Quantum Inner Product Scoring with Grid-Based Maps for Structure-Based Virtual Screening

Structure-based virtual screening is fundamentally constrained by the combinatorial growth of configurational spaces arising from receptor conformations, ligand identities, conformations, and spatial degrees of freedom. We reformulate protein-ligand interaction energy calculation as a linear-algebraic problem defined on shared Cartesian grids. Within this framework, electrostatic and van der Waals interaction energies are expressed as inner products between receptor potential maps and ligand charge and atom-type occupancy vectors. Ligand translations and rotations are represented as unitary operations acting on independent spatial registers, enabling systematic reuse of grid information across large pose ensembles within a unified computational formulation while explicitly evaluating interaction energies for each receptor-ligand configuration via inner products. We implement inner-product estimation using the Hadamard test and validate the formulation through systematic comparisons with classical atom-based and map-based energy evaluations. Across multiple receptor-ligand systems, we demonstrate that the proposed representation preserves energetic ordering in the low-energy regime relevant to structure-based virtual screening, while remaining robust under finite-sampling conditions. By exposing the tensorized structure underlying interaction-energy evaluation, this work establishes a representation-level formulation for map-based virtual screening compatible with both classical and quantum computational paradigms.