Advertisement

Unusual Solutions of Usual Problems

  • Rajendra K. BeraEmail author
Chapter
  • 82 Downloads
Part of the Undergraduate Lecture Notes in Physics book series (ULNP)

Abstract

This chapter describes how certain problems that may be computationally solved on a Universal Turing Machine have a superior algorithmic solution in quantum computing. As examples, inter alia, we describe the Deutsch, the Deutsch–Jozsa, the Elitzur–Vaidman, and a few other algorithms. These problems and their related solution algorithms are easy to understand. They are also a convenient way of introducing certain frequently used computational steps in developing quantum algorithms, e.g., computing a function in parallel for multiple values of its argument.

References

  1. 1.
    H.C. von Baeyer, Tangled tales. The Sciences, Spring 2001, pp. 14–17Google Scholar
  2. 2.
    K. Bartkiewicz et al., Experimental quantum forgery of quantum optical money. arXiv:1604.04453v2 [quant-ph], 2 Mar 2017. https://arxiv.org/pdf/1604.04453.pdf
  3. 3.
    G. Brassard, Brief history of quantum cryptography: a personal perspective. arXiv:quant-ph/0604072v1, 11 Apr 2006. https://arxiv.org/pdf/quant-ph/0604072.pdf
  4. 4.
    R. Cleve, A. Ekert, C. Macchiavllo, M. Mosca, Quantum algorithms revisited. Proc. R. Soc. Lond. A 454, 339–354 (1998). See preprint at: arXiv:quant-ph/9708016, v1 8 Aug 1997, http://arxiv.org/PS_cache/quant-ph/pdf/9708/9708016v1.pdf
  5. 5.
    D. Deutsch, Quantum theory, the Church-Turing principle and the universal quantum computer. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 400(1818), 97–117 (1985). http://www.ceid.upatras.gr/tech_news/papers/quantum_theory.pdf
  6. 6.
    D. Deutsch, R. Jozsa, Rapid solutions of problems by quantum computation. Proc. R. Soc. Lond. A 439, 553–558 (1992). http://www.qudev.ethz.ch/phys4/studentspresentations/djalgo/DeutschJozsa.pdf
  7. 7.
    A.J. DeWeerd, Interaction-free measurement. Am. J. Phys. 70(3), 272–275 (2002). http://bulldog2.redlands.edu/facultyfolder/deweerd/research/IFM-AJP.pdf
  8. 8.
    A.C. Elitzur, L. Vaidman, Quantum mechanical interaction-free measurements. Found. Phys. 23, 987–97 (1993). Preprint available at http://arxiv.org/PS_cache/hep-th/pdf/9305/9305002v2.pdf
  9. 9.
    L. Hardy, Nonlocality for two particles without inequalities for almost all entangled states. Phys. Rev. Lett. 71(11), 1665–1668 (1993). https://pdfs.semanticscholar.org/f940/11b5ad26ac9b8c8a7f1e336d3d1f85450b31.pdf
  10. 10.
    P.G. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, M. Kasevich, Experimental realization of “Interaction-Free” measurements, in Symposium, on the Foundations of Modern Physics, 1994: 70 Years of Matter Waves, ed. by K.V. Laurikainen, C. Montonen, K. Sunnarborg (Frontières, 1994) pp. 129–138. http://www.univie.ac.at/qfp/publications3/pdffiles/1994-08.pdf
  11. 11.
    P. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, M. Kasevich, Interaction-free measurement. Phys. Rev. Lett. 74, 4763–4766 (1995a). https://vcq.quantum.at/fileadmin/Publications/1995-03.pdf
  12. 12.
    P.G. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, M. Kasevich, Experimental realization of interaction-free measurement, in Proceedings of the Conference on Fundamental Problems in Quantum Theory, held in honor of Prof. J.A. Wheeler, UMBC, Baltimore, Maryland June 19–22, 1995. Annals of the New York Academy of Sciences, ed. by D.M. Greenberger, J.A. Wheeler, A. Zeilinger, vol. 755, (1995b). http://vcq.quantum.at/fileadmin/Publications/1994-08.pdf
  13. 13.
    L. Mach, Ueber einen Interferenzrefraktor. Zeitschrift für Instrumentenkunde 12, 89–93 (1892)Google Scholar
  14. 14.
    M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000). Errata at http://www.squint.org/qci/
  15. 15.
    R. Penrose, Shadows of the Mind (Oxford University Press, Oxford, 1994) (Vintage paperback)Google Scholar
  16. 16.
    L. Vaidman, The Meaning of the Interaction-Free Measurements. Foundations of Physics, 33 (3), 491–510 (2003) http://www.tau.ac.il/~vaidman/lvhp/m87.pdf
  17. 17.
    S. Wiesner, Conjugate coding. Sigact News 15(1), 78–88 (1983). https://doi.org/10.1145/1008908.1008920 (Original manuscript written circa 1970)
  18. 18.
    L. Zehnder, Ein neuer Interferenzrefraktor. Zeitschrift für Instrumentenkunde 11, 275–285 (1891)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Acadinnet Education Services IndiaBangaloreIndia

Personalised recommendations