please show me how to take the derivative of a quantum circuit I don’t understand how a circuit has a derivative

Hi @AstroQFT, great question! It sounds crazy that circuits can have a gradient but in fact they can.

The gradient is similar to the derivative. It’s a vector that points in the direction of highest increase of a function. We use quantum circuits to calculate a function of certain parameters (for instance rotations). So if we can find the direction of highest increase of the function we have the gradient.

In order to do this we vary some of the parameters in the function. This gives us similar functions that combined together in a linear combination give the gradient of the original function! This image from the docs (link below) can further illustrate this concept.

This entry in the docs goes into a lot more detail in case you want a more technical explanation. https://pennylane.readthedocs.io/en/user-docs-refactor/concepts/autograd_quantum.html#id5

Please let me know if this answered your question! I would be happy to answer more questions if you have any.

thank you @CatalinaAlbornoz that is helpful so the gradient is not of the circuit but of the function of the circuit parameter that gets measurecd at the output right

Hi @AstroQFT. The gradient is in fact of the circuit. Mathematically a circuit is a function **f** which has some parameters **theta** and which receives some inputs **x**. The output of the function is the measurement of the quantum circuit. The gradient of this function that represents the circuit is the gradient of the circuit!

You can think of the circuit as a black box with some parameters you can tweek. The way we find the gradient is by tweeking the parameters to create new circuits that combine together to give the gradient of the original one.

Please let me know if this answers your question!

ohh i see, that makes sense now, thank you so much!