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In the past few years there has been a tumultuous activity aimed atintroducing novel conceptual schemes for quantum computing. The approachproposed in (Marzuoli A and Rasetti M 2002, 2005a) relies on the (re)couplingtheory of SU(2) angular momenta and can be viewed as a generalization toarbitrary values of the spin variables of the usual quantum-circuit model basedon `qubits' and Boolean gates. Computational states belong tofinite-dimensional Hilbert spaces labelled by both discrete and continuousparameters, and unitary gates may depend on quantum numbers ranging over finitesets of values as well as continuous (angular) variables. Such a framework isan ideal playground to discuss discrete (digital) and analogic computationalprocesses, together with their relationships occuring when a consistentsemiclassical limit takes place on discrete quantum gates. When working withpurely discrete unitary gates, the simulator is naturally modelled as familiesof quantum finite states--machines which in turn represent discrete versions oftopological quantum computation models. We argue that our model embodies a sortof unifying paradigm for computing inspired by Nature and, even moreambitiously, a universal setting in which suitably encoded quantum symbolicmanipulations of combinatorial, topological and algebraic problems might findtheir `natural' computational reference model.Comment: 17 pages, 1 figure; Workshop `Natural processes and models of  computation' Bologna (Italy) June 16-18 2005; to appear in Natural Computin

Coupling of quantum angular momenta: an insight into analogic/discrete and local/global models of computation