GHZ quantum circuit in Qiskit.

ghz.md

A GHZ quantum circuit is a quantum computing system that includes 3 entangled qubits.

A Greenberger–Horne–Zeilinger state (GHZ state) is a certain type of entangled quantum state that involves at least three subsystems.

Demo in IBM Quantum Composer.

ghz.py

def ghz():
    """
    Create a GHZ (entangled 3-qubit system) quantum circuit.
    """
    qc = QuantumCircuit(3)
    qc.h(0)
    qc.cx(0, 1)
    qc.cx(0, 2)
    qc.measure_all()

    job = qiskit.execute(qc, qiskit.BasicAer.get_backend('qasm_simulator'), shots=1000)
    print(job.result().get_counts())

output.txt

{'000': 481, '111': 519}

I think the correct way to create a 3-qubit GHZ state would be as follows :

    qc.h(0)
    qc.cx(0, 1)
    qc.cx(1, 2)

Great comment. In fact, both configurations are valid GHZ circuits.

The difference between the two GHZ state configurations lies in the order of the CNOT gates applied and which qubits serve as control and target. However, both methods result in the same final state.

Config 1

• The first CNOT gate is applied between the first and second qubits.
• The second CNOT gate is applied between the first and third qubits.

Config 2

• The first CNOT gate is applied between the first and second qubits.
• The second CNOT gate is applied between the second and third qubits.

Both sequences of CNOT gates achieve the ghz entanglement. Thank you.