  The aim of the paper is to provide an method to obtain representations of the
braid group through a set of quasitriangular Hopf algebras. In particular,
these algebras may be derived from group algebras of cyclic groups with
additional algebraic structures. In this context, by using the flip operator,
it is possible to construct R-matrices that can be regarded as quantum logic
gates capable of preserving quantum entanglement.
