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Genetic and Evolutionary Computation Conference

GECCO 2003: Genetic and Evolutionary Computation — GECCO 2003 pp 390–400Cite as

Evolving Hogg’s Quantum Algorithm Using Linear-Tree GP

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2723))

Abstract

Intermediate measurements in quantum circuits compare to conditional branchings in programming languages. Due to this, quantum circuits have a natural linear-tree structure. In this paper a Genetic Programming system based on linear-tree genome structures developed for the purpose of automatic quantum circuit design is introduced. It was applied to instances of the 1-SAT problem, resulting in evidently and “visibly” scalable quantum algorithms, which correspond to Hogg’s quantum algorithm.

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References

  1. H. Barnum, H. Bernstein, and L. Spector, Better-than-classical circuits for OR and AND/OR found using genetic programming, 1999, LANL e-preprint quantph/9907056.

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  3. D. Deutsch, Quantum theory, the Church-Turing principle and the universal quantum computer, Proc. R. Soc. London A, 400 (1985), pp. 97–117.

    Article  MATH  MathSciNet  Google Scholar 

  4. D. Deutsch and R. Jozsa, Rapid solution of problems by quantum computation, Proc. R. Soc. London A, 439 (1992), pp. 553–558.

    MATH  MathSciNet  Google Scholar 

  5. Y. Ge, L. Watson, and E. Collins, Genetic algorithms for optimization on a quantum computer, in Proceedings of the 1st International Conference on Unconventional Models of Computation (UMC), C. Calude, J. Casti, and M. Dinneen, eds., DMTCS, Auckland, New Zealand, Jan. 1998, Springer, Singapur, pp. 218–227.

    Google Scholar 

  6. L. Grover, A fast quantum mechanical algorithm for database search, in Proceedings of the 28th Annual ACM Symposium on Theory of Computing (STOC), ACM, ed., Philadelphia, Penn., USA, May 1996, ACM Press, New York, pp. 212–219, LANL e-preprint quant-ph/9605043.

    Google Scholar 

  7. J. Gruska, Quantum Computing, McGraw-Hill, London, 1999.

    Google Scholar 

  8. M. Hirvensalo, Quantum Computing, Natural Computing Series, Springer-Verlag, 2001.

    Google Scholar 

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

    Article  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  11. W. Kantschik and W. Banzhaf, Linear-tree GP and its comparison with other GP structures, in Proceedings of the 4th European Conference on Genetic Programming (EUROGP), J. Miller, M. Tomassini, P. Lanzi, C. Ryan, A. Tettamanzi, and W. Langdon, eds., vol. 2038 of LNCS, Lake Como, Italy, Apr. 2001, Springer, Berlin, pp. 302–312.

    Google Scholar 

  12. M. Nielsen and I. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, 2000.

    Google Scholar 

  13. X. Peng, X. Zhu, X. Fang, M. Feng, M. Liu, and K. Gao, Experimental implementation of Hogg’s algorithm on a three-quantum-bit NMR quantum computer, Phys. Rev. A, 65 (2002).

    Google Scholar 

  14. B. Rubinstein, Evolving quantum circuits using genetic programming, in Proceedings of the 2001 Congress on Evolutionary Computation, IEEE, ed., Seoul, Korea, May 2001, IEEE Computer Society Press, Silver Spring, MD, USA, pp. 114–151. The first version of this paper already appeared in 1999.

    Google Scholar 

  15. L. Spector, Quantum computation — a tutorial, in GECCO-99: Proceedings of the Genetic and Evolutionary Computation Conference, W. Banzhaf, J. Daida, A. Eiben, M. H. Garzon, V. Honavar, M. Jakiela, and R. Smith, eds., Orlando, Florida, USA, Jul. 1999, Morgan Kaufmann Publishers, San Francisco, pp. 170–197.

    Google Scholar 

  16. L. Spector, The evolution of arbitrary computational processes, IEEE Intelligent Systems, (2000), pp. 80–83.

    Google Scholar 

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

    Chapter  Google Scholar 

  18. L. Spector, H. Barnum, H. Bernstein, and N. Swamy, Quantum Computing Applications of Genetic Programming, in Advances in Genetic Programming, L. Spector, U.-M. O’Reilly, W. Langdon, and P. Angeline, eds., vol. 3, MIT Press, Cambridge, MA, USA, 1999, pp. 135–160.

    Google Scholar 

  19. A. Steane, Quantum computation, Reports on Progress in Physics, 61 (1998), pp. 117–173, LANL e-preprint quant-ph/9708022.

    MathSciNet  Google Scholar 

  20. A. Surkan and A. Khuskivadze, Evolution of quantum algorithms for computer of reversible operators, in Proceedings of the 2002 NASA/DoD Conference on Evolvable Hardware (EH), IEEE, ed., Alexandria, Virginia, USA, Jul. 2002, IEEE Computer Society Press, Silver Spring, MD, USA, pp. 186–187.

    Chapter  Google Scholar 

  21. C. Williams and A. Gray, Automated Design of Quantum Circuits, in Explorations in Quantum Computing, C. Williams and S. Clearwater, eds., Springer, New York, 1997, pp. 113–125.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, Chair of Systems Analysis, University of Dortmund, 44221, Dortmund, Germany

    André Leier & Wolfgang Banzhaf

Authors
  1. André Leier
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  2. Wolfgang Banzhaf
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Editor information

Editors and Affiliations

  1. Lawrence Livermore National Laboratory, Center for Applied Scientific Computing (CASC), 7000 East Avenue, L-561, Livermore, CA, 94550, USA

    Erick Cantú-Paz

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Leier, A., Banzhaf, W. (2003). Evolving Hogg’s Quantum Algorithm Using Linear-Tree GP. In: Cantú-Paz, E., et al. Genetic and Evolutionary Computation — GECCO 2003. GECCO 2003. Lecture Notes in Computer Science, vol 2723. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45105-6_48

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  • DOI: https://doi.org/10.1007/3-540-45105-6_48

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40602-0

  • Online ISBN: 978-3-540-45105-1

  • eBook Packages: Springer Book Archive

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