# How does noise affect the implementation of quantum gates?

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?

• I think the easiest way is to consider the action of simple noise models like the phase damping map, which transforms the Bloch sphere to an ellipsoid along the $x$-axis; the depolarizing map which shrinks the Bloch sphere towards the origin (i.e., the maximally mixed state), etc. Then, one can understand more "complex" kinds of noise in terms of these "elementary" ones. For more details, I'll refer you to: Sec. VIIA of Lidar's notes. – keisuke.akira Aug 7 at 5:55