ABSTRACT To improve data analysis and feature learning, this study compares the effectiveness of quantum dimensionality reduction (qDR) techniques to classical ones. In this study, we investigate several qDR techniques on a variety of datasets such as quantum Gaussian distribution adaptation (qGDA), quantum principal component analysis (qPCA), quantum linear discriminant analysis (qLDA), and quantum t‐SNE (qt‐SNE). The Olivetti Faces, Wine, Breast Cancer, Digits, and Iris are among the datasets used in this investigation. Through comparison evaluations against well‐established classical approaches, such as classical PCA (cPCA), classical LDA (cLDA), and classical GDA (cGDA), and using well‐established metrics like loss, fidelity, and processing time, the effectiveness of these techniques is assessed. The findings show that cPCA produced positive results with the lowest loss and highest fidelity when used on the Iris dataset. On the other hand, quantum uniform manifold approximation and projection (qUMAP) performs well and shows strong fidelity when tested against the Wine dataset, but ct‐SNE shows mediocre performance against the Digits dataset. Isomap and locally linear embedding (LLE) function differently depending on the dataset. Notably, LLE showed the largest loss and lowest fidelity on the Olivetti Faces dataset. The hypothesis testing findings showed that the qDR strategies did not significantly outperform the classical techniques in terms of maintaining pertinent information from quantum datasets. More specifically, the outcomes of paired t‐tests show that when it comes to the ability to capture complex patterns, there are no statistically significant differences between the cPCA and qPCA, the cLDA and qLDA, and the cGDA and qGDA. According to the findings of the assessments of mutual information (MI) and clustering accuracy, qPCA may be able to recognize patterns more clearly than standardized cPCA. Nevertheless, there is no discernible improvement between the qLDA and qGDA approaches and their classical counterparts.
ABSTRACT To improve data analysis and feature learning, this study compares the effectiveness of quantum dimensionality reduction (qDR) techniques to classical ones. In this study, we investigate several qDR techniques on a variety of datasets such as quantum Gaussian distribution adaptation (qGDA), quantum principal component analysis (qPCA), quantum linear discriminant analysis (qLDA), and quantum t‐SNE (qt‐SNE). The Olivetti Faces, Wine, Breast Cancer, Digits, and Iris are among the datasets used in this investigation. Through comparison evaluations against well‐established classical approaches, such as classical PCA (cPCA), classical LDA (cLDA), and classical GDA (cGDA), and using well‐established metrics like loss, fidelity, and processing time, the effectiveness of these techniques is assessed. The findings show that cPCA produced positive results with the lowest loss and highest fidelity when used on the Iris dataset. On the other hand, quantum uniform manifold approximation and projection (qUMAP) performs well and shows strong fidelity when tested against the Wine dataset, but ct‐SNE shows mediocre performance against the Digits dataset. Isomap and locally linear embedding (LLE) function differently depending on the dataset. Notably, LLE showed the largest loss and lowest fidelity on the Olivetti Faces dataset. The hypothesis testing findings showed that the qDR strategies did not significantly outperform the classical techniques in terms of maintaining pertinent information from quantum datasets. More specifically, the outcomes of paired t‐tests show that when it comes to the ability to capture complex patterns, there are no statistically significant differences between the cPCA and qPCA, the cLDA and qLDA, and the cGDA and qGDA. According to the findings of the assessments of mutual information (MI) and clustering accuracy, qPCA may be able to recognize patterns more clearly than standardized cPCA. Nevertheless, there is no discernible improvement between the qLDA and qGDA approaches and their classical counterparts.
