Non-Clifford Removal

[nabe98]

Implements non-Clifford removal method.

• method to convert ZXGraphState into phase-gadget form (see Prop.4.16 in [1])
• method to remove the YZ node with a single neighbor (see Lem. 4.17)
• method to merge YZ nodes with the same neighbors (see Lem. 4.18)
• repeat the above methods if these processes result in any new internal Clifford vertices (see Thm. 4.21)
• add a demo in examples/
• fix test_euler.py
• fix local complementation and pivot
  • replace measurement_action based impl. into LocalClifford based impl.
  • update test_zxgraphstate

Ref.
[1] M. Backens et al., Quantum 5, 421 (2021)

closes #8

[masato-fuk]

@nabe98 Could you add a demo in examples/ after you finish the implementation?

[nabe98]

@masato-fuk
Thanks for the review! I've fixed all the issues you pointed out.

As for the tests, there are no problems with the current ones, but in order to fully cover all the conditional branches implemented in zxgraphstate.py, three additional tests are needed. (I already have drafts for them, but the calculations still need to be revised.)
These additional tests are planned to be included in a subsequent PR.

[masa10-f]

Please check my comments

_update_node_measurement seems not to be used.

[masa10-f]

@nabe98
The ZXGraphState class has too many private methods. Can you simplify them? We have to update gflow inside the routines afterwards, so the simple implementation will help us

[nabe98]

@masato-fuk
Thanks for the review!
The main changes are as follows:

1. Removed some private methods to improve readability
2. Simplified the preprocessing logic for remove_clifford

[Copilot]

Pull Request Overview

This PR implements the "Non-Clifford Removal" feature by adding methods for converting ZXGraphState forms, removing specific Clifford nodes, and merging YZ nodes based on recent theoretical results. Key changes include:

• Refactoring local Clifford removal logic and measurement update routines in ZXGraphState.
• Updating and expanding tests related to local complementation, pivot operations, and measurement basis updates.
• Adding a new function in random_objects and a demo in examples to showcase the graph simplification process.

Reviewed Changes

Copilot reviewed 6 out of 6 changed files in this pull request and generated no comments.

Show a summary per file

File	Description
tests/test_euler.py	Updated test cases for local complementation and pivot functions.
graphix_zx/zxgraphstate.py	Refactored and extended Clifford node removal and merging logic.
graphix_zx/random_objects.py	Added new function to generate random MBQC circuits.
graphix_zx/graphstate.py	Added properties to expose inner-to-node mappings.
examples/zxgraph_simplification.py	Provided a demo example for ZX-diagram simplification.