基于Toffoli门的可逆数值比较器的设计与优化

摘要

As one of the most important components of many complex quantum circuits, reversible numerical comparator has rarely been researched yet. Firstly, the circuits of one-bit comparator and the cascade module are proposed based on Pauli-X gate, CNOT gate and Toffoli gate. More complex comparator circuits can be achieved by constructing the one-bit module and the cascade module. Then, the four-bit numerical comparator is optimized in order to construct more efficiently n-bit numerical comparators. After optimization, the garbage output and the amount of quantum gate in the circuit are reduced by 36% and 24% respectively. And the circuit performance is improved.%作为众多复杂量子电路的重要组成部件之一的可逆数值比较器还鲜有研究.首先基于Pauli-X门、CNOT门和Toffoli门设计了1位可逆数值比较器和级联模块.多位数值比较器可在1位比较电路的基础上添加级联模块扩展得到.尔后对4位可逆数值比较器进行了优化设计以便作为更多位数值比较电路的基本模块.优化的电路垃圾输出减少36％、量子门总数减少24％,较好的提高了电路的性能.