Research Data Accompanying the Publication: "Quantum Computing and Tensor Networks for Laminate Design: A Novel Approach to Stacking Sequence Retrieval"

This data repository contains generated data files from the experiments in the paper:A. Wulff <em>et al.</em>: Comput. Methods Appl. Mech. Eng. 432 (2024) 117380,doi: 10.1016/j.cma.2024.117380<br><strong>Abstract:</strong>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, which is typically the second phase in a common bi-level optimization procedure for minimizing the weight of composite structures. To adapt stacking sequence retrieval 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 numerical state-vector simulations of two variational quantum algorithms and additionally chose a classical tensor network algorithm, the DMRG algorithm, to numerically validate our approach. For the DMRG algorithm, we derived a matrix product operator representation of the loss function Hamiltonian and the penalty terms. Although this work primarily concentrates on quantum computation, the application of tensor network algorithms presents a novel quantum-inspired approach for stacking sequence retrieval.<br>For further information on the data in this repository, view the 'README.md' file.

本数据集仓库包含该论文实验所生成的数据文件：A. Wulff等人：《Comput. Methods Appl. Mech. Eng.》432 (2024) 117380，DOI: 10.1016/j.cma.2024.117380

**摘要：**正如工程领域的诸多任务一样，结构设计往往需要应对复杂且计算成本高昂的问题。其中一个典型案例便是层合复合材料的重量优化——由于配置空间呈指数级增长且存在非线性约束，该问题至今仍是一项极具挑战性的任务。快速发展的量子计算领域或许能为解决这类复杂问题提供全新路径。然而，在将任意量子算法应用于特定问题之前，需要先将问题转换为兼容量子计算机底层运算的形式。
本研究聚焦于采用层合参数的铺层序列检索任务，这通常是最小化复合材料结构重量的常见双层优化流程中的第二阶段。为了使铺层序列检索适配量子计算方法，我们将所有可能的铺层序列映射至量子态空间。进一步地，我们在该空间中推导得到了一个线性算子——哈密顿量（Hamiltonian），它封装了铺层序列检索问题固有的损失函数。此外，我们演示了如何将铺层序列的制造约束作为惩罚项纳入哈密顿量中。
这种量子表示形式适用于多种经典与量子算法，用于求解量子哈密顿量的基态。为进行实际验证，我们对两种变分量子算法开展了数值态矢仿真，同时选取经典张量网络算法——密度矩阵重整化群（DMRG）算法——来对我们的方法进行数值验证。针对DMRG算法，我们推导了损失函数哈密顿量与惩罚项的矩阵乘积算子表示形式。
尽管本研究主要围绕量子计算展开，但张量网络算法的应用为铺层序列检索提供了一种全新的类量子计算路径。

如需了解本仓库中数据集的更多细节，请查看"README.md"文件。