Skip to main content

A quantum-implementable neural network model

Abstract

A quantum-implementable neural network, namely quantum probability neural network (QPNN) model, is proposed in this paper. QPNN can use quantum parallelism to trace all possible network states to improve the result. Due to its unique quantum nature, this model is robust to several quantum noises under certain conditions, which can be efficiently implemented by the qubus quantum computer. Another advantage is that QPNN can be used as memory to retrieve the most relevant data and even to generate new data. The MATLAB experimental results of Iris data classification and MNIST handwriting recognition show that much less neuron resources are required in QPNN to obtain a good result than the classical feedforward neural network. The proposed QPNN model indicates that quantum effects are useful for real-life classification tasks.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

References

  1. 1.

    Nielsen, M., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  2. 2.

    Shor, P.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997)

    MathSciNet  Article  MATH  Google Scholar 

  3. 3.

    Childs, A.M., Landahl, A.J., Parrilo, P.A.: Quantum algorithms for the ordered search problem via semidefinite programming. Phys. Rev. A 75, 032335 (2007)

    ADS  Article  Google Scholar 

  4. 4.

    Farhi, E., Goldstone, J., Gutmann, S., Lapan, J., Lundgren, A., Preda, D.: A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem. Science 292, 472 (2001)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  5. 5.

    Murphy, K.P.: Machine Learning: A Probabilistic Perspective. MIT Press, Cambridge (2012)

    MATH  Google Scholar 

  6. 6.

    Cristina Diamantini, M., Trugenberger, C.A.: High-capacity quantum associative memories (2015). arXiv:1506.01231v1

  7. 7.

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

    ADS  Article  MATH  Google Scholar 

  8. 8.

    Wiebe, N., Kapoor, A., Svore, K.: Quantum deep learning. arXiv preprint arXiv:1412.3489 (2014)

  9. 9.

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

    ADS  Article  Google Scholar 

  10. 10.

    Lloyd, S., Mohseni, M., Rebentrost, P.: Quantum algorithms for supervised and unsupervised machine learning (2013). arXiv:1307.0411

  11. 11.

    Menneer, T., Narayanan, A.: Quantum artificial neural networks vs classical artificial neural networks: experiments in simulation. In: Proceedings of the IEEE Fourth International Conference on Computational Intelligence and Neuroscience, pp. 757–759 (2000)

  12. 12.

    Ventura, D., Martinez, T.: Quantum associative memory. Inf. Sci. 124(1–4), 273–296 (2000)

    MathSciNet  Article  Google Scholar 

  13. 13.

    Pagiamtis, K., Sheikholeslami, A.: Content-addressable memory (CAM) circuits and architectures: a tutorial and survey. IEEE J. Solid State Circuits 41(3), 712–727 (2006)

    Article  Google Scholar 

  14. 14.

    Behrman, E.C., Nash, L.R., Steck, J.E., Chandrashekar, A.A., Skinner, S.R.: Simulations of quantum neural networks. Inf. Sci. 128(3), 257–269 (2000)

    MathSciNet  Article  MATH  Google Scholar 

  15. 15.

    Panella, M., Martinelli, G.: Neural networks with quantum architecture and quantum learning. Int. J. Circuit Theory Appl. 39, 61–77 (2011)

    Article  MATH  Google Scholar 

  16. 16.

    Schuld, M., Sinayskiy, I., Petruccione, F.: The quest for A quantum neural network. Quantum Inf. Process. 13(11), 2567–2586 (2014)

    MathSciNet  Article  MATH  Google Scholar 

  17. 17.

    Sahni, V., Patvardhan, C.: Iris data classification using quantum neural networks. In: AIP Conference Proceedings, vol. 864, p. 219 (2006)

  18. 18.

    Fei, L., Baoyu Z.: A study of quantum neural networks. In: IEEE International Conference on Neural Networks and Signal Processing, December (2003)

  19. 19.

    Weinberg, S.: Precision tests of quantum mechanics. Phys. Rev. Lett. 62, 485–488 (1989)

    ADS  Article  Google Scholar 

  20. 20.

    Silva, A.J.D., Ludermir, T.B., Oliveira, W.R.D.: Quantum perceptron over a field and neural network architecture selection in a quantum computer. Neural Netw. 76, 55–64 (2016)

    Article  Google Scholar 

  21. 21.

    Schuld, M., Sinayskiy, I., Petruccione, F.: Simulating a perceptron on a quantum computer (2014). arXiv:1412.3635

  22. 22.

    Iris flower data set. https://en.wikipedia.org/wiki/Iris_flower_data_set

  23. 23.

    THE MNIST DATABASE of handwritten digits website. http://yann.lecun.com/exdb/mnist/

  24. 24.

    Chen, J., Wang, L., Charbon, E., Wang, B.: A programmable architecture for quantum computing. Phys. Rev. A 88, 022311 (2013)

    ADS  Article  Google Scholar 

  25. 25.

    Brown, K.L., Thesis, P.D.: Using the Qubus for Quantum Computing. University of Leeds, Leeds (2011)

    Google Scholar 

  26. 26.

    https://en.wikipedia.org/wiki/Einstein_notation

  27. 27.

    Jesse, A.: Garman: A Heuristic Review of Quantum Neural Networks, master paper of Imperial College London (2011)

  28. 28.

    Brassard, G., Hoyer, P., Mosca, M., Tapp, A.: Quantum amplitude amplification and estimation (2000). arXiv:quantum-ph/0005055

  29. 29.

    Spiller, T.P., Nemoto, K., Braunstein, S.L., Munro, W.J., van Loock, P., Milburn, G.J.: Quantum computation by communication. New J. Phys. 8, 30 (2006)

    ADS  Article  Google Scholar 

  30. 30.

    Raussendorf, R., Briegel, H.J.: A one-way quantum computer. Phys. Rev. Lett. 86, 5188 (2001)

    ADS  Article  Google Scholar 

  31. 31.

    Raussendorf, R., Browne, D.E., Briegel, H.J.: Measurement-based quantum computation with cluster states. Phys. Rev. A 68, 022312 (2003)

    ADS  Article  Google Scholar 

  32. 32.

    Shende, V.V., Bullock, S.S., Markov, I.L.: Synthesis of quantum logic circuits. In: IEEE Transaction on CAD, vol. 25, no. 6 (2006)

  33. 33.

    Shwartz, S.S., David, S.B.: Understanding Machine Learning. Cambridge University Press, Cambridge (2014)

    Book  MATH  Google Scholar 

  34. 34.

    Deng, L.: The MNIST database of handwritten digit images for machine learning research. IEEE Signal Process. Mag. 29, 141 (2012)

    ADS  Article  Google Scholar 

  35. 35.

    Srivastava, N., Hinton, G., Krizhevsky, A., Sutskever, I., Salakhutdinov, R.: Dropout: a simple way to prevent neural networks from overfitting. http://jmlr.org/papers/v15/srivastava14a.html, http://www.cs.toronto.edu/~hinton/absps/dropout.pdf

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Lingli Wang.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Chen, J., Wang, L. & Charbon, E. A quantum-implementable neural network model. Quantum Inf Process 16, 245 (2017). https://doi.org/10.1007/s11128-017-1692-x

Download citation

Keywords

  • Feedforward neural network
  • Quantum probability neural network
  • Quantum neuron
  • Iris and MNIST experiments