For historical reasons, people usually use to represent the quantum Not gate (see Pauli matrices).

When taking and states, the quantum Not gate does the same thing as the classic NOT gate:

When the quantum Not gate act on a superposition state , it interchange the roles of and :

There’s an alternate representation, the quantum circuit representation. In a quantum circuit we depict an gate as follows: X_gate.png The line from left to right is what’s called a quantum wire. A quantum wire represents a single qubit.

A third representation of the gate is the matrix notation:

The inverse of the Not Gate is itself.