  The Clifford algebra over the three-dimensional real linear space includes
its linear structure and its exterior algebra, the subspaces spanned by
multivectors of the same degree determine a gradation of the Clifford algebra.
Through these geometric notions, natural one-to-one and two-to-one
homomorphisms from $\mbox{SO}(3)$ into $\mbox{SU}(2)$ are built conventionally,
and the set of qubits, is identified with a subgroup of $\mbox{SU}(2)$. These
constructions are suitable to be extended to corresponding tensor powers. The
notions of qubits, quregisters and qugates are translated into the language of
symmetry groups. The corresponding elements to entangled states in the tensor
product of Hilber spaces. realise a notion of entanglement in the tensor
product of symmetry groups.
