Update QuantumScriptSerializer.serialize_observables to better handle new operator arithmetic

[mudit2812]

Context:
This PR is implementing some technical debt that was left behind after #649 was merged.

Description of the Change:

• Update order of operations when serializing operators. Pauli reps are now always prioritized unless we're serializing a Hamiltonian. While Hamiltonian now does have a pauli rep, it behaves lazily. I also assumed that there might be pipelines in lightning that take advantage of Hamiltonian.grouping_indices. If this is not a major concern, I can update to also use the pauli rep with Hamiltonian.
  • One issue I ran into is figuring out how to serialize Prod when the operands might have overlapping wires. In the case of Paulis, this is handled automatically by the pauli rep. However, in other cases, we end up in an infinite recursion as simplifying does not lead to any changes to the operands. If anyone has an idea about this, I would love to hear it. The current solutions I have in mind are to either raise an error, or fallback to treating the observable as a Hermitian (although the matrix might not actually be hermitian).
• Unpinned cmake since there is now a release with the bug fix that was causing trouble (See here for context).

Benefits:
More optimized pipeline for serialization with new operator arithmetic.

Possible Drawbacks:

Related GitHub Issues:

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 98.70%. Comparing base (404bd2d) to head (8f770d9).
Report is 1 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #670      +/-   ##
==========================================
+ Coverage   97.09%   98.70%   +1.60%     
==========================================
  Files         149      173      +24     
  Lines       19387    24399    +5012     
==========================================
+ Hits        18824    24082    +5258     
+ Misses        563      317     -246     

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[mudit2812]

[sc-59698]

[maliasadi]

Nice work @mudit2812!

[mudit2812]

I'm not sure what's going on with the codecov warnings. I added tests specifically targeting the "uncovered" lines and I know that those lines are being covered locally. My guess is that the warnings are artifacts of the continuously updated coverage that happens due to the way that coverage data is uploaded to codecov.

The checks window also says that 100% patch coverage has been achieved.

[vincentmr]

I'm not sure what's going on with the codecov warnings. I added tests specifically targeting the "uncovered" lines and I know that those lines are being covered locally. My guess is that the warnings are artifacts of the continuously updated coverage that happens due to the way that coverage data is uploaded to codecov.

The checks window also says that 100% patch coverage has been achieved.

I have encountered that in the past. I would say feel free to ignore it.

[vincentmr]

Looks good to me, thanks @mudit2812 !

[AmintorDusko]

Nice work, @mudit2812 !

[maliasadi]

🪂