Support wire labels in qinfo transforms

[eddddddy]

Context:
Taken from #4318:

Other functions are affected by this discrepancy between wire indices and wire labels:

• qinfo.fidelity, qinfo.reduced_dm, qinfo.vn_entropy, qinfo.mutual_info, qinfo.relative_entropy raise an error when passed wire labels
• qinfo.purity uses wrong wires. It is not possible to compute the purity w.r.t, say, a string-labeled qubit. Importantly, no error is raised in this case.

Users may expect the following code to work:

dev = qml.device("default.qubit", wires=[0, "a", 12])

@qml.qnode(dev)
def circuit0(x):
    qml.RX(x, 0)
    return qml.state()

@qml.qnode(dev)
def circuit1(x):
    qml.RX(x, "a")
    return qml.state()

x = np.array(1.3)
qml.qinfo.fidelity(circuit0, circuit1, [0], ["a"])((x,), (x,)) # raises an error
qml.qinfo.reduced_dm(circuit1, ["a"])((x,), (x,)) # raises an error
qml.qinfo.vn_entropy(circuit, wires=["a"])(x) # raises an error
qml.qinfo.mutual_info(circuit0, [0], [12])(x) # raises an error, already because of the _existence_ of a custom label
qml.qinfo.relative_entropy(circuit0, circuit1, [0], ["a"])((x,), (x,)) # raises an error

Likewise, users may try to compute a purity w.r.t a custom-labeled qubit:

dev = qml.device("default.mixed", wires=[0, "a", 12])

@qml.qnode(dev)
def circuit(x):
    qml.DepolarizingChannel(x, "a")
    return qml.state()

x = np.array(0.2)

qml.qinfo.purity(circuit, wires=["a"])(x) # returns 1, which is incorrect, interpreting `wires` as labels
qml.qinfo.purity(circuit, wires=[1])(x) # returns 1, which is incorrect, interpreting `wires` as indices into the labels

Description of the Change:
Support custom wire labels in all qinfo transforms.

Related GitHub Issues:
Fixes #4318

[github-actions]

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[codecov]

Codecov Report

Merging #4331 (360ec4d) into master (10cae8d) will increase coverage by 0.00%.
The diff coverage is 100.00%.

@@           Coverage Diff           @@
##           master    #4331   +/-   ##
=======================================
  Coverage   99.79%   99.79%           
=======================================
  Files         351      351           
  Lines       32087    32096    +9     
=======================================
+ Hits        32020    32029    +9     
  Misses         67       67           

Impacted Files	Coverage Δ
pennylane/qinfo/transforms.py	100.00% <100.00%> (ø)

[dwierichs]

Thanks for the super quick fix @eddddddy 💯
Thorough test additions 😎
I only have two very minor suggestions.

[mudit2812]

I think the PR looks good. But two things concern me w.r.t the new device API:

• The new device doesn't have wires, so qnode.device.wires can't be used for wire mapping.
• The new device also does not have a C_DTYPE or R_DTYPE attribute, which I'm seeing being used in the qinfo transforms.

Tagging @albi3ro for thoughts.

Once these are addressed, I'm happy to approve. Everything else looked good :)

[timmysilv]

I think the qinfo module (and various other ones) are still incompatible with the new device API, and it'll be quite a bit of work to get things caught up unfortunately. I'd prefer that this PR isn't blocked by that, since it'll need to be handled at a larger scale anyway

[eddddddy]

I agree with @timmysilv. There are still some things to work out for compatibility with the new device API and I'd rather we do those in a separate PR that includes everything else.

[albi3ro]

[sc-41189]

[mudit2812]

🚀

[albi3ro]

As others have pointed out, these transforms will cause issues with the new device API. I've created a new shortcut ticket to resolve these issues, the most tricky of which will be the wire order for a state vector with non-standard labels.

But that shouldn't block this bugfix right now, as long as the other open questions are resolved before the next release.

Thanks for fixing this up :)