Investigating Quantum Teleportation With Python And Qiskit

Introduction

Quantum teleportation is a fascinating concept in the field of quantum computing. It is a process of transferring the quantum state of a qubit from one location to another without physically transporting the qubit itself. In this blog post, we will explain the basics of quantum teleportation and demonstrate how to implement it using Python and the Qiskit library.

Quantum Teleportation Protocol

The quantum teleportation protocol involves three main steps:

1. Preparation of entangled qubits
2. Bell measurement
3. Conditional state transformation

Let's break down each step:

1. Preparation of entangled qubits

Alice and Bob share a pair of qubits in an entangled state known as a Bell state. This state is represented as:

|Ψ⟩ = (1/√2)(|00⟩ + |11⟩)

2. Bell measurement

Alice performs a Bell measurement on her qubit and the qubit she wants to teleport. This measurement collapses their joint state into one of the four Bell states. Alice then sends the classical result of her measurement to Bob.

3. Conditional state transformation

Based on Alice's transmitted classical information, Bob applies a corresponding transformation to his qubit, successfully teleporting the quantum state.

Implementing Quantum Teleportation in Qiskit

To implement quantum teleportation in Qiskit, follow these steps:

Step 1: Import required libraries

import numpy as np
from qiskit import QuantumCircuit, transpile, assemble, Aer, QuantumRegister, ClassicalRegister
from qiskit.visualization import plot_histogram, plot_bloch_multivector

Step 2: Create a quantum circuit

qr = QuantumRegister(3)    # Protocol uses 3 qubits
crz = ClassicalRegister(1) # and 2 classical bits
crx = ClassicalRegister(1) # in 2 different registers
qc = QuantumCircuit(qr, crz, crx)

Step 3: Prepare entangled qubits

def create_bell_pair(qc, a, b):
    qc.h(a) # Apply a H-gate to the first qubit
    qc.cx(a, b) # Apply a CNOT gate to the qubits

create_bell_pair(qc, 1, 2)
qc.barrier()

Step 4: Perform Bell measurement

def bell_measurement(qc, a, b, c, d):
    qc.cx(a, b)
    qc.h(a)
    qc.measure(a, c)
    qc.measure(b, d)
    
bell_measurement(qc, 0, 1, 0, 1)
qc.barrier()

Step 5: Apply conditional transformations

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

Step 6: Execute and visualize the circuit

sim = Aer.get_backend('statevector_simulator')
result = sim.run(qc).result()
statevector_out = result.get_statevector()

# Visualize the output state vector
plot_bloch_multivector(statevector_out)

This implementation will perform quantum teleportation, and by visualizing the output state vector, you'll see the successful transfer of the quantum state between qubits.

Conclusion

Quantum teleportation is an essential concept in quantum computing and plays a vital role in future quantum communication systems. Through the Qiskit library, you can easily create quantum circuits simulating teleportation, deepening your understanding of this fascinating process.