Add primitives.containers.BitArray container class

[ihincks]

Summary

This PR introduces the BitArray class whose purpose is to store an array of bit values, and be the fundamental result type inside for SamplerV2 for those circuit outputs that are bit valued.

Instances of this object contain a single, contiguous block of data that represents an array of bitstrings. The last axis is over packed bits, the second last axis is over shots, and the preceding axes correspond to the shape of the pub that was executed to sample these bits.

There are helper functions for converting from/to other formats, as well as for performing bitwise operations directly on the data chunk.

Details and comments

See also Qiskit/RFCs#56

[qiskit-bot]

One or more of the the following people are requested to review this:

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

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[chriseclectic]

I think the main open question is do we use shots or samples terminology here and in SamplerV2?

[t-imamichi]

This PR looks good. I wait for the discussion of shots v.s. samples.

[ihincks]

I am in favour of using shots.

Pros:

• long standing tradition in quantum to mean individual outcomes measured from a system
• long standing convention in IBM APIs
• samples is used elsewhere in our stack to refer to randomly chosen circuits, etc

Cons:

• The thing is called Sampler and so it's catchy for it to produce samples

IMO these pros outweigh the cons and is the path of least confusion.

[ElePT]

I have to side with @ihincks here, shots is the established convention, and I believe that changing the term will be more confusing than beneficial. On top of this, "samples" is already pretty overloaded within IBM quantum projects, for example, to refer to the sub-experiments using circuit knitting techniques, or to refer to pulse samples. A quick search of samples on the qiskit repo yields 69 results in the codebase.

[chriseclectic]

I think "samples" being used heavily in the pulse layer is a good argument for sticking with "shots". I would also say we could go further and look to remove the terminology of using samples in twirling/circuit knitting and use a different name eg "randomizations" would be more descriptive for twirling

[chriseclectic]

Couple of comments

[chriseclectic]

LGTM