Abstract: 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 includ e three-valued quantum NOT gate,three-valued quantum controlled-NOT gate,three-valued Hadamard gate,three-valued quantum SWAP gate and three-valued CR_k 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.

Key words: Quantum computation,Three-valued quantum elementary gates,Quantum Fourier transform,Synthesis of quantum circuit