Optimize Dependent Chain Collection Routine in PauliFrame

[masa10-f]

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• Make sure you have tests for the new code and that test passes (run pytest)
• If applicable, add a line to the [unreleased] part of CHANGELOG.md, following keep-a-changelog.
• Format added code by ruff
• Type checking by mypy and pyright
• Make sure the checks (github actions) pass.
• Check that the docs compile without errors (run make html in ./docs/ - you may need to install dependency for sphinx docs, see docs/requirements.txt.)

Then, please fill in below:

Context (if applicable):

The PauliFrame._collect_dependent_chain method was too slow for practical FT-MBQC compilation.

Description of the change:

• Added Pauli axis cache to avoid redundant basis computations
• Implemented chain memoization cache to prevent recalculating dependent chains
• Optimized set operations for better performance in large graph states

Related issue:

NA

[codecov]

Codecov Report

❌ Patch coverage is 86.66667% with 2 lines in your changes missing coverage. Please review.
✅ Project coverage is 67.58%. Comparing base (c2a052e) to head (cff07ea).
⚠️ Report is 1 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #118      +/-   ##
==========================================
+ Coverage   66.81%   67.58%   +0.76%     
==========================================
  Files          21       21              
  Lines        1962     1968       +6     
  Branches      300      300              
==========================================
+ Hits         1311     1330      +19     
+ Misses        603      590      -13     
  Partials       48       48              

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[d1ssk]

Looks good, huge improvement!