Interactive model
QA: Bloch Sphere Explorer
Adjust qubit angles and view Bloch sphere gate rotations interactively.
This interactive page treats the Bloch sphere as a coordinate picture for a normalized single-qubit state. Adjust θ and φ to move the state vector, then adjust the camera yaw and pitch to rotate only the view.
The gate visual uses the same initial state and camera view as the sphere above it. The before and after vectors show how selected single-qubit gates can be represented as rotations of the Bloch vector.
Interactive model
Bloch sphere state explorer
|psi> = 0.866 |0>
+ (0.354 + 0.354i) |1>
Bloch vector = [0.612, 0.612, 0.5]
Basic operations
Gate action as rotations
X rotates the Bloch vector by 180 degrees around the x-axis.
The camera view and initial before-state are synchronized with the Bloch sphere explorer above.
Linear Algebra Interpretation
A pure qubit state can be written as
with normalization
The Bloch sphere removes global phase and draws the remaining state information as a point on a unit sphere. It is a geometric model of the state description, not a replacement for the underlying two-dimensional complex vector space.