发表机构
Korea University（高丽大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对多角度量子近似优化算法（maQAOA）求解最大独立集问题，提出坐标式训练框架，通过解析傅里叶级数逐参数优化，显著降低训练成本并提升收敛可靠性。
AI 中文摘要
约束组合优化为建模广泛的现实决策问题提供了数学框架，包括能源网络运行、金融投资组合优化、物流、路由和资源分配。本文研究了应用于最大独立集问题（一个典型的约束图优化任务）的多角度量子近似优化算法（maQAOA）的参数优化。我们提出了一种maQAOA的坐标式训练框架，该框架通过求解一系列一维优化子问题，每次更新一个变分参数。对于每个选定的坐标，该方法重建目标函数对该参数的依赖关系，并直接移动到使训练目标最小化（或等价地使相应的期望解质量最大化）的参数值。虽然该方法专门在maQAOA上进行了演示，但其基本理论原理——即相对于给定参数的期望值可以解析地表示为有限傅里叶级数——广泛适用于通过参数化量子电路求解的一般任务。在连通的Erdős-Rényi图基准上的实证评估表明，与标准的基于梯度、随机和无导数基线相比，这种解析方法显著降低了达到目标近似比所需的计算训练成本，并产生了更优越的收敛可靠性。
英文摘要
Constrained combinatorial optimisation provides a mathematical framework for modelling a wide range of practical decision making problems, including energy network operation, financial portfolio optimisation, logistics, routing, and resource allocation. This paper studies parameter optimisation for the multi angle quantum approximate optimisation algorithm (maQAOA) applied to the maximum independent set problem, a canonical constrained graph based optimisation task. We propose a coordinate wise training framework for maQAOA that updates one variational parameter at a time by solving a sequence of one dimensional optimisation subproblems. For each selected coordinate, the method reconstructs the objective dependence on that parameter and moves directly to the parameter value that minimises the training objective, or equivalently maximises the corresponding expected solution quality. While demonstrated specifically on maQAOA, the underlying theoretical principle, that the expectation value with respect to a given parameter can be analytically expressed as a finite Fourier series, is broadly applicable to general tasks solved via parameterised quantum circuits. Empirical evaluations on connected ErdHos Renyi graph benchmarks demonstrate that this analytic approach significantly reduces the computational training cost required to reach target approximation ratios and yields superior convergence reliability compared to standard gradient based, stochastic, and derivative free baselines.
