Quantum preconditioning for constrained optimization problems

We study the effect of quantum preconditioning on constrained combinatorial optimization problems, focusing on balanced graph bi-partitioning. The proposed approach uses two-point correlations between decision variables derived from the Quantum Approximate Optimization Algorithm (QAOA) to construct a modified objective function that is subsequently provided to mixed-integer programming (MIP) solvers. The results support a hybrid optimization framework in which quantum algorithms provide problem-specific information to guide classical exact MIP solvers.