Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1411.5949 · Quantum Information Processing

Quantum arithmetic with the quantum Fourier transform

Lidia Ruiz, Juan Carlos García-Escartín

Published Apr 28, 2017• 201 citations
arXivHTMLPDF
DOI
10.1007/s11128-017-1603-1

Related papers

Fourier Transforms and Quantum Computation

Umesh V. Vazirani

Lecture notes in computer science•Jan 1, 2002•5 citations

Quantum Fourier Transform‐Based Arithmetic Logic Unit on a Quantum Processor

Selçuk Çakmak, Murat Kurt, Azmi Gençten

Abstract This study proposes and construct a primitive quantum arithmetic logic unit (qALU) based on the quantum Fourier transform (QFT). The qALU is capable of performing arithmetic ADD (addition) and logic NAND gate operations. It designs a scalable quantum circuit and presents the circuits for driving ADD and NAND operations on two‐input and four‐input quantum channels, respectively. By comparing the required number of quantum gates for serial and parallel architectures in executing arithmetic addition, it evaluates the performance. It also execute the proposed quantum Fourier transform‐based qALU design on real quantum processor hardware provided by IBM. The results demonstrate that the proposed circuit can perform arithmetic and logic operations with a high success rate. Furthermore, it discusses in detail the potential implementations of the qALU circuit in the field of computer science, highlighting the possibility of constructing a soft‐core processor on a quantum processing unit.

arXiv:2306.09560•Annalen der Physik•Dec 15, 2023•6 citations

Algorithms Using Quantum Fourier Transform

Robert Hundt

The quantum Fourier transform is another fundamental quantum algorithm. The section begins with a simple phase-kick circuit and expands to quantum phase estimation before detailing the quantum Fourier transform itself. A short section on arithmetic in the quantum domain introduces techniques that are used in a final detailed section on Shor’s famous algorithm for number factorization.

Cambridge University Press eBooks•Nov 20, 2025•0 citations

The Quantum Fourier Transform and Its Applications

WORLD SCIENTIFIC eBooks•Aug 27, 2026•0 citations

The Quantum Fourier Transform

Marco O. Lanzagorta, Jeffrey K. Uhlmann

Synthesis lectures on quantum computing•Jan 1, 2008•2 citations

Quantum arithmetic operations based on quantum fourier transform on signed integers

Engin Şahin

The quantum Fourier transform (QFT) brings efficiency in many respects, especially usage of resource, for most operations on quantum computers. In this study, the existing QFT-based and non-QFT-based quantum arithmetic operations are examined. The capabilities of QFT-based addition and multiplication are improved with some modifications. The proposed operations are compared with the nearest quantum arithmetic operations. Furthermore, novel QFT-based subtraction, division and exponentiation operations are presented. The proposed arithmetic operations can perform nonmodular operations on all signed numbers without any limitation by using less resources. In addition, novel quantum circuits of two’s complement, absolute value and comparison operations are also presented by using the proposed QFT-based addition and subtraction operations.

arXiv:2005.00443•International Journal of Quantum Information•Sep 1, 2020•35 citations
Abstract This study proposes and construct a primitive quantum arithmetic logic unit (qALU) based on the quantum Fourier transform (QFT). The qALU is capable of performing arithmetic ADD (addition) and logic NAND gate operations. It designs a scalable quantum circuit and presents the circuits for driving ADD and NAND operations on two‐input and four‐input quantum channels, respectively. By comparing the required number of quantum gates for serial and parallel architectures in executing arithmetic addition, it evaluates the performance. It also execute the proposed quantum Fourier transform‐based qALU design on real quantum processor hardware provided by IBM. The results demonstrate that the proposed circuit can perform arithmetic and logic operations with a high success rate. Furthermore, it discusses in detail the potential implementations of the qALU circuit in the field of computer science, highlighting the possibility of constructing a soft‐core processor on a quantum processing unit.
The quantum Fourier transform (QFT) brings efficiency in many respects, especially usage of resource, for most operations on quantum computers. In this study, the existing QFT-based and non-QFT-based quantum arithmetic operations are examined. The capabilities of QFT-based addition and multiplication are improved with some modifications. The proposed operations are compared with the nearest quantum arithmetic operations. Furthermore, novel QFT-based subtraction, division and exponentiation operations are presented. The proposed arithmetic operations can perform nonmodular operations on all signed numbers without any limitation by using less resources. In addition, novel quantum circuits of two’s complement, absolute value and comparison operations are also presented by using the proposed QFT-based addition and subtraction operations.