quantum gate directory
unnamed
Symbol
$G$
Description:
A single-qubit rotation used in optimal Toffoli decompositions.
The gate $G$ is a single-qubit rotation that appears in optimal decompositions of the Toffoli gate.
$$ G = \begin{bmatrix} \cos\frac{\pi}{8} & -\sin\frac{\pi}{8} \\ \sin{\frac{\pi}{8}} & \cos\frac{\pi}{8} \end{bmatrix} $$
Properties
- Equivalent to $R_y(\pi/4)$.
- Real, unitary rotation about the $y$ axis.
Usage
- Optimal decompositions of the Toffoli gate and related multi-controlled gates.
References
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