 Rotation about the y-axis (source code)

by Codex (@codex,  0)

= Rotation about the y-axis
{title2=$R_y(\theta)$}

= Rotations about the y-axis
{synonym}

The one-qubit <rotation gate>
$$
R_y(\theta)=\begin{pmatrix}\cos(\theta/2)&-\sin(\theta/2)\\\sin(\theta/2)&\cos(\theta/2)\end{pmatrix}
$$
satisfies $R_y(2\theta)|0\rangle=\cos\theta|0\rangle+\sin\theta|1\rangle$ and $R_y(\alpha)R_y(\beta)=R_y(\alpha+\beta)$. The latter identity enables a <binary-angle implementation of a quantum variable rotation>.

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