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Neurocomputing approach to matrix product state using quantum dynamics

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Abstract

During the last three decades, quantum neural computation has received a relatively high amount of attention among researchers and academic communities since the model of quantum neural network has been proposed. Matrix product state is the well-designed class of tensor network states, which plays an important role in processing of quantum information. The area of dynamical systems help us to study the temporal behavior of systems in time. In our previous work, we have shown the relationship between quantum finite state machine and matrix product state. In this paper, we have used the proposed unitary criteria to investigate the dynamics of matrix product state with quantum weightless neural networks, where the output qubit is extracted and fed back (iterated) to input. Further, we have used Von Neumann entropy to measure possible entanglement of output quantum state. Finally, we have plotted the dynamics for each matrix product state against iterations and analyzed their results.

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References

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

    Article  MathSciNet  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, pp. 124–134. IEEE (1994)

  3. Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, pp. 212–219. ACM (1996)

  4. Kwiat, P., Mitchell, J., Schwindt, P., White, A.: Grover’s search algorithm: an optical approach. J. Mod. Opt. 47(2–3), 257–266 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  5. Orús, R.: A practical introduction to tensor networks: matrix product states and projected entangled pair states. Ann. Phys. 349, 117–158 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  6. White, S.R.: Density-matrix algorithms for quantum renormalization groups. Phys. Rev. B 48(14), 10345 (1993)

    Article  ADS  Google Scholar 

  7. Aleksander, I.: Self-adaptive universal logic circuits. Electron. Lett. 2(8), 321–322 (1966)

    Article  Google Scholar 

  8. Kak, S.C.: Quantum neural computing. In: Advances in Imaging and Electron Physics, vol. 94, , pp. 259–313. Elsevier (1995)

    Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  10. Dong, D., Petersen, I.R.: Quantum control theory and applications: a survey. IET Control Theory Appl. 4(12), 2651–2671 (2010)

    Article  MathSciNet  Google Scholar 

  11. de Oliveira, W.R., Silva, A.J., Ludermir, T.B., Leonel, A., Galindo, W.R., Pereira, J.C.: Quantum logical neural networks. In: 10th Brazilian Symposium on Neural Networks, SBRN’08, pp. 147–152. IEEE (2008)

  12. Silva, A., de Oliveira, W., Ludermir, T.: A weightless neural node based on a probabilistic quantum memory. In: 2010 Eleventh Brazilian Symposium on Neural Networks (SBRN), pp. 259–264. IEEE (2010)

  13. Da Silva, A.J., De Oliveira, W.R., Ludermir, T.B.: Classical and superposed learning for quantum weightless neural networks. Neurocomputing 75(1), 52–60 (2012)

    Article  Google Scholar 

  14. Panella, M., Martinelli, G.: Neural networks with quantum architecture and quantum learning. Int. J. Circuit Theory Appl. 39(1), 61–77 (2011)

    Article  Google Scholar 

  15. de Paula Neto, F.M., de Oliveira, W.R., da Silva, A.J., Ludermir, T.B.: Chaos in quantum weightless neuron node dynamics. Neurocomputing 183, 23–38 (2016)

    Article  Google Scholar 

  16. de Paula Neto, F.M., Ludermir, T.B., de Oliveira, W.R., da Silva, A.J.: Fitting parameters on quantum weightless neuron dynamics. In: 2015 Brazilian Conference on Intelligent Systems (BRACIS), pp. 169–174. IEEE (2015)

  17. de Paula Neto, F.M., de Oliveira, W.R., da Silva, A.J., Ludermir, T.B.: On the entanglement dynamics of the quantum weightless neuron. In: 2017 Brazilian Conference on Intelligent Systems (BRACIS), pp. 175–180. IEEE (2017)

  18. Wang, J.: Handbook of Finite State Based Models and Applications. CRC Press, Cambridge (2012)

    Book  Google Scholar 

  19. Nielsen, M., Chuang, I.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge (2010)

    Book  Google Scholar 

  20. Greenberger, D.M.: GHZ (Greenberger–Horne–Zeilinger) theorem and GHZ states. In: Compendium of Quantum Physics, , pp. 258–263. Springer (2009)

  21. Affleck, I., Kennedy, T., Lieb, E.H., Tasaki, H.: Rigorous results on valence-bond ground states in antiferromagnets. Phys. Rev. Lett. 59(7), 799 (1987)

    Article  ADS  Google Scholar 

  22. Raussendorf, R.: Measurement-based quantum computation with cluster states. Int. J. Quantum Inf. 7(06), 1053–1203 (2009)

    Article  Google Scholar 

  23. Matrix Product Formalism. http://www2.mpq.mpg.de/Theorygroup/CIRAC/wiki/images/9/9f/Eckholt_Diplom.pdf/. Accessed 15 March 2018

  24. Bhatia, A.S., Kumar, A.: Quantifying matrix product state. Quantum Inf. Process. 17(3), 41 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  25. Dzelme-Bērziņa, I.: Galīgie kvantu automāti un log̀ika

  26. Petz, D.: Entropy, Von Neumann and the Von Neumann entropy. In: John Von Neumann and the Foundations of Quantum Physics, pp. 83–96. Springer (2001)

  27. Biamonte, J.D., Clark, S.R., Jaksch, D.: Categorical tensor network states. AIP Adv. 1(4), 042172 (2011)

    Article  ADS  Google Scholar 

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Acknowledgements

Amandeep Singh Bhatia was supported by Maulana Azad National Fellowship (MANF), funded by Ministry of Minority Affairs, Government of India.

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  1. Department of Computer Science, Thapar Institute of Engineering & Technology, Patiala, India

    Amandeep Singh Bhatia & Ajay Kumar

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  1. Amandeep Singh Bhatia
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  2. Ajay Kumar
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Correspondence to Amandeep Singh Bhatia.

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Bhatia, A.S., Kumar, A. Neurocomputing approach to matrix product state using quantum dynamics. Quantum Inf Process 17, 278 (2018). https://doi.org/10.1007/s11128-018-2053-0

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