Molecular docking via quantum annealing: modelling π−stacking interactions as a QUBO problem

Molecular docking is a fundamental technique in computational biology and drug design, aimed at predicting the most stable configuration between a ligand and a biological receptor. In recent years, there has been growing interest in integrating advanced computational paradigms - such as quantum annealing and high-performance computing (HPC) - into docking workflows, with the goal of improving both accuracy and efficiency. This work contributes to this line of research by proposing the inclusion of a term capable of capturing pi-stacking interactions within the global energy function used in ligand–receptor docking problems. Pi-stacking interactions, which arise from non-covalent forces between aromatic systems, play a crucial role in biomolecular recognition processes but are often overlooked or treated simplistically in traditional models. In the first part of the work, computational chemistry simulations were performed on HPC infrastructures to generate detailed energy profiles of the interaction between benzene rings. Building on previous QUBO models based on graph representations of molecular docking, a new Hamiltonian term was formulated to account for pi-stacking interactions, while respecting the constraints imposed by the discrete framework. Particular attention was paid to integrating this term in a way that is compatible with the discrete nature of subgraph isomorphism problems. Finally, simulated annealing computations were carried out to validate the model. Tests were conducted on systems involving benzene interacting with aromatic residues such as tyrosine, phenylalanine, and tryptophan. The results confirmed that the newly introduced term significantly influences the predicted binding configuration, guiding the ligand toward the correct spatial orientation. These findings demonstrate the relevance of incorporating pi-stacking interactions into docking models and pave the way for future improvements in physically-informed molecular optimization.