This study proposes a novel structural optimization framework based on quantum variational circuits, in which the multiplier acting on the cross-sectional area of each rod in a truss structure as an updater is used as a design variable. Specifically, we employ a classical processor for structural analysis with the finite element method, and the Quantum Approximate Optimization Algorithm (QAOA) is subsequently performed to update the cross-sectional area so that the compliance is minimized. The advantages of this framework can be seen in three key aspects. First, by defining design variables as multipliers, rather than simply reducing the design variable to a binary candidate of inclusion or exclusion (corresponding to qubit states, ``0" and ``1"), it provides greater flexibility in adjusting the cross-sectional area of the rod at each iteration of the optimization process. Second, the multipliers acting on rods are encoded with on-off encoding, eliminating additional constraints in the convergence judgement. As a result, the objective function is in a simple format, enabling efficient optimization using QAOA.Third, a fixed linear ramp schedule (FLRS) for variational parameter setting bypasses the classical optimization process, thereby improving the operational efficiency of the framework. In the two structural cases investigated in this study, the proposed approach highlights the feasibility and applicability potential of quantum computing in advancing engineering design and optimization. Numerical experiments have demonstrated the effectiveness of this framework, providing a firm foundation for future research on quantum-assisted optimization methods in engineering fields.

翻译：本研究提出了一种基于量子变分电路的新型结构优化框架，其中将作用于桁架结构各杆件横截面积的乘子作为设计变量进行更新。具体而言，我们采用经典处理器通过有限元法进行结构分析，随后执行量子近似优化算法（QAOA）以更新横截面积，从而使柔度最小化。该框架的优势体现在三个关键方面。首先，通过将设计变量定义为乘子，而非简单地将其简化为包含或排除的二元候选（对应于量子比特状态“0”和“1”），该框架在优化过程的每次迭代中为调整杆件横截面积提供了更大的灵活性。其次，作用于杆件的乘子采用开关编码进行编码，消除了收敛判断中的额外约束。因此，目标函数形式简洁，能够利用QAOA实现高效优化。第三，用于变分参数设置的固定线性斜坡调度（FLRS）绕过了经典优化过程，从而提高了框架的运行效率。在本研究探讨的两个结构案例中，所提方法凸显了量子计算在推进工程设计与优化方面的可行性与应用潜力。数值实验证明了该框架的有效性，为未来工程领域量子辅助优化方法的研究奠定了坚实基础。