For decades, the promise of quantum computing has outpaced its theoretical foundations — algorithms were built on intuition as much as proof, and hope as much as rigor. Now, a team of researchers has closed a meaningful gap: variational quantum algorithms, long used to approximate the ground-state properties of complex quantum systems, have been given rigorous mathematical guarantees of convergence and generalization. By anchoring the learning process to guiding states and mapping its dynamics onto well-understood kernel models, they have transformed a promising heuristic into a method with pr