Quantum Interaction Manifolds for Cancer Genomics: A Theoretical Framework and Proof-of-Concept Quantum Machine Learning for Early Diagnosis and Drug Response Modeling

Understanding and predicting cancer phenotypes from genomic data requires models capableof capturing high-order interactions among genes and biological pathways. We introduce Quantum Interaction Manifolds (QIMs), a theoretical framework that represents gene expression profiles as quantumstates evolved under biologically informed Hamiltonians. We show that QIM embeddings induce hypothesisclasses that cannot be efficiently approximated by classical learners under standard complexity assumptions,providing a principled quantum advantage in representing nonlinear genomic dependencies. Using noisysimulations on reduced-dimensional datasets, we demonstrate that QIM-based quantum kernels achievecompetitive accuracy in cancer classification tasks, while variational quantum models trained on QIMrepresentations learn continuous drug response signals with stable convergence. Together, these results establish QIMs as a quantum-native approach for modeling genomic interactions and highlight the potentialof structured quantum machine learning to support future developments in computational oncology