This work presents a fully quantum approach to support vector machine (SVM) learning by integrating gate-based quantum kernel methods with quantum annealing-based optimization. We explore the construction of quantum kernels using various feature maps and qubit configurations, evaluating their suitability through Kernel-Target Alignment (KTA). The SVM dual problem is reformulated as a Quadratic Unconstrained Binary Optimization (QUBO) problem, enabling its solution via quantum annealers. Our experiments demonstrate that a high degree of alignment in the kernel and an appropriate regularization parameter lead to competitive performance, with the best model achieving an F1-score of 90%. These results highlight the feasibility of an end-to-end quantum learning pipeline and the potential of hybrid quantum architectures in quantum high-performance computing (QHPC) contexts.
This work presents a fully quantum approach to support vector machine (SVM) learning by integrating gate-based quantum kernel methods with quantum annealing-based optimization. We explore the construction of quantum kernels using various feature maps and qubit configurations, evaluating their suitability through Kernel-Target Alignment (KTA). The SVM dual problem is reformulated as a Quadratic Unconstrained Binary Optimization (QUBO) problem, enabling its solution via quantum annealers. Our experiments demonstrate that a high degree of alignment in the kernel and an appropriate regularization parameter lead to competitive performance, with the best model achieving an F1-score of 90%. These results highlight the feasibility of an end-to-end quantum learning pipeline and the potential of hybrid quantum architectures in quantum high-performance computing (QHPC) contexts.
Quantum machine learning is one of the fields where quantum computers are expected to bring advantages over classical methods. However, the limited size of current computers restricts the exploitation of the full potential of quantum machine learning methods. Additionally, different computing paradigms, both quantum and classical, each have their own strengths and weaknesses. Obtaining optimal results with algorithms thus requires algorithms to be tweaked to the underlying computational paradigm, and the tasks to be optimally distributed over the available computational resources. In this work, we explore the potential gains from combining different computing paradigms to solve the complex task of data classification for three different datasets. We use a gate-based quantum model to implement a quantum kernel and implement a complex feature map. Next, we formulate a quadratic unconstrained optimisation problem to be solved on quantum annealing hardware. We then evaluate the losses on classical hardware and reconfigure the model parameters accordingly. We tested this so-called triple-hybrid quantum support vector machine on various data sets, and find that it achieves higher precision than other support vector machines (both quantum and classical) on complex quantum data, whereas it achieves varying performance on simple classical data using limited training. For the complex data sets, the triple-hybrid version converges faster, requiring fewer circuit evaluations.
Classification is a fundamental task in machine learning that aims to categorize input samples into predefined classes based on their features. It has widespread applications in areas such as spam detection and image classification. Support Vector Machines (SVM) are a widely-used supervised learning method that seeks to maximize the margin between decision boundaries, particularly excelling in non-linear classification tasks through kernel functions. In this study, the SVM classification problem is reformulated as an optimization problem and represented using Quadratic Unconstrained Binary Optimization (QUBO) to leverage quantum computing for solving. To enhance the solution process, the simulated annealing algorithm is employed, improving convergence speed and boosting both the efficiency and performance of the classification task.
In recent years, quantum computers have emerged as promising candidates for implementing kernels. Quantum Embedding Kernels embed data points into quantum states and calculate their inner product in a high-dimensional Hilbert Space by computing the overlap between the resulting quantum states. Variational Quantum Circuits (VQCs) are typically used for this end, with Kernel Target Alignment (KTA) as cost function. The optimized kernels can then be deployed in Support Vector Machines (SVMs) for classification tasks. However, both classical and quantum SVMs scale poorly with increasing dataset sizes. This issue is exacerbated in quantum kernel methods, as each inner product requires a quantum circuit execution. In this paper, we investigate KTA-trained quantum embedding kernels and employ a low-rank matrix approximation, the Nyström method, to reduce the quantum circuit executions needed to construct the Kernel Matrix. We empirically evaluate the performance of our approach across various datasets, focusing on the accuracy of the resulting SVM and the reduction in quantum circuit executions. Additionally, we examine and compare the robustness of our model under different noise types, particularly coherent and depolarizing noise.
Quantum annealers natively minimize quadratic unconstrained binary optimization (QUBO) problems, yet faithfully compiling continuous convex objectives into discrete binary forms with formal guarantees remains challenging. We present a complete, algebraically verifiable pipeline for training a linear squared-hinge support vector machine on quantum annealing hardware. The construction comprises four stages with rigorous justification: (i) an exact epigraph reformulation eliminating the hinge nonlinearity, (ii) equality conversion via surplus variables with a quadratic penalty whose exactness on the finite binary domain is formally established, (iii) closed-form QUBO coefficients and a provably energy-preserving Ising mapping, and (iv) a moment-based three-component decoder that reconstructs continuous parameters from noisy annealer samples using empirical first- and second-order statistics. We execute this pipeline end-to-end on D-Wave Advantage systems and evaluate under a rigorous protocol with 30 stratified splits, bootstrap confidence intervals, paired tests, and effect sizes. The feature-wise solver achieves 87-89% test accuracy on the Iris benchmark, competitive with classical baselines at this scale. We contribute a fully auditable reduction from convex SVM training to Ising optimization rather than claiming quantum advantage, and explicitly characterize limitations from discretization, embedding overhead, and feature-wise decomposition.
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)) to (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 introduces a generalized quantum-classical dual kernel learning method for Support Vector Machines (SVMs), extending its application to both classification and regression tasks. Our method combines quantum and classical kernels via an adaptively weighted linear combination, forming a dual kernel learning technique that outperforms models relying solely on either kernel type. In this paper, we demonstrate the effectiveness of our approach on several real-world datasets in terms of classification accuracy and for regression, highR2-score and low Root Mean Square Error (RMSE). Furthermore, we evaluate the dual kernel model on both ideal and noisy quantum backends using the IBM Qiskit toolkit. Under ideal conditions, the dual kernel method consistently maintains superior performance compared to purely classical or quantum kernels. While the presence of noise may affect performance, the dual kernel still achieves results that are competitive with the best individual kernels, underscoring its robustness and practical viability in real-world applications.