Determining Ground-State Phase Diagrams on Quantum Computers via a Generalized Application of Adiabatic State Preparation

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