Geodesic
An application of Khovanov homology to quantum codes
Annales de l’Institut Henri Poincaré D, Tome 1 (2014) no. 2, pp. 185-223

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We use Khovanov homology to define families of LDPC quantum error-correcting codes: unknot codes with asymptotical parameters [[3 2ℓ+1 8πℓ;1;2 ℓ ]]; unlink codes with asymptotical parameters [[3 2πℓ6 ℓ ;2 ℓ ;2 ℓ ]] and (2,ℓ)-torus link codes with asymptotical parameters [[n;1;d n ]] where d n >n 1.62.

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DOI : 10.4171/aihpd/6
Classification : 81-XX, 57-XX, 94-XX
Keywords: quantum codes, CSS codes, LDPC codes, Khovanov homology 
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     title = {An application of {Khovanov} homology to quantum codes},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
     pages = {185--223},
     volume = {1},
     number = {2},
     year = {2014},
     doi = {10.4171/aihpd/6},
     mrnumber = {3229943},
     zbl = {1309.81055},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/aihpd/6/}
}
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Audoux, Benjamin. An application of Khovanov homology to quantum codes. Annales de l’Institut Henri Poincaré D, Tome 1 (2014) no. 2, pp. 185-223. doi: 10.4171/aihpd/6

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