A control qubit determines whether a controlled gate operates on its target qubits. When every control qubit is in |1⟩, the gate acts on the targets; if any control is |0⟩, the state remains unchanged. section 2.3.1
Controlled-gate behavior follows these rules:
- Apply the target operation to each basis-state component whose controls are all |1⟩. section 2.3.1
- Leave basis-state components unchanged when at least one control is |0⟩. section 2.3.1
- Extend the rule to superpositions by applying the gate linearly to every term. section 2.3.1
CNOT as the simplest case
With the left qubit as control and the right as target, CNOT maps |10⟩ to |11⟩ and |11⟩ to |10⟩, while leaving |00⟩ and |01⟩ unchanged. section 2.3.1
