This paper presents a new structural design framework, developed based on iterative optimization via quantum annealing (QA). The novelty lies in its successful design update using an unknown design multiplier obtained by iteratively solving the optimization problems with QA. In addition, to align with density-based approaches in structural optimization, multipliers are multiplicative to represent design material and serve as design variables. In particular, structural analysis is performed on a classical computer using the finite element method, and QA is utilized for topology updating. The primary objective of the framework is to minimize compliance under an inequality volume constraint, while an encoding process for the design variable is adopted, enabling smooth iterative updates to the optimized design. The proposed framework incorporates both penalty methods and slack variables to transform the inequality constraint into an equality constraint and is implemented in a quadratic unconstrained binary optimization (QUBO) model through QA. To demonstrate its performance, design optimization is performed for both truss and continuum structures. Promising results from these applications indicate that the proposed framework is capable of creating an optimal shape and topology similar to those benchmarked by the optimality criteria (OC) method on a classical computer.

翻译：本文提出了一种基于量子退火（QA）迭代优化的新型结构设计框架。其创新之处在于，通过使用量子退火迭代求解优化问题所获得的未知设计乘子，成功实现了设计更新。此外，为与结构优化中的密度法保持一致，乘子采用乘法形式以表征设计材料并作为设计变量。具体而言，结构分析在经典计算机上使用有限元方法进行，而拓扑更新则利用量子退火实现。该框架的主要目标是在不等式体积约束下最小化柔度，同时采用设计变量的编码过程，以实现对优化设计的平滑迭代更新。所提出的框架结合了惩罚函数法与松弛变量，将不等式约束转化为等式约束，并通过量子退火在二次无约束二进制优化（QUBO）模型中实现。为验证其性能，本文对桁架结构和连续体结构分别进行了设计优化。这些应用所取得的良好结果表明，所提出的框架能够生成与经典计算机上基于最优性准则（OC）方法基准测试相似的优化形状与拓扑。