Set the stage for Opflow and QI deprecation

[ElePT]

What should we add?

Ideally, we would like to begin the process of deprecating opflow and quantum instance in the 0.24 release with this PR: #9176

In general terms, the quantum instance can be replaced by the primitives, and the opflow functionality can be replaced by a combination of quantum_info operators, primitives, and new algorithms. However, there will not be a 1-1 correspondence, and we should identify what we want to do with the missing pieces.

The idea of this epic is to gather all of the necessary tasks to set the stage for the deprecation. I have identified a group of tasks, but I know that my knowledge is not complete. As we progress through the list, it is likely that new items will be added.

I wanted to expose this process publicly to encourage feedback and suggestions, so feel free to comment any missing functionality or roadblocks you identify, and I will add them to the list.

• Add Opflow Migration Guide #9484
• Remove opflow dependency in EvolvedOperatorAnsatz #9516
• Add Quantum Instance Migration Guide #9517

Good to have:

• Migrate the commutator utilities from opflow to quantum_info #9490

Related tutorial issues (good to have):

• Add a Variational Quantum Time Evolution Tutorial qiskit-tutorials#1391
• Update Gradient Framework tutorial to use primitives qiskit-tutorials#1390
• Add a State Fidelities tutorial qiskit-tutorials#1442

Other related issues:

• Implement SparsePauliOp.assign_parameters #8966

[woodsp-ibm]

I'm sure this is known by us, but stating it here for others, this deprecation and removal needs to be coordinated with the deprecation and removal of the algorithms (or aspects thereof) that were built with and used opflow and quantum instance, as it cannot be removed before that function which still uses it as well. The new/refactored algorithms are in place, since 0.22, and the pre-existing opflow/QI logic is currently pending deprecation awaiting migration guide work before they will be switched to deprecated. Ideally this should be done for the 0.24.0 as well.

Also there are a number of issues and a couple of PRs labelled mod: opflow which eventually we will want to close off.

[ElePT]

Given that the missing items are good to have, and have been documented in their respective issues in qiskit-tutorials, this issue can be closed.