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Many-body localization enables iterative quantum optimization.

Hanteng Wang1,2, Hsiu-Chung Yeh3, Alex Kamenev3,4

  • 1School of Physics and Astronomy, University of Minnesota, Minneapolis, MN, 55455, USA. wanghanteng@sjtu.edu.cn.

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This study introduces a quantum approximate optimization algorithm that improves problem-solving by cycling near the many-body localization (MBL) transition. The novel approach offers a scalable solution for complex discrete optimization challenges.

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Area of Science:

  • Quantum Computing
  • Condensed Matter Physics
  • Computational Complexity

Background:

  • Many discrete optimization problems are computationally intractable due to complex energy landscapes with numerous local minima.
  • Quantum computation offers a potential nhưng has shown limited success in addressing these hard problems.
  • The many-body localization (MBL) transition presents a unique physical phenomenon with potential applications in computation.

Purpose of the Study:

  • To develop a novel quantum approximate optimization algorithm (QAOA) for efficiently solving hard discrete optimization problems.
  • To leverage the properties of the many-body localization (MBL) transition, specifically its tricritical point, for improved optimization.
  • To demonstrate a scalable and systematically improvable approach to quantum optimization.

Main Methods:

  • The proposed algorithm involves repetitive cycling around the tricritical point of the many-body localization (MBL) transition.
  • Each cycle consists of 'quantum melting' of the glassy state via a first-order transition, followed by reentrance through a second-order MBL transition.
  • The optimization performance is enhanced by maintaining the reentrance path close to the tricritical point.

Main Results:

  • The algorithm systematically improves optimization outcomes by carefully navigating the MBL transition.
  • The computational time complexity scales algebraically with system size and required precision.
  • The critical exponents of the continuous MBL transition are found to be relevant to the algorithm's performance.

Conclusions:

  • The developed quantum approximate optimization algorithm offers a promising new direction for tackling computationally hard discrete optimization problems.
  • The algorithm's efficiency and scalability are linked to the fundamental physics of many-body localization transitions.
  • This work provides a theoretical framework for utilizing critical phenomena in quantum computation for practical applications.