# Quantum Y gate
**Quantum Y gate** (or **Pauli-Y gate**) is a quantum gate. It rotates the quantum state by $\pi$ degrees around the Y-axis on the Bloch sphere. In matrix form, it is equivalent to Pauli matrix $\sigma_y$ which is why it's commonly called Pauli-Y gate.

$$Y = \begin{pmatrix}0 & -i\\ i & 0\end{pmatrix}$$

In some ways, it acts as an alternative to [[quantum-x-gate]], but it induces a phase rotation by $\pi / 2$ (or $i$).

$$Y\lvert 1\rangle = \lvert 0\rangle\qquad Y\lvert 0\rangle = \lvert 1 \rangle$$
And it does so for interference states as well (basis states on the X-axis):
$$Y\lvert +\rangle = \lvert -\rangle\qquad Y\lvert -\rangle = \lvert +\rangle$$
The phase states (basis states on the Y-axis) are eigen states of Y gate and they are unaffected by it
$$Y\lvert i\rangle = \lvert i\rangle\qquad Y\lvert -i\rangle = \lvert -i\rangle$$