The X (NOT) Gate

The Pauli-X gate is the quantum version of the classical NOT: it swaps the amplitudes of $|0\rangle$ and $|1\rangle$. On a basis state it simply flips the bit,

$X|0\rangle = |1\rangle, \qquad X|1\rangle = |0\rangle,$

and its matrix is

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

Unlike a classical NOT, $X$ acts linearly on superpositions too: $X\big(\alpha|0\rangle + \beta|1\rangle\big) = \beta|0\rangle + \alpha|1\rangle$. Because $X^2 = I$, applying it twice returns the original state — $X$ is its own inverse.

Try it

Flip the qubit from $|0\rangle$ to $|1\rangle$, then press Run and Check.

After running, all the probability sits on $|1\rangle$ — the Bloch vector now points at the south pole.

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