Simulating the transverse-field Ising model on the kagome lattice using a programmable quantum annealer

The presence of competing interactions arising from geometry