Clifford group is not a semidirect product in dimensions N divisible by four
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F23%3A00370155" target="_blank" >RIV/68407700:21230/23:00370155 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21340/23:00370155
Result on the web
<a href="https://doi.org/10.1088/1751-8121/acd891" target="_blank" >https://doi.org/10.1088/1751-8121/acd891</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1088/1751-8121/acd891" target="_blank" >10.1088/1751-8121/acd891</a>
Alternative languages
Result language
angličtina
Original language name
Clifford group is not a semidirect product in dimensions N divisible by four
Original language description
The paper is devoted to projective Clifford groups of quantum N-dimensional systems (with configuration space Z(N)). Clearly, Clifford gates allow only the simplest quantum computations which can be simulated on a classical computer (Gottesmann-Knill theorem). However, it may serve as a cornerstone of full quantum computation. As to its group structure it is well-known that-in N-dimensional quantum mechanics-the Clifford group is a natural semidirect product provided the dimension N is an odd number. For even N special results on the Clifford groups are scattered in the mathematical literature, but they mostly do not concern the semidirect structure. Using appropriate group presentation of SL(2, ZN) it is proved that for even N the projective Clifford groups are not natural semidirect products if and only if N is divisible by four.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10100 - Mathematics
Result continuities
Project
<a href="/en/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Center for advanced applied science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Physics A: Mathematical and Theoretical
ISSN
1751-8113
e-ISSN
1751-8121
Volume of the periodical
56
Issue of the periodical within the volume
27
Country of publishing house
GB - UNITED KINGDOM
Number of pages
29
Pages from-to
1-29
UT code for WoS article
001015472600001
EID of the result in the Scopus database
2-s2.0-85163408693