Creating thermal distributions from diabatic excitations in ion-trap-based quantum simulation

The goal of adiabatic ground-state preparation is to start a simple quantum system in its ground state and adiabatically evolve the Hamiltonian to a complex one, maintaining the ground state throughout the evolution. In ion-trap-based quantum simulations, coherence times are too short to allow for adiabatic evolution for large chains, so the system evolves diabatically, creating excitations to higher energy states. Because the probability for diabatic excitation depends exponentially on the excitation energy and because the thermal distribution also depends exponentially on the excitation energy, we investigate whether the diabatic excitation can create 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 such a thermal state.