On Clifford Groups in Quantum Computing

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F18%3A00324445" target="_blank" >RIV/68407700:21340/18:00324445 - isvavai.cz</a>

Výsledek na webu

<a href="http://iopscience.iop.org/issue/1742-6596/1071/1" target="_blank" >http://iopscience.iop.org/issue/1742-6596/1071/1</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1742-6596/1071/1/012022" target="_blank" >10.1088/1742-6596/1071/1/012022</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On Clifford Groups in Quantum Computing

Popis výsledku v původním jazyce

The term Clifford group was introduced in 1998 by D. Gottesmann in his investigation of quantum error-correcting codes. The simplest Clifford group in multiqubit quantum computation is generated by a restricted set of unitary Clifford gates - the Hadamard, $pi/4$-phase and controlled-X gates. Because of this restriction the Clifford model of quantum computation can be efficiently simulated on a classical computer (the Gottesmann-Knill theorem). However, this fact does not diminish the importance of the Clifford model, since it may serve as a suitable starting point for a full-fledged quantum computation. In the general case of a single or composite quantum system with finite-dimensional Hilbert space the finite Weyl-Heisenberg group of unitary operators defines the quantum kinematics and the states of the quantum register. Then the corresponding Clifford group is defined as the group of unitary operators leaving the Weyl-Heisenberg group invariant. The aim of this contribution is to show that our comprehensive results on symmetries of the Pauli gradings of quantum operator algebras -- covering any single as well as composite finite quantum systems -- directly correspond to Clifford groups defined as quotients with respect to U(1).

Název v anglickém jazyce

On Clifford Groups in Quantum Computing

Popis výsledku anglicky

The term Clifford group was introduced in 1998 by D. Gottesmann in his investigation of quantum error-correcting codes. The simplest Clifford group in multiqubit quantum computation is generated by a restricted set of unitary Clifford gates - the Hadamard, $pi/4$-phase and controlled-X gates. Because of this restriction the Clifford model of quantum computation can be efficiently simulated on a classical computer (the Gottesmann-Knill theorem). However, this fact does not diminish the importance of the Clifford model, since it may serve as a suitable starting point for a full-fledged quantum computation. In the general case of a single or composite quantum system with finite-dimensional Hilbert space the finite Weyl-Heisenberg group of unitary operators defines the quantum kinematics and the states of the quantum register. Then the corresponding Clifford group is defined as the group of unitary operators leaving the Weyl-Heisenberg group invariant. The aim of this contribution is to show that our comprehensive results on symmetries of the Pauli gradings of quantum operator algebras -- covering any single as well as composite finite quantum systems -- directly correspond to Clifford groups defined as quotients with respect to U(1).

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název statě ve sborníku

Journal of Physics: Conference Series

ISBN

—

ISSN

1742-6596

e-ISSN

1742-6596

Počet stran výsledku

11

Strana od-do

1-11

Název nakladatele

Institute of Physics Publishing

Místo vydání

Bristol

Místo konání akce

Bregenz

Datum konání akce

30. 7. 2017

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

—