发表机构
Rigetti Computing; Davidson School of Chemical Engineering, Purdue University（瑞吉蒂计算; 普渡大学戴维森化学工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对平衡图二分等约束组合优化问题，提出基于QAOA两点相关性的量子预处理方法，可加快混合整数规划求解器获得近优解的速度，为量子-经典混合优化框架提供支撑。
AI 中文摘要
我们研究量子预处理对约束组合优化问题的影响，重点关注平衡图二分问题。所提方法利用量子近似优化算法（QAOA）得到的决策变量之间的两点相关性，构建修正目标函数，随后将其提供给混合整数规划（MIP）求解器。预处理后的MIP公式保留原始硬约束，所有 incumbent 解均在原始目标下评估。对密集加权完全图实例的计算实验表明，预处理后的问题实例能更快达到近优解，且在测试的最浅QAOA深度时已实现大部分收益。求解器回调轨迹显示，这源于求解搜索过程中更早发现高质量incumbent解。这些结果支持一种混合优化框架，其中量子算法提供特定问题信息以指导经典精确MIP求解器。
英文摘要
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.
Comments24 pages, 8 figures
