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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 Grovers 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.
The quantum Hall effect is a remarkable manifestation of quantized transport in a two-dimensional electron gas. Given its technological relevance, it is important to understand its development in realistic nanoscale devices. In this work we present h
We measure graphene coplanar waveguides from direct current (DC) to 13.5GHz and show that the apparent resistance (in the presence of parasitic impedances) has an quadratic frequency dependence, but the intrinsic conductivity (without the influence o
Previous studies of photon-assisted tunneling through normal-metal-insulator-superconductor junctions have exhibited potential for providing a convenient tool to control the dissipation of quantum-electric circuits in-situ. However, the current liter
The quantum localization in the quantum Hall regime is revisited using Graphene monolayers with accurate measurements of the longitudinal resistivity as a function of temperature and current. We experimentally show for the first time a cross-over fro
We discuss control of the quantum-transport properties of a mesoscopic device by connecting it in a coherent feedback loop with a quantum-mechanical controller. We work in a scattering approach and derive results for the combined scattering matrix of