  We expand a set of notions recently introduced providing the general setting
for a universal representation of the quantum structure on which quantum
information stands. The dynamical evolution process associated with generic
quantum information manipulation is based on the (re)coupling theory of SU(2)
angular momenta. Such scheme automatically incorporates all the essential
features that make quantum information encoding much more efficient than
classical: it is fully discrete; it deals with inherently entangled states,
naturally endowed with a tensor product structure; it allows for generic
encoding patterns. The model proposed can be thought of as the non-Boolean
generalization of the quantum circuit model, with unitary gates expressed in
terms of 3nj coefficients connecting inequivalent binary coupling schemes of
n+1 angular momentum variables, as well as Wigner rotations in the eigenspace
of the total angular momentum. A crucial role is played by elementary j-gates
(6j symbols) which satisfy algebraic identities that make the structure of the
model similar to "state sum models", employed in discretizing Topological
Quantum Field Theories and quantum gravity. The spin network simulator can thus
be viewed also as a Combinatorial QFT model for computation. The semiclassical
limit (large j's) is discussed.
