Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

Quantum Fractional Fourier Transform

Not Accessible

Your library or personal account may give you access

Abstract

Fourier transform has taken place in different areas and applications, in this paper has been revised an important new form of application in the paradigm of quantum computing. Quantum Fourier transforms have gained increased attention with the rise of quantum walks, boson sampling, and quantum metrology [2]. In the Shor’s Algorithm it is used for find discrete logarithms on a quantum computer with two modular exponentiations and two quantum Fourier transforms [1]. Our propose consist in show a new quantum gate that can perform the Fractional Fourier Transform defined by Namias as a tool to solve the differential equation of the quantum mechanical oscillator [3], which it can satisfy the condition of to be unitary. We apply the quantum gate in different states through of a real quantum computer offered by IBM for check that it carry out the transform successfully, it results were compared with results of Quantum Fourier Transform for can understand its application. In the geometric point of view showed in the figure (2a) and (2c) through of Bloch Sphere, we can see the difference between the application of Quantum Fourier Transform (QFT) and Quantum Fractional Fourier Transform (with our quantum gate) to the basis state |0〉, while in the figure (2b) and (2d) is possible see with a theoretical result that probability density is equal for both.

© 2018 The Author(s)

PDF Article
More Like This
Implementation of Quantum and Classical Discrete Fractional Fourier Transforms

Armando Perez-Leija, Steffen Weimann, Maxime Lebugle, Markus Gräfe, Rene Heilmann, Stefan Nolte, Hector Moya-Cessa, Demetrios N. Christodoulides, and Alexander Szameit
FTh2D.4 Frontiers in Optics (FiO) 2015

Implementation of quantum discrete fractional Fourier transform

Markus Gräfe, Steffen Weimann, Armando Perez-Leija, Maxime Lebugle, Robert Keil, René Heilmann, Stefan Nolte, Gregor Weihs, Demetrios N. Christodoulides, and Alexander Szameit
QW6B.4 Quantum Information and Measurement (QIM) 2017

Fractional Fourier Transform In Time-Frequency Domain Using Quantum Memory

Marcin Jastrzebski, Bartosz Niewelt, Stanislaw Kurzyna, Jan Nowosielski, Wojciech Wasilewski, Mateusz Mazelanik, and Michał Parniak
FW1C.2 Frontiers in Optics (FiO) 2023

Poster Presentation

Media 1: PDF (340 KB)     
Select as filters


Select Topics Cancel
© Copyright 2024 | Optica Publishing Group. All Rights Reserved