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.

本数据仓库包含来自下述论文实验所生成的数据文件：A. Wulff 等：《应用力学与工程中的计算机方法（Comput. Methods Appl. Mech. Eng.）》432卷（2024年）第117380号文章，DOI: 10.1016/j.cma.2024.117380

**摘要：**
与诸多工程任务一样，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（laminated composite materials）的重量优化问题，由于构型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，需要先将该问题转换为可适配量子计算机底层运算的形式。

我们的研究聚焦于基于铺层参数（lamination parameters）的铺层序列检索（stacking sequence retrieval）问题，该问题通常是最小化复合结构重量的常见双层优化（bi-level optimization）流程中的第二阶段。为了使铺层序列检索可适配量子计算方法，我们将所有可能的铺层序列映射至量子态空间（quantum state space）中。我们进一步在该态空间中推导出一个线性算符——哈密顿量（Hamiltonian），其封装了铺层序列检索问题固有的损失函数（loss function）。此外，我们还演示了如何将铺层序列的制造约束（manufacturing constraints）作为惩罚项（penalty terms）纳入哈密顿量中。该量子表示形式适用于多种用于求解量子哈密顿量基态（ground state）的经典与量子算法。

为开展实际演示，我们针对两种变分量子算法（variational quantum algorithms）进行了数值态矢（state-vector）模拟，同时还选取了经典张量网络算法（tensor network algorithm）——密度矩阵重整化群（Density Matrix Renormalization Group, 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符（matrix product operator）表示形式。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铺层序列检索提供了一种全新的量子启发式路径。

如需了解本仓库中数据的更多详情，请查看「README.md」文件。