Upgrade qchem to use fermionic operators

[soranjh]

Context:
The qchem module is upgraded to use the fermionic operators of the fermi module.

Description of the Change:
The function fermionic_observable is modified to optionally return a FermiSentence.
The function qubit_observable is modified to optionally accept a FermiSentence as input.

Benefits:

Possible Drawbacks:

Related GitHub Issues:

[github-actions]

Hello. You may have forgotten to update the changelog!
Please edit doc/releases/changelog-dev.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

Merging #4336 (101bd33) into master (d28df54) will increase coverage by 0.00%.
The diff coverage is 100.00%.

@@           Coverage Diff           @@
##           master    #4336   +/-   ##
=======================================
  Coverage   99.77%   99.77%           
=======================================
  Files         351      351           
  Lines       32411    32435   +24     
=======================================
+ Hits        32338    32362   +24     
  Misses         73       73           

Impacted Files	Coverage Δ
pennylane/qchem/hamiltonian.py	100.00% <100.00%> (ø)
pennylane/qchem/observable_hf.py	100.00% <100.00%> (ø)
pennylane/qchem/tapering.py	99.51% <100.00%> (-0.01%)	⬇️

[lillian542]

Thanks @soranjh! Looks like things are working and the demo notebooks run without warnings. 🚀

I left a few comments/questions, and I was wondering if a few more tests would be in order :)

[trbromley]

Thanks @soranjh! Please could you add an entry to the deprecations page, as I've realized that this upgrade effectively contains a deprecation of the old behaviour.

[Jaybsoni]

Just some small changes, looks good overall.

Since we are deprecating the default functionality, we should also make sure to test that the warnings we raise are actually being raised. This might be a bit overkill as the warning will be removed soon aswell, but shouldn't take too long

[soranjh]

Just some small changes, looks good overall.

Since we are deprecating the default functionality, we should also make sure to test that the warnings we raise are actually being raised. This might be a bit overkill as the warning will be removed soon aswell, but shouldn't take too long

Added tests for warnings.

[lillian542]

Looks good to me! Thanks @soranjh 🚀

[Jaybsoni]

Looks good to me!

[trbromley]

[SC-39865]