The action of a quantum singly controlled gate, denoted Λ(G)">, where a single qubit's value controls the application of G">, can be understood by looking at the following example of a product state input:
That is to say, the controlled gate applies G"> to the register containing ψ"> if and only if the control qubit takes the value 1">. In general, such controlled operations are described in circuit diagrams as
Here the black circle denotes the quantum bit on which the gate is controlled and a vertical wire denotes the unitary that is applied when the control qubit takes the value . For the special cases where G=X and G=Z, the following notation is used to describe the controlled version of the gates (note that the controlled-X gate is the CNOT gate):
