Microwave experiments simulating quantum search and directed transport in artificial graphene

B�hm, Julian; Bellec, Matthieu; Mortessagne, Fabrice; Kuhl, Ulrich; Barkhofen, Sonja; Gehler, Stefan; St�ckmann, Hans-J�rgen; Foulger, Iain; Gnutzmann, Sven; Tanner, Gregor

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.

Citation

Böhm, J., Bellec, M., Mortessagne, F., Kuhl, U., Barkhofen, S., Gehler, S., Stöckmann, H.-J., Foulger, I., Gnutzmann, S., & Tanner, G. (2015). Microwave experiments simulating quantum search and directed transport in artificial graphene. Physical Review Letters, 114(11), Article 110501. https://doi.org/10.1103/PhysRevLett.114.110501

• Journal Article Type: Article
• Acceptance Date: Sep 8, 2014
• Publication Date: Mar 17, 2015
• Deposit Date: Sep 25, 2017
• Publicly Available Date: Sep 25, 2017
• 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
• DOI: https://doi.org/10.1103/PhysRevLett.114.110501
• Public URL: https://nottingham-repository.worktribe.com/output/747462
• Publisher URL: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.110501
• Additional Information: ©2015 American Physical Society.
• Contract Date: Sep 25, 2017