How do I visualize the action of Pauli $X$ and $Y$ gates on $|0\rangle$?

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I visualize Pauli Gates making rotations by π radians about the x, y, and z axes on the Bloch sphere.

If this is the case, then how Pauli-X and Pauli-Y gates applied to $|0\rangle$ differ? As both should rotate the $|0\rangle$ state to same location.

Abhinav

Posted 2020-10-05T04:32:09.550

Reputation: 209

Answers

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Applying X gate to the $|0\rangle$ state gives you $|1\rangle$, and applying Y gate to the $|0\rangle$ state gives you $i|1\rangle$. These states differ only by a global phase (the $i$ scalar multiplier in the second case), so they are not physically distinguishable (you cannot set up an experiment to observe the difference between them). Bloch sphere represents all states that differ by a global phase as one point on it, so you won't be able to see the difference using it.

X and Y gates differ in their effect on most other states, though (except $|1\rangle$, which will give you the same issue).

Mariia Mykhailova

Posted 2020-10-05T04:32:09.550

Reputation: 6 616