An application of Khovanov homology to quantum codes

Abstract

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 $d_n>\frac{\sqrt{n}}{1.62}$.