基于控制K次平方根非门的类Toffoli门构造方法

在量子电路综合算法中，由于非置换量子门比置换量子门具有更复杂的规则，直接使用非置换量子门会大幅度提高综合算法的复杂性，因此可先使用非置换量子门生成相应的置换量子门，然后再用这些置换量子门综合所求量子可逆逻辑电路，从而提高算法性能。本文重点研究如何用非置换量子门构造新的置换量子门，为此吸收了格雷码的思想，提出了一种高效的递归构造方法，实现使用控制非门和控制K次平方根非门(非置换量子门)，快速生成最优的类Toffoli门(置换量子门)。

Realization of Toffoli-Like Gates Using Controlled K-th-Root-of-NOT Quantum Gates

Since non-permutative quantum gates have more complex rules than permutative quantum gates, direct use of non-permutative quantum gates can greatly increase the complexity of the synthesis algorithm, so given quantum gates should be used to create new permutative quantum gates, and then these permutative gates are used to synthesize the desired quantum reversible logic circuit, thus improving the algorithm performance. This paper focuse on how to use non-permutative quantum gates to construct new permutative gates, therefore, we absorb the idea of Gray code and present an efficient recursive construction which can use controlled-NOT gates and controlled K-th-root-of-NOT gates (non-permutative quantum gates) to construct the optimal Toffoli-like gates (permutative quantum gates).