Quantum Teleportation

We have seen in films about people teleport from place A to B without traversing through physical space, but will it remain as a science fiction forever? Human kind is embracing science and technology like never before and things that were considered to be a fiction centuries ago is getting materialized. Even scientists and futurists predict that human kind may become immortal in future. So, there is every possibility that humans will teleport from A location to B location, at least in centuries to come.

Scientists have discovered that quantum particles can teleport from A to B without traversing through physical space. When quantum particles can teleport, humans can also teleport since the building blocks of matter in universe is atoms. Quantum particles may be an electron / photon / ion which are building blocks of an atom.

Teleportation portrayal

Quantum Teleportation Theory

Quantum Teleportation is a quantum communication protocol where we send qubits by using classical bits. It is just a flip of super dense coding where we send two classical bits using a single qubit. The advantage of quantum teleportation lies in its ability to send quantum information arbitrarily far distances without exposing quantum states to thermal decoherence from the environment or other adverse effects.

Quantum Teleportation Protocol

Circuit for Quantum Teleportation

Let us consider Alice wants to send a qubit of state C to Bob. She takes advantage of two classical bits and an entangled qubit pair. Alice can transfer qubit and in the end Bob will have the qubit of state C. Now we can say qubit C has been teleported. Alice won’t have the qubit of the state C anymore. Quantum teleportation requires three qubits and two classical bits to teleport an unknown quantum state. You can ask me a question, why Alice can’t create a copy of qubit state C? The answer is NO, because you cannot create a copy of a qubit state (in superposition) as per no cloning theorem. We can create a copy of only the classical states. Alice and Bob should use a third party also called as Telamon to send them an entangled qubit pair. Below are the steps involved in quantum teleportation:

1. Generate a pair of entangled qubits A, B and sending A to Alice and B to Bob
2. Alice applies a CNOT gate to the qubit (A) controlled by C and then she applies a Hadamard gate to qubit C
3. Alice measures the state of qubits and stores the result in the classical bits and sends it to Bob
4. Bob who has the entangled qubit B, applies quantum gates based on the bits received.

00: Identity

01: Apply 𝑋 gate

10: Apply Z gate

11: Apply 𝑍𝑋 gate

5. Use quantum simulator to test quantum teleportation

Quantum Teleportation using Qiskit

# Import the required libraries
from qiskit import QuantumCircuit, Aer, execute
from qiskit.visualization import plot_histogram

# Create 3 qubits and 3 classical bits
qc = QuantumCircuit(3, 3)

# Assign NOT gate to qubit 0
qc.x(0)

# Create a barrier
qc.barrier()

# Create a bell state by entangling the qubits 1 and 2 by using hadamard gate and CNOT gate
qc.h(1)
qc.cx(1, 2)

# Create a barrier
qc.barrier()

# Create a plot of the circuit
qc.draw(output="mpl")

# Apply CNOT gate to the qubit 0
qc.cx(0, 1)

# Apply hadamard gate to circuit 0
qc.h(0)

# create a barrier
qc.barrier()

# Create a plot
qc.draw(output="mpl")

# Measure the qubits 0, 1
qc.measure([0, 1], [0, 1])

# Create a barrier
qc.barrier()

# Create a plot
qc.draw(output="mpl")

# Apply CNOT gate on qubits 1, 2
qc.cx(1, 2)

# Apply CNOT gate on qubits 0, 2
qc.cz(0, 2)

# Measure the second qubit
qc.measure([2], [2])

# Draw the circuit
qc.draw(output="mpl")

# create a qasm simulator
backend = Aer.get_backend("qasm_simulator")

# Execute the circuit and the get counts
result = execute(qc, backend, shots=1024).result().get_counts(qc)

# plot the histogram
plot_histogram(result)

We can see from the above histogram, there is a 100% chance of measuring qubit B in state |1> (Look at the left most bits in the x-axis). We can conclude that quantum teleportation is working fine.

Below is my Github link for quantum computing examples which contains the single qubit gates, multi qubit gates and quantum protocol like Teleportation and Super Dense Coding.

GitHub - sampathkumaran90/Quantum-Computing