QFT 基于QFT的同质化 (QFT-based Homogenization)

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.

翻译：高效数字定性是综合材料分析中的一个关键问题。为了跟踪图像成像成像法的准确性改进,已经开发出数字定性的记忆高效方法。其中,Molinec和Suquet(1994,1998年)提出了一个基于FFFT的求解器,使FFFT的复杂性降低数字定性复杂性。然而,最近开发的断层感应器使记忆要求和计算时间达到了另一个水平。为了避免这一瓶颈,使用了量子计算领域的新跳跃。本文件将介绍Quantum Fourier变换(QFT)的应用,以取代Mourinec和Suquet算法中的快速四面形变(FFT) 。它将主要侧重于如何解读储存在量子状态中的四面形系数。首先,用最有可能的振荡估计(MLQAE) 重新制作的哈达马德测试算法来确定量系数。第二,在镜像域的材料定性中提出了避免哈达米德测试的改进。最后,该算法将应用于材料同质化,以确定基本地理结构的准确性。