Advertisement

Quantum Computation

  • Adriano Barenco
  • Artur Ekert
  • G. Massimo Palma
  • Kalle-Antti Suominen
Conference paper

Abstract

Computers solve problems following a precise set of instructions that can be mechanically applied to yield the solution to any given instance of a particular problem. A specification of this set of instruction is called an algorithm. Examples of algorithms are the procedures taught in elementary schools for adding and multiplying whole numbers; when these procedures are mechanically applied, they always yield the correct result for any pair of whole numbers. However, any operation on numbers is performed by physical means and what can be clone to a number depends on the physical representation of this number and the underlying physics of computation. For example, when numbers are encoded in quantum states then quantum computers, i.e. physical devices whose unitary dynamics can be regarded as the performance of computation, can accept states which represent a coherent superposition of many different numbers (inputs) and evolve them into another superposition of numbers (outputs). In this case computation, i.e. a sequence of unitary transformations, affects simultaneously each element of the superposition allowing a massive parallel data, processing albeit, within one piece of quantum hardware. As the result quantum computers can efficiently solve sonic problems which are believed to be intractable on any classical computer [1, 2, 3, 4] (for an elementary introduction to quantum computation see [5]).

Keywords

Discrete Fourier Transform Logic Gate Coherent Superposition Quantum Logic Gate Quantum Factoring 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    D. Deutsch and R..lozsa, Proc. R. Soc. Lond. Ser. A -1:39.. 5. 53 (1992).Google Scholar
  2. [2]
    E. Bernstein and U. Vazirani. in Proc. 25th A(’ì11 Symposium on the Theory of Computation, p. 11 (1993).Google Scholar
  3. [3]
    D.S. Sinon, in Proceedings of the:35th Annual Symposium on lin’ Foundations of Computer Science, edited by S. Goldwasser (IEEE Computer Society Press. Los Alamitos, CA), p. 116 (1991).Google Scholar
  4. [4]
    P.W. Shor, in Proceedings of the 3.511i Anneal Symposium on the Foundations of Computer Science, edited by S. Goldwasser (IEEE Computer Society Press, Los Alamitos, CA), p. 12,1 (1991).Google Scholar
  5. [5]
    A.li. Ekert, in Proc. I1`1’ ICAP, edited by D. AVineland cf al., Atomic Physics 11, AIP Press (1995).Google Scholar
  6. [6]
    R. Rivest, A. Shamir, and L. Adleinan, `On Digital Signatures and Public-Key Cryptosysteius“, MiT Laboratory for Computer Science, Technical Report, MIT/LCS/TR-212 (. January 1979 ).Google Scholar
  7. [7]
    R.D. Silvernman, Math. (’onmp. -15,: 329 (1957).Google Scholar
  8. [8]
    A.K. Leustra,, 1–1.\V. Lenstra.Jr., M.S. D1anasse, and.1.1\1. Pollard, in Proc. 22nd ACM Symposium ou the Theory of Computing, p.:5(í I (1990).Google Scholar
  9. [9]
    D. Welsh, “(’odes and Cryptography”, Clarendon Press. Oxford (195$).Google Scholar
  10. [10]
    C.II. Papa.dimitrion, “Computational Complexity”, Addison-Wesley Publishing Company (1991).Google Scholar
  11. [11]
    A.K. Ekert and R. Jozsa. to appear in Rev-. Mod. Phys. (199.5).Google Scholar
  12. [12]
    D. Deutsch, Proc. R. Soc. Lond. Ser. A -125, 7: 3 (1959).Google Scholar
  13. [13]
    D.P. DiVincenzo, Phys. Rev. A 51, 1015 (1995).Google Scholar
  14. [14]
    A. Barenco, Proc. Roy. Soc. Loud. Ser. A 449, 679 (1995).CrossRefzbMATHGoogle Scholar
  15. [15]
    T. Sleator and H. Weiufurter, Phys. Rev. Lett. 74, 1087 (1995).CrossRefGoogle Scholar
  16. [16]
    D. Deutsch, A. Barenco, and A. Ekert, Proc. R.. Soc. Lond. Ser. A 4: 19, 669 (1995).MathSciNetCrossRefGoogle Scholar
  17. [17]
    S. Lloyd, “Almost any quantum logic gate is universal”, to appear in Phys. Rev. Lett. (1995).Google Scholar
  18. [18]
    A. Barenco, D. Deutsch, A. Ekert, and R. Jozsa, Phys. Rev. Lett. 719,: 1083 (1995).Google Scholar
  19. [19]
    V.B. Braginsky, Yu. I. Vorontsov, and F. Ya.. Ebalili, Zh. Eksp. Theo. Fiz. 73, 1310 [Sov. Phys. JETP 46, 705 (19 77)].Google Scholar
  20. [20]
    S.L. Braunstein, A. Mann, and \I. Revzen, Phys. Rev. Lett. 68.: 3259 (1992).Google Scholar
  21. [21]
    C.H. Bennett, G. Brassard, C. (’r(“Teau, 11..lozsa, A. Peres, and W. N. AVootters, Phys. Rev. Lett. 70, 1895 (1993).MathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    C.H. Bennett and 5..1. Wiesner, Puys. Rev. Lett. 69. 2881 (1992).CrossRefzbMATHGoogle Scholar
  23. [23]
    A. Barenco, C.H. Bennett, R. Cleve, D.P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, and 11. AVeinfurter. “Elementary gates for quantum computation”, to appear in Phys. Rev. A (1995).Google Scholar
  24. [24]
    D.E. Knuth, “The Art of’ Computer Programming, Volume 2: Seininumnerical Algorithms”, Addison-Wesley Publishing Company (1981).Google Scholar
  25. [25]
    D. Deutsch, unpublished (199–1).Google Scholar
  26. [26]
    R. Cleve, “A Note on Computing Fourier Transformation In Quantum Programs”, University of Calgary preprint (199–1).Google Scholar
  27. [27]
    W.H. Zurek, Physics Today, October, p. 36 (1991).Google Scholar
  28. [28]
    W. Unruh, Phys. Rev. A 51, 992 (1995).Google Scholar
  29. [29]
    G.M. Palma, N.-A. Suominen, A. Ekert. “Quantum Computers and Dissipation”, to appear in Proc. R. Soc. Loud. Ser. A (1995).Google Scholar
  30. [30]
    Q.A. Turchette. (’..1. Hooch A\’. Lange, H. iMabnchi. and 11.. 1. Nimble. “Measurement of conditional phase shift l’or quant inn logic”, siilunitted to Phys. Rev. Lett. (1995).Google Scholar
  31. [31]
    M. Brune et al., Phys. Rev. Lett. 72, 33: 39 (1991).Google Scholar
  32. [32]
    J.I. Cirac and P. Zoller, Phys. Rev. Lett. 71, -1091 (1995).Google Scholar
  33. [33]
    D. Deutsch, “The Fabric of Reality” Viking-Penguin Publishers, to appeau (1996).Google Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Adriano Barenco
    • 1
  • Artur Ekert
    • 1
  • G. Massimo Palma
    • 1
  • Kalle-Antti Suominen
    • 1
  1. 1.Clarendon LaboratoryUniversity of OxfordOxfordUK

Personalised recommendations