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Topological Quantum Computation

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Formal Methods for Dynamical Systems (SFM 2013)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 7938))

Abstract

This pedagogical introduction to topological quantum computation includes the following parts. First we provide an introduction to anyons and topological models. In particular we consider the properties of anyons and their relation to topological quantum computation. Then we present the quantum double models. These are stabiliser codes, that can be described very much like quantum error correcting codes. They include the toric code and various Abelian and non-Abelian extensions. Next the Jones polynomials are presented, which are topological invariants of links and knots that are related to anyons. Their evaluations by classical algorithms is computationally complex, but their approximation by quantum algorithms is efficient. Finally, we presenter an overview of the current state of topological quantum computation and present some open questions.

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Author information

Authors and Affiliations

  1. School of Physics and Astronomy, Univesrity of Leeds, Leeds, LS2 9JT, UK

    Jiannis K. Pachos

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  1. Jiannis K. Pachos
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Editors and Affiliations

  1. Dipartimento di Scienze di Base e Fondamenti, Università di Urbino "Carlo Bo", , ,, Piazza della Repubblica 13, 61029, Urbino, Italy

    Marco Bernardo

  2. Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, Den Dolech 2, 5612 AZ, Eindhoven, The Netherlands

    Erik de Vink

  3. Dipartimento di Informatica,, Università di Verona, Ca’ Vignal 2, Strada le Grazie 15, 37134, Verona, Italy

    Alessandra Di Pierro

  4. Department of Computing, Imperial College London, Huxley Building,180 Queen’s Gate, SW7 2BZ, London, UK

    Herbert Wiklicky

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Pachos, J.K. (2013). Topological Quantum Computation. In: Bernardo, M., de Vink, E., Di Pierro, A., Wiklicky, H. (eds) Formal Methods for Dynamical Systems. SFM 2013. Lecture Notes in Computer Science, vol 7938. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38874-3_5

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  • DOI: https://doi.org/10.1007/978-3-642-38874-3_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38873-6

  • Online ISBN: 978-3-642-38874-3

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