Advertisement

Distributed Quantum Programming

  • Ellie D’Hondt
  • Yves Vandriessche
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5715)

Abstract

In this paper we explore the structure and applicability of the Distributed Measurement Calculus (DMC), a formal assembly language for distributed measurement-based quantum computations. We describe its syntax and semantics, both operational and denotational, and state several properties that are crucial to the practical usability of our language, such as equivalence of our semantics, as well as compositionality and context-freeness of DMC programs. We show how to put these properties to use by constructing a composite program that implements distributed controlled operations, and demonstrate that the semantics of this program does not change under the various composition operations. Our formal model is meant to be the basis of a virtual machine for distributed quantum computations, where programming execution no longer needs to be analysed by hand, while at the same time formal properties may be relied upon. Several insights on how to move towards this virtual level are given.

Keywords

Virtual Machine Quantum Computation Operational Semantic Denotational Semantic Share Control 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [AM05]
    Adão, P., Mateus, P.: A process algebra for reasoning about quantum security. In: Selinger, P. (ed.) Proceedings of the 3rd Workshop on Quantum Programming Languages (QPL 2004), pp. 3–20 (2005)Google Scholar
  2. [BA81]
    Brock, J.D., Ackerman, W.B.: Scenarios: A model of non-determinate computation. Formalizations of Programming Concepts 107 (1981)Google Scholar
  3. [BVK98]
    Bose, S., Vedral, V., Knight, P.L.: Multiparticle generalization of entanglement swapping. Phys. Rev. A 57(2), 822–829 (1998)CrossRefGoogle Scholar
  4. [DDKP05]
    Danos, V., D’Hondt, E., Kashefi, E., Panangaden, P.: Distributed measurement-based quantum computation. In: Selinger, P. (ed.) Proceedings of the 3rd International Workshop on Quantum Programming Languages (QPL 2005). ENTCS, vol. 170, pp. 73–94 (2005); quant-ph/0506070Google Scholar
  5. [D’H05]
    D’Hondt, E.: Distributed quantum computation – A measurement-based approach. PhD thesis, Vrije Universiteit Brussel (2005)Google Scholar
  6. [DKP07]
    Danos, V., Kashefi, E., Panangaden, P.: The measurement calculus. Journal of the ACM 54(2) (2007); quant-ph/0704.1263v1Google Scholar
  7. [GN04]
    Gay, S.J., Nagarajan, R.: Communicating quantum processes. In: Selinger, P. (ed.) Proceedings of the 2nd Workshop on Quantum Programming Languages (QPL 2004), Turku, Finland. Turku Centre for Computer Science, TUCS General Publication No 33 (2004)Google Scholar
  8. [GNP05]
    Gay, S.J., Nagarajan, R., Papanikolaou, N.: Probabilistic model-checking of quantum protocols (2005)Google Scholar
  9. [JL05]
    Jorrand, P., Lalire, M.: Toward a quantum process algebra. In: Proceedings of the first conference on computing frontiers, pp. 111–119. ACM Press, New York (2005)Google Scholar
  10. [Kni96]
    Knill, E.: Conventions for quantum pseudocode. Technical Report LAUR-96-2724, Los Alamos National Laboratory (1996)Google Scholar
  11. [LJ04]
    Lalire, M., Jorrand, P.: A process algebraic approach to concurrent and distributed quantum computation: operational semantics. In: Selinger, P. (ed.) Proceedings of the 2nd Workshop on Quantum Programming Languages (QPL 2004), Turku, Finland. Turku Centre for Computer Science, TUCS General Publication No 33 (2004)Google Scholar
  12. [NC00]
    Nielsen, M.A., Chuang, I.: Quantum computation and quantum information. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  13. [RBB03]
    Raussendorf, R., Browne, D.E., Briegel, H.J.: Measurement-based quantum computation on cluster states. Phys. Rev. A 68(2), 022312 (2003)CrossRefGoogle Scholar
  14. [RMR+06]
    De Raedt, K., Michielsen, K., De Raedt, H., Trieu, B., Arnold, G., Richter, M., Lippert, T., Watanabe, H., Ito, N.: Massive parallel quantum computer simulator. quant-ph/0608239 (2006)Google Scholar
  15. [SAC+06]
    Svore, K.M., Aho, A.V., Cross, A.W., Chuang, I.L., Markov, I.L.: A layered software architecture for quantum computing design tools. IEEE Computer 39(1), 74–83 (2006)CrossRefGoogle Scholar
  16. [Sel03]
    Selinger, P.: Towards a quantum programming language. Mathematical Structures in Computer Science (2003) (to appear)Google Scholar
  17. [YL05]
    Yimsiriwattana, A., Lomonaco, S.J.: Generalized GHZ states and distributed quantum computing. AMS Contemporary Mathematics (2005)Google Scholar
  18. [ZZHE93]
    Zukowski, M., Zeilinger, A., Horne, M.A., Ekert, A.: Event-ready detectors. Bell experiment via entanglement swapping. Phys. Rev. Lett. 71(26), 4287–4290 (1993)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Ellie D’Hondt
    • 1
  • Yves Vandriessche
    • 1
  1. 1.Vrije Universiteit BrusselBelgium

Personalised recommendations