  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.
