A general quantum search algorithm with arbitrary unitary transformations and
an arbitrary initial state is considered in this work. To serach a marked state
with certainty, we have derived, using an SU(2) representation: (1) the
matching condition relating the phase rotations in the algorithm, (2) a concise
formula for evaluating the required number of iterations for the search, and
(3) the final state after the search, with a phase angle in its amplitude of
unity modulus. Moreover, the optimal choices and modifications of the phase
angles in the Grover kernel is also studied.Comment: 8 pages, 2 figure
