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中文摘要：
本文将通用量子线路分为两类，给出了每类中两种线路的酉算子表达式；根据矩阵张量积转置相似定理，实现了两类线路酉算子间的转换．引入矩阵的直和运算并将其扩展到向量上，以简洁的形式直观地表示出量子线路对输入向量的作用．在将量子线路抽象为受控酉运算嵌套的基础上，提出了仿真量子线路的分治算法．相较于其他基于状态向量的仿真算法，该算法避免了通过张量积运算生成酉矩阵，从而节省了存储空间；并且在仿真非平凡的量子线路时具有更好的时间复杂度．
英文摘要：
Quantum circuits are divided into two classes, and unitary operator expressions for two kinds of circuits in each class are offered. Transformation of unitary operators between two classes is presented according to tensor product transposition similaxity theory. Besides, direct sum operation of matrices is adopted and expanded to vectors to elegantly represent the functions of quantum circuits on input vectors. On the basis of abstracting quantum circuits as controlled unitary operations, divide and conquer algorithms are proposed to simulate quantum circuits. In contrast to other algorithms based on state vector, our algorithms avoid generating matrix operators by tensor product, thus are considerably economy of memory space;and we also show that they are more time-efficient while simulating nontrivial quantum circuits.
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