ENTANGLEMENT, QUANTUM PHASE TRANSITIONS AND QUANTUM ALGORITHMSAuthor:
ORÚS LACORT ROMÁN ÓSCAR.
Year:
2005.
University:
BARCELONA [
www.ub.es].
Place of defense: FACULTAT DE FÍSICA.
Place of preparation: FACULTAT DE FÍSICA, UNIVERSITAT DE BARCELONA.
Summary: Since the pioneering ideas Feynman until today, information and quantum computing has evolved so fast. Being quantum mechanics in its origins regarded primarily as a theoretical framework in which to explain certain fundamental processes acontecían in Nature, it was during the 80's and 90 when they started thinking about the inherently quantum behavior of world in which we live as a tool with which to develop information technology more powerful, based on the same principles of quantum physics. As Landauer said, the information is physically, and therefore should not be at all surprised that the attempt to receive communion with the mechanical theory of information. And nothing could be further from reality, it soon became apparent that it was possible to use the laws of quantum physics to perform tasks unthinkable from a classic. For example, the discovery of teleportation, coding superdensa, quantum cryptography, the factoring algorithm Shor and Grover search algorithm, constitute some of the remarkable achievements that have attracted the attention of many people, inside and outside science. It is quantum information, thus acting as a field genuinely plurisdiciplinar, which concentrated researchers from different branches of physics, mathematics and engineering. While its origins were in the quantum information and those who benefited from knowledge of other fields, today the tools developed within the framework of the quantum theory of information may also be used in the study of problems of different areas, such as physics many bodies or quantum field theory. This is because of the detailed study that quantum information develops in the quantum correlations, or intertwining quantum. Any physical system described by the laws of quantum mechanics can therefore consider the perspective of the theory of quantum information theory through the intertwining. The work presented in this thesis, and we try to distill some of the most important aspects in this summary is at the interface between information and quantum computing, quantum theory of many bodies, and the quantum field theory. We use these tools to analyze three disciplines couple problems that appear in its intersection. Specifically, in Section 1 consider the irreversibility of the group renormalización terms of the quantum theory of information through the use of the theory of mayorización and fields under the theory. In section 2 we estimate intertwining of a copy of a bipartisan pair a wide variety of models with the help of techniques and theory of fields under matrices Toeplitz. The intertwining of entropy model Lipkin, Meshkoy and Glick is preserved in section 3, showing many analogy with which appears in quantum system in (1 +1) dimensions. In section 4 we apply the ideas of the laws of quantum scale correlations in quantum phase transitions to the study of quantum algorithms, especially factoring algorithm Shor quantum algorithms and evolutionary diabática that solves a problem NP- full and the problem of searching a database disorderly, respectively. Similarly, we use techniques insperiadas originally in condensed matter physics simulations to perform classical, through state product matrix, a quantum algorithm adiabatic in section 5. Finally, section 6 considers the behavior of some families of quantum algorithms under the standpoint of the theory of mayorización and section 7 collect some possible future directions from this work.
