Quantum Dynamics of Optimization Problems
Abstract
In this letter, by establishing the Schr\"odinger equation of the optimization problem, the optimization problem is transformed into a constrained state quantum problem with the objective function as the potential energy. The mathematical relationship between the objective function and the wave function is established, and the quantum interpretation of the optimization problem is realized. Under the black box model, the Schr\"odinger equation of the optimization problem is used to establish the kinetic equation, i.e., the Fokker-Planck equation of the time evolution of the optimization algorithm, and the basic iterative structure of the optimization algorithm is given according to the interpretation of the Fokker-Planck equation. The establishment of the Fokker-Planck equation allows optimization algorithms to be studied using dynamic methods and is expected to become an important theoretical basis for algorithm dynamics.
Keywords
Cite
@article{arxiv.2012.03312,
title = {Quantum Dynamics of Optimization Problems},
author = {Peng Wang and Gang Xin and Yuwei Jiao},
journal= {arXiv preprint arXiv:2012.03312},
year = {2021}
}
Comments
We corrected some errors in the theoretical part of the paper, especially the quantum interpretation part corresponding to the approximation of the objective function. At the same time, we have added some comparative experiments and quantum effect experiments of skeleton algorithms, and hope to publish them in a new paper (arXiv:2106.13927)