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量子可逆逻辑电路综合技术是构建量子计算机的关键技术之一.本文提出基于数组正反变换的量子可逆逻辑电路双向综合算法.该算法依据两个数字间的汉明距离,利用邻接矩阵的电路转化规则,从正反两个方向,生成任意给定置换的量子可逆逻辑电路.理论分析表明,该方法综合n量子电路最多需要(n-1)·2n+1个扩展通用Toffoli门.与其它同类算法相比,由于不需要穷尽搜索,该算法的时间复杂度和空间复杂度都有大幅度降低.此外,由于合理采用了扩展通用Toffoli门,该算法可综合任一置换(包括奇置换和偶置换)的量子可逆逻辑电路,且电路中量子门的数量大幅减少.
Quantum reversible logic circuit synthesis technology is one of the key technologies for constructing quantum computer.In this paper, we propose a two-way synthesis algorithm of quantum reversible logic circuit based on the forward and inverse transform of the array.The algorithm relies on the Hamming distance between two numbers, Rule, a quantum reversible logic circuit with arbitrary given permutations is generated from both the positive and negative directions.The theoretical analysis shows that this method requires a maximum of (n-1) · 2n + 1 generalized Toffoli gates to be integrated with the n-quantum circuit. Compared with the algorithm, the proposed algorithm can reduce the time complexity and space complexity greatly because it does not need exhaustive search. In addition, due to the rational use of extended universal Toffoli gate, the algorithm can combine either permutation (including singular permutation and even Replacement) quantum reversible logic circuit, and the number of quantum gates in the circuit drastically reduced.