Make templates valid Pytrees

[dwierichs]

Context:
Most templates are operations themselves. Therefore they should be valid PyTrees, but some are not.

Description of the Change:
This PR adapts the parameters and/or hyperparameters, as well as the methods _flatten and/or _unflatten for a number of parameters.
It adds standard_validity tests to all template test files where assert_valid is not being called on the respective template yet.
Explicit flatten/unflatten tests are removed, because they are contained in assert_valid.

Benefits:
Code quality/self-consistency and consistency of templates with PL functionality.
Test suite quality.

Possible Drawbacks:

Related GitHub Issues:
This helps us go forward with capturing of templates, because primitive_bind_call can be created in a way that is consistent with __init__ and _unflatten.

[sc-63810]

[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 (f5b805b) to head (4bf0ac5).
Report is 264 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #5698      +/-   ##
==========================================
- Coverage   99.67%   99.66%   -0.02%     
==========================================
  Files         416      416              
  Lines       38686    38742      +56     
==========================================
+ Hits        38562    38613      +51     
- Misses        124      129       +5     

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[albi3ro]

So I still think there's some issues with QDrift._flatten/ _unflatten. If we bind new parameters for the hamiltonian coefficients, then the decomposition should be appropriately updated. Right now it's not updated. But this might need to be resolved in tandem with the algorithms team.

But other than that issue, this is looking great 🎉

It does bring up the issue of templates being prone to unexpected edge cases. Since it seems like SymbolicOp wasn't actually very helpful with resolving these issues, maybe we could develop a NestedTemplate operator to help with these things. But that is definitely a task for later.

[albi3ro]

👍

Feel free to modify the seed behavior of QDrift so that it's stays None. I approve both options.

[Jaybsoni]

Great work! The updates to assert valid will make it very simple to have one test checking for everything!