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Simulation of a Multidimensional Input Quantum Perceptron

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Abstract

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).

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References

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

  3. Simon, D.R.: On the power of quantum computation. In: 35th Annual Symposium on Foundations of Computer Science, 1994 Proceedings, pp. 116–123

  4. Overall Technology Roadmap Characteristics. International Technology Roadmap for Semiconductors (2010). http://www.itrs2.net/itrs-reports.html

  5. Bernstein, D.J., Buchmann, J., Dahmen, E.: Post-Quantum Cryptography, 1st edn. Springer, Berlin. ISBN 978-3-540-88702-7 (2009)

  6. Witten, I.H., Frank, E.: Data Mining: Practical Machine Learning Tools and Techniques. Morgan Kaufmann, Los Altos (2005)

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  8. Hagan, M., Demuth, H., Beale, M.: Neural Network Design. PWS Publishing Company, Boston (1996)

    Google Scholar 

  9. Minsky, M., Papert, S.: Perceptrons: An Introduction to Computational Geometry. MIT Press, Cambridge (1969)

    MATH  Google Scholar 

  10. Hopfield, J.J.: Artificial neural networks. IEEE Circuits Devices Mag. 4(5), 3–10 (1988)

    Article  Google Scholar 

  11. Gallant, S.I.: Perceptron-based learning algorithms. IEEE Trans. Neural Netw. I(2), 179191 (1990)

    Google Scholar 

  12. Cybenko, G.: Approximation by superpositions of a sigmoidal function. Math. Control Signals Syst. 2, 303–314 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  13. Lewenstein, M.: Quantum perceptrons. J. Mod. Opt. 41(12), 2491–2501 (1994)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. Jones, J.A.: Quantum Information, Computation and Communication, 1st edn. Cambridge: Cambridge University Press. ISBN 978-1-107-01446-6 (2012)

  15. Zhou, R.: Quantum competitive neural network. Int. J. Theor. Phys. 49, 110–119 (2010)

    Article  MATH  Google Scholar 

  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)

  17. Ventura, D., Martinez, T.: Quantum associative memory. Inf. Sci. 5124, 273–296 (2000)

    Article  MathSciNet  Google Scholar 

  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)

  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)

    Article  MATH  Google Scholar 

  20. Kak, S.C.: Quantum neural computing. Adv. Imaging Electron. Phys. 94, 259–314 (1995)

    Article  Google Scholar 

  21. Shafee, F.: Neural networks with quantum gated nodes. Eng. Appl. Artif. Intell. 20(4), 429–437 (2007)

    Article  Google Scholar 

  22. De Vos, A.: Reversible Computing: Fundamentals, Quantum Computing, and Applications. Wiley, London (2011)

    MATH  Google Scholar 

  23. Abdessaied, Nabila, Drechsler, R.: Reversible and Quantum Circuits: Optimization and Complexity Analysis. Springer, Berlin (2016)

    Book  MATH  Google Scholar 

  24. Perumalla, K.S.: Introduction to Reversible Computing. CRC Press, Boca Raton (2013)

    Google Scholar 

  25. Schuld, M., Sinayskiy, I., Petruccione, F.: Simulating a perceptron on a quantum computer. Phys. Lett. A 379(7), 660–663 (2015)

    Article  MATH  Google Scholar 

  26. Schuld, M., Sinayskiy, I., Petruccione, F.: The quest for a quantum neural network. Quantum Inf. Process. 13(11), 25672586 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  27. Kitaev, A.Y., Shen, A.H., Vyalyi, M.N.: Classical and Quantum Computation, vol. 47. American Mathematical Society, Providence (2002)

    MATH  Google Scholar 

  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)

  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)

    Article  Google Scholar 

  30. Poggio, T., Bizzi, E.: Generalization in vision and motor control. Nature 431(7010), 768 (2004)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX, 77843, USA

    Alexandre Y. Yamamoto, Peng Li & H. Rusty Harris

  2. Department of Physics, San Diego State University, San Diego, CA, 92182, USA

    Kyle M. Sundqvist

Authors
  1. Alexandre Y. Yamamoto
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  2. Kyle M. Sundqvist
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  3. Peng Li
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  4. H. Rusty Harris
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Correspondence to H. Rusty Harris.

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Yamamoto, A.Y., Sundqvist, K.M., Li, P. et al. Simulation of a Multidimensional Input Quantum Perceptron. Quantum Inf Process 17, 128 (2018). https://doi.org/10.1007/s11128-018-1858-1

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