In the Quantum-Train (QT) framework, mapping quantum state measurements to classical neural network weights is a critical challenge that affects the scalability and efficiency of hybrid quantum-classical models. The traditional QT framework employs a multi-layer perceptron (MLP) for this task, but it struggles with scalability and interpretability. To address these issues, we propose replacing the MLP with a tensor network-based model and introducing a distributed circuit ansatz designed for large-scale quantum machine learning with multiple small quantum processing unit nodes. This approach enhances scalability, efficiently represents high-dimensional data, and maintains a compact model structure. Our enhanced QT framework retains the benefits of reduced parameter count and independence from quantum resources during inference. Experimental results on benchmark datasets demonstrate that the tensor network-based QT framework achieves competitive performance with improved efficiency and generalization, offering a practical solution for scalable hybrid quantum-classical machine learning.
In the Quantum-Train (QT) framework, mapping quantum state measurements to classical neural network weights is a critical challenge that affects the scalability and efficiency of hybrid quantum-classical models. The traditional QT framework employs a multi-layer perceptron (MLP) for this task, but it struggles with scalability and interpretability. To address these issues, we propose replacing the MLP with a tensor network-based model and introducing a distributed circuit ansatz designed for large-scale quantum machine learning with multiple small quantum processing unit nodes. This approach enhances scalability, efficiently represents high-dimensional data, and maintains a compact model structure. Our enhanced QT framework retains the benefits of reduced parameter count and independence from quantum resources during inference. Experimental results on benchmark datasets demonstrate that the tensor network-based QT framework achieves competitive performance with improved efficiency and generalization, offering a practical solution for scalable hybrid quantum-classical machine learning.
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/ .
Recently, there has been growing interest in medical image analysis methods based on multi-layer perceptron (MLP), which have demonstrated remarkable performance in this field. Typically, the MLP has been employed to flatten feature maps along the channel and spatial dimensions and encode them to capture the overall feature information. However, for MLP-based architecture, the whole learning process requires high computational complexity, a large number of parameters, and large-scale training datasets. Meanwhile, quantum tensor network (QTN), derived from quantum many-body systems, have gained popularity in machine learning due to their ability to reduce the number of parameters and explore the correlation of remote elements in an image through a tensor contraction operation. In this paper, we propose a novel framework named QTN-MLP based on QTN and MLP to tackle the weaknesses of MLP. This paper has been extensively validated on the COVID-CT dataset and ISIC 2018 dataset, and the experiments show that our method competes with state-of-the-art methods with lower computational complexity and fewer parameters.
Tensor networks can compactly represent high-dimensional data in the form of low-rank tensor decompositions, which helps capture complex structures and correlations within the data. However, their inherently multilinear nature limits their potential as universal approximators. To address this limitation, tensor networks are combined with classical neural network layers, introducing nonlinear elements to enhance the model’s expressive power. The Hybrid Tensor Networks (HTN) system encompasses two prevalent tensor network configurations, Matrix Product States and Tree Tensor Networks, which facilitates the adaptable design of models customized for particular machine learning applications. This framework has been validated on classification and image reconstruction tasks, demonstrating its potential to handle complex data structures and its applicability within the machine learning field. Employing this approach, the goal is to establish a foundation for future research on hybrid quantum-classical models, thereby opening up avenues for the realm of quantum machine learning.
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.
In this paper, we introduce Quantum-Train-Based Distributed Multi-Agent Reinforcement Learning (Dist-QTRL), a novel approach to addressing the scalability challenges of traditional Reinforcement Learning (RL) by integrating quantum computing principles. Quantum-Train Reinforcement Learning (QTRL) leverages parameterized quantum circuits to efficiently generate neural network parameters, achieving a poly(log(N))reduction in the dimensionality of trainable parameters while harnessing quantum entanglement for superior data representation. The framework is designed for distributed multi-agent environments, where multiple agents, modeled as Quantum Processing Units (QPUs), operate in parallel, enabling faster convergence and enhanced scalability. Additionally, the Dist-QTRL framework can be extended to high-performance computing (HPC) environments by utilizing distributed quantum training for parameter reduction in classical neural networks, followed by inference using classical CPUs or GPUs. This hybrid quantumHPC approach allows for further optimization in real-world applications. In this paper, we provide a mathematical formulation of the Dist-QTRL framework and explore its convergence properties, supported by empirical results demonstrating performance improvements over centric QTRL models. The results highlight the potential of quantum-enhanced RL in tackling complex, highdimensional tasks, particularly in distributed computing settings, where our framework achieves significant speedups through parallelization without compromising model accuracy. This work paves the way for scalable, quantum-enhanced RL systems in practical applications, leveraging both quantum and classical computational resources.
In this work, we introduce the Federated Quantum-Train (QT) framework, which integrates the QT model into federated learning to leverage quantum computing for distributed learning systems. Quantum client nodes employ Quantum Neural Networks (QNNs) and a mapping model to generate local target model parameters, which are updated and aggregated at a central node. Testing with a VGG-like convolutional neural network on the CIFAR-10 dataset, our approach significantly reduces qubit usage from 19 to as low as 8 qubits while reducing generalization error. The QT method mitigates overfitting observed in classical models, aligning training and testing accuracy and improving performance in highly compressed models. Notably, the Federated QT framework does not require a quantum computer during inference, enhancing practicality given current quantum hardware limitations. This work highlights the potential of integrating quantum techniques into federated learning, paving the way for advancements in quantum machine learning and distributed learning systems.