Add Pauli-flow extraction from pattern corrections

[CrewRiz]

Summary

Adds XZCorrections.to_pauli_flow() and Pattern.extract_pauli_flow() so Pauli flow can be extracted directly from pattern X/Z corrections without rerunning Pauli-flow extraction on the underlying open graph. The converter reconstructs compatible correction sets by solving the Pauli-flow parity constraints over GF(2), then validates with the existing PauliFlow.check_well_formed() checks.

Closes #432.

Tests

• uv run --with pytest --with pytest-benchmark pytest tests/test_flow_core.py::TestFlowPatternConversion::test_corrections_to_pauli_flow tests/test_pattern.py::TestPattern::test_extract_pauli_flow
• uv run --with pytest --with pytest-benchmark pytest tests/test_flow_core.py tests/test_pattern.py
• uv run --with pytest --with pytest-benchmark pytest (3162 passed, 151 skipped, 2 xfailed)
• uv run --with ruff==0.15.16 ruff check graphix/flow/core.py graphix/flow/exceptions.py graphix/pattern.py tests/test_flow_core.py tests/test_pattern.py
• uv run --with ruff==0.15.16 ruff format --check graphix/flow/core.py graphix/flow/exceptions.py graphix/pattern.py tests/test_flow_core.py tests/test_pattern.py
• uv run --with pyright --with pytest pyright graphix/flow/core.py graphix/pattern.py tests/test_flow_core.py tests/test_pattern.py (0 errors, 0 warnings)
• uv run --with mypy==2.1.0 --with pytest --with pytest-benchmark --with types-networkx==3.6.1.20260518 --with types-setuptools --with scipy-stubs mypy graphix/flow/core.py graphix/flow/exceptions.py graphix/pattern.py tests/test_flow_core.py tests/test_pattern.py

Disclosure

Travis Crew (CrewRiz) used AI-assisted coding support while preparing this PR.

[codecov]

Codecov Report

❌ Patch coverage is 98.30508% with 2 lines in your changes missing coverage. Please review.
✅ Project coverage is 89.09%. Comparing base (6edaaef) to head (6671969).

Files with missing lines	Patch %	Lines
graphix/flow/core.py	98.21%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #539      +/-   ##
==========================================
+ Coverage   88.85%   89.09%   +0.23%     
==========================================
  Files          49       49              
  Lines        7135     7253     +118     
==========================================
+ Hits         6340     6462     +122     
+ Misses        795      791       -4     

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[thierry-martinez]

Thank you for your contribution. As you may have noticed, two other pull requests (#526 and #534) already address the same issue.

The overall approach of your PR is very similar to the others: the Pauli‑flow definition yields a system of GF(2) equations, where the anachronical corrections are the unknowns, and solving this system provides the correction sets.

Could you clarify how your contribution differs from, or improves upon, the previous works? Specifically, please explain why you consider your approach to be better.

[thierry-martinez]

The CI broke because of a new Matplotlib release. It was fixed in #541, which has now been merged. Could you merge the current master into your branch?

[CrewRiz]

Addressed both outstanding items in the latest push.

• Merged current master, so the branch includes Pin matplotlib==3.10.9 for extra dev dependencies #541.
• Aligned the reconstruction with Graphix's existing GF(2) tooling: MatGF2.gauss_elimination plus solve_f2_linear_system, with no private bitmask solver.
• Kept the runtime path narrower: the unknowns are only admissible non-future X/Y nodes, the empty pattern returns the trivial flow, incompatible corrections raise FlowGenericError(NoPauliFlow), and XZCorrections.to_pauli_flow no longer calls pf.check_well_formed() in production.
• Added focused tests for the empty and incompatible-corrections paths.

On #526/#534: I agree the core method is the same GF(2) reconstruction; I am not claiming a fundamentally different algorithm. This branch's current value is that it is small, uses Graphix's existing linear-algebra machinery, and keeps the correctness evidence focused on exact X/Z corrections round trips plus the new edge cases. I am glad to adapt this branch toward whichever implementation shape maintainers prefer.

Local verification:

• ruff format --check / ruff check
• mypy graphix/flow/core.py graphix/flow/exceptions.py graphix/pattern.py tests/test_flow_core.py tests/test_pattern.py
• pyright graphix/flow/core.py graphix/flow/exceptions.py graphix/pattern.py tests/test_flow_core.py tests/test_pattern.py (0 errors, 0 warnings)
• pytest -q (3269 passed, 23 skipped, 26 xfailed)