Fig. 2

Sketch of the main circuit: Qubits in the main circuit can be divided into two groups: L-qubits to represent the sub labels, and will play the role of control bits and the V-qubits to represent a given vector. Initially, L-qubits will be prepared at state \((\frac {|0\rangle +|1\rangle }{\sqrt {2}})^{\otimes N}\), where there are N qubits representing the sub labels. The minimum N=⌈log2n⌉, and n is the total number of sub labels. In sum n control rotation gates are needed