Improved handling for Identities on no wires

[albi3ro]

Context:

While we have added the ability to have qml.I() on no wires to better reflect the wire-independent nature of the identity and create operations again from a simplified form, we don't necessarily have extensive support and coverage for this new style of observable yet.

Description of the Change:

This PR extends support for qml.I() for devices.qubit measurement pathways measure and measure_with_samples. It also allows us to calculate the eigenvalues for composite ops that contain an operator on no wires. And finally, it adds support for observables with no wires to qml.pauli.group_observables.

Throughout, I assume an observable with no wires commutes with everything, as qml.I does in fact commute with everything.

Benefits:

Possible Drawbacks:

Related GitHub Issues:

[sc-61509] Fixes #5532

[Qottmann]

Awesome! Seems to fix my issues with qnodes that compute expectation values with CompositeOps that contain I() instances 👌

@qml.qnode(qml.device("default.qubit"))
def qnode():
    return qml.expval(I() + Z(0))

qnode()

[Qottmann]

Awesome, thanks so much @albi3ro

Just missing one integration test with a qnode perhaps? Otherwise happy to approve!

[Qottmann]

One minor point about straight I() not being allowed to be measured

[Qottmann]

Great PR, thanks so much for the fix @albi3ro ! 🥂

My main concern of Hamiltonians/Sums containing I() being able to be handled is solved with this 👍

Would be good to also be able to directly measure I() as well, but for the moment this will do!

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.68%. Comparing base (9151477) to head (8247bc9).
Report is 3 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #5570      +/-   ##
==========================================
- Coverage   99.69%   99.68%   -0.01%     
==========================================
  Files         410      411       +1     
  Lines       38278    38030     -248     
==========================================
- Hits        38161    37912     -249     
- Misses        117      118       +1     

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