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Introduction to Quantum Computation

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Fundamentals of Quantum Information

Part of the book series: Lecture Notes in Physics ((LNP,volume 587))

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Abstract

A computation is a physical process. It may be performed by a piece of electronics or on an abacus, or in your brain, but it is a process that takes place in nature and as such it is subject to the laws of physics. Quantum computers are machines that rely on characteristically quantum phenomena, such as quantum interference and quantum entanglement in order to perform computation. In this series of lectures I want to elaborate on the computational power of such machines.

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References

  1. The term was coined by B. Schumacher. See, for example, Phys. Rev. A 51 2738 (1995).

    ADS  MathSciNet  Google Scholar 

  2. D. Deutsch, Proc. R. Soc. Lond. A 425 73 (1989).

    ADS  MathSciNet  Google Scholar 

  3. W. K. Wootters and W. H. Zurek, Nature 299 802 (1982).

    Article  ADS  Google Scholar 

  4. A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. W. Shor, T. Sleator, J. Smolin and H. Weinfurter, Phys. Rev. A 52 3457 (1995).

    ADS  Google Scholar 

  5. D. Deutsch, A. Barenco and A. Ekert, Proc. R. Soc. Lond. A 449 669 (1995).

    ADS  MathSciNet  Google Scholar 

  6. A. Barenco, D. Deutsch, A. Ekert and R. Jozsa, Phys. Rev. Lett. 74 4083 (1995).

    Article  ADS  Google Scholar 

  7. D. P. DiVincenzo, Phys. Rev. A 51 1015 (1995).

    ADS  Google Scholar 

  8. S. Lloyd, Phys. Rev. Lett. 75 346 (1995).

    Article  ADS  Google Scholar 

  9. G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers (Oxford University Press, Oxford, 1979).

    MATH  Google Scholar 

  10. T. Toffoli, Mathematical Systems Theory 14 13 (1981).

    Article  MATH  MathSciNet  Google Scholar 

  11. C. H. Papadimitriou, Computational Complexity (Addison-Wesley, 1994).

    Google Scholar 

  12. D. Coppersmith, IBMR esearch report (1994).

    Google Scholar 

  13. R. Solovay and V. Strassen, SIAMJ. Comp. 6 84 (1977).

    Article  MATH  MathSciNet  Google Scholar 

  14. R. Motwani and P. Raghavan, Randomised Algorithms (Cambridge University Press, 1995).

    Google Scholar 

  15. P. W. Shor, “Algorithms for quantum computation: Discrete logarithms and factoring” Proc. 35th Annual Symposium on the Foundations of Computer Science, p. 124 edited by S. Goldwasser (IEEE Computer Society Press, Los Alamitos, CA 1994). Expanded version of this paper is available at LANL quant-ph archive.

    Google Scholar 

  16. R. P. Feynman, Int. J. of Theor. Phys. 21 467 (1982).

    Article  MathSciNet  Google Scholar 

  17. R. Cleve, A. Ekert, C. Macchiavello and M. Mosca, Proc. R. Soc. Lond. A 454 339 (1998).

    ADS  MathSciNet  Google Scholar 

  18. D. Deutsch, Proc. R. Soc. Lond. A 400 97 (1985).

    ADS  MathSciNet  Google Scholar 

  19. L. K. Grover, “A fast quantum mechanical algorithm for database search”, Proc. 28th Annual ACM Symposium on the Theory of Computing (STOC’96), p. 212 (ACM, Philadelphia, Pennsylvania, 1996).

    Google Scholar 

  20. M. Boyer, G. Brassard, P. Hoyer, A. Tapp, Proc. of the Workshop on Physics and Computation (PhysComp96) 36 (1996).

    Google Scholar 

  21. T. Hogg, Physica D120 102 (1998).

    ADS  Google Scholar 

  22. C. Zalka, Physical Review A60 2746 (1999).

    ADS  Google Scholar 

  23. A. Y. Kitaev, LANL quant-ph archive, quant-ph/9511026 (1995).

    Google Scholar 

  24. V. Vedral, A. Barenco and A. Ekert, Phys. Rev. A 54 147 (1996).

    ADS  MathSciNet  Google Scholar 

  25. D. Beckman, A. Chari, S. Devabhaktuni and J. Preskill, Phys. Rev. A 54 1034 (1996).

    ADS  MathSciNet  Google Scholar 

  26. A. Ekert and R. Jozsa, Rev. Mod. Phys. 68 733 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  27. D. Kahn, The Codebreakers: The Story of Secret Writing, (Macmillan, New York, 1967).

    Google Scholar 

  28. D. Stinson, Cryptography: Theory and Practice (CRC Press, 1995).

    Google Scholar 

  29. G. S. Vernam, J. AIEE 45 109 (1926).

    Google Scholar 

  30. C. E. Shannon, Bell Syst. Tech. J. 28 657 (1949).

    Google Scholar 

  31. W. Diffe and M. E. Hellman, IEEE Transactions on Information Theory 22 644 (1976).

    Article  Google Scholar 

  32. R. L. Rivest, A. Shamir and L. M. Adleman, Communication of the ACM 21 120 (1978).

    Article  MATH  MathSciNet  Google Scholar 

  33. J. H. Ellis, Tech. report Communications-Electronics Security Group, United Kingdom (1970).

    Google Scholar 

  34. C. Cocks, Tech. report Communications-Electronics Security Group, United Kingdom (1973).

    Google Scholar 

  35. C. H. Bennett and G. Brassard, Proc. IEEE Int. Conference on Computers, Systems and Signal Processing (IEEE, New York, 1984).

    Google Scholar 

  36. C. H. Bennett, Phys. Rev. Lett. 68 3121 (1992).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  37. A. Ekert, Phys. Rev. Lett. 67, 661 (1991).

    Article  MATH  ADS  MathSciNet  Google Scholar 

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Authors
  1. Artur Ekert
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Editors and Affiliations

  1. Department of Physics, University of Stellenbosch, 7602, Matieland, South Africa

    Dieter Heiss

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© 2002 Springer-Verlag Berlin Heidelberg

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Ekert, A. (2002). Introduction to Quantum Computation. In: Heiss, D. (eds) Fundamentals of Quantum Information. Lecture Notes in Physics, vol 587. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45933-2_3

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  • DOI: https://doi.org/10.1007/3-540-45933-2_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43367-5

  • Online ISBN: 978-3-540-45933-0

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