Quantum Process Calculus for Linear Optical Quantum Computing

  • Sonja Franke-Arnold
  • Simon J. Gay
  • Ittoop V. Puthoor
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7948)


We extend quantum process calculus in order to describe linear optical elements. In all previous work on quantum process calculus a qubit was considered as the information encoded within a 2 dimensional Hilbert space describing the internal states of a localised particle, most often realised as polarisation information of a single photon. We extend quantum process calculus by allowing multiple particles as information carriers, described by Fock states. We also consider the transfer of information from one particular qubit realisation (polarisation) to another (path encoding), and describe post-selection. This allows us for the first time to describe linear optical quantum computing (LOQC) in terms of quantum process calculus. We illustrate this approach by presenting a model of an LOQC CNOT gate.


Formal methods quantum computing linear optics semantics quantum process calculus 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press (2000)Google Scholar
  2. 2.
  3. 3.
  4. 4.
    Knill, E., Laflamme, R., Milburn, G.J.: A scheme for efficient quantum computation with linear optics. Nature 409, 46 (2001)CrossRefGoogle Scholar
  5. 5.
    O’Brien, J.L., Pryde, G.J., White, A.G., Ralph, T.C., Branning, D.: Demonstration of an all-optical quantum controlled-not gate. Nature 426, 264 (2003)CrossRefGoogle Scholar
  6. 6.
    Politi, A., Cryan, M.J., Rarity, J.G., Yu, S., O’Brien, J.L.: Silica-on-silicon waveguide quantum circuits. Science 320, 646 (2008)CrossRefGoogle Scholar
  7. 7.
    Gay, S.J., Nagarajan, R.: Communicating Quantum Processes. In: Proceedings of the 32nd Annual ACM Symposium on Principles of Programming Languages, pp. 145–157. ACM (2005)Google Scholar
  8. 8.
    Jorrand, P., Lalire, M.: Toward a quantum process algebra. In: CF 2004: Proceedings of the 1st Conference on Computing Frontiers, pp. 111–119. ACM Press (2004)Google Scholar
  9. 9.
    Feng, Y., Duan, R., Ji, Z., Ying, M.: Probabilistic bisimilarities between quantum processes arXiv:cs.LO/0601014 (2006)Google Scholar
  10. 10.
    Milner, R.: Communication and Concurrency. Prentice-Hall (1989)Google Scholar
  11. 11.
    Myers, C.R., Laflamme, R.: Linear optics quantum computation: an overview arXiv: quant-ph/0512104v1 (2005)Google Scholar
  12. 12.
    Ralph, T.C., Lanford, N.K., Bell, T.B., White, A.G.: Linear optical controlled-not gate in the coincidence basis. Physical Review Letters A 65, 62324–1 (2002)Google Scholar
  13. 13.
    Milner, R.: Communicating and Mobile Systems: the Pi-Calculus. Cambridge University Press (1999)Google Scholar
  14. 14.
    Milner, R., Parrow, J., Walker, D.: A calculus of mobile processes, I. Information and Computation 100(1), 1–40 (1992)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Gay, S.J., Nagarajan, R.: Types and Typechecking for Communicating Quantum Processes. Mathematical Structures in Computer Science 16(3), 375–406 (2006)MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    Davidson, T.A.S.: Formal Verification Techniques using Quantum Process Calculus. PhD thesis, University of Warwick (2011)Google Scholar
  17. 17.
    Davidson, T.A.S., Gay, S.J., Nagarajan, R., Puthoor, I.V.: Analysis of a quantum error correcting code using quantum process calculus. EPTCS 95, 67–80 (2011)CrossRefGoogle Scholar
  18. 18.
    Wright, A.K., Felleisen, M.: A syntactic approach to type soundness. Information and Computation 115(1), 38–94 (1994)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Sonja Franke-Arnold
    • 1
  • Simon J. Gay
    • 2
  • Ittoop V. Puthoor
    • 1
    • 2
  1. 1.School of Physics and AstronomyUniversity of GlasgowUK
  2. 2.School of Computing ScienceUniversity of GlasgowUK

Personalised recommendations