Fig. 6

Sketch of the main circuit for Method II: Qubits in the main circuit can be divided into two groups: One group will represent the sub labels, and will play the role of control bits, as the L part in the figure. The other will represent the given vector, as the V part in the circuit. Furthermore, qubits representing the vectors are divided into a few groups (In this Figure, 2 groups), and the sublabel qubits will control them respectively. We need to measure all of them to get our results. Connection between the V qubits are not required in this circuit