A gate for a Quantum Computer

Let XX be an Operator.

X=(0110)=i e−iπ2XX = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} = i\,e^{-i\frac{\pi}{2}X}

Example: If you put state ∣0⟩\ket{0} or ∣1⟩\ket{1} through them

X∣0⟩=∣1⟩,X∣1⟩=∣0⟩X\ket{0} = \ket{1}, \qquad X\ket{1} = \ket{0}