Quantum-inspired kernels for scarce ECG labels

The decision: make the reference part of similarity

A similarity function is a modeling choice. In the QADK study, ECG beats are summarized by eight descriptors and encoded before a support-vector model uses the resulting kernel matrix. The kernel combines angular fidelity with a reference-relative term. Those terms ask different questions: how closely do two encoded states align, and how do their projections differ relative to the reference?

The interactive worked example deliberately reduces this geometry to two real dimensions. At input angles 60° and 90°, fidelity is about 0.933. Moving to 10° and 40° preserves the angular separation, so fidelity is unchanged, while the reference-projection gap changes. This is a way to inspect the definition, not evidence about ECG classification accuracy.

The consequence: the weights define the geometry

Increasing the fidelity weight changes which pairwise differences dominate the kernel. The site constrains the two weights to sum to one so that this trade-off can be explored with a single slider. That convenience is not the paper’s hyperparameter procedure: the study tunes the terms separately.

A fair interpretation therefore separates three objects: the published kernel definition, the parameter settings selected by an evaluation protocol, and the toy settings used to explain the idea. A visually appealing matrix cannot substitute for testing the fitted model against relevant classical baselines.

What the evaluation must protect

The portfolio’s verified record identifies the PTB ECG setting and patient-level evaluation. That distinction matters because beats from one person are not interchangeable with independent people. If the intended claim concerns new patients, the patient is the relevant unit of separation.

The practical audit is to keep the split boundary visible throughout feature construction, preprocessing, parameter selection, and final reporting. The browser lab does none of those operations; it helps formulate questions to ask of the archived experiment.

• Check how the normal reference is chosen and whether any held-out information can influence it.
• Compare kernels under the same patient-level split and tuning budget.
• Keep state-vector or quantum-inspired computation distinct from evidence of hardware advantage.

The boundary of the small reproduction

The downloadable check evaluates fidelity, reference gap, and their weighted sum for one two-dimensional example using only Python’s standard library. Its passing result establishes arithmetic agreement with the supplied expected values. It does not reproduce ECG descriptors, learned parameters, patient-level performance, or clinical utility.

The paper-associated Zenodo archive remains the place to inspect the larger computational workflow. This note does not invent installation steps for an archive that was not executed during the portfolio update.