Do quantum gates rotate a qubit around the Bloch sphere?

Or do quantum gates rotate the Bloch sphere around a qubit?

"The simplest quantum gates are the Paulis: X, Y, and Z. Their action is to perform a half rotation of the Bloch sphere around the x, y, and z axes."

What does this mean?


2 Answers 2


This question can similarly be asked in a non-quantum context: does a translation mean that your coordinates move while your objects remain in place or that your objects move within a fixed coordinate system? It turns out that these two operations are physically equivalent and so you can use either one to describe the same situation, so long as you keep track of everything. The trick is that moving an object in one direction is like moving the coordinate system in the opposite direction (see for example the last sentence in this section of wikipedia).

You can think about this using the earth as an example: if you walk east by 10 metres and look around, you'll see the same thing as if you were suspended in one place and the world rotated toward the west by 10 metres. If you try this with the night sky, you can see why it was originally believed that the earth stood still while the constellations rotated around it: this leads to the same physical observations as the earth rotating in the opposite direction while the constellations stand still.

In my experience, most people talk about gates rotating the vectors around the Bloch sphere and they keep the orientation of the Bloch sphere fixed. But it is always possible for people to use other conventions, hence my lengthy response as to why both conventions are physically legitimate.


Bloch sphere represent states of a qubit. Rotating Bloch sphere means rotating (states of) qubit.


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