In this paper, we present an approach for enhancing quantum tensor networks through the method of data re-uploading. The proposed framework integrates multiple layers of classical data encoding into tensor network architectures, thereby improving their approximation capacity and reducing the impact of barren plateaus in training. The model construction relies on tree tensor networks combined with RX, RZ, and RY rotational gates and CNOT entanglement, while optimization is performed using differential evolution as a gradient-free algorithm. Experimental evaluation was carried out on the iris and wine datasets, comparing baseline tensor networks with architectures incorporating one to three re-uploading layers. The results demonstrate a consistent reduction in training and test loss, with accuracy, recall, and precision reaching 100% on the iris dataset for three layers and improvements of up to 40% in prediction quality on the wine dataset. These findings confirm that data re-uploading significantly enhances the performance and expressiveness of tensor network-based quantum models.
In this paper, we present an approach for enhancing quantum tensor networks through the method of data re-uploading. The proposed framework integrates multiple layers of classical data encoding into tensor network architectures, thereby improving their approximation capacity and reducing the impact of barren plateaus in training. The model construction relies on tree tensor networks combined with RX, RZ, and RY rotational gates and CNOT entanglement, while optimization is performed using differential evolution as a gradient-free algorithm. Experimental evaluation was carried out on the iris and wine datasets, comparing baseline tensor networks with architectures incorporating one to three re-uploading layers. The results demonstrate a consistent reduction in training and test loss, with accuracy, recall, and precision reaching 100% on the iris dataset for three layers and improvements of up to 40% in prediction quality on the wine dataset. These findings confirm that data re-uploading significantly enhances the performance and expressiveness of tensor network-based quantum models.
We introduce the Tree Tensor Network-enhanced Quantum-Classical Neural Network (TTN-QNet), a hybrid architecture that leverages the hierarchical structure of Tree Tensor Networks for efficient parameter representation and Variational Quantum Circuits (VQC) for expressive modeling. Unlike Tensor Ring Networks, TTNs reduce parameter redundancy through a tree-based topology, enabling scalable and interpretable computation. The proposed TTN-QNet is evaluated on the Iris, MNIST, and CIFAR-10 datasets, achieving classification accuracies of 93.2%, 85.24%, and 81.67%, respectively, on binary classification tasks. TTN-QNet demonstrates rapid convergence and robustness against barren plateaus, offering a promising direction for deep quantum learning.
Data re-uploading quantum circuits (DRQC) are a key approach to implementing quantum neural networks and have been shown to outperform classical neural networks in fitting high-frequency functions. However, their practical application is limited by the scalability of current quantum hardware. In this paper, we introduce the mathematical paradigm of DRQC into classical models by proposing a quantum-inspired data re-uploading network (Q-RUN), which retains the Fourier-expressive advantages of quantum models without any quantum hardware. Experimental results demonstrate that Q-RUN delivers superior performance across both data modeling and predictive modeling tasks. Compared to the fully connected layers and the state-of-the-art neural network layers, Q-RUN reduces model parameters while decreasing error by approximately one to three orders of magnitude on certain tasks. Notably, Q-RUN can serve as a drop-in replacement for standard fully connected layers, improving the performance of a wide range of neural architectures. This work illustrates how principles from quantum machine learning can guide the design of more expressive artificial intelligence.
Quantum machine learning models incorporating data re-uploading circuits have garnered significant attention due to their exceptional expressivity and trainability. However, their ability to generate accurate predictions on unseen data, referred to as the predictive performance, remains insufficiently investigated. This study reveals a fundamental limitation in predictive performance when deep encoding layers are employed within the data re-uploading model. Concretely, we theoretically demonstrate that when processing high-dimensional data with limited-qubit data re-uploading models, their predictive performance progressively degenerates to near random-guessing levels as the number of encoding layers increases. In this context, the repeated data uploading cannot mitigate the performance degradation. These findings are validated through experiments on both synthetic linearly separable datasets and real-world datasets. Our results demonstrate that when processing high-dimensional data, the quantum data re-uploading models should be designed with wider circuit architectures rather than deeper and narrower ones.
