Factoring 51 and 85 with 8 qubits

We construct simplified quantum circuits for Shor's order-finding algorithm for composites N given by products of the Fermat primes 3, 5, 17, 257, and 65537. Such composites, including the previously studied case of 15, as well as 51, 85, 771, 1285, 4369, … have the simplifying property that th...

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Detalles Bibliográficos
Autores principales: Geller, Michael R., Zhou, Zhongyuan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group 2013
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3808816/
https://www.ncbi.nlm.nih.gov/pubmed/24162074
http://dx.doi.org/10.1038/srep03023
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author Geller, Michael R.
Zhou, Zhongyuan
author_facet Geller, Michael R.
Zhou, Zhongyuan
author_sort Geller, Michael R.
collection PubMed
description We construct simplified quantum circuits for Shor's order-finding algorithm for composites N given by products of the Fermat primes 3, 5, 17, 257, and 65537. Such composites, including the previously studied case of 15, as well as 51, 85, 771, 1285, 4369, … have the simplifying property that the order of a modulo N for every base a coprime to N is a power of 2, significantly reducing the usual phase estimation precision requirement. Prime factorization of 51 and 85 can be demonstrated with only 8 qubits and a modular exponentiation circuit consisting of no more than four CNOT gates.
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spelling pubmed-38088162013-10-28 Factoring 51 and 85 with 8 qubits Geller, Michael R. Zhou, Zhongyuan Sci Rep Article We construct simplified quantum circuits for Shor's order-finding algorithm for composites N given by products of the Fermat primes 3, 5, 17, 257, and 65537. Such composites, including the previously studied case of 15, as well as 51, 85, 771, 1285, 4369, … have the simplifying property that the order of a modulo N for every base a coprime to N is a power of 2, significantly reducing the usual phase estimation precision requirement. Prime factorization of 51 and 85 can be demonstrated with only 8 qubits and a modular exponentiation circuit consisting of no more than four CNOT gates. Nature Publishing Group 2013-10-28 /pmc/articles/PMC3808816/ /pubmed/24162074 http://dx.doi.org/10.1038/srep03023 Text en Copyright © 2013, Macmillan Publishers Limited. All rights reserved http://creativecommons.org/licenses/by-nc-sa/3.0/ This work is licensed under a Creative Commons Attribution-NonCommercial-ShareALike 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/
spellingShingle Article
Geller, Michael R.
Zhou, Zhongyuan
Factoring 51 and 85 with 8 qubits
title Factoring 51 and 85 with 8 qubits
title_full Factoring 51 and 85 with 8 qubits
title_fullStr Factoring 51 and 85 with 8 qubits
title_full_unstemmed Factoring 51 and 85 with 8 qubits
title_short Factoring 51 and 85 with 8 qubits
title_sort factoring 51 and 85 with 8 qubits
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3808816/
https://www.ncbi.nlm.nih.gov/pubmed/24162074
http://dx.doi.org/10.1038/srep03023
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