Bloch sphere

A geometric representation of pure single-qubit states as points on the surface of a unit sphere.

Any pure qubit state can be parameterized as:

|\psi\rangle = \cos(\tfrac{\theta}{2})|0\rangle + e^{i\phi}\sin(\tfrac{\theta}{2})|1\rangle.

The angles $(\theta,\phi)$ map to a point on the sphere.