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 [[3^(2l+1)/sqrt(8{\pi}l);1;2^l]]; unlink codes with asymptotical parameters [[sqrt(2/2{\pi}l)6^l;2^l;2^l]] and (2,l)-torus link codes with asymptotical parameters [[n;1;d_n]] where d_n>\sqrt(n)/1.62.