Comparative Analysis of Quantum Kernel Methods and Deep Neural Networks for Heart Disease Prediction

Abstract

Relative to the proposed methods for better clinical prediction on small tabular cohorts, quantum kernel methods are often proposed, but published comparisons rarely control input dimensionality, hyperparameter search budget or even the classical kernel baseline that a fidelity kernel directly replaces. We present a combined pre-registered style comparison of quantum kernel methods, deep neural networks, and five classical baseline models on three different cardiac cohorts (UCI datasets combined, n=917; Cleveland: n=297; Z-Alizadeh Sani: n=303), under an identical single protocol including 55 repeated stratified nested cross-validation, fold-fitted preprocessing and dimensionality reduction with consistent eight-dimensional input subspace across compared models, equal search time budget of 20 candidates per model. The quantum kernel did not outperform the radial-basis-function support vector machine (its direct classical analogue) in any of the three cohorts (AUC=−0.006, −0.014, −0.014), and ℓ2-regularised logistic regression reached the highest mean ROC-AUC across 84 pairwise comparisons on ROC-AUC compared to other methods for each of two out of three cohorts, with 29 surviving Holm correction, and only one exceeding the standard deviation at fold-level. A sample–efficiency analysis finds the crossover where the network surpasses the quantum kernel at n≈93 and n≈123 patients for both UCI cohorts, lower than any clinically viable trial size. We also demonstrate that amplitude encoding - the best-performing quantum configuration whose fidelity kernel analytically reduces to a squared cosine similarity and is therefore not, functionally, a quantum feature map - actually yields exponentially concentrating operators directly measurable: off-diagonal Gram variance decreases from 1.06×10−2 for four qubits to 2.22×10−4 at ten (the second-order Pauli map yielding MCC=0.000 in one cohort). The collapse of the model is detected by threshold-dependent metrics long before the ROC-AUC. With batched state vector construction, Gram assembly is reduced from O(n^2 ) circuit executions to O (n) + dense product, and the complete 25-fold protocol is feasible. Our conclusions are that there is no tangible benefit of using quantum kernel methods for clinical tabular prediction at the cohort sizes and qubit budgets accessible today, and we highlight the diagnostics for any future such claim.