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arXiv · 2608.28842

Quantum Preconditioning For Constrained Optimization Problems

Anurag Ramesh·Bhuvanesh Sundar·Maxime Dupont·David E. Bernal Neira
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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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Anurag Ramesh, Bhuvanesh Sundar, Maxime Dupont, David E. Bernal Neira. 2026-08-28. Quantum Preconditioning For Constrained Optimization Problems. https://arxiv.org/abs/2608.28842

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