Differences

This shows you the differences between two versions of the page.

--- i-gate [May 25, 2026 at 10:14] – Ivan Janevski
+++ i-gate [June 15, 2026 at 15:22] (current) – Ivan Janevski
@@ Line 1: / Line 1: @@
-# I gate
+# $I$ gate (Identity 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 Identity gate is represented by a 2x2 identity matrix.
+**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.
 $$I = \begin{pmatrix}1 & 0\\ 0 & 1\end{pmatrix}$$
-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 $\lvert\psi\rangle = a\lvert 0\rangle + b\lvert 1\rangle$
+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)]]
-$$I\lvert\psi\rangle = \begin{pmatrix}1 & 0\\ 0 & 1\end{pmatrix}\begin{pmatrix}a\\b\end{pmatrix} = \begin{pmatrix}1a + 0b\\ 0a + 1b\end{pmatrix} = \begin{pmatrix}a\\b\end{pmatrix} = \lvert\psi\rangle$$