Abstract This research explores the potential of quantum computing in data analysis, focusing on the efficient analysis of high-dimensional quantum datasets using dimensionality reduction techniques. The study aims to fill the knowledge gap by developing robust quantum dimensionality reduction techniques that can mitigate noise and errors. The research methodology involved a comprehensive review and analysis of existing quantum dimensionality reduction techniques, such as quantum principal component analysis, quantum linear discriminant analysis and quantum generative models. The study also explored the limitations imposed by NISQ devices and proposed strategies to adapt these techniques to work efficiently within these constraints. The key results demonstrate the potential of quantum dimensionality reduction techniques to effectively reduce the dimensionality of high-dimensional quantum datasets while preserving critical quantum information. The evaluation of quantum principal component analysis, quantum linear discriminant analysis and quantum generative models showed their effectiveness in improving quantum data analysis, particularly in improving simulation speed and predicting properties. Despite the challenges posed by noise and errors, robust quantum dimensionality reduction methods showed promise in mitigating these effects and preserving quantum information. Finally, this research contributes to the advancement of quantum data analysis by presenting a comprehensive analysis of quantum dimensionality reduction techniques and their applications. It highlights the importance of developing robust quantum feature learning methods that can operate efficiently in noisy quantum environments, especially in the NISQ era.
Breast cancer, the unruly development of abnormal cells in breasts, is a pressing public health issue and needs early detection for improving survival rates. Machine learning algorithms have shown promising results in breast cancer classification and detection. This study evaluates the performances of traditional and quantum machine learning techniques for data classification of breast cancer, emphasizing their effectiveness in discerning patterns using reduced set of features. An approach is proposed to reduce 30-dimensional features to 2-dimensional features using widely applied Principal Component Analysis (PCA), Incremental PCA, Truncated Singular Value Decomposition and Kernel PCA techniques. This study aims to provide an insight on the impact of reduction of features on the classification of breast cancer using classical and quantum machine learning techniques.
Breast cancer is rated as one of the top leading diagnosed and deadliest cancers affecting women worldwide and causing high mortality rate among cancers. With the data-driven applications, hybrid quantum-classical machine learning models have evolved as significant alternatives for handling complex feature spaces with the growing interest in quantum computing. This paper presents a systematic comparative study of classical and quantum machine learning approaches for breast cancer classification using the Wisconsin Breast Cancer Dataset. In this architecture we have preprocessed classical feature vectors using standard normalized techniques and parallelly quantum states are mapped through data embedding techniques which relies on parameterized rotational gates. In this work we have implemented all quantum models using the Pennylane library, resulting in hybrid quantum–classical optimization on near-term quantum simulators. The comparison results in multiple classical and quantum models. In classical we have Support Vector Machine (SVM), K-Nearest Neighbors (KNN) and Convolutional Neural Networks (CNN), which are compared with the quantum-based models such as the Variational Quantum Classifier (VQC), Quantum Support Vector Machine (QSVM) and Quantum Convolutional Neural Network (QCNN). In QSVM, we have performed dimensionality reduction using Principal Component Analysis (PCA) before to quantum embedding, and quantum-generated features are used to train a classical linear SVM. The evaluation metrics results in accuracy, precision, recall, F1-score, ROC curves and confusion matrices. The classical models achieves the accuracy in the range of 94%-96%, whereas competitive performance of quantum models demonstrate depending on the embedding strategy and circuit configuration. In the implemented quantum models, the variational quantum classifier achieved the highest classification accuracy of 96.06%, surpassing other evaluated models. These results demonstrate quantum embedding combined with variational quantum circuits can effectively capture discriminative patterns in medical datasets, indicating the implementation of quantum machine learning models for breast cancer diagnosis with the present quantum simulating platforms.
