  We study the construction of both universal quantum computation and
multi-partite entangled states in the topological diagrammatical approach to
quantum teleportation. Our results show that the teleportation-based quantum
circuit model admits a space-time topological interpretation which makes the
construction of both quantum gates and four-partite entangled states more
intuitive and simpler. Our results state a deeper link between the space-time
non-locality and the quantum non-locality which are the two-fold character of
the topological diagrammatical representation.
