This study introduces a novel framework that brings together two main Quantum Programming methodologies, gate-based Quantum Computing and Quantum Annealing, by applying the Model-Driven Engineering principles. This aims to enhance the adaptability, design and scalability of quantum programs, facilitating their design and operation across diverse computing platforms. A notable achievement of this research is the development of a mapping method for programs between gate-based quantum computers and quantum annealers which can lead to the automatic transformation of these programs. Specifically, this method is applied to the Variational Quantum Eigensolver Algorithm and Quantum Anneling Ising Model, targeting ground state solutions. Finding ground-state solutions is crucial for a wide range of scientific applications, ranging from simulating chemistry lab experiments to medical applications, such as vaccine development. The success of this application demonstrates Model-Driven Engineering for Quantum Programming frameworks's practical viability and sets a clear path for quantum Computing's broader use in solving intricate problems.