QFT-based Homogenization

TL;DR

This paper introduces a quantum computing approach using Quantum Fourier Transform (QFT) to enhance the efficiency of numerical homogenization in composite materials, replacing classical FFT methods to handle larger datasets.

Contribution

It presents a novel application of QFT in material homogenization, including methods for reading quantum Fourier coefficients and improving computational efficiency.

Findings

QFT-based algorithm can replace FFT in homogenization tasks.

Quantum methods reduce memory and computation time for large datasets.

Application demonstrated on effective stiffness calculation of basic geometries.

Abstract

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.