连续时间量子行走算法在截断单形晶格上的搜索研究

Research on Continuous-time Quantum Walk Algorithm Searching on Truncated Simplex Lattices

为证明连续时间量子行走算法在结构型数据库上的搜索可以实现二次加速的效果,对结构型数据库中的截断单形晶格类型,进行了连续时间量子行走算法的应用研究。首先对截断单形晶格进行对称性分析,确定系统演化所处的希尔伯特空间,然后用哈密顿量本征态与基础态的平方叠加、和简并微扰理论两种方法来求解系统演化需要的临界跳跃率。最后通过对图中的边进行加权的方法,合并了量子搜索的步骤,缩短了系统演化的时间,从而实现了平方加速的效果,并表明了边的权重对量子搜索过程的影响。

To demonstrate the quadratic speedup effect of the continuous-time quantum walk algorithm searching in structural database,this study delves into its application specifically for the truncated simplex lattice within structural databases.Initially,the determination of the Hilbert space in which the system evolves is based on an analysis of the symmetry of the truncated simplex lattice.Subsequently,the critical jumping rate for system evolution is derived by utilizing the square overlaps between the eigenstates of the Hamiltonian and the basis states,and employing degenerate perturbation theory.Ultimately,by assigning weights to the graph's edges,the stages of the quantum search are merged,thereby shortening the system evolution time and manifesting a quadratic speedup.This exploration elucidates the impact of weighted edges on the quantum search process.