. Mohamed, A.-B.A.: Bipartite non-classical correlations for a lossy two connected qubit–cavity systems: trace distance discord and Bell’s non-locality. Quantum Inform. Process. 17, 1 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  29. Mohamed, A.A., Joshi, A., Hassan, S.: Bipartite non-local correlations in a double-quantum-dot excitonic system. J. Phys. A: Math. Theor. 47, 335301 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  30. Mohamed, A.-B.A.: Non-local correlations via Wigner–Yanase skew information in two SC-qubit having mutual interaction under phase decoherence. Euro. Phys. J. D 71, 1 (2017)

    Article  Google Scholar 

  31. Mohamed, A.A., Eleuch, H.: Quantum correlation control for two semiconductor microcavities connected by an optical fiber. Physica Scripta 92, 065101 (2017)

    Article  ADS  Google Scholar 

  32. Mohamed, A.-B., Eleuch, H., Ooi, C.R.: Non-locality correlation in two driven qubits inside an open coherent cavity: trace norm distance and maximum Bell function. Sci. Rep. 9, 1 (2019)

    Article  Google Scholar 

  33. Adhikary, S., Dangwal, S., Bhowmik, D.: Supervised learning with a quantum classifier using multi-level systems. Quantum Inform. Process. 19, 89 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  34. A. Mari, T. R. Bromley, J. Izaac, M. Schuld, and N. Killoran, Transfer learning in hybrid classical-quantum neural networks arXiv preprint arXiv:1912.08278 ( 2019)

  35. Bishop, C.M.: Pattern recognition and machine learning pattern recognition and machine learning. Springer, Berlin (2006)

    MATH  Google Scholar 

  36. Haykin, S.: Neural networks and learning machines 3/E neural networks and learning machines 3/E. Pearson Education, India (2010)

    Google Scholar 

  37. M. Ostaszewski, E. Grant, and M. Benedetti, Quantum circuit structure learning arXiv preprint arXiv:1905.09692 ( 2019)

  38. Wiebe, N., Braun, D., Lloyd, S.: Quantum algorithm for data fitting. Phys. Rev. Lett. 109, 050505 (2012)

    Article  ADS  Google Scholar 

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

  40. Pérez-Salinas, A., Cervera-Lierta, A., Gil-Fuster, E., Latorre, J.I.: Data re-uploading for a universal quantum classifier. Quantum 4, 226 (2020)

    Article  Google Scholar 

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

    Article  Google Scholar 

  42. https://quantumcomputing.ibm.com

  43. Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880 (1969)

    Article  ADS  MATH  Google Scholar 

  44. Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V., Wehner, S.: Bell nonlocality. Rev. Mod. Phys. 86, 419 (2014)

    Article  ADS  Google Scholar 

  45. Gisin, N.: Bell’s inequality holds for all non-product states. Phys. Lett. A 154, 201 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  46. Cirel’son, B.S.: Quantum generalizations of Bell’s inequality. Lett. Math. Phys. 4, 93 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  47. Braunstein, S.L., Mann, A., Revzen, M.: Maximal violation of Bell inequalities for mixed states. Phys. Rev. Lett. 68, 3259 (1992)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  48. UCI repository of machine learning databases, organization Department of Information and Computer Science, University of California Irvine ( 2020), https://archive.ics.uci.edu/ml/datasets/Iris

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

  50. Collins, D., Gisin, N., Linden, N., Massar, S., Popescu, S.: Bell inequalities for arbitrarily high-dimensional systems. Phys. Rev. Lett. 88, 040404 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  51. Sandhir, R.P., Adhikary, S., Ravishankar, V.: CGLMP and Bell–CHSH formulations of non-locality: a comparative study. Quantum Inform. Process. 16, 263 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The author thanks V. Ravishankar, Sooryansh Asthana, Siddharth Dangwal and Rajni Bala for fruitful discussions. The author also thanks the unknown reviewers for making useful comments which helped in improving the manuscript.

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Correspondence to Soumik Adhikary.

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Adhikary, S. Entanglement assisted training algorithm for supervised quantum classifiers. Quantum Inf Process 20, 254 (2021). https://doi.org/10.1007/s11128-021-03179-w

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