Microwave Experiments Simulating Quantum Search and Directed Transport in Artificial Graphene

TL;DR

This paper demonstrates wave search algorithms and directed transport in an artificial graphene lattice using microwave experiments, providing a proof of principle for quantum search techniques in physical systems with Dirac points.

Contribution

It presents the first experimental implementation of wave search algorithms and directed transport in a microwave artificial graphene lattice, validating theoretical predictions.

Findings

Successful wave search in a microwave honeycomb lattice.

Observation of directed wave transport near Dirac points.

Experimental scaling behavior analysis in linear chains.

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.