🔔 HelloBell

A quantum computing "hello world" — creating a Bell state with Qiskit.

HelloBell is the quantum analogue of printing "hello, world". It builds the simplest entangled state in quantum computing — the Bell state

$$|\Phi^+\rangle = \frac{|00\rangle + |11\rangle}{\sqrt{2}}$$

using a Hadamard gate followed by a CNOT gate, then verifies entanglement via:

• Expectation values — $\langle ZZ \rangle = 1$, $\langle XX \rangle = 1$, $\langle ZI \rangle = \langle IZ \rangle = 0$
• Measurement sampling — a 50/50 split between $|00\rangle$ and $|11\rangle$

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🚀 Getting Started

# Activate the virtual environment
source .venv/bin/activate

# Run the hello world
python hello_bell.py

Expected output:

Expectation values (ideal Bell state):
  ⟨ZZ⟩ = 1.0000   (should be  1.0000)
  ⟨ZI⟩ = 0.0000   (should be  0.0000)
  ⟨IZ⟩ = 0.0000   (should be  0.0000)
  ⟨XX⟩ = 1.0000   (should be  1.0000)

Measurement counts (1024 shots):
  |00⟩:  542  (52.9%)
  |11⟩:  482  (47.1%)

📁 Project Structure

HelloBell/
├── hello_bell.py      # Bell-state circuit + verification
├── .venv/             # Python virtual environment
├── .gitignore
└── README.md

🔬 What's Happening?

Gate	Qubit 0	Qubit 1	Effect
H	─┤H├─	─────	Creates superposition: $
CX	─■───	─┤X├─	CNOT flips q₁ when q₀ = $

The result is a maximally entangled two-qubit state — measuring one qubit instantly tells you the outcome of the other.

📦 Requirements

• Python 3.12+
• Qiskit 2.x (installed in .venv/)

📄 License

This project is for educational purposes. Feel free to use, share, and modify.