Scalable physical systems that enable trapping and coherent manipulation of quantum matter lie at the heart of quantum information processing (QIP). Solid-state approaches benefit from rapidly evolving nanotechnology and provide a way towards efficient on-chip quantum devices. In this thesis we show how key ideas from quantum optics can inspire novel setups and implementations for QIP in solid-state settings. To this end, we develop strategies for the realization of well-defined lattices for

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... ctrons and other quasiparticles in semiconductors. The theoretical proposals presented in this thesis may serve as novel platforms for controlling and studying quantum many-body systems. In an introductory passage, we provide a brief summary of goals, recent advances and future directions in quantum information science, highlighting the significant progress that has been made in related fields during the past years. The core of the thesis consists of two parts, one dedicated to quantum systems interacting with elastic waves in solids, and another related to a novel class of two-dimensional semiconductors. In the first part, we theoretically investigate how surface acoustic waves (SAWs) may be used to create well-defined potentials for mobile electrons and other semiconductor quasiparticles. We develop an effective description of electrons coupled to SAW-driven time-dependent electromagnetic fields by modelling their dynamics within a Floquet framework. The underlying physical coupling mechanisms can be based on piezoelectric, piezomagnetic or strain fields, respectively, and we discuss the implications of each. We show that these systems bear striking similarities with atomic, molecular and optical implementations, such as trapped ions and cold neutral atoms in optical lattices. Specific to the solid-state environment are couplings to various sorts of impurities and bulk phonons, which possibly degrade the quality of SAW-based traps. We thus take into account these effects, and investigate the influence of thermal bulk pho [...]