<p>The discovery of causal relations from observed data has attracted significant interest from disciplines such as economics, social sciences, and biology. In practical applications, knowledge of underlying systems is often unavailable, and real data are usually associated with nonlinear causal structures, which makes direct use of most conventional causality analysis methods difficult. This study proposes a novel quantum Peter-Clark (qPC) algorithm for causal discovery that requires no assumptions about underlying model structures. Based on conditional independence tests in the reproducing kernel Hilbert spaces characterized by quantum circuits, the proposed <i>qPC</i> algorithm can explore causal relations from observed data drawn from arbitrary distributions. We conducted extensive experiments on the fundamental graph components of causal structures, demonstrating that the qPC algorithm exhibits better performance, particularly with small sample sizes, compared to its classical counterpart. Furthermore, we proposed an optimization approach based on Kernel Target Alignment (KTA) for determining hyperparameters of quantum kernels. This method effectively reduced false positives in causal discovery, enabling more reliable inference. Our theoretical and experimental results demonstrate that the proposed quantum algorithm can facilitate robust inference in causal discovery, supporting it in regimes where classical algorithms typically fail to perform. In addition, the effectiveness of this method was validated using datasets on Boston housing prices, heart disease, and biological signaling systems as real-world applications. These findings highlight the potential of quantum circuit-based causal discovery methods in addressing practical challenges in small-sample scenarios where traditional approaches show significant limitations.</p>