Support differentiable coefficients for observables

[albi3ro]

Context:

With legacy operator arithmetic, we supported trainable coefficients using the hadamard_grad transform. This doesn't really work anymore with generic operator arithmetic.

Description of the Change:

Uses the split_to_single_terms transform in gradient preprocessing if any of the observables have trainable coefficients.

In order to get this to pass tests, various bugs in split_non_commuting needed fixing.

Benefits:

Possible Drawbacks:

Related GitHub Issues:

[sc-71490]

[github-actions]

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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.60%. Comparing base (2147813) to head (9f0a1a1).
Report is 3 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #6598      +/-   ##
==========================================
- Coverage   99.60%   99.60%   -0.01%     
==========================================
  Files         476      476              
  Lines       45237    45215      -22     
==========================================
- Hits        45060    45035      -25     
- Misses        177      180       +3     

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[astralcai]

With legacy operator arithmetic, we supported trainable coefficients using the hadamard_grad transform. This doesn't really work anymore with generic operator arithmetic.

Should we deprecate/remove hamiltonian_grad?

[albi3ro]

With legacy operator arithmetic, we supported trainable coefficients using the hadamard_grad transform. This doesn't really work anymore with generic operator arithmetic.

Should we deprecate/remove hamiltonian_grad?

Potentially worth considering now.