[Return-types #7] QNode integration with custom gradient and autograd

[rmoyard]

Context:

This PR makes possible to use return types with QNodes and custom derivatives (finite-diff, param shift and adjoint) with Autograd.

Description of the Change:

1. Implement a new custom_vjp functions which is now separated between multi and single measurment custom_vjp_single, custom_vjp_multi.
2. Clean the autograd interface and adapt it to the new return types.
3. Update test from test_autograd.py, test_autograd_qnode.py and test_vjp.py

Benefits:

The new return types system is almost fully compatible with Autograd. (no ragged arrays)

Possible Drawbacks:

1. Users must apply autograd.numpy.hstack for multiple measurements or for second derivative.

2. Potential slowdown due to post-processing.

TODO:

1. Change the batch transform post processing function.
2. Add CV derivatives
3. Warning shots and state quantities entropies Vn entropy and mutual info shot vec validation check #3180

[sc-25813]

[github-actions]

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[codecov]

Codecov Report

Merging #3041 (26d8324) into master (37a4024) will increase coverage by 0.00%.
The diff coverage is 100.00%.

@@           Coverage Diff            @@
##           master    #3041    +/-   ##
========================================
  Coverage   99.69%   99.69%            
========================================
  Files         275      275            
  Lines       24012    24170   +158     
========================================
+ Hits        23938    24097   +159     
+ Misses         74       73     -1     

Impacted Files	Coverage Δ
pennylane/_grad.py	100.00% <ø> (ø)
pennylane/gradients/__init__.py	100.00% <100.00%> (ø)
pennylane/gradients/finite_difference.py	100.00% <100.00%> (ø)
pennylane/gradients/parameter_shift.py	100.00% <100.00%> (ø)
pennylane/gradients/vjp.py	100.00% <100.00%> (ø)
pennylane/interfaces/autograd.py	100.00% <100.00%> (ø)
pennylane/interfaces/execution.py	100.00% <100.00%> (ø)
pennylane/qnode.py	100.00% <100.00%> (ø)
pennylane/math/utils.py	100.00% <0.00%> (+0.88%)	⬆️

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[eddddddy]

Great job @rmoyard 💯!

I gave my first pass and left a few comments. Nothing too major from my side other than some questions and small suggestions.

[antalszava]

A massive effort, congrats @rmoyard! 👏 💪 Overall no major blockers, I've made some comments where I thought some smaller changes could be made to improve the changes.

A couple of general comments:

• I think shapes and types have been checked at many places already and made some comments at further spots. Overall I think we have to be more careful with these than before because this is of more importance;
• The documentation and commenting in the PR is looking top-notch and the code overall looks very clean 💯

[rmoyard]

@eddddddy @antalszava It is ready for a new round of reviews!

Two things I could not solve is:

1. @antalszava Why numpy array with shape () are converted to float, single measurment and single params. I would appreciate your input here.
2. @eddddddy The sum with axis 0 is not working with ArrayBox and differentiation, see my comment above. I could not simplify compute_vjp more.

Also pls go through the open comments and close the one where my answer was sufficient.

[antalszava]

Looks good! 💪 🌟 Remaining comments are minor.

[eddddddy]

Thanks for the changes @rmoyard 💯

Looks good to me as long as the rest of @antalszava's comments are addressed. 🙂

[rmoyard]

[sc-28429]