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.
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.
Fuzzy Cognitive Maps (FCMs) were originally introduced as a framework for modeling complex systems and have since evolved into powerful pattern recognition models capable of capturing intricate causal relationships within data. Despite their potential, the application of FCMs in computer vision remains limited, primarily because they are not inherently designed to process high-dimensional visual representations and therefore rely on external feature extraction methods. In this work, we propose a quantum-enhanced architecture for image classification, termed QFCM-QCNN, in which a Quantum Convolutional Neural Network (QCNN) extracts compact feature representations that are subsequently processed by a Quantum Fuzzy Cognitive Map (QFCM) head for final prediction. To validate the proposed quantum approach, we also implement its classical counterpart, FCM-CNN, where a conventional CNN backbone feeds a differentiable FCM head. Both architectures are trained end-to-end via backpropagation through differentiable FCM and QFCM layers, enabling a unified learning framework that maps images directly to predictions. The proposed models are evaluated on ten medical imaging datasets using standard classification metrics as well as Degree of Confidence (DoC) prediction scores. Experimental results show that QFCM-QCNN achieves classification performance comparable to FCM-CNN-64D across most benchmarks while operating on only 8-dimensional feature representations instead of 64-dimensional ones, with 87.5% reduction in feature dimensionality. QFCM-QCNN produces the highest prediction confidence on seven out of the ten datasets.
As Quantum Machine Learning (QML) continues to mature, there is an increasing demand for novel architectures that broaden the ways quantum models learn from data, represent knowledge, and perform inference. In this work, we address this need by introducing a hybrid Quantum Fuzzy Cognitive Map (QFCM) model for pattern recognition, in which the core arithmetic operations of the classical Fuzzy Cognitive Map (FCM) inference mechanism are replaced by a parameterized quantum circuit. The proposed model preserves the structural foundations and causal inference principles of classical FCMs, while leveraging quantum computation to model and process interactions among concepts. The proposed QFCM was evaluated on six benchmark datasets, demonstrating competitive performance and achieving a 9.37% increase in prediction confidence compared to the classical FCM. Overall, this work contributes to the growing QML ecosystem by embedding the fundamental principles of FCMs into a quantum circuit–based formulation, thereby extending their representational and computational capabilities.
Quantum Machine Learning (QML) has emerged as a groundbreaking approach within the rapidly evolving field of Quantum Computing (QC), leveraging quantum phenomena such as superposition and entanglement to surpass classical models in representational power, optimization speed, and computational efficiency. This paradigm shift paves the way for transformative applications across diverse domains while simultaneously confronting the inherent complexities of quantum mechanics and hardware limitations. Among the powerful computational models used for decision-making and pattern recognition, Fuzzy Cognitive Maps (FCMs) have demonstrated exceptional capabilities in modeling complex systems. Researchers have continually refined the traditional FCM framework by integrating novel features to enhance its effectiveness. However, despite its potential, the integration of quantum computing with FCMs remains largely unexplored, with only a limited number of studies addressing this intersection. This work provides a comprehensive theoretical algorithmic evaluation of the integration between Quantum Computing and FCMs, investigating potential advancements, challenges, and novel applications. Additionally, we present a systematic review of existing research on Quantum Fuzzy Cognitive Maps (QFCMs), offering new insights into their theoretical foundations and future directions. By bridging the gap between quantum computing and cognitive modeling, this study aims to unlock new possibilities for intelligent decision-making systems in the quantum era.
Quantum kernel methods are a promising branch of quantum machine learning, but their per- formance across data types and encoding choices remains incompletely understood. To address this gap, we developed an algorithmic framework for variational quantum kernels utilizing resource- efficient ansätze for complex classification tasks and introduced a parameter scaling technique to accelerate convergence. We conducted a comprehensive benchmark of this framework on eight chal- lenging, real-world and high-dimensional datasets covering tabular, image, time series, and graph data. Our results show that the proposed quantum kernel demonstrated competitive classification accuracy compared to standard classical kernels in classical simulation, such as the radial basis function (RBF) kernel. This work demonstrates that properly designed quantum kernels can func- tion as versatile, high-performance tools, laying a foundation for quantum-enhanced applications in machine learning. Further research is needed to fully assess the practical performance of quantum methods.
Remote sensing applications increasingly rely on multimodal Earth observation data to improve land-cover classification. However, conventional kernel methods may struggle to capture complex nonlinear relationships between modalities such as synthetic aperture radar (SAR) and multispectral optical imagery. In this work, we investigate a quantum kernel learning framework based on data reuploading feature maps for fused Sentinel-1 and Sentinel-2 data. Input features are first reduced using Tucker decomposition and mapped into quantum states via a parameterized multi-layer circuit consisting of non-commuting rotations and entangling operations. The feature map repeatedly encodes classical data across multiple layers with layer-specific scaling, enabling richer representations than shallow embeddings. Pairwise overlaps between quantum states define a kernel matrix used in a classical support vector machine for classification. We benchmark the proposed quantum kernel against classical linear, polynomial, and radial basis function kernels using multiple evaluation metrics, including accuracy, macro F1-score, and Matthews correlation coefficient. Results indicate that deeper quantum feature maps achieve competitive performance but do not consistently outperform well-tuned classical kernels. These findings highlight the importance of feature map design and parameterization in quantum kernel methods.
Abstract Quantum kernel methods have emerged as a powerful paradigm for extending classical machine learning into high-dimensional quantum Hilbert spaces, offering potential advantages in complex, nonlinear pattern recognition. However, their performance on near-term quantum devices remains constrained by circuit depth, noise sensitivity, and suboptimal parameterization of quantum feature maps. This paper introduces an Adaptive Quantum Kernel Optimization (AQKO) framework that integrates circuit-level adaptability, hybrid optimization, and regularization to enhance both expressivity and robustness in quantum kernel learning. The proposed method employs Adaptive Quantum Feature Maps (AQFM) that dynamically adjust rotation and phase parameters through a hybrid gradient-based optimization routine, reducing overfitting and improving generalization. Furthermore, a regularized quantum kernel objective is formulated to stabilize eigenvalue spectra under Noisy Intermediate-Scale Quantum (NISQ) conditions. Extensive experiments on nonlinear benchmark datasets — including Moons , Circles , and Iris — demonstrate that AQKO achieves up to 8.5% higher classification accuracy and 32% lower circuit depth compared to static quantum kernels. Hardware validation using IBM’s ibmq_quito device confirms AQKO’s resilience under depolarizing noise (p = 0.02) with a 41% error mitigation efficiency gain. These findings highlight AQKO’s potential as a scalable and noise-tolerant foundation for real-world quantum-enhanced learning, bridging the gap between theoretical quantum kernel models and practical NISQ implementations.