Algoritmos quânticos para o problema do isomorfismo de grafos

Abstract

The graph isomorphism problem has applications in several areas of science. This problem has not an efficient solution to its general case. In this work, we present the basic concepts of group theory, graph theory and quantum mechanics. We introduce the hidden subgroup problem and a known polynomial reduction of the graph isomorphism problem in its general case to the hidden subgroup problem on the symmetric group. We use a method that reduces the graph isomorphism problem to the group intersection problem. This method combines results from quantum computing and solvable group theory providing a efficient solution through a quantum algorithm to the graph isomorphism problem for the particular class of graphs.