An SO(3) picture for quantum searching

An SO(3) picture of the generalized Grover quantum searching algorithm is constructed. In this picture, various aspects of quantum searching, the phase matching requirement in particular, are easily understood. It also offers a simple quantitative description of quantum searching. Exact formulae for the rotation angle and rotational axis are given. The probability of finding the marked state is just the projection of the state vector onto the z-axis in this picture. Applications of the picture to the standard Grover algorithm and to a generalized quantum search algorithm with arbitrary phase rotations are given.