Amplitude amplification for known state but unknown amplitude

Asked Aug 22 '20 at 06:04

Active Aug 24 '20 at 09:18

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I have a circuit that prepares a state $|s\rangle$ which is a superposition of the basis states $$\sum_{x=0}^{2^{n-1}}\alpha_x|x\rangle$$ with amplitude $\alpha_x$ for a circuit of $n$ qubits. Particularly, the solution to the problem I'm looking is on the state $|0\rangle$.

The challenge is that, $|0\rangle$ usually has a really low probability (and sometimes its not even present in the superposition).

I was wondering if there was a simple way to boost the amplitude of $|0\rangle$ given I know specifically location of my solution?

edited Aug 24 '20 at 09:18

glS

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asked Aug 22 '20 at 06:04

César Leonardo Clemente López

Is $|0\rangle$ a subset of the $n$ qubits? If it’s only $k\le n$ of these qubits why not use a conditional rotation based on these? – Mark Spinelli Aug 23 '20 at 02:53
You mean a conditional rotation if state 0 is present? Could you please elaborate a little bit more on what kind of rotation you mean – César Leonardo Clemente López Aug 23 '20 at 06:37
Are you familiar with the idea that amplitude amplification and Grover's search are essentially the same thing? Are you aware that Grover's search can be used when there's an unknown number of solutions (making use of phase estimation)? You can put the two together... – DaftWullie Aug 26 '20 at 07:39
Is this on the main paper? – César Leonardo Clemente López Aug 28 '20 at 15:07

Amplitude amplification for known state but unknown amplitude

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