Project 2: Spooky Action - Creating an Entangled Bell State

Build a circuit that creates a Bell pair and verifies correlation.

Project Overview

Attribute Value
Difficulty Level 1: Beginner
Time Estimate Weekend
Main Language Python
Alternative Languages Q#, Java
Knowledge Area Entanglement
Tools Qiskit or Cirq
Main Book “Quantum Computation and Quantum Information” by Nielsen & Chuang

What you’ll build: A two-qubit circuit that generates a Bell state and measures perfect correlation.

Why it teaches quantum: Entanglement is the non-classical feature that powers quantum algorithms.

Core challenges you’ll face:

  • Building the entangling gate sequence
  • Measuring correlations
  • Interpreting joint probabilities

Real World Outcome

You will measure outcomes where 00 and 11 dominate, with almost no 01 or 10.

Example Output:

$ python bell.py --shots 1000
Counts: 00=510, 11=490

Verification steps:

  • Confirm correlated outcomes
  • Increase shots to see stability

The Core Question You’re Answering

“How can two qubits act as one system?”

This is the heart of entanglement.

Concepts You Must Understand First

Stop and research these before coding:

  1. Entangled states
    • Why can’t a Bell state be written as a product of single-qubit states?
    • Book Reference: Nielsen & Chuang, Ch. 2
  2. CNOT gate
    • How does CNOT create entanglement?
    • Book Reference: Nielsen & Chuang, Ch. 4
  3. Measurement correlations
    • Why do measurements match even when qubits are apart?
    • Book Reference: Nielsen & Chuang, Ch. 2

Questions to Guide Your Design

  1. Measurement basis
    • Will you measure in the Z basis only?
    • What happens if you measure in X basis?
  2. Visualization
    • How will you show correlation (histogram, table)?
    • Will you compute correlation coefficients?

Thinking Exercise

Bell Circuit

List the gate sequence to create Phi+> from 00>.

Questions while working:

  • Which qubit is the control for CNOT?
  • What outcomes are expected?

The Interview Questions They’ll Ask

Prepare to answer these:

  1. “What is entanglement?”
  2. “How do you create a Bell state?”
  3. “Why do Bell states show perfect correlation?”
  4. “What is CNOT used for?”
  5. “How do you verify entanglement experimentally?”

Hints in Layers

Hint 1: Starting Point Apply Hadamard to qubit 0.

Hint 2: Next Level Apply CNOT with qubit 0 as control.

Hint 3: Technical Details Measure both qubits in the same basis.

Hint 4: Tools/Debugging Plot measurement histograms and compute correlation.

Books That Will Help

Topic Book Chapter
Entanglement Nielsen & Chuang Ch. 2
CNOT Nielsen & Chuang Ch. 4
Correlations Nielsen & Chuang Ch. 2

Implementation Hints

  • Use a simulator for consistent results.
  • Increase shots for stable correlations.
  • Keep circuits minimal to avoid confusion.

Learning Milestones

  1. First milestone: You can build a Bell circuit.
  2. Second milestone: You can measure correlations correctly.
  3. Final milestone: You can explain why entanglement is non-classical.