Quantum I gate (or Identity gate) is a quantum gate that leaves the quantum state unchanged. In quantum circuits it's commonly written as wire. In matrix form, it's equivalent to the identity matrix.

$$I = \begin{pmatrix} 1 & 0\\ 0 & 1\end{pmatrix}$$

For states along the Z-axis: $$I\lvert 0\rangle =\lvert 0\rangle\qquad I\lvert 1\rangle = \lvert 1 \rangle$$

For states along the X-axis: $$I\lvert i\rangle =\lvert i\rangle\qquad I\lvert -i\rangle = \lvert -i \rangle$$

For states along the Y-axis: $$I\lvert +\rangle =\lvert +\rangle\qquad I\lvert -\rangle = \lvert - \rangle$$