Anyonic quantum walks

Brennen, Gavin K. and Ellinas, Demosthenes and Kendon, Viv and Pachos, Jiannis K. and Tsohantjis, Ioannis and Wang, Zhenghan (2010) Anyonic quantum walks. Annals of Physics, 325 (3). pp. 664-681. ISSN 0003-4916 (https://doi.org/10.1016/j.aop.2009.12.001)

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Abstract

The one dimensional quantum walk of anyonic systems is presented. The anyonic walker performs braiding operations with stationary anyons of the same type ordered canonically on the line of the walk. Abelian as well as non-Abelian anyons are studied and it is shown that they have very different properties. Abelian anyonic walks demonstrate the expected quadratic quantum speedup. Non-Abelian anyonic walks are much more subtle. The exponential increase of the system's Hilbert space and the particular statistical evolution of non-Abelian anyons give a variety of new behaviors. The position distribution of the walker is related to Jones polynomials, topological invariants of the links created by the anyonic world-lines during the walk. Several examples such as the SU(2)k and the quantum double models are considered that provide insight to the rich diffusion properties of anyons.

  • Item type:Article
    ID code:79029
    Dates:
    Date
    Event
    31 March 2010
    Published
    6 December 2009
    Published Online
    3 December 2009
    Accepted
    Subjects:Science > Physics
    Department:Faculty of Science > Physics
    Depositing user: Pure Administrator
    Date deposited:22 Dec 2021 11:40
    Last modified:18 Apr 2024 00:30
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/79029
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