基于矩阵变换的线性最近邻量子线路综合与优化

Linear Nearest Neighbor Quantum Circuit Synthesis and Optimization Based on the Matrix

为了构造线性最近邻量子线路,降低线性量子可逆线路的量子代价,提出了一种基于矩阵变换的线性量子线路综合与优化方法.该方法给出了线路的矩阵表示和基于矩阵的近邻CNOT(Controlled NOT Gate)门判定,并提出矩阵分组的最佳方案,保证了线路综合中CNOT门数量最优.为了实现量子线路近邻化,提出了swap门的矩阵表示及线路近邻化规则,证明了两种swap门添加方式的等效性;提出了不同情况下swap门的消除规则,降低了近邻化后量子线路的量子代价.选择benchmark例题库中具有代表性的线路进行实验,与已有的量子线路近邻化算法相比,线路量子代价平均优化率为34.31%.

In order to construct linear nearest neighbor(LNN)quantum circuit and reduce its total quantum cost,a matrix-based synthesis and optimization method is proposed.The linear reversible circuit is represented by matrix,and the CNOT(Controlled NOT Gate)analysis based on the matrix is put forward.The best strategy of matrix partition is given,which ensures the number of CNOT gate used in the circuit synthesis is optimal.The matrix representation of swap gate and the NN(Nearest Neighbor)rules are proposed to realize the LNN circuits.The equivalence of two insertion methods of swap gates is proven.Deletion rules of swap gates which are used to make gates adjacent to NN in different cases are proposed,and they can reduce the quantum cost.Experimental results on typical benchmark circuits and comparison against previous algorithms for LNN quantum circuit optimization,the average optimization rate in quantum cost is 34.31%.