We address the problem of implementing bottleneck layers from classical pretrained neural networks on a quantum computer, with the goal of exploring intrinsically quantum ansatz for representing large linear layers within hybrid classical-quantum models. Our approach begins with a compression step in which the target linear layer is represented as an effective matrix product operator (MPO) without degrading model performance. The MPO is then further disentangled into a more compact form. This enables a hybrid classical-quantum execution scheme, where the disentangling circuits are deployed on a quantum computer while the remainder of the network—including the disentangled MPO—runs on classical hardware. We introduce two complementary algorithms for MPO disentangling: (1) an disentangling variational method leveraging standard tensor network optimization techniques and (2) an disentangling gradient-descent-based approach. We validate these methods through a proof-of-concept translation of simple classical neural networks for MNIST and CIFAR-10 image classification into a hybrid classical-quantum form.
We address the problem of implementing bottleneck layers from classical pretrained neural networks on a quantum computer, with the goal of exploring intrinsically quantum ansatz for representing large linear layers within hybrid classical-quantum models. Our approach begins with a compression step in which the target linear layer is represented as an effective matrix product operator (MPO) without degrading model performance. The MPO is then further disentangled into a more compact form. This enables a hybrid classical-quantum execution scheme, where the disentangling circuits are deployed on a quantum computer while the remainder of the network—including the disentangled MPO—runs on classical hardware. We introduce two complementary algorithms for MPO disentangling: (1) an disentangling variational method leveraging standard tensor network optimization techniques and (2) an disentangling gradient-descent-based approach. We validate these methods through a proof-of-concept translation of simple classical neural networks for MNIST and CIFAR-10 image classification into a hybrid classical-quantum form.
We introduce a framework for seamlessly integrating quantum computing into pretrained large language models (LLMs). The key idea is to construct a hybrid quantum-classical representation that exactly reproduces the original model, providing a principled starting point from which quantum resources can only improve performance. Our approach replaces the weight matrices in self-attention and multilayer perceptron layers with two variational quantum circuits coupled to a matrix product operator (MPO). Tensor network disentanglers transfer much of each layer's information into the quantum circuits, enabling the remaining tensor network to be compressed to a bond-dimension-one MPO with over three orders of magnitude fewer classical parameters (in our experiments, from 110,592 to approximately 36 for the replaced layer) and less than a 0.3\% increase in perplexity. Training an added unitary adapter on top of this representation then surpasses the original model, reducing perplexity by up to 1.6\%. Finally, we validate the hybrid architecture on a real quantum processor, demonstrating a practical route towards quantum-enhanced language models.
Abstract Image classification, a pivotal task in multiple industries, faces computational challenges due to the burgeoning volume of visual data. This research addresses these challenges by introducing two quantum machine learning models that leverage the principles of quantum mechanics for effective computations. Our first model, a hybrid quantum neural network with parallel quantum circuits, enables the execution of computations even in the noisy intermediate-scale quantum era, where circuits with a large number of qubits are currently infeasible. This model demonstrated a record-breaking classification accuracy of 99.21% on the full MNIST dataset, surpassing the performance of known quantum–classical models, while having eight times fewer parameters than its classical counterpart. Also, the results of testing this hybrid model on a Medical MNIST (classification accuracy over 99%), and on CIFAR-10 (classification accuracy over 82%), can serve as evidence of the generalizability of the model and highlights the efficiency of quantum layers in distinguishing common features of input data. Our second model introduces a hybrid quantum neural network with a Quanvolutional layer, reducing image resolution via a convolution process. The model matches the performance of its classical counterpart, having four times fewer trainable parameters, and outperforms a classical model with equal weight parameters. These models represent advancements in quantum machine learning research and illuminate the path towards more accurate image classification systems.
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.
In recent years, the field of machine learning has witnessed a paradigm shift with the emergence of hybrid quantum-classical neural networks. These networks combine the power of classical neural networks with the computational advantages offered by quantum variational circuits. This study presents a comprehensive survey of hybrid quantum-classical machine learning algorithms, focusing on their architecture, performance, and hyperparameter optimization techniques. Introducing the concept of hybrid quantum-classical machine learning and its significance in contemporary image classification tasks. It explores the theoretical foundations of quantum variational circuits and their integration with classical neural network architectures. Special attention is given to prominent algorithms such as Quantum Convolutional Neural Networks, Quanvolutional Neural Networks, and Quantum ResNet, each offering unique advantages in image classification tasks. A major aspect covered in this study is the hyperparameter optimization techniques employed in hybrid quantum-classical machine learning. The chapter discusses quantum-inspired optimization methods tailored for efficiently tuning the hyperparameters of complex neural network models. Through comparative analysis, the effectiveness of these optimization techniques is demonstrated in reducing computational overhead and improving model performance. Moreover, the study also delves into experimental results obtained from benchmarking hybrid quantum-classical models against traditional classical approaches. It highlights the accuracy variations observed across different quantum architectures and explores the impact of architectural permutations on model convergence. Insights gained from these experiments provide valuable guidance for researchers and practitioners seeking to leverage hybrid quantum-classical neural networks in real-world applications.
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.
In the last decade, quantum computing (QC) has shown its great potential in advancing research in many fields. Here we introduce a new quantum-classical neural network, by combining quantum computing and classical computing in a hybrid neural network (HNN) that can be trained to perform image classification. The HNN on the basis of the classic convolutional neural network (CNN) with quantum circuit is considered for image classification problem. The various configurations of HNN were investigated where QC with different number of qubits were used and compared. The HNN configurations were trained, validated, and tested on the more complex CIFAR10 and CIFAR100 datasets in addition to our previous attempts on the simpler MNIST, notMNIST, MNIST Fashion datasets. Performance of HNN was compared for multiclass classification on these datasets for different number of classes (from 2 to 10) using QCs with correspondent number of qubits (from 2 to 4). The metrics measured (accuracy and loss) during these experiments support our assumption about feasibility of HNN application for multiclass classification problems.