Clifford group is not a semidirect product in dimensions N divisible by four

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/68407700:21340/23:00370155

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Clifford group is not a semidirect product in dimensions N divisible by four

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Clifford group is not a semidirect product in dimensions N divisible by four

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10100 - Mathematics

Projekt

<a href="/cs/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Centrum pokročilých aplikovaných přírodních věd</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Journal of Physics A: Mathematical and Theoretical

ISSN

1751-8113

e-ISSN

1751-8121

Svazek periodika

56

Číslo periodika v rámci svazku

27

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

29

Strana od-do

1-29

Kód UT WoS článku

001015472600001

EID výsledku v databázi Scopus

2-s2.0-85163408693