One broad goal of quantum simulation is to start a simple quantum system in its ground state and slowly evolve the Hamiltonian to a complex one, maintaining the ground state throughout the evolution (called adiabatic state preparation). This provides a natural setting to create a highly entangled and correlated quantum state if the final Hamiltonian supports such a ground state. In ion-trap-based quantum simulations, coherence times are too short to allow for such ground-state evolution for large chains, because the rapid evolution of the system creates excitations to higher energy states. Because the probability for this excitation depends exponentially on the excitation energy and because the thermal distribution also depends exponentially on the excitation energy, we investigate whether this so-called diabatic excitation can create the analog of a thermal distribution; as this could serve as an alternative for creating thermal states of complex quantum systems without requiring contact with a heat bath. In this work, we explore this relationship and determine situations where diabatic excitation can approximately create thermal
states.
