Phase diagram of the Schwinger model by adiabatic preparation of states on a quantum simulator

We argue the feasibility of studying the phase structure of a quantum physical system on quantum devices via adiabatic preparation of states. We introduce a method and successfully test it in application to the Schwinger model in the presence of a topological $\ensuremath{\theta}$ term. We explore the first-order-phase-transition and the no-transition regions of the corresponding phase diagram. The core idea of the method is to separately evolve the ground and the first excited states with a time-dependent Hamiltonian, the time dependence of which interpolates between different values of $\ensuremath{\theta}$. Despite our approach being a direct application of the adiabatic theorem, in some cases we are able to demonstrate its advantages in comparison to a different method from the literature that also employs adiabatic state preparation.