  Recent experimental advances have inspired the development of theoretical
tools to describe the non-equilibrium dynamics of quantum systems. Among them
an exact representation of quantum spin systems in terms of classical
stochastic processes has been proposed. Here we provide first steps towards the
extension of this stochastic approach to bosonic systems by considering the
one-dimensional quantum quartic oscillator. We show how to exactly parameterize
the time evolution of this prototypical model via the dynamics of a set of
classical variables. We interpret these variables as stochastic processes,
which allows us to propose a novel way to numerically simulate the time
evolution of the system. We benchmark our findings by considering analytically
solvable limits and providing alternative derivations of known results.
