| BONANOME, Marianna, Mark HILLERY and Vladimír BUŽEK. Applications of quantum algorithms to the study of group automorphisms. Physical Review A. New York: American Physical Society, 2007, Vol. 76, No. 1, p. A012324, 6 pp. ISSN 1050-2947. |
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@article{747032,
author = {Bonanome, Marianna and Hillery, Mark and Bužek, Vladimír},
article_location = {New York},
article_number = {No. 1},
keywords = {quantum information processing; group automorphism; quantum algorithms},
language = {eng},
issn = {1050-2947},
journal = {Physical Review A},
note = {arXiv:0708.2560},
title = {Applications of quantum algorithms to the study of group automorphisms},
volume = {Vol. 76},
year = {2007}
}
TY - JOUR
ID - 747032
AU - Bonanome, Marianna - Hillery, Mark - Bužek, Vladimír
PY - 2007
TI - Applications of quantum algorithms to the study of group automorphisms
JF - Physical Review A
VL - Vol. 76
IS - No. 1
SP - A012324
EP - A012324
PB - American Physical Society
SN - 10502947
N1 - arXiv:0708.2560
KW - quantum information processing
KW - group automorphism
KW - quantum algorithms
N2 - 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. In particular, quantum programs that specify control over data can be treated using methods of quantum information theory.
ER -
BONANOME, Marianna, Mark HILLERY and Vladimír BUŽEK. Applications of quantum algorithms to the study of group automorphisms. \textit{Physical Review A}. New York: American Physical Society, 2007, Vol. 76, No. 1, p.~A012324, 6 pp. ISSN~1050-2947.
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