Design of p-Valued Deutsch Quantum Gates with Multiple Control Signals and Mixed Polarity

  • Claudio MoragaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9720)


This paper presents a detailed study of the realization of p–valued Deutsch quantum gates with n > 2 controlling signals, both under conjunctive and disjunctive control, and including zero or mixed polarity of the controlling signals. It is shown that the realization complexity is in O(p n  1). The realization comprises only Muthukrishnan-Stroud elementary quantum gates.


p-valued Deutsch gate Multi-control Mixed polarity Quantum computing 


  1. 1.
    Aharonov, D., Ben-Or, M.: Fault-tolerant quantum computation with constant error rate. SIAM J. Comput. 38(4), 1207–1282 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Barenco, A., Bennett, C.H., Cleve, R., Di Vincenzo, D.P., Margolus, N., Shor, P., Sleator, T., Smolin, J.A., Weinfurter, H.: Elementary gates for quantum computation. Phys. Rev. A 52, 3457–3467 (1995)CrossRefGoogle Scholar
  3. 3.
    Deutsch, D.: Quantum computational networks. Proc. Roy. Soc. Lond. A 425, 73–90 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Moraga, C.: Aspects of reversible and quantum computing in a p-valued domain. IEEE JETCAS 6(1) (2016, in press). doi: 10.1109/JETCAS.2016.2528658
  5. 5.
    Moraga, C.: Realization of p-valued Deutsch quantum gates under multi-control and mixed polarity. Research report 851, Faculty of Computer Science, TU Dortmund University. ISSN 0933-6192 (2016)Google Scholar
  6. 6.
    Muthukrishnan, A., Stroud, C.R.: Multiplevalued logic gates for quantum computation. Phys. Rev. A 62, 052309 (2000)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Szyprowski, M., Kerntopf, P.: Optimal 4-bit reversible mixed-polarity Toffoli circuits. In: Glück, R., Yokoyama, T. (eds.) RC 2012. LNCS, vol. 7581, pp. 138–151. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  8. 8.
    Toffoli, T.: Reversible computing, Tech. Memo MIT/ /LCS/TM-151, MIT Lab. for Comp. Sci. (1980)Google Scholar
  9. 9.
    Yuttanan, B., Nirat, C.: Roots of matrices. Songklanakarin J. Sci. Technol. 27(3), 659–665 (2005)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Chair Informatics 1TU Dortmund UniversityDortmundGermany

Personalised recommendations