Exploring phase transitions in a quantum dimer using a quantum annealer

It is well known that problems with exponentially decreasing gaps can cause adiabatic quantum computation (AQC) to fail. However, this does not imply that open-system quantum annealing (QA) will also fail for these problems. We consider an archetypical problem that is classically trivial, but difficult for AQC: an Ising ladder exhibiting a first-order phase transition with an exponentially closing gap, and a second-order phase transition with a polynomially closing gap. We investigate the performance of QA at these quantum phase transitions/ gap scalings theoretically using open quantum systems theory and experimentally using the D-Wave quantum annealer.