Forbush decreases (FDs)—transient reductions in galactic cosmic ray intensity driven by interplanetary coronal mass ejections—are key observables in space weather monitoring, yet their automated detection from multivariate solar wind and neutron monitor time series remains a challenging classification problem. Here we report a systematic benchmark of quantum kernel support vector machines (QKSVM) for FD detection, in which the FD magnitude threshold emerges as the governing factor separating two distinct classification regimes. Using 2971 confirmed events from the Forbush Effects and Interplanetary Disturbances (FEID) catalog, combined with hourly OMNI solar wind parameters—including interplanetary magnetic field (IMF) components, solar wind speed, proton density, proton temperature, and the Kp and Dst geomagnetic indices—and galactic cosmic ray count rates from the Jungfraujoch neutron monitor station (JUNG, NMDB), we construct a balanced FD versus quiet-time classification dataset and extract 121 statistical features across eleven physical channels. A ZZFeatureMap quantum kernel with 4–8 qubits is benchmarked against a classical radial basis function (RBF) SVM across 180 experimental configurations spanning FD magnitude thresholds of 0%–7%, circuit depths of 1–3 repetitions, and quantum training sizes of 50–250 samples. We find that below a magnitude threshold of 4%, the classical kernel consistently outperforms the quantum alternative (mean Δ AUC = − 0.100 at min_magn = 0 %). Above this threshold, the relationship inverts: at min_magn ≥ 4 % the quantum kernel achieves positive mean Δ AUC in 72% of configurations, rising to 100% of configurations at min_magn ≥ 5 % (mean Δ AUC = + 0.074 , peak AUC = 1.000 with 4–8 qubits), indicating that the entanglement structure of the ZZFeatureMap captures non-linear correlations between IMF dynamics and cosmic ray modulation that the RBF kernel cannot represent. The magnitude threshold of 4% thus constitutes a physically interpretable boundary between a noise-dominated regime where classical methods suffice and a signal-rich regime where quantum kernels provide measurable and statistically significant advantage ( p < 0.001 , Wilcoxon signed-rank test). These results establish FD magnitude as a key predictor of quantum classification performance, and suggest that near-term quantum machine learning applications in heliophysics should preferentially target high-amplitude space weather events.
Forbush decreases (FDs)—transient reductions in galactic cosmic ray intensity driven by interplanetary coronal mass ejections—are key observables in space weather monitoring, yet their automated detection from multivariate solar wind and neutron monitor time series remains a challenging classification problem. Here we report a systematic benchmark of quantum kernel support vector machines (QKSVM) for FD detection, in which the FD magnitude threshold emerges as the governing factor separating two distinct classification regimes. Using 2971 confirmed events from the Forbush Effects and Interplanetary Disturbances (FEID) catalog, combined with hourly OMNI solar wind parameters—including interplanetary magnetic field (IMF) components, solar wind speed, proton density, proton temperature, and the Kp and Dst geomagnetic indices—and galactic cosmic ray count rates from the Jungfraujoch neutron monitor station (JUNG, NMDB), we construct a balanced FD versus quiet-time classification dataset and extract 121 statistical features across eleven physical channels. A ZZFeatureMap quantum kernel with 4–8 qubits is benchmarked against a classical radial basis function (RBF) SVM across 180 experimental configurations spanning FD magnitude thresholds of 0%–7%, circuit depths of 1–3 repetitions, and quantum training sizes of 50–250 samples. We find that below a magnitude threshold of 4%, the classical kernel consistently outperforms the quantum alternative (mean Δ AUC = − 0.100 at min_magn = 0 %). Above this threshold, the relationship inverts: at min_magn ≥ 4 % the quantum kernel achieves positive mean Δ AUC in 72% of configurations, rising to 100% of configurations at min_magn ≥ 5 % (mean Δ AUC = + 0.074 , peak AUC = 1.000 with 4–8 qubits), indicating that the entanglement structure of the ZZFeatureMap captures non-linear correlations between IMF dynamics and cosmic ray modulation that the RBF kernel cannot represent. The magnitude threshold of 4% thus constitutes a physically interpretable boundary between a noise-dominated regime where classical methods suffice and a signal-rich regime where quantum kernels provide measurable and statistically significant advantage ( p < 0.001 , Wilcoxon signed-rank test). These results establish FD magnitude as a key predictor of quantum classification performance, and suggest that near-term quantum machine learning applications in heliophysics should preferentially target high-amplitude space weather events.
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.
We present a systematic design for large-scale quantum kernel classification, demonstrated through a quantum support vector classifier (QSVC) for particle-track classification using centroid-based CLAS12 drift-chamber features. Each event is encoded into a six-qubit state via a fully entangled ZZFeatureMap, whose fidelities define a quantum kernel within a standard SVM framework. By decoupling state preparation from kernel construction and distributing evaluation across a multi-node MPI-based HPC allocation, the approach scales to 1.0x10^5 training and 4.0x10^5 test events with an exactly constructed kernel matrix, to our knowledge more than an order of magnitude larger than prior high-energy-physics quantum-kernel studies.
Benchmarked against linear, polynomial, RBF, and sigmoid SVM kernels and extremely randomized trees (ERT), the ideal QSVC achieves the highest recall (99.99%) among all models. Under a calibrated hardware noise model (FakeMumbaiV2, 500 training / 2,000 test events), AUC falls from 0.9985 to 0.9671 and peak significance improvement falls from 17.5 to ~3.5, yet recall remains at 99.51% -- indicating this signal-retention advantage is attenuated but not eliminated by circuit-level decoherence.
Geometric analysis of the quantum embedding shows near-orthogonal inter-class states with coherent intra-class neighborhoods under ideal simulation; under noise this structure compresses toward the maximally mixed state while preserving its relative ordering.
