quantum gate directory
Pauli-X
Symbol
$X$
Description:
Bit-flip gate that swaps $|0\rangle$ and $|1\rangle$.
Alternate notations:
- $X$
- $\sigma_x$
- $\sigma_1$
- $\mathrm{NOT}$
The Pauli-$X$ gate is the quantum analog of a classical NOT.
| Matrix | $\begin{bmatrix}0 & 1 \\ 1 & 0 \end{bmatrix}$ |
| Arity | 1 |
| Group | $\mathsf{U}(2)$ |
Properties
- Hermitian and self-inverse: $X^\dagger = X$ and $X^2 = I$.
- Equivalent to a $R_x(\pi)$ up to global phase.
Usage
- Bit flips and toggling computational basis states.
Groups
This gate is contained in the following groups:
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