Abstract We present a comprehensive investigation into the learning capabilities of a simple d-level system (qudit). Our study is specialized for classification tasks using real-world databases, specifically the Iris, breast cancer, and MNIST datasets. We explore various learning models in the metric learning framework, along with different encoding strategies. In particular, we employ data re-uploading techniques and maximally orthogonal states to accommodate input data within low-dimensional systems. Our findings reveal optimal strategies, indicating that when the dimension of input feature data and the number of classes are not significantly larger than the qudit’s dimension, our results show favorable comparisons against the best classical models. This trend holds true even for small quantum systems, with dimensions d < 5 and utilizing algorithms with a few layers ( L = 1 , 2 ). However, for high-dimensional data such as MNIST, we adopt a hybrid approach involving dimensional reduction through a convolutional neural network. In this context, we observe that small quantum systems often act as bottlenecks, resulting in lower accuracy compared to their classical counterparts.
Abstract We present a comprehensive investigation into the learning capabilities of a simple d-level system (qudit). Our study is specialized for classification tasks using real-world databases, specifically the Iris, breast cancer, and MNIST datasets. We explore various learning models in the metric learning framework, along with different encoding strategies. In particular, we employ data re-uploading techniques and maximally orthogonal states to accommodate input data within low-dimensional systems. Our findings reveal optimal strategies, indicating that when the dimension of input feature data and the number of classes are not significantly larger than the qudit’s dimension, our results show favorable comparisons against the best classical models. This trend holds true even for small quantum systems, with dimensions d < 5 and utilizing algorithms with a few layers ( L = 1 , 2 ). However, for high-dimensional data such as MNIST, we adopt a hybrid approach involving dimensional reduction through a convolutional neural network. In this context, we observe that small quantum systems often act as bottlenecks, resulting in lower accuracy compared to their classical counterparts.
Abstract Quantum two-level systems, i.e., qubits, form the basis for most quantum machine learning approaches that have been proposed throughout the years. However, higher dimensional quantum systems constitute a promising alternative and are increasingly explored in theory and practice. Here, we explore the capabilities of multi-level quantum systems, so-called qudits, for their use in a quantum machine learning context. We formulate classification and regression problems with the data re-uploading approach and demonstrate that a quantum circuit operating on a single qudit is able to successfully learn highly non-linear decision boundaries of classification problems such as the MNIST digit recognition problem. We demonstrate that the performance strongly depends on the relation between the qudit states representing the labels and the structure of labels in the training data set. Such a bias can lead to substantial performance improvement over qubit-based circuits in cases where the labels, the qudit states, and the operators employed to encode the data are well-aligned. Furthermore, we elucidate the influence of the choice of the elementary operators and show that a squeezing operator is necessary to achieve good performances. We also show that there exists a trade-off for qudit systems between the number of circuit-generating operators in each processing layer and the total number of layers needed to achieve a given accuracy. Finally, we compare classification results from numerically exact simulations and their equivalent implementation on actual IBM quantum hardware. The findings of our work support the notion that qudit-based algorithms exhibit attractive traits and constitute a promising route to increasing the computational capabilities of quantum machine learning approaches.
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.
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.
Quantum machine learning holds the potential to revolutionize cancer treatment and diagnostic imaging by uncovering complex patterns beyond the reach of classical methods. This study explores the effectiveness of quantum convolutional layers in classifying ultrasound breast images for cancer detection. By encoding classical data into quantum states through angle embedding and employing a robustly entangled 9-qubit circuit design with an SU(4) gate, we developed a Quantum Convolutional Neural Network (QCNN) and compared it to a classical CNN of similar architecture. Our QCNN model, leveraging two quantum circuits as convolutional layers, achieved an impressive peak training accuracy of 76.66% and a validation accuracy of 87.17% at a learning rate of 1 × 10−2. In contrast, the classical CNN model attained a training accuracy of 77.52% and a validation accuracy of 83.33%. These compelling results highlight the potential of quantum circuits to serve as effective convolutional layers for feature extraction in image classification, especially with small datasets.
Abstract Quantum Machine Learning (QML) has emerged as a promising paradigm that leverages the principles of quantum mechanics—such as superposition and entanglement—to overcome the limitations of classical machine learning in handling complex, high-dimensional data. However, practical challenges such as limited coherence times of qubits and the integration of quantum circuits with classical architectures have hindered the full realization of QML’s potential. To address these challenges, this paper proposes a novel hybrid architecture, termed the Classical-Quantum Hybrid Convolutional Neural Network (CQHCNN), which integrates quantum-inspired layers into conventional deep learning frameworks. These quantum layers utilize quantum information processing to extract complex features, while the classical components perform feature extraction and classification. This paper evaluates the performance of our model on several benchmark datasets, including MNIST, Fashion-MNIST, CIFAR-10 and COVID-19 Radiography, demonstrating its ability to outperform some other Quantum Convolutional Neural Networks (QCNNs) in terms of many metrics. Experimental results indicate that the hybrid model achieves significant improvements in classification accuracy and computational efficiency, highlighting the potential of quantum-inspired techniques to enhance classical machine learning models.
This paper presents a hybrid quantum-classical machine learning model for classification tasks, integrating a 4-qubit quantum circuit with a classical neural network. The quantum circuit is designed to encode the features of the Iris dataset using angle embedding and entangling gates, thereby capturing complex feature relationships that are difficult for classical models alone. The model, which we term a Quantum Convolutional Neural Network (QCNN), was trained over 20 epochs, achievinga perfect 100% accuracy on the Iris dataset test set on 16 epoch. Our results demonstrate the potential of quantum-enhanced models in supervised learning tasks, particularly in efficiently encoding and processing data using quantum resources. We detail the quantum circuit design, parameterizedgate selection, and the integration of the quantum layer with classical neural network components.This work contributes to the growing body of research on hybrid quantum-classical models and theirapplicability to real-world datasets.