In the documentation for “Parameter-shift rules” it talks about constructing partial derivatives by evaluating the same circuit with different parameters:

How is this any different than numerical differentiation though, mentioned here?

I see one mention towards this on the page:

“While this construction bears some resemblance to the numerical finite-difference method for computing derivatives, here s is finite rather than infinitesimal.”

What’s a concrete example of s (i.e. what’s the significance of calling it out as finite vs. infinitesimal)?

Adding a little bit more to this as I read more through the documentation. The page on quantum gradient mentions:

“This means that quantum gradients can be computed by quantum computers,”

By *computed* here does it mean that the gradient function itself is being output as the result of the computation or that simply the gradient is being computed on a quantum computer by calling the circuit multiple times with a parameter shift?