ExperimentsExperiment 2 · Quantum basics

Qubits

Steer a qubit and see amplitude, probability and phase.

① What is the problem?

What exactly is a qubit, and how is it different from a bit?

② How does a classical computer approach it?

A bit is 0 or 1 — you can read it without disturbing it.

③ How does the quantum approach differ?

A qubit's state |ψ⟩ = α|0⟩ + β|1⟩ has two amplitudes. Measuring gives 0 with probability |α|² and 1 with probability |β|².

Qubit state on the Bloch sphere

(0.80, 0.00, 0.60)

Probability of 0

80.0%

Probability of 1

20.0%

θ — tilt (changes the probabilities)53°

φ — phase (hidden angle)0°

A qubit can be tilted anywhere between 0 and 1. When you look at it you always get 0 or 1 — the tilt sets how likely each one is.

A qubit is like an arrow that can point anywhere on a globe. North = 0, south = 1. Measuring snaps it to 0 or 1.

④ What is happening mathematically?

|α|² + |β|² = 1. With angles: α = cos(θ/2), β = e^{iφ} sin(θ/2). θ sets the probabilities, φ is the relative phase.

⑤ What does the simulation show?

A Bloch-sphere arrow and probability bars, computed from the simulated state as you move the sliders.

⑥ What did we learn?

A qubit is described by amplitudes, not by a hidden 0 or 1. Phase does not change the probabilities directly, but matters for interference.

⑦ What can you experiment with?

Find the θ that gives an 80% / 20% split. Then change φ — do the probabilities change?

📓 Record: my lab notebook

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