As with many tasks in engineering, structural design frequently involves navigating complex and computationally expensive problems. A prime example is the weight optimization of laminated composite materials, which to this day remains a formidable task, due to an exponentially large configuration space and non-linear constraints. The rapidly developing field of quantum computation may offer novel approaches for addressing these intricate problems. However, before applying any quantum algorithm to a given problem, it must be translated into a form that is compatible with the underlying operations on a quantum computer. Our work specifically targets stacking sequence retrieval with lamination parameters. To adapt this problem for quantum computational methods, we map the possible stacking sequences onto a quantum state space. We further derive a linear operator, the Hamiltonian, within this state space that encapsulates the loss function inherent to the stacking sequence retrieval problem. Additionally, we demonstrate the incorporation of manufacturing constraints on stacking sequences as penalty terms in the Hamiltonian. This quantum representation is suitable for a variety of classical and quantum algorithms for finding the ground state of a quantum Hamiltonian. For a practical demonstration, we chose a classical tensor network algorithm, the DMRG algorithm, to numerically validate our approach. For this purpose, we derived a matrix product operator representation of the loss function Hamiltonian and the penalty terms. Numerical trials with this algorithm successfully yielded approximate solutions, while exhibiting a tradeoff between accuracy and runtime. Although this work primarily concentrates on quantum computation, the application of tensor network algorithms presents a novel quantum-inspired approach for stacking sequence retrieval.

翻译：与工程中的许多任务一样，结构设计经常需要应对复杂且计算成本高昂的问题。一个典型的例子是层合复合材料结构的重量优化，由于存在指数级增长的构型空间和非线性约束，该问题至今仍是一项艰巨的任务。快速发展的量子计算领域可能为解决这些复杂问题提供新途径。然而，在将任何量子算法应用于特定问题之前，必须将其转化为与量子计算机基本操作兼容的形式。本研究专门针对基于层合参数的堆叠序列检索问题。为适配量子计算方法，我们将可能的堆叠序列映射到量子态空间。我们进一步在该态空间中推导出一个线性算子（哈密顿量），该算子封装了堆叠序列检索问题固有的损失函数。此外，我们展示了如何将堆叠序列的制造约束作为惩罚项纳入哈密顿量。这种量子表示适用于多种用于寻找量子哈密顿量基态的经典和量子算法。在实用验证中，我们选择了经典张量网络算法——密度矩阵重整化群（DMRG）算法来数值验证本方法。为此，我们推导了损失函数哈密顿量和惩罚项的矩阵乘积算子表示。使用该算法的数值试验成功获得了近似解，同时表现出精度与运行时间之间的权衡关系。尽管本研究主要聚焦量子计算，但张量网络算法的应用为堆叠序列检索提供了一种新颖的量子启发式方法。