Geometric Phase in Geometric Algebra Qubit Formalism

He who undertakes to deal with questions of natural sciences without the help of geometry is attempting the infeasible. (Galileo Galilei). Though having been existed for a while the geometric algebra formalism even in the most simple intuitively clear three dimensional case causes very often by physiological reasons rejection in physics scientist community starting from allegations on using of incorrect linear operations and up to accusations of attempts to eliminate complex numbers from physics.