Skip to main content
SpringerLink
Log in

Quantum Adiabatic Evolution Algorithm for a Quantum Neural Network

  • Conference paper
  • First Online:
Book cover Artificial Neural Networks and Neural Information Processing — ICANN/ICONIP 2003 (ICANN 2003, ICONIP 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2714))

Abstract

In this paper, a new quantum algorithm for solving the combinatorial optimization problems is discussed. It is based on the quantum adiabatic evolution algorithm. We propose a new method for synthesizing a Hamiltonian inspired by a Hopfield network in order to improve calculation cost. The quantum system given by a new Hamiltonian has neuron-like interactions and shows quantum behavior. We present simulation results of the new algorithm for the 4-queen problem.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Shor, P.W.: Polynomial-time algorithm for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, (1997) 1484.

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  4. Farhi, E., Goldstone, J., Gutmann, S., Sipser, M.: Quantum computation by adiabatic evolution. quant-ph/0001106.

    Google Scholar 

  5. Farhi, E., Goldstone, J., Gutmann, S.: A numerical study of the performance of a quantum adiabatic evolution algorithm for satisfiability. quant-ph/0007071.

    Google Scholar 

  6. Farhi, E., Goldstone, J., Gutmann, S., Lapan, J., Lundgren, A., Preda, D.: A quantum adiabatic evolution algorithm applied to random instances of an NPcomplete problem. quant-ph/0104129.

    Google Scholar 

  7. Messiah, A.: Quantum Mechanics. Dover, New York, (1999) p. 739.

    Google Scholar 

  8. Kinjo, M., Sato, S., Nakajima, K.: Advantage and disadvantage of the quantum adiabatic evolution algorithm for combinatorial optimization problems. Abstracts of the 10th JST International Symposium (ISQC), Tokyo, Japan, March, (2002), P-2.

    Google Scholar 

  9. Tank, D.W., Hopfield, J.J.: Simple ‘neural’ optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit. IEEE Trans. Circuits Syst. 35, (1988) 1273.

    Article  Google Scholar 

  10. Loss, D., DiVincenzo, D.P.: Quantum computation with quantum dots. Phys. Rev. A, 57, (1997), 120–126.

    Article  Google Scholar 

  11. Kane, B.E.: A silicon-based nuclear spin quantum computer. Nature, 393, (1998) 133–137.

    Article  Google Scholar 

  12. Golub, G.H., van Loan, C.F.: Matrix Computations, 3rd Ed. Johns Hopkins University, Baltimore, MD, (1996) 572.

    MATH  Google Scholar 

  13. Tagliarini, G.A., Page, E.W.: Solving constraint satisfaction problems with neural networks. Proceedings of the IEEE International Conference on Neural Networks, 3, (1987) 741–747.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. PRESTO, Japan Science and Technology Co., Kawaguchi, 332-0012, Japan

    Mitsunaga Kinjo & Shigeo Sato

  2. Research Institute of Electrical Communication, Tohoku University, Sendai, 980-8577, Japan

    Shigeo Sato & Koji Nakajima

Authors
  1. Mitsunaga Kinjo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shigeo Sato
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Koji Nakajima
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Bogazici University, Bebek, 34342, Istanbul, Turkey

    Okyay Kaynak  & Ethem Alpaydin  & 

  2. Laboratory of Computer and Information Science, Helsinki University of Technology, P.O.B. 5400, 02015, Finland

    Erkki Oja

  3. Department of Computer Science and Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong

    Lei Xu

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kinjo, M., Sato, S., Nakajima, K. (2003). Quantum Adiabatic Evolution Algorithm for a Quantum Neural Network. In: Kaynak, O., Alpaydin, E., Oja, E., Xu, L. (eds) Artificial Neural Networks and Neural Information Processing — ICANN/ICONIP 2003. ICANN ICONIP 2003 2003. Lecture Notes in Computer Science, vol 2714. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44989-2_113

Download citation

  • DOI: https://doi.org/10.1007/3-540-44989-2_113

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40408-8

  • Online ISBN: 978-3-540-44989-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation