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

Computer

Watts Humphrey Award Nomination

Published Aug 1, 2022• 0 citations
Publisher

Abstract

Shor's algorithm can find the frequency, and therefore the period, in polynomial time by using quantum computing as a way that allows the undesirable frequencies to cancel out, leaving the one frequency that leads to the correct period.
DOI
10.1109/mc.2022.3188065

Related papers

A short note on Shor's factoring algorithm

Harry Buhrman

This note shows that Shor's algorithm for factoring in polynomial time on a quantum computer can be made to work with zero error probability.

ACM SIGACT News•Mar 1, 1996•8 citations

Shor's algorithm without partial fractions

Nolan R. Wallach

The purpose of this note was to give a proof that Shor's algorithm for period search is polynomial using only the standard $2^{n}$ quantum Fourier thansform and some simple trigonometry. There is an error that was pointed out to the author by Pavel Wocjan.

arXiv:1208.1987•Aug 9, 2012•0 citations

Implementation of Shor’s Algorithm in QISKIT by Quantum Computing using IBMQ

Quantum machine learning is the combination of quantum computing and classical machine learning. It helps in solving the problems of one field to another field. Shor’s algorithm is used for factoring the integers in polynomial time. Since the bestknown classical algorithm requires super polynomial time to factor the product of two primes, the widely used cryptosystem, RSA, relies on factoring being impossible for large enough integers. In this paper we will focus on the quantum part of Shor’s algorithm, which actually solves the problem of period finding. In polynomial time factoring problem can be turned into a period finding problem so an efficient period finding algorithm can be used to factor integers efficiently.

International Journal of Advanced Trends in Computer Science and Engineering•Apr 5, 2021•0 citations

Analysis of Innovative Quantum Optimization Solutions for Shor’s Period Finding Algorithm Applied to the Computation of

Kaleb Dias Antoine KODO, Eugène Cokou Ezin

In the rapidly evolving domain of quantum computing, Shor’s algorithm has emerged as a groundbreaking innovation with far-reaching implications for the field of cryptographic security. However, the efficacy of Shor’s algo... | Find, read and cite all the research you need on Tech Science Press

Journal of quantum computing•Jan 1, 2025•0 citations

Simulations of Shor's algorithm with implications to scaling and quantum error correction

Simon J. Devitt, Austin G. Fowler, Lloyd C. L. Hollenberg

The publication in 1994 of Shor's algorithm, which allows factorisation of composite number N in a time polynomial in its binary length L has been the primary catalyst for the race to construct a functional quantum computer. However, it seems clear that any practical system that may be developed will not be able to perform completely error free quantum gate operations or shield even idle qubits from inevitable error effects. Hence, the practicality of quantum algorithms needs to be investigated to not only determine limitations on such algorithms in a noisy quantum computer, but also to estimate what demands must be made of quantum error correction (QEC). Shor's algorithm is a combination of both classical pre and post-processing, and also a quantum period finding subroutine (QPF) which allows for the exponential speed up of this algorithm on a quantum device. This paper will look at the stability of this quantum subroutine under the effects of several error models. Direct simulation of the entire QPF subroutine required to factorise a given composite number N in the presence of errors shows that the circuit required to implement Shor's algorithm is very sensitive to a small number of errors within the entire calculation. Well designed and efficient error correction codes, quick gate times and very low gate error rates will be essential for any physical realisation of Shor's factoring algorithm.

arXiv:quant-ph/0408081•Aug 12, 2004•5 citations

IMPLEMENTATION OF PERIOD-FINDING ALGORITHM BY MEANS OF SIMULATING QUANTUM FOURIER TRANSFORM

Moghareh Abed Zohreh, Ashoorian Mohsen, Kiumars Ghowsi

•Jan 1, 2010•0 citations
The purpose of this note was to give a proof that Shor's algorithm for period search is polynomial using only the standard 2n2^{n}2n quantum Fourier thansform and some simple trigonometry. There is an error that was pointed out to the author by Pavel Wocjan.
Quantum machine learning is the combination of quantum computing and classical machine learning. It helps in solving the problems of one field to another field. Shor’s algorithm is used for factoring the integers in polynomial time. Since the bestknown classical algorithm requires super polynomial time to factor the product of two primes, the widely used cryptosystem, RSA, relies on factoring being impossible for large enough integers. In this paper we will focus on the quantum part of Shor’s algorithm, which actually solves the problem of period finding. In polynomial time factoring problem can be turned into a period finding problem so an efficient period finding algorithm can be used to factor integers efficiently.
The publication in 1994 of Shor's algorithm, which allows factorisation of composite number N in a time polynomial in its binary length L has been the primary catalyst for the race to construct a functional quantum computer. However, it seems clear that any practical system that may be developed will not be able to perform completely error free quantum gate operations or shield even idle qubits from inevitable error effects. Hence, the practicality of quantum algorithms needs to be investigated to not only determine limitations on such algorithms in a noisy quantum computer, but also to estimate what demands must be made of quantum error correction (QEC). Shor's algorithm is a combination of both classical pre and post-processing, and also a quantum period finding subroutine (QPF) which allows for the exponential speed up of this algorithm on a quantum device. This paper will look at the stability of this quantum subroutine under the effects of several error models. Direct simulation of the entire QPF subroutine required to factorise a given composite number N in the presence of errors shows that the circuit required to implement Shor's algorithm is very sensitive to a small number of errors within the entire calculation. Well designed and efficient error correction codes, quick gate times and very low gate error rates will be essential for any physical realisation of Shor's factoring algorithm.