Adaptive Quantum Kernel Learning with Alignment-Trained Feature Maps for High-Dimensional ECG Segment Classification

Quantum fidelity kernels embed classical data in the state space of a parameterised circuit and are attractive for small biomedical datasets, but the encoding is normally fixed in advance, forcing a hand-crafted dimensionality reduction and an arbitrary angle scaling, and the resulting kernel can concentrate towards a constant in a way that finite-shot estimation cannot resolve. This paper develops an adaptive quantum kernel for five-class (N, S, V, F, Q) classification of 10-s single-lead ECG segments in which a 77-dimensional feature vector, produced by a classical conditioning, QRS-detection and feature-extraction stage, is mapped to rotation angles through a trainable projection and per-qubit bandwidth and encoded by a layered Hadamard–rotation–ring-ZZ circuit. The projection, bandwidths and entangling strengths are learned by maximising the centred kernel–target alignment with gradient back-propagation through a state-vector simulator. Three properties are proved and numerically verified: the centred alignment is invariant to global depolarising noise, the expected squared Frobenius error of a finite-shot kernel estimate has a closed form bounded by N2/4M, and an exact-kernel SVM on a globally depolarised Gram matrix coincides with a clean-kernel SVM whose box constraint is scaled by (1 − p). On 500 segments derived from the MIT-BIH Arrhythmia Database under 3×5-fold stratified cross-validation, alignment training raises the training alignment from 0.54 to 0.96 and the accuracy from 89.4 % (fixed map) to 95.4 % at eight qubits, where it matches scalar bandwidth tuning, and exceeds bandwidth tuning by 3.4 points at four qubits; a tuned RBF-SVM on the same features remains higher at 97.9 %, so no quantum advantage is claimed. The adaptive kernel is, however, insensitive to sampling noise: with 128 shots per entry and depolarising strength 0.4 its accuracy stays at 94.9 %, whereas the bandwidth-tuned kernel loses up to 2.1 points and post-processing recovers only part of that, an effect explained by the within-/between-class kernel contrast that alignment training produces and by the strongly regularised SVM it supports. Limitations of segment-level evaluation and future hardware experiments are discussed.