Clarification in is_hermitian property

[PietropaoloFrisoni]

Context: The docstring of the is_hermitian function was not entirely clear. Specifically, there are some edge cases where this property returns the wrong result. Now this limitation is documented.

Description of the Change: As above.

Benefits: More clarity.

Possible Drawbacks: None that I can think of.

Related GitHub Issues: None.

[sc-95920]

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 99.68%. Comparing base (bd07c01) to head (11ecd35).
⚠️ Report is 419 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #7946      +/-   ##
==========================================
- Coverage   99.68%   99.68%   -0.01%     
==========================================
  Files         542      542              
  Lines       55622    55622              
==========================================
- Hits        55449    55448       -1     
- Misses        173      174       +1     

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[isaacdevlugt]

I know there was a discussion about this on slack, but is this behaviour not fixable? It's odd that we have a user-facing operator property that we know gives incorrect results.

[PietropaoloFrisoni]

@isaacdevlugt Yeah I agree that this is odd. At least now this is documented : )

It seems to me that the only 'secure' way would be to compare the matrix of the operator with the adjoint matrix (which is what qml.is_hermitian does). Maybe it makes sense to schedule this property for deprecation?

[albi3ro]

I know there was a discussion about this on slack, but is this behaviour not fixable? It's odd that we have a user-facing operator property that we know gives incorrect results.

If it was 100% accurate, it would be too expensive to be useful, since the only real way to be accurate is by using the full matrix. But potentially we could just remove it entirely.

[isaacdevlugt]

This PR is fine to merge, but I would strongly consider deprecating and removing op.is_hermitian because of this behaviour 😅