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Diagnosing Quantum Kernel Failures: Spectral Audit, Dequantization, and the Dual Concentration Bottleneck

Neil Suarez

Published Aug 19, 2026• 0 citations
Publisher

Abstract

We present ThylerSpectral-Audit-Q, a three-layer automated diagnostic framework for quantum kernel pathologies, validated across 124 configurations spanning 7 data domains plus a systematic six-family quantum kernel survey: tabular (digits, diabetes, California housing, covtype), clinical (Iris, Wine, Breast Cancer), quantum-native (V0/V1 ZZFeatureMap, V2 IQPFeatureMap), molecular graph (MUTAG, PTC_FM), industrial (semiconductor proxy, Steel Plates Faults, satellite proxy), time series (AR2, ECG5000 via ZZFeatureMap, QHMM, and TSHK kernels). The kernel survey applies six encoding families (PauliFeatureMap, AngleEncoding, AmplitudeEncoding, EfficientSU2, RandomCircuitKernel, QFTFeatureMap) to three tabular benchmark datasets at n ∈ {4, 6, 8}. Contribution 1 — Diagnostic framework. Three sequential layers — exponential concentration (EC) detection (Shannon effective rank ratio r_eff; five-tier spectral taxonomy), dequantization filter (Tang-Chia eigenvalue truncation), and kernel-target alignment evaluation (centered KTA) — combine into a composite PROCEED/CAUTION/ABORT Spectral Health Card. All four primary datasets (breast cancer, make_moons, Iris, Wine) yield ABORT or CAUTION verdicts under ZZFeatureMap. The framework generalizes: IQPFeatureMap reproduces EC_COLLAPSE at n=8 (r_eff=0.943) without recalibration. A data-kernel structural sensitivity is also detected: the same kernel yields LIKELY_DEQUANTIZABLE on molecular graph data (r_eff=0.153) versus CONFIRMED_DEQUANTIZABLE on tabular data (r_eff=0.095) — a distinction invisible to kernel architecture inspection alone. Contribution 2 — Advantage regime, retired at n_train=150 (v19). At n_train=50, Hamming Quantum Kernel (HQK) on quantum-native data produced the paper's only non-ABORT signal: large effect sizes over SVM-Linear on V2 (IQPFeatureMap) data (d=+0.949–1.015; under the corrected resampled t-test for repeated-CV dependence, p_NB=0.0605 for λ=0.5 and p_NB=0.0485 for λ=0.1 — marginal). Because the pre-registered robustness criterion required corrected significance in both λ configurations, a recovery experiment at n_train=150 was pre-registered (exploracion_010) and has now been executed (S052). Result: every V2 effect size reverses sign — λ=0.5: d=−0.215 (p_NB=0.6375, ns); λ=0.1: d=−1.243 (p_NB=0.0189 — a significant disadvantage, HQK now performing worse than SVM-Linear/RBF) — and the pre-registered effect-size-floor control (d≥0.5 in both λ, designed to distinguish gradual collapse from sign reversal) fails in both configurations. The secondary same-architecture V0/V1 arm also reverses sign (d=+0.27→−0.374 vs Linear, ns). Per the pre-registered decision rule, the cross-architecture advantage claim is retired, not restored. This converges with exploracion_012's finding that V6 — a circuit verified diagonal-unitary by construction but structurally distinct from V0/V1/V2's ZZ/IQP coupling — also shows significant disadvantage at n_train=150 (d=−1.10 to −1.13, p_NB<0.05 in both λ): at the matched n_train=150 standard, no HQK configuration tested in this paper shows a robust advantage over classical baselines. The dual concentration bottleneck — global EC (fidelity collapse) and local EC (Pauli-Z observables ⟨Z_i⟩→0 as n increases) — disables both fidelity kernels and projected quantum kernels simultaneously, and this negative result is now the paper's consistent empirical picture rather than a partial exception to it. A complementary negative structural result: exhaustive hyperparameter optimization over ZZFeatureMap (63 grid configurations: γ × reps × entanglement, plus 100-step continuous variational search) on classical time series data (AR2_n4, r_eff=0.2975) finds zero configurations with Δ_kta > 0 in full audit, confirming that quantum-native data is a necessary but not sufficient structural condition for any advantage signal under the full three-layer audit within the ZZFeatureMap family. The D6 kernel survey further shows that K2 (AngleEncoding) achieves Δ_kta>0 on classical tabular data, but is blocked from PROCEED by the dequantization filter, confirming that Layers 1–2 are essential to prevent false PROCEED verdicts. Contribution 3 — Quantum kernel phase diagram. The 124 audited configurations form a quantum kernel phase diagram in (r_eff × Δ_acc × n_qubits) space with two robustly confirmed empirical phases (ABORT, CAUTION) and measurable phase boundaries, plus a third, provisional phase (PROCEED, 7/124 configs) that has not been re-verified at the n_train=150 standard that retired Contribution 2 above. Seven geometric patterns are observable, including a cross-domain discovery: the STRUCTURED_LOW_RANK regime (0.10 < r_eff ≤ 0.35) appears independently in molecular graph data (r_eff ∈ [0.036, 0.312]) and industrial quality-control data (r_eff=0.22), despite no domain relationship — a finding invisible to kernel architecture inspection alone. Contribution 4 — Domain-agnostic spectral classification. A k-nearest-neighbor classifier trained exclusively on spectral audit features achieves F1-macro=1.000 and MCC=1.000 on an external test set of 20 configurations from three entirely unseen domains: molecular graphs, industrial QC, and time series. Random Forest feature importance reveals dataset_type_code=0% — the framework's diagnostic accuracy is domain-invariant by construction. To the best of our knowledge, ThylerSpectral-Audit-Q is the only pre-execution diagnostic tool integrating EC detection, dequantization filtering, and structural alignment evaluation into a single automated pipeline with an empirical multi-domain phase diagram, validated across 124 configurations spanning 7 data domains and a systematic six-family quantum kernel survey.

