Controlled Operator

A **controlled operator** is a quantum operation that acts on a target qubit (or system) **only if** one or more control qubits are in a specific state (usually (|1\rangle)). It’s represented as ( C(U) ), where (U) is the operator applied conditionally. For example, the **CNOT gate** is a controlled-(X) operator: it flips the target qubit only when the control qubit is (|1\rangle).