- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:04:49
Annales de l’Institut Henri Poincaré D
Ann. Inst. Henri Poincaré Comb. Phys. Interact.
AIHPD
2308-5827
2308-5835
General
Combinatorics
Quantum theory
10.4171/AIHPD
http://www.ems-ph.org/doi/10.4171/AIHPD
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
1
2014
2
An application of Khovanov homology to quantum codes
Benjamin
Audoux
Technopole Chateau Gombert, Marseille cedex 13, FRANCE
quantum codes, CSS codes, LDPC codes, Khovanov homology
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 $d_n>\frac{\sqrt{n}}{1.62}$.
Quantum theory
Manifolds and cell complexes
Information and communication, circuits
185
223
10.4171/AIHPD/6
http://www.ems-ph.org/doi/10.4171/AIHPD/6