Skip to main content

Rewriting Measurement-Based Quantum Computations with Generalised Flow

  • Conference paper
Automata, Languages and Programming (ICALP 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6199))

Included in the following conference series:

  • 1434 Accesses

Abstract

We present a method for verifying measurement-based quantum computations, by producing a quantum circuit equivalent to a given deterministic measurement pattern. We define a diagrammatic presentation of the pattern, and produce a circuit via a rewriting strategy based on the generalised flow of the pattern. Unlike other methods for translating measurement patterns with generalised flow to circuits, this method uses neither ancilla qubits nor acausal loops.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Raussendorf, R., Briegel, H.J.: A one-way quantum computer. Phys. Rev. Lett. 86, 5188–5191 (2001)

    Article  Google Scholar 

  2. Anne Broadbent, J.F., Kashefi, E.: Universal blind quantum computation. In: Proc. FoCS 2009 (2009)

    Google Scholar 

  3. Browne, D.E., Kashefi, E., Perdrix, S.: Computational depth complexity of measurement-based quantum computation (2009) preprint: arXiv:0909.4673

    Google Scholar 

  4. Coecke, B., Duncan, R.: Interacting quantum observables. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 298–310. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  5. Danos, V., Kashefi, E., Panangaden, P.: The measurement calculus. J. ACM 54(2) (2007)

    Google Scholar 

  6. Danos, V., Kashefi, E.: Determinism in the one-way model. Phys. Rev. A 74(052310) (2006)

    Google Scholar 

  7. Browne, D., Kashefi, E., Mhalla, M., Perdrix, S.: Generalized flow and determinism in measurement-based quantum computation. New J. Phys. 9 (2007)

    Google Scholar 

  8. Duncan, R.: Verifying the measurement calculus by rewriting. In: DCM 2007 (2007) (Oral presentation)

    Google Scholar 

  9. Kashefi, E.: Lost in translation. In: Proc. DCM 2007 (2007)

    Google Scholar 

  10. Abramsky, S., Coecke, B.: A categorical semantics of quantum protocols. In: Proc. LiCS 2004, pp. 415–425. IEEE Computer Society Press, Los Alamitos (2004)

    Google Scholar 

  11. Coecke, B., Pavlovic, D.: Quantum measurements without sums. In: Chen, G., Kauffman, L.H., Lomonaco Jr., S.J. (eds.) The Mathematics of Quantum Computation and Technology. Taylor and Francis, Abington (2007)

    Google Scholar 

  12. Coecke, B., Paquette, E.O.: POVMs and Naimark’s theorem without sums. In: Proceedings of QPL 2006 (2006)

    Google Scholar 

  13. Dixon, L., Duncan, R., Kissinger, A.: Quantomatic. Project home page, http://dream.inf.ed.ac.uk/projects/quantomatic/

  14. Duncan, R.: Types for Quantum Computing. PhD thesis, Oxford University (2006)

    Google Scholar 

  15. Dixon, L., Duncan, R.: Graphical reasoning in compact closed categories for quantum computation. Ann. Math. Artif. Intel. 56(1), 23–42 (2009)

    Article  MATH  Google Scholar 

  16. Duncan, R., Perdrix, S.: Graph states and the necessity of Euler decomposition. In: Ambos-Spies, K., Löwe, B., Merkle, W. (eds.) CiE 2009. LNCS, vol. 5635, pp. 167–177. Springer, Heidelberg (2009)

    Google Scholar 

  17. Kissinger, A.: Graph rewrite systems for complementary classical structures in \(\dag\)-symmetric monoidal categories. Master’s thesis, Oxford University (2008)

    Google Scholar 

  18. Lack, S.: Composing PROPs. Theor. Appl. Categ. 13(9), 147–163 (2004)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Duncan, R., Perdrix, S. (2010). Rewriting Measurement-Based Quantum Computations with Generalised Flow. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds) Automata, Languages and Programming. ICALP 2010. Lecture Notes in Computer Science, vol 6199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14162-1_24

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14162-1_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14161-4

  • Online ISBN: 978-3-642-14162-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics