quantum gate directory
Pauli-Z
Symbol
$Z$
Description:
Phase-flip gate that leaves $|0\rangle$ unchanged and flips the phase of $|1\rangle$.
Alternate notations:
- $Z$
- $\sigma_z$
- $\sigma_3$
The Pauli-$Z$ gate applies a relative phase of $-1$ to the $|1\rangle$ component.
| Matrix | $\begin{bmatrix}1 & 0 \\ 0 & -1 \end{bmatrix}$ |
| Arity | 1 |
| Group | $\mathsf{U}(2)$ |
Properties
- Hermitian and self-inverse: $Z^\dagger = Z$ and $Z^2 = I$.
- Equivalent to a $\pi$ rotation about $z$ up to global phase.
- Diagonal in the computational basis.
Groups
This gate is contained in the following groups:
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