Demonstration of Shor’s factoring algorithm for N $$=$$ = 21 on IBM quantum processors

Abstract We report a proof-of-concept demonstration of a quantum order-finding algorithm for factoring the integer 21. Our demonstration involves the use of a compiled version of the quantum phase estimation routine, and builds upon a previous demonstration. We go beyond this work by using a configu...

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Autores principales:	Unathi Skosana, Mark Tame
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/83ad215236954f3fa443398042bc8bfa
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spelling	oai:doaj.org-article:83ad215236954f3fa443398042bc8bfa2021-12-02T18:51:53ZDemonstration of Shor’s factoring algorithm for N $$=$$ = 21 on IBM quantum processors10.1038/s41598-021-95973-w2045-2322https://doaj.org/article/83ad215236954f3fa443398042bc8bfa2021-08-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-95973-whttps://doaj.org/toc/2045-2322Abstract We report a proof-of-concept demonstration of a quantum order-finding algorithm for factoring the integer 21. Our demonstration involves the use of a compiled version of the quantum phase estimation routine, and builds upon a previous demonstration. We go beyond this work by using a configuration of approximate Toffoli gates with residual phase shifts, which preserves the functional correctness and allows us to achieve a complete factoring of $$N=21$$ N = 21 . We implemented the algorithm on IBM quantum processors using only five qubits and successfully verified the presence of entanglement between the control and work register qubits, which is a necessary condition for the algorithm’s speedup in general. The techniques we employ may be useful in carrying out Shor’s algorithm for larger integers, or other algorithms in systems with a limited number of noisy qubits.Unathi SkosanaMark TameNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-12 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Unathi Skosana Mark Tame Demonstration of Shor’s factoring algorithm for N $$=$$ = 21 on IBM quantum processors
description	Abstract We report a proof-of-concept demonstration of a quantum order-finding algorithm for factoring the integer 21. Our demonstration involves the use of a compiled version of the quantum phase estimation routine, and builds upon a previous demonstration. We go beyond this work by using a configuration of approximate Toffoli gates with residual phase shifts, which preserves the functional correctness and allows us to achieve a complete factoring of $$N=21$$ N = 21 . We implemented the algorithm on IBM quantum processors using only five qubits and successfully verified the presence of entanglement between the control and work register qubits, which is a necessary condition for the algorithm’s speedup in general. The techniques we employ may be useful in carrying out Shor’s algorithm for larger integers, or other algorithms in systems with a limited number of noisy qubits.
format	article
author	Unathi Skosana Mark Tame
author_facet	Unathi Skosana Mark Tame
author_sort	Unathi Skosana
title	Demonstration of Shor’s factoring algorithm for N $$=$$ = 21 on IBM quantum processors
title_short	Demonstration of Shor’s factoring algorithm for N $$=$$ = 21 on IBM quantum processors
title_full	Demonstration of Shor’s factoring algorithm for N $$=$$ = 21 on IBM quantum processors
title_fullStr	Demonstration of Shor’s factoring algorithm for N $$=$$ = 21 on IBM quantum processors
title_full_unstemmed	Demonstration of Shor’s factoring algorithm for N $$=$$ = 21 on IBM quantum processors
title_sort	demonstration of shor’s factoring algorithm for n $$=$$ = 21 on ibm quantum processors
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/83ad215236954f3fa443398042bc8bfa
work_keys_str_mv	AT unathiskosana demonstrationofshorsfactoringalgorithmforn21onibmquantumprocessors AT marktame demonstrationofshorsfactoringalgorithmforn21onibmquantumprocessors
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Demonstration of Shor’s factoring algorithm for N $$=$$ = 21 on IBM quantum processors

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