A quantum graph-based differential model for drug-drug interaction prediction

Predicting clinically significant drug-drug interactions (DDIs) continues to be an unresolved challenge in contemporary pharmacovigilance, primarily due to the inadequacy of current computational frameworks in addressing the nonlinear, multi-scale characteristics of simultaneous drug metabolism. This paper presents the Quantum Graph-Differential (QGD) model an exact mathematical framework that combines quantum-inspired graph theory with a set of interconnected fractional differential equations to describe and forecast pairwise drug-drug interactions (DDIs). The principal component of our construction is the quantum interaction graph [Formula: see text], wherein the vertex set represents distinct drug molecules as quantum states within a finite-dimensional Hilbert space, and the complex-valued edge weights are obtained from the overlap of shared metabolic pathways and transporter affinity profiles.A Schrödinger-type equation on [Formula: see text] governs drug-drug coupling, and the graph Hamiltonian [Formula: see text] is constructed from a novel fractional quantum graph Laplacian [Formula: see text], [Formula: see text]. A hybrid quantum-classical dynamical model is created by coupling the time evolution of the interaction wavefunction [Formula: see text] to a compartmental pharmacokinetic/pharmacodynamic (PK/PD) ordinary differential equation system. Using Banach fixed-point and semigroup theory, we prove existence, uniqueness, and long-time asymptotic stability of solutions. Using the QGD framework on a selected dataset of 7,428 clinically confirmed DDI pairs from DrugBank v5.1, TWOSIDES, and FAERS, our model outperforms five established baselines by 1.5-13.9 percentage points in AUC, with an average precision of 0.948 and an AUC of 0.962. Quantum edge weighting alone explains a 3.7% relative F1 gain over unweighted graph methods, according to ablation experiments. These results show that quantifiable, interpretable improvements in DDI prediction can be obtained by incorporating quantum mechanical concepts into graph-differential frameworks.