  Tracking the behaviour of stochastic systems is a crucial task in the
statistical sciences. It has recently been shown that quantum models can
faithfully simulate such processes whilst retaining less information about the
past behaviour of the system than the optimal classical models. We extend these
results to general temporal and symbolic dynamics. Our systematic protocol for
quantum model construction relies only on an elementary description of the
dynamics of the process. This circumvents restrictions on corresponding
classical construction protocols, and allows for a broader range of processes
to be modelled efficiently. We illustrate our method with an example exhibiting
an apparent unbounded memory advantage of the quantum model compared to its
optimal classical counterpart.
