  We introduce a framework for the calculation of ground and excited state
energies of bosonic systems suitable for near-term quantum devices and apply it
to molecular vibrational anharmonic Hamiltonians. Our method supports generic
reference modal bases and Hamiltonian representations, including the ones that
are routinely used in classical vibrational structure calculations. We test
different parametrizations of the vibrational wave function, which can be
encoded in quantum hardware, based either on heuristic circuits or on the
bosonic Unitary Coupled Cluster Ansatz. In particular, we define a novel
compact heuristic circuit and demonstrate that it provides the best compromise
in terms of circuit depth, optimization costs, and accuracy. We evaluate the
requirements, number of qubits and circuit depth, for the calculation of
vibrational energies on quantum hardware and compare them with state-of-the-art
classical vibrational structure algorithms for molecules with up to seven
atoms.
