Generalize qml.probs() to compute probabilities with respect to an eigenbasis

[rmoyard]

Context:

Previously qml.probs() was not able to accept an Hermitian observable, in order to give the probabilities in another basis than the computational one.

Description of the Change:

Now it is possible to give an optional Hermitian observable that will be used to rotate the circuit before measuring the probabilities. Then we receive the probabilities of the state in the Hermitian eigenbasis.

H = 1 / np.sqrt(2) * np.array([[1, 1], [1, -1]])

@qml.qnode(dev)
def circuit():
    qml.PauliZ(wires=0)
    qml.PauliX(wires=1)
    return qml.probs(op=qml.Hermitian(H, wires=0))

print(circuit())

Related GitHub Issues:

This is a user requested feature, closes #1468

[github-actions]

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[codecov]

Codecov Report

Merging #1692 (64d7fae) into master (06972e8) will increase coverage by 0.00%.
The diff coverage is 100.00%.

@@           Coverage Diff           @@
##           master    #1692   +/-   ##
=======================================
  Coverage   99.22%   99.22%           
=======================================
  Files         207      207           
  Lines       15579    15587    +8     
=======================================
+ Hits        15458    15466    +8     
  Misses        121      121           

Impacted Files	Coverage Δ
pennylane/measure.py	99.03% <100.00%> (+0.08%)	⬆️

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[antalszava]

[ch7663]

[albi3ro]

Why are we limiting this to just qml.Hermitian observables? Why not any kind of Observable?

Also, MeasurementProcess uses obs, but then some of the creation functions use op. Since we can only pass in observables, and only one observable, maybe we should standardize the use of ob across the file. Names do matter since the user does have to pass operation in as a keyword argument.

I think we should actually look into using multiple dispatch for these MeasurementProcess factory methods,, but that would be outside the scope of this PR.

Also, a general comment on the formatting changes to files that aren't actually affected by a given PR. Might want to revert default_qubit and _qubit_device.

[josh146]

Why are we limiting this to just qml.Hermitian observables? Why not any kind of Observable?

It might be worth asking @cvjjm for more details on the exact use case they were considering in the original issue :)

[cvjjm]

I suppose every kind of observable that define diagonalizing_gates() can be supported. Even better, a list of jointly measurable observables could probably be supported as well without too much effort.

[cvjjm]

... because then it should be possible to use the exact same pre-measurement rotation machinery that PL also uses for things like expval and var.

[albi3ro]

Just some minor wording changes, but after that, this PR seems to get the job done so I'll approve it.

[albi3ro]

Glad to have this 😃