Computing Library › Quantum Logic Gates
Quantum Logic Gates
CNOT Gate (Controlled-X)
The CNOT flips the target qubit if the control is |1⟩ — the two-qubit gate that creates entanglement and anchors nearly every quantum circuit.
Matrix
Unitary matrix
1000010000010010
Circuit symbol
Action on basis states
| input | output |
|---|---|
| |00⟩ | |00⟩ |
| |01⟩ | |01⟩ |
| |10⟩ | |11⟩ |
| |11⟩ | |10⟩ |
How it works
CNOT (CX) is Clifford and, with H, turns a product state into a Bell state: H on the control then CNOT gives (|00⟩+|11⟩)/√2. With arbitrary single-qubit gates it is universal. It is the standard entangler and the syndrome-extraction workhorse of error correction.
In code (Qiskit)
python
qc = QuantumCircuit(2)
qc.h(0)
qc.cx(0, 1) # Bell statetwo-qubitCliffordentangling