Microwave Experiments Simulating Quantum Search and Directed Transport in Artificial Graphene

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.

5 pages, 5 figures, supplementary material: 4 videos

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• Multiparameter estimation of continuous-time Quantum Walk Hamiltonians through Machine Learning
• A classical limit of Grover's algorithm induced by dephasing: Coherence vs entanglement
• The electronic structure and intervalley coupling of artificial and genuine graphene superlattice
• Staggered Quantum Walk on Hexagonal Lattices
• Unifying quantum spatial search, state transfer and uniform sampling on graphs: simple and exact
• Stern-Gerlach splitters for lattice quasispin
• Dimerized Decomposition of Quantum Evolution on an Arbitrary Graph
• Temporal nonclassicality in continuous-time quantum walks