Allow Identity() to have no wires

[Qottmann]

Allows Identity() to have no wires, similar to e.g. GlobalPhase

Also updating PauliWord.operation() to return qml.Identity() and PauliSentence.operation() to return qml.s_prod(0, qml.Identity()) in case of empty word and sentence, respectively.

As a temporary fix, we explicitly dont allow expvals of Identity(), but plan to fix this by updating hamiltonian_expand and sum_expand immediately after.

[github-actions]

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[Qottmann]

[sc-55334]

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (bfd0352) 99.69% compared to head (d95f03b) 99.68%.
Report is 1 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #5106      +/-   ##
==========================================
- Coverage   99.69%   99.68%   -0.01%     
==========================================
  Files         394      394              
  Lines       35979    35711     -268     
==========================================
- Hits        35868    35599     -269     
- Misses        111      112       +1     

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[albi3ro]

Mind adding some integration tests with "default.qubit"? We might also want to make an associated test to the lightning repo adding an integration test for support for qml.Identity().

[Qottmann]

For the moment, we don't allow measuring qml.Identity() as there are some non-trivial concerns for who should handle the case (pennylane or the device). Trying to measure qml.Identity() on default qubit raises ValueError: Cannot set an empty list of wires.. However, the lightning error is cryptic and needs to be improved: ValueError: shapes (2,) and (1,) not aligned: 2 (dim 0) != 1 (dim 0)

[trbromley]

What will the repr look like for qml.Identity()?

[Qottmann]

Together with #5116 it would be

>>> qml.Identity()
I()

as that would also be the copy-and-paste-able version

(see changes in pennylane/ops/identity.py in #5116)

[albi3ro]

This may require some follow up work, both with hamiltonian_expand, and sum_expand and unknown unknowns, but I definitely think this will help in working in working with pauli sentences.

[timmysilv]

looks great! left an optional comment, but otherwise good to go

[trbromley]

Does that include something like qml.expval(qml.PauliX(0) @ qml.Identity()) or just strictly qml.expval(qml.Identity())?

[Qottmann]

Good point, this case is in fact not handled. Though it should also not appear accidentally since Identities are stripped from PauliWords upon initialization:

>>> pw = PauliWord({0:"X", 1:"I"})
>>> pw
X(0)
>>> pw.operation()
PauliX(wires=[0])

It could occur with still if a user specifically tries to compute qml.expval(qml.PauliX(0) @ qml.Identity()) though 😬 Luckily, a fix to handle empty-wire Identities is under way already anyway.