DOI
10.5281/zenodo.22020064

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We present ThylerSpectral-Audit-Q, a three-layer automated diagnostic framework for quantum kernel pathologies, validated across 124 configurations spanning 7 data domains plus a systematic six-family quantum kernel survey: tabular (digits, diabetes, California housing, covtype), clinical (Iris, Wine, Breast Cancer), quantum-native (V0/V1 ZZFeatureMap, V2 IQPFeatureMap), molecular graph (MUTAG, PTC_FM), industrial (semiconductor proxy, Steel Plates Faults, satellite proxy), time series (AR2, ECG5000 via ZZFeatureMap, QHMM, and TSHK kernels). The kernel survey applies six encoding families (PauliFeatureMap, AngleEncoding, AmplitudeEncoding, EfficientSU2, RandomCircuitKernel, QFTFeatureMap) to three tabular benchmark datasets at n ∈ {4, 6, 8}. Contribution 1 — Diagnostic framework. 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At n_train=50, Hamming Quantum Kernel (HQK) on quantum-native data produced the paper's only non-ABORT signal: large effect sizes over SVM-Linear on V2 (IQPFeatureMap) data (d=+0.949–1.015; under the corrected resampled t-test for repeated-CV dependence, p_NB=0.0605 for λ=0.5 and p_NB=0.0485 for λ=0.1 — marginal). Because the pre-registered robustness criterion required corrected significance in both λ configurations, a recovery experiment at n_train=150 was pre-registered (exploracion_010) and has now been executed (S052). Result: every V2 effect size reverses sign — λ=0.5: d=−0.215 (p_NB=0.6375, ns); λ=0.1: d=−1.243 (p_NB=0.0189 — a significant disadvantage, HQK now performing worse than SVM-Linear/RBF) — and the pre-registered effect-size-floor control (d≥0.5 in both λ, designed to distinguish gradual collapse from sign reversal) fails in both configurations. The secondary same-architecture V0/V1 arm also reverses sign (d=+0.27→−0.374 vs Linear, ns). Per the pre-registered decision rule, the cross-architecture advantage claim is retired, not restored. This converges with exploracion_012's finding that V6 — a circuit verified diagonal-unitary by construction but structurally distinct from V0/V1/V2's ZZ/IQP coupling — also shows significant disadvantage at n_train=150 (d=−1.10 to −1.13, p_NB<0.05 in both λ): at the matched n_train=150 standard, no HQK configuration tested in this paper shows a robust advantage over classical baselines. The dual concentration bottleneck — global EC (fidelity collapse) and local EC (Pauli-Z observables ⟨Z_i⟩→0 as n increases) — disables both fidelity kernels and projected quantum kernels simultaneously, and this negative result is now the paper's consistent empirical picture rather than a partial exception to it. A complementary negative structural result: exhaustive hyperparameter optimization over ZZFeatureMap (63 grid configurations: γ × reps × entanglement, plus 100-step continuous variational search) on classical time series data (AR2_n4, r_eff=0.2975) finds zero configurations with Δ_kta > 0 in full audit, confirming that quantum-native data is a necessary but not sufficient structural condition for any advantage signal under the full three-layer audit within the ZZFeatureMap family. The D6 kernel survey further shows that K2 (AngleEncoding) achieves Δ_kta>0 on classical tabular data, but is blocked from PROCEED by the dequantization filter, confirming that Layers 1–2 are essential to prevent false PROCEED verdicts. Contribution 3 — Quantum kernel phase diagram. The 124 audited configurations form a quantum kernel phase diagram in (r_eff × Δ_acc × n_qubits) space with two robustly confirmed empirical phases (ABORT, CAUTION) and measurable phase boundaries, plus a third, provisional phase (PROCEED, 7/124 configs) that has not been re-verified at the n_train=150 standard that retired Contribution 2 above. Seven geometric patterns are observable, including a cross-domain discovery: the STRUCTURED_LOW_RANK regime (0.10 < r_eff ≤ 0.35) appears independently in molecular graph data (r_eff ∈ [0.036, 0.312]) and industrial quality-control data (r_eff=0.22), despite no domain relationship — a finding invisible to kernel architecture inspection alone. Contribution 4 — Domain-agnostic spectral classification. A k-nearest-neighbor classifier trained exclusively on spectral audit features achieves F1-macro=1.000 and MCC=1.000 on an external test set of 20 configurations from three entirely unseen domains: molecular graphs, industrial QC, and time series. Random Forest feature importance reveals dataset_type_code=0% — the framework's diagnostic accuracy is domain-invariant by construction. To the best of our knowledge, ThylerSpectral-Audit-Q is the only pre-execution diagnostic tool integrating EC detection, dequantization filtering, and structural alignment evaluation into a single automated pipeline with an empirical multi-domain phase diagram, validated across 124 configurations spanning 7 data domains and a systematic six-family quantum kernel survey.
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.
