Simulation of a Multidimensional Input Quantum Perceptron

  • Alexandre Y. Yamamoto
  • Kyle M. Sundqvist
  • Peng Li
  • H. Rusty HarrisEmail author


In this work, we demonstrate the improved data separation capabilities of the Multidimensional Input Quantum Perceptron (MDIQP), a fundamental cell for the construction of more complex Quantum Artificial Neural Networks (QANNs). This is done by using input controlled alterations of ancillary qubits in combination with phase estimation and learning algorithms. The MDIQP is capable of processing quantum information and classifying multidimensional data that may not be linearly separable, extending the capabilities of the classical perceptron. With this powerful component, we get much closer to the achievement of a feedforward multilayer QANN, which would be able to represent and classify arbitrary sets of data (both quantum and classical).


Perceptron Quantum machine learning Quantum Artificial Neural Network Quantum information Quantum Perceptron 


  1. 1.
    Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: 35th Annual Symposium on Foundations of Computer Science, 1994 Proceedings. Santa Fe, NM, pp. 124–134 (1994)Google Scholar
  3. 3.
    Simon, D.R.: On the power of quantum computation. In: 35th Annual Symposium on Foundations of Computer Science, 1994 Proceedings, pp. 116–123Google Scholar
  4. 4.
    Overall Technology Roadmap Characteristics. International Technology Roadmap for Semiconductors (2010).
  5. 5.
    Bernstein, D.J., Buchmann, J., Dahmen, E.: Post-Quantum Cryptography, 1st edn. Springer, Berlin. ISBN 978-3-540-88702-7 (2009)Google Scholar
  6. 6.
    Witten, I.H., Frank, E.: Data Mining: Practical Machine Learning Tools and Techniques. Morgan Kaufmann, Los Altos (2005)zbMATHGoogle Scholar
  7. 7.
    Wittek, P.: Quantum Machine Learning: What Quantum Computing Means to Data Mining. Academic Press, London (2014)zbMATHGoogle Scholar
  8. 8.
    Hagan, M., Demuth, H., Beale, M.: Neural Network Design. PWS Publishing Company, Boston (1996)Google Scholar
  9. 9.
    Minsky, M., Papert, S.: Perceptrons: An Introduction to Computational Geometry. MIT Press, Cambridge (1969)zbMATHGoogle Scholar
  10. 10.
    Hopfield, J.J.: Artificial neural networks. IEEE Circuits Devices Mag. 4(5), 3–10 (1988)CrossRefGoogle Scholar
  11. 11.
    Gallant, S.I.: Perceptron-based learning algorithms. IEEE Trans. Neural Netw. I(2), 179191 (1990)Google Scholar
  12. 12.
    Cybenko, G.: Approximation by superpositions of a sigmoidal function. Math. Control Signals Syst. 2, 303–314 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Lewenstein, M.: Quantum perceptrons. J. Mod. Opt. 41(12), 2491–2501 (1994)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Jones, J.A.: Quantum Information, Computation and Communication, 1st edn. Cambridge: Cambridge University Press. ISBN 978-1-107-01446-6 (2012)Google Scholar
  15. 15.
    Zhou, R.: Quantum competitive neural network. Int. J. Theor. Phys. 49, 110–119 (2010)CrossRefzbMATHGoogle Scholar
  16. 16.
    Sagheer, A., and Metwally, N.: Communication via quantum neural networks. In: The 2nd World Congress on Nature and Biologically Inspired Computing, NaBIC. IEEE, pp. 418–422 (2010)Google Scholar
  17. 17.
    Ventura, D., Martinez, T.: Quantum associative memory. Inf. Sci. 5124, 273–296 (2000)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Zhou, R., Qin, L., Jiang, N. (2006). Quantum perceptron network. In: The 16th International Conference on Artificial Neural Networks, ICANN , LNCS, vol. 4131, pp. 651–657 (2006)Google Scholar
  19. 19.
    Li, C., Li, S.: Learning algorithm and application of quantum BP neural networks based on universal quantum gates. J. Syst. Eng. Electron. 19(1), 167–174 (2008)CrossRefzbMATHGoogle Scholar
  20. 20.
    Kak, S.C.: Quantum neural computing. Adv. Imaging Electron. Phys. 94, 259–314 (1995)CrossRefGoogle Scholar
  21. 21.
    Shafee, F.: Neural networks with quantum gated nodes. Eng. Appl. Artif. Intell. 20(4), 429–437 (2007)CrossRefGoogle Scholar
  22. 22.
    De Vos, A.: Reversible Computing: Fundamentals, Quantum Computing, and Applications. Wiley, London (2011)zbMATHGoogle Scholar
  23. 23.
    Abdessaied, Nabila, Drechsler, R.: Reversible and Quantum Circuits: Optimization and Complexity Analysis. Springer, Berlin (2016)CrossRefzbMATHGoogle Scholar
  24. 24.
    Perumalla, K.S.: Introduction to Reversible Computing. CRC Press, Boca Raton (2013)Google Scholar
  25. 25.
    Schuld, M., Sinayskiy, I., Petruccione, F.: Simulating a perceptron on a quantum computer. Phys. Lett. A 379(7), 660–663 (2015)CrossRefzbMATHGoogle Scholar
  26. 26.
    Schuld, M., Sinayskiy, I., Petruccione, F.: The quest for a quantum neural network. Quantum Inf. Process. 13(11), 25672586 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Kitaev, A.Y., Shen, A.H., Vyalyi, M.N.: Classical and Quantum Computation, vol. 47. American Mathematical Society, Providence (2002)zbMATHGoogle Scholar
  28. 28.
    Sopena, J.M., Romero, E., Alquezar, R.: Neural networks with periodic and monotonic activation functions: a comparative study in classification problems. In: Ninth International Conference on Artificial Neural Networks, 1999, ICANN 99 (Conference Publications No. 470), vol. 1. IET (1999)Google Scholar
  29. 29.
    Johansson, J.R., Nation, P.D., Nori, F.: QuTiP: an open-source Python framework for the dynamics of open quantum systems. Comput. Phys. Comm. 183, 17601772 (2012)CrossRefGoogle Scholar
  30. 30.
    Poggio, T., Bizzi, E.: Generalization in vision and motor control. Nature 431(7010), 768 (2004)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Alexandre Y. Yamamoto
    • 1
  • Kyle M. Sundqvist
    • 2
  • Peng Li
    • 1
  • H. Rusty Harris
    • 1
    Email author
  1. 1.Department of Electrical and Computer EngineeringTexas A&M UniversityCollege StationUSA
  2. 2.Department of PhysicsSan Diego State UniversitySan DiegoUSA

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