Greedy Scheduling Algorithm, Feedforward Optimization, and Additional Pattern metrics

[masa10-f]

Before submitting, please check the following:

• 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:

Description of the change:

This PR significantly enhances the MBQC pattern scheduling functionality
and adds feedforward optimization capabilities.

• Greedy Scheduler Implementation: Fast heuristic schedulers as
  alternatives to CP-SAT solver (updated the previous algorithms I have implemented in Graphix)
  • greedy_minimize_time: Greedy scheduler prioritizing minimal execution time
  • greedy_minimize_space: Greedy scheduler prioritizing minimal qubit usage
  • Useful for large-scale graphs or when optimality is not critical
  • Added max_qubit_count constraint support to schedulers
• Feedforward Optimization: Pauli simplification for
  feedforward optimization
  • pauli_simplification: Removes redundant Pauli corrections (originally proposed in the measurement calculus, and I have reimplemented it in the pure feedforward layer)
• New Pattern Properties: Additional metrics for pattern evaluation
  • volume: Sum of space across all timeslices
  • max_volume: Maximum volume (max_space × depth)
  • idle_times: Idle time for each qubit
  • throughput: Number of measurements per TICK

Related issue:

[codecov]

Codecov Report

❌ Patch coverage is 67.93478% with 59 lines in your changes missing coverage. Please review.
✅ Project coverage is 75.32%. Comparing base (4c26208) to head (cebc457).

❌ Your patch check has failed because the patch coverage (67.93%) is below the target coverage (75.00%). You can increase the patch coverage or adjust the target coverage.

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #131      +/-   ##
==========================================
- Coverage   76.00%   75.32%   -0.69%     
==========================================
  Files          21       22       +1     
  Lines        2209     2391     +182     
  Branches      378      428      +50     
==========================================
+ Hits         1679     1801     +122     
- Misses        456      510      +54     
- Partials       74       80       +6     

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.