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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing...
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Related Experiment Video

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Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices
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Quantum search on graphene lattices.

Iain Foulger1, Sven Gnutzmann1, Gregor Tanner1

  • 1School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.

Physical Review Letters
|March 4, 2014
PubMed
Summary

We developed a continuous-time quantum search algorithm for graphene lattices. This quantum search efficiently finds marked sites faster than classical methods, also enabling state transfer.

Area of Science:

  • Quantum computing
  • Condensed matter physics
  • Materials science

Background:

  • Quantum search algorithms offer speedups over classical searches.
  • Graphene's unique electronic properties, particularly near the Dirac point, are of significant interest.
  • Implementing quantum algorithms on physical systems remains a key challenge.

Purpose of the Study:

  • To present a continuous-time quantum search algorithm specifically designed for a graphene lattice.
  • To demonstrate an efficient quantum search implementation on a two-dimensional lattice.
  • To explore the potential applications of this algorithm beyond search, such as state transfer.

Main Methods:

  • Utilizing the linear dispersion relation of graphene near the Dirac point.
  • Developing a continuous-time quantum walk on a graphene lattice model.

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  • Analyzing the performance of the quantum search against classical search algorithms.

    • Main Results:

    • The proposed quantum search algorithm demonstrates faster searching capabilities on a graphene lattice compared to classical approaches.
    • The algorithm successfully leverages the unique electronic structure of graphene.
    • The study confirms the algorithm's applicability for quantum state transfer and communication.

    Conclusions:

    • A novel continuous-time quantum search algorithm for graphene lattices has been successfully developed and presented.
    • This algorithm offers a significant speed advantage for searching marked sites on a 2D graphene lattice.
    • The findings open avenues for quantum information processing and communication applications utilizing graphene's properties.