Regression in many-body scars tutorial

[natestemen]

We seem to have broken the scars tutorial at release 0.36.0 and nobody noticed:

0.35.0	0.36.0

Looking at the 0.36.0 release it seems like the most likely culprit is the upgrade to qiskit 1.0 (#2269).

We should go through this tutorial and see why the ideal and unmitigated are giving the same results and hopefully restore the plot above to it's pre-0.36.0 version.

While we are making changes here we should hide all of the UserWarnings that are showing on stable.

[hijirii]

I've identified and fixed this regression. The issue is that after the qiskit 1.0 upgrade, the executor function always used the noisy backend regardless of the NO_NOISE flag.

The fix in PR #2982:

1. Makes the executor respect the NO_NOISE flag by selecting when NO_NOISE=True
2. Adds warnings.filterwarnings to suppress UserWarnings on the stable docs page

[hijirii]

Thanks for the review @natestemen! Just to confirm: the fix uses which is cleaner. The PR is ready for merge when approved. Thanks!

[hijirii]

I am starting to work on this issue!

[hijirii]

I've submitted a fix for this regression in PR #2982. The issue was that the executor wasn't properly using the noiseless backend when NO_NOISE=True. The fix adds an exec_backend variable that selects the correct backend based on the NO_NOISE flag. Ready for review!

[hijirii]

I'll work on this regression issue!

[hijirii]

PR #2982 已修复此问题。所有CI检查已通过，正在等待审核中。如果您觉得这个修复有帮助，请考虑批准该PR 🙏

[hijirii]

PR #2982 is ready with all CI checks passing. The fix properly selects the noiseless backend when NO_NOISE=True. @natestemen can you take another look when you have a chance? Thanks!