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中国物理学会期刊

一种战术行动中平台聚类编组问题的基于QAOA的量子增强求解方法

A QAOA-based quantum enhanced method for solving platform clustering and grouping problems in tactical operations

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  • 针对战术行动中平台聚类编组的复杂约束问题,本文提出一种基于量子近似优化算法(Quantum Approximation Optimization Algorithm, QAOA)的两阶段量子增强求解方法。首先,将问题拆分为资源匹配与平台归属两个关联子问题:第一阶段基于整数背包问题构建量子伊辛模型,设计QAOA量子线路并优化参数,生成满足任务簇资源需求的候选平台簇集合;第二阶段以精确覆盖问题为框架,构建对应的量子模型并优化求解,筛选满足平台唯一归属且全集覆盖的全局最优分簇方案。通过经典问题向量子伊辛模型的映射,结合参数化量子线路与经典优化器协同优化,实现复杂约束下平台聚类的高效求解。在基于Python3框架下的量子软件开发环境和量子计算云服务平台中完成实验,实验结果表明,所提方法在平台分配效率上较传统算法提升显著,并且在时间复杂度上明显优于其他传统算法。与传统的多维动态列表规划法和多优先级列表动态规划法相比,时间复杂度由O(n2)降低到O(5n + 5k)。

    To address the challenge of complex multi-resource constraints in platform grouping for tactical operations, this study develops a quantum-enhanced solution optimization framework using the Quantum Approximate Optimization Algorithm (QAOA). By decomposing the problem into sequential phases of resource matching and cluster optimization, and leveraging a hybrid quantum-classical approach, the framework is designed to efficiently generate optimal platform grouping schemes. As shown in Fig.1, First, the problem was decomposed into two interrelated subproblems: resource matching and platform assignment. A quantum Ising model was formulated for the integer knapsack problem, and a QAOA quantum circuit was designed. Parameter optimization was then performed to generate candidate platform clusters that satisfy task cluster resource requirements; Second, leveraging the exact set cover problem as a framework, a corresponding quantum model was formulated and optimally solved using hybrid quantum-classical optimization. This process identified the globally optimal clustering scheme that ensures both platform uniqueness and complete set coverage; Finally, an efficient solution for platform clustering under complex constraints was developed by reformulating the classical problem into a quantum Ising model and integrating a parameterized quantum circuit with classical optimizers through hybrid quantum-classical optimization. The experiments were conducted in a Python3-based quantum software development environment and quantum computing cloud service platform. The experimental results demonstrate that the proposed quantum-enhanced optimization framework significantly outperforms traditional algorithms in platform allocation efficiency, with the time complexity reduced from O(n2) to O(5n + 5k) compared to conventional multi-dimensional dynamic list programming and multi-priority list dynamic programming methods, illustrating a distinct advantage. The study confirms that the QAOA-based framework can effectively address complex platform clustering and grouping problems in tactical operations, thereby laying a foundation for the application of quantum computing in command-and-control and resource optimization domains.

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