## Bijection between Fibre Bundle and Hilbert Space

Show that the collection of all unit vectors in $H$ ( $H$ is a Hilbert space) is in bijection with $S^1$ (a fibre bundle) over the Bloch sphere.

So I have that a unit vector in $H$ is of the form, $\alpha|0\rangle + \beta|1\rangle$, where $|\alpha|^2 + |\beta|^2 = 1$. How do I relate this to the fibre bundle.