# $I$ 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)]]