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Statements

Subject Item
n2:RIV%2F00216224%3A14330%2F07%3A00020702%21RIV10-GA0-14330___
rdf:type
skos:Concept n11:Vysledek
dcterms: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.
dcterms:title
Applications of quantum algorithms to the study of group automorphisms Applications of quantum algorithms to the study of group automorphisms
skos:prefLabel
Applications of quantum algorithms to the study of group automorphisms Applications of quantum algorithms to the study of group automorphisms
skos:notation
RIV/00216224:14330/07:00020702!RIV10-GA0-14330___
n3:aktivita
n9:P n9:Z
n3:aktivity
P(GA201/07/0603), Z(MSM0021622419)
n3:cisloPeriodika
No. 1
n3:dodaniDat
n4:2010
n3:domaciTvurceVysledku
Hillery, Mark n17:4347196
n3:druhVysledku
n19:J
n3:duvernostUdaju
n13:S
n3:entitaPredkladatele
n5:predkladatel
n3:idSjednocenehoVysledku
410573
n3:idVysledku
RIV/00216224:14330/07:00020702
n3:jazykVysledku
n18:eng
n3:klicovaSlova
quantum information processing; group automorphism; quantum algorithms
n3:klicoveSlovo
n10:group%20automorphism n10:quantum%20information%20processing n10:quantum%20algorithms
n3:kodStatuVydavatele
US - Spojené státy americké
n3:kontrolniKodProRIV
[FADCA8E69005]
n3:nazevZdroje
Physical Review A
n3:obor
n15:IN
n3:pocetDomacichTvurcuVysledku
2
n3:pocetTvurcuVysledku
3
n3:projekt
n14:GA201%2F07%2F0603
n3:rokUplatneniVysledku
n4:2007
n3:svazekPeriodika
Vol. 76
n3:tvurceVysledku
Hillery, Mark Bonanome, Marianna Bužek, Vladimír
n3:wos
000248486600062
n3:zamer
n12:MSM0021622419
s:issn
1050-2947
s:numberOfPages
6
n7:organizacniJednotka
14330