Abstract We introduce a hybrid model combining a quantum-inspired tensor network and a variational quantum circuit to perform supervised learning tasks. This architecture allows for the classical and quantum parts of the model to be trained simultaneously, providing an end-to-end training framework. We show that compared to the principal component analysis, a tensor network based on the matrix product state with low bond dimensions performs better as a feature extractor for the input data of the variational quantum circuit in the binary and ternary classification of MNIST and Fashion-MNIST datasets. The architecture is highly adaptable and the classical-quantum boundary can be adjusted according to the availability of the quantum resource by exploiting the correspondence between tensor networks and quantum circuits.
Abstract We introduce a hybrid model combining a quantum-inspired tensor network and a variational quantum circuit to perform supervised learning tasks. This architecture allows for the classical and quantum parts of the model to be trained simultaneously, providing an end-to-end training framework. We show that compared to the principal component analysis, a tensor network based on the matrix product state with low bond dimensions performs better as a feature extractor for the input data of the variational quantum circuit in the binary and ternary classification of MNIST and Fashion-MNIST datasets. The architecture is highly adaptable and the classical-quantum boundary can be adjusted according to the availability of the quantum resource by exploiting the correspondence between tensor networks and quantum circuits.
One key step in performing quantum machine learning (QML) on noisy intermediate-scale quantum (NISQ) devices is the dimension reduction of the input data prior to their encoding. Traditional principle component analysis (PCA) and neural networks have been used to perform this task; however, the classical and quantum layers are usually trained separately. A framework that allows for a better integration of the two key components is thus highly desirable. Here we introduce a hybrid model combining the quantum-inspired tensor networks (TN) and the variational quantum circuits (VQC) to perform supervised learning tasks, which allows for an end-to-end training. We show that a matrix product state based TN with low bond dimensions performs better than PCA as a feature extractor to compress data for the input of VQCs in the binary classification of MNIST dataset. The architecture is highly adaptable and can easily incorporate extra quantum resource when available.
The advent of noisy intermediate-scale quantum (NISQ) computers raises a crucial challenge to design quantum neural networks for fully quantum learning tasks. To bridge the gap, this work proposes an end-to-end learning framework named QTN-VQC, by introducing a trainable quantum tensor network (QTN) for quantum embedding on a variational quantum circuit (VQC). The architecture of QTN is composed of a parametric tensor-train network for feature extraction and a tensor product encoding for quantum embedding. We highlight the QTN for quantum embedding in terms of two perspectives: (1) we theoretically characterize QTN by analyzing its representation power of input features; (2) QTN enables an end-to-end parametric model pipeline, namely QTN-VQC, from the generation of quantum embedding to the output measurement. Our experiments on the MNIST dataset demonstrate the advantages of QTN for quantum embedding over other quantum embedding approaches.
Abstract There have been numerous quantum neural networks reported, but they struggle to match traditional neural networks in accuracy. Given the huge improvement of the neural network models’ accuracy by two-dimensional tensor network (TN) states in classical tensor network machine learning (TNML), it is promising to explore whether its application in quantum machine learning can extend the performance boundary of the models. Here, we transform two-dimensional TNs into quantum circuits for supervised learning. Specifically, we encode two-dimensional TNs into quantum circuits through rigorous mathematical proofs for constructing model ansätze, including string-bond states, entangled-plaquette states and isometric TN states. In addition, we propose adaptive data encoding methods and combine with TNs. We construct a tensor-network-inspired quantum circuit (TNQC) supervised learning framework for transferring TNML from classical to quantum, and build several novel two-dimensional TN-inspired quantum classifiers based on this framework. Finally, we propose a parallel quantum machine learning method for multi-class classification to construct 2D TNQC-based multi-class classifiers. Classical simulation results on the MNIST benchmark dataset show that our proposed models achieve the state-of-the-art accuracy performance, significantly outperforming other quantum classifiers on both binary and multi-class classification tasks, and beat simple convolutional classifiers on a fair track with identical inputs. The noise resilience of the models makes them successfully run and work in a real quantum computer.
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.
Hybrid quantum-classical neural networks have emerged as a promising approach for leveraging quantum computing in machine learning while mitigating current hardware limitations. This paper presents Sim-HVQC, a hybrid Deep Quantum Neural Network that couples an adaptive, parameter-free SimAM weighting module with classical feature extraction to preserve class-discriminative information prior to encoding into a Variational Quantum Circuit (VQC). Previous studies are restricted to binary classification [1] [2] [3] [4] [5]. In contrast, the proposed framework is trained and evaluated on various multi-class datasets(MNIST, KMNIST, Fashion-MNIST, and EMNIST). The framework further demonstrates reproducibility, parameter efficiency, and interpretability through multi-seed evaluation, parameter analysis, and latent/quantum feature inspection. The source code is publicly available at https://github.com/Dilli822/ SimAM-HVQC
We implement a hybrid quantum-classical model for image classification that compresses MNIST digit images into a low-dimensional feature space and then maps these features onto a 5-qubit quantum state. First, an autoencoder compresses each 28×28 image (784 pixels) into a 64-dimensional latent vector, preserving salient features of the digit with minimal reconstruction error. We further reduce the latent representation to 5 principal components using Principal Component Analysis (PCA), to match the 5 available qubits. These 5 features are encoded as rotation angles in a quantum circuit with 5 qubits. The quantum feature map applies single-qubit rotations (Ry gates) proportional to the feature values, followed by a Hadamard gate and a cascade of entangling CNOT gates to produce a non-product entangled state. Measuring the 5-qubit state yields a 32-dimensional probability distribution over basis outcomes, which serves as a quantum-enhanced feature vector for classification. A classical neural network with a softmax output is then trained on these 32-dimensional quantum feature vectors to predict the digit class. We evaluate the hybrid model on the MNIST dataset and compare it to a purely classical baseline that uses the 64-dimensional autoencoder latent features for classification. The results show that the hybrid model can successfully classify digits, demonstrating the feasibility of integrating quantum computing in the classification pipeline, although its accuracy (about 75\% on test data) currently falls below the classical baseline (about 98\% on the same compressed data).