  Molecular vibrations underpin important phenomena such as spectral
properties, energy transfer, and molecular bonding. However, obtaining a
detailed understanding of the vibrational structure of even small molecules is
computationally expensive. While several algorithms exist for efficiently
solving the electronic structure problem on a quantum computer, there has been
comparatively little attention devoted to solving the vibrational structure
problem with quantum hardware. In this work, we discuss the use of quantum
algorithms for investigating both the static and dynamic vibrational properties
of molecules. We introduce a physically motivated unitary vibrational coupled
cluster ansatz, which also makes our method accessible to noisy, near-term
quantum hardware. We numerically test our proposals for the water and sulfur
dioxide molecules.
