Phase condition for the Grover algorithm

摘要

For the Grover algorithm, we derive the exact formula of the norm of the amplitude in the marked state in a sine-function form and use this formula, to derive the necessary and sufficient phase condition sin Delta <= vertical bar beta vertical bar for this algorithm with arbitrary phase rotations. We show that the condition of identical rotation angles theta = phi, which is a special case of our condition, is a sufficient but not necessary, phase condition.