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.

翻译：基于热力学的统计与随机分析一直是随机全局优化的主流分析框架。随着近期量子退火或量子隧穿算法在全局优化中的出现，我们亟需构建新的全局优化算法研究框架。本文基于薛定谔方程对量化优化方法进行分析，以揭示量子力学中何种特性赋予了全局优化能力。研究表明，量化优化中由薛定谔方程导出的隧穿效应能够使算法逃离局部极小值。此外，我们证实该隧穿效应与基于量子力学的全局优化方法具有相同的本质特性。基于标准多峰基准函数的实验验证了所提分析方法的有效性。