$G$
misc & legacy 1 qubit
unnamed
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
The unitary, drawn
Every entry of the matrix as a disc. The area is the transition probability $|U_{jk}|^2$; the colour and the hand are the phase. Rows are outputs $\langle j|$, columns inputs $|k\rangle$, in the computational basis.
Phase
Disc area $= |U_{jk}|^2$. Hover an entry for its value, or take the JSON.