Entanglement and Bell States

The same H + CNOT combination that builds a Bell state in Qiskit builds one in Cirq too, entanglement is a property of the physics, not of any particular SDK.

Building and inspecting a Bell state

import cirq

q0, q1 = cirq.LineQubit.range(2)

circuit = cirq.Circuit([
    cirq.H(q0),
    cirq.CNOT(q0, q1),
])

simulator = cirq.Simulator()
result = simulator.simulate(circuit)
print(result.dirac_notation())
print(abs(result.final_state_vector) ** 2)  # ~[0.5, 0, 0, 0.5] for |00>, |01>, |10>, |11>

The probability vector has 4 entries, one per possible 2-qubit outcome in order 00, 01, 10, 11. Just like Qiskit's Bell state, only 00 and 11 have non-zero probability, 01/10 are impossible: measure either qubit and you instantly know the other's outcome.

Verifying with repeated measurement

circuit_measured = cirq.Circuit([
    cirq.H(q0),
    cirq.CNOT(q0, q1),
    cirq.measure(q0, q1, key='result'),
])

result = simulator.run(circuit_measured, repetitions=1000)
print(result.histogram(key='result'))

cirq.measure(q0, q1, key='result') measures both qubits under one shared key, and .run(circuit, repetitions=1000) (Cirq's equivalent of Qiskit's shots) executes the circuit 1000 times. result.histogram(key='result') tallies the outcomes, covered in full in the next lesson.