  In recent years, generative artificial neural networks based on restricted
Boltzmann machines (RBMs) have been successfully employed as accurate and
flexible variational wave functions for clean quantum many-body systems. In
this article we explore their use in simulations of disordered quantum spin
models. The standard dense RBM with all-to-all inter-layer connectivity is not
particularly appropriate for large disordered systems, since in such systems
one cannot exploit translational invariance to reduce the amount of parameters
to be optimized. To circumvent this problem, we implement sparse RBMs, whereby
the visible spins are connected only to a subset of local hidden neurons, thus
reducing the amount of parameters. We assess the performance of sparse RBMs as
a function of the range of the allowed connections, and compare it with the one
of dense RBMs. Benchmark results are provided for two sign-problem free
Hamiltonians, namely pure and random quantum Ising chains. The RBM ansatzes are
trained using the unsupervised learning scheme based on projective quantum
Monte Carlo (PQMC) algorithms. We find that the sparse connectivity facilitates
the training process and allows sparse RBMs to outperform the dense
counterparts. Furthermore, the use of sparse RBMs as guiding functions for PQMC
simulations allows us to perform PQMC simulations at a reduced computational
cost, avoiding possible biases due to finite random-walker populations. We
obtain unbiased predictions for the ground-state energies and the magnetization
profiles with fixed boundary conditions, at the ferromagnetic quantum critical
point. The magnetization profiles agree with the Fisher-de Gennes scaling
relation for conformally invariant systems, including the scaling dimension
predicted by the renormalization-group analysis.
