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Microwave experiments simulating quantum search and directed transport in artificial graphene
Julian Böhm1, Matthieu Bellec1, Fabrice Mortessagne1
1Laboratoire de Physique de la Matière Condensée, UMR 7336, Université Nice Sophia Antipolis, CNRS, Parc Valrose, 06100 Nice, France.
Physical Review Letters
|April 4, 2015
Summary
This study demonstrates a novel wave search algorithm using artificial graphene, achieving efficient spatial searching by resonating localized states with lattice properties near Dirac points. The findings show potential for faster information retrieval in complex systems.
Area of Science:
- Quantum computing and information science
- Condensed matter physics
- Wave phenomena
Background:
- Quantum search algorithms offer speedups over classical methods, with spatial searches on lattices being a key extension.
- Theoretical work suggests searches are possible in 2D and 3D lattices with Dirac points, particularly in tight-binding models.
- Dirac points in lattice spectra are crucial for enabling efficient quantum searches.
Purpose of the Study:
- To experimentally implement and validate wave search algorithms and directed wave transport.
- To demonstrate these concepts in a graphene lattice arrangement, specifically artificial graphene.
- To investigate the scaling behavior of these search algorithms.
Main Methods:
- Utilizing classical waves in a microwave setup with dielectric resonators arranged in a honeycomb lattice (artificial graphene).
- Implementing a proof-of-principle experiment to achieve resonance between localized search states and extended lattice states.
- Focusing on the energy region near Dirac points, characterized by low spectral density.
- Experimentally examining the scaling behavior using linear chains.
Main Results:
- Successful implementation of wave search algorithms and directed wave transport in artificial graphene.
- Demonstration of localized states resonating with extended lattice states near Dirac points.
- Experimental validation of the theoretical predictions for searchability in lattices with Dirac points.
- Investigation into the scaling properties of the implemented search algorithms.
Conclusions:
- The experiment provides a proof of principle for wave search algorithms in artificial graphene structures.
- Resonating localized states with extended lattice states near Dirac points is an effective strategy for spatial searching.
- The findings support the potential of using lattice properties, like Dirac points, for enhanced search capabilities in classical and quantum systems.
