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Grover Search as a Naturally Occurring Phenomenon.

Mathieu Roget1, Stéphane Guillet1, Pablo Arrighi2

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Fermions with 1/2 spin can act as a Grover search, naturally finding topological defects in materials. This quantum walk (QW) behavior offers new ways to explore material properties without specific search algorithms.

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Area of Science:

  • Quantum physics
  • Condensed matter physics
  • Quantum computing

Background:

  • Discrete-time quantum walks (QWs) model particle evolution on lattices.
  • Certain QWs can mimic the Dirac equation, describing free propagation of 1/2-spin fermions.
  • Topological defects in materials are areas of interest for novel electronic properties.

Purpose of the Study:

  • To investigate if 1/2-spin fermions, via quantum walks, can naturally perform a search for topological defects.
  • To explore the potential of using freely propagating particles for defect detection.
  • To identify novel quantum computing applications for quantum walk search.

Main Methods:

  • Studied two specific Dirac quantum walks on square and triangular lattices.
  • Employed numerical simulations to observe particle behavior.
  • Analyzed walker localization and probability around defects.

Main Results:

  • Quantum walks of 1/2-spin fermions demonstrated Grover search-like behavior.
  • Walker localization around topological defects occurred in O(sqrt[N]) steps.
  • Probability of finding defects was O(1/logN).
  • This occurs naturally without a specific oracle step.

Conclusions:

  • 1/2-spin fermions can naturally search for topological defects in materials using quantum walks.
  • This finding suggests practical implementations using freely propagating particles.
  • Opens new avenues for quantum computing applications, focusing on topological properties.