  Quantum particle simulations have largely been based on time-independent,
split-operator schemes in which kinetic and potential operators are interwoven
to provide accurate approximations to system dynamics. These simulations can be
very expensive in terms of the number of gates required, although individual
cases, such as tunneling, have been found where prethreshold simulations are
possible. By prethreshold, we mean a quantum computation or simulation with an
existing architecture and not requiring error correction. In the case of
molecular collisions, switching to a time-dependent formulation can reduce the
system dimensionality significantly and provide an opportunity for
pre-threshold simulation. Here, we study the efficiency of gate-based quantum
simulation of a set of molecular collisions of increasing complexity. We show
that prethreshold quantum simulation of such systems is feasible up to Hilbert
space dimension 8, but beyond that error correction would be required.
