Data complexity signature predicts quantum projected learning benefit for antibiotic resistance

Abstract: This study presents the first large-scale empirical evaluation of quantum machine learning for predicting antibiotic resistance in clinical urine cultures. Antibiotic resistance is amongst the top threats to humanity, and inappropriate antibiotic use is a main driver of resistance. We developed a Quantum Projective Learning (QPL) approach and executed 60 qubit experiments on IBM Eagle and Heron quantum processing units. While QPL did not consistently outperform classical baselines, potentially reflecting current quantum hardware limitations, it did achieve parity or superiority in specific scenarios, notably for the antibiotic nitrofurantoin and selected data splits, revealing that quantum advantage may be data-dependent. Analysis of data complexity measures uncovered a multivariate signature, which comprised Shannon entropy, Fisher Discriminant Ratio, standard deviation of kurtosis, number of low-variance features, and total correlations. The multivariate model accurately (AUC = 0.88, $p$-value = 0.03) distinguished cases wherein QPL executed on quantum hardware would outperform classical models. This signature suggests that quantum kernels excel in feature spaces with high entropy and structural complexity. These findings point to complexity-driven adaptive model selection as a promising strategy for optimizing hybrid quantum-classical workflows in healthcare. Overall, this investigation marks the first application of quantum machine learning in urology, and in antibiotic resistance prediction. Further, this work highlights conditional quantum utility and introduces a principled approach for leveraging data complexity signatures to guide quantum machine learning deployment in biomedical applications.