# Quantum arithmetic with the quantum Fourier transform

@article{RuizPerez2017QuantumAW, title={Quantum arithmetic with the quantum Fourier transform}, author={Lidia Ruiz-Perez and Juan Carlos Garc{\'i}a-Escart{\'i}n}, journal={Quantum Information Processing}, year={2017}, volume={16}, pages={1-14} }

The quantum Fourier transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing quantum Fourier transform adders and multipliers and comment some simple variations that extend their capabilities. These modified circuits can perform modular and non-modular arithmetic operations and work with signed integers. Among the operations, we discuss a quantum method to compute the weighted average of a series of inputs in the transform domain. One of the…

## 69 Citations

Integer numeric multiplication using quantum Fourier transform

- Computer Science, PhysicsQuantum Studies: Mathematics and Foundations
- 2021

A generic structure for the multiplication of any two integers using quantum Fourier transform is proposed, applicable for different quantum applications.

Quantum arithmetic operations based on quantum Fourier transform on signed integers

- PhysicsArXiv
- 2020

The proposed arithmetic operations can perform non-modular operations on all signed numbers without any limitation by using less resources and are compared with the nearest quantum arithmetic operations.

Quantum arithmetic operations based on quantum fourier transform on signed integers

- PhysicsInternational Journal of Quantum Information
- 2020

Novel quantum circuits of two’s complement, absolute value and comparison operations are presented by using the proposed QFT based addition and subtraction operations.

Quantum Amplitude Arithmetic

- Physics
- 2020

Quantum algorithm involves the manipulation of amplitudes and computational basis, of which manipulating basis is largely a quantum analogue of classical computing that is always a major contributor…

The multiplier based on quantum Fourier transform

- PhysicsCCF Trans. High Perform. Comput.
- 2020

The circuit analysis shows that the proposed multiplier could reduce the number of qubits in ancillary, and the multiplication result of finite qubits can be directly obtained by using fewer quantum gates, which has reduced the resource cost of quantum multiplier greatly.

Performance Evaluations of Noisy Approximate Quantum Fourier Arithmetic

- Computer Science2022 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW)
- 2022

Efficient techniques to implement QFT-based integer addition and multiplications, fundamental to various quantum applications including Shor's algorithm, weighted sum optimization problems in data processing and machine learning, and quantum algorithms requiring inner products are utilized.

3-Qubit Circular Quantum Convolution Computation using Fourier Transform with Illustrative Examples

- Physics
- 2022

In this work, we describe examples for calculating the 1-D circular convolution of signals represented by 3-qubit superpositions. The case is considered, when the discrete Fourier transform of one of…

Quantum Fourier Operators and Their Application

- Computer ScienceReal Perspective of Fourier Transforms and Current Developments in Superconductivity
- 2021

This work reviews the structure of the quantum Fourier transform and its implementation, and provides a permutation structure for putting the QFT within the context of universal computation.

Quantum Fourier transform in computational basis

- Computer ScienceQuantum Inf. Process.
- 2017

A new quantum scheme to encode Fourier coefficients in the computational basis, with fidelity 1 - \delta $$1-δ and digit accuracy ϵ for each Fourier coefficient is detailed.

Applications of Universal Parity Quantum Computation

- Computer Science
- 2022

We demonstrate the applicability of a universal gate set in the parity encoding, which is a dual to the standard gate model, by exploring several quantum gate algorithms such as the Quantum Fourier…

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