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Tutorial: Graphical Calculus for Quantum Circuits

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Reversible Computation (RC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 7581))

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Abstract

We explain the graphical zx-calculus for reasoning about qubits without any reference to the underlying categorical semantics, and illustrate its use on quantum circuits.

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References

  1. Backens, M.: The ZX-calculus is complete for stabilizer quantum mechanics. In: Proceedings of Quantum Physic and Logic IX (2012)

    Google Scholar 

  2. 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 

  3. Coecke, B., Duncan, R.: Interacting quantum observables: categorical algebra and diagrammatics. New Journal of Physics 13, 043016 (2011), arXiv:0906.4725

    Article  MathSciNet  Google Scholar 

  4. Coecke, B., Duncan, R., Kissinger, A., Wang, Q.: Strong complementarity and non-locality in categorical quantum mechanics. In: Chiribella, G., Spekkens, R.W. (eds.) Proceedings of 27th IEEE Conference on Logic in Computer Science (LiCS). Extended version to appear in: Quantum Theory: Informational Foundations and Foils. Springer (2012)

    Google Scholar 

  5. Coecke, B., Edwards, B., Spekkens, R.W.: Phase groups and the origin of non-locality for qubits. ENTCS 271(2), 15–36 (2011), arXiv:1003.5005

    Google Scholar 

  6. Danos, V., Kashefi, E., Panangaden, P.: The measurement calculus. Journal of the ACM 54(2) (2007), arXiv:quant-ph/0412135

    Google Scholar 

  7. 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)

    Chapter  Google Scholar 

  8. 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 

  9. Gottesman, D.: Stabilizer codes and quantum error correction. Ph.D. Thesis, Caltech (2007), arXiv:quant-ph/9705052

    Google Scholar 

  10. Hillebrand, A.: Quantum protocols involving multiparticle entanglement and their representations in the ZX-calculus. MSc. thesis, University of Oxford (2011)

    Google Scholar 

  11. Horsman, C.: Quantum picturalism for topological cluster-state computing. New Journal of Physics 13, 095011 (2011), arXiv:1101.4722

    Article  Google Scholar 

  12. Zamdzhiev, V.N.: An abstract approach towards quantum secret sharing. MSc. thesis, University of Oxford (2012)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Oxford University and Université Libre de Bruxelles, UK

    Bob Coecke & Ross Duncan

Authors
  1. Bob Coecke
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  2. Ross Duncan
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Editor information

Editors and Affiliations

  1. DIKU, Department of Computer Science, University of Copenhagen, Universitetsparken 1, 2100, Copenhagen, Denmark

    Robert Glück

  2. Department of Software Engineering, Nanzan University, 489-0863, Seto, Japan

    Tetsuo Yokoyama

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Coecke, B., Duncan, R. (2013). Tutorial: Graphical Calculus for Quantum Circuits. In: Glück, R., Yokoyama, T. (eds) Reversible Computation. RC 2012. Lecture Notes in Computer Science, vol 7581. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36315-3_1

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  • DOI: https://doi.org/10.1007/978-3-642-36315-3_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36314-6

  • Online ISBN: 978-3-642-36315-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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