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IEEE Access

Comparative Analysis of a Quantum SVM With an Optimized Kernel Versus Classical SVMs

Matheus Cammarosano Hidalgo

Published Jan 1, 2025• 10 citations
Publisher

Abstract

SupportVector Machine (SVM) is a widely used algorithm for classification, valued for its flexibility with kernels that effectively handle non-linear problems and high-dimensional data. Businesses across industries face challenges in improving customer retention and reducing churn, making predictive models essential for identifying at-risk customers and enhancing revenue. This paper investigates an optimized quantum embedding kernel for SVM (Quantum SVM - QSVM) applied to a public bank customer dataset, featuring variables on customer relationships and churn indicators. While focused on the financial sector, the methodology is broadly applicable for reducing churn and boosting revenue across industries. QSVM performance is compared to SVMs with established kernels, including Radial Basis Function (RBF), linear, polynomial, and sigmoid. Experiments varied the number of variables from two to seven to evaluate their impact on model performance and kernel behavior. The experiments were conducted on quantum simulators, which faced scalability challenges addressed using reduced datasets. Even so, this study sheds light on the potential of QSVMs to effectively manage increasing numbers of variables in predictive models, offering valuable insights into their capability to handle complex, high-dimensional data and their applicability in real-world scenarios.

DOI
10.1109/access.2025.3567352

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SupportVector Machine (SVM) is a widely used algorithm for classification, valued for its flexibility with kernels that effectively handle non-linear problems and high-dimensional data. Businesses across industries face challenges in improving customer retention and reducing churn, making predictive models essential for identifying at-risk customers and enhancing revenue. This paper investigates an optimized quantum embedding kernel for SVM (Quantum SVM - QSVM) applied to a public bank customer dataset, featuring variables on customer relationships and churn indicators. While focused on the financial sector, the methodology is broadly applicable for reducing churn and boosting revenue across industries. QSVM performance is compared to SVMs with established kernels, including Radial Basis Function (RBF), linear, polynomial, and sigmoid. Experiments varied the number of variables from two to seven to evaluate their impact on model performance and kernel behavior. The experiments were conducted on quantum simulators, which faced scalability challenges addressed using reduced datasets. Even so, this study sheds light on the potential of QSVMs to effectively manage increasing numbers of variables in predictive models, offering valuable insights into their capability to handle complex, high-dimensional data and their applicability in real-world scenarios.
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Churn prediction of customers is highly significant in banking as the cost of retention is much lower than the cost of acquisition. Usually individuals operate with the standard ML frameworks, such as SVM, although they have a ceiling when the data is of high dimension and extremely non-linear - they become more and more sluggish and are inadequate to actually model all the complexity. The paper presents a Quantum Support Vector Machine (QSVM) that is used to predict the customers who are going to leave the bank. Unlike The preprocessing in classical code, such as clean up the data, encoding of categories, scaling and then PCA to reduce the feature set to one that fits within the small number of qubits, all proceeds as normal. Then we apply the shrunk data to a quantum state, using ZZFeatureMap, and compute a quantum kernel which informs us of the similarity between data points in Hilbert space. Initialization of the QSVM in Python using Qiskit and then running it on the Qiskit Aer simulator. It is reasonably good: overall accuracy of around 88 percent and good scores on non-churn customer identification and fair adequacy in identifying churners. These figures demonstrate that quantum-enhanced ML might be a viable alternative to quantum hardware in the realm of real business analytics and is going to become even more feasible as quantum technology advances.
Quantum Machine Learning (QML) provides a pathway for analysing nonlinear relationships through quantum- enhanced feature spaces. Although quantum models are theoreti- cally well suited for high-complexity data, current hardware and simulator limitations restrict their use to small datasets. For this reason, the original large Web Phishing Detection Dataset was reduced to 200 representative samples through dimensionality reduction, allowing controlled experimentation and enabling evaluation of quantum behaviour with manageable computational cost. QML research commonly follows this approach, testing algorithms on small datasets first, because quantum feature maps can generate exponentially expressive Hilbert-space embeddings even from limited inputs. In this study, multiple Quantum Support Vector Machine (QSVM) models were implemented using fidelity-based quantum kernels and Pauli feature maps. Models with 2 to 10 qubits were evaluated to observe how circuit width affects performance. The two-qubit QSVM achieved the best quantum result with 72 % accuracy, whereas deeper circuits showed declining performance, indicating overfitting and reduced generalization on limited data. In contrast, the classical SVM attained 97 % accuracy with significantly lower computational effort. These findings highlight the challenges and potential of QML for cybersecurity tasks. Future work will explore circuit- expressivity tuning, optimized quantum kernels, hybrid quantum- classical approaches, and scalability to larger phishing datasets as quantum hardware evolves.
Abstract Support vector machines (SVMs) are widely used for classification, but become computationally expensive as datasets grow and data become high-dimensional or nonlinearly separable. Quantum support vector machines (QSVMs) enhance the traditional SVMs by replacing conventional feature mappings with quantum-implemented embeddings that project data into high-dimensional Hilbert spaces, potentially improving expressive power and efficiency. However, training QSVMs on current noisy intermediate-scale quantum (NISQ) devices remains challenging, as constructing the quantum kernel matrix requires repeated circuit executions and scales quadratically with dataset size. We propose NQ-SVM , a hybrid quantum-classical method that incorporates the Nystr\"om approximation to enhance the scalability of QSVMs. By selecting a small set of landmark points, the Nystr\"om method yields a low-rank kernel approximation, reducing complexity from (O(n2))(O(n^2))(O(n2)) to (O(nm))(O(nm))(O(nm)), while preserving the quantum advantages in handling high-dimensional, non-linear data. Extensive simulations demonstrate that NQ-SVM achieves comparable classification accuracy to classical SVMs and full QSVMs, while substantially reducing training time and kernel evaluation costs. These results underscore the potential of NQ-SVM as a scalable and practical hybrid framework for near-term quantum machine learning (QML).
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.
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.