多值逻辑量子置换门的酉矩阵表示

Unitary Matrix of Multiple-Valued Quantum Permutation Gate

理论上量子可逆电路不存在能量耗散问题,因此量子计算系统对环境产生的负面影响可以达到最低.多值逻辑量子置换门是构建多值逻辑量子电路的基本单元.该文从数学的角度研究多值逻辑量子置换门的酉矩阵,提出了一种构造多值逻辑量子置换门酉矩阵的方法,并对其正确性进行了讨论.在此基础之上,又给出了构造混合多值逻辑量子置换门酉矩阵的框架,利用此框架可以方便地构造任何混合逻辑量子置换门的酉矩阵.酉矩阵是量子门的数学模型,可以清晰地反映出量子门的数学性质.研究量子门的酉矩阵对验证量子门的正确性和可靠性,分析量子状态在电路中的演化过程及发展趋势具有一定的意义.

The negative effects to environment arose from quantum computing system can reach minimum in theory because there is no power dissipation in quantum reversible circuits.Multiple-valued quantum permutation gate is the basic unit to construct multiple-valued quantum circuits.In this paper,the unitary matrix of multiple-valued quantum permutation gate is studied from the view of mathematics.A method constructing the unitary matrix of multiple-valued quantum permutation gate is put forward,and its correctness is discussed constructively by permutation matrix.On the basis of it,a framework by which the unitary matrix of any hybrid quantum gate can be constructed is presented.Unitary matrix is mathematical model of quantum gate and can reflect quantum gate＇s mathematical properties clearly.The research on quantum gate＇s unitary matrix is significant to verify the correctness and reliability of quantum gate and to analyze the evolution process and development trend of quantum state in quantum circuits.