# X-gate
**X-gate** (or **Pauli-X gate** / **Quantum NOT gate**) is a 1-qubit quantum gate that serves as the quantum equivalent of logical NOT. It's represented by the following 2x2 matrix.

$$ X = \begin{pmatrix}0 & 1\\ 1 & 0\end{pmatrix}$$

The gate flips $\lvert 0\rangle$ to $\lvert 1\rangle$, and $\lvert 1\rangle$ to $\lvert 0\rangle$, which is why it's called the quantum equivalent of NOT.

On the Bloch sphere, it rotates the state by $\pi$ radians (180 degrees) around the X-axis.