Kernel-based one-class classification (OCC) methods leverage kernel functions and are widely used for anomaly detection due to their ability to map data into high-dimensional feature spaces. One such model is Least Squares Support Vector Data Description (LS-SVDD), which aims to construct a minimum volume hypersphere that encompasses the target class observations. A pivotal component in the construction of the hypersphere is the choice of kernel. In this study, the Radial Basis Function (RBF) kernel is compared to a quantum kernel constructed through quantum feature maps. The two kernel methods are compared across four distributional shift scenarios—mean shift, rotating covariance, correlation drift, and Gaussian mixture—at three dimensionalities through simulations. Additionally, the two kernel methods are also evaluated using real-world data through an illustrative example. Furthermore, the Harrow-Hassidim-Lloyd (HHL) quantum algorithm was examined as a potential speedup for solving linear systems of equations within the LS-SVDD framework in quantum space.
Kernel-based one-class classification (OCC) methods leverage kernel functions and are widely used for anomaly detection due to their ability to map data into high-dimensional feature spaces. One such model is Least Squares Support Vector Data Description (LS-SVDD), which aims to construct a minimum volume hypersphere that encompasses the target class observations. A pivotal component in the construction of the hypersphere is the choice of kernel. In this study, the Radial Basis Function (RBF) kernel is compared to a quantum kernel constructed through quantum feature maps. The two kernel methods are compared across four distributional shift scenarios—mean shift, rotating covariance, correlation drift, and Gaussian mixture—at three dimensionalities through simulations. Additionally, the two kernel methods are also evaluated using real-world data through an illustrative example. Furthermore, the Harrow-Hassidim-Lloyd (HHL) quantum algorithm was examined as a potential speedup for solving linear systems of equations within the LS-SVDD framework in quantum space.
Abstract We compare two quantum approaches that use support vector machines for multi-class classification on a reduced Sloan Digital Sky Survey () dataset: the quantum kernel-based QSVM and the Harrow-Hassidim-Lloyd least-squares SVM (HHL LS-SVM). Both one-vs-rest and two-step hierarchical classification schemes were implemented. The QSVM involves angle encoding of ten features, two unitary operator blocks consisting of rotational operator gates, and a projective measurement that projects the final state to the zero state. The HHL-based method involves solving a system of linear equations using the HHL algorithm and using the solution in a support vector machine approach. The results indicate that the QSVM outperforms HHL LS-SVM in most cases. HHL LS-SVM performs somewhat competitively in selected cases, particularly when isolating galaxies (majority), however, it also performs poorly in others, especially when isolating QSOs (minority). Comparisons with classical SVMs confirm that quantum and classical methods achieve broadly similar performance, with classical models performing slightly ahead overall. Scaling analysis reveals a trade-off: QSVM performance suffers from quadratic scaling with the number of samples and features, but benefits from explicit feature representation during training, while HHL LS-SVM scales essentially constantly, with moderate fluctuations, but suffers from limited representative elements. The HHL-based method is also highly noise-sensitive. These results suggest that QSVM performs better overall under the experimental conditions considered here and is likely to be more amenable to near-term hardware execution in terms of circuit depth and structure, while the more efficient scaling of HHL LS-SVM makes it a useful option for larger datasets beyond the NISQ era.
Abstract Least Squares Support Vector Machine (LS-SVM) is a reformulation of the Support Vector Machine(SVM) algorithm that uses a hyperplane to classify elements in a dataset, with the coefficients of the hyperplane being determined by solving a linear system of equations. A quantum algorithm, the Harrow-Hassidim-Lloyd (HHL) algorithm, has the potential to offer exponential advantages over classical algorithms for solving linear systems, although an efficient implementation is yet to be developed. The current era of quantum computing presents a series of technical challenges for implementing and executing circuits, with smaller circuits being less susceptible to noise. In response to this scenario, circuit reduction optimizations have been developed to enhance execution quality. This paper presents the process of using optimized HHL quantum circuits to generate LS-SVMs applied to the classification of pulsar candidates, where the quantum generated SVMs closely matched the performance of their classical counterparts and obtained competitive results against other Quantum Machine Learning methods even when using a real quantum device, with the optimized circuits having a significant execution speedup over the original quantum circuits.
