The discovery of causal relationships from observed data has attracted significant interest from disciplines such as economics, social sciences, epidemiology, and biology. In practical applications, considerable knowledge of the underlying systems is often unavailable, and real data are often associated with nonlinear causal structures, which make the direct use of most conventional causality analysis methods difficult. This study proposes a novel quantum Peter-Clark (qPC) algorithm for causal discovery that does not assume any underlying model structures. Based on the independence conditional tests in a class of reproducing kernel Hilbert spaces characterized by quantum circuits, the proposed qPC algorithm can explore causal relationships from the observed data drawn from arbitrary distributions. We conducted systematic experiments on fundamental graph parts of causal structures, demonstrating that the qPC algorithm exhibits a significantly better performance, particularly with smaller sample sizes compared to its classical counterpart. Furthermore, we proposed a novel optimization approach based on Kernel Target Alignment (KTA) for determining hyperparameters of quantum kernels. This method effectively reduced the risk of false positives in causal discovery, enabling more reliable inference. Our theoretical and experimental results demonstrate that the proposed quantum algorithm can empower classical algorithms for robust and accurate inference in causal discovery, supporting them in regimes where classical algorithms typically fail. Additionally, the effectiveness of this method was validated using the Boston Housing dataset as a real-world application. These findings demonstrate the new potential of quantum circuit-based causal discovery methods in addressing practical challenges, particularly in small-sample scenarios where traditional approaches have shown limitations.

本研究针对在小样本情况下因果关系发现的困难，提出了一种新的量子彼得-克拉克（qPC）算法，该算法不依赖任何假设的模型结构。通过在量子电路特征化的再生核希尔伯特空间中进行条件独立性检验，qPC算法在小样本情况下表现出显著优于传统方法的性能，进一步通过基于核目标对齐（KTA）的方法优化量子核的超参数，从而降低了假阳性的风险，强化了因果推断的可靠性。 

量子增强的小样本因果发现