Unify Lightning Kokkos device and Lightning Qubit device under a Lightning Base device

[LuisAlfredoNu]

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!

• [X] 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.

• [X] 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.

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---

Context: Following the design of *Lightning Qubit uses the New Device API end to end, we can now migrate lightning.kokkos device to the new device API.

Description of the Change: Increase the reusability of the code by creating base classes for Lightning StateVector, Measurements, and AjointJacobian. Create a new device base class for LightningQubit and LightningKokkos.

Benefits: Improve the maintenance and readability of the Python front-end devices for LQ and LK.

Possible Drawbacks:

Related GitHub Issues:

[sc-71783]

[github-actions[bot]]

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[bot]]

Codecov Report

Attention: Patch coverage is 35.72895% with 313 lines in your changes missing coverage. Please review.

Project coverage is 61.36%. Comparing base (db98cbc) to head (efa3005). Report is 1 commits behind head on master.

Files with missing lines	Patch %	Lines
pennylane_lightning/core/_measurements_base.py	24.24%	100 Missing :warning:
pennylane_lightning/core/_adjoint_jacobian_base.py	28.86%	69 Missing :warning:
pennylane_lightning/core/lightning_newAPI_base.py	45.33%	41 Missing :warning:
pennylane_lightning/core/_state_vector_base.py	56.25%	28 Missing :warning:
...ylane_lightning/lightning_qubit/lightning_qubit.py	28.57%	20 Missing :warning:
...ane_lightning/lightning_kokkos/lightning_kokkos.py	30.76%	18 Missing :warning:
...nylane_lightning/lightning_kokkos/_state_vector.py	20.00%	12 Missing :warning:
...ane_lightning/lightning_qubit/_adjoint_jacobian.py	38.88%	11 Missing :warning:
...ne_lightning/lightning_kokkos/_adjoint_jacobian.py	36.36%	7 Missing :warning:
...nnylane_lightning/lightning_qubit/_state_vector.py	50.00%	3 Missing :warning:
... and 2 more

:exclamation: There is a different number of reports uploaded between BASE (db98cbc) and HEAD (efa3005). Click for more details.

HEAD has 45 uploads less than BASE

| Flag | BASE (db98cbc) | HEAD (efa3005) | |------|------|------| ||52|7|

Additional details and impacted files

```diff @@ Coverage Diff @@ ## master #876 +/- ## =========================================== - Coverage 96.50% 61.36% -35.14% =========================================== Files 208 24 -184 Lines 28812 2146 -26666 =========================================== - Hits 27805 1317 -26488 + Misses 1007 829 -178 ```

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[AmintorDusko]

@LuisAlfredoNu, it looks like you still have problems with the formatting check.

[LuisAlfredoNu]

@AmintorDusko All the suggestions are done or commented on. Could you make a second review, please? :smile: