Bell-States-and-Quantum-Teleportation--Qiskit

Quantum Teleportation of All Bell States using IBM Quantum Composer & Qiskit

This repository presents a complete implementation of Quantum Teleportation for all four Bell states using both:

• 🧪 IBM Quantum Composer (GUI)
• 💻 Qiskit (Python)

The project demonstrates:

• Creation of all Bell states
• Quantum teleportation protocol with mid-circuit measurement
• Classical feed-forward correction (X and Z gates)
• Simulation results with histogram plots

This work serves as a practical demonstration of one of the most fundamental protocols in quantum information science.

---

🔹 Bell States Implemented

The four maximally entangled Bell states are:

Bell State	Name
Bell 1	Φ⁺ (Phi Plus)
Bell 2	Φ⁻ (Phi Minus)
Bell 3	Ψ⁺ (Psi Plus)
Bell 4	Ψ⁻ (Psi Minus)

Each of these states is teleported from Alice to Bob using the standard quantum teleportation protocol.

---

🔹 Project Features

✔ Creation of all four Bell states
✔ Quantum teleportation with entanglement
✔ Mid-circuit measurement and classical feed-forward correction
✔ Implementation using IBM Quantum Composer
✔ Qiskit code for each Bell state
✔ Simulation using AerSimulator
✔ Histogram plots verifying teleportation success

---

🔹 Project Structure

Quantum-Teleportation-Bell-States/

│ ├── README.md

│ ├── circuits/ │ ├── bell1_phi_plus_composer.png │ ├── bell2_phi_minus_composer.png │ ├── bell3_psi_plus_composer.png │ └── bell4_psi_minus_composer.png │

├── code/ │ ├── bell1_phi_plus.py │ ├── bell2_phi_minus.py │ ├── bell3_psi_plus.py │ └── bell4_psi_minus.py │

├── qasm/ │ ├── bell1.qasm │ ├── bell2.qasm │ ├── bell3.qasm │ └── bell4.qasm │

├── results/ │ ├── bell1_histogram.png │ ├── bell2_histogram.png │ ├── bell3_histogram.png │ └── bell4_histogram.png │

└── report/ └── Quantum_Teleportation_Report.pdf

---

🔹 Tools & Technologies Used

• IBM Quantum Composer (GUI circuit design)
• Qiskit (Python quantum programming framework)
• Qiskit AerSimulator (quantum circuit simulation)
• Matplotlib (histogram visualization)
• Python 3
• Google Collab

---

🔹 Teleportation Protocol Overview

The teleportation protocol follows these steps:

1. Prepare a Bell state between qubits q1 and q2
2. Entangle the input qubit q0 with q1
3. Measure Alice’s qubits (q0, q1)
4. Apply classical feed-forward corrections on Bob’s qubit (q2):
   • If c1 = 1 → apply X
   • If c0 = 1 → apply Z
5. Measure q2 to recover the teleported quantum state

This protocol guarantees perfect reconstruction of the original entangled state at Bob’s location.

---

🔹 How to Run the Code

1️⃣ Install Dependencies

pip install qiskit qiskit-aer matplotlib

2️⃣ Run Any Bell State Teleportation

Example for Bell State Φ⁺:

python code/bell1_phi_plus.py

This will:

a.) Run the teleportation circuit on the simulator

b.) Display the measurement histogram

c.) Save the histogram image (if enabled in code)

🔹 Expected Results

Each Bell state reproduces the expected correlations after teleportation:

Bell State	Expected Dominant Outputs
Φ⁺	000 , 111
Φ⁻	000 , 111 (with phase inversion)
Ψ⁺	010 , 101
Ψ⁻	010 , 101 (with phase inversion)

Successful teleportation is verified when these outcomes appear with approximately 50% probability each.

🔹 Screenshots & Results :

a.) Circuit diagrams from IBM Quantum Composer are available in circuits/

b.) Histogram plots from Qiskit simulations are available in results/

These confirm correct implementation of quantum teleportation for all Bell states.

🔹 Future Extensions

a.) Run teleportation on real IBM Quantum hardware

b.) Compute teleportation fidelity

c.) Extend to teleportation of arbitrary single-qubit states

d.) Add noise models and error analysis

🔹 Author

Abhishek Kumar

B.Tech Computer Science Engineering

Quantum Computing Enthusiast

🔗 GitHub: https://github.com/abhiiiisheek

🔗 LinkedIn: https://linkedin.com/in/abhishek-kumar-6a458b329

🔹 Acknowledgements

a.) IBM Quantum Platform

b.) Qiskit Documentation

c.) Nielsen & Chuang — Quantum Computation and Quantum Information

⭐ If you find this project useful, consider giving it a star!