Smith, JacobWhen a system thermalizes it loses all memory of its initial conditions. Even within a closed quantum system, subsystems usually thermalize using the rest of the system as a heat bath. Exceptions to quantum thermalization have been observed, but typically require inherent symmetries or noninteracting particles in the presence of static disorder. The prediction of many-body localization (MBL), in which disordered quantum systems can fail to thermalize despite strong interactions and high excitation energy, was therefore surprising and has attracted considerable theoretical attention. We experimentally generate MBL states by applying an Ising Hamiltonian with long-range interactions and programmably random disorder to ten spins initialized far from equilibrium with respect to the Hamiltonian. Using experimental and numerical methods we observe the essential signatures of MBL: initial state memory retention, Poissonian distributed many-body energy level spacings, and evidence of long-time entanglement growth. Our platform can be scaled to more spins, where detailed modeling of MBL becomes impossible.enDissertationPhysicsMany-body localizationQuantum computationQuantum physicsQuantum simulationQuantum thermalizationTrapped ions