Add some utilities for T-rex error mitigation

[ddddddanni]

This PR introduces the initial building blocks and helper functions required to support T-REX error mitigation in
pauli expectation calculation.

The change includes:
Implement _get_trex_twirled_basis_gate to fetch the appropriate rotation gates (Rx, Ry, X, I) based on the target Pauli basis and flip state.
Implement _generate_random_boolean_choices to generate randomized 2D boolean arrays for twirling operations.
Implement _build_trex_twirled_pauli_circuits to append the appropriate basis twirling gates and joint measurements to a base circuit.

[obriente]

Thanks for submitting! The code seems ok, but I'm worried about some forward-compatibility issues, as well as making the workflow as easy as possible to combine with other error mitigation techniques. Would defer to other people on the team whether this is a significant issue or something that we can deal with later.

[mhucka]

@obriente Would you be willing to act as reviewer for this PR? I mean, you basically have been already :-). Can we assign you to this PR?

[obriente]

All of my comments were addressed, LGTM

[mhucka]

Spotted some possible minor issues.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 99.60%. Comparing base (74abd87) to head (76fe571).
⚠️ Report is 22 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff            @@
##             main    #8095    +/-   ##
========================================
  Coverage   99.60%   99.60%            
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  Files        1118     1118            
  Lines      100951   101213   +262     
========================================
+ Hits       100551   100812   +261     
- Misses        400      401     +1     

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[mhucka]

@ddddddanni Thank you for working on this!

I hate to be a nag, but could you click on the "Resolve conversation" button for those review items that are, in fact, resolved? I think they all are, but can't be 100% sure myself.

[ddddddanni]

@ddddddanni Thank you for working on this!

I hate to be a nag, but could you click on the "Resolve conversation" button for those review items that are, in fact, resolved? I think they all are, but can't be 100% sure myself.

Sure! I think this is resolved since Tom has approved the PR.

[mhucka]

Thank you for working on this, and I'm sorry to make more requests …

[mhucka]

@ddddddanni Thank you for all the hard work on this and addressing my comments! LGTM.