These results demonstrate a scalable, reproducible workflow for quantum kernel experimentation at HEP-relevant scale, quantifying the practical cost of realistic hardware noise on quantum-enhanced classification.
Detecting credit card fraud is notoriously difficult because fraudulent charges make up less than 0.2% of total transactions. Quantum Machine Learning (QML), particularly Quantum Kernel Support Vector Machines (QSVM), promises richer feature representations by embedding classical data into high-dimensional Hilbert spaces. However, whether this theoretical advantage holds up when managing real-world financial data bottlenecks remains unclear. We designed a controlled benchmark comparing three quantum encodings, Angle, ZZFeatureMap, and IQP against classical models while keeping sample sizes, feature counts, and scaling strictly matched. To handle class skew without corrupting quantum state overlaps, we embedded synthetic minority oversampling (SMOTE) directly into the quantum Gram matrix workflow, raising PR-AUC scores by roughly +0.04 across feature maps. When trained on the full European credit card dataset with 30 features, classical baselines reached a top PR-AUC of 0.983. However, restricting classical models to match QSVM hardware constraints (500 samples, 4 PCA features) dropped their PR-AUC to 0.750. This puts our best quantum result 0.730 PR-AUC using IQP encoding on 150 samples into realistic context. Testing on physical quantum hardware reduced performance further to 0.62 due to CNOT gate errors and thermal noise. Overall, our findings pinpoint two main operational bottlenecks for near-term quantum kernels: the scaling of Gram matrix evaluation and heavy information loss from squeezing features onto small qubit registers.
Abstract Quantum kernel methods offer a potential advantage for classification tasks in high-dimensional feature spaces, yet their practical benefit critically depends on how input features are prepared. We compare five dimensionality reduction strategies—principal component analysis (PCA), Gaussian random projection (RP Gaussian), sparse random projection (RP Sparse), partial least squares (PLS), and uniform manifold approximation and projection (UMAP) — as pre-processing steps for quantum kernel support vector machines (SVMs) applied to trabecular bone classification from synthetic micro-computed tomography (micro-CT) data. Using a custom procedural generator based on Gaussian random field zero-crossings, we produced 500 synthetic trabecular bone volumes with controlled morphometric properties such as bone volume fraction (BV/TV), trabecular thickness (Tb.Th), number (Tb.N) and spacing (Tb.Sp). Texture features extracted from grayscale slices are reduced to 8-dimensional quantum circuit inputs via each method, then classified using both classical radial basis function (RBF)-SVMs and quantum kernel SVMs with ZZ feature maps on a statevector simulator, both evaluated with 5 × 5 repeated stratified cross-validation (25 folds). Our results show that UMAP is the only reduction method where the quantum kernel remains competitive with the classical baseline. Under repeated cross-validation, UMAP showed a +0.032 accuracy gap favouring the quantum kernel (Dietterich 5 × 2 CV p = 0.177); however, validation on 10 fully independent datasets—each with independently generated samples, separate reduction fits, and separate kernel matrices — reversed the sign to −0.030 (paired t -test p = 0.123; Wilcoxon p = 0.193; quantum wins 3/10 datasets), indicating that the apparent advantage was likely inflated by fold dependence. Nevertheless, UMAP’s gap remains small and non-significant in both analyses, whereas all linear methods (PCA, RP Gaussian, PLS) show substantial quantum deficits of −0.090 to −0.116 across BV/TV classification, with PCA and PLS remaining significant under corrected tests (5 × 2 CV p = 0.004 and p = 0.007 respectively). We additionally evaluate quantum kernel ridge regression for continuous morphometric prediction, finding that ZZ quantum kernels fail uniformly at regression (negative R 2 for all methods except PLS at 4 qubits), suggesting that the ZZ kernel captures decision boundaries but not smooth metric structure. These findings provide practical guidance for feature engineering in near-term quantum machine learning pipelines and demonstrate that the choice of dimensionality reduction can determine whether quantum kernels remain competitive with classical baselines.
Quantum kernel methods utilize high-dimensional quantum feature spaces as a theoretically motivated strategy to address data scarcity in supervised classification. However, theoretical analyses predict exponential concentration of quantum kernel similarity values as qubit count increases. This study presents the first statistically controlled empirical evaluation of fixed-feature-map quantum support vector machines (QSVMs) for few-shot keyword spotting. The ZZFeatureMap and PauliFeatureMap circuits (2 to 3 qubits, PCA-compressed MFCC features, ~51% variance retained) were evaluated across 24 configurations and four low-resource regimes (5–30 samples per class) on the Google Speech Commands dataset, using ten independent seeds with Wilcoxon signed-rank tests and Bonferroni correction. Across all configurations and sample sizes, QSVM accuracy remained close to the five-class random baseline (19.3% at 30 samples per class; random baseline 20%), while RBF SVM achieved 38.7% and a compact CNN achieved 65.3%. Direct kernel similarity measurement confirmed severe concentration, where the 3-qubit QSVM produced near-identical same-class and different-class similarity means (both approximately 0.192), with 94.1% overlap. Under matched MFCC+PCA features, all classical kernels outperformed QSVM, including linear SVM (Cliff’s δ=−0.98 , p=0.002 ) and RBF SVM ( δ=−0.82 , p=0.002 , Bonferroni-corrected α=0.003 ), with CNN achieving complete stochastic dominance ( δ=−1.00 ). These results empirically validate quantum kernel concentration in structured acoustic classification within evaluated NISQ constraints, and apply specifically to the fixed-feature-map paradigm, not quantum kernel methods in general. The identified failure modes, namely exponential concentration, geometric misalignment, and limited circuit expressivity, provide concrete directions for future research into trainable quantum feature maps and hybrid quantum-classical architectures.