Grover Search as a Naturally Occurring Phenomenon

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.