Experiments on 'quantum' search and directed transport in microwave artificial graphene

Description

A series of quantum search algorithms has been proposed recently providing an algebraic speed-up compared to classical search algorithms from N to N where N is the number of items in the search space. In particular, devising searches on regular lattices have become popular 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 possess 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 in 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. We furthermore investigate the scaling behavior experimentally using linear chains.

Abstract

International audience

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