Applications of quantum algorithms to the study of group automorphisms

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F07%3A00020702" target="_blank" >RIV/00216224:14330/07:00020702 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Applications of quantum algorithms to the study of group automorphisms

Original language 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 qu

Czech name

Aplikace kvantových algoritmů při studiu automorfismů grup

Czech description

Analýza tří aplikací efektivních kvantových algoritmů pro určení vlastností permutací a automorfismů grup.

Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

IN - Informatics

OECD FORD branch

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Project

<a href="/en/project/GA201%2F07%2F0603" target="_blank" >GA201/07/0603: Quantum multipartite computation, communication and security</a><br>

Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2007

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Physical Review A

ISSN

1050-2947

e-ISSN

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Volume of the periodical

Vol. 76

Issue of the periodical within the volume

No. 1

Country of publishing house

US - UNITED STATES

Number of pages

6

Pages from-to

"A012324"

UT code for WoS article

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EID of the result in the Scopus database

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