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--- quantum-y-gate [May 11, 2026 at 11:44] – yanevskiv
+++ quantum-y-gate [May 14, 2026 at 11:38] (current) – external edit 127.0.0.1
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+# 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
+$$Y\lvert i\rangle = \lvert i\rangle\qquad Y\lvert -i\rangle = \lvert -i\rangle$$