# How to "eliminate" some components of the state vector?

I have $$n*k$$ qubits. At the very beginning the length of the state vector is $$2^{nk}$$. After some manipulations (Qiskit circuit) I reduce it to $$k^n$$ and it looks like $$a|1...\rangle +a|0...\rangle ...$$ Now I want to "eliminate " the $$|0...\rangle$$ components, and keep only the $$|1...\rangle$$ ones, if possible with the same coefficient for all (equiprobability).

Applying Grover I can find $$c|1...\rangle +d|0...\rangle ...$$

with $$c >> d$$, but I guess there is a simpler and more efficient method. But which one?

• From my understanding, there isn't really a more asymptotically efficient method than Grover's. You can do the repeat-until-success methods, or finally you can use some sequence of controlled $R_y$ rotations. But the last option is dependent on your coefficients $a$ and which states you have already zeroed out. In general it is exponential in gate depth, but you can always give it a shot and see if in practice it works OK for your situation. But I believe in general the problem you are posing does not have an easy trick to solve it Commented Nov 16, 2023 at 8:49
• Commented Mar 14 at 20:30