Pauli-X Quantum Gate

quantum-computing

Definition

Pauli- $X$ Quantum Gate

The Pauli-$X$ quantum gate is the pauli matrix

$$X=\left(\begin{array}{cc}0& 1\\ 1& 0\end{array}\right).$$

It acts as the quantum analogue of NOT:

$$\begin{array}{rl}X|0⟩& =|1⟩\\ X|1⟩& =|0⟩\end{array}$$

Examples

General State

For a general state

$$|\psi ⟩=\alpha |0⟩+\beta |1⟩$$

we get

$$X|\psi ⟩=\beta |0⟩+\alpha |1⟩.$$

So it swaps amplitudes.