Pauli X-gate

Last updated Jun 23, 2022

• Type atom
• Status good

The Pauli X-gate, or NOT Gate, turns $\ket 0$ into $\ket 1$, and $\ket 1$ into $\ket 0$ [^1[]]: $$\displaylines{
X\ket0 = \ket 1, \newline
X\ket1 = \ket 0.
}$$
If we apply the X-gate twice, we rotate around the $x$-axis of the Bloch sphere by $360^\circ$, which does nothing. Then, $X^2 = I$. It’s Matrix representation is: $$X = \begin{pmatrix}0 & 1 \\ 1 & 0 \end{pmatrix}.$$