Bump to qiskit 1.1

[t-imamichi]

Summary

Bump to Qiskit 1.1 and replace Backend Primitives V2 with those of Qiskit 1.1

TODO: We need to take a benchmark using the local mode just in case

Details and comments

Fixes #1631
Fixes #1690
Fixes #1702
Closes #1678

[ihincks]

In order to fully close #1690, we'll need to do things like stop using make_data_bin and _FIELDS. We could also descope that issue, open a new one, and make those changes in a different PR.

[t-imamichi]

Thank you for pointing out them, Ian. I should have made a PR carefully. I will take a look at those items and identify whether I can include them in this PR or I need a separate PR.

[coveralls]

Pull Request Test Coverage Report for Build 9192822147

Details

• 7 of 7 (100.0%) changed or added relevant lines in 1 file are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage decreased (-0.5%) to 82.212%

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Totals
Change from base Build 9184945052:	-0.5%
Covered Lines:	5990
Relevant Lines:	7286

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💛 - Coveralls

[kt474]

Thank you for pointing out them, Ian. I should have made a PR carefully. I will take a look at those items and identify whether I can include them in this PR or I need a separate PR.

Let me know if I can help with some of the work that needs to be split out into a separate PR

[ihincks]

I think it will be cleanest if we have 1) this PR, 2) a PR for DataBin access (_FIELDS -> keys() etc), 3) stop using make_data_bin (possible encoder changes).

[ihincks]

I've de-scoped #1690 and added #1702, #1703, #1704.

This PR now closes #1690 and #1702 (as well as the other two listed at the top).

@kt474 all of these can be listed in this sprint, so please feel free to take either or both of the last ones, if you'd like :)

[t-imamichi]

Thank you for reorganizing issues. I updated the description to align them. I think this PR should focus on #1702.
I will work on the other items as separate PRs.

[ihincks]

These changes look correct to me, thank you.