  We present a quantum algorithm for calculating the vibronic spectrum of a
molecule, a useful but classically hard problem in chemistry. We show several
advantages over previous quantum approaches: vibrational anharmonicity is
naturally included; after measurement, some state information is preserved for
further analysis; and there are potential error-related benefits. Considering
four triatomic molecules, we numerically study truncation errors in the
harmonic approximation. Further, in order to highlight the fact that our
quantum algorithm's primary advantage over classical algorithms is in
simulating anharmonic spectra, we consider the anharmonic vibronic spectrum of
sulfur dioxide. In the future, our approach could aid in the design of
materials with specific light-harvesting and energy transfer properties, and
the general strategy is applicable to other spectral calculations in chemistry
and condensed matter physics.
