Zhongtian Dong, Marçal Comajoan Cara, Gopal Ramesh Dahale, Roy T. Forestano, S. V. Gleyzer, Daniel Justice, Kyoungchul Kong, Tom Magorsch, Konstantin Tzvetanov Matchev, Katia Matcheva, Eyup B. Unlu
This paper presents a comparative analysis of the performance of Equivariant Quantum Neural Networks (EQNNs) and Quantum Neural Networks (QNNs), juxtaposed against their classical counterparts: Equivariant Neural Networks (ENNs) and Deep Neural Networks (DNNs). We evaluate the performance of each network with three two-dimensional toy examples for a binary classification task, focusing on model complexity (measured by the number of parameters) and the size of the training dataset. Our results show that the Z2×Z2 EQNN and the QNN provide superior performance for smaller parameter sets and modest training data samples.
This paper presents a comparative analysis of the performance of Equivariant Quantum Neural Networks (EQNNs) and Quantum Neural Networks (QNNs), juxtaposed against their classical counterparts: Equivariant Neural Networks (ENNs) and Deep Neural Networks (DNNs). We evaluate the performance of each network with three two-dimensional toy examples for a binary classification task, focusing on model complexity (measured by the number of parameters) and the size of the training dataset. Our results show that the Z2×Z2 EQNN and the QNN provide superior performance for smaller parameter sets and modest training data samples.
Abstract In this study, we compare the performance of randomized classical and quantum neural networks (NNs) as well as classical and quantum-classical hybrid convolutional neural networks (CNNs) for the task of supervised binary image classification. We keep the employed quantum circuits compatible with near-term quantum devices and use two distinct methodologies: applying randomized NNs on dimensionality-reduced data, and applying CNNs to full image data. We evaluate these approaches on three fully-classical data sets of increasing complexity: an artificial hypercube data set, MNIST handwritten digits and industrial images of practical relevance. Our study’s central goal is to shed more light on how quantum and classical models perform for various binary classification tasks and on what defines a good quantum model. To this end, our study involves a correlation analysis between classification accuracy and quantum model hyperparameters, and an analysis on the role of entanglement in quantum models, as well as on the impact of initial training parameters. We find classical and quantum-classical hybrid models achieve statistically-equivalent classification accuracies across most data sets with no approach consistently outperforming the other. Interestingly, we observe that quantum NNs show lower variance with respect to initial training parameters and that the role of entanglement is nuanced. While incorporating entangling gates seems to be generally advantageous, we also observe that their (optimizable) entangling power is not correlated with model performance. We also observe an inverse proportionality between the number of entangling gates and the average gate entangling power. Our study provides an industry perspective on quantum machine learning for practical binary image classification tasks, highlighting both current limitations and potential avenues for further research in quantum circuit design, entanglement utilization, and model transferability across varied applications.
Quantum neural network architectures that have little to no inductive biases are known to face trainability and generalization issues. Inspired by a similar problem, recent breakthroughs in machine learning address this challenge by creating models encoding the symmetries of the learning task. This is materialized through the usage of equivariant neural networks the action of which commutes with that of the symmetry. In this work, we import these ideas to the quantum realm by presenting a comprehensive theoretical framework to design equivariant quantum neural networks (EQNNs) for essentially any relevant symmetry group. We develop multiple methods to construct equivariant layers for EQNNs and analyze their advantages and drawbacks. Our methods can find unitary or general equivariant quantum channels efficiently even when the symmetry group is exponentially large or continuous. As a special implementation, we show how standard quantum convolutional neural networks (QCNNs) can be generalized to group-equivariant QCNNs where both the convolution and pooling layers are equivariant to the symmetry group. We then numerically demonstrate the effectiveness of a S U ( 2 ) -equivariant QCNN over symmetry-agnostic QCNN on a classification task of phases of matter in the bond-alternating Heisenberg model. Our framework can be readily applied to virtually all areas of quantum machine learning. Lastly, we discuss about how symmetry-informed models such as EQNNs provide hopes to alleviate central challenges such as barren plateaus, poor local minima, and sample complexity. Published by the American Physical Society 2024
Machine learning algorithms are heavily relied on to understand the vast amounts of data from high-energy particle collisions at the CERN Large Hadron Collider (LHC). The data from such collision events can naturally be represented with graph structures. Therefore, deep geometric methods, such as graph neural networks (GNNs), have been leveraged for various data analysis tasks in high-energy physics. One typical task is jet tagging, where jets are viewed as point clouds with distinct features and edge connections between their constituent particles. The increasing size and complexity of the LHC particle datasets, as well as the computational models used for their analysis, have greatly motivated the development of alternative fast and efficient computational paradigms such as quantum computation. In addition, to enhance the validity and robustness of deep networks, we can leverage the fundamental symmetries present in the data through the use of invariant inputs and equivariant layers. In this paper, we provide a fair and comprehensive comparison of classical graph neural networks (GNNs) and equivariant graph neural networks (EGNNs) and their quantum counterparts: quantum graph neural networks (QGNNs) and equivariant quantum graph neural networks (EQGNN). The four architectures were benchmarked on a binary classification task to classify the parton-level particle initiating the jet. Based on their area under the curve (AUC) scores, the quantum networks were found to outperform the classical networks. However, seeing the computational advantage of quantum networks in practice may have to wait for the further development of quantum technology and its associated application programming interfaces (APIs).
