Bachelor and diploma theses

The adiabatic theorem tells us that evolving an eigenstate with a weakly time-dependent Hamiltonian results in a state near an instantaneous eigenstate, if some conditions are met. In this diploma thesis, we will first analyze these conditions in some depth. Second, we will look for computational applications of such processes, and their generalizations (quantum annealing). We will focus on stoquastic Hamiltonians, in particular those related to continuous-time quantum walks.