Return qchem Hamiltonians with real dtype coeffs

[soranjh]

Context:
The qchem Hamiltonians built with the new qml.jordan_wigner function have complex coefficients with zero imaginary components. This PR removes the imaginary part if it is less than a pre-defined tolerance.

Description of the Change:
The qml.jordan_wigner function is modified to optionally remove the imaginary components of the computed qubit operator.

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.
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[soranjh]

[sc-44462]

[codecov]

Codecov Report

All modified lines are covered by tests ✅

Comparison is base (ea7e1d4) 99.63% compared to head (3588acd) 99.63%.

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #4639   +/-   ##
=======================================
  Coverage   99.63%   99.63%           
=======================================
  Files         376      376           
  Lines       33672    33678    +6     
=======================================
+ Hits        33548    33554    +6     
  Misses        124      124           

Files	Coverage Δ
pennylane/fermi/conversion.py	100.00% <100.00%> (ø)
pennylane/qchem/dipole.py	100.00% <100.00%> (ø)
pennylane/qchem/observable_hf.py	100.00% <100.00%> (ø)

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[lillian542]

Right now tol=0 behaves the same as tol=None; I would expect tol=0 to remove complex terms that were exactly 0, so I think this should be updated.

I guess it's being indirectly tested through the observable_hf test file, but could we add a small test explicitly testing just this for tol of None, 0, and something small? Something that would catch the current behaviour where 0 is treated as None.

Also needs a changelog entry :)

[timmysilv]

I second Lillian's sentiment - keeping the default to None but changing if tol to if tol is not None should meet the requirements you're describing (preferring opt-in over opt-out to this behaviour), and that would work for me

[soranjh]

Right now tol=0 behaves the same as tol=None; I would expect tol=0 to remove complex terms that were exactly 0, so I think this should be updated.

I guess it's being indirectly tested through the observable_hf test file, but could we add a small test explicitly testing just this for tol of None, 0, and something small? Something that would catch the current behaviour where 0 is treated as None.

Also needs a changelog entry :)

Added the test and the changelog.

[timmysilv]

🎉

[lillian542]

🚀