Bloch Sphere Visualizer

    Interactive 3D visualization of single-qubit states on the Bloch sphere

    Quick States

    Interactive Bloch Sphere

    θ (Polar Angle)0°
    0° (|0⟩)90°180° (|1⟩)
    φ (Azimuthal Angle)0°
    0°90°180°270°360°
    Quantum State
    |ψ⟩ = (1.0000)|0⟩ + (0.0000)|1⟩
    P(|0⟩)100.0%
    P(|1⟩)0.0%
    x
    0.0000
    y
    0.0000
    z
    1.0000

    About the Bloch Sphere

    The Bloch sphere is a geometric representation of a single qubit's pure state space. Every point on the sphere corresponds to a unique qubit state |ψ⟩ = cos(θ/2)|0⟩ + e^(iφ)sin(θ/2)|1⟩.

    The north pole represents |0⟩, the south pole |1⟩, and points on the equator are equal superpositions with varying relative phase. The Bloch vector (x, y, z) equals (⟨σₓ⟩, ⟨σᵧ⟩, ⟨σ_z⟩), the expectation values of the Pauli matrices.

    Quantum gates correspond to rotations on the Bloch sphere: X-gate rotates π around x-axis, Z-gate rotates π around z-axis, and Hadamard rotates π around the axis (x+z)/√2.

    Related Tools