  In the past few years there has been a tumultuous activity aimed at
introducing novel conceptual schemes for quantum computing. The approach
proposed in (Marzuoli A and Rasetti M 2002, 2005a) relies on the (re)coupling
theory of SU(2) angular momenta and can be viewed as a generalization to
arbitrary values of the spin variables of the usual quantum-circuit model based
on `qubits' and Boolean gates. Computational states belong to
finite-dimensional Hilbert spaces labelled by both discrete and continuous
parameters, and unitary gates may depend on quantum numbers ranging over finite
sets of values as well as continuous (angular) variables. Such a framework is
an ideal playground to discuss discrete (digital) and analogic computational
processes, together with their relationships occuring when a consistent
semiclassical limit takes place on discrete quantum gates. When working with
purely discrete unitary gates, the simulator is naturally modelled as families
of quantum finite states--machines which in turn represent discrete versions of
topological quantum computation models. We argue that our model embodies a sort
of unifying paradigm for computing inspired by Nature and, even more
ambitiously, a universal setting in which suitably encoded quantum symbolic
manipulations of combinatorial, topological and algebraic problems might find
their `natural' computational reference model.
