Exact amplitude amplification
= Exact amplitude amplification
If the initial good amplitude $p=\sin\theta$ is known, an ancillary qubit can reduce it to $\sin\theta'=p c$ with $\theta'=\pi/(4k+2)$ and $0<c\leq1$. After $k$ ordinary amplitude-amplification iterations the good amplitude is $\sin((2k+1)\theta')=1$, so the target state is prepared exactly.