Deprecate PrimitivesV1 reference implementations and their utils

[LeanderCS]

Fixes #12497

Summary

Deprecate

• BaseEstimatorV1
• BaseSamplerV1
• Estimator
• Sampler
• BackendEstimator
• BackendSampler
• init_circuit function
• init_observable function
• final_measurement_mapping function

Update

• BasePrimitive docstrings

Details and comments

[qiskit-bot]

Thank you for opening a new pull request.

Before your PR can be merged it will first need to pass continuous integration tests and be reviewed. Sometimes the review process can be slow, so please be patient.

While you're waiting, please feel free to review other open PRs. While only a subset of people are authorized to approve pull requests for merging, everyone is encouraged to review open pull requests. Doing reviews helps reduce the burden on the core team and helps make the project's code better for everyone.

One or more of the following people are relevant to this code:

• @Qiskit/terra-core
• @ajavadia
• @levbishop
• @t-imamichi

[coveralls]

Pull Request Test Coverage Report for Build 9662438342

Warning: This coverage report may be inaccurate.

This pull request's base commit is no longer the HEAD commit of its target branch. This means it includes changes from outside the original pull request, including, potentially, unrelated coverage changes.

• For more information on this, see Tracking coverage changes with pull request builds.
• To avoid this issue with future PRs, see these Recommended CI Configurations.
• For a quick fix, rebase this PR at GitHub. Your next report should be accurate.

Details

• 20 of 20 (100.0%) changed or added relevant lines in 9 files are covered.
• 182 unchanged lines in 8 files lost coverage.
• Overall coverage decreased (-0.02%) to 89.761%

---

Files with Coverage Reduction	New Missed Lines	%
qiskit/circuit/library/generalized_gates/permutation.py	1	92.86%
qiskit/circuit/library/standard_gates/u2.py	1	96.88%
qiskit/transpiler/passes/synthesis/unitary_synthesis.py	2	88.2%
qiskit/circuit/library/standard_gates/u3.py	3	96.91%
crates/qasm2/src/lex.rs	4	93.13%
qiskit/circuit/library/standard_gates/u1.py	5	94.85%
crates/circuit/src/circuit_instruction.rs	18	95.81%
crates/circuit/src/operations.rs	148	71.77%

Totals
Change from base Build 9616513556:	-0.02%
Covered Lines:	63797
Relevant Lines:	71074

---

💛 - Coveralls

[t-imamichi]

I asked some questions about the agreement #12497 (comment). So, let's wait for answers about other base classes and the result classes.

[t-imamichi]

I reverted SamplerResult, EstimatorResult and BasePrimitive.

[ElePT]

Thanks a lot for the changes @t-imamichi, the deprecated classes seem to follow the recent discussion outcomes. The only missing point is fixing the current lint complaint, which I believe might require modifying the primitives __init__ to deal with the BaseEstimator/BaseSampler alias import (probably re-raising the warning in the __init__? you may be able to find a better solution than me)

[t-imamichi]

I thought the revised version of BaseSampler and BaseEstimator was smarter (copied #11054). But as CI showed, it caused complicated import issues. It's not easy for me to resolve because BaseSampler and BaseEstimator are imported by qiskit.primitives.__init__.py and qiskit.primitives.bases.__init__.py. I don't think it's a good idea to update all init files.
So, I reverted the change. I check pylint locally. I hope CI passes finally.

[ElePT]

LGTM, thanks for the effort taking the PR past the finish line!