  Quantum simulation of complex quantum systems and their properties often
requires the ability to prepare initial states in an eigenstate of the
Hamiltonian to be simulated. In addition, to compute the eigenvalues of a
Hamiltonian is in general a non-trivial problem. Here, we propose a hybrid
quantum-classical probabilistic method to compute eigenvalues and prepare
eigenstates of Hamiltonians which are simulatable with a trapped-ion quantum
processor.
