Implement qompiler

[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.)

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Context (if applicable):

Description of the change:

Implemented

• Pauli frame, tracking applied Pauli byproduct so that feedforward can be clearly managed.
• Qompiler modules, which convert graph+flowlike into a pattern with Pauli frame

Chnaged

• I have removed feedforward instructions from M, X, and Z commands. Now, it is completely managed in Pauli frame.

Related issue:

[Copilot]

Pull Request Overview

This PR introduces a new “qompiler” module and Pauli frame tracking to compile graph-state circuits into MBQC patterns, refactors command objects, and updates documentation/configuration.

• Add qompiler.py and pauli_frame.py to initialize and track Pauli frames during pattern compilation.
• Extend Pattern to carry a PauliFrame and update qompile* routines accordingly.
• Remove classical-bit control fields from M, X, and Z commands and update their __str__ representations; update docs, examples, and project config.

Reviewed Changes

Copilot reviewed 13 out of 14 changed files in this pull request and generated no comments.

Show a summary per file

File	Description
tests/test_pattern.py	Removed existing pattern tests—new tests needed for Pattern.pauli_frame and qompiler
pyproject.toml	Added an “D” entry under examples; verify correctness
graphix_zx/qompiler.py	New qompiler implementation; compiles graph states into Pattern
graphix_zx/pauli_frame.py	New PauliFrame class to track byproduct corrections
graphix_zx/pattern.py	Extended Pattern dataclass to include pauli_frame
graphix_zx/command.py	Removed s_cbit/t_cbit fields from commands; updated __str__
graphix_zx/focus_flow.py	Reversed topo_order in place
examples/pattern_generation.py	New example showing qompile_from_flow usage
docs/source/*.rst	Added/removed references for qompiler and pauli_frame modules
docs/requirements.txt	Added matplotlib

Comments suppressed due to low confidence (5)

graphix_zx/command.py:69

• Removing s_cbit/t_cbit from M, X, and Z commands is a breaking API change; consider updating the changelog and bumping the major version to signal this change to downstream users.

    """

graphix_zx/qompiler.py:196

• This comment mentions removing local Clifford commands, but no such logic is present. Please either implement the removal or update/delete the comment to accurately reflect the current behavior.

    # NOTE: currently, we remove local Clifford commands

pyproject.toml:76

• [nitpick] The entry "D" under examples/*.py looks incomplete or missing a file extension. Verify that this matches an actual example file or remove it to avoid confusion.

  "D",

graphix_zx/focus_flow.py:107

• [nitpick] This in-place list.reverse() differs from the reversed() calls used in other modules. Consider unifying the approach for clarity and consistency across the codebase.

    topo_order.reverse()  # children first

[d1ssk]

Putting fault tolerance aside for now and focusing only on MBQC, I believe the branching between a2b_dag and a_flip (where a, b = x or z) is redundant. If we have four types of a2b_dag, then the measurement plane information is already encoded, so a single flip function should suffice, applying the flip operation to the target of any a2b_dag. Conversely, if we separate x_flip and z_flip, then the measurement plane is already being referenced when deciding which one to execute, so there's no need to have four versions of dag—two (for 2b_dag) should be enough.

[d1ssk]

As shown in the example, when the gflow is passed directly as an argument to qompile, there can be nodes whose xflow acts on themselves. However, those are not being properly excluded from the X correction DAG.

[masa10-f]

@d1ssk

1. DAGs in PauliFrame
   As we discussed today, the current implementation is insufficient for a fault-tolerant one, although it's enough for the feedforward in MBQC. I noticed that xflow and zflow with meas_flip method are sufficient in the conventional case, as in 488716b. Anyway, we should consider how to deal with decoder output in FT regime.

2. self-loop in xflow
   In 18c98ae, I allowed self-loops both in xflow and zflow because the formal definition of generalized flow does so. In PauliFrame, self-loop is not a problem because it's not a physical operation. For consistency in runtime, I will flip the Pauli frame if the measurement outcome is -1, so that self-loop correction will cancel it out.

[masa10-f]

@d1ssk Could you quickly review again? If there's no problem, please approve this PR.

[d1ssk]

Looks good!