Today artificial neural networks are applied in various fields - engineering, data analysis, robotics. While they represent a successful tool for a variety of relevant applications, mathematically speaking they are still far from being conclusive. In particular, they suffer from being unable to find the best configuration possible during the training process (local minimum problem). In this paper, we focus on this issue and suggest a simple, but effective, post-learning strategy to allow the search for improved set of weights at a relatively small extra computational cost. Therefore, we introduce a novel technique based on analogy with quantum effects occurring in nature as a way to improve (and sometimes overcome) this problem. Several numerical experiments are presented to validate the approach.