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