  Mapping out phase diagrams of quantum systems using classical simulations can
be challenging or intractable due to the computational resources required to
simulate even small quantum systems far away from the thermodynamic limit. We
investigate using quantum computers and the Variational Quantum Eigensolver
(VQE) for this task. In contrast to the task of preparing the exact ground
state using VQE, sketching phase diagrams might require less quantum resources
and accuracy, because low fidelity approximations to the ground state may be
enough to correctly identify different phases. We used classical numerical
simulations of low-depth VQE circuits to compute order parameters for four
well-studied spin and fermion models which represent a mix of 1D and 2D, and
exactly-solvable and classically hard systems. We find that it is possible to
predict the location of phase transitions up to reasonable accuracy using
states produced by VQE even when their overlap with the true ground state is
small. Further, we introduce a model-agnostic predictor of phase transitions
based on the speed with which the VQE energy improves with respect to the
circuit depth, and find that in some cases this is also able to predict phase
transitions.
