Deep learning is a powerful technique for data-driven learning in the era of Big Data. However, most deep learning models are deterministic models that ignore the uncertainty of data. Fuzzy neural networks are proposed to tackle this type of problem. In this article, we proposed a novel quantum assisted hierarchical fuzzy neural network (QA-HFNN). Different from classical fuzzy neural networks, QA-HFNN uses quantum neural networks (QNNs) to learn fuzzy membership functions. The model is a multifeature fusion learning algorithm with a parallel structural design that integrates quantum and classical neural networks. The classical network is used to capture high-dimensional neural features, the QNNs are designed to capture fuzzy logic features of the data, then, the two features are fused to form the final features to be classified. The experiment is performed on a classical computer, and the quantum circuit is built through a simulated quantum environment. The results indicate that the accuracy of QA-HFNN can equal to or even surpass classical methods in image classification tasks. The quantum circuit utilizes only a single qubit which is easy to implement. In addition, the fidelity of quantum circuit in a quantum noise environment is assessed, demonstrating that QA-HFNN has strong robustness. The time and computational complexity of QNNs was analyzed, further proving the effectiveness of the model.
Deep learning is a powerful technique for data-driven learning in the era of Big Data. However, most deep learning models are deterministic models that ignore the uncertainty of data. Fuzzy neural networks are proposed to tackle this type of problem. In this article, we proposed a novel quantum assisted hierarchical fuzzy neural network (QA-HFNN). Different from classical fuzzy neural networks, QA-HFNN uses quantum neural networks (QNNs) to learn fuzzy membership functions. The model is a multifeature fusion learning algorithm with a parallel structural design that integrates quantum and classical neural networks. The classical network is used to capture high-dimensional neural features, the QNNs are designed to capture fuzzy logic features of the data, then, the two features are fused to form the final features to be classified. The experiment is performed on a classical computer, and the quantum circuit is built through a simulated quantum environment. The results indicate that the accuracy of QA-HFNN can equal to or even surpass classical methods in image classification tasks. The quantum circuit utilizes only a single qubit which is easy to implement. In addition, the fidelity of quantum circuit in a quantum noise environment is assessed, demonstrating that QA-HFNN has strong robustness. The time and computational complexity of QNNs was analyzed, further proving the effectiveness of the model.
Neural network is a powerful learning paradigm for data feature learning in the era of big data. However, most neural network models are deterministic models that ignore the uncertainty of data. Fuzzy neural networks are proposed to address this problem. FDNN is a hierarchical deep neural network that derives information from both fuzzy and neural representations, the representations are then fused to form representation to be classified. FDNN perform well on uncertain data classification tasks. In this paper, we proposed a novel hierarchical fused quantum fuzzy neural network (HQFNN). Different from classical FDNN, HQFNN uses quantum neural networks to learn fuzzy membership functions in fuzzy neural network. We conducted simulated experiment on two types of datasets (Dirty-MNIST and 15-Scene), the results show that the proposed model can outperform several existing methods. In addition, we demonstrate the robustness of the proposed quantum circuit.
Classical deep neural network models struggle to represent data uncertainty and capture dependencies between features simultaneously, especially under fuzzy or noisy conditions. Although a quantum-assisted hierarchical fuzzy neural network (QA-HFNN) was proposed to learn fuzzy membership for each feature, it cannot model dependencies between features due to its single-qubit encoding. To address this, this paper proposes a dual-qubit hierarchical fuzzy neural network (DQ-HFNN), encoding feature pairs onto a pair of entangled qubits, which extends the single-feature fuzzy model to a joint fuzzy representation. By introducing quantum entanglement, the dual-qubit circuit can encode non-classical correlations, enabling the model to directly learn relationship patterns between feature pairs. Experiments on benchmarks show that DQ-HFNN demonstrates higher classification accuracy than QA-HFNN, as well as classical deep learning baselines. Furthermore, ablation studies after controlling for circuit depth and parameter counts show that the performance gain mainly stems from the relational modeling capability enabled by entanglement rather than enhanced expressivity. The proposed DQ-HFNN model exhibits high parameter efficiency and fast inference speed. Experiments under noisy conditions suggest that it is robust against noise and has the potential to be implemented on noisy intermediate-scale quantum devices.
