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.