The CNOT (controlled-NOT) gate is the most widely used two-qubit gate in quantum computing. It takes two inputs — a control qubit and a target qubit — and flips the target qubit (applies X gate) if and only if the control qubit is in state |1⟩. When the control qubit is in superposition, the CNOT creates entanglement: applying CNOT to a control qubit in state (|0⟩+|1⟩)/√2 and a target qubit in state |0⟩ produces the Bell state (|00⟩+|11⟩)/√2, maximally entangled.
The CNOT gate, combined with arbitrary single-qubit gates, forms a universal gate set — any quantum computation can be decomposed into sequences of CNOT and single-qubit operations. This makes CNOT a natural compilation target, and quantum circuit complexity is often measured by CNOT count. However, the CNOT is not always the native gate of the hardware — IBM processors natively implement the cross-resonance gate (equivalent to CNOT up to single-qubit rotations), while Google's processors use CZ gates, and Quantinuum uses ZZ gates.
CNOT gates can only be performed between physically connected qubits, and qubit connectivity varies by processor architecture. IBM's heavy-hex topology connects each qubit to 2-3 neighbors; Google's grid topology provides 4 neighbors; trapped-ion systems offer all-to-all connectivity. When a CNOT is needed between non-adjacent qubits, SWAP operations (each requiring 3 CNOTs) must be inserted to route information, increasing circuit depth and error accumulation. Efficient CNOT routing is a major focus of quantum circuit compilation research.