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The One Way to Quantum Computation

  • Vincent Danos
  • Elham Kashefi
  • Prakash Panangaden
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4052)

Abstract

Measurement-based quantum computation has emerged from the physics community as a new approach to quantum computation where measurements rather than unitary transformations are the main driving force of computation. Among measurement-based quantum computation methods the recently introduced one-way quantum computer [RB01] stands out as basic and fundamental.

In this work we a concrete syntax and an algebra of these patterns derived from a formal semantics. We developed a rewrite theory and proved a general standardization theorem which allows all patterns to be put in a semantically equivalent standard form.

Keywords

Entangle State Quantum Computation Denotational Semantic Concrete Syntax Pauli Operator 
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. [BBC+93]
    Bennett, C., Brassard, G., Crepeau, C., Jozsa, R., Peres, A., Wootters, W.: Teleporting an unknown quantum state via dual classical and EPR channels. Phys Rev Lett 10(5), 1895–1899 (1993), citeseer.ist.psu.edu/bennett93teleporting.html CrossRefMathSciNetGoogle Scholar
  2. [Deu87]
    Deutsch, D.: Quantum computers. Computer Bulletin 3(2), 24 (1987)MathSciNetGoogle Scholar
  3. [DKP]
    Vincent Danos, Elham Kashefi, and Prakash Panangaden. The measurement calculus. Available from www.cs.mcgill.ca/~prakash/pubs.html
  4. [DKP05]
    Danos, V., Kashefi, E., Panangaden, P.: Robust and parsimonious realisations of unitaries in the one-way model. Phys. Rev. A 72 (2005)Google Scholar
  5. [GC99]
    Gottesman, D., Chuang, I.L.: Quantum teleportation is a universal computational primitive. Nature, 390–402 (1999)Google Scholar
  6. [Gro98]
    Grover, L.K.: A framework for fast quantum mechanical algorithms. In: Proceedings of STOC 1998 – Symposium on Theory of Computing, pp. 53–62 (1998)Google Scholar
  7. [NC00]
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  8. [Nie04]
    Nielsen, M.A.: Optical quantum computation using cluster states. Phys. Rev. Lett. 93(4), 40503 (2004)CrossRefGoogle Scholar
  9. [RB01]
    Raussendorf, R., Briegel, H.-J.: A one-way quantum computer. Physical Review Letters 86(5188) (2001)Google Scholar
  10. [RBB03]
    Raussendorf, R., Browne, D.E., Briegel, H.-J.: Measurement-based quantum computation on cluster states. Phys. Rev. A 68(022312) (2003)Google Scholar
  11. [Sel04]
    Selinger, P.: Towards a quantum programming language. Mathematical Structures in Computer Science 14(4), 527 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  12. [Sho94]
    Shor, P.W.: Algorithms for quantum computation: Discrete logarithms and factoring. In: Proceedings of FOCS 1994 – Symposium on Foundations of Computer Science, p. 124 (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Vincent Danos
    • 1
  • Elham Kashefi
    • 2
  • Prakash Panangaden
    • 3
  1. 1.Université Paris 7 & CNRS 
  2. 2.IQCUniversity of Waterloo & Christ ChurchOxford
  3. 3.School of Computer ScienceMcGill UniversityMontréalCanada

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