Quantum Teleportation Algorithm Always Ends in State $|0\rangle$

Question

I'm trying to put together a demo using the Quantum Teleportation example provided by qiskit. The quantum circuit runs as intended when it's initialized to the state $|0\rangle$, and the measured result clearly sees the qubit $q_2$ taking on the state $|q_0\rangle$.

On the other hand, initializing $q_0$ to any other state will still yield $|0\rangle$ when measuring the state of $q_2$ at the end of the circuit, even after applying the inverse of the initialization operation as in this example. Is this correct?

Here's my code for the circuit:

# entangle two qubits
def create_bell_pair(qc: QuantumCircuit, a: int, b: int) -> None:
    qc.h(a)
    qc.cx(a, b)

def alice_gates(qc: QuantumCircuit, psi: int, a: int) -> None:
    qc.cx(psi, a)
    qc.h(psi)

def measure_and_send(qc: QuantumCircuit, a: int, b: int) -> None:
    qc.measure(a,0)
    qc.measure(b,1)

def bob_gates(qc: QuantumCircuit, qubit: int, crz: ClassicalRegister, crx: ClassicalRegister):
    qc.x(qubit).c_if(crx, 1) 
    qc.z(qubit).c_if(crz, 1) 


def teleportation_circuit(init_v: list[complex] = None) -> QuantumCircuit:
    qr = QuantumRegister(3, name="q")
    crz, crx = ClassicalRegister(1, name="crz"), ClassicalRegister(1, name="crx")
    qc = QuantumCircuit(qr, crz, crx)
    
    # initialize values
    psi = random_statevector(2)
    init_v = psi if init_v is None else init_v
    init_gate = Initialize(init_v)
    init_gate.label = "init gate"
    
    qc.append(init_gate, [0])
    qc.barrier()
    
    create_bell_pair(qc, 1, 2)
    qc.barrier()
    
    # send qubits to alice & bob
    alice_gates(qc, 0, 1)
    qc.barrier()
    
    # send classical bits to bob
    measure_and_send(qc, 0, 1)
    qc.barrier()
    
    # bob receives the classical bits 
    bob_gates(qc, 2, crz, crx)
    
    # bob reverse the initialization gate
    inverse_init_gate = init_gate.gates_to_uncompute()
    qc.append(inverse_init_gate, [2])

    # place result into a classical gate
    cr_result = ClassicalRegister(1)
    qc.add_register(cr_result)
    qc.measure(2,2)

    return qc

Here's the circuit rendered as a drawing:

After running the above circuit with $q_0$ initialized to $|1\rangle$, I get the following counts:

{'0 0 0': 256, '0 0 1': 232, '0 1 0': 232, '0 1 1': 280}

The circuit above is initialized to state $|1\rangle$, but I still measure $q_2$ to be $|0\rangle$ when running it on IBM's simulators, as well as ibmq_lima.

Could someone please tell me what I'm doing wrong? Thanks!

Answer 1

This is because of these lines of code:

    # bob reverse the initialization gate
    inverse_init_gate = init_gate.gates_to_uncompute()
    qc.append(inverse_init_gate, [2])

These two lines add the gates that set $q_2$ back to $|0\rangle$. Just remove them and the output should look like:

{'1 1 1': 266, '1 0 0': 261, '1 1 0': 240, '1 0 1': 257}