  Several quantum hardware platforms, while being unable to perform fully
fault-tolerant quantum computation, can still be operated as analogue quantum
simulators for addressing many-body problems. However, due to the presence of
errors, it is not clear to what extent those devices can provide us with an
advantage with respect to classical computers. In this work we consider the use
of noisy analogue quantum simulators for computing physically relevant
properties of many-body systems both in equilibrium and undergoing dynamics. We
first formulate a system-size independent notion of stability against extensive
errors, which we prove for Gaussian fermion models, as well as for a restricted
class of spin systems. Remarkably, for the Gaussian fermion models, our
analysis shows the stability of critical models which have long-range
correlations. Furthermore, we analyze how this stability may lead to a quantum
advantage, for the problem of computing the thermodynamic limit of many-body
models, in the presence of a constant error rate and without any explicit error
correction.
