Remove runtime program, quantum instance, and opflow

[t-imamichi]

Summary

This PR removes runtime clients, which have been already removed at IBM Quantum Platform, and QuantumInstance-based algorithms.

• remove QuantumInstance-based legacy algorithms
• remove VQEClient, QAOAClient, and VQERuntimeResult
• remove Opflow
• update tutorials
• reno

Details and comments

It still uses opflow-based PauliSumOp somewhere for the compatibility. E.g., to_ising function to return PauliSumOp with the default option (option opflow=False returns SparsePauliOp). Should I remove them all as well?
→ Opflow is also removed.

[coveralls]

Pull Request Test Coverage Report for Build 6032830758

• 23 of 27 (85.19%) changed or added relevant lines in 7 files are covered.
• 7 unchanged lines in 1 file lost coverage.
• Overall coverage increased (+0.6%) to 93.022%

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Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
qiskit_optimization/algorithms/grover_optimizer.py	10	14	71.43%

Files with Coverage Reduction	New Missed Lines	%
qiskit_optimization/algorithms/optimization_algorithm.py	7	90.15%

Totals
Change from base Build 6021123767:	0.6%
Covered Lines:	4146
Relevant Lines:	4457

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💛 - Coveralls

[woodsp-ibm]

It still uses opflow-based PauliSumOp somewhere for the compatibility. E.g., to_ising function to return PauliSumOp with the default option (option opflow=False returns SparsePauliOp). Should I remove them all as well?

Yes, the intent is to cease use of deprecated function like that so supporting just SparsePauliOp is all that should be done.

In terms of other deprecated code in Opt, I did a quick search and this was all that came up for me. We should remove this too - in this case its time is up anyway (could have been removed last release)

qiskit-optimization/qiskit_optimization/applications/graph_optimization_application.py

Lines 83 to 89 in e2855f2

	@staticmethod
	@deprecate_method(
	"0.3.0", DeprecatedType.FUNCTION, "networkx.gnm_random_graph", "in NetworkX, directly"
	)
	def random_graph(num_nodes: int, num_edges: int, seed: Optional[int] = None) -> nx.Graph:
	"""
	Args:

[t-imamichi]

I removed opflow and updated tutorials and reno following Steve's feedback.

[woodsp-ibm]

This is just a comment on this. Given that a Sampler is now the only option with the removal of QI we could have defaulted the Sampler to the qiskit.primitives one if it was None in the constructor (and noted this for the sampler param there). That way the default value does not lead to an error - which seems strange. I get why it was done having to support both QI and Sampler. Since that is more of an improvement, and the GroverOptimizer was being looked at to be improved anyway, I think we can live with it like this, so as I said just a comment.

[t-imamichi]

Yes, we can make Sampler mandatory. But we need to change the argument order (need to move sampler first or second). Do you think whether we can change the argument order of GroverOptimizer.__init__?

[woodsp-ibm]

I was not talking about that much of a change. Leave it default to None and in the constructor do something like this

   if sampler is None:
      sampler = Sampler() # qiskit.primitives.Sampler

se we default it to the reference Sampler, and say we do this for the sampler param docstring. I think for the GroverOptimizer there had been some work done, not sure how far it went, to look at the issue raised some while back which was to have this use Grover rather than contain similar code. I think I would leave any more radical change until such a time as that might be done.

As I mentioned I am fine with leaving it like it is - its not that the GroverOptimizer is used much. Its not so great having an invalid default value as such but it is what it is due to this QI migration. The internal creating an instance of the default Sampler, if it were None, I thought more a simple improvement that might be done.

[t-imamichi]

Sorry. I got it. I leave it as is. I will then work on #537 after merging this PR tomorrow.

[woodsp-ibm]

Seems good to me. I left a comment above but its just that a comment - I don't see it blocking this.