Quantum Preconditioning For Constrained Optimization Problems

• URL: http://arxiv.org/abs/2608.28842v1
• Date: Fri, 28 Aug 2026 20:23:37 GMT
• Title: Quantum Preconditioning For Constrained Optimization Problems
• Abstract summary: We study the effect of quantum preconditioning on constrained optimization problems.<n>The proposed approach uses two-point correlations between decision variables to construct a modified objective function.<n>Experiments on dense, weighted complete-graph instances show that the preconditioned problem instances reach near-optimal solutions faster.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 preconditioned MIP formulation retains the original hard constraint, and all incumbent solutions are evaluated under the original objective. Computational experiments on dense, weighted complete-graph instances show that the preconditioned problem instances reach near-optimal solutions faster, with most of the benefit already realized at the shallowest QAOA depth tested. Solver callback trajectories show this arises from earlier discovery of high-quality incumbents during the solution search. These results support a hybrid optimization framework in which quantum algorithms provide problem-specific information to guide classical exact MIP solvers.

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