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--- i-gate [May 13, 2026 at 12:46] – yanevskiv
+++ i-gate [June 15, 2026 at 15:22] (current) – Ivan Janevski
@@ Line 1: / Line 1: @@
+# $I$ gate (Identity gate)
+**I gate** (or **identity gate**) is a single-qubit quantum gate that leaves the state of a qubit unchanged. It is represented by the $2 \times 2$ identity matrix and drawn as a plain wire in quantum circuit diagrams.
+$$I = \begin{pmatrix}1 & 0\\ 0 & 1\end{pmatrix}$$
+The identity gate is trivial on its own but appears in multi-qubit notation to indicate that a qubit is carried through a time step without any operation being applied. For example, applying $H$ to the first qubit and nothing to the second is written as $H \otimes I$. It is also one of the four [[pauli-gates|Pauli gates]].
+## List of code implementations
+- [[i-gate-qiskit|I gate (Qiskit)]]
+- [[i-gate-custatevec|I gate (cuStateVec)]]
+- [[i-gate-cudaq|I gate (CUDA-Q)]]