Appears in collection : Combinatorics and Arithmetic for Physics: special days 2023

The quantum double model has been introduced by Kitaev in order to propose a model of quantum computing based on anyonic excitations, thus stable against perturbations. We propose a deformation of this model, induced by an external 3 form. In this model, the role of the quantum double is replaced by its twisted version, a quasi Hopf algebra introduced in orbifold models by Dijkgraaf, Pasquier and Roche.