Warm start adiabatic state preparation

State preparation is a critical prerequisite for running any quantum algorithm. Adiabatic state preparation is a promising heuristic algorithm for state preparation. However, warm-starting adiabatic state preparation using classical simulation methods remains challenging. A main obstacle to warm-starting is that we lack a systematic approach to embed arbitrary classical states into the ground states of Hamiltonians that are efficient to simulate on quantum computers. Here, we present two methods to embed any preparable state onto the ground state of a simulatable Hamiltonian. We compare these methods to existing approaches in the literature and find they can improve the total adiabatic time.