In this paper, we propose a novel quantum Peter-Clark (qPC) algorithm for discovering causal relationships in real-world data with non-linear causal structures. Unlike existing causal analysis methods that require assumptions about the underlying model structure, the qPC algorithm explores causal relationships from observation data drawn from random distributions based on conditional independence tests in the reproducible kernel Hilbert space characterized by quantum circuits. Experimental results show that the qPC algorithm outperforms existing algorithms, especially in small sample sizes, and enables reliable inference by effectively reducing false positives through a novel optimization approach based on Kernel Target Alignment (KTA). We verify its effectiveness through practical application studies using Boston housing prices, heart disease, and biological signaling system datasets.
