We present a quantum annealing-based solution method for topology optimization (TO). In particular, we consider TO in a more general setting, i.e., applied to structures of continuum domains where designs are represented as distributed functions, referred to as continuum TO problems. According to the problem's properties and structure, we formulate appropriate sub-problems that can be solved on an annealing-based quantum computer. The methodology established can effectively tackle continuum TO problems formulated as mixed-integer nonlinear programs. To maintain the resulting sub-problems small enough to be solved on quantum computers currently accessible with small numbers of quits and limited connectivity, we further develop a splitting approach that splits the problem into two parts: the first part can be efficiently solved on classical computers, and the second part with a reduced number of variables is solved on a quantum computer. By such, a practical continuum TO problem of varying scales can be handled on the D-Wave quantum annealer. More specifically, we concern the minimum compliance, a canonical TO problem that seeks an optimal distribution of materials to minimize the compliance with desired material usage. The superior performance of the developed methodology is assessed and compared with the state-of-the-art heuristic classical methods, in terms of both solution quality and computational efficiency. The present work hence provides a promising new avenue of applying quantum computing to practical designs of topology for various applications.

翻译：我们提出了一种基于量子退火的拓扑优化（TO）求解方法。具体而言，我们将TO置于更一般的设定中，即应用于连续体结构的设计问题（其中设计变量表示为分布函数），称为连续拓扑优化问题。根据问题的特性与结构，我们构建了可在退火量子计算机上求解的合适子问题。所建立的方法可有效处理表述为混合整数非线性规划的连续拓扑优化问题。为使得子问题规模足够小以适应当前比特数少且连接性有限的量子计算机，我们进一步开发了一种分裂方法：将问题分为两部分——第一部分可在经典计算机上高效求解，第二部分则通过量子计算机求解（其变量数量已大幅缩减）。通过这种方式，不同规模的实用连续拓扑优化问题可在D-Wave量子退火器上处理。具体而言，我们关注最小柔度问题——这一经典拓扑优化问题旨在满足材料用量约束下寻求最优材料分布以最小化结构柔度。从求解质量与计算效率两方面，我们评估了所提出方法的优越性能，并与现有最先进的经典启发式方法进行了对比。因此，本研究为将量子计算应用于各类实际拓扑设计提供了富有前景的新途径。