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.

基于热力学的统计和随机分析已经成为随机全局优化的主要分析框架。最近，出现了用于全局优化的量子退火或量子隧穿算法，我们需要一个新的研究框架来研究全局优化算法。在本文中，我们基于薛定谔方程提供了基于量子化的优化的分析，以揭示量子力学中的哪种性质使全局优化成为可能。我们证明了基于量子化的优化中由薛定谔方程推导出的隧穿效应能够逃离局部最小值。此外，我们确认这种隧穿效应是包含在以量子力学为基础的全局优化中的相同性质。对于标准的多模态基准函数的实验表明了所提分析的有效性。