Quantum erasure-correcting codes and percolation on regular tilings of the hyperbolic plane

Nicolas Delfosse (1) , Gilles Zemor (1)

1 IMB - Institut de Mathématiques de Bordeaux

We are interested in percolation for a family of self-dual tilings of the hyperbolic plane. We achieve an upper bound on the critical probability for these tilings by taking appropriate finite quotients and associating them with a family of quantum CSS codes. We then relate the probability of percolation to the probability of a decoding error for these codes on the quantum erasure channel.

Domaines: Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]

Nicolas Delfosse, Gilles Zemor. Quantum erasure-correcting codes and percolation on regular tilings of the hyperbolic plane. 2011. ⟨hal-00632255⟩