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 performed state-vector simulations of two variational quantum algorithms and additionally chose a classical tensor network algorithm, the DMRG algorithm, to numerically validate our approach. 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类似，结构设计常常涉及处理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的重量优化，由于存在指数级庞大的配置空间和非线性约束，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底层操作兼容的形式。我们的工作特别针对基于层合参数的堆叠顺序检索问题。为使该问题适应量子计算方法，我们将可能的堆叠顺序映射到量子态空间。我们进一步在该态空间内推导了一个线性算子——哈密顿量，该算子封装了堆叠顺序检索问题固有的损失函数。此外，我们展示了将堆叠顺序的制造约束作为惩罚项纳入哈密顿量的方法。这种量子表示适用于寻找量子哈密顿量基态的各种经典和量子算法。为进行实际验证，我们对两种变分量子算法进行了态矢量模拟，并额外选择了一种经典张量网络算法——DMRG算法，以数值方式验证我们的方法。尽管本研究主要聚焦于量子计算，但张量网络算法的应用为堆叠顺序检索提供了一种新颖的量子启发式方法。