Registre quantique

Dans le domaine de l'informatique quantique, un registre quantique est un registre composé de plusieurs qubits^[1]. Il est l'équivalent quantique d'un registre classique.

Définition

Un registre quantique de taille $n$ est un système quantique comprenant $n$ qubits.

Il peut être représenté sous la forme d'un espace de Hilbert, ${\mathcal {H}}$ , dans lequel les données stockées sont sous la forme:

${\mathcal {H}}={\mathcal {H_{n-1}}}\otimes {\mathcal {H_{n-2}}}\otimes \ldots \otimes {\mathcal {H_{0}}}$ ^[2].

Registre quantique vs. registre classique

Tout d'abord, il y a une différence conceptuelle entre le registre quantique et classique.

Un registre classique de taille $n$ se compose d'un tableau de $n$ bascules. Un registre quantique de taille $n$ est simplement une collection de $n$ qubits.

De plus, alors qu'un registre classique de taille $n$ est capable de stocker une seule valeur de la $2^{n}$ possibilités engendrées par $n$ bits, un registre quantique est capable de stocker tous les $2^{n}$ possibilités engendrées par ses qubits en même temps.

Par exemple, prenons un registre de 2 bits. Un registre classique est capable de stocker une seule des valeurs possibles représentées par 2 bits - $00,01,10,11\quad (0,1,2,3)$ en conséquence.

Si nous prenons 2 qubits dans un état de superposition:

$|a_{0}\rangle ={\frac {1}{\sqrt {2}}}(|0\rangle +|1\rangle )$ et $|a_{1}\rangle ={\frac {1}{\sqrt {2}}}(|0\rangle -|1\rangle )$

Sa définition implique que:

$|a\rangle =|a_{0}\rangle \otimes |a_{1}\rangle ={\frac {1}{2}}(|00\rangle -|01\rangle +|10\rangle -|11\rangle )$

On observe donc que le qubit est implicitement capable de stocker toutes les valeurs simultanément.

Références

↑ (en) Auteur inconnu, « Basic concepts in quantum computation », .
↑ Günther W., V.N. Gheorghe, F.G. Major, Charged particle traps II : applications, Berlin, Springer, 2009 (ISBN 978-3540922605), p. 220

Voir aussi

Sphère de Bloch

Portail de l’informatique

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