ExperimentsExperiment 3 · Quantum basics

Superposition

Apply a Hadamard, then measure — or apply it twice and see interference.

① What is the problem?

What does it mean for a qubit to be in a superposition?

② How does a classical computer approach it?

A classical coin mid-air is still secretly heads or tails — we just don't know yet.

③ How does the quantum approach differ?

After H, the qubit is (|0⟩+|1⟩)/√2. Applying H again returns exactly |0⟩ — the |1⟩ parts cancel. A secretly-decided coin can't do that.

🔮 Make a prediction

Start in |0⟩ and apply H twice. What is P(0)?

Tip: select any gate to learn what it does.

|ψ⟩ = 1.000|0⟩ + 0.000|1⟩

P(0)

100.0%

P(1)

0.0%

Sampled so far: 0 × 0, 1 × 0 (fresh copies of |ψ⟩ each time)

The Hadamard gate puts the qubit into an equal mix of 0 and 1. Measuring gives 0 or 1 at random.

④ What is happening mathematically?

H|0⟩ = (|0⟩+|1⟩)/√2, H|1⟩ = (|0⟩−|1⟩)/√2, and H·H = I.

⑤ What does the simulation show?

Amplitude bars (with sign) and probability bars from the simulated state, and real sampled measurements.

⑥ What did we learn?

Superposition is not ignorance: amplitudes can cancel (interfere). That is the resource algorithms like Grover use.

⑦ What can you experiment with?

Predict: after H, H what is P(0)? Then try it.

📓 Record: my lab notebook

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