Aura115™ Bell Pair Circuit — QCL Governed Entanglement

⚛ Circuit Diagram — H · CNOT · MEASURE

Ideal Bell state |Φ⁺⟩ — concurrence = 1.0 · fully entangled · ZZ correlation = +1

📐 Ideal State Verification

Amplitudes

State	Re(ψ)	\|ψ\|²
\|00⟩	0.7071	0.5000
\|01⟩	0	0
\|10⟩	0	0
\|11⟩	0.7071	0.5000

Verification Checks

✅ Normalized — Σ|ψ|² = 1
✅ Anti-correlated invalid states are zero (|01⟩ = |10⟩ = 0)
✅ |Φ⁺⟩ structure — P(00) = P(11) = 0.5
✅ Concurrence = 1.0 (maximally entangled)
✅ ZZ correlation = +1

📊 Ideal Probability Distribution

|00⟩

50.00%

|01⟩

0.00%

|10⟩

0.00%

|11⟩

50.00%

QCL-3 Boundary Status

Coherence lock ACTIVE — Q_L within viability kernel K

Saturn Ring audit log — Ring 0 cleared

Route: /api/cirq-bell-pair · Node serverless

🎲 Measurement Sampler — POST /api/cirq-bell-pair

Shots

🐍 Cirq Extension — Python Source

# Aura115™ Cirq Extension Example
# Path: Aura115_CURRENT/cirq/examples/aura_cirq_bell_pair.py
# Run: python -m pip install cirq && python aura_cirq_bell_pair.py

import cirq

def build_bell_pair_circuit() -> cirq.Circuit:
    q0, q1 = cirq.LineQubit.range(2)
    circuit = cirq.Circuit(
        cirq.H(q0),
        cirq.CNOT(q0, q1),
        cirq.measure(q0, q1, key="m"),
    )
    return circuit

def simulate(circuit, repetitions=1000):
    simulator = cirq.Simulator()
    result = simulator.run(circuit, repetitions=repetitions)
    return result

circuit = build_bell_pair_circuit()
result = simulate(circuit)
print(circuit)
print(result.histogram(key="m"))

API Route — Node Serverless Draft

// GET /api/cirq-bell-pair
// Returns: draft circuit, ideal verification, amplitude map

// POST /api/cirq-bell-pair  { "shots": 1024 }
// Returns: draft + verification + sampled measurement counts

targetState: "(|00> + |11>) / sqrt(2)"
steps: [
  { order: 1, gate: "H",     target:  "q0" },
  { order: 2, gate: "CNOT", control: "q0", target: "q1" },
  { order: 3, gate: "MEASURE", targets: ["q0", "q1"], key: "m" }
]

Bell Pair Circuit