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For Students · Bloch Sphere

Bloch Sphere for a wavefunction collapse

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a wavefunction collapse live below — adjust the inputs and watch it respond, right in your browser.

Bloch SphereLive

the state of a qubit

Controls

Presets

Polar angle θ (°)

Azimuth φ (°)

Every pure state of a single qubit is a point on the Bloch sphere. The north pole is |0⟩, the south |1⟩, and the equator holds equal superpositions differing only in phase φ. Quantum gates rotate this arrow — the geometric picture behind all single-qubit quantum computing.

▶ Run in Python

Data Inspector

P(|0⟩)0.750

P(|1⟩)0.250

Amplitude α0.866

Amplitude β0.50∠45°

Governing equation

∣ ψ ⟩ = cos \frac{θ}{2} ∣0 ⟩ + e^{i ϕ} sin \frac{θ}{2} ∣1 ⟩ = 0.87 ∣0 ⟩ + e^{i (4 5^{\circ})} 0.50 ∣1 ⟩

Reading this result: Polar angle θ sets the measurement odds: P(|0⟩)=cos²(θ/2)=0.75, so tilting toward a pole biases the qubit while φ only twists its phase.

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Frequently asked questions

Is this good for students?: Yes — this version of "Bloch Sphere for a wavefunction collapse" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.