Quantum Teleportation in Qiskit

The Quantum Teleportation Circuit: A Quick Review

Let's start with a visual reminder of the circuit we're about to build. This diagram shows the three qubits and the sequence of operations we discussed in the previous lesson.

Our task is to construct this circuit in Qiskit.

Building the Circuit, Step-by-Step

We'll build the teleportation protocol in stages, just as we described it theoretically. A great resource for this is the Qiskit documentation itself, which provides clean, commented code. We'll use it as our guide.

The resource you just read introduced two useful Qiskit features:

• barrier(): This is a visual element in the circuit diagram that also acts as a directive to the compiler, preventing it from merging gates across the barrier. It helps keep our logical steps separate and readable.
• if_test(): This is the modern Qiskit syntax for making a quantum gate conditional on the value of a classical bit. In our case, Bob applies an X gate only if Alice's first classical bit is 1, and a Z gate only if her second classical bit is 1. This directly implements the correction table from our last lesson.

Now, let's watch a video that walks through this exact coding process. Seeing it built in real-time can help solidify your understanding.

Verifying the Teleportation

We've built the circuit, but how do we confirm it works? We can't simply measure Bob's final qubit, because that would just give us a 0 or 1, destroying the teleported state.

The standard verification method is a clever "round trip" test:

1. Prepare an initial state: Instead of starting with an unknown state $|\psi ⟩$, we'll create a specific, known state by applying a gate to a qubit that starts as $|0⟩$. To make the test general, we'll use a random unitary gate, $U$. The state to be teleported is now $|\psi ⟩=U|0⟩$.
2. Run the protocol: Execute the teleportation circuit to send $|\psi ⟩$ to Bob's qubit.
3. Apply the inverse gate: If the protocol worked, Bob's qubit is now in the state $U|0⟩$. To check this, he can apply the inverse gate, $U^{-1}$. Since quantum gates are unitary, their inverse is simply their conjugate transpose, denoted $U^{†}$. Applying it should return his qubit to the initial state: $U^{†}(U|0⟩)=|0⟩$.
4. Measure: Finally, Bob measures his qubit. If the teleportation was successful, he should measure 0 with 100% certainty.

This process provides a powerful way to confirm that the state was transmitted with high fidelity. The fact that every gate $U$ has a corresponding inverse $U^{†}$ is a direct consequence of the unitarity of quantum evolution, a concept you've noted as important.

Let's see how this verification is implemented in Qiskit.

To see this verification in action, let's return to the Qiskit video.

By combining these steps, you now have a complete Qiskit program to both implement and verify the quantum teleportation protocol.

Conclusion

In this lesson, we bridged the gap between theory and practice. You've seen how to translate the abstract steps of the quantum teleportation protocol into concrete Qiskit code.

Key Takeaways:

• Quantum and classical registers (QuantumRegister, ClassicalRegister) are used to define the resources for the circuit.
• The teleportation circuit is built by adding gates (h, cx, measure) in the same sequence as the theoretical protocol.
• The barrier() function improves readability and controls circuit compilation.
• Classically controlled operations are implemented using if_test(), allowing Bob's actions to depend on Alice's measurement outcomes.
• A robust verification method involves preparing a random state with a unitary gate $U$, running the protocol, applying the inverse gate $U^{†}$, and measuring to confirm the qubit has returned to $|0⟩$.

Preview of the Next Lesson:
We've now seen that teleportation works and how to build it. In the next lesson, we will revisit a crucial question we touched upon briefly: "Why doesn't quantum teleportation enable faster-than-light communication?". We will formalize the argument and ensure the distinction between the instantaneous collapse of the wavefunction and the speed of information transfer is perfectly clear.