Position-dependent and cooperative quantum Parrondo walks

David Bulger*, James Freckleton, Jason Twamley

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    14 Citations (Scopus)
    6 Downloads (Pure)


    This work is a study on quantum computational formulations of Parrando walks, that is, positively trending random walks formed as combinations of negatively trending random walks. We reanalyse the position-dependent walk proposed by Košík et al (2007 J. Mod. Opt. 54 2275), correcting the parameter choices in that paper to achieve the Parrando effect. We also devise a quantum analogue of the cooperative Parrando walk of Toral (2002 Fluct. Noise Lett. 2 L305), in which it is the interaction between multiple participants, rather than position-dependence, that allows the Parrando effect to occur. We give a general formulation of a quantum analogue of the classical walk of Toral (2002 Fluct. Noise Lett. 2 L305), and demonstrate the Parrando effect numerically. Lastly, we highlight a qualitative difference in asymptotic behaviour between quantum Parrando walks and their classical counterparts. In particular, we draw attention to an intuitive but unreliable assumption, based on classical random walks, which may pose extra challenges for applications of the Parrando effect in the quantum setting seeking to separate or classify data or particles.

    Original languageEnglish
    Article number093014
    Pages (from-to)1-16
    Number of pages16
    JournalNew Journal of Physics
    Publication statusPublished - 12 Sep 2008

    Bibliographical note

    Copyright 2008 IOP Publishing Ltd from New journal of physics. This material is posted here with the permission of IOP Publishing Ltd and the authors. Use of this material is permitted for personal, research and non-commercial uses. Further information regarding the copyright applicable to this article can be viewed at http://www.iop.org/EJ/abstract/1367-2630/10/9/093014


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