ExperimentsExperiment 13 · Quantum information

Quantum Randomness

Pseudo-random numbers vs measurement-based randomness.

1. Learn
2. Watch
3. Interact
4. Predict
5. Run
6. Observe
7. Record
8. Answer
9. Research

① What is the problem?

Where do random numbers come from?

② How does a classical computer approach it?

Pseudo-random generators are deterministic formulas: the same seed always gives the same sequence.

③ How does the quantum approach differ?

Measuring H|0⟩ gives outcomes that are fundamentally unpredictable on real hardware.

Classical pseudo-random

Seed42

Quantum measurement-based

Each number = 4 measurements of a qubit in H|0⟩ (4 random bits).

Honesty note

These “quantum” measurements are simulated: the Born-rule sampling uses your computer's cryptographic entropy source. On a real quantum device the unpredictability comes from physics itself. Both histograms look uniform — statistics alone cannot prove where randomness came from.

④ What is happening mathematically?

Chi-square test: χ² = Σ (Oᵢ−Eᵢ)²/Eᵢ checks whether counts look uniform.

⑤ What does the simulation show?

Histograms and uniformity statistics for both sources, plus a seed-replay demonstration.

⑥ What did we learn?

Statistics can't prove randomness. Quantum RNGs matter because their unpredictability comes from physics. Note: here quantum measurements are simulated, so they rely on your computer's entropy source.

⑦ What can you experiment with?

Generate with the same seed twice. What do you notice?

📓 Record: my lab notebook

Write your observations. Notes are saved only in this browser.