Discrete Fourier Transform in Nanostructures using Scattering

TL;DR

This paper introduces a novel method to perform discrete Fourier transforms by scattering a coherent beam off a 2D potential, enabling efficient and fault-tolerant Fourier analysis in nanostructures.

Contribution

It demonstrates that Fourier transforms can be realized through scattering in nanostructures, offering a new approach for optical and quantum information processing.

Findings

Fourier transform performed via scattering off 2D potentials.

Method is fault-tolerant due to wavelength-dependent accuracy.

Potential applications in nanostructure analysis and quantum computing.

Abstract

In this paper we show that the discrete Fourier transform can be performed by scattering a coherent particle or laser beam off a two-dimensional potential that has the shape of rings or peaks. After encoding the initial vector into the two-dimensional potential, the Fourier-transformed vector can be read out by detectors surrounding the potential. The wavelength of the laser beam determines the necessary accuracy of the 2D potential, which makes our method very fault-tolerant.