Accurate traffic forecasting plays a crucial role in modern Intelligent Transportation Systems (ITS), as it enables real-time traffic flow management, reduces congestion, and improves the overall efficiency of urban transportation networks. With the rise of Quantum Machine Learning (QML), it has emerged a new paradigm possessing the potential to enhance predictive capabilities beyond what classical machine learning models can achieve. In the present work we pursue a heuristic approach to explore the potential of QML, and focus on a specific transport issue. In particular, as a case study we investigate a traffic forecast task for a major urban area in Athens (Greece), for which we possess high-resolution data. In this endeavor we explore the application of Quantum Neural Networks (QNN), and, notably, we present the first application of quantum data re-uploading in the context of transport forecasting. This technique allows quantum models to better capture complex patterns, such as traffic dynamics, by repeatedly encoding classical data into a quantum state. Aside from providing a prediction model, we spend considerable effort in comparing the performance of our hybrid quantum-classical neural networks with classical deep learning approaches. We observe that, in fully connected network settings, hybrid quantum-classical models consistently underperform, with median scores approximately 10% worse than their purely classical counterparts across different configurations. In contrast, recursive architectures with data re-uploading show the opposite trend: hybrid models achieved up to 5% better median scores under comparable complexity settings. Additionally, these hybrid models converged in fewer training epochs, indicating improved training efficiency. Our results show that hybrid models achieve competitive accuracy with state-of-the-art classical methods, especially when the number of qubits and re-uploading blocks is increased. While the classical models demonstrate lower computational demands, we provide evidence that increasing the complexity of the quantum model improves predictive accuracy. These findings indicate that QML techniques, and specifically the data re-uploading approach, hold promise for advancing traffic forecasting models and could be instrumental in addressing challenges inherent in ITS environments.
Abstract Quantum machine learning researchers often rely on incorporating tensor networks (TN) into deep neural networks (DNN) and variational optimization. However, the standard optimization techniques used for training the contracted trainable weights of each model layer suffer from the correlations and entanglement structure between the model parameters in classical implementations. To address this issue, a multi-layer design of a tensor ring optimized variational quantum learning classifier (Quan-TR) comprising cascading entangling gates replacing the fully connected (dense) layers of a TN is proposed, and it is referred to as tensor ring optimized quantum-enhanced tensor neural networks (TR-QNet). TR-QNet parameters are optimized using the stochastic gradient descent algorithm on qubit measurements. The proposed TR-QNet is evaluated on three distinct datasets, namely Iris, MNIST, and CIFAR-10, to demonstrate the enhanced precision achieved for binary classification. In quantum simulations, the proposed TR-QNet achieves promising precision of 94.5% 94.5 % , 86.16% 86.16 % , and 83.54% 83.54 % on the Iris, MNIST, and CIFAR-10 datasets. Benchmark studies have been conducted on state-of-the-art quantum and classical implementations of TN models to show the efficacy of the proposed TR-QNet. Moreover, the scalability of TR-QNet highlights its potential for exhibiting in deep learning applications on a large scale. The PyTorch implementation of TR-QNet is available on Github https://github.com/konar1987/TR-QNet/ .
ABSTRACT Background Quantum machine learning is an emerging field that may offer unique advantages over classical machine learning but has not been extensively studied with real-world healthcare data of practical size. This study evaluates the performance of a recently proposed quantum machine learning algorithm—quantum circuits with data re-uploading—compared to classical machine learning and other common quantum algorithms, using both benchmarking data and real-world laboratory medicine data. Methods Four datasets containing between 2 and 30 features were selected for evaluation. The quantum re-uploading algorithm was compared against variational quantum classifiers, quantum neural networks and four, commonly used classical machine learning algorithms. Initial, baseline comparisons of classification performance (F1 score) were conducted using all algorithms across the four datasets. Configuration parameters were then optimized for the quantum data re-uploading algorithm using a previously published dataset of plasma amino acid profiles to determine the impact of optimization on classification performance, followed by a final comparison against classical ML algorithms. Results Baseline comparisons of quantum re-uploading showed superior classification performance on lower-dimensional datasets compared to quantum and linear ML algorithms. However, performance declined significantly as the number of input features increased. While optimization improved classification performance, marked variability was observed. Following optimization, the quantum re- uploading algorithm again performed comparably to linear algorithms but had lower classification performance on the plasma amino acid dataset compared to non-linear classical algorithms. Conclusion This study suggests that quantum data-reuploading algorithms can achieve classification performance comparable to some classical methods on lower-dimensional datasets, presenting opportunities for early research applications in laboratory medicine. However, while optimizing configuration parameters can improve classification performance, further advancements in quantum hardware and algorithm design will likely be necessary for quantum machine learning to become practically viable in laboratory medicine, and biomedical research more broadly.