Advertisement

Quantum Information Processing

, Volume 1, Issue 1–2, pp 129–134 | Cite as

Qubit Geometry and Conformal Mapping

  • Jae-weon LeeEmail author
  • Chang Ho Kim
  • Eok Kyun Lee
  • Jaewan Kim
  • Soonchil Lee
Article

Abstract

Identifying the Bloch sphere with the Riemann sphere (the extended complex plane), we obtain relations between single qubit unitary operations and Möbius transformations on the extended complex plane.

PACS: 03.67.-a, 03.67.Lx, 03.67.Hk

quantum computing bloch sphere qubit geometry conformal mapping stereographic projection 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    For a review see, for example, M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge Press, Cambridge, 2000), D. Eckert and A. Zeilinger, eds., The Physics of Quantum Information (Springer Verlag, Berlin, 2000).Google Scholar
  2. 2.
    P. Benio., J. Stat. Phys. 22, 563 (1980).Google Scholar
  3. 3.
    W. Rindler and R. Penrose, Spinors and Space-Time Vol.1 (Cambridge Monographs on Math Physics) (Cambridge University Press, 1986)Google Scholar
  4. 4.
    H. Urbantke, Am. J. Phys. 59, 503 (1991).Google Scholar
  5. 5.
    R. Mosser and R. Dandolo., quant-ph/0108137.Google Scholar
  6. 6.
    F. Frescura and B. Hiley, Am. J. Phys. 49, 152 (1981); T. Havel and C. Doran, quant-ph/ 0004031.Google Scholar
  7. 7.
    See, for example, M. A. Porter, The Hopf fibration and its applications, found at http://www.cam.cornell.edu/ mason/researchGoogle Scholar
  8. 8.
    B. Hatfield, Quantum Field Theory of Point Particles and Strings (Addison-Wesley Publishing Company, 1992).Google Scholar
  9. 9.
    R. P. Feynman, Frank L. Vernon, and Robert W. Hellwarth, J. Applied Physics 65 (1957).Google Scholar
  10. 10.
    P. Ginsparg, "Applied confomal field theories" in LES HOUCHES Lectures, by E. Br ezin and J. Zinn-Justin, eds. (1988)Google Scholar

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • Jae-weon Lee
    • 1
    Email author
  • Chang Ho Kim
    • 1
  • Eok Kyun Lee
    • 1
  • Jaewan Kim
    • 2
  • Soonchil Lee
    • 2
  1. 1.Department of Chemistry, School of Molecular Science (BK 21)Korea Advanced Institute of Science and TechnologyTaejonKorea
  2. 2.Department of PhysicsKorea Advanced Institute of Science and TechnologyTaejonKorea

Personalised recommendations