一种求倒数近似值的量子算法及其量子电路-《计算机技术与发展》

文章信息/Info

Title:: A Quantum Algorithm for Finding Reciprocal Approximation andIts Quantum Circuit

Author(s):: ZHU Jia-liang; YE Bin; JI Wen; School of Information and Control Engineering,China University of Mining and Technology,Xuzhou 221116,China

Keywords:: quantum algorithm; quantum circuit; reciprocal; quantum adder; quantum multiplier

摘要:: 求取一个无符号数的倒数在数值计算中有着重要的应用。如何在量子电路中高效准确地求出倒数, 影响着许多量子算法的性能。在此提出了一种求倒数近似值的量子算法及其量子电路的设计方法。首先将输入的二进制数存储在输入寄存器中;通过添加 Toffoli 门将两个 n 位二进制数每一位相乘的结果保存在 2n 个辅助量子比特中;再重复利用基础量子门设计出的 n 位量子全加器对辅助量子比特进行低位置零的移位相加;用控制非门设计置零电路对辅助寄存器进行置零操作以重复利用辅助量子比特,最后设计出了一种量子电路宽度较小的量子乘法器。应用牛顿迭代法解得一个求倒数近似值的系统图,然后在上述量子全加器和量子乘法器的基础上,设计出系统中各模块的量子电路图,最后连接各模块电路图,形成一个完整的求倒数量子算法的量子电路。通过分析,该量子电路提高了辅助量子比特的利用率,并且具有较低的计算复杂性。

Abstract:: Finding the reciprocal of an unsigned number plays an important role in numerical calculations. How to find the reciprocal efficiently and accurately in quantum circuits affects the performance of many quantum algorithms. A quantum algorithm is proposed to calculate the approximation of the reciprocal and the corresponding quantum circuits are designed. Firstly, the input binary number is stored in the input register. Then,the multiplication results of two n-bit binary numbers are stored in 2n auxiliary qubits by adding Toffoli gate.After the least significant auxiliary bits are set to 0,the n-bit quantum? full adder designed by the basic quantum gate is reused to shift and add the auxiliary qubits. The zero setting circuit is designed by the CNOT gate to zero the auxiliary register,so the auxiliary qubit can be reused. Finally,a multiplier with small quantum circuit width is designed. Newton iterative method is used to obtain a system diagram for reciprocal approximation. Then based on the above - mentioned quantum full adder and quantum multiplier, each module of the system diagram is designed. Finally,each module is connected to form a complete reciprocal quantum circuit. Through analysis,it can be seen that the quantum circuit improves the utilization rate of auxiliary qubits and has low computational complexity.