Hopf fibration is a connection between state vector representation of a qubit $\lvert\psi\rangle = a\lvert 0\rangle + b\lvert 1\rangle$ and points on the Bloch sphere $(x, y, z)$.

$$\pi(\lvert\psi\rangle) = \langle\psi\lvert\sigma_i\lvert\psi\rangle $$