When Do Quantum Kernels Help? An Interaction-Order Criterion and Null Results Across Three Biomedical Cohorts

Quantum kernel methods are increasingly applied to clinical prediction, but reported advantages rarely come with ablations, confidence intervals or negative controls. We benchmark a hybrid quantum-classical stacking model under nested cross-validation on three public biomedical cohorts: CRyPTIC tuberculosis drug resistance (12,287 isolates, six drugs), Duke DCE-MRI radiogenomics (n = 922, five endpoints) and MIAS mammography (322 images). Against an all-classical ensemble, the quantum branches change AUC by between -0.0024 and +0.0048 on every tuberculosis and Duke endpoint. Of twenty-four paired comparisons none significantly favours the hybrid, and the one nominally significant difference (p = 0.012, the hybrid below logistic regression on mammography) does not survive correction for multiplicity. Two measurements explain the null: fidelity-kernel off-diagonals decay as 0.5037^n (R^2 = 0.99), and a 277-fold increase in simulated entanglement moves AUC by 0.0148. We recast the inductive-bias argument for quantum kernels as a screen that needs no quantum computation: a quantum feature map can help only if the target depends on high-order feature interactions. The screen measured all six tuberculosis drugs as first-order before any quantum model was run. On synthetic controls an entangling map overtakes tuned classical baselines only at maximal interaction order, and its margin grows with sample size, against the common small-data claim. We also document three evaluation failures in our own pipeline, including a feature-label leak (0.918 AUC where the rebuild gives 0.54-0.59) and stacking leakage worth up to 0.09 AUC. All features, predictions and code are released. Data: https://doi.org/10.5281/zenodo.23344459 . Code: https://doi.org/10.5281/zenodo.23344193 .