Bloch sphere qubit visualiser
Every pure state of a single qubit is a point on the surface of a sphere. The poles are |0⟩ and |1⟩, and everything else is a superposition. Gates are rotations of the sphere, which makes them far easier to picture than matrices.
Interactive, free and runs in your browser. Part of the Quantum Mechanics simulations.
What you will see
A glass sphere with the state vector drawn as a glowing arrow. A latitude ring shows the polar angle θ and an amber arc shows the phase φ. The sphere glows brightest where a measurement is most likely to land, and gate buttons rotate the state smoothly so you can watch what each one does.
Try this
- From |0⟩, press H: the state swings down to the equator, a 50/50 superposition.
- Press Z on the equator and watch φ jump by π while the probabilities do not change.
- Press X twice and see that two half-turns bring you back.
Common misconception
A superposition is not the qubit secretly being 0 or 1. The phase φ has no effect on a single measurement in the 0/1 basis, but it changes the outcome of interference, which is why gates like H after Z give different results.
Exam-style question
A qubit is at θ = π/3, φ = 0. What is the probability of measuring |0⟩?
P(0) = cos²(θ/2) = cos²(π/6) = (√3/2)² = 0.75, so 75%. P(1) = sin²(π/6) = 25%.
Key equations
|ψ⟩ = cos(θ/2)|0⟩ + e^{iφ} sin(θ/2)|1⟩P(0) = cos²(θ/2)
Curriculum
AQA A-level physics, IB Physics HL C.3 and E.1.