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Reversibility in Extended Measurement-Based Quantum Computation

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Reversible Computation (RC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9138))

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Abstract

When applied on some particular quantum entangled states, measurements are universal for quantum computing. In particular, despite the fondamental probabilistic evolution of quantum measurements, any unitary evolution can be simulated by a measurement-based quantum computer (MBQC). We consider the extended version of the MBQC where each measurement can occur not only in the \(\{X,Y\}\)-plane of the Bloch sphere but also in the \(\{X,Z\}\)- and \(\{Y,Z\}\)-planes. The existence of a gflow in the underlying graph of the computation is a necessary and sufficient condition for a certain kind of determinism. We extend the focused gflow (a gflow in a particular normal form) defined for the \(\{X,Y\}\)-plane to the extended case, and we provide necessary and sufficient conditions for the existence of such normal forms.

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References

  1. Broadbent, A., Kashefi, E.: Parallelizing quantum circuits. Theoretical computer science 410 (26), 2489–2510

    Google Scholar 

  2. Browne, D.E., Kashefi, E., Mhalla, M., Perdrix, S.: Generalized flow and determinism in measurement-based quantum computation. New J. Phys. 9, 250 (2007)

    Article  Google Scholar 

  3. Danos, V., Kashefi, E.: Determinism in the one-way model. Physical Review A 74 (2006)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  5. Danos, V., Kashefi, E., Panangaden, P., Perdrix, S.: Extended measurement calculus. In: Chapter in Semantic Techniques in quantum Computation. Cambridge University Press (2010)

    Google Scholar 

  6. Duncan, R., Perdrix, S.: Rewriting measurement-based quantum computations with generalised flow. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6199, pp. 285–296. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  7. Dias da Silva, R., Pius, E., Kashefi, E.: Global Quantum Circuit Optimization. arXiv:1301.0351

  8. Hein, M., Eisert, J., Briegel, H.J.: Multi-party entanglement in graph states. Phys. Rev. A 69, 062311 (2004)

    Article  MathSciNet  Google Scholar 

  9. Kashefi, E., Markham, D., Mhalla, M., Perdrix, S.: Information flow in secret sharing protocols. In: Developments in Computational Models (DCM 2009), EPTCS 9, pp. 87–97 (2009)

    Google Scholar 

  10. Mhalla, M., Murao, M., Perdrix, S., Someya, M., Turner, P.S.: Which graph states are useful for quantum information processing? In: Bacon, D., Martin-Delgado, M., Roetteler, M. (eds.) TQC 2011. LNCS, vol. 6745, pp. 174–187. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  11. Mhalla, M., Perdrix, S.: Finding optimal flows efficiently. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 857–868. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  12. Mhalla, M., Perdrix, S.: Graph States, Pivot Minor, and Universality of (X, Z)-measurements. IJUC 9(1–2), 153–171 (2013)

    Google Scholar 

  13. Prevedel, R., Walther, P., Tiefenbacher, F., Bohi, P., Kaltenbaek, R., Jennewein, T., Zeilinger, A.: High-speed linear optics quantum computing using active feed-forward. Nature 445(7123), 65–69 (2007)

    Article  Google Scholar 

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

    Article  Google Scholar 

  15. Raussendorf, R., Browne, D.E., Briegel, H.J.: Measurement-based quantum computation with cluster states. Physical Review A 68, 022312 (2003)

    Article  Google Scholar 

  16. Walther, P., Resch, K.J., Rudolph, T., Schenck, E., Weinfurter, H., Vedral, V., Aspelmeyer, M., Zeilinger, A.: Experimental one-way quantum computing. Nature 434(7030), 169–176 (2005)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Telecom ParisTech, Paris, France

    Nidhal Hamrit

  2. CNRS, Villers-lès-Nancy, France

    Simon Perdrix

  3. LORIA, UMR 7503, CNRS, Inria, Université de Lorraine, Nancy, France

    Nidhal Hamrit & Simon Perdrix

Authors
  1. Nidhal Hamrit
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  2. Simon Perdrix
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Corresponding author

Correspondence to Simon Perdrix .

Editor information

Editors and Affiliations

  1. CNRS and Université Paris Diderot, Paris, France

    Jean Krivine

  2. Inria, St. Ismier Cedex, France

    Jean-Bernard Stefani

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Hamrit, N., Perdrix, S. (2015). Reversibility in Extended Measurement-Based Quantum Computation. In: Krivine, J., Stefani, JB. (eds) Reversible Computation. RC 2015. Lecture Notes in Computer Science(), vol 9138. Springer, Cham. https://doi.org/10.1007/978-3-319-20860-2_8

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  • DOI: https://doi.org/10.1007/978-3-319-20860-2_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20859-6

  • Online ISBN: 978-3-319-20860-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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