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--- i-gate [May 13, 2026 at 12:50] – yanevskiv
+++ i-gate [May 14, 2026 at 11:38] (current) – external edit 127.0.0.1
@@ Line 1: / Line 1: @@
+# I gate
+**I gate** (or **Identity gate**) is a quantum gate that leaves the state vector unchanged. In other words, it does nothing. It's commonly drawn as a wire. Its matrix representation is equivalent to the identity matrix. For a single qubit, the gate is simply a 2x2 identity matrix.
+$$I = \begin{pmatrix}1 & 0\\ 0 & 1\end{pmatrix}$$
+You apply the identity gate $I$ to a state vector $\lvert\psi\rangle$ by multiplying it the state vector from the left $I\lvert\psi\rangle$. The following is a worked example where the state vector is a single qubit $\lvert\psi\rangle = a\lvert 0\rangle + b\lvert 1\rangle$
+$$I\lvert\psi\rangle = \begin{pmatrix}1 & 0\\ 0 & 1\end{pmatrix}\begin{pmatrix}a\\b\end{pmatrix} = \begin{pmatrix}1a + 0b\\ 0a + 1b\end{pmatrix} = \begin{pmatrix}a\\b\end{pmatrix} = \lvert\psi\rangle$$