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Suppose I have three different operators $U_1, U_2,U_3$. Now, these three operators will be applied if my current state of the system is $|\psi_0\rangle,|\psi_1\rangle $ and $|\psi_2\rangle$ respectively.

Now suppose I started with some initial state $|\psi_{initial}\rangle$ and after applying two unitary operations it will be converted to one of the states above and on the basis of that the respective unitary operator needs to applied.

I know we can't measure the state as it will collapse the system. So, what method can be applied here?

what method can be applied to do what? – glS – 2020-11-27T19:09:34.420

It's mention in the question. An operator conditioned on the current state of system. If after doing some operations the current state of the system comes out to be $|\psi_0\rangle$ then I want to apply operator $U_1$ and so on. – Binshumesh sachan – 2020-11-28T03:58:48.873

you just stated that $U_i$ are applied to $|\psi_i\rangle$, that you start with $|\psi_{initial}\rangle$ and that you apply two unitary operations to it sending it to some $|\psi_i\rangle$ and that you then apply $U_i$ to this state. I see no question here. Also, it would be great if you could provide the context on why you want to do this – glS – 2020-11-28T10:25:14.990