  Geometric frustration in two-dimensional Ising models allows for a wealth of
exotic universal behavior, both Ising and non-Ising, in the presence of quantum
fluctuations. In particular, the triangular antiferromagnet and Villain model
in a transverse field can be understood through distinct XY pseudospins, but
have qualitatively similar phase diagrams including a quantum phase transition
in the (2+1)-dimensional XY universality class. While the quantum dynamics of
modestly-sized systems can be simulated classically using tensor-based methods,
these methods become infeasible for larger lattices. Here we perform both
classical and quantum simulations of these dynamics, where our quantum
simulator is a superconducting quantum annealer. Our observations on the
triangular lattice suggest that the dominant quench dynamics are not described
by the quantum Kibble-Zurek scaling of the quantum phase transition, but rather
a faster coarsening dynamics in an effective two-dimensional XY model in the
ordered phase. Similarly, on the Villain model, the scaling exponent does not
match the Kibble-Zurek expectation. These results demonstrate the ability of
quantum annealers to simulate coherent quantum dynamics and scale beyond the
reach of classical approaches.
