5.4.1 Circuits with multiple gates

Single-qubit gates and two-qubit gates can be combined in a structured sequence to give a quantum circuit containing multiple quantum gates. Consider as an example the circuit shown in Figure 11, which depicts a sequence of gates acting on two qubits, labelled and . Remember that each qubit enters its circuit from the left; first, a Hadamard gate is applied to qubit . Then a CNOT is applied to and , where the control C is and the target T is . Finally, a NOT gate is applied to .

The circuit in Figure 11 is a sequence of operations applied to qubits and can be analysed using the methods already introduced, with extra subscripts labelling the single-qubit gates and operations so that the qubit each operation is acting on is clear. Thus acts only on the qubit , leaving unchanged. Therefore, using as a sample input the calculation becomes:

Now acts only on , so

This means that

Next comes the effect of the CNOT gate, courtesy of and gives

Finally, observe that acts on only, so flip of each ket in the superposition: