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.
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.
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.
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.
As image datasets grow in scale and complexity, classical convolutional neural networks (CNNs) increasingly face limitations in computational efficiency, scalability, and generalisation in low-data regimes. Quantum machine learning (QML) offers a promising alternative, with quantum convolutional neural networks (QCNNs) exploiting quantum parallelism and entanglement for feature extraction. This paper introduces the Novel Quantum Convolutional Neural Network (No-QCNN), which differs from recent hybrid QCNN/QCQ-CNN architectures by employing an end-to-end quantum convolution-pooling pipeline without inserting an intermediate classical CNN block. No-QCNN is a hybrid quantum-classical model that employs a variational quantum classifier (VQC) optimised via the COBYLA algorithm and is designed for binary and multiclass classification of low-resolution colour images on near-term quantum devices. A key innovation is a problem-specific quantum feature map that pre-processes each image into a structured three-dimensional block-matrix representation, jointly encoding pixel colour (R, G, B) and spatial position before mapping this information into a hierarchical ZZFeatureMap. This encoding captures spatial-chromatic correlations at shallow circuit depth, making it compatible with noisy intermediate-scale quantum (NISQ) constraints. The model is implemented using IBM-Qiskit on a local quantum simulator and benchmarked against a classical CNN. For a six-class classification task on a 50-image dataset, No-QCNN achieves a validation accuracy of 82.05%, substantially outperforming the classical CNN's 40.00%, indicating improved generalisation and reduced overfitting in low-data, multiclass settings. Conversely, for a simpler binary classification task, the classical CNN achieves perfect validation accuracy of 100%, surpassing the No-QCNN's 89.7%. We further observe that No-QCNN performance declines with increasing dataset size and training time due to limited circuit expressibility, data-encoding overhead, and finite-sampling noise inherent to NISQ models. Overall, these results position No-QCNN as a complementary framework best suited to low-data, correlation-rich classification tasks, defining a realistic niche for quantum-enhanced artificial vision and quantum perception in the NISQ era.
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.
Convolutional Neural Networks (CNNs) are extensively utilized for image classification due to their ability to exploit data correlations effectively. However, traditional CNNs encounter several challenges, including limitations in accuracy improvement, computational efficiency, explain ability, and generalization. As data dimensionality or model complexity increases, CNNs often become more difficult to train efficiently, leading to slower processing times. To overcome these challenges, Quantum Convolutional Neural Networks (QCNNs) offer a promising quantum-based approach to enhance existing models, particularly by improving training efficiency and reducing processing times. This paper provides a comparative analysis of classical CNNs and a novel quantum circuit architecture tailored for image-based tasks. The analysis emphasizes the adaptability and potential of quantum circuits to enhance feature extraction, recognition accuracy, and processing efficiency.We applied various QCNN architectures to the Chinese-MNIST dataset and compared their performance with traditional CNN models. Although QCNNs achieved slightly lower accuracy, they demonstrated significantly greater stability. These findings high- light QCNNs’ potential to overcome the computational limitations of conventional deep learning, offering a promising pathway for quantum-enhanced solutions in computer vision. Future work will focus on refining quantum circuit designs, developing hybrid quantum-classical models, and extending QCNN applications to larger and more diverse datasets.
In the field of image processing, a well-known model is the Convolutional Neural Network, or CNN. The unique benefit that sets this model apart is its exceptional ability to use the correlation information included in the data. Even with their amazing accomplishment, conventional CNNs could have trouble improving further in terms of generalization, accuracy, and computing economy. However, it could be challenging to train CNN correctly and process information quickly if the model or data dimensions are too large. This is since it will cause the data processing to lag. The Quantum Convolutional Neural Network, or QCNN for short, is a novel proposed quantum solution that might either enhance the functionality of an existing learning model or solve a problem requiring the combination of quantum computing with CNN. To highlight the flexibility and versatility of quantum circuits in improving feature extraction capabilities, this paper compares deep quantum circuit architecture designed for image-based tasks with classical Convolutional Neural Networks (CNNs) and a novel quantum circuit architecture. The covidx-cxr4 dataset was used to train quantum-CNN models, and their results were compared against those of other models. The results show that when paired with innovative feature extraction methods, the suggested deep Quantum Convolutional Neural Network (QCNN) outperformed the conventional CNN in terms of processing speed and recognition accuracy. Even though it required more processing time, QCNN outperformed CNN in terms of recognition accuracy. When training on the covidx-cxr4 dataset, this dominance becomes much more apparent, demonstrating how deeper quantum computing has the potential to completely transform image classification problems.