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Abstract
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.