Skip to main content
SpringerLink
Log in

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

  • Conference paper
  • First Online:
Reversible Computation (RC 2016)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9720))

Included in the following conference series:

  • 662 Accesses

Abstract

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.

Work leading to this paper was partially supported by the EU COST-Action IC-1405 on Reversible Computation – Extending Horizons of Computing.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    X represents a Muthukrishnan-Stroud (MS) gate realizing a p-valued Pauli matrix shifting by 1 (modulo p) the state of its input qupit when its controlling qupits are in the state |p − 1〉.

References

  1. Aharonov, D., Ben-Or, M.: Fault-tolerant quantum computation with constant error rate. SIAM J. Comput. 38(4), 1207–1282 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  3. Deutsch, D.: Quantum computational networks. Proc. Roy. Soc. Lond. A 425, 73–90 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  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

    Google Scholar 

  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. Muthukrishnan, A., Stroud, C.R.: Multiplevalued logic gates for quantum computation. Phys. Rev. A 62, 052309 (2000)

    Article  MathSciNet  Google Scholar 

  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)

    Chapter  Google Scholar 

  8. Toffoli, T.: Reversible computing, Tech. Memo MIT/ /LCS/TM-151, MIT Lab. for Comp. Sci. (1980)

    Google Scholar 

  9. Yuttanan, B., Nirat, C.: Roots of matrices. Songklanakarin J. Sci. Technol. 27(3), 659–665 (2005)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Chair Informatics 1, TU Dortmund University, 44227, Dortmund, Germany

    Claudio Moraga

Authors
  1. Claudio Moraga
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Claudio Moraga .

Editor information

Editors and Affiliations

  1. National Institute of Informatics, Tokyo, Japan

    Simon Devitt

  2. University of Bologna/Inria, Bologna, Italy

    Ivan Lanese

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Moraga, C. (2016). Design of p-Valued Deutsch Quantum Gates with Multiple Control Signals and Mixed Polarity. In: Devitt, S., Lanese, I. (eds) Reversible Computation. RC 2016. Lecture Notes in Computer Science(), vol 9720. Springer, Cham. https://doi.org/10.1007/978-3-319-40578-0_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-40578-0_13

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40577-3

  • Online ISBN: 978-3-319-40578-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation