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--- quantum-i-gate [May 11, 2026 at 11:29] – yanevskiv
+++ quantum-i-gate [May 14, 2026 at 11:38] (current) – external edit 127.0.0.1
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+# Quantum I gate
+**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.
+$$I = \begin{pmatrix} 1 & 0\\ 0 & 1\end{pmatrix}$$
+## Effect
+### Z basis states
+For states along the Z-axis:
+$$I\lvert 0\rangle =\lvert 0\rangle\qquad I\lvert 1\rangle = \lvert 1 \rangle$$
+### X basis states
+For states along the X-axis:
+$$I\lvert i\rangle =\lvert i\rangle\qquad I\lvert -i\rangle = \lvert -i \rangle$$
+### Y basis states
+For states along the Y-axis:
+$$I\lvert +\rangle =\lvert +\rangle\qquad I\lvert -\rangle = \lvert - \rangle$$