Introduction: In recent years, high-dimensional clinical and genomic data have gained significant importance for prognosis and personalized medicine in breast cancer. But the use of quantum machine learning (QML) on such data is limited by the availability of few qubits, the computation time of quantum simulation, and dimensionality reduction. This work systematically compares several QML architectures for breast cancer classification in the presence of realistic and simulator constraints. Methods: The experiments were performed on a dataset of METABRIC breast cancer patients (2,509 patients). After handling missing values and one-hot encoding, there were 63 features in the processed data set. The feature space was reduced by Principal Component Analysis (PCA) to 12, 4 and 2 components for the implementations of quantum computers, respectively, with 56.10 ± 0.14%, 26.78 ± 0.57% and 16.23 ± 0.33% of the variance retained. Three QML models were tested: Quantum Neural Networks (QNN), Quantum K-Nearest Neighbors (QKNN), and Quantum Support Vector Machines (QSVM), with the models being simulated. Seven classical classification models were tested: Logistic Regression, SVM with RBF kernel, K-Nearest Neighbors, Random Forest, XGBoost, LightGBM and Multilayer Perceptron, both with PCA-matched and full 63-feature representation. All primary results are reported with 5-fold cross validation. Results: Among the evaluated QML architectures, QKNN using 12 principal components achieved the strongest performance, attaining an accuracy of **75.11% ± 3.76%**, an F1-score of **0.7088 ± 0.0433**, and a ROC-AUC of **0.8148 ± 0.0394**. Even though all of the QML models performed significantly poorly in comparison to classical models trained on the entire 63-feature data set, the latter models were able to achieve about **94% accuracy** with XGBoost, Random Forest, and Logistic Regression. The comparison also showed the effect of information loss due to PCA is significant in predictive performance in both classical and quantum models. Discussion: The results show that for high dimensional breast cancer data, currently available simulator-based QML models can learn meaningful patterns with limited quantum resources, but are not as effective as powerful classical machine learning models when complete feature representations are available. The study does not report any sort of quantum advantage or clinical use, but rather a benchmark of current QML architectures that has been rigorously calculated and repeated, with a focus on the impact of dimensionality reduction, validation approaches, and simulator limitations, as well as outlining challenges that need to be overcome prior to practical implementation on real quantum hardware.
Obesity, characterized by an excessive increase in body fat, is not only a significant disease but also a condition that serves as the basis for many other illnesses. Therefore, early intervention and necessary precautions for diagnosing and treating obesity are of paramount importance. Classical machine learning algorithms are actively utilized in medical fields to expedite prediction processes. However, the increasing volume of data renders even effective classification algorithms inadequate for experts to diagnose diseases. Quantum computing-based algorithms come into play at this point, offering a new perspective in machine learning by utilizing quantum physics, which is contrary to the rules of classical physics. Dimensionality reduction techniques required for the use of quantum-based algorithms play an essential role in both classical and quantum applications. In this study, Linear Discriminant Analysis (LDA) and Principal Component Analysis (PCA), classical dimensionality reduction methods, were applied to the obesity dataset and analyzed with Quantum Support Vector Machine (QSVM) and Support Vector Machine (SVM) algorithms. To conduct QSVM studies, the comparison of three different quantum feature maps providing the qubit transformation of classical bit data is also included in this study. As a result of the analysis, it was determined that the proposed method as LDA-QSVM achieved 100% success when used with Z and Pauli X feature maps. This success, which is rare in literature studies on obesity data, emphasizes the future potential of quantum-based algorithms in obesity diagnosis and treatment.
This paper evaluates the performance of two quantum machine learning algorithms: Quantum Support Vector Machine (QSVM) and Quantum Principal Component Analysis (Q-PCA). The scalability of QSVM is analyzed across increasing dataset sizes and feature dimensions, revealing faster-than-linear growth in kernel evaluation and SVM training times. However, this computational overhead is accompanied by a notable decline in classification accuracy, highlighting challenges in applying QSVM to larger or more complex datasets. In contrast, Q-PCA demonstrates near-linear scalability with dataset size and qubit count, leveraging the independence of quantum circuit execution and structured operations to maintain efficiency. A QNN-based implementation of Q-PCA further validates its ability to align data with principal components, maximize variance, and enable effective dimensionality reduction. These findings emphasize the potential of Q-PCA for efficient quantum-enhanced data analysis while underscoring the need for optimization in QSVM and further exploration of Q-PCA’s capabilities for real-world quantum computing applications.