Quantum Hidden Subgroup Algorithms: An Algorithmic Toolkit

Simple item page
dc.creatorLomonaco Jr., Samuel J.
dc.creatorKauffman, Louis H.
dc.date2006-07-06
dc.date.accessioned2026-07-07T07:22:53Z
dc.date.available2026-07-07T07:22:53Z
dc.descriptionOne of the most promising and versatile approaches to creating new quantum algorithms is based on the quantum hidden subgroup (QHS) paradigm, originally suggested by Alexei Kitaev. This class of quantum algorithms encompasses the Deutsch-Jozsa, Simon, Shor algorithms, and many more. In this paper, our strategy for finding new quantum algorithms is to decompose Shor's quantum factoring algorithm into its basic primitives, then to generalize these primitives, and finally to show how to reassemble them into new QHS algorithms. Taking an "alphabetic building blocks approach," we use these primitives to form an "algorithmic toolkit" for the creation of new quantum algorithms, such as wandering Shor algorithms, continuous Shor algorithms, the quantum circle algorithm, the dual Shor algorithm, a QHS algorithm for Feynman integrals, free QHS algorithms, and more. Toward the end of this paper, we show how Grover's algorithm is most surprisingly "almost" a QHS algorithm, and how this result suggests the possibility of an even more complete "algorithmic tookit" beyond the QHS algorithms.
dc.description34 pages, 8 figures
dc.identifierhttps://arxiv.org/abs/quant-ph/0607046
dc.identifierhttp://arxiv.org/abs/quant-ph/0607046
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115820
dc.subjectQuantum Physics
dc.titleQuantum Hidden Subgroup Algorithms: An Algorithmic Toolkit
dc.typetext

Files

Collections

arXiv