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Annales de l’Institut Henri Poincaré D

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Volume 1, Issue 2, 2014, pp. 185–223
DOI: 10.4171/AIHPD/6

Published online: 2014-07-03

An application of Khovanov homology to quantum codes

Benjamin Audoux[1]

(1) Technopole Chateau Gombert, Marseille, France

We use Khovanov homology to define families of LDPC quantum error-correcting codes: unknot codes with asymptotical parameters $[[ \frac{3^{2 \ell+1}}{\sqrt{8\pi\ell}};1;2^\ell]]$; unlink codes with asymptotical parameters $[[\sqrt{\frac{3}{2\pi \ell}}6^\ell;2^\ell;2^\ell ]]$ and $(2,\ell)$-torus link codes with asymptotical parameters $[[n;1;d_n]]$ where $d_n>\frac{\sqrt{n}}{1.62}$.

Keywords: quantum codes, CSS codes, LDPC codes, Khovanov homology

Audoux Benjamin: An application of Khovanov homology to quantum codes. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 1 (2014), 185-223. doi: 10.4171/AIHPD/6