 Controlled NOT gate

The controlled-NOT gate is a two-qubit unitary operator that flips a target qubit when its control is in $|1⟩$. In the ordered labels below, $a$ denotes the control, $b$ the target, and $\oplus$ is addition modulo two.

The controlled-NOT gate maps $|a,b⟩$ to $|a,b\oplus a⟩$.

The basis rule extends linearly to quantum superpositions. For example, it sends $|+⟩|0⟩$ to $(|00⟩+|11⟩)/\sqrt{2}$, a Bell state. The control is not first measured: its quantum coherence can become entanglement between the two qubits. Applying the controlled-NOT gate twice returns the original state. ^[ref]

A Controlled NOT gate, commonly referred to as a CNOT gate or CX gate, is an essential component in quantum computing. It is a two-qubit gate that performs a NOT operation (also known as a bit-flip) on a target qubit only when a control qubit is in the state \(|1\rangle\).