Search Algorithm Based on Permutation Group by Quantum Walk on Hypergraphes

Because a significant number of algorithms in computational science include search challenges and a large number of algorithms that can be transformed into search problems have garnered significant attention, especially the time rate and accuracy of search, a quantum walk search algorithm on hypergraphs, whose aim is to reduce time consumption and increase the readiness and controllability of search, is proposed in this paper. First, the data points are divided into groups and then isomorphic to the permutation set. Second, the element coordinates in the permutation set are adopted to mark the position of the data points. Search the target data by the controllable quantum walk with multiparticle on the ring. By controlling the coin operator of quantum walk, it is determined that search algorithm can increase the accuracy and controllability of search. It is determined that search algorithm can reduce time consumption by increasing the number of search particles. It also provides a new direction for the design of quantum walk algorithms, which may eventually lead to entirely new algorithms.