Analysis on effects of coin operators in search algorithms based on quantum walk

To study the performance of search algorithms based on different marking coins,the negative identity operator I,Grover diffusion operator D and quantum Fourier transform operator F are used as marking coin operators to construct search algorithms based on operators - I,- D and - F (SAI,SAD and SAF). Numerical simulations are used to explore the performance of these algorithms when searching for multiple target vertices on symmetric and random graphs. The effects of SAI and SAD in one-step quantum walk are analyzed,and state transition on the root of a Cayley tree is investigated using the nonrepeating quantum walk. The results show that the success probability curves of SAI are close to the square of sinusoidal curve,and the success probabilities are greater than 0. 5 on dense graphs. SAD is equivalent to SAI when searching for nonadjacent multiple targets,while the success probability curves have double peaks when searching for hybrid vertices on Johnson graph and some random graphs. The performance of SAF when searching for adjacent targets depends on the order of each vector in the basis states of coin space of the target vertices. Finally,periodic state transfer is realized using nonrepeating coin on the root of 4-Cayley tree with generation g using 2g steps. © 2023 Southeast University. All rights reserved.