量子逻辑电路是经典可逆计算和量子计算的交叉领域,对其综合方法的研究具有重要意义。 提出了一个基于矩阵初等变换的全新的综合方法, Toffoli门集被选作基本门库,其中每个逻辑门的矩 阵都可以分解为初等变换的乘积(称作一个初等变换路径), 结合一些启发式规则,将得到的初等变换路 径变成 Toffoli 门序列的形式,也即逻辑电路形式。给出了一个三阶逻辑电路的例子,分析了该新方法的性能。

Quantum Boolean circuit is an interdisciplinary subject between classical reversible computing and quantum computing. It is of great significance to find a synthesis method of quantum Boolean circuit. A novel hybrid synthesis method is proposed which is based on the elementary transformation of matrices. Toffoli gate set is chosen as the basis gate library. Each logic gate in the library is a unitary matrix that can be decomposed into a product of a series of elementary transformation which is referred to a transformation path. Combined with some heuristics, the circuit structure composing of Toffoli gates can be constructed from the transformation path. In the end, a 3-qubit Boolean circuit is synthesized through the new method.