  Variational Monte Carlo with neural network quantum states has proven to be a
promising avenue for evaluating the ground state energy of spin Hamiltonians.
Based on anecdotal evidence, it has been claimed repeatedly in the literature
that neural network quantum state simulations are insensitive to the sign
problem. We present a detailed and systematic study of restricted Boltzmann
machine (RBM) based variational Monte Carlo for quantum spin chains, resolving
exactly how relevant stoquasticity is in this setting. We show that in most
cases, when the Hamiltonian is phase connected with a stoquastic point, the
complex RBM state can faithfully represent the ground state, and local
quantities can be evaluated efficiently by sampling. On the other hand, we
identify a number of new phases that are challenging for the RBM Ansatz,
including non-topological robust non-stoquastic phases as well as stoquastic
phases where sampling is nevertheless inefficient. Our results suggest that
great care needs to be taken with neural network quantum state based
variational Monte Carlo when the system under study is highly frustrated.
