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Quantum kernel support vector machines for trabecular bone classification: comparing feature reduction strategies on synthetic micro-CT data

Isabella Florez, Ahmed Farhat, James Le Houx, Edoardo Altamura, Gianluca Tozzi

Published May 7, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.64898/2026.05.04.722627

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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 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.
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=0.05α= 0.05α=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≥0.976r \geq 0.976r≥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\varepsilon^2 = 0.73ε2=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.
This paper examines the application of a Quantum Support Vector Machine (QSVM) for radarbased aerial target classification using micro-Doppler signatures. Classical features are extracted and reduced via Principal Component Analysis (PCA) to enable efficient quantum encoding. The reduced feature vectors are embedded into a quantum kernel-induced feature space using a fully entangled ZZFeatureMap and classified using a kernel based QSVM. Performance is first evaluated on a quantum simulator and subsequently validated on NISQ-era superconducting quantum hardware, specifically the IBM Torino (133-qubit) and IBM Fez (156-qubit) processors. Experimental results demonstrate that the QSVM achieves competitive classification performance relative to classical SVM baselines while operating on substantially reduced feature dimensionality. Hardware experiments reveal the impact of noise and decoherence and measurement shot count on quantum kernel estimation, and further show improved stability and fidelity on newer Heron r2 architecture. This study provides a systematic comparison between simulator-based and hardware-based QSVM implementations and highlights both the feasibility and current limitations of deploying quantum kernel methods for practical radar signal classification tasks.
Quantum kernel methods are often proposed as a route to improved medical image classification because quantum feature maps can embed data into high-dimensional Hilbert spaces. However, their practical value remains unclear when compared with strong classical kernels under leakage-controlled conditions. This study benchmarks two simulated quantum kernel support vector machines, QSVM-ZZ and QSVM-Pauli, against logistic regression, linear SVM, fixed-default RBF-SVM, and a compact multi-layer perceptron on BrainTumorMRI and BreastMNIST. All models used identical frozen ResNet18 features, train-only standardisation, PCA compression to four and eight dimensions, three random seeds, and matched classifier-training budgets where applicable. Across 24 seed-level matched comparisons, the best quantum kernel model never outperformed the best classical model. The mean quantum-minus-classical macro-F1 gap was - 0.2230, with all 24 gaps negative. Fixed pairwise comparisons confirmed that RBF-SVM exceeded both quantum kernels individually. QSVMs also required approximately 50 × to more than 220 × higher runtime. These findings show that, for compressed ResNet18 medical image features under noiseless simulation, the tested QSVM-ZZ and QSVM-Pauli kernels did not provide a practical advantage over fixed-default RBF-SVM.
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