Although intervention practices like mindfulness meditation have proven effective in treating psychosis, there is no clarity on the mechanism of information propagation in the brain. In this study, we formulated a network optimization problem and searched for the optimal solution using Digital Annealer developed by Fujitsu Ltd. This is inspired by quantum computing and is effective in solving large-scale combinatorial optimization problems to find the information propagation pathway in the brain that contributes to the realization of mindfulness. Specifically, we defined the optimal network state as the state of the brain network that is considered to be associated with the mindfulness state. We formulated the problem into two network optimization problems — the minimum vertex-cover problem and the maximum-flow problem — to search for the information propagation pathway that is important for realizing the state. In the minimum vertex-cover problem, we aimed to identify brain regions that are important for the realization of the mindfulness state, and identified eight regions, including four that were suggested to be consistent with previous studies. We formulated the problem as a maximum-flow problem to identify the information propagation pathways in the brain that contribute to the activation of these four identified regions. As a result, approximately 30% of the connections in the brain network structure of this study were identified, and the pathway with the highest flow rate was considered to characterize the bottom-up emotion regulation during mindfulness. The findings of this study could be useful for more direct interventions in the context of mindfulness, which are being investigated by neurofeedback and other methods. This is because existing studies have not clarified the information propagation pathways that contribute to the realization of the brain network states that characterize mindfulness states. In addition, this approach may be useful as a methodology to identify information propagation pathways in the brain that contribute to the realization of higher-order human cognitive activities, such as mindfulness, within large-scale brain networks.