  We analyze the accuracy and sample complexity of variational Monte Carlo
approaches to simulate the dynamics of many-body quantum systems classically.
By systematically studying the relevant stochastic estimators, we are able to:
(i) prove that the most used scheme, the time-dependent Variational Monte Carlo
(tVMC), is affected by a systematic statistical bias or exponential sample
complexity when the wave function contains some (possibly approximate) zeros,
an important case for fermionic systems and quantum information protocols; (ii)
show that a different scheme based on the solution of an optimization problem
at each time step is free from such problems; (iii) improve the sample
complexity of this latter approach by several orders of magnitude with respect
to previous proofs of concept. Finally, we apply our advancements to study the
high-entanglement phase in a protocol of non-Clifford unitary dynamics with
local random measurements in 2D, first benchmarking on small spin lattices and
then extending to large systems.
