Systematic Data-Driven Penalty Calibration for Constrained Quantum Optimization with Application to Molecular Docking

Abstract This paper describes MMP, a three-stage framework for systematic quantum optimization of constrained molecular docking problems. The protocol addresses the “formulation bottleneck”—the critical challenge of translating constrained optimization problems into valid QUBO (Quadratic Unconstrained Binary Optimization) formulations for quantum solvers. MMP replaces heuristic penalty tuning with data-driven calibration through: (1) classical solution-space analysis to validate fragment libraries before quantum deployment, (2) systematic penalty sweeps to identify optimal “Goldilocks Zone” coefficients, and (3) MAC-QAOA (MMP Adaptive Constraint QAOA) with layer-dependent penalty decay. Preliminary benchmarks on synthetic constrained optimization problems demonstrate 99.7% solution validity at identified elbow points and 25.5% improvement in solution quality over static-penalty QAOA. MMP is hardware-agnostic but designed for near-term devices including Pasqal’s Orion Gamma (140+ qubits). The theoretical framework, algorithmic details, and preliminary validation results of the protocol are discussed, establishing a systematic methodology for quantum-augmented optimization workflows for drug discovery. All benchmarks are conducted on synthetic constrained optimization instances that reproduce structural features of docking formulations; application to real molecular docking targets is left for future work.