Coined quantum walks on percolation graphs

Leung, Godfrey and Knott, Paul and Bailey, Joe and Kendon, Viv (2010) Coined quantum walks on percolation graphs. New Journal of Physics, 12. 123018. ISSN 1367-2630 (https://doi.org/10.1088/1367-2630/12/12/123018)

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Abstract

Quantum walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing properties of quantum walks compared with their classical counterparts have been well studied on regular structures and also shown to be sensitive to defects and imperfections in the lattice. As a simple example of a disordered system, we consider percolation lattices, in which edges or sites are randomly missing, interrupting the progress of the quantum walk. We use numerical simulation to study the properties of coined quantum walks on these percolation lattices in one and two dimensions. In one dimension (the line), we introduce a simple notion of quantum tunnelling and determine how this affects the properties of the quantum walk as it spreads. On two-dimensional percolation lattices, we show how the spreading rate varies from linear in the number of steps down to zero as the percolation probability decreases towards the critical point. This provides an example of fractional scaling in quantum-walk dynamics. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

  • Item type:Article
    ID code:78836
    Dates:
    Date
    Event
    9 December 2010
    Published
    10 June 2010
    Accepted
    Subjects:Science > Physics
    Department:Faculty of Science > Physics
    Depositing user: Pure Administrator
    Date deposited:08 Dec 2021 16:51
    Last modified:09 Apr 2024 02:53
    URI:https://strathprints.strath.ac.uk/id/eprint/78836
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