Rotation about the y-axis ($R_y(\theta )$)

The one-qubit rotation gatesatisfies $R_y(2\theta )|0⟩=\cos \theta |0⟩+\sin \theta |1⟩$ and $R_y(\alpha )R_y(\beta )=R_y(\alpha +\beta )$. The latter identity enables a binary-angle implementation of a quantum variable rotation.