  We discuss in details the role of Wigner 6j symbol as the basic building
block unifying such different fields as state sum models for quantum geometry,
topological quantum field theory, statistical lattice models and quantum
computing. The apparent twofold nature of the 6j symbol displayed in quantum
field theory and quantum computing -a quantum tetrahedron and a computational
gate- is shown to merge together in a unified quantum-computational SU(2)-state
sum framework.