Anomaly detection, an important task in data analysis, involves identifying observations or events that deviate in some way from the rest of the data. Machine learning techniques have shown success in automating this process by detecting hidden patterns and deviations in large-scale data. The potential of quantum computing for machine learning has been widely recognized, leading to extensive research efforts to develop suitable quantum machine learning (QML) algorithms. In particular, the search for QML algorithms for near-term NISQ devices is in full swing. However, NISQ devices pose additional challenges due to their limited qubit coherence times, low number of qubits, and high error rates. Kernel methods based on quantum kernel estimation have emerged as a promising approach to QML on NISQ devices, offering theoretical guarantees, versatility, and compatibility with NISQ constraints. Especially support vector machines (SVM) utilizing quantum kernel estimation have shown success in various supervised learning tasks. However, in the context of anomaly detection, semisupervised learning is of great relevance, and yet there is limited research published in this area. This paper introduces an approach to semisupervised anomaly detection based on the reconstruction loss of a support vector regression (SVR) with quantum kernel. This novel model is an alternative to the variational quantum and quantum kernel one-class classifiers, and is compared to a quantum autoencoder as quantum baseline and a SVR with radial-basis-function (RBF) kernel as well as a classical autoencoder as classical baselines. The models are benchmarked extensively on 10 real-world anomaly detection data sets and one toy data set and it is shown that our SVR model with quantum kernel performs better than the SVR with RBF kernel as well as all other models, achieving highest mean AUC over all data sets. In addition, our QSVR outperforms the Quantum autoencoder on 9 out of 11 data sets.
One-class classification (OCC) is a fundamental problem in machine learning with numerous applications, such as anomaly detection and quality control. With the increasing complexity and dimensionality of modern datasets, there is a growing demand for advanced OCC techniques with better expressivity and efficiency. We introduce Neural Quantum Support Vector Data Description (NQSVDD), a classical-quantum hybrid framework for OCC that performs end-to-end optimized hierarchical representation learning. NQSVDD integrates a classical neural network with trainable quantum data encoding and a variational quantum circuit, enabling the model to learn nonlinear feature transformations tailored to the OCC objective. The hybrid architecture maps input data into an intermediate high-dimensional feature space and subsequently projects it into a compact latent space defined through quantum measurements. Importantly, both the feature embedding and the latent representation are jointly optimized such that normal data form a compact cluster, for which a minimum-volume enclosing hypersphere provides an effective decision boundary. Experimental evaluations on benchmark datasets demonstrate that NQSVDD achieves competitive or superior AUC performance compared to classical Deep SVDD and quantum baselines, while maintaining parameter efficiency and robustness under realistic noise conditions.
Abstract Quantum kernel approaches have been touted as a possible way to gain representational advantages over classical machine learning techniques however most comparative work only looks at classification accuracy leaving the geometric structure of the kernels unexplored. We carry out a comprehensive kernel-level comparison between classical support vector machines (SVMs) with radial basis function (RBF) kernels and quantum support vector classifiers that use ZZFeatureMap and PauliFeatureMap fidelity kernels, tested on two synthetic and two real-world two-dimensional datasets. After applying centred kernel alignment(CKA), the Hilbert-Schmidt Independence Criterion (HSIC), eigenvalue spectrum analysis, spectral entropy, and effective rank. Firstly, shallow quantum kernels form a moderately aligned band with RBF across all datasets and conditions that is quite stable (CKA : 0.41 → 0.57), whereas going deeper in the circuit to two repetitions largely mismatches both alignment and accuracy with no representational gain (e.g. Iris cross-validation accuracy: 0.920 → 0.670, p = 0.0004). Secondly, depolarising noise surprisingly increases the quantum-classical kernel alignment, which means that near-term hardware kernels are structurally closer to RBF than noiseless simulations suggest. Thirdly, the scenarios that lead to maximum apparent quantum-classical divergence, small sample sizes and low noise, are precisely those most used to benchmark quantum kernel advantage. Kernel-level structural analysis is essential for meaningful evaluation of quantum machine learning methods.
Quantum kernel methods have been proposed as a promising approach for leveraging near-term quantum computers for supervised learning, yet rigorous benchmarks against strong classical baselines remain scarce. We present a comprehensive empirical study of quantum kernel support vector machines (QSVMs) across nine binary classification datasets, four quantum feature maps, three classical kernels, and multiple noise models, totalling 970 experiments with strict nested cross-validation.
Our analysis spans four phases: (i) statistical significance testing, revealing that none of 29 pairwise quantum-classical comparisons reach significance at α=0.05; (ii) learning curve analysis over six training fractions, showing steeper quantum slopes on six of eight datasets that nonetheless fail to close the gap to the best classical baseline; (iii) hardware validation on IBM ibm_fez (Heron r2), demonstrating kernel fidelity r≥0.976 across six experiments; and (iv) seed sensitivity analysis confirming reproducibility (mean CV 1.4%).
A Kruskal-Wallis factorial analysis reveals that dataset choice dominates performance variance (ε2=0.73), while kernel type accounts for only 9%. Spectral analysis offers a mechanistic explanation: current quantum feature maps produce eigenspectra that are either too flat or too concentrated, missing the intermediate profile of the best classical kernel, the radial basis function (RBF). Quantum kernel training (QKT) via kernel-target alignment yields the single competitive result -- balanced accuracy 0.968 on breast cancer -- but with ~2,000x computational overhead.
Our findings provide actionable guidelines for quantum kernel research. The complete benchmark suite is publicly available to facilitate reproduction and extension.