  A growing body of work has established the modelling of stochastic processes
as a promising area of application for quantum techologies; it has been shown
that quantum models are able to replicate the future statistics of a stochastic
process whilst retaining less information about the past than any classical
model must -- even for a purely classical process. Such memory-efficient models
open a potential future route to study complex systems in greater detail than
ever before, and suggest profound consequences for our notions of structure in
their dynamics. Yet, to date methods for constructing these quantum models are
based on having a prior knowledge of the optimal classical model. Here, we
introduce a protocol for blind inference of the memory structure of quantum
models -- tailored to take advantage of quantum features -- direct from
time-series data, in the process highlighting the robustness of their structure
to noise. This in turn provides a way to construct memory-efficient quantum
models of stochastic processes whilst circumventing certain drawbacks that
manifest solely as a result of classical information processing in classical
inference protocols.
