So I am trying to implement non-unitary operations on Qiskit.
There is an option to perform conditional operations in Qiskit.
Suppose I prepare a qubit state in superposition. $|\psi\rangle=\sqrt{\frac{1}{2}}\left(|0\rangle+|1\rangle\right)$
Then I measure it in computational basis. The output will be randomly 0 or 1.
I then give an instruction to apply bit flip if the output is 1 and do nothing if the output is 0. I can use the conditional if statement here.
Using this I guarantee that my output will always be $|0\rangle$ state no matter what. The entire operation can be represented by
$O=\sqrt{2}|0\rangle\langle0|$ matrix (which is non-unitary)
Is this kind of operation a basic example of doing non-unitary operation on a quantum computer which uses only unitary gates?
This is the diagram of the circuit.