Unlocking Nonlinear Dynamics in Fuzzy Cognitive Maps: A Quantum Kernel Approach

Fuzzy cognitive maps (FCMs) offer an interpretable framework for causal modeling but struggle to represent nonlinear relationships in high‐dimensional data. This work proposes the kernelized quantum FCM (QKFCM), a hybrid quantum–classical model that integrates variational quantum kernels into the FCM architecture. By extending classical kernelized FCMs and replacing fixed radial basis function kernels with a trainable quantum kernel based on a shallow data reuploading feature map, the model enables task‐adaptive similarity learning in a high‐dimensional Hilbert space. Experimental evaluation on multiple benchmark datasets of diverse complexity demonstrates that the QKFCM consistently achieves lower training loss (up to 54% reduction) and improved training stability compared to classical FCMs, while yielding competitive or superior classification accuracy (up to 7% improvement) on high‐dimensional and large‐scale datasets. These results highlight the effectiveness of quantum‐enhanced kernels for scalable and interpretable hybrid learning.