本文给出了量子门的符号化表示形式,将n量子线路表示成一个控制位符号向量和一个低阶受控量子门的组合,避免了使用高维矩阵的巨大存储开销.对无循环格雷码生成算法进行扩展,提出了n元k定位二进制数生成算法.提出了快速量子仿真算法FQSA,将输入状态向量分组,用同一酉算子对各组进行矩阵向量乘积运算,从而快速产生输出状态向量.相比其他通用量子仿真算法,FQSA节省了存储空间,并具有最优的时间复杂度.仿真QFT表明,较当前最好的分治算法,FQSA极大降低了运行时间,提高了可仿真量子比特数.

We introduce symbolic representation for quantum circuit,and show how n-qubit circuit can be described as a control qubit symbolic vector and a lower-order controlled gate,instead of the representation of higher-order unitary matrix.We extend the loopless Gray code binary generation algorithm and propose n elements k position binary generation algorithm.Besides,a fast quantum simulation algorithm (FQSA) is presented,it divides a qubit state vector into several operand groups,each group is multiplied by the same unitary matrix,and then the output can be given quickly.In contrast to any other state vector based algorithm,FQSA requires less memory,and has an optimal time complexity.The experimental result of QFT indicates that FQSA is more time-efficient and it can provide more qubits circuit simulation under the same condition.