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.
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.
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.
This research presents a new architecture for structured picture categorization problems called Hierarchical Fused Quantum Fuzzy Neural Network (HFQ-FNN). It combines the ideas of quantum computing with fuzzy logic and neural networks. With an accuracy of 84.04%, the suggested HFQ-FNN beats CNN and FDNN, two industry standards, on the Dirty-MNIST dataset, by a margin of 2.9% and 1.4%, respectively. Also, on the 15-Scene dataset, HFQ-FNN achieves an accuracy of 74.27% and shows a considerably higher F1 value, which is 3.0% better than DNN and 0.6% better than FDNN. The robustness analysis shows that HFQ-FNN is resilient against quantum noise, with a fidelity of 0.95 at a 0.1 noise probability. These findings show that HFQ-FNN is a powerful tool for improving picture classification accuracy through the use of quantum computing, which could lead to major developments in the field of complicated data classification.
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.
Neural network is one of the AI algorithms commonly used to process data, and has an extremely important position in scenarios such as image recognition, classification, and machine translation. With the increase of data volume explosion, the required computing power of neural networks is also significantly increased. The emergence of quantum neural networks improves the computational power of neural networks, but the accuracy of neural networks and quantum neural networks is not high in the face of the complexity and uncertainty of big data. In order to improve the efficiency and accuracy, the cross-fusion of "fuzzy number theory + quantum neural network" is proposed to study the quantum fuzzy neural network (FQNN) based on fuzzy number. The Gaussian fuzzy function is used to generate the corresponding fuzzy affiliation matrix to describe the uncertain information in the data. The fuzzy independent variables are trained through the FQNN model, and the model is output after changing the parameters of the quantum forward propagation layer. Simulation experiments show that the quantum fuzzy neural network model based on fuzzy number is more efficient and accurate in this study compared with the quantum neural network model.
This paper introduces a new type of deep learning method named Deep Quantum Network (DQN) for classification. DQN inherits the capability of modeling the structure of a feature space by fuzzy sets. At first, we propose the architecture of DQN, which consists of quantum neuron and sigmoid neuron and can guide the embedding of samples divisible in new Euclidean space. The parameter of DQN is initialized through greedy layer-wise unsupervised learning. Then, the parameter space of the deep architecture and quantum representation are refined by supervised learning based on the global gradient-descent procedure. An exponential loss function is introduced in this paper to guide the supervised learning procedure. Experiments conducted on standard datasets show that DQN outperforms other feed forward neural networks and neuro-fuzzy classifiers.