  Quantum phase transitions materialize as level crossings in the ground-state
energy when the parameters of the Hamiltonian are varied. The resulting
ground-state phase diagrams are straightforward to determine by exact
diagonalization on classical computers, but are challenging on quantum
computers because of the accuracy needed and the near degeneracy of competing
states close to the level crossings. In this work, we use a local adiabatic
ramp for state preparation to allow us to directly compute ground-state phase
diagrams on a quantum computer via time evolution. This methodology is
illustrated by examining the ground states of the XY model with a magnetic
field in the z-direction in one dimension. We are able to calculate an accurate
phase diagram on both two and three site systems using IBM quantum machines.
