3

I had a question earlier about generating the superposition of all the possible states: Here. In that case, we could apply $H^{\otimes n}$ to the state $|0\rangle^{\otimes n}$, and each state has the same amplitude in the superposition: $|0\rangle^{\otimes n} \to \dfrac{1}{\sqrt{2^n}}\sum_{i=0}^{2^n-1} |i\rangle $. However, it is possible for us to tune the amplitude of certain states in the superposition? Say if I have 4 qubits and 4 Hadamard gates (one on each), that would generate a superposition of 16 states. Can I add some additional procedures to increase the amplitude of $|0110\rangle$ and $|1001\rangle$ and the rest states have the same and reduced amplitude?

Thanks!!

3This one of the things Grover's Algorithm does; the Wikipedia Page is quite good at outlining the algorithm. – Bertrand Einstein IV – 2021-01-26T18:39:26.897

@Bertrand Einstein IV Thank you!! – Zhengrong – 2021-01-26T20:35:28.847