Appears in collection : 2014 - T1 - WS1 - Asymptotic properties of groups

A family of quantum error correcting codes (QECC) is constructed out of congruence quotients of the 4- dimensional hyperbolic space. The parameters of these codes are expressed by some aymptotic properties of the manifolds and their fundamental groups. By estimating these parameters, we disprove a conjecture of Zémor who predicted that such homological QECC do not exist. All notions will be defined and explained. A joint work with Larry Guth.