Quantum error-correcting codes and their geometries
Annales de l’Institut Henri Poincaré D, Tome 10 (2023) no. 2, pp. 337-405.
Le texte intégral des articles récents est réservé aux abonnés de la revue. Consultez l'article sur le site de la revue.

This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum error-correcting codes allow the negation of these effects in order to successfully restore the original quantum information. We briefly describe the necessary quantum-mechanical background to be able to understand how quantum error correction works. We go on to construct quantum codes: firstly qubit stabilizer codes, then qubit non-stabilizer codes, and finally codes with a higher local dimension. We will delve into the geometry of these codes. This allows one to deduce the parameters of the code efficiently, deduce the inequivalence between codes that have the same parameters, and presents a useful tool in deducing the feasibility of certain parameters. We also include sections on quantum maximum distance separable codes and the quantum MacWilliams identities.

Accepté le :
Publié le :
DOI : 10.4171/aihpd/160
Classification : 81-XX, 94-XX
Mots-clés : Quantum error-correcting codes 
@article{AIHPD_2023__10_2_337_0,
     author = {Ball, Simeon and Centelles, Aina and Huber, Felix},
     title = {Quantum error-correcting codes and their geometries},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
     pages = {337--405},
     volume = {10},
     number = {2},
     year = {2023},
     doi = {10.4171/aihpd/160},
     mrnumber = {4581446},
     zbl = {1522.81064},
     language = {en},
     url = {http://www.numdam.org/articles/10.4171/aihpd/160/}
}
TY  - JOUR
AU  - Ball, Simeon
AU  - Centelles, Aina
AU  - Huber, Felix
TI  - Quantum error-correcting codes and their geometries
JO  - Annales de l’Institut Henri Poincaré D
PY  - 2023
SP  - 337
EP  - 405
VL  - 10
IS  - 2
UR  - http://www.numdam.org/articles/10.4171/aihpd/160/
DO  - 10.4171/aihpd/160
LA  - en
ID  - AIHPD_2023__10_2_337_0
ER  - 
%0 Journal Article
%A Ball, Simeon
%A Centelles, Aina
%A Huber, Felix
%T Quantum error-correcting codes and their geometries
%J Annales de l’Institut Henri Poincaré D
%D 2023
%P 337-405
%V 10
%N 2
%U http://www.numdam.org/articles/10.4171/aihpd/160/
%R 10.4171/aihpd/160
%G en
%F AIHPD_2023__10_2_337_0
Ball, Simeon; Centelles, Aina; Huber, Felix. Quantum error-correcting codes and their geometries. Annales de l’Institut Henri Poincaré D, Tome 10 (2023) no. 2, pp. 337-405. doi : 10.4171/aihpd/160. http://www.numdam.org/articles/10.4171/aihpd/160/

Cité par Sources :