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Microwave experiments simulating quantum search and directed transport in artificial graphene

Böhm, Julian; Bellec, Matthieu; Mortessagne, Fabrice; Kuhl, Ulrich; Barkhofen, Sonja; Gehler, Stefan; Stöckmann, Hans-Jürgen; Foulger, Iain; Gnutzmann, Sven; Tanner, Gregor

Authors

Julian Böhm

Matthieu Bellec

Fabrice Mortessagne

Ulrich Kuhl

Sonja Barkhofen

Stefan Gehler

Hans-Jürgen Stöckmann

Iain Foulger iain.foulger2004@gmail.com

GREGOR TANNER GREGOR.TANNER@NOTTINGHAM.AC.UK
Professor of Applied Mathematics



Abstract

A series of quantum search algorithms have been proposed recently providing an algebraic speedup compared to classical search algorithms from N to \sqrt{N}, where N is the number of items in the search space. In particular, devising searches on regular lattices has become popular in extending Grover’s original algorithm to spatial searching. Working in a tight-binding setup, it could be demonstrated, theoretically, that a search is possible in the physically relevant dimensions 2 and 3 if the lattice spectrum possesses Dirac points. We present here a proof of principle experiment implementing wave search algorithms and directed wave transport in a graphene lattice arrangement. The idea is based on bringing localized search states into resonance with an extended lattice state in an energy region of low spectral density—namely, at or near the Dirac point. The experiment is implemented using classical waves in a microwave setup containing weakly coupled dielectric resonators placed in a honeycomb arrangement, i.e., artificial graphene. Furthermore, we investigate the scaling behavior experimentally using linear chains.

Journal Article Type Article
Publication Date Mar 17, 2015
Journal Physical Review Letters
Print ISSN 0031-9007
Electronic ISSN 1079-7114
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 114
Issue 11
Article Number 110501
APA6 Citation Böhm, J., Bellec, M., Mortessagne, F., Kuhl, U., Barkhofen, S., Gehler, S., …Tanner, G. (2015). Microwave experiments simulating quantum search and directed transport in artificial graphene. Physical Review Letters, 114(11), https://doi.org/10.1103/PhysRevLett.114.110501
DOI https://doi.org/10.1103/PhysRevLett.114.110501
Publisher URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.110501
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information ©2015 American Physical Society.

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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