  We study how chaos, introduced by a weak perturbation, affects the
reliability of the output of analog quantum simulation. As a toy model, we
consider the Lipkin-Meshkov-Glick (LMG) model. Inspired by the semiclassical
behavior of the order parameter in the thermodynamic limit, we propose a
protocol to measure the quantum phase transition in the ground state and the
dynamical quantum phase transition associated with quench dynamics. We show
that the presence of a small time-dependent perturbation can render the
dynamics of the system chaotic. We then show that the estimates of the critical
points of these quantum phase transitions, obtained from the quantum simulation
of its dynamics, are robust to the presence of this chaotic perturbation, while
other aspects of the system, such as the mean magnetization are fragile, and
therefore cannot be reliably extracted from this simulator. This can be
understood in terms of the simulated quantities that depend on the global
structure of phase space vs. those that depend on local trajectories.
