{c}
{title2=$X$}
{wiki=Pauli_matrices}

The Pauli $X$ gate interchanges $|0\rangle$ and $|1\rangle$.


Pauli X gate

{c}

= Quantum NOT gate
{synonym}
{title2}

The <quantum NOT gate> swaps the state of $\ket{0}$ and $\ket{1}$, i.e. it maps:
$$
x \ket{0} + y \ket{y} \to y \ket{0} + x \ket{y}
$$
As a result, this gate also inverts the probability of measuring 0 or 1, e.g.
* if the old probability of 0 was 0, then it becomes 1
* if the old probability of 0 was 0.2, then it becomes 0.8

$$
\begin{bmatrix}
0 & 1 \\
1 & 0 \\
\end{bmatrix}
$$
{title=<Quantum NOT gate> <matrix>}

\Image[https://upload.wikimedia.org/wikipedia/commons/9/91/Qcircuit_CNOT.svg]
{title=<Quantum NOT gate> symbol}


 Pauli-X gate

ID: pauli-x-gate