Bloch Sphere & Quantum Gates

Interactive qubit state visualization

Every qubit state maps to a point on the Bloch sphere. Apply Pauli gates (X, Y, Z), the Hadamard gate, phase gates (S, T), and arbitrary rotations. Watch the state vector move on the sphere and track the amplitudes, probabilities, and Bloch coordinates in real time.

Preset States

Standard Gates

Rotation Angle: 0.25pi

State Vector

α = 1.000|α|² = 1.0000

β = 0|β|² = 0.0000

Bloch Coordinates

x=0.000 y=0.000 z=1.000

θ=0.000 rad φ=0.000 rad

|\psi\rangle = \cos\tfrac{\theta}{2}\,|0\rangle + e^{i\varphi}\sin\tfrac{\theta}{2}\,|1\rangle

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