Quantum Angle-distance kernel for ECG classification and anomaly detection: a quantum-inspired framework for biomedical signal analysis.

Reliable, clear and lightweight ECG classification is important for immediate medical and wearable applications, yet challenges due to confounding signals, rare, labeled examples as well as high model complexity. Our method introduces a Quantum Angle–Distance Kernel (QADK), inspired by quantum principles, combining angular alignments in Hilbert space along with displacements relative to a reference point, thereby increasing class resolution without loss of transparency. We represent heartbeats using descriptive features rather than raw data; these are mapped into fixed-length complex vectors using a simulated quantum coding scheme. Comparisons between such encoded patterns use a balanced mixture of squared similarity scores and projection gaps, creating a stable kernel matrix that works directly with common learning tools. We test QADK on a large ECG heartbeat dataset using strict patient-wise splits on 100 Monte-Carlo measurements; comparisons include linear SVM, RBF SVM, 1D CNN, MLP, and single-class anomaly detection methods. During supervised classification, QADK-SVM achieves an average AUC-ROC of 0.977 ± 0.003, macro F1 of 0.923 ± 0.005, accuracy of 0.937 ± 0.004 – clearly beating linear SVM while matching the best performing RBF after embedding adjustment. In the single-class setting, QADK yields AUC = 0.884 ± 0.005 Ablation with nested cross-validation shows that both components contribute to performance in our pipeline: adding a reference term to the fidelity-only kernel resulted in an average pairwise increase in AUC of +2.4% points under the reported PTB distribution. The fidelity term primarily improved specificity in these experiments. Through sensitivity checks, we found that m = 32 offers a usable embedding size that preserves results without excessive computation time for upcoming quantum devices. Computational analysis shows that Gram construction is the main cost driver – scaling roughly as Θ(n2), yet remains manageable for medium-sized groups, especially when using low-level methods to increase efficiency. While all empirical validations in this study were performed using classical simulation, our theoretical resource analysis demonstrates that QADK is natively compatible with NISQ hardware, requiring only 11 qubits and standard swap tests. This confirms the framework’s suitability for a future shift from simulation to real device implementation. Unlike deep networks, QADK achieves, which combines strong classification accuracy, high interpretability, and compatibility with capacity-constrained systems, making it suitable for ECG tasks in wearable or resource-constrained clinical environments.