  We numerically test an optimization method for deep neural networks (DNNs)
using quantum fluctuations inspired by quantum annealing. For efficient
optimization, our method utilizes the quantum tunneling effect beyond the
potential barriers. The path integral formulation of the DNN optimization
generates an attracting force to simulate the quantum tunneling effect. In the
standard quantum annealing method, the quantum fluctuations will vanish at the
last stage of optimization. In this study, we propose a learning protocol that
utilizes a finite value for quantum fluctuations strength to obtain higher
generalization performance, which is a type of robustness. We demonstrate the
performance of our method using two well-known open datasets: the MNIST dataset
and the Olivetti face dataset. Although computational costs prevent us from
testing our method on large datasets with high-dimensional data, results show
that our method can enhance generalization performance by induction of the
finite value for quantum fluctuations.
