.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "gallery/nonunitary_parity_projection.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_gallery_nonunitary_parity_projection.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_gallery_nonunitary_parity_projection.py:

Non-Unitary Parity Projection in MBQC
========================================

A 3-node star graph implements the Kraus branch

.. math::

    K_s = \frac{I + (-1)^s\, Z_0 Z_1}{2}

on the two data qubits when the central ancilla is measured in the
:math:`X` basis. Starting from :math:`|{+}{+}\rangle`, the two
branches produce Bell states:

.. math::

    s = 0 &\;\longrightarrow\; |\Phi^+\rangle = \frac{|00\rangle + |11\rangle}{\sqrt{2}} \\
    s = 1 &\;\longrightarrow\; |\Psi^+\rangle = \frac{|01\rangle + |10\rangle}{\sqrt{2}}

This demonstrates **measurement-induced entanglement**: a genuinely
non-unitary operation realised by a single MBQC measurement.

.. GENERATED FROM PYTHON SOURCE LINES 24-34

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from graphqomb.common import Axis, AxisMeasBasis, MeasBasis, Sign
    from graphqomb.graphstate import GraphState
    from graphqomb.pattern import print_pattern
    from graphqomb.qompiler import qompile
    from graphqomb.simulator import PatternSimulator, SimulatorBackend
    from graphqomb.visualizer import visualize








.. GENERATED FROM PYTHON SOURCE LINES 35-36

Build the star graph: two data qubits connected to one ancilla.

.. GENERATED FROM PYTHON SOURCE LINES 36-63

.. code-block:: Python

    nodes = ["q0", "q1", "anc"]
    edges = [("q0", "anc"), ("q1", "anc")]
    inputs = ["q0", "q1"]
    outputs = ["q0", "q1"]

    meas_bases: dict[str, MeasBasis] = {
        "anc": AxisMeasBasis(Axis.X, Sign.PLUS),
    }

    graph, node_map = GraphState.from_graph(
        nodes=nodes,
        edges=edges,
        inputs=inputs,
        outputs=outputs,
        meas_bases=meas_bases,
        coordinates={"q0": (0.0, 0.0), "q1": (2.0, 0.0), "anc": (1.0, 1.0)},
    )

    # No corrective feedforward: keep the genuine non-unitary branch.
    xflow: dict[int, set[int]] = {}

    pattern = qompile(graph, xflow)
    print("pattern depth        :", pattern.depth)
    print("pattern max space    :", pattern.max_space)
    print("pattern active volume:", pattern.active_volume)
    print_pattern(pattern)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    pattern depth        : 2
    pattern max space    : 3
    pattern active volume: 7
    N: node=2, coord=(1.0, 1.0)
    E: nodes=(0, 2)
    E: nodes=(1, 2)
    TICK
    M: node=2, plane=Plane.XY, angle=0
    TICK
    X: node=0
    Z: node=0
    X: node=1
    Z: node=1
    0 more commands truncated. Change lim argument of print_pattern() to show more




.. GENERATED FROM PYTHON SOURCE LINES 64-65

Visualize the star graph.

.. GENERATED FROM PYTHON SOURCE LINES 65-69

.. code-block:: Python

    ax = visualize(graph, show_node_labels=True)
    ax.set_title("Star graph for parity projection")
    plt.show()




.. image-sg:: /gallery/images/sphx_glr_nonunitary_parity_projection_001.png
   :alt: Star graph for parity projection
   :srcset: /gallery/images/sphx_glr_nonunitary_parity_projection_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 70-71

Reference Bell states for verification.

.. GENERATED FROM PYTHON SOURCE LINES 71-98

.. code-block:: Python

    PHI_PLUS = np.array([1, 0, 0, 1], dtype=complex) / np.sqrt(2)
    PSI_PLUS = np.array([0, 1, 1, 0], dtype=complex) / np.sqrt(2)

    anc_node = node_map["anc"]


    def run(seed: int) -> None:
        """Run the pattern once and report which Bell state appears."""
        sim = PatternSimulator(pattern, SimulatorBackend.StateVector)
        sim.simulate(rng=np.random.default_rng(seed))

        out = sim.state.state().ravel()

        overlap_phi = abs(np.vdot(PHI_PLUS, out))
        overlap_psi = abs(np.vdot(PSI_PLUS, out))

        s = int(sim.results[anc_node])
        print(f"seed={seed}, ancilla result s={s}")
        print(f"  |<Phi+|out>| = {overlap_phi:.6f}")
        print(f"  |<Psi+|out>| = {overlap_psi:.6f}")
        print()


    # These two seeds give the two different branches with NumPy's default_rng.
    run(seed=0)
    run(seed=2)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    seed=0, ancilla result s=0
      |<Phi+|out>| = 1.000000
      |<Psi+|out>| = 0.000000

    seed=2, ancilla result s=1
      |<Phi+|out>| = 0.000000
      |<Psi+|out>| = 1.000000






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.124 seconds)


.. _sphx_glr_download_gallery_nonunitary_parity_projection.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: nonunitary_parity_projection.ipynb <nonunitary_parity_projection.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: nonunitary_parity_projection.py <nonunitary_parity_projection.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: nonunitary_parity_projection.zip <nonunitary_parity_projection.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_