Abstract

In this paper a programming language, qGCL, is presented for the expression of quantum algorithms. It contains the features required to program a ‘universal’ quantum computer (including initialisation and observation), has a formal semantics and body of laws, and provides a refinement calculus supporting the verification and derivation of programs against their specifications. A representative selection of quantum algorithms are expressed in the language and one of them is derived from its specification.

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References

  1. 1.
  2. 2.
    Barenco, A., et al.: Elementary gates of quantum computation. Physical Review A 52(5), 3457–3467 (1995)CrossRefGoogle Scholar
  3. 3.
    Barenco, A.: A universal two-bit gate for quantum computation. Proc. R. Soc. Lond. A 449, 679–683 (1995)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Boyer, M., Brassard, G., Hoyer, P., Tapp, A.: Tight bounds on quantum searching. In: Toffoli, T., Biaford, M., Lean, J. (eds.) Fourth Workshop on Physics and Computation, New England Complex System Institute, pp. 36–43 (1996)Google Scholar
  5. 5.
    Butler, M., Hartel, P.: Reasoning about Grover’s quantum search algorithm using probabilistic wp. University of Southampton technical report DSSETR- 98-10 (1998)Google Scholar
  6. 6.
    Cleve, R., Ekert, A., Macchiavello, C., Mosca, M.: Quantum algorithms revisited. Proc. R. Soc. Lond., A. 454, 339–354 (1998)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Deutsch, D.: Quantum theory, the Church-Turing principle and the universal quantum computer. Proc. R. Soc. Lond. A 400, 97–117 (1985)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Deutsch, D.: Quantum computational networks. Proc. R. Soc. Lond. A 425, 73–90 (1989)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Deutsch, D., Barenco, A., Ekert, A.: Universality in quantum computation. Proc. R. Soc. Lond. A 449, 669–677 (1995)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Deutsch, D., Jozsa, R.: Rapid solution of problems by quantum computation. Proc. R. Soc. Lond. A 439, 553–558 (1992)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Dijkstra, E.W.: A Discipline of Programming. Prentice-Hall International, Englewood Cliffs (1976)MATHGoogle Scholar
  12. 12.
    Elitzur, A.C., Vaidman, L.: Quantum mechanical interaction-free measurements. Foundations of Physics 32(7), 987–997 (1993)CrossRefGoogle Scholar
  13. 13.
    Feynman, R.P.: The Feynman Lectures on Physics, vol. 3. Addison-Wesley, Reading (1964)Google Scholar
  14. 14.
    Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the 28th ACM STOC, pp. 212–219 (1996)Google Scholar
  15. 15.
    Gruska, J.: Quantum Computing. Advanced Topics in Computer Science. McGraw-Hill International, UK (1999)Google Scholar
  16. 16.
    Jifeng, H., Seidel, K., McIver, A.K.: Probabilistic models for the guarded command language. Science of Computer Programming 28, 171–192 (1997)MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Hoare He Jifeng, C.A.R.: The weakest prespecification. parts I and II. Fundamenta Informatica IX, 51–84 (1986)Google Scholar
  18. 18.
    Isham, C.J.: Lectures on Quantum Theory. Imperial College Press, London (1995)MATHGoogle Scholar
  19. 19.
    Josza, R.: Characterising classes of functions computable by quantum parallelism. Proc. R. Soc. Lond. A 435, 563–574 (1991)CrossRefGoogle Scholar
  20. 20.
    Morgan, C.: Programming from Specifications, 2nd edn. Prentice-Hall International, Englewood Cliffs (1994)MATHGoogle Scholar
  21. 21.
    Seidel, K., Morgan, C.C., McIver, A.K.: Probabilistic imperative programming: a rigorous approach (1996), Available at http://www.comlab.ox.ac.uk/oucl/research/areas/probs/bibliography.html
  22. 22.
    Morgan, C., McIver, A., Seidel, K.: Annabelle McIver and Karen Seidel. Probabilistic predicate transformers. TOPLAS 18(3), 325–353 (1996)Google Scholar
  23. 23.
    Morgan, C., McIver, A.: pGCL: formal reasoning for random algorithms. South African Computer Journal 22, 14–27 (1999)Google Scholar
  24. 24.
    Morgan, C., McIver, A.K.: Demonic, angelic and unbounded probabilistic choices in sequential programs. To appear in Acta Informatica; see the site at [23]Google Scholar
  25. 25.
    Mosca, M., Ekert, A.: The hidden subgroup problem and eigenvalue estimation on a quantum computer. In: Williams, C.P. (ed.) QCQC 1998. LNCS, vol. 1509, p. 174. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  26. 26.
  27. 27.
    Peres, A.: Quantum Theory: Concepts and Methods. Kluwer Academic Publishers, Dordrecht (1998)Google Scholar
  28. 28.
    Schumacher, B.: Quantum coding. Physical Review A 51(4), 2738–2747 (1995)CrossRefMathSciNetGoogle Scholar
  29. 29.
    Shor, P.W.: Algorithms for quantum computation: discrete log and factoring. In: Proceedings of the 35th IEEE FOCS, pp. 124–134 (1994)Google Scholar
  30. 30.
    Simon, D.R.: On the power of quantum computation. In: Proceedings of the 35th IEEE FOCS, pp. 116–123 (1994)Google Scholar
  31. 31.
    Williams, C.P., Clearwater, S.H.: Explorations in Quantum Computing. Springer, New York (1998)Google Scholar
  32. 32.
    Zuliani, P.: DPhil Thesis. Oxford University. (in preparation)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • J. W. Sanders
    • 1
  • P. Zuliani
    • 1
  1. 1.Programming Research GroupOxford University Computing LaboratoryOxfordEngland

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