  Quantum gas systems are ideal analog quantum simulation platforms for
tackling some of the most challenging problems in strongly correlated quantum
matter. However, they also expose the urgent need for new theoretical
frameworks. Simple models in one dimension, well studied with conventional
methods, have received considerable recent attention as test cases for new
approaches. Ladder models provide the logical next step, where established
numerical methods are still reliable, but complications of higher dimensional
effects like gauge fields can be introduced. In this paper, we investigate the
application of the recently developed neural-network quantum states in the
two-leg Bose-Hubbard ladder under strong synthetic magnetic fields. Based on
the restricted Boltzmann machine and feedforward neural network, we show that
variational neural networks can reliably predict the superfluid-Mott insulator
phase diagram in the strong coupling limit comparable with the accuracy of the
density-matrix renormalization group. In the weak coupling limit, neural
networks also diagnose other many-body phenomena such as the vortex, chiral,
and biased-ladder phases. Our work demonstrates that the two-leg Bose-Hubbard
model with magnetic flux is an ideal test ground for future developments of
neural-network quantum states.