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\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 (RBF). The complete benchmark suite is publicly available to facilitate reproduction and extension.
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 map clinical features into exponentially large Hilbert spaces where overlapping biological markers can become more separable than in fixed-dimensional classical feature spaces, but existing work evaluates single quantum feature maps, ignores barren-plateau failure modes, and relies on single train-test splits vulnerable to data leakage. Classical diagnostics for Parkinson's disease, breast cancer, and diabetes remain limited by the Specificity-Recall trade-off that fixed-dimensional kernels impose on overlapping biomarker distributions. We propose an adaptive hybrid quantum framework routing clinical data through three distinct quantum feature maps, namely Angle, Amplitude, and ZZ-entanglement, computing fidelity-based Gram matrices for Quantum SVM and Quantum KNN classifiers. A Logistic Regression meta-learner, trained on strictly out-of-fold predictions from nested cross-validation (5-fold inner, 10-fold outer), learns which quantum kernel generalizes on each dataset and suppresses those that do not. Evaluated on Parkinson's (195 patients), Breast Cancer (569), and Diabetes (768) with 1,000-iteration bootstrapping, the ensemble raised Parkinson's Specificity from 0.585 to 0.813 ([Formula: see text]) while maintaining Recall above 0.95, matched classical RBF-SVM on Breast Cancer (all [Formula: see text]), and improved Diabetes Recall from 0.553 to 0.621 ([Formula: see text]). A standalone Variational Quantum Classifier failed on all datasets (ROC-AUC 0.51 to 0.57), confirming barren plateau limitations. Explainability via SHAP, LIME, and Permutation Importance revealed dataset-dependent kernel trust: the meta-learner suppressed QKNN Amplitude on Diabetes (coefficient [Formula: see text]) while amplifying it on Parkinson's (1.761). PCA-based feature backtracking recovered established biomarkers including Insulin and Glucose for Diabetes, vocal perturbation measures for Parkinson's, and nucleus geometry for Breast Cancer. Noise simulations confirmed graceful degradation under NISQ conditions. The framework performs data-driven kernel selection, removing the need to pre-specify an encoding strategy.
Quantum kernel techniques aim to leverage quantum computational capabilities on social data. However, their application to natural language processing tasks faces formidable obstacles, such as extreme dimensionality reduction (D=384→k=8), concentration of measure in quantum feature spaces, and the lack of theoretical understanding of when quantum advantages occur in kernel-based text classification. Filling this gap, we provide a comprehensive study of quantum kernels for text classification that addresses three major challenges in existing studies: general data compression approaches that ignore class structure, the lack of a predictive diagnostic toolkit, and overlooked approaches for handling concentration effects. Our main contributions include a supervised contrastive data compression approach with theoretical guarantees of kernel alignment, a five-diagnostic toolkit connecting theoretical insights with practical performance, the discovery of a small-data regime (n≤200) in which quantum methods perform comparably to classical approaches, and a transparent demonstration that quantum kernels require carefully designed settings to remain competitive with classical counterparts. Across four datasets, evaluated using five random seeds and exact paired statistical testing, we observe that quantum projected kernels achieve an accuracy of 84.5% compared to 85.1% for the classical RBF kernel (p>0.05, not statistically significant) under supervised compression settings. However, quantum methods lag behind by approximately 2%–4% at larger scales due to concentration effects, reflected in reduced off-diagonal kernel variance (0.003 vs. 0.025).
Fidelity-based quantum kernels provide a direct interface between quantum feature maps and classical kernel methods, but they can exhibit exponential concentration: with increasing system size or circuit expressivity, the Gram matrix approaches the identity and suppresses informative similarity structure. We present an empirical study of two mitigation strategies implemented in Qiskit: (i) local (patch-wise) kernels that aggregate subsystem similarities, and (ii) multi-scale kernels that mix local and global similarity across patch granularities. We benchmark baseline, local, and multi-scale kernels under matched preprocessing, splits, and SVM protocols on several tabular datasets, sweeping the feature dimension d∈{4,6,…,20}d\in\{4,6,\dots,20\}d∈{4,6,…,20}. We report concentration diagnostics based on off-diagonal kernel statistics, spectral richness via effective rank, and centered alignment with labels. Across datasets, local and multi-scale constructions consistently mitigate concentration and yield richer kernel spectra relative to the global fidelity baseline, while the impact on classification accuracy depends on the dataset and dimension.