Abstract This work focuses on investigating an end-to-end learning approach for quantum neural networks (QNN) on noisy intermediate-scale quantum devices. The proposed model combines a quantum tensor network (QTN) with a variational quantum circuit (VQC), resulting in a QTN-VQC architecture. This architecture integrates a QTN with a horizontal or vertical structure related to the implementation of quantum circuits for a tensor-train network. The study provides theoretical insights into the quantum advantages of the end-to-end learning pipeline based on QTN-VQC from two perspectives. The first perspective refers to the theoretical understanding of QTN-VQC with upper bounds on the empirical error, examining its learnability and generalization powers; The second perspective focuses on using the QTN-VQC architecture to alleviate the Barren Plateau problem in the training stage. Our experimental simulation on CPU/GPUs is performed on a handwritten digit classification dataset to corroborate our proposed methods in this work.
Abstract This work focuses on investigating an end-to-end learning approach for quantum neural networks (QNN) on noisy intermediate-scale quantum devices. The proposed model combines a quantum tensor network (QTN) with a variational quantum circuit (VQC), resulting in a QTN-VQC architecture. This architecture integrates a QTN with a horizontal or vertical structure related to the implementation of quantum circuits for a tensor-train network. The study provides theoretical insights into the quantum advantages of the end-to-end learning pipeline based on QTN-VQC from two perspectives. The first perspective refers to the theoretical understanding of QTN-VQC with upper bounds on the empirical error, examining its learnability and generalization powers; The second perspective focuses on using the QTN-VQC architecture to alleviate the Barren Plateau problem in the training stage. Our experimental simulation on CPU/GPUs is performed on a handwritten digit classification dataset to corroborate our proposed methods in this work.
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.
Resource constraints and imperfect quantum operations remain major challenges for quantum machine learning (QML) on noisy intermediate-scale quantum (NISQ) devices, particularly for fault-diagnosis tasks involving imbalanced and heterogeneous data. This work proposes QTN-RQNN, a Quantum Tensor Network-Based Recurrent Quantum Neural Network that integrates tensor-network-inspired nearest-neighbor interactions with recurrent quantum processing. The model sequentially encodes input features while propagating quantum memory across recurrent steps and incorporates QSMOTE for class balancing. QTN-RQNN is evaluated on four heterogeneous fault-diagnosis datasets SPID, CWRUBD, EFDD, and SFDD and compared with QNN, QTN-QNN, and RQNN baselines through classification, ablation, multi-seed, convergence, and quantum-resource analyses. Results show dataset-dependent predictive behavior, indicating that increased quantum architectural complexity does not universally improve classification. On SPID, QTN-RQNN improves the RQNN F1-score from 0.3077 to 0.4516 and ROC-AUC from 0.4485 to 0.6970, while the remaining datasets exhibit different performance-resource trade-offs and sensitivity to recurrent timesteps and circuit depth. Across all datasets, QTN-RQNN reduces the two-qubit-gate count from 32 to 24 per sample relative to RQNN, corresponding to a 25% reduction without increasing the four-qubit requirement; the same relative reduction is obtained for QTN-QNN over QNN. These findings establish QTN-RQNN as a resource-conscious recurrent quantum architecture and highlight the need to jointly consider predictive performance and circuit-resource requirements for near-term quantum fault diagnosis.
Abstract The noisy intermediate-scale quantum devices enable the implementation of the variational quantum circuit (VQC) for quantum neural networks (QNN). Although the VQC-based QNN has succeeded in many machine learning tasks, the representation and generalization powers of VQC still require further investigation, particularly when the dimensionality of classical inputs is concerned. In this work, we first put forth an end-to-end QNN, TTN-VQC, which consists of a quantum tensor network based on a tensor-train network (TTN) for dimensionality reduction and a VQC for functional regression. Then, we aim at the error performance analysis for the TTN-VQC in terms of representation and generalization powers. We also characterize the optimization properties of TTN-VQC by leveraging the Polyak-Lojasiewicz condition. Moreover, we conduct the experiments of functional regression on a handwritten digit classification dataset to justify our theoretical analysis.
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.
Quantum neural networks (QNNs) have recently attracted remarkable attention as a potential alternative to classical and deep neural network (NN) models particularly under constraints imposed by noisy intermediate-scale quantum (NISQ) devices, which support only shallow circuits with few quantum bits (qubits) and limited variational depth. However, applying QNNs to natural language processing (NLP) remains challenging because text representations are typically high-dimensional, while NISQ classifiers can only encode a small number of features at a time, requiring classical compression to enable stable training and flexible circuit configuration. In addition, many existing studies integrate QNNs into rich-text representation pipelines, where the quantum circuit is often implemented as a variational quantum circuit (VQC). Here, the VQC acts as an additional component within a larger model, and it remains unclear how the quantum component improves the classification task. Therefore, in this work, we propose a fully reproducible and compact QNN pipeline that provides a controlled setting for studying the contribution of the VQC to text classification. The model is trained end-to-end with a lightweight classical compression layer, and the overall study is supported by systematic ablation analyses of the compression layer, the classifier heads under a shared frozen low-dimensional representation, and quantum circuit structure. Our model uses the term frequency-inverse document frequency (TF-IDF) features with linear compression followed by a shallow four-qubit, two-layer VQC, implemented in PyTorch and PennyLane for end-to-end training. It is evaluated on five benchmark text classification datasets against classical baselines, including logistic regression and multilayer perceptron (MLP) models. Experimental results show that the proposed QNN achieves a competitive performance across all evaluated datasets, yielding the best results on three of the five benchmark datasets.
Recent advancements in machine learning have revolutionised research across various fields. Despite their success, conventional learning techniques are hindered by their significant computational resources and energy requirements. Prompted by recent experimental breakthroughs in quantum computing, variational quantum machine learning (QML) – machine learning integrated with variational quantum circuits (VQCs) – has emerged as a promising alternative. Nonetheless, the theoretical framework underpinning the advantages of variational QML is still rudimentary. Specifically, the training of VQCs faces several challenges, such as the barren plateau problem, where the gradient diminishes exponentially with an increasing qubits. A related issue arises in variational QML training, where the convergence rate is exponentially small. In this thesis, we present theoretically guaranteed solutions to these challenges. First, we construct innovative circuit architectures to address the vanishing gradient problem in deep VQCs. We propose quantum controlled-layer and quantum ResNet structures, demonstrating that the expected gradient norm's lower bound is unaffected by the increase in qubits and circuit depth. Next, we introduce an initialization strategy to mitigate the vanishing gradient issue in general deep quantum circuits. We prove that Gaussian-initialized parameters ensure the gradient norm's decay rate remains inversely polynomial despite the increase in qubit numbers and circuit depth. Finally, we propose a novel and effective theory for analysing the training of quantum neural networks with moderate depths. We prove that, under certain randomness conditions in the circuits and datasets, training converges linearly with a rate inversely proportional to the dataset size. Our approach surpasses previous results, achieving exponentially larger convergence rates with modest depth, or conversely, requiring exponentially less depth for equivalent rates.