$I$
The identity gate $I_n$ acts on $n$ qubits and leaves all basis states unchanged.
$$ I_2 = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} $$
Properties
- Identity element of the unitary group; it commutes with all gates.
The unitary, drawn
Every entry of the matrix as a disc. The area is the transition probability $|U_{jk}|^2$; the colour and the hand are the phase. Rows are outputs $\langle j|$, columns inputs $|k\rangle$, in the computational basis.
Phase
Disc area $= |U_{jk}|^2$. Hover an entry for its value, or take the JSON.
SDK support
How to call this gate in each framework. Hover a ⓘ for a note; the support matrix compares every gate at once.
| SDK | Name |
|---|---|
| Qiskit | qiskit.circuit.library.IGate |
| PennyLane | pennylane.Identity |
| Cirq | cirq.I ⓘ |
| Q# | Std.Intrinsic.I |
| PyQuil | pyquil.gates.I |
| Braket | braket.circuits.gates.I |
| BQSKit | bqskit.ir.gates.IdentityGate |
| Qibo | qibo.gates.I ⓘ |
| pytket | pytket.circuit.OpType.noop ⓘ |
| Stim | I |
| OpenQASM | stdgates.inc: id ⓘ |