  Agent-based models are a powerful tool for studying the behaviour of complex
systems that can be described in terms of multiple, interacting ``agents''.
However, because of their inherently discrete and often highly non-linear
nature, it is very difficult to reason about the relationship between the state
of the model, on the one hand, and our observations of the real world on the
other. In this paper we consider agents that have a discrete set of states
that, at any instant, act with a probability that may depend on the environment
or the state of other agents. Given this, we show how the mathematical
apparatus of quantum field theory can be used to reason probabilistically about
the state and dynamics the model, and describe an algorithm to update our
belief in the state of the model in the light of new, real-world observations.
Using a simple predator-prey model on a 2-dimensional spatial grid as an
example, we demonstrate the assimilation of incomplete, noisy observations and
show that this leads to an increase in the mutual information between the
actual state of the observed system and the posterior distribution given the
observations, when compared to a null model.
