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We have the situation where a 50/50 split between $|1\rangle$ and $|0\rangle$. This was done using a $H$-Gate. Now, when measuring in qiskit, if my understanding is correct, we collapse onto the Z-plane which then results in either a 0 or a 1.

So my question now would be, what's the practical usage of any rotation that isn't a Y-Rotation? As far as I can see, the Y-Rotation changes the amplitudes/probabilities of the measurement, where as a Z-Rotation does not.

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    $\begingroup$ A $Z$ rotation affects the phase of the state, which can be useful to get constructive/destructive interference later on. $\endgroup$
    – epelaaez
    Oct 25 at 9:09
  • $\begingroup$ Does that have any implications on quantum circuits? From my understanding it allows us to use even more of the complete state-space, but that isn't per se directly measurable, and there for, usable to construct algorithms with. $\endgroup$
    – Redimo
    Oct 25 at 10:17
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    $\begingroup$ Yes it has. Take for example the quantum Fourier transform, it uses the controlled Phase gate, which is a controlled rotation around the Z axis (in Qiskit’s implementation, it differs from the normal CRZ by a relative phase) $\endgroup$
    – epelaaez
    Oct 25 at 10:25

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