JournalsaihpdVol. 1, No. 2pp. 185–223

An application of Khovanov homology to quantum codes

  • Benjamin Audoux

    Technopole Chateau Gombert, Marseille, France
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Abstract

We use Khovanov homology to define families of LDPC quantum error-correcting codes: unknot codes with asymptotical parameters [[32+18π;1;2]][[ \frac{3^{2 \ell+1}}{\sqrt{8\pi\ell}};1;2^\ell]]; unlink codes with asymptotical parameters [[32π6;2;2]][[\sqrt{\frac{3}{2\pi \ell}}6^\ell;2^\ell;2^\ell ]] and (2,)(2,\ell)-torus link codes with asymptotical parameters [[n;1;dn]][[n;1;d_n]] where dn>n1.62d_n>\frac{\sqrt{n}}{1.62}.

Cite this article

Benjamin Audoux, An application of Khovanov homology to quantum codes. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 1 (2014), no. 2, pp. 185–223

DOI 10.4171/AIHPD/6