NOT Quantum Gate

quantum-computing

Definition

NOT Quantum Gate

The NOT quantum gate is the [[Knowledge/Pauli-X Quantum Gate|Pauli-$X$ gate]]: a one-qubit gate that flips the basis states

$$\begin{array}{rl}|0⟩& \mapsto |1⟩,\\ |1⟩& \mapsto |0⟩,\end{array}$$

and on a general state swaps the amplitudes:

$$X(\alpha |0⟩+\beta |1⟩)=\beta |0⟩+\alpha |1⟩.$$

It is its own unitary inverse: $X^2=I$.