I am trying to think about quantum noise visually here. If, for example, one wants to implement an X-gate to perform a 180-degree rotation around the Bloch Sphere. In a perfect world, the X-gate will move the quantum state from the |0> state to the |1> state.
My question is, how does the existence of noise affect the implementation of gates (i.e. the X-gate)?
Does it make the quantum state rotate some angle that's is slightly greater than or smaller than 180 degrees? In short, how can one visualize noise on the Bloch Sphere?