Legacy device API handles Prod observables

[astralcai]

Context:
The legacy device API has special handling of Tensor and Sum as observables, but Prod is not covered by that.

Description of the Change:

• Prod observables are expanded if they simplify to a Sum
• In check_validity, the operands of Prod observables are checked.

Possible Drawbacks:
simplify is called on Prod observables many times, which might be inefficient

Related Shortcut Story:
[sc-60584]

[github-actions]

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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.66%. Comparing base (b2b0c36) to head (d946dd2).
Report is 5 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #5475      +/-   ##
==========================================
- Coverage   99.67%   99.66%   -0.01%     
==========================================
  Files         404      404              
  Lines       37833    37567     -266     
==========================================
- Hits        37709    37442     -267     
- Misses        124      125       +1     

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[Qottmann]

Great work! Thanks @astralcai !

I left mostly questions for now :)

Concerning the renaming of the mock devices in the test I dont have an opinion and would refer to someone from core to judge whether changing all of them is a good idea or not.

[astralcai]

Concerning the renaming of the mock devices in the test I dont have an opinion and would refer to someone from core to judge whether changing all of them is a good idea or not.

@Qottmann The renaming was because multiple test cases were using different mock devices that were exact duplicates of one another. I removed the duplicates, and changed all these test cases to use just the one that was left.

[lillian542]

Looks good @astralcai! Left a couple of small comments about tests.

[Qottmann]

Thanks @astralcai

My questions are mostly answered and I am overall happy with the PR.
The only thing left to discuss is the simplify. Why do we need it?

[astralcai]

Thanks @astralcai

My questions are mostly answered and I am overall happy with the PR. The only thing left to discuss is the simplify. Why do we need it?

@Qottmann The purpose of this is to expand a nested Prod out into either a Prod or a Sum. For example if the observable was qml.X(0) @ qml.Y(1) @ qml.Z(2), we get a Prod with two operands, a Prod and a Z, or if the observable was qml.X(0) @ (qml.Y(1) + qml.Z(2)), we would also want to flatten out the nested structure. I know simplify does this, but do you know if there is another less expensive alternative?

[Qottmann]

Looks good to me for now, happy to move on and revisit later for a better solution with simplify 👍

Thanks @astralcai great work!

[lillian542]

What @Qottmann said 🚀