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Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light
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Anderson localization makes adiabatic quantum optimization fail.

Boris Altshuler1, Hari Krovi, Jérémie Roland

  • 1Department of Physics, Columbia University, New York, NY 10027, USA. bla@phys.columbia.edu

Proceedings of the National Academy of Sciences of the United States of America
|July 10, 2010
PubMed
Summary
This summary is machine-generated.

Adiabatic quantum optimization, a method for solving complex computational problems, is hindered by small energy gaps. These gaps, similar to Anderson localization, cause quantum computers to get trapped, limiting their effectiveness for NP-complete problems.

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Area of Science:

  • Quantum Computing
  • Computer Science
  • Statistical Mechanics

Background:

  • NP-complete problems are a major challenge in computer science.
  • Adiabatic quantum optimization offers a quantum approach to these problems.
  • The efficiency of adiabatic quantum optimization is limited by spectral gaps.

Purpose of the Study:

  • To analyze the statistics of spectral gaps in adiabatic quantum optimization.
  • To investigate the implications of these gaps for solving NP-complete problems.

Main Methods:

  • Analysis of gap statistics using concepts from quantum disordered systems.
  • Application of Anderson localization phenomena to quantum computing Hamiltonians.
  • Study of large random instances of NP-complete problems.

Main Results:

  • Exponentially small spectral gaps emerge near the end of the adiabatic algorithm.
  • A phenomenon analogous to Anderson localization is responsible for these small gaps.
  • These small gaps lead to the system becoming trapped in local minima.

Conclusions:

  • Adiabatic quantum optimization is shown to fail for large random NP-complete problems.
  • The findings suggest limitations in using current adiabatic quantum optimization techniques.
  • Further research is needed to overcome the spectral gap limitations.