  The Grover search algorithm is one of the two key algorithms in the field of
quantum computing, and hence it is of significant interest to describe it in
the most efficient mathematical formalism. We show firstly, that Clifford's
formalism of geometric algebra, provides a significantly more efficient
representation than the conventional Bra-ket notation, and secondly, that the
basis defined by the states of maximum and minimum weight in the Grover search
space, allows a simple visualization of the Grover search as the precession of
a spin-1/2 particle. Using this formalism we efficiently solve the exact search
problem, as well as easily representing more general search situations.

Quantum Physics;Data Structures and Algorithms