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 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.
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.
Quantum Machine Learning (QML) represents a paradigm shift in computational approaches, offering the potential to surpass classical machine learning algorithms in complex data analysis. This paper investigates the application of QML to the identification of non-linear patterns, focusing on leveraging quantum states to uncover hidden correlations and anomalies within datasets. We propose a novel framework that utilizes quantum entanglement and superposition to enhance pattern recognition capabilities. The core mechanism centers on harnessing the inherent properties of quantum states to provide a fundamentally different approach to data analysis, specifically designed to address the challenges posed by non-linear data. This research explores the potential of quantum algorithms to improve pattern detection and anomaly detection, and investigates the influence of quantum characteristics on pattern recognition processes. The paper will detail the implementation of a quantum model for pattern recognition, discuss its performance compared to classical models, and explore the fundamental principles underpinning its effectiveness. We argue that this work introduces a new perspective on pattern recognition, offering the possibility of enhanced accuracy, robustness, and the ability to identify subtle patterns within complex datasets. The core claim posits that quantum machine learning can effectively identify and interpret non-linear patterns, offering significant advantages over conventional methods.
Machine Learning (ML) has been widely applied across numerous domains due to its ability to automatically identify informative patterns from data for various tasks. The availability of large-scale data and advanced computational power enables the development of sophisticated models and training strategies, leading to state-of-the-art performance, but it also introduces substantial challenges. Quantum Computing (QC), which exploits quantum mechanisms for computation, has attracted growing attention and significant global investment as it may address these challenges. Consequently, Quantum Machine Learning (QML), the integration of these two fields, has received increasing interest, with a notable rise in related studies in recent years. We are motivated to review these existing contributions regarding quantum circuit-based learning models for classical data analysis and highlight the identified potentials and challenges of this technique. Specifically, we focus not only on QML models, both kernel-based and neural network-based, but also on recent explorations of their integration with classical machine learning layers within hybrid frameworks. Moreover, we examine both theoretical analysis and empirical findings to better understand their capabilities, and we also discuss the efforts on noise-resilient and hardware-efficient QML that could enhance its practicality under current hardware limitations. In addition, we cover several emerging paradigms for advanced quantum circuit design and highlight the adaptability of QML across representative application domains. This study aims to provide an overview of the contributions made to bridge quantum computing and machine learning, offering insights and guidance to support its future development and pave the way for broader adoption in the coming years.
The integration of quantum computing principles with classical deep learning architectures has emerged as a promising direction for advancing image recognition systems beyond the limitations of purely classical convolutional neural networks (CNNs). This study proposes and analyzes a hybrid quantum–classical deep learning framework based on quanvolutional neural network (QNN) principles, where quantum circuits are embedded within convolutional feature extraction layers to enhance representation capability. The research investigates how quantum-enhanced filters, particularly quanvolutional layers, contribute to improved feature diversity, non-linear transformation capacity, and classification accuracy in image recognition tasks. Building upon established convolutional architectures and quantum machine learning theories, the proposed framework integrates quantum random circuit encoding with classical deep neural networks to evaluate performance gains in comparison to conventional CNN models. The study further incorporates theoretical insights from hybrid quantum-classical learning systems, emphasizing the role of parameterized quantum circuits in feature mapping and optimization stability. The methodology is grounded in NISQ-era quantum computing constraints and leverages hybrid optimization strategies to ensure computational feasibility. Experimental evaluation demonstrates that quanvolution-based models can provide improved robustness in feature extraction, particularly in high-dimensional image spaces, while maintaining competitive computational efficiency. However, scalability limitations and noise sensitivity in quantum circuits remain key challenges. Overall, this work contributes to the growing field of quantum-enhanced machine learning by providing a structured performance analysis of hybrid quanvolutional architectures and highlighting their potential role in next-generation intelligent visual recognition systems.