Single-Qubit State Preparation

Prepare a qubit in any pure state and watch it live on the Bloch sphere, with the axes and the six reference states clearly marked.

State preparation

θ (polar angle)

φ (relative phase)

Amplitudes

|ψ⟩ = 1|0⟩ + 0|1⟩

P(0) = 1.000 · P(1) = 0.000

Note on global phase. Only θ and φ affect where the state sits on the sphere. An overall phase in front of |ψ⟩ moves nothing here — it's unobservable, by design.

Bloch sphere drag to rotate view · scroll to zoom

x = 0.000 y = 0.000 z = 1.000

x — |+⟩ ↔ |−⟩ y — |i⟩ ↔ |−i⟩ z — |0⟩ ↔ |1⟩

Copy failed

Why this fails. Cloning would need one operation that works for every possible input state at once. Run the linearity of quantum evolution through two different states and the results contradict each other — so no such operation exists for an unknown state. This is the no-cloning theorem, and it's not a hardware limitation. It's built into the math.