Computación cuántica : problemas de correspondencia y asignación de recursos

Abstract

Resumen original en inglés: Many important technological problems such as facility assignment, medium ac- cess management, dynamic spectrum allocation, can be addressed as decision or mat- ching problems. The usual classic algorithms, heuristics, etc. may become less efficient when the amount of resources or agents involved in the decision matching problem grow beyond a certain amount. Quantum computing takes advantage of quantum mechanical effects such as entanglement and superposition to provide massive per- formance speedup in certain types of computation problems such as data searching, factorization and encryption. In the course of this thesis quantum decision models are developed and studied as a tool for solving classic decision problems more effi- ciently. As a generic model of decision problem a quantum dating market model is proposed. The quantum matching model stability is analyzed through Von Neumann entropy calculus and the information about the different possible strategies leading to stable and unstable states is obtained. The performance of quantum and classic strategies is compared showing that the agents capitalizing a Grover quantum search based strategy achieve a much bigger success rate than those playing classics as the number of players grows. Entanglement between player strategies lead to outcomes in the quantum model that are totally unexpected in the decision problem classic formulation. Finally, game theory applied to wireless communications is studied. In- terference problems are analysed from the viewpoint of game theory and quantum game solutions allowing fair and efficient resources sharing are proposed. Besides, the medium access problem is treated as a quantum minority game and novel results are presented.