Quantum Topology Optimization via Quantum Annealing
Quantum Topology Optimization via Quantum Annealing
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DOI：
10.1109/tqe.2023.3266410
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发表时间：
2023-01
影响因子：
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通讯作者：
Zisheng Ye;Xiaoping Qian;W. Pan
中科院分区：
文献类型：
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作者：
Zisheng Ye;Xiaoping Qian;W. Pan
提出了一种基于量子退火的拓扑优化求解方法。特别地，我们在更一般的设置中考虑TO，即，应用于连续域的结构，其中设计被表示为分布式函数，称为连续TO问题。根据问题的性质和结构，我们制定了适当的子问题，可以解决基于退火的量子计算机。所建立的方法可以有效地解决连续TO问题制定为混合整数非线性规划。为了保持所产生的子问题足够小，以便在目前可用少量量子位和有限连接的量子计算机上解决，我们进一步开发了一种分裂方法，将问题分为两部分：第一部分可以在经典计算机上有效解决，第二部分在量子计算机上解决，变量数量减少。通过这样，可以在D-Wave量子退火机上处理不同尺度的实际连续TO问题。更具体地说，我们关注的最小的顺应性，一个典型的TO问题，寻求最佳的材料分配，以尽量减少所需的材料使用的顺应性。所开发的方法的上级性能进行评估和比较与国家的最先进的启发式经典方法，在解决方案的质量和计算效率。因此，目前的工作提供了一个很有前途的新途径，应用量子计算的实际设计的拓扑结构的各种应用。
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 subproblems 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 subproblems small enough to be solved on quantum computers currently accessible with small numbers of qubits 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.