# If I have a state $a|0000\rangle+b|0011\rangle$, how do you change it to make $b>a$?

How to increase the amplitude of a specific quantum state?

If my quantum circuit produces the state $$a|0000\rangle+b|0011\rangle$$, how to make $$b>a$$?

• how does "how to make" mean? You mean what gate/circuit can be used to change this state into another one with $b>a$? – glS Aug 1 at 11:26
• yes, is there any gate or circuit can do that? – Ebtehal Ali Aug 1 at 11:46
• You could invert about the mean. This is tagged grovers-algorithm. What do you know of Grover's algorithm? Are you getting confused about a specific step? – Mark S Aug 1 at 12:21

You don't specify whether or not the parameters $$a,b$$ are known. If they are, then the task is trivial. First, apply a controlled-not from qubit 3 to qubit 4, leaving you in the state $$|00\rangle(a|0\rangle+b|1\rangle)|0\rangle.$$ Now apply a unitary on qubit 3 (e.g. a Y-rotation by some angle of your choosing), so that you change to a state $$|00\rangle(c|0\rangle+d|1\rangle)|0\rangle.$$ Then you apply controlled-not again to give the final state $$|00\rangle(c|00\rangle+d|11\rangle).$$ However, I suppose this is not what you had in mind?
Alternatively, I might infer that you're intending $$a>b$$, perhaps you don't know $$a,b$$, but all you care about is changing the coefficients so that the amplitude of the 11 component is larger than that of the 00 component. In that case, it's even easier: apply Pauli X on both qubits 3 and 4. It'll convert you to $$|00\rangle(b|00\rangle+a|11\rangle),$$ satisfying those requirements.