In [Phys. Rev. Lett. 113, 210501 (2014)], to achieve the optimal fixed-point quantum search in the case of unknown fraction (denoted by $lambda$) of target items, the analytical multiphase matching (AMPM) condition has been proposed. In this paper, we find out that the AMPM condition can also be used to design the exact quantum search algorithm in the case of known $lambda$, and the minimum number of iterations reaches the optimal level of existing exact algorithms. Experiments are performed to demonstrate the proposed algorithm on IBMs quantum computer. In addition, we theoretically find two coincidental phases with equal absolute value in our algorithm based on the AMPM condition and that algorithm based on single-phase matching. Our work confirms the practicability of the AMPM condition in the case of known $lambda$, and is helpful to understand the mechanism of this condition.
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