Implement SimulatorBackend and Statevec

[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:

Context (if applicable):

I have implemented simulator_backend and statevec for the basic numerical calculation. Currently, simulator_backend has a minimum set of abstract methods, which will be extended in future PRs.
I added flip and conjugate methods in common.MeasBasis.

Description of the change:

Related issue:

[Copilot]

Pull Request Overview

This PR introduces a new BaseSimulatorBackend interface and a concrete StateVector simulator backend with core operations (evolution, measurement, tensoring, etc.), extends measurement bases with flip and conjugate methods, and adds corresponding tests and documentation.

• Implement BaseSimulatorBackend abstract class
• Add StateVector class with numerical routines (evolve, measure, entangle, ...)
• Extend MeasBasis with flip/conjugate and update docs/tests

Reviewed Changes

Copilot reviewed 8 out of 8 changed files in this pull request and generated 1 comment.

Show a summary per file

File	Description
tests/test_statevec.py	Add unit tests for StateVector; covers init, evolve, measure, etc.
graphix_zx/statevec.py	Implement StateVector methods and state-management logic
graphix_zx/simulator_backend.py	Introduce BaseSimulatorBackend interface
graphix_zx/matrix.py	Add is_hermitian helper
graphix_zx/common.py	Add abstract flip/conjugate to MeasBasis and implement in two subclasses
docs/source/statevec.rst	Document StateVector module
docs/source/simulator_backend.rst	Document simulator_backend module
docs/source/references.rst	Register the new modules in the reference guide

Comments suppressed due to low confidence (6)

graphix_zx/statevec.py:119

• [nitpick] The parameter num_qubits shadows the num_qubits property, which can be confusing. Consider renaming to something like count or new_qubits.

    def add_node(self, num_qubits: int) -> None:

graphix_zx/statevec.py:158

• [nitpick] The example in the docstring is unclear about the permutation convention. Clarify whether the list represents a mapping from old-to-new or new-to-old axes so users aren't confused.

        if permutation is [2, 0, 1], then

graphix_zx/statevec.py:155

• The reorder method is new but lacks any unit tests. Consider adding tests to cover common permutations and verify that qubit ordering is handled correctly.

    def reorder(self, permutation: Sequence[int]) -> None:

graphix_zx/statevec.py:130

• The entangle (and by extension add_node) methods are not exercised by the existing tests. Adding coverage for these operations would help prevent regressions.

    def entangle(self, qubits: tuple[int, int]) -> None:

graphix_zx/matrix.py:39

• It’s safer to first check that mat is square (shape[0] == shape[1]) before comparing to its conjugate transpose, to avoid unexpected broadcasting.

def is_hermitian(mat: NDArray[T]) -> bool:

graphix_zx/common.py:121

• The new flip and conjugate methods on measurement bases lack direct unit tests. Consider adding tests to validate their behavior for each basis type.

    def flip(self) -> PlannerMeasBasis:

[EarlMilktea]

Almost there!