This dataset contains the complete experimental results and supporting data generated in the study of quantum feature maps and their impact on kernel geometry, expressivity, and classification performance. The experiments investigate quantum kernel methods based on the Loschmidt Echo formulation, implemented using PennyLane, and evaluate multiple quantum embeddings across different datasets and input dimensions. For each configuration (dataset × embedding × dimension), the dataset includes: - quantum kernel matrices,- classification results (SVM with precomputed kernels),- kernel target alignment (KTA),- effective dimension of the kernel,- model complexity measures,- geometric difference metrics,- aggregated statistical summaries,- configuration snapshots ensuring full reproducibility. The dataset is structured to support full reproducibility of the experimental pipeline and enables independent analysis of quantum kernel geometry and learning performance. All results correspond to benchmark experiments conducted on datasets from the PennyLane QML benchmark collection. This dataset accompanies a study on the relationship between quantum embeddings, kernel geometry, and machine learning performance.
This dataset contains the complete experimental results and supporting data generated in the study of quantum feature maps and their impact on kernel geometry, expressivity, and classification performance. The experiments investigate quantum kernel methods based on the Loschmidt Echo formulation, implemented using PennyLane, and evaluate multiple quantum embeddings across different datasets and input dimensions. For each configuration (dataset × embedding × dimension), the dataset includes: - quantum kernel matrices,- classification results (SVM with precomputed kernels),- kernel target alignment (KTA),- effective dimension of the kernel,- model complexity measures,- geometric difference metrics,- aggregated statistical summaries,- configuration snapshots ensuring full reproducibility. The dataset is structured to support full reproducibility of the experimental pipeline and enables independent analysis of quantum kernel geometry and learning performance. All results correspond to benchmark experiments conducted on datasets from the PennyLane QML benchmark collection. This dataset accompanies a study on the relationship between quantum embeddings, kernel geometry, and machine learning performance.
The support vector machine algorithm with a quantum kernel estimator (QSVM-Kernel), as a leading example of a quantum machine learning technique, has undergone significant advancements. Nevertheless, its integration with classical data presents unique challenges. While quantum computers primarily interact with data in quantum states, embedding classical data into quantum states using feature mapping techniques is essential for leveraging quantum algorithms Despite the recognized importance of feature mapping, its specific impact on data classification outcomes remains largely unexplored. This study addresses this gap by comprehensively assessing the effects of various feature mapping methods on classification results, taking medical data analysis as a case study. In this study, the QSVM-Kernel method was applied to classification problems in two different and publicly available medical datasets, namely, the Wisconsin Breast Cancer (original) and The Cancer Genome Atlas (TCGA) Glioma datasets. In the QSVM-Kernel algorithm, quantum kernel matrices obtained from 9 different quantum feature maps were used. Thus, the effects of these quantum feature maps on the classification results of the QSVM-Kernel algorithm were examined in terms of both classifier performance and total execution time. As a result, in the Wisconsin Breast Cancer (original) and TCGA Glioma datasets, when Rx and Ry rotational gates were used, respectively, as feature maps in the QSVM-Kernel algorithm, the best classification performances were achieved both in terms of classification performance and total execution time. The contributions of this study are that (1) it highlights the significant impact of feature mapping techniques on medical data classification outcomes using the QSVM-Kernel algorithm, and (2) it also guides undertaking research for improved QSVM classification performance.
Reproducibility archive (code + manuscript) for the paper "Benchmarking Quantum Kernel Support Vector Machines Against Classical Baselines on Tabular Data: A Rigorous Empirical Study with Hardware Validation" (arXiv:2604.18837). The archive contains the full Python benchmark framework, experiment configurations, unit tests, and the compiled manuscript. 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; (ii) learning curve analysis; (iii) hardware validation on IBM ibm_fez (Heron r2); and (iv) seed sensitivity analysis. 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 (RBF). The complete benchmark suite is publicly available to facilitate reproduction and extension.
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.
Quantum kernels are among the most promising methods in quantum machine learning, providing a natural way to embed data into high-dimensional Hilbert spaces via quantum circuits and capturing non-linear relationships in data. Their learning behaviour is governed by the function class they represent, which is formally characterized by the structure of the associated Reproducing Kernel Hilbert Space (RKHS). However, a theoretical characterization of this function class, and of how it depends on the choice of feature map and its hyperparameters, is still lacking. In this work, we focus on the Instantaneous Quantum Polynomial (IQP) feature map and derive a Fourier representation of the associated RKHS generators as finite sums of trigonometric functions evaluated on polynomially transformed input variables, with a finite set of accessible frequencies determined by the circuit construction and scaled by the bandwidth hyperparameter. This representation identifies three bandwidth regimes with qualitatively distinct expressive properties from localised, through multimodal, to periodic. Numerical experiments on synthetic datasets with controlled periodic and multimodal structure, across data dimensions and feature-map configurations, reproduce the three regimes in both supervised classification and unsupervised anomaly detection, benchmarked against a classical Gaussian kernel. These results make the relationship between expressivity and data structure explicit for IQP kernels: expressive power translates into a practical benefit only when the accessible frequencies match with the structure of the data, which provides a criterion for selecting the bandwidth when the periodic or multimodal structure of data is known.
Quantum-enhanced machine learning is a rapidly evolving field that aims to leverage the unique properties of quantum mechanics to enhance classical machine learning. However, the practical applicability of these methods remains an open question, particularly beyond the context of specifically crafted toy problems, and given the current limitations of quantum hardware. This study focuses on quantum kernel methods in the context of classification tasks. In particular, it examines the performance of quantum kernel estimation and quantum kernel training (QKT) in connection with two quantum feature mappings, namely, ZZFeatureMap and CovariantFeatureMap. Remarkably, these feature maps have been proposed in the literature under the conjecture of possible near-term quantum advantage and have shown promising performance in ad hoc datasets. This study aims to evaluate their versatility and generalization capabilities in a more general benchmark, encompassing both artificial and established reference datasets. Classical machine learning methods, specifically support vector machines and logistic regression, are also incorporated as baseline comparisons. Experimental results indicate that quantum methods exhibit varying performance across different datasets. Despite outperforming classical methods in ad hoc datasets, mixed results are obtained for the general case among standard classical benchmarks. The experimental data call into question a general added value of applying QKT optimization, for which the additional computational cost does not necessarily translate into improved classification performance. Instead, it is suggested that a careful choice of the quantum feature map in connection with proper hyperparameterization may prove more effective.
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.