Document a list of examples of which primitives to use in specific situations (support team request)

[beckykd]

URL, if applicable

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Describe the new content you are requesting.

we've had some users having some trouble understanding a little bit all the primitives living everywhere - document which type of situation we should use which primitives

Noiseless simulation = exact simulation without sampling noise
https://qiskit.github.io/qiskit-aer/stubs/qiskit_aer.primitives.Sampler.html#qiskit_aer.primitives.Sampler using sampler.run(…, shots=None) (old samplerV1 interface)
Shotnoise simulation = shot-based ideal simulation, only noise is the sampling
StatevectorSampler https://docs.quantum.ibm.com/api/qiskit/qiskit.primitives.StatevectorSampler
https://qiskit.github.io/qiskit-aer/stubs/qiskit_aer.primitives.Sampler.html#qiskit_aer.primitives.Sampler (old samplerV1 interface)
https://docs.quantum.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.SamplerV2 + ideal aer simulator https://docs.quantum.ibm.com/api/migration-guides/local-simulators#aersimulator
Simulated device noise
https://qiskit.github.io/qiskit-aer/stubs/qiskit_aer.primitives.Sampler.html#qiskit_aer.primitives.Sampler (old samplerV1 interface)
https://docs.quantum.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.SamplerV2 + fake backend or aer simulator with noise
Running on actual hardware
https://docs.quantum.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.SamplerV2 + real backend from QiskitRuntimeService
Not in this list :

Sampler v1 of Qiskit.primitives and qiskit-ibm-runtime : bound to be deprecated
BaseSampler V1/V2 : abstract base class for each version that define a common interface for implementing primitives
BackendSampler https://docs.quantum.ibm.com/api/qiskit/qiskit.primitives.BackendSampler ==> not that useful when running within the ibm quantum ecosystem
Questions :

Are the aer primitives going to be updated to v2? Qiskit/qiskit-aer#2078
For case 2 : which one for what?
For case 3 : which one for what?
For case 2 and 3 : several ways to do the same thing, is there a plan to have only one in the future?

If this new content request is accepted, do you want to write the content?

I will write a draft of the proposed content

Here's the formatting of @LenaPer's original message