  Quantum algorithms are promising candidates for the enhancement of
computational efficiency for a variety of computational tasks, allowing for the
numerical study of physical systems intractable to classical computers. In the
Noisy Intermediate Scale Quantum (NISQ) era of quantum computing, however,
quantum resources are limited and thus quantum algorithms utilizing such
resources efficiently are highly coveted. We present a resource-efficient
quantum algorithm for bosonic quantum simulations using the Variational Quantum
Eigensolver algorithm with the Unitary Coupled Cluster ansatz. Our algorithm
proves to significantly increase accuracy with a simultaneous large reduction
of required quantum resources, exhibiting increased performance for all
relevant parameters compared to current approaches. It provides a shorter route
to achieve a quantum advantage in bosonic quantum simulations along with a
flexible method to tailor the utilized quantum resources of a quantum computer.
While being specifically feasible for NISQ devices, the advantages of our
algorithm are independent of hardware parameters, maintaining its superiority
for future fault tolerant quantum devices. The study of vibrational properties
of molecular systems is crucial in a variety of contexts, such as spectroscopy,
fluorescence, chemical reaction dynamics and transport properties. Thus, our
algorithm provides a resource-efficient flexible approach to study such
applications in the context of quantum computational chemistry on quantum
computers.
