9

2

I've created a simple circuit in Q-Kit to understand conditional gates and outputted states on each step:

- In the beginning there is clear 00 state, which is the input
- The first qubit is passed through the Hadamard gate, it gets into superposition, 00 and 10 become equally possible
- The first qubit CNOTs the second one, probability of 00 is unchanged, but 10 and 11 are swapped
- The first qubit passes Hadamard again and
**probability of 00 is splited between 00 and 10, and 11 between 01 and 11**as if first qubit stepped into superposition from a fixed state

Shouldn't the result be equally distributed 00 and 01? The first qubit passes Hadamard twice, which should put it into superposition and back to initial 0. The CNOT gate does not affect controller qubit, so its existence shouldn't affect first qubit at all, but in fact it makes it act like it wasn't in superposition any more. **Does usage of qubit as a controller collapse its superposition?**