About: Applications of quantum algorithms to the study of group automorphisms

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We discuss three applications of efficient quantum algorithms to determining properties of permutations and group automorphisms. The first uses the Bernstein-Vazirani algorithm to determine an unknown homomorphism from $Z_{p-1}^{m}$ to $Aut(Z_{p})$ where $p$ is prime. The remaining two make use of modifications of the Grover search algorithm. The first finds the fixed point of a permutation or an automorphism (assuming it has only one besides the identity). It can be generalized to find cycles of a specified size for permutations or orbits of a specified size for automorphisms. The second finds which of a set of permutations or automorphisms maps one particular element of a set or group onto another. This has relevance to the conjugacy problem for groups. We show how two of these algorithms can be implemented via programmable quantum processors. This approach opens new perspectives in quantum information processing, wherein both the data and the programs are represented by states of quantum registers. We discuss three applications of efficient quantum algorithms to determining properties of permutations and group automorphisms. The first uses the Bernstein-Vazirani algorithm to determine an unknown homomorphism from $Z_{p-1}^{m}$ to $Aut(Z_{p})$ where $p$ is prime. The remaining two make use of modifications of the Grover search algorithm. The first finds the fixed point of a permutation or an automorphism (assuming it has only one besides the identity). It can be generalized to find cycles of a specified size for permutations or orbits of a specified size for automorphisms. The second finds which of a set of permutations or automorphisms maps one particular element of a set or group onto another. This has relevance to the conjugacy problem for groups. We show how two of these algorithms can be implemented via programmable quantum processors. This approach opens new perspectives in quantum information processing, wherein both the data and the programs are represented by states of quantum registers. (en)
Title	Applications of quantum algorithms to the study of group automorphisms Applications of quantum algorithms to the study of group automorphisms (en)
skos:prefLabel	Applications of quantum algorithms to the study of group automorphisms Applications of quantum algorithms to the study of group automorphisms (en)
skos:notation	RIV/00216224:14330/07:00020702!RIV10-GA0-14330___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/07/0603), Z(MSM0021622419)
http://linked.open...iv/cisloPeriodika	No. 1
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Bužek, Vladimír Hillery, Mark
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Masarykova univerzita / Fakulta informatiky
http://linked.open...dnocenehoVysledku	410573
http://linked.open...ai/riv/idVysledku	RIV/00216224:14330/07:00020702
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	quantum information processing; group automorphism; quantum algorithms (en)
http://linked.open.../riv/klicoveSlovo	quantum algorithms quantum information processing group automorphism
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[FADCA8E69005]
http://linked.open...i/riv/nazevZdroje	Physical Review A
http://linked.open...in/vavai/riv/obor	IN
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Quantum multipartite computation, communication and security
http://linked.open...UplatneniVysledku	2007
http://linked.open...v/svazekPeriodika	Vol. 76
http://linked.open...iv/tvurceVysledku	Bužek, Vladimír Bonanome, Marianna Hillery, Mark
http://linked.open...ain/vavai/riv/wos	000248486600062
http://linked.open...n/vavai/riv/zamer	Highly Parallel and Distributed Computing Systems
issn	1050-2947
number of pages	6 (xsd:int)
http://localhost/t...ganizacniJednotka	14330
is http://linked.open...avai/riv/vysledek of	Applications of quantum algorithms to the study of group automorphisms Applications of quantum algorithms to the study of group automorphisms Applications of quantum algorithms to the study of group automorphisms

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