This study explores the performance of Quantum Support Vector Classifiers (QSVCs) and Quantum Neural Networks (QNNs) in comparison to classical models for machine learning tasks. By evaluating these models on the Iris and MNIST-PCA datasets, we find that quantum models tend to outperform classical approaches as the problem complexity increases. While QSVCs generally provide more consistent results, QNNs exhibit superior performance in higher-complexity tasks due to their increased quantum load. Additionally, we analyze the impact of hyperparameter tuning, showing that feature maps and ansatz configurations significantly influence model accuracy. We also compare the PennyLane and Qiskit frameworks, concluding that Qiskit provides better optimization and efficiency for our implementation. These findings highlight the potential of Quantum Machine Learning (QML) for complex classification problems and provide insights into model selection and optimization strategies
Abstract Geometric deep learning refers to the scenario in which the symmetries of a dataset are used to constrain the parameter space of a neural network and thus, improve their trainability and generalization. Recently, this idea has been incorporated into the field of quantum machine learning, which has given rise to equivariant quantum neural networks (EQNNs). In this work, we investigate the role of classical-to-quantum embedding on the performance of equivariant quantum convolutional neural networks (EQCNNs) for the classification of images. We discuss the connection between the data embedding method and the resulting representation of a symmetry group and analyze how changing representation affects the expressibility of an EQCNN. We numerically compare the classification accuracy of EQCNNs with three different basis-permuted amplitude embeddings to the one obtained from a non-equivariant quantum convolutional neural network (QCNN). Our results show a clear dependence of classification accuracy on the underlying embedding, especially for initial training iterations. The improvement in classification accuracy of EQCNN over non-equivariant QCNN may be present or absent depending on the particular embedding and dataset used. The noisy simulation using simple noise models shows that certain EQCNNs are more robust to noise than non-equivariant QCNNs. It is expected that the results of this work can be useful to the community for a better understanding of the importance of data embedding choice in the context of geometric quantum machine learning.
The rapid growth of computer vision and increasingly complex image recognition tasks has exposed fundamental computational limitations of classical machine learning models, motivating the exploration of quantum computing as an emerging new paradigm. This paper presents a comprehensive benchmarking study of classical and quantum machine learning models for image recognition on the MNIST handwritten digit dataset, evaluating both traditional models, a Classical Support Vector Machine (CSVM) and a Quantum Support Vector Machine (QSVM), and deep neural network models, a Classical Convolutional Neural Network (CCNN) and a Quantum Convolutional Neural Network (QCNN), across four performance dimensions: classification accuracy, computational runtime, parameter count, and memory requirements. Experiments are conducted as functions of both feature dimensionality and sample size, and across CPU and GPU execution environments, providing a controlled, multidimensional comparison to address gaps in prior work. For the SVM-based models, QSVM consistently outperforms CSVM in accuracy, reaching ∼ 0.90 versus ∼ 0.85 at 1,000 samples, with a higher computational cost. A feature count of 10 qubits and a sample size in the range of 200 -- 500 emerge as practical operating points that balance accuracy and runtime. For the neural network models, CCNN and QCNN achieve comparable classification accuracy, both exceeding 0.96 at 64 features and 60,000 samples, yet QCNN offers superior parameter and memory efficiency at higher feature counts, while incurring higher runtime. Across both model families, quantum models consistently outperform classical models by greater margins in accuracy as feature dimensionality or sample size increases.