Remove opflow classes from primitives

[mberna]

Summary

PauliSumOp class has been deprecated since 0.24.0. This PR removes PauliSumOp support from the primitives.

Details and comments

Updated the tests accordingly.

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[t-imamichi]

Opflow is being removed by #11111. It contains the same changes as this PR.

[coveralls]

Pull Request Test Coverage Report for Build 6779944663

• 0 of 0 changed or added relevant lines in 0 files are covered.
• 4 unchanged lines in 1 file lost coverage.
• Overall coverage increased (+0.02%) to 86.949%

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Files with Coverage Reduction	New Missed Lines	%
crates/qasm2/src/lex.rs	4	91.16%

Totals
Change from base Build 6774672560:	0.02%
Covered Lines:	74344
Relevant Lines:	85503

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💛 - Coveralls

[t-imamichi]

You don't need to test SparsePauliOp(SparsePauliOp(...)). The test of SparsePauliOp(...) is enough.

[ElePT]

Thanks @mberna, as @t-imamichi mentioned we were planning to do this as part of #11111, which should be ready as soon as the algorithms removal is merged. Is there any particular reason why this should be done earlier?

[mberna]

Since #11111 is still a draft and also marked as on-hold until #11086 is merged, would it be possible to merge this PR first? This will enable the removal of PauliSumOp from https://github.com/Qiskit/qiskit-ibm-runtime

[jakelishman]

Even if we merged this right now, it won't be in even a pre-release version of Qiskit until a couple of days before Summit, so I'm not certain that it'll accelerate your timelines.

#11111 is only in draft / on hold as a marker that it's not the first step in the process of safe removal of opflow. It's expected to be just about ready to go. We're working through that process, but we need to take care that it's done safely, so we don't inadvertently break seemingly unrelated code that other Summit demos might be relying on - for example, the recent release of Aer 0.13 showed that there's still some surprising dependence on some old Aqua-inherited / opflow-related code in qiskit.utils that we're also unravelling.

The full timeline of things that happen to remove opflow is this:

• qiskit-nature and qiskit-machine-learning put out new releases that stop relying on qiskit.algorithms. This code is all already written, it just needs a release cutting, and should happen within a day or two.
• qiskit.algorithms is removed from Qiskit (Remove deprecated qiskit.algorithms module #11086)
• qiskit.opflow is removed from Qiskit (Remove deprecated opflow module, QuantumInstance and related utils #11111)

Of these, the removal of qiskit.algorithms is all ready to go as soon as we can be sure that all our downstream projects are safe with the migration (while it's Nature we explicitly test against, this is a proxy that all uses can be replaced). After that, the opflow-removal PR (#11111) is pretty immediately ready to go, and that complete covers this PR.

This PR shouldn't merge before opflow is removed, because until it actually is, it would be a backwards incompatible change to remove the inputs from the primitives. The only reason we're allowed to remove the input from the primitives at all is because it wouldn't be possible to construct an opflow object; until that time, it must remain valid as an input. This PR is also currently missing several of the references to opflow objects that exist within the primitives-validation code.

[ElePT]

#11111 Has finally been merged 🎉 , so this PR is no longer necessary. Thanks for your patience :)