Update qml.generator's "hamiltonian" method to follow new operator arithmetic

[lillian542]

Context:
We are generally treating "Hamiltonian" as meaning alternately qml.ops.Hamiltonian or qml.ops.LinearCombination depending on whether or not new_opmath is enabled.

The current implementation of qml.generator(op, format="hamiltonian") mostly respects that, but uses convert_to_legacy_H if the generator is a Sum, Prod or SProd even with new_opmath is enabled, breaking the convention.

Description of the Change:
We add convert_to_H, which converts any arithmetic operator to a conceptual Hamiltonian - either qml.ops.Hamiltonian or qml.ops.LinearCombination. We use the new convert_to_H function in the qml.generator method. The convert_to_legacy_H function continues to convert specifically to a legacy Hamiltonian regardless of the global setting for new_opmath.

Benefits:
Consistency, no one will ask for a generator with new_opmath enabled and get a legacy Hamiltonian.

[github-actions]

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[lillian542]

[sc-57982]

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.48%. Comparing base (c290f28) to head (68e9e14).

Additional details and impacted files

@@            Coverage Diff             @@
##           ham-tests    #5421   +/-   ##
==========================================
  Coverage      99.47%   99.48%           
==========================================
  Files            400      400           
  Lines          37143    37146    +3     
==========================================
+ Hits           36949    36954    +5     
+ Misses           194      192    -2     

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[Qottmann]

I am in favor of this change, i.e. enforcing that generators are Hamiltonian-like instances for consistency

[lillian542]

I am in favor of this change, i.e. enforcing that generators are Hamiltonian-like instances for consistency

I wouldn't say we're enforcing anything per se. This changes it specifically if you call qml.generator(op, format="hamiltonian"). Calls of qml.generator in general will still default to the prefactor format.

[PietropaoloFrisoni]

Thank you so much for this @lillian542 ! Tests seem to have issues, but it is most certainly just random fluctuations

[Qottmann]

The test failures came from ham-tests. Should be good now though 👍

[PietropaoloFrisoni]

@Qottmann Yep, I have the same issue in my PR (which is why I am still waiting to merge).