quantum gate directory
Pauli-Y
Symbol
$Y$
Description:
Bit-and-phase flip combining $X$ and $Z$ with a phase.
Alternate notations:
- $Y$
- $\sigma_y$
- $\sigma_2$
The Pauli-$Y$ gate is a $\pi$ rotation around the $y$ axis of the Bloch sphere.
| Matrix | $\begin{bmatrix}0 & -i \\ i & 0 \end{bmatrix}$ |
| Arity | 1 |
| Group | $\mathsf{U}(2)$ |
Properties
- Hermitian and self-inverse: $Y^\dagger = Y$ and $Y^2 = I$.
- Equivalent to a $\pi$ rotation about $y$ up to global phase.
Usage
- Phase-sensitive bit flips and basis changes.
Groups
This gate is contained in the following groups:
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