BugFix: Controlled.generator correctly projects with control values

[astralcai]

Context:

Controlled.generator always projects onto the $\ket{1}$ space of the control wire without considering control values.

Description of the Change:

Now Controlled.generator correctly projects the operator based on the control value specified

Benefits:

Fixes a bug

[codecov]

Codecov Report

Attention: 2 lines in your changes are missing coverage. Please review.

Comparison is base (c01cb4b) 99.67% compared to head (116ef54) 99.66%.
Report is 19 commits behind head on master.

Files	Patch %	Lines
pennylane/workflow/jacobian_products.py	91.30%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #5068      +/-   ##
==========================================
- Coverage   99.67%   99.66%   -0.01%     
==========================================
  Files         394      394              
  Lines       35670    35461     -209     
==========================================
- Hits        35554    35343     -211     
- Misses        116      118       +2     

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[albi3ro]

We should also add some tests to ensure this definition of the generator agrees with the qml.exp(op.generator(), 1j*op.data[0]) convention for a generator. op and that exponential operator should have the same form.

We could potentially even add this check to assert_valid:

https://github.com/PennyLaneAI/pennylane/blob/master/pennylane/ops/functions/assert_valid.py

to test generators more generally, but for now we should just check those two forms have the same matrix.

[astralcai]

We should also add some tests to ensure this definition of the generator agrees with the qml.exp(op.generator(), 1j*op.data[0]) convention for a generator. op and that exponential operator should have the same form.

We could potentially even add this check to assert_valid:

https://github.com/PennyLaneAI/pennylane/blob/master/pennylane/ops/functions/assert_valid.py

to test generators more generally, but for now we should just check those two forms have the same matrix.

I added a quick check for this in the test case, is checking matrix equivalence the proper way of doing this?

[albi3ro]

Thanks for finding this and making a fix 🎉

[timmysilv]

looks good!

[Alex-Preciado]

Awesome!! Just Linking to Shortcut story: [sc-55065]