Study On The Related Properties Of Some Kinds Of Quantum Walk On Graphs

This master thesis aims to explain the relationship between rotation operator and basic quantum gate.Using Fourier transform,the related properties of analytical solutions of quantum walk on cycle,two-dimensional lattice and hypercube are studied.As follows:In section 1,based on the importance of rotation operator and quantum gate,we obtain the relationship between quantum gate and rotation operator about the coordinate axis,and the relationship between quantum gate and general rotation operator.In section 2,based on Fourier transform,we obtain properties of the analytical solution of quantum walk on finite graphs.It mainly includes properties of the analytical solution of general state of quantum walk on cycle,the unbiasedness of special quantum walk on two-dimensional lattice and the relationship between the initial condition of quantum walk on hypercube and a set of basis in an invariant subspace.