Suppose we have a qubit in the state $|q\rangle = a |0\rangle + b |1\rangle$, and another ancilla qubit $= |0\rangle$.
I wish to have the following black-box gate:
if |a| > 0.8, then turn the ancilla to |1⟩ else leave the ancilla unchanged at |0⟩.
Is it possible to construct such a black-box gate?
(Background information: I do not want to use measurement on $|q\rangle$ because that will terminate the quantum process. I need to continue the quantum process. In my case, the resulting ancilla state is used to control the subsequent quantum computing as part of a larger quantum system where computation process will differ depending on whether the ancilla qubit is 0 or 1.)