  We adapt the robust phase estimation algorithm to the evaluation of energy
differences between two eigenstates using a quantum computer. This approach
does not require controlled unitaries between auxiliary and system registers or
even a single auxiliary qubit. As a proof of concept, we calculate the energies
of the ground state and low-lying electronic excitations of a hydrogen molecule
in a minimal basis on a cloud quantum computer. The denominative robustness of
our approach is then quantified in terms of a high tolerance to coherent errors
in the state preparation and measurement. Conceptually, we note that all
quantum phase estimation algorithms ultimately evaluate eigenvalue differences.
