From f23a5593818575e04dc844e5aecf1ff378b1fbd3 Mon Sep 17 00:00:00 2001
From: Masato Fukushima <masa1063fuk@gmail.com>
Date: Sun, 12 Apr 2026 16:07:14 +0900
Subject: [PATCH] Add non-unitary parity projection example

Demonstrate measurement-induced entanglement via a 3-node star graph
that implements the Kraus branch K_s = (I + (-1)^s Z0 Z1) / 2.
The ancilla X-measurement produces Bell states from |++> input,
showing genuinely non-unitary MBQC operations with the existing
statevector simulator.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
---
 CHANGELOG.md                             |  4 +
 examples/nonunitary_parity_projection.py | 98 ++++++++++++++++++++++++
 2 files changed, 102 insertions(+)
 create mode 100644 examples/nonunitary_parity_projection.py

diff --git a/CHANGELOG.md b/CHANGELOG.md
index 8309786f..7504c8cf 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -7,6 +7,10 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ## [Unreleased]
 
+### Added
+
+- **Non-Unitary Parity Projection Example**: Added `examples/nonunitary_parity_projection.py` demonstrating measurement-induced entanglement via a 3-node star graph parity projector
+
 ## [0.3.0] - 2026-04-08
 
 ### Added
diff --git a/examples/nonunitary_parity_projection.py b/examples/nonunitary_parity_projection.py
new file mode 100644
index 00000000..0708bff2
--- /dev/null
+++ b/examples/nonunitary_parity_projection.py
@@ -0,0 +1,98 @@
+r"""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.
+"""
+
+# %%
+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
+
+# %%
+# Build the star graph: two data qubits connected to one ancilla.
+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)
+
+# %%
+# Visualize the star graph.
+ax = visualize(graph, show_node_labels=True)
+ax.set_title("Star graph for parity projection")
+plt.show()
+
+# %%
+# Reference Bell states for verification.
+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)
+
+# %%