Abstract The high-dimensional linear separability of the classic support vector machine is achieved through the kernel method, which maps data to a high-dimensional space. However, the kernel method involves estimating multiple parameters, which reduces the model's computational efficiency. To address this, some related works use quantum kernel estimation to replace the classic kernel method, thus reducing the computational load associated with parameter estimation in quantum support vector machines. Despite these improvements, quantum support vector machines face the challenge of establishing correlations between different data points through quantum entanglement to effectively capture the distribution characteristics of the data. Consequently, the model's accuracy is low when performing regression analysis on large datasets with complex distributions. To address this issue, an improved quantum backpropagation algorithm is introduced, utilizing controlled-Z gates to entangle qubits representing different data points. Additionally, to enhance the entanglement between qubits, the absolutely maximally entangled state is employed to further optimize the quantum backpropagation algorithm. This enhancement enables the algorithm to better capture the distribution characteristics of the data. Building on this, the quantum support vector machine model is improved to overcome the shortcomings of the existing model. A new algorithm is proposed, and the parameter count of the new algorithm's circuit is analyzed. Experimental results demonstrate that optimizing the quantum backpropagation algorithm to improve the quantum support vector machine leads to higher accuracy in regression analysis on real-world problems. Specifically, strengthening the degree of quantum entanglement makes the model more capable of capturing the distribution characteristics of complex datasets, resulting in more accurate fitting outcomes.
Abstract The high-dimensional linear separability of the classic support vector machine is achieved through the kernel method, which maps data to a high-dimensional space. However, the kernel method involves estimating multiple parameters, which reduces the model's computational efficiency. To address this, some related works use quantum kernel estimation to replace the classic kernel method, thus reducing the computational load associated with parameter estimation in quantum support vector machines. Despite these improvements, quantum support vector machines face the challenge of establishing correlations between different data points through quantum entanglement to effectively capture the distribution characteristics of the data. Consequently, the model's accuracy is low when performing regression analysis on large datasets with complex distributions. To address this issue, an improved quantum backpropagation algorithm is introduced, utilizing controlled-Z gates to entangle qubits representing different data points. Additionally, to enhance the entanglement between qubits, the absolutely maximally entangled state is employed to further optimize the quantum backpropagation algorithm. This enhancement enables the algorithm to better capture the distribution characteristics of the data. Building on this, the quantum support vector machine model is improved to overcome the shortcomings of the existing model. A new algorithm is proposed, and the parameter count of the new algorithm's circuit is analyzed. Experimental results demonstrate that optimizing the quantum backpropagation algorithm to improve the quantum support vector machine leads to higher accuracy in regression analysis on real-world problems. Specifically, strengthening the degree of quantum entanglement makes the model more capable of capturing the distribution characteristics of complex datasets, resulting in more accurate fitting outcomes.
Classical machine learning, extensively utilized across diverse domains, faces limitations in speed, efficiency, parallelism, and processing of complex datasets. In contrast, quantum machine learning algorithms offer significant advantages, including exponentially faster computations, enhanced data handling capabilities, inherent parallelism, and improved optimization for complex problems. In this study, we used the entanglement enhanced quantum kernel in a quantum support vector machine to train complex respiratory datasets. Compared to classical algorithms, our findings reveal that quantum support vector machine (QSVM) performs better with higher accuracy (45%) for complex respiratory datasets while maintaining comparable performance with linear datasets in contrast to their classical counterparts executed on a 2-qubit system. Through our study, we investigate the efficacy of the QSVM-Kernel algorithm in harnessing the enhanced dimensionality of the quantum Hilbert space for effectively training complex datasets.
Classical machine learning, extensively utilized across diverse domains, faces limitations in speed, efficiency, parallelism, and processing of complex datasets. In contrast, quantum machine learning algorithms offer significant advantages, including exponentially faster computations, enhanced data handling capabilities, inherent parallelism, and improved optimization for complex problems. In this study, we used the entanglement-enhanced quantum kernel in quantum support vector machine to train complex respiratory data sets. Compared to classical algorithms, our findings reveal that QSVM performs better with 45% higher accuracy for complex respiratory data sets while maintaining comparable performance with linear datasets in contrast to their classical counterparts executed on a 2-qubit system. Through our study, we investigate the efficacy of the QSVM-Kernel algorithm in harnessing the enhanced dimensionality of the quantum Hilbert space for effectively training complex datasets.
Quantum machine learning has emerged as a promising frontier, leveraging the principles of quantum computing to enhance classical algorithms. This paper proposes an optimized Quantum Support Vector Classifier (QSVC) for the classification of the MNIST dataset (a benchmark in handwritten digit recognition). We employ a Chebyshev Parameterized Quantum Circuit (PQC) with an increased number of qubits and layers, and utilize an existing projected quantum kernel method to effectively capture the complex patterns in the data. To enhance model robustness, data augmentation techniques are applied, and dimensionality reduction is performed using Principal Component Analysis (PCA). The proposed QSVC demonstrates competitive accuracy on both the training and testing datasets, highlighting the potential of quantum kernel methods in practical machine learning applications. A comparative analysis with classical Support Vector Machines (SVM) demonstrates the feasibility of quantum methods for high-dimensional classification tasks. Additionally, we investigate the impact of varying the number of qubits in the quantum circuit, providing in-depth insights into the scalability and performance trade-offs of quantum kernel methods.
Quantum Machine Learning (QML) has emerged as a paradigm that combines the computational advantages of quantum computing with the predictive capabilities of machine learning to address complex data classification problems. As data dimensionality increases rapidly and classical learning algorithms face scalability constraints, QML leverages quantum parallelism, entanglement, and high-dimensional Hilbert space representations to enhance learning performance. This paper reviews and analyses advanced QML algorithms, including Quantum Support Vector Machines (QSVM), Variational Quantum Circuits (VQC), Quantum Neural Networks (QNN), and Quantum Kernel Estimation, for optimizing both binary and multi-class classification tasks under high-complexity conditions. The proposed QML framework is evaluated on benchmark datasets like MNIST, the Breast Cancer Wisconsin (BCW) dataset, and synthetic nonlinear datasets, and is compared against classical machine learning baselines, including Support Vector Machines (SVM), Random Forests (RF), and Deep Neural Networks (DNN). The results demonstrate notable improvements in classification accuracy (up to 96.8%), decision margins, and computational efficiency in quantum-suitable data regimes, while also highlighting current limitations related to noise, circuit depth, and hardware constraints. Overall, the study presents a unified QML framework, theoretical formulations, and experimental evaluations that illustrate the potential of quantum algorithms for next-generation classification tasks.
Support Vector Machines (SVMs) are powerful machine learning models widely used for classification and regression tasks. However, their performance can be significantly impacted by the choice of the kernel function, which defines how data points are mapped into a higher-dimensional space. Traditional kernels often struggle to capture complex, non-linear relationships effectively, leading to suboptimal results. This paper proposes a novel approach to kernel design inspired by quantum mechanical principles. Specifically, we leverage concepts of quantum entanglement and superposition to generate kernels that can potentially capture richer and more nuanced data patterns. Our core claim is that employing these quantum-inspired designs can improve SVM performance and scalability. We present a theoretical framework outlining how quantum mechanical effects can be translated into kernel functions. The proposed method is based on constructing kernel functions that implicitly encode correlations between data points, mimicking the inherent interconnectedness observed in quantum systems. We explore specific kernel formulations based on these principles and discuss their potential advantages and challenges. The ultimate goal is to demonstrate that quantum inspiration can unlock new avenues for kernel design, leading to more effective SVM models.
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.