Add C++ decomposition with scipy_openblas32

[multiphaseCFD]

Before submitting

Please complete the following checklist when submitting a PR:

• All new features must include a unit test.
  If you've fixed a bug or added code that should be tested, add a test to the
  tests directory!

• All new functions and code must be clearly commented and documented.
  If you do make documentation changes, make sure that the docs build and
  render correctly by running make docs.

• Ensure that the test suite passes, by running make test.

• Add a new entry to the .github/CHANGELOG.md file, summarizing the
  change, and including a link back to the PR.

• Ensure that code is properly formatted by running make format.

When all the above are checked, delete everything above the dashed
line and fill in the pull request template.

---

Context:

[sc-78187] & [sc-53754]

The blas/lapack support is a long standing issue for lightning. The main challenge is the wheels building for the windows platform, which does not support a fortran compiler natively. Recently, the scipy team release the standalone scipy-openblas32 wheel for linux, windows and macos platform. This could solve the win support issue.

There are a few technical discussions on how to add the scipy-openblas32 support to lightning:

• Dynamic loading vs static linking? Dynamic loading was chosen and the relative path to the libscipy_openblas is added to the runpath of the shared lib object of installations from wheel. In this case, scipy-openblas32 is required to be installed in the same site-packages dir. However, for the direct C++ usage as well as pip editable install, the absolute path to libscipy_openblas is still needed to ensure the libscipy_openblas lib can be found and loaded.
• As a result, scipy-openblas32 is a dependency of lightning.
• This implementation does not support conda-forge.

This PR also brings a few other changes:

• BLASLib loading is handled by a singleton class BLASLibLoaderManager, instead of the compute_diagonalizing_gates API.
• The openblas support is tested against macos, linux and windows for the C++ tests on CIs and integration with catalyst locally.
• An additional cmake option: PY_INSTALL is added to identify if the pip installation is editable or not. This PY_INSTALL is ON if not self.editable_mode.

Description of the Change:

Benefits:

Possible Drawbacks:

Related GitHub Issues:

[github-actions]

Hello. You may have forgotten to update the changelog!
Please edit .github/CHANGELOG.md with:

• A one-to-two sentence description of the change. You may include a small working example for new features.
• A link back to this PR.
• Your name (or GitHub username) in the contributors section.

[codecov]

Codecov Report

Attention: Patch coverage is 95.00000% with 2 lines in your changes missing coverage. Please review.

Project coverage is 92.20%. Comparing base (f9e8f62) to head (4342619).
Report is 1 commits behind head on master.

Files with missing lines	Patch %	Lines
..._lightning/core/src/utils/BLASLibLoaderManager.hpp	88.88%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #995      +/-   ##
==========================================
- Coverage   94.44%   92.20%   -2.24%     
==========================================
  Files         229      178      -51     
  Lines       38841    27390   -11451     
==========================================
- Hits        36682    25254   -11428     
+ Misses       2159     2136      -23     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[josephleekl]

awesome work @multiphaseCFD ! Just added some comments/questions, happy to look over it again and approve once answered!

[josephleekl]

also have you updated the changelog?

[LuisAlfredoNu]

Thank you @multiphaseCFD
Only a couple of comments 👍

[maliasadi]

LGTM! 🏆 Happy to approve after addressing the last round of concerns and suggestions.

[maliasadi]

Thanks @multiphaseCFD! 🎉

[josephleekl]

LGTM, thanks @multiphaseCFD for this addition!