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Applied Physics B

, Volume 98, Issue 4, pp 623–633 | Cite as

Entanglement generation of Clifford quantum cellular automata

Article

Abstract

Clifford quantum cellular automata (CQCAs) are a special kind of quantum cellular automata (QCAs) that incorporate Clifford group operations for the time evolution. Despite being classically simulable, they can be used as basic building blocks for universal quantum computation. This is due to the connection to translation-invariant stabilizer states and their entanglement properties. We will give a self-contained introduction to CQCAs and investigate the generation of entanglement under CQCA action. Furthermore, we will discuss finite configurations and applications of CQCAs.

Keywords

Spin Chain Symplectic Form Stabilizer Generator Binary String Pauli Matrice 
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.

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References

  1. 1.
    D.M. Schlingemann, H. Vogts, R.F. Werner, J. Math. Phys. 49 (2008) Google Scholar
  2. 2.
    J. Gütschow, S. Uphoff, R.F. Werner, Z. Zimborás, J. Math. Phys. (2009, submitted) Google Scholar
  3. 3.
    B. Schumacher, R.F. Werner, Preprint, 2004 Google Scholar
  4. 4.
    D. Shepherd, T. Franz, R.F. Werner, Phys. Rev. Lett. 97 (2006) Google Scholar
  5. 5.
    R. Raussendorf, Phys. Rev. A 72 (2005) Google Scholar
  6. 6.
    R. Raussendorf, H.J. Briegel, Phys. Rev. Lett. 86, 5188 (2001) ADSCrossRefGoogle Scholar
  7. 7.
    R. Raussendorf, Phys. Rev. A 72 (2005) Google Scholar
  8. 8.
    J. Fitzsimons, J. Twamley, Phys. Rev. Lett. 97, 090502 (2006) ADSCrossRefGoogle Scholar
  9. 9.
    D. Gottesman, Ph.D. thesis, California Institute of Technology, Pasadena, CA, 1997 Google Scholar
  10. 10.
    D. Fattal, T.S. Cubitt, Y. Yamamoto, S. Bravyi, I.L. Chuang, Preprint, 2004 Google Scholar
  11. 11.
    M. Fekete, Math. Z. 17, 228 (1923) MathSciNetCrossRefGoogle Scholar
  12. 12.
    J. Fitzsimons, L. Xiao, S.C. Benjamin, J.A. Jones, Phys. Rev. Lett. 99, 030501 (2007) MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Institut für Theoretische PhysikUniversität HannoverHannoverGermany

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