  We investigate the non-equilibrium dynamics of isolated quantum spin systems
via an exact mapping to classical stochastic differential equations. We show
that one can address significantly larger system sizes than recently obtained,
including two-dimensional systems with up to 49 spins. We demonstrate that the
results for physical observables are in excellent agreement with exact results
and alternative numerical techniques where available. We further develop a
hybrid stochastic approach involving matrix product states. In the presence of
finite numerical sampling, we show that the non-Hermitian character of the
stochastic representation leads to the growth of the norm of the time-evolving
quantum state and to departures for physical observables at late times. We
demonstrate approaches that correct for this and discuss the prospects for
further development.
