Transform to split sums into single terms

[lillian542]

Context:
Some simulators can handle non-commuting observables but don't take multi-term observables.

Description of the Change:
We add a transform that splits the observables on a tape up into single-term observables. This transform relies heavily on the no_grouping functionality already implemented in split_non_commuting. However, instead of splitting the measurements across many tapes, all of the measurements are returned on a single tape.

measurements = [qml.expval(qml.X(0) + 0.2 * qml.X(1)), qml.expval(qml.X(1) + qml.Z(1))]
tape = qml.tape.QuantumScript(measurements=measurements)
tapes, processing_fn = qml.transforms.split_to_single_terms(tape)

>>> tapes[0].measurements
[expval(X(0)), expval(X(1)), expval(Z(1))]

>>> dev = qml.device("default.qubit", wires=2)
>>> results = dev.execute(tapes)
>>> results
((0.0, 0.0, 1.0),)

>>> processing_fn(results)
(0.0, 1.0)

[lillian542]

[sc-60187]

[lillian542]

[sc-60188]

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.67%. Comparing base (dbb26f2) to head (446e9eb).
Report is 1 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #5884      +/-   ##
==========================================
- Coverage   99.67%   99.67%   -0.01%     
==========================================
  Files         425      426       +1     
  Lines       40926    40660     -266     
==========================================
- Hits        40793    40526     -267     
- Misses        133      134       +1     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[albi3ro]

All comments from me are minor and non-blocking. No concerns from my side :)

[astralcai]

Looks good to me! Although with this much overlap between this and split_non_commuting, I wonder if it is worth it to unify the two at some point in the future.

[lillian542]

with this much overlap between this and split_non_commuting, I wonder if it is worth it to unify the two at some point in the future

Then we'd have to rename it, since this doesn't split things that don't commute... perhaps we could call it sum_expand 🤣

[lillian542]

@trbromley I added a note on each transform that I hope clarifies