Implement FABLE as a Template (issue #4848)

[austingmhuang]

Context: Implemented a new template for issue 4848

Description of the Change: Implements FABLE as a template to efficiently encodes the block matrix.

Benefits:

Possible Drawbacks:

Related GitHub Issues: https://github.com/PennyLaneAI/pennylane/issues/4848

[codecov[bot]]

Codecov Report

Attention: 6 lines in your changes are missing coverage. Please review.

Comparison is base (5cfdedd) 99.36% compared to head (fab4792) 99.67%. Report is 15 commits behind head on master.

Files	Patch %	Lines
pennylane/templates/subroutines/fable.py	90.62%	6 Missing :warning:

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #5107      +/-   ##
==========================================
+ Coverage   99.36%   99.67%   +0.30%     
==========================================
  Files         392      395       +3     
  Lines       35850    35774      -76     
==========================================
+ Hits        35623    35656      +33     
+ Misses        227      118     -109     

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[Jaybsoni]

Hi @austingmhuang, great work so far! There are just some failures in the CI to fix and some comments from reviewers to address and it should be in good condition to merge into PennyLane! Could please do the following:

• We have formatting tests which check that any new code committed to Pennylane is standardized under some conventions. You can automatically fix these formatting issues by pip installing the contents of requirements-dev.txt, and running the command make format in your terminal inside the pennyLane repo.
• CodeCov, is a CI tool responsible for ensuring that every line of code is tested to some extent. This ensures we aren't committing un-tested code which might introduce bugs. Could you please add test cases for the lines of code highlighted by Codecov. You can find these lines annotated under the "Files changed" heading here on GitHub.

Looking forward to having this in PennyLane, Cheers,

[codecov-commenter]

Codecov Report

All modified and coverable lines are covered by tests :white_check_mark:

Project coverage is 99.66%. Comparing base (1089bb3) to head (245a6f5). Report is 4 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #5107      +/-   ##
==========================================
- Coverage   99.66%   99.66%   -0.01%     
==========================================
  Files         402      404       +2     
  Lines       37635    37554      -81     
==========================================
- Hits        37510    37428      -82     
- Misses        125      126       +1     

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[austingmhuang]

Hi everybody,

Sorry it took so long to get things done, I had been travelling a lot the last two weeks. I've added all the relevant tests for autograd and jax as well as tests to cover all the code. The test cases are a bit limited but I could add more test cases if needed. From what I can tell the docs are building properly and is accessible as well. If there's anything else that needs to be added to the PR, please let me know.

[austingmhuang]

[sc-50347]