Many-body localization enables iterative quantum optimization

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.