Differentiable pulse programming with qubits in PennyLane

[Qottmann]

Pulse programming in PennyLane demonstration with the following table of contents
a) Introduction to pulse gates, relates it to channels and other hardware terms. Explains time-dependent Schrodinger equation and such
b) Demonstrate how this can be done in PennyLane
c) Explains gradients (maybe mention parameter shift, showcase backprop capabilities for now)
d) runs ctrl-VQE

TODO

• Intro material
• PennyLane functionality
• Gradients
• Small ctrl-VQE demonstration
• update using official convenience functions
• polish
• use larger molecule
• Restrict / normalize pulse amplitude (in 2210.15812 eq. (8) they propose normalizing through the differentiable normalization function $N(z) = S(|z|) z/|z|$ with $S(x) = \frac{1-e^{-x}}{1+e^{x}}$)

[alvaro-at-xanadu]

Really good tutorial that I'll be referencing quite a bit 😃

• Minor changes in style and some grammar/typos

[Qottmann]

Thanks for the quick and helpful review @alvaro-at-xanadu and @KetpuntoG . I updated the demo with your suggestions

[Qottmann]

Switching back to dev branch since the master branch still has the broken autoray incompatibility (see https://github.com/PennyLaneAI/qml/actions/runs/4363669469/jobs/7630059782)

Edit: Just updated the requirements

[alvaro-at-xanadu]

Ready to go!

[KetpuntoG]

Great! ready to go @Qottmann 😉