Heterotic Computing

  • Viv Kendon
  • Angelika Sebald
  • Susan Stepney
  • Matthias Bechmann
  • Peter Hines
  • Robert C. Wagner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6714)


Non-classical computation has tended to consider only single computational models: neural, analog, quantum, etc. However, combined computational models can both have more computational power, and more natural programming approaches, than such ‘pure’ models alone. Here we outline a proposed new approach, which we term heterotic computing. We discuss how this might be incorporated in an accessible refinement-based computational framework for combining diverse computational models, and describe a range of physical exemplars (combinations of classical discrete, quantum discrete, classical analog, and quantum analog) that could be used to demonstrate the capability.


Nuclear Magnetic Resonance Experiment Control Layer Nuclear Magnetic Resonance Parameter Nuclear Magnetic Resonance System Nuclear Magnetic Resonance Quantum 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abramsky, S., Coecke, B.: A categorical semantics of quantum protocols. In: Proc. IEEE Symp. Logic in Comp. Sci., pp. 415–425 (2004)Google Scholar
  2. 2.
    Anders, J., Browne, D.: Computational power of correlations. Phys. Rev. Lett. 102, 050502 (2009)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Banach, R., Jeske, C., Fraser, S., Cross, R., Poppleton, M., Stepney, S., King, S.: Approaching the formal design and development of complex systems: The retrenchment position. In: WSCS, IEEE ICECCS 2004 (2004)Google Scholar
  4. 4.
    Banach, R., Jeske, C., Poppleton, M., Stepney, S.: Retrenching the purse. Fundamenta Informaticae 77, 29–69 (2007)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Banach, R., Poppleton, M.: Retrenchment: an engineering variation on refinement. In: Bert, D. (ed.) B 1998. LNCS, vol. 1393, pp. 129–147. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  6. 6.
    Banach, R., Poppleton, M., Jeske, C., Stepney, S.: Engineering and theoretical underpinnings of retrenchment. Sci. Comp. Prog. 67(2-3), 301–329 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Bechmann, M., Sebald, A., Stepney, S.: From binary to continuous gates – and back again. In: Tempesti, G., Tyrrell, A.M., Miller, J.F. (eds.) ICES 2010. LNCS, vol. 6274, pp. 335–347. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  8. 8.
    Blakey, E.: Unconventional complexity measures for unconventional computers. Natural Computing (2010), doi:10.1007/s11047-010-9226-9Google Scholar
  9. 9.
    Chuang, I.L., Vandersypen, L.M.K., Zhou, X., Leung, D.W., Lloyd, S.: Experimental realization of a quantum algorithm. Nature 393(6681), 143–146 (1998)CrossRefGoogle Scholar
  10. 10.
    Clark, J.A., Stepney, S., Chivers, H.: Breaking the model: finalisation and a taxonomy of security attacks. ENTCS 137(2), 225–242 (2005)Google Scholar
  11. 11.
    Collins, D., et al.: NMR quantum computation with indirectly coupled gates. Phys. Rev. A 62(2), 022304 (2000)CrossRefGoogle Scholar
  12. 12.
    Cooper, D., Stepney, S., Woodcock, J.: Derivation of Z refinement proof rules: forwards and backwards rules incorporating input/output refinement. Tech. Rep. YCS-2002-347, Department of Computer Science, University of York (December 2002)Google Scholar
  13. 13.
    Cory, D.G., et al.: NMR based quantum information processing: Achievements and prospects. Fortschritte der Physik 48(9–11), 875–907 (2000)CrossRefGoogle Scholar
  14. 14.
    d’Hondt, E., Panangaden, P.: Quantum weakest preconditions. Math. Struct. Comp. Sci. 16(3), 429–451 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    DiVincenzo, D.P.: The physical implementation of quantum computation. Fortschritte der Physik 48(9-11), 771–783 (2000), arXiv:quant-ph/0002077v3 CrossRefzbMATHGoogle Scholar
  16. 16.
    Dusold, S., Sebald, A.: Dipolar recoupling under magic-angle spinning conditions. Annual Reports on NMR Spectroscopy 41, 185–264 (2000)CrossRefGoogle Scholar
  17. 17.
    Hines, P.: The categorical theory of self-similarity. Theory and Applications of Categories 6, 33–46 (1999)MathSciNetzbMATHGoogle Scholar
  18. 18.
    Hines, P.: A categorical framework for finite state machines. Mathematical Structures in Computer Science 13, 451–480 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Jones, J.A.: NMR quantum computation. Progress in Nuclear Magnetic Resonance Spectroscopy 38(4), 325–360 (2001)CrossRefGoogle Scholar
  20. 20.
    Lambek, J., Scott, P.: An introduction to higher-order categorical logic. Cambridge University Press, Cambridge (1986)zbMATHGoogle Scholar
  21. 21.
    Levitt, M.H.: Composite pulses. In: Grant, D.M., Harris, R.K. (eds.) Encyclopedia of Nuclear Magnetic Resonance, vol. 2, pp. 1396–1441. Wiley, Chichester (1996)Google Scholar
  22. 22.
    Linden, N., Barjat, H., Freeman, R.: An implementation of the Deutsch-Jozsa algorithm on a three-qubit NMR quantum computer. Chemical Physics Letters 296(1-2), 61–67 (1998)CrossRefGoogle Scholar
  23. 23.
    Mac Lane, S.: Categories for the working mathematician. Springer, Heidelberg (1971)CrossRefzbMATHGoogle Scholar
  24. 24.
    Roselló-Merino, M., Bechmann, M., Sebald, A., Stepney, S.: Classical computing in nuclear magnetic resonance. IJUC 6(3-4), 163–195 (2010)Google Scholar
  25. 25.
    Sebald, A., Bechmann, M., Calude, C.S., Abbott, A.A.: NMR-based classical implementation of the de-quantisation of Deutsch’s problem (work in progress)Google Scholar
  26. 26.
    Spiller, T.P., Nemoto, K., Braunstein, S.L., Munro, W.J., van Loock, P., Milburn, G.J.: Quantum computation by communication. New J. Phys. 8(2), 30 (2006)CrossRefGoogle Scholar
  27. 27.
    Stepney, S.: The neglected pillar of material computation. Physica D: Nonlinear Phenomena 237(9), 1157–1164 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Wagner, R.C., Everitt, M.S., Jones, M.L., Kendon, V.M.: Universal continuous variable quantum computation in the micromaser. In: Calude, C.S., Hagiya, M., Morita, K., Rozenberg, G., Timmis, J. (eds.) Unconventional Computation. LNCS, vol. 6079, pp. 152–163. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  29. 29.
    Wegner, P.: Why interaction is more powerful than algorithms. CACM 40, 80–91 (1997)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Viv Kendon
    • 1
  • Angelika Sebald
    • 2
  • Susan Stepney
    • 3
  • Matthias Bechmann
    • 2
  • Peter Hines
    • 3
  • Robert C. Wagner
    • 1
  1. 1.School of Physics and AstronomyUniversity of LeedsUK
  2. 2.Department of ChemistryUniversity of YorkUK
  3. 3.Department of Computer ScienceUniversity of YorkUK

Personalised recommendations