feature: add PauliString sums

[dorakingx]

Closes #1256.

Summary

• Adds PauliSum, a weighted container for PauliString terms.
• Supports Pauli string addition/subtraction, scalar multiplication, distributed multiplication by Pauli strings or other Pauli sums, indexing, membership checks, and commuting checks.
• Adds conversion helpers to and from weighted term lists and Braket Observable.Sum objects built from Pauli observables.
• Re-exports PauliSum from braket.quantum_information.

Validation

• uv run pytest test/unit_tests/braket/quantum_information/test_pauli_string.py -q
• uvx ruff check src/braket/quantum_information/pauli_string.py src/braket/quantum_information/__init__.py
• uvx ruff format --check src/braket/quantum_information/pauli_string.py src/braket/quantum_information/__init__.py test/unit_tests/braket/quantum_information/test_pauli_string.py

AI assistance disclosure: I used Codex as a coding assistant, then inspected the generated changes and ran the validation commands above.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 100.00%. Comparing base (a5ee47d) to head (444efa5).

Additional details and impacted files

@@            Coverage Diff             @@
##              main     #1283    +/-   ##
==========================================
  Coverage   100.00%   100.00%            
==========================================
  Files          169       169            
  Lines        10963     11109   +146     
  Branches      1412      1439    +27     
==========================================
+ Hits         10963     11109   +146     

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[dorakingx]

I pushed an update to address the Codecov failures.

Changes:

• Added tests for PauliSum edge cases and error paths that Codecov reported as missing.
• Added support for PauliString * PauliSum so multiplication distributes consistently in both directions.

Local validation:

uv run python -m coverage erase
PYTEST_ADDOPTS="" uv run python -m coverage run -m pytest -o addopts="" test/unit_tests/braket/quantum_information/test_pauli_string.py -q
uv run python -m coverage report -m src/braket/quantum_information/pauli_string.py

This now reports src/braket/quantum_information/pauli_string.py at 100% coverage locally.

I also ran:

uvx tox -e linters_check
uvx tox -e unit-tests -- test/unit_tests/braket/quantum_information/test_pauli_string.py -q

The targeted tox unit-test run passed with 65 passed and 32 xfailed.