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Evolving Hogg’s Quantum Algorithm Using Linear-Tree GP

  • André Leier
  • Wolfgang Banzhaf
Conference paper
Part of the Lecture Notes in Computer Science book series (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.

Keywords

Quantum Algorithm Quantum Circuit Quantum Gate Intermediate Measurement Genetic Program System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [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. [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.zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    D. Deutsch, Quantum theory, the Church-Turing principle and the universal quantum computer, Proc. R. Soc. London A, 400 (1985), pp. 97–117.zbMATHMathSciNetCrossRefGoogle Scholar
  4. [4]
    D. Deutsch and R. Jozsa, Rapid solution of problems by quantum computation, Proc. R. Soc. London A, 439 (1992), pp. 553–558.zbMATHMathSciNetGoogle Scholar
  5. [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. [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. [7]
    J. Gruska, Quantum Computing, McGraw-Hill, London, 1999.Google Scholar
  8. [8]
    M. Hirvensalo, Quantum Computing, Natural Computing Series, Springer-Verlag, 2001.Google Scholar
  9. [9]
    T. Hogg, Highly structured searches with quantum computers, Phys. Rev. Lett., 80 (1998), pp. 2473–2476.CrossRefGoogle Scholar
  10. [10]
    T. Hogg, Solving highly constrained search problems with quantum computers, J. Artificial Intelligence Res., 10 (1999), pp. 39–66.zbMATHMathSciNetGoogle Scholar
  11. [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. [12]
    M. Nielsen and I. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, 2000.Google Scholar
  13. [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. [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. [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. [16]
    L. Spector, The evolution of arbitrary computational processes, IEEE Intelligent Systems, (2000), pp. 80–83.Google Scholar
  17. [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.CrossRefGoogle Scholar
  18. [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. [19]
    A. Steane, Quantum computation, Reports on Progress in Physics, 61 (1998), pp. 117–173, LANL e-preprint quant-ph/9708022.MathSciNetGoogle Scholar
  20. [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.CrossRefGoogle Scholar
  21. [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

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • André Leier
    • 1
  • Wolfgang Banzhaf
    • 1
  1. 1.Dept. of Computer Science, Chair of Systems AnalysisUniversity of DortmundDortmundGermany

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