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

Fluctuations and Non-Hermiticity in the Stochastic Approach to Quantum Spins