Iris
Lab

Bloch Sphere

Any pure qubit state can be represented as a point on the surface of the Bloch sphere. Apply quantum gates and watch the state vector rotate in 3D. Click "Measure" to collapse the state probabilistically.

|ψ⟩ = 1.00|0⟩
θ = 0.00°   φ = 0.00°
Quantum Gates
Custom Rotation
Rx angle 0°
Ry angle 0°
Rz angle 0°
Gate History

    The Bloch Sphere

    The Bloch sphere is a geometric representation of a single qubit's pure state space. The north pole represents |0⟩ and the south pole |1⟩. Points on the equator are equal superpositions with different relative phases: |+⟩ and |−⟩ on the x-axis, |i⟩ and |−i⟩ on the y-axis.

    Quantum Gates

    Each gate is a unitary rotation on the Bloch sphere. The Hadamard (H) gate rotates 180° around the axis halfway between x and z. Pauli-X, Y, Z are 180° rotations around their respective axes. S is a 90° z-rotation, T is a 45° z-rotation.

    Measurement

    Measurement collapses the state to |0⟩ or |1⟩ with probabilities cos²(θ/2) and sin²(θ/2) respectively. This is the Born rule in action.