Quantization-based Optimization with Perspective of Quantum Mechanics

• URL: http://arxiv.org/abs/2308.11594v3
• Date: Wed, 18 Oct 2023 04:02:41 GMT
• Title: Quantization-based Optimization with Perspective of Quantum Mechanics
• Authors: Jinwuk Seok, and Changsik Cho
• Abstract summary: We provide the analysis for quantization-based optimization based on the Schr"odinger equation. We show that the tunneling effect derived by the Schr"odinger equation in quantization-based optimization enables to escape of a local minimum.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Statistical and stochastic analysis based on thermodynamics has been the main analysis framework for stochastic global optimization. Recently, appearing quantum annealing or quantum tunneling algorithm for global optimization, we require a new researching framework for global optimization algorithms. In this paper, we provide the analysis for quantization-based optimization based on the Schr\"odinger equation to reveal what property in quantum mechanics enables global optimization. We present that the tunneling effect derived by the Schr\"odinger equation in quantization-based optimization enables to escape of a local minimum. Additionally, we confirm that this tunneling effect is the same property included in quantum mechanics-based global optimization. Experiments with standard multi-modal benchmark functions represent that the proposed analysis is valid.

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