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An application of Khovanov homology to quantum codes (1307.4677v1)
Published 17 Jul 2013 in cs.IT, math.GT, math.IT, and quant-ph
Abstract: We use Khovanov homology to define families of LDPC quantum error-correcting codes: unknot codes with asymptotical parameters [[32l+1/sqrt(8{\pi}l);1;2l]]; unlink codes with asymptotical parameters [[sqrt(2/2{\pi}l)6l;2l;2l]] and (2,l)-torus link codes with asymptotical parameters [[n;1;d_n]] where d_n>\sqrt(n)/1.62.