Skip to main content

Comparison of Selection Strategies for Evolutionary Quantum Circuit Design

  • Conference paper
Genetic and Evolutionary Computation – GECCO 2004 (GECCO 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3103))

Included in the following conference series:

Abstract

Evolution of quantum circuits faces two major challenges: complex and huge search spaces and the high costs of simulating quantum circuits on conventional computers. In this paper we analyze different selection strategies, which are applied to the Deutsch-Jozsa problem and the 1-SAT problem using our GP system. Furthermore, we show the effects of adding randomness to the selection mechanism of a (1,10) selection strategy. It can be demonstrated that this boosts the evolution of quantum algorithms on particular problems.

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

Access this chapter

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.: Algorithms for quantum computation: discrete logarithm and factoring. In: IEEE (ed.) Proceedings of the 35th Annual IEEE Symp. on Foundations of Computer Science (FOCS), Silver Spring, MD, USA, pp. 124–134. IEEE Computer Society Press, Los Alamitos (1994)

    Chapter  Google Scholar 

  2. Grover, L.: A fast quantum mechanical algorithm for database search. In: ACM (ed.) Proceedings of the 28th Annual ACM Symposium on Theory of Computing (STOC), pp. 212–219. ACM Press, New York (1996)

    Google Scholar 

  3. Hogg, T.: Solving highly constrained search problems with quantum computers. J. Artificial Intelligence Res. 10, 39–66 (1999)

    MATH  MathSciNet  Google Scholar 

  4. van Dam, W., Hallgren, S.: Efficient quantum algorithms for shifted quadratic character problems (2000)

    Google Scholar 

  5. Hallgren, S.: Polynomial-time quantum algorithms for pell’s equation and the principal ideal problem. In: ACM (ed.) Proceedings of the 34rd Annual ACM Symposium on Theory of Computing (STOC), ACM Press, New York (2002)

    Google Scholar 

  6. van Dam, W., Seroussi, G.: Efficient quantum algorithms for estimating Gauss sums (2002)

    Google Scholar 

  7. Williams, C., Gray, A.: Automated Design of Quantum Circuits, pp. 113–125. Springer, New York (1997)

    Google Scholar 

  8. Spector, L., Barnum, H., Bernstein, H., Swamy, N.: Quantum Computing Applications of Genetic Programming, vol. 3, pp. 135–160. MIT Press, Cambridge (1999)

    Google Scholar 

  9. Spector, L., Barnum, H., Bernstein, H., Swamy, N.: Finding a better-thanclassical quantum AND/OR algorithm using genetic programming. In: Angeline, P., Michalewicz, Z., Schoenauer, M., Yao, X., Zalzala, A. (eds.) Proceedings of the 1999 Congress on Evolutionary Computation, Silver Spring, MD, USA, pp. 2239–2246. IEEE Computer Society Press, Los Alamitos (1999)

    Google Scholar 

  10. Barnum, H., Bernstein, H., Spector, L.: Better-than-classical circuits for OR and AND/OR found using genetic programming (1999)

    Google Scholar 

  11. Barnum, H., Bernstein, H., Spector, L.: Quantum circuits for OR and AND of ORs. J. Phys. A: Math. Gen. 33, 8047–8057 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  12. Leier, A., Banzhaf, W.: Evolving hogg’s quantum algorithm using linear-tree gp. In: Cantú-Paz, E., Foster, J.A., Deb, K., Davis, L., Roy, R., O’Reilly, U.-M., Beyer, H.-G., Kendall, G., Wilson, S.W., Harman, M., Wegener, J., Dasgupta, D., Potter, M.A., Schultz, A., Dowsland, K.A., Jonoska, N., Miller, J., Standish, R.K. (eds.) GECCO 2003. LNCS, vol. 2723, pp. 390–400. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  13. Leier, A., Banzhaf, W.: Exploring the search space of quantum programs. In: Sarker, R., Reynolds, R., Abbass, H., Tan, K., McKay, B., Essam, D., Gedeon, T. (eds.) Proceedings of the 2003 Congress on Evolutionary Computation, Piscataway, NJ, USA, vol. I, pp. 170–177. IEEE Computer Society Press, Los Alamitos (2003)

    Chapter  Google Scholar 

  14. Gruska, J.: Quantum Computing. McGraw-Hill, London (1999)

    Google Scholar 

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

    MATH  Google Scholar 

  16. Hirvensalo, M.: Quantum Computing. Natural Computing Series. Springer, Berlin (2001)

    MATH  Google Scholar 

  17. Wagner, G., Stadler, P.: Complex adaptations and the structure of recombination spaces. Technical Report 97-03-029, Santa Fe Institute (1998)

    Google Scholar 

  18. Schwefel, H.P.: Evolution and Optimum Seeking. Sixth-Generation Computer Technology Series. John-Wiley & Sons, New York, USA (1995)

    Google Scholar 

  19. Rechenberg, I.: Evolutionsstrategie 1993. Frommann Verlag, Stuttgart, Germany (1994)

    Google Scholar 

  20. Rudolph, G.: An evolutionary algorithm for integer programming. In: Davidor, Y., Männer, R., Schwefel, H.-P. (eds.) PPSN 1994. LNCS, vol. 866, pp. 139–148. Springer, Heidelberg (1994)

    Google Scholar 

  21. Cleve, R., Ekert, A., Macchiavello, C., Mosca, M.: Quantum algorithms revisited. Proc. R. Soc. London A 454, 339–354 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  22. Hogg, T.: Highly structured searches with quantum computers. Phys. Rev. Lett. 80, 2473–2476 (1998)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Leier, A., Banzhaf, W. (2004). Comparison of Selection Strategies for Evolutionary Quantum Circuit Design. In: Deb, K. (eds) Genetic and Evolutionary Computation – GECCO 2004. GECCO 2004. Lecture Notes in Computer Science, vol 3103. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24855-2_65

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-24855-2_65

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22343-6

  • Online ISBN: 978-3-540-24855-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics