  We reformulate the full quantum dynamics of spin systems using a phase space
representation based on SU(2) coherent states which generates an exact mapping
of the dynamics of any spin system onto a set of stochastic differential
equations. The new representation is superior in practice to an earlier phase
space approach based on Schwinger bosons, with the numerical effort scaling
only linearly with system size. By also implementing extrapolation techniques
from quasiclassical equations to the full quantum limit, we are able to extend
useful simulation times several fold. This approach is applicable in any
dimension including cases where frustration is present in the spin system. The
method is demonstrated by simulating quenches in the transverse field Ising
model in one and two dimensions
