Encoding Choice Is Associated with Large Differences in Variational Quantum Classifier Performance on Cancer Data Under a Fixed Training Budget

Abstract

Variational quantum classifiers (VQCs) are often reported to perform poorly on biomedical tabular data, but such conclusions depend on the encoding circuit, the training budget, and the comparison protocol. Methods. We compared 4-qubit VQCs, a quantum-kernel SVM (QSVM), a majority-class control, and tuned classical models (on four PCA features and on all features) on Wisconsin breast cancer (n = 569), Coimbra biomarkers (n = 116), Golub leukemia gene expression (n = 72, 7,129 genes), and SEER breast-cancer registry data (n = 4,024; 15% deaths). All models were evaluated on identical blocks of 5-fold × 5-seed stratified cross-validation with preprocessing fitted on training folds, nested tuning, and Nadeau–Bengio-corrected inference with Holm correction. Trained classifiers were also evaluated on three IBM Quantum devices. Results. On the three small datasets, a VQC with the conventional two-repetition ZZ feature map was close to chance (accuracy 0.688, 0.594, 0.509), whereas a product (Z) feature map reached 0.900, 0.797, and 0.658; at matched repetition counts the Z-minus-ZZ gap was +0.12 to +0.21 and, after Holm correction, significant on Wisconsin only. More evaluations (up to 1,500) and six initializations did not close the ZZ deficit on Wisconsin. With the encoding chosen by inner cross-validation, the VQC exceeded the majority control on Wisconsin and Golub and stayed below classical models on Wisconsin and in several Golub contrasts. No statistically significant difference was detected between the encoding-selected VQC and the classical baselines on Coimbra, or between the Z-map QSVM and PCA-4 classical models; Bayesian equivalence analysis supported practical equivalence only for the QSVM on Wisconsin. On SEER the encoding mattered little: the VQC exceeded the majority control in balanced accuracy (0.548 versus 0.500) but ranked patients worse than logistic regression and random forest (ROC-AUC 0.678 versus 0.745 and 0.733). Full-feature classical models were strongest overall. On hardware (class-balanced test subsets, not natural-prevalence performance), accuracy relative to noise-free simulation changed by −0.071 to +0.048 per run (pooled ibm_fez, Wisconsin: −0.024, 95% CI −0.060 to +0.008), using 5.5 QPU-minutes. Conclusions. Under a fixed training budget, encoding choice was associated with large differences in VQC accuracy on small datasets, so single-encoding negative results should not be generalized; because the Z and ZZ maps also differ in entanglement structure, we do not attribute the gap to encoding alone. No quantum advantage was observed.