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It is easy to see how $\theta$ (rotation from the positive z-axis) and $\varphi$ (rotation from the positive z-axis) affect the initial state of the qubit when looking at the Bloch sphere but I have been playing around with different $\lambda$ values and can't see a clear transformation. Geometrically, how does lambda transform the state?

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$\lambda$ is also a rotation around the $z$ axis. However, there is an ordering issue. There's a sequence of $z$-rotation ($\lambda$), $y$-rotation ($\theta$), $z$-rotation ($\varphi$).

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  • $\begingroup$ Is it a typo we don't have any x-rotation here? $\endgroup$ – user9318 yesterday
  • $\begingroup$ no. This question was (implicitly) about the u3 rotation in qiskit, which is essentially a sequence of rotations z-y-z. $\endgroup$ – DaftWullie yesterday
  • $\begingroup$ I see, thank you! $\endgroup$ – user9318 yesterday

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