International Journal of Theoretical Physics

, Volume 51, Issue 3, pp 705–723 | Cite as

Quantum Associative Neural Network with Nonlinear Search Algorithm

  • Rigui Zhou
  • Huian Wang
  • Qian Wu
  • Yang Shi


Based on analysis on properties of quantum linear superposition, to overcome the complexity of existing quantum associative memory which was proposed by Ventura, a new storage method for multiply patterns is proposed in this paper by constructing the quantum array with the binary decision diagrams. Also, the adoption of the nonlinear search algorithm increases the pattern recalling speed of this model which has multiply patterns to \(O( {\log_{2}}^{2^{n -t}} ) = O( n - t )\) time complexity, where n is the number of quantum bit and t is the quantum information of the t quantum bit. Results of case analysis show that the associative neural network model proposed in this paper based on quantum learning is much better and optimized than other researchers’ counterparts both in terms of avoiding the additional qubits or extraordinary initial operators, storing pattern and improving the recalling speed.


Quantum neural network Associative memory Binary decision diagrams Quantum nonlinear algorithm Quantum learning 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Kak, S.C.: On quantum neural computing. Inf. Sci. 83(3–4), 143–160 (1995) CrossRefGoogle Scholar
  2. 2.
    Ventura, D., Martinez, T.R.: Quantum associative memory. Inf. Sci. 124(1–4), 273–296 (2000) MathSciNetCrossRefGoogle Scholar
  3. 3.
    Ezhov, A.A., Nifanova, A.V., Ventura, D.: Quantum associative memory with distributed queries. Inf. Sci. 128(3–4), 271–293 (2000) MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Loo, C.K., Perus, M., Bischof, H.: Associative memory based image and object recognition by quantum holography. Open Syst. Inf. Dyn. 11(5), 277–289 (2004) MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Rigatos, G.G., Tzafestas, S.G.: Quantum learning for associative memories. Fuzzy Syst. 157(13), 1797–1813 (2006) MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Li, P.C., Li, S.Y.: Learning algorithm and application of quantum BP neural networks based on universal quantum gates. J. Syst. Eng. Electron. 19(1), 167–174 (2008) MATHGoogle Scholar
  7. 7.
    Panella, M., Martinelli, G.: Neural networks with quantum architecture and quantum learning. Int. J. Circuit Theory Appl. 39(1), 61–77 (2009) CrossRefGoogle Scholar
  8. 8.
    Panella, M., Martinelli, G.: Neurofuzzy networks with nonlinear quantum learning. IEEE Trans. Fuzzy Syst. 17(3), 698–710 (2009) CrossRefGoogle Scholar
  9. 9.
    Zhou, R., Ding, Q.: Quantum pattern recognition with probability of 100%. Int. J. Theor. Phys. 47(5), 1278–1285 (2008) MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Zhou, R., Jiang, N., Ding, Q.: Model and training of QNN with weight. Neural Process. Lett. 24(3), 261–269 (2006) CrossRefGoogle Scholar
  11. 11.
    Zhou, R., Ding, Q.: Quantum M-P neural network. Int. J. Theor. Phys. 46(12), 3209–3215 (2007) MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Zhou, R.: Quantum competitive neural network. Int. J. Theor. Phys. 49(1), 110–119 (2010) MATHCrossRefGoogle Scholar
  13. 13.
    Abrams, D., Lloyd, S.: Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and #P problems. Phys. Rev. Lett. 81(18), 3992–3995 (1998) ADSCrossRefGoogle Scholar
  14. 14.
    Czachor, M.: Notes on nonlinear quantum algorithms. arXiv:quant-ph/9802051v2, 23 February (1998)
  15. 15.
    Czachor, M.: Local modification of the Abrams–Lloyd nonlinear algorithm. arXiv:quant-ph/9803019v1, 9 March (1998)
  16. 16.
    Rosenbaum, D.: Binary superposed quantum decision diagrams. Quantum Inf. Process. 9(4), 463–496 (2010) MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Nielsen, M., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000) MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.College of Information EngineeringEast China JiaoTong UniversityNanchangPR China
  2. 2.Key Laboratory of Intelligent Computing & Information Processing of Ministry of EducationXiangtan UniversityXiangtanChina

Personalised recommendations