  The earlier approach is used for description of qubits and geometric phase
parameters, the things critical in the area of topological quantum computing.
The used tool, Geometric (Clifford) Algebra is the most convenient formalism
for that case. Generalization of formal complex plane to an an arbitrary plane
in three dimensions and of usual Hopf fibration to the map generated by an
arbitrary unit value element of even sub-algebra of the three-dimensional
Geometric Algebra are resulting in more profound description of qubits compared
to quantum mechanical Hilbert space formalism.
