Given a quantum state $\left|\Psi\right> = \sum_{i=0}^{2^n-1} \alpha_i\left|i \right>$, for which I know that the probabilities ($|\alpha_i|^2$) follow a sine/cosine like distribution as in the following picture. enter image description here

It is important to note that I do not know for which basis states the probability is maximal or minimal, I just know that the distribution follows such a sine/cosine wave.

Now, how can I amplify those probabilities that are above some threshold $\tau$? I just need to "spike" the distribution a little more. I suspect I can do amplitude estimation to write the amplitudes in an ancilla register, mark those states that are above the threshold $\tau$ and then do amplitude amplification. This works for any state $\left|\Psi\right>$, but is there a simpler, more efficient algorithm to spike the probabilities, given that I know how the state looks like?



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