Exact Transfer-Matrix Evaluation Reveals Operating-Point Limits and Opportunities for Fidelity Quantum Kernels in Biomedical Abstract Screening

<title>Abstract</title> <p>Quantum kernel methods promise expressive similarity measures, but their practical value on high-dimensional biomedical language data remains uncertain. We evaluated fidelity quantum support vector classification (QSVC) for biomedical abstract screening using PubMedBERT embeddings compressed by principal component analysis and encoded with a diagonal $R_z$ plus nearest-neighbour $ZZ$ feature map. For this circuit family, we derive an exact line-transfer evaluator: each overlap is a one-dimensional complex Ising partition function computed by a $2\times2$ transfer recursion in $\mathcal{O}(n)$ time, without storing $2^n$-dimensional state vectors. The evaluator matched dense simulation to $5.3\times10^{-15}$ and enabled sweeps up to 32 qubits. Scaling experiments showed concentration-like behaviour, with declining kernel--target alignment and class-conditional separation as qubit count increased beyond the useful range. A centred-product interaction, $\phi_{ij}=\alpha x_i x_j$, acted as a bandwidth control and improved threshold-local specificity. At validation target sensitivity 0.95, the validation-selected QSVC improved test specificity over logistic regression by +0.032, but transported to test sensitivity 0.945 and did not exceed the radial basis function (RBF) support vector machine specificity. At the 0.99 target, selected 24-qubit QSVC configurations improved specificity over compressed classical baselines, although classical baselines retained higher area under the receiver-operating-characteristic curve. These results support a qualified conclusion: structured quantum-inspired kernels can improve operating-point utility, but fidelity QSVC did not provide global ranking superiority over strong classical baselines.</p>