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Quantum systems undergoing non-unitary adiabatic evolution present unique characteristics with applications in the field of Quantum Computation. In this dissertation, we study the formalism of quantum open systems, the theory of dynamical semigroups and Lindblad operators. We enunciate and prove the adiabatic theorem as formulated by T. Kato in order to understand the main idea and formalism behind adiabatic evolutions. We use these results to describe the optimization problem of adiabatic paths in dispersive quantum systems (whose dynamics is given by a class of Lindblad operators) and, following the outline designed by Avron et al. [8], we obtain the conditions so that this optimization is unique and we apply this result in quantum search algorithms.

Parametrizações otimais de trajetórias adiabáticas em sistemas quânticos dissipativos