Quantum walks and quantum search on graphene lattices

Foulger, Iain, Gnutzmann, Sven and Tanner, Gregor (2015) Quantum walks and quantum search on graphene lattices. Physical Review A, 91 (6). 062323/1-062323/15. ISSN 2469-9934

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Quantum walks have been very useful in developing search algorithms in quantum information, in particular for devising of spatial search algorithms. However, the construction of continuous-time quantum search algorithms in two-dimensional lattices has proved difficult, requiring additional degrees of freedom. Here, we demonstrate that a continuous-time quantum walk search is possible in two dimensions by changing the search topology to a graphene lattice, utilizing the Dirac point in the energy spectrum. This is made possible by making a change to standard methods of marking a particular site in the lattice. Various ways of marking a site are shown to result in successful search protocols. We further establish that the search can be adapted to transfer probability amplitude across the lattice between specific lattice sites thus establishing a line of communication between these sites.

Item Type: Article
RIS ID: https://nottingham-repository.worktribe.com/output/754156
Additional Information: ©2015 American Physical Society
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1103/PhysRevA.91.062323
Depositing User: Tanner, Prof Gregor
Date Deposited: 25 Sep 2017 08:25
Last Modified: 04 May 2020 17:10
URI: https://eprints.nottingham.ac.uk/id/eprint/46594

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