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--- y-gate [May 25, 2026 at 10:23] – Ivan Janevski
+++ y-gate [August 22, 2026 at 15:22] (current) – external edit 127.0.0.1
@@ Line 1: / Line 1: @@
-# Y-gate
+# Y gate
-**Y-gate** (or **Pauli-Y gate**, **phase gate**) is a single qubit quantum gate. It is represented by the following 2x2 matrix.
+**Y gate** (or **Pauli-Y gate**) is a single-qubit gate represented by the second Pauli matrix. It combines the actions of the [[x-gate|X gate]] (bit flip) and the [[z-gate|Z gate]] (phase flip), and additionally multiplies the amplitude by $i$. It is one of the three [[pauli-gates|Pauli gates]].
 $$Y = \begin{pmatrix}0 & -i \\ i & 0\end{pmatrix}$$
+The gate maps the computational basis states with an accompanying imaginary factor, and its eigenstates are the $Y$-axis states on the [[bloch-sphere|Bloch sphere]]:
+$$Y\lvert 0\rangle = i\lvert 1\rangle \qquad Y\lvert 1\rangle = -i\lvert 0\rangle$$
+$$Y\lvert i\rangle = \lvert i\rangle \qquad Y\lvert{-i}\rangle = \lvert{-i}\rangle$$
+On the Bloch sphere, $Y$ corresponds to a $\pi$ rotation about the $y$-axis. Like all Pauli gates it is Hermitian, unitary, and satisfies $Y^2 = I$. The $Y$ gate can be decomposed as $Y = iXZ$. In quantum error correction, a $Y$ error on a qubit means both a bit flip and a phase flip occurred simultaneously.
+## List of code implementations
+- [[y-gate-qiskit|Y gate (Qiskit)]]
+- [[y-gate-custatevec|Y gate (cuStateVec)]]
+- [[y-gate-cudaq|Y gate (CUDA-Q)]]