Deep learning vision systems excel at pattern recognition yet falter when inputs are noisy or the model must explain its own confidence. Fuzzy inference, with its graded memberships and rule transparency, offers a remedy, while parameterized quantum circuits can embed features in richly entangled Hilbert spaces with striking parameter efficiency. Bridging these ideas, this study introduces a innovative Highly Quantized Fuzzy Neural Network (HQFNN) that realises the entire fuzzy pipeline inside a shallow quantum circuit and couples the resulting quantum signal to a lightweight CNN feature extractor. Each image feature is first mapped to a single qubit membership state through repeated angle reuploading. Then a compact rule layer refines these amplitudes, and a clustered CNOT defuzzifier collapses them into one crisp value that is fused with classical features before classification. Evaluated on standard image benchmarks, HQFNN consistently surpasses classical, fuzzy enhanced and quantum only baselines while using several orders of magnitude fewer trainable weights, and its accuracy degrades only marginally under simulated depolarizing and amplitude damping noise, evidence of intrinsic robustness. Gate count analysis further shows that circuit depth grows sublinearly with input dimension, confirming the model's practicality for larger images. These results position the model as a compact, interpretable and noise tolerant alternative to conventional vision backbones and provide a template for future quantum native fuzzy learning frameworks.
Image classification is an important application for deep learning. With the advent of quantum technology, quantum neural networks (QNNs) have become the focus of research. Traditional deep learning-based image classification involves using a convolutional neural network (CNN) to extract features from the image and a multi-layer perceptron (MLP) network to create the decision boundaries. However, quantum circuits with parameters can extract rich features from images and also create complex decision boundaries. This paper proposes a hybrid QNN (H-QNN) model designed for binary image classification that capitalizes on the strengths of quantum computing and classical neural networks. Our H-QNN model uses a compact, two-qubit quantum circuit integrated with a classical convolutional architecture, making it highly efficient for computation on noisy intermediate-scale quantum (NISQ) devices that are currently leading the way in practical quantum computing applications. Our H-QNN model significantly enhances classification accuracy, achieving a 90.1% accuracy rate on binary image datasets. In addition, we have extensively evaluated baseline CNN and our proposed H-QNN models for image retrieval tasks. The obtained quantitative results exhibit the generalization of our H-QNN for downstream image retrieval tasks. Furthermore, our model addresses the issue of overfitting for small datasets, making it a valuable tool for practical applications.
Modern vision networks achieve high accuracy but depend on millions of weights and offer limited insight into prediction confidence. Fuzzy reasoning produces graded rule strengths that quantify uncertainty, and variational quantum circuits add compact expressive power, yet quantum neural networks and fuzzy reasoning rarely appear together in a unified model. We present the Intensively Quantized Integrated Fuzzy Neural Network (IQI-FNN), a quantized architecture that replaces the membership and defuzzification blocks of a classical fuzzy neural network with a shallow parameterized quantum circuit while retaining only minimal classical layers. Its quantum-fuzzy module merges single-qubit membership encoding, angle reuploading, a lightweight rule layer and a clustered-CNOT defuzzifier, which keeps gate count linear in feature dimension. Across standard image classification benchmarks IQI-FNN surpasses relevant state-of-the-art models and attains peak accuracy with modest hyperparameter tuning. Complexity analysis shows gate depth and parameter size grow gently with input dimension, the network stays lightweight, and fidelity remains high under representative gate-level noise in simulation. IQI-FNN therefore offers a compact, interpretable and noise-resilient alternative to conventional vision backbones and advances quantum-native fuzzy learning.
Image classification is a fundamental task in deep learning, and recent advances in quantum computing have generated significant interest in quantum neural networks. Traditionally, Convolutional Neural Networks (CNNs) are employed to extract image features, while Multilayer Perceptrons (MLPs) handle decision making. However, parameterized quantum circuits offer the potential to capture complex image features and define sophisticated decision boundaries. In this paper, we present a novel Hybrid Quantum–Classical Neural Network (H-QNN) for image classification, and demonstrate its effectiveness using the MNIST dataset. Our model combines quantum computing with classical supervised learning to enhance classification accuracy and computational efficiency. In this study, we detail the architecture of the H-QNN, emphasizing its capability in feature learning and image classification. Experimental results demonstrate that the proposed H-QNN model outperforms conventional deep learning methods in various training scenarios, showcasing its effectiveness in high-dimensional image classification tasks. Additionally, we explore the broader applicability of hybrid quantum–classical approaches in other domains. Our findings contribute to the growing body of work in quantum machine learning, and underscore the potential of quantum-enhanced models for image recognition and classification.