Algoritmos quânticos e o problema da clique máxima em grafos

• Main Author: Dias, Matheus Giovanni
• Publication Date: 2022
• Format: Bachelor thesis
• Language: por
• Source: Repositório Institucional da UTFPR (da Universidade Tecnológica Federal do Paraná (RIUT))
• Download full: http://repositorio.utfpr.edu.br/jspui/handle/1/33230
• topic: Computação quântica; Algorítmos computacionais; Algoritmos em grafos; Complexidade computacional; Quantum computing; Computer algorithms; Graph algorithms; Computational complexity; CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO

Determining the cardinality of the maximum clique on a simple graph is a NP-hard problem with several applications of interest. The best know classical algorithm for this problem has (3/3) time complexity. Classical computing uses phenomena from classical physics to model, store and process information. Consequently, the entire model of classical computing is bounded superiorly by the limits of classical physics. As an alternative, Quantum Computing has been developed to take advantage of quantum phenomena and provide the constructions of circuits capable of performing certain computations more efficiently. In this paper, two quantum solutions to the maximum clique problem will be proposed and analyzed, based on the Grover Quantum Search algorithms and the Quantum Minimal Search Algorithm, comparing their respective time complexities with the best known classical solution.