Simple Sets of Measurements for Universal Quantum Computation and Graph State Preparation

  • Yasuhiro Takahashi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6519)


We show that the set of observables \(\{Z\otimes X, (\cos\theta) X + (\sin\theta) Y \ {\rm all} \ \theta \in [0,2\pi)\}\) with one ancillary qubit is universal for quantum computation. The set is simpler than a previous one in the sense that one-qubit projective measurements described by the observables in the set are ones only in the (X,Y) plane of the Bloch sphere. The proof of the universality implies a simple set of observables that is approximately universal for quantum computation. Moreover, it implies a simple set of observables for efficient graph state preparation.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Raussendorf, R., Briegel, H.J.: A One-Way Quantum Computer. Phys. Rev. Lett. 86, 5188–5191 (2001)CrossRefGoogle Scholar
  2. 2.
    Nielsen, M.A.: Quantum Computation by Measurement and Quantum Memory. Phys. Lett. A 308, 96–100 (2003)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Perdrix, S.: State Transfer Instead of Teleportation in Measurement-Based Quantum Computation. International Journal of Quantum Information 3(1), 219–223 (2005)CrossRefGoogle Scholar
  4. 4.
    Childs, A.M., Leung, D.W., Nielsen, M.A.: Unified Derivation of Measurement-Based Schemes for Quantum Computation. Phys. Rev. A 71, 032318 (2005)CrossRefGoogle Scholar
  5. 5.
    Leung, D.W.: Quantum Computation by Measurements. International Journal of Quantum Information 2(1), 33–43 (2004)CrossRefMATHGoogle Scholar
  6. 6.
    Jorrand, P., Perdrix, S.: Unifying Quantum Computation with Projective Measurements Only and One-Way Quantum Computation. In: SPIE Quantum Informatics 2004, vol. 5833, pp. 44–51 (2005)Google Scholar
  7. 7.
    Perdrix, S.: Towards Minimal Resources of Measurement-Based Quantum Computation. New Journal of Physics 9, 206 (2007)CrossRefGoogle Scholar
  8. 8.
    Høyer, P., Mhalla, M., Perdrix, S.: Resources Required for Preparing Graph States. In: Asano, T. (ed.) ISAAC 2006. LNCS, vol. 4288, pp. 638–649. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  9. 9.
    Nielsen, M.A., Chuang, I.L.: Quantum Information and Quantum Computation. Cambridge University Press, Cambridge (2000)MATHGoogle Scholar
  10. 10.
    Danos, V., Kashefi, E., Panangaden, P.: Parsimonious and Robust Realizations of Unitary Maps in the One-Way Model. Phys. Rev. A 72, 064301 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Yasuhiro Takahashi
    • 1
  1. 1.NTT Communication Science LaboratoriesNTT CorporationAtsugiJapan

Personalised recommendations