Algorithms and Platforms for Quantum Science and Technology

Abstract

The field of quantum science and technology has seen tremendous recent progress. Despite this, building large-scale quantum devices remains daunting as fault tolerance is a distant goal in all current experimental platforms. This dissertation discusses two complementary avenues towards practically relevant quantum technologies. In the first part, we explore physically inspired quantum algorithms that run on near-term devices without quantum error correction. We investigate the robustness of adiabatic quantum algorithms, placing stringent requirements on noise induced by the environment. In addition, we construct quantum algorithms that sample from classical Gibbs distributions. These algorithms elucidate connections between computational complexity and phase transitions and provide physical insight into the origin of quantum speedup. The second part focuses on novel platforms and optical interfaces for quantum applications. We demonstrate that optical resonances in ordered arrays of atoms and atomically thin semiconductors offer a powerful tool to control and manipulate light at both the classical and single-photon level. We further study interactions between optical excitations and charge carriers in two-dimensional semiconductors, which give rise to complex quantum many-body dynamics in a largely unexplored regime.