中文摘要：

将经典的对称二分法应用于多线量子可逆逻辑门的分解中,证明当量子位数n≥5且3≤k≤n-2时,任意多线量子可逆逻辑门（′k-′CNOT门）可以在没有辅助位的情况下由少于[4﹂log2（k-2）」＋1-3（2﹂log2（k-2）」＋1-k＋1）2﹂log2（k-2）」]个′2-′CNOT门（Toffoli门）构成.利用该方法可以使由多线量子可逆逻辑门分解而生成的物理电路门阵列数大幅下降.与Yang等报道的实验结果相比,′2-′CNOT门的数量级由O（2k）减少为O（k2）.

英文摘要：

The classical symmetric dichotomy is applied to the decomposition of a multi-line quantum reversible logic gate.A conclusion is proved that any multi-line quantum reversible logic gate ′k′-CNOT can be constituted by less than [4﹂log2（k-2）」＋1-3（2﹂log2（k-2）」＋1-k＋1）2﹂log2（k-2）」] ′2′-CNOT gates（Toffoli gate） without auxiliary bit under the condition that the quantum bit n≥5 and 3≤k≤n-2.This method can make a substantial decrease in the number of the gate array corresponding circuit generated by the decomposition of a multi-line reversible quantum logic gate.Compared with the experimental results presented by Yang et al.,the number of the ′2′-CNOT gates is cut down from O（2k） to O（k2）.