三值量子基本门及其对量子Fourier变换的电路实现

Three-valued Quantum Elementary and Implementation of Quantum Fourier Transform Circuit

理论上可以把量子基本门组合在一起来实现任何量子电路和构建可伸缩的量子计算机。但由于构建量子线路的量子基本门数量庞大,要正确控制这些量子门十分困难。因此,如何减少构建量子线路的基本门数量是一个非常重要和非常有意义的课题。提出采用三值量子态系统构建量子计算机,并给出了一组三值量子基本门的功能定义、算子矩阵和量子线路图。定义的基本门主要包括三值量子非门、三值控制非门、三值Hadamard门、三值量子交换门和三值控制CRk门等。通过把量子Fourier变换推广到三值量子态,成功运用部分三值量子基本门构建出能实现量子Fourier变换的量子线路。通过定量分析发现,三值量子Fourier变换的线路复杂度比二值情况降低了至少50%,表明三值量子基本门在降低量子计算线路复杂度方面具有巨大优势。

In theory,quantum elementary gates can be put together to implement any quantum circuit and build a scalable quantum computer.Because the number of quantum elementary gates required to build quantum logic circuits is too large,exactly controlling them is not easy.Therefore,how to reduce the number of quantum elementary gates to build quantum circuits is a very important and significant topic.Three-level quantum system was proposed to build quantum computer in this paper,and a set of three-valued quantum elementary gates were defined,including function,operator matrix,quantum circuit diagram.These elementary gates mainly include three-valued quantum NOT gate,three-valued quantum controlled-NOT gate,three-valued Hadamard gate,three-valued quantum SWAP gate and three-valued CRk gate and so on.This paper extended the quantum Fourier transform（QFT）to three-valued quantum states,and quantum circuits were successfully built to implement QFT with partial three-valued quantum elementary gates.By the quantitative analysis,the complexity of three-valued QFT circuit is lower than two-valued case at least 50%.The result indicates that the three-valued quantum elementary gates have a huge advantage in respect of reducing the circuit complexity about quantum computation.