论文标题
基于QFT的均质化
QFT-based Homogenization
论文作者
论文摘要
有效的数值表征是复合材料分析中的关键问题。为了遵循图像层析成像的准确性提高，已经开发了数值表征的记忆有效方法。其中，Moulinec和Suquet（1994,1998）提出了一个基于FFT的求解器，将数值表征的复杂性降低到FFT复杂性。然而，最近的层析成像传感器的最新发展使记忆需求和计算时间达到了另一个水平。为了避免这种瓶颈，已经使用了量子计算领域的新飞跃。本文将介绍量子傅立叶变换（QFT）的应用，以替换毛琳克和suquet算法中快速傅立叶变换（FFT）。它将主要集中于如何读取存储在量子状态的傅立叶系数。首先，使用大多数可能性振幅估计（MLQAE）应用的重新设计的Hadamard测试算法来确定量子系数。其次，在镜像域上的材料表征的情况下，提出了避免HADAMARD测试的改进。最后，将最后一个算法应用于材料均质化，以确定碱性几何形状的有效刚度。
Efficient numerical characterization is a key problem in composite material analysis. To follow accuracy improvement in image tomography, memory efficient methods of numerical characterization have been developed. Among them, an FFT based solver has been proposed by Moulinec and Suquet (1994,1998) bringing down numerical characterization complexity to the FFT complexity. Nevertheless, recent development of tomography sensors made memory requirement and calculation time reached another level. To avoid this bottleneck, the new leaps in the field of Quantum Computing have been used. This paper will present the application of the Quantum Fourier Transform (QFT) to replace the Fast Fourier Transform (FFT) in Moulinec and Suquet algorithm. It will mainly focused on how to read out Fourier coefficients stored in a quantum state. First, a reworked Hadamard test algorithm applied with Most likelihood amplitude estimation (MLQAE) is used to determine the quantum coefficients. Second, an improvement avoiding Hadamard test is presented in case of Material characterization on mirrored domain. Finally, this last algorithm is applied to Material homogenization to determine effective stiffness of basic geometries.
