  In this paper, after a brief presentation of the physical 2+1 dimensional
place where the anyons evolve, there is established the links creation
probability for the anyons. The departure point is the celebrated Laughlin wave
function. Then, two cases of quantum links are emphasized, considering two and
three anyons. In the first case a two qubits register is attached. The unitary
transformation (e.g. the UCNOT unitary transformation) can map not-entangled
quantum states to the quantum and topological entangled states, as there are
highlighted in this paper for the two anyons link case. The six qubit register
which is attached to the three anyons link is only shortly presented since it
represents a work in progress. The topologic and quantum states are represented
by ket vectors and correspondingly by diagrams.
