Fix qml.GellMann observable data

[mudit2812]

Context:
Fixes #4341 .

Description of the Change:

• Update Observable._obs_data() to include the index of qml.GellMann in the parameter list.
• Update Hamiltonian._obs_data() to include the index of qml.GellMann in the parameter list.

Note:
I would still recommend using the new operator arithmetic with qutrits. The generators of parametric qutrit gates are instances of Prod and Sum, not qml.Hamiltonian. So, try using qml.dot instead of qml.Hamiltonian with qutrit observables.

Benefits:
Comparison of instances of qml.GellMann, Hamiltonians and Tensors containing qml.GellMann is correct.

Possible Drawbacks:

Related GitHub Issues:
#4341

[mudit2812]

[sc-41597]

[codecov]

Codecov Report

Merging #4366 (55cf2b7) into master (fa58441) will increase coverage by 0.00%.
The diff coverage is 100.00%.

@@           Coverage Diff           @@
##           master    #4366   +/-   ##
=======================================
  Coverage   99.77%   99.77%           
=======================================
  Files         351      351           
  Lines       32407    32411    +4     
=======================================
+ Hits        32334    32338    +4     
  Misses         73       73           

Impacted Files	Coverage Δ
pennylane/pulse/parametrized_evolution.py	96.55% <ø> (ø)
pennylane/pulse/transmon.py	100.00% <ø> (ø)
pennylane/operation.py	96.81% <100.00%> (+<0.01%)	⬆️
pennylane/ops/qubit/hamiltonian.py	100.00% <100.00%> (ø)

[timmysilv]

being honest, I don't love seeing qml.GellMan in such base/unrelated files as operation.py and hamiltonian.py. Did you consider any other ways of getting this done? I do appreciate how concise the change is, but it seems like a circular dependency that we kinda just get away with today.

[mudit2812]

it seems like a circular dependency that we kinda just get away with today.

I agree, and I wasn't particularly happy with the change. I tried just overloading GellMann._obs_data() but both Hamiltonian and Observable _obs_data supersede it. The alternate solution is to always use new op math, which I've recommended in the PR description as well.

If we want to correctly support it in Hamiltonian, adding a special case for it would be required as there are no other observables which justify having hyperparameters stored in _obs_data. That being said, I think that saying "Don't use Hamiltonian; use qml.dot" is also a valid solution.

[timmysilv]

do we need to plan anything to have this removed in the future? I suspect it will happen naturally once we switch to arithmetic ops everywhere since that seems to be the only place this is used (Sum/Prod aren't even Observable objects!)

[timmysilv]

given the circumstances, adding 2 lines in each file ain't too bad. thanks for this!

[albi3ro]

Simple enough fix.

Would this actually work in a measurement?

[mudit2812]

Would this actually work in a measurement?

It should. The issue was that calling Hamiltonian.simplify relied on Hamiltonian.compare, which was not taking the index of GellMann into account. Since this change is contained to one exception in terms of comparison for GellMann, measurements shouldn't be affected. Moreover, support for Hamiltonian measurements is basically non-existent in default.qutrit, so it doesn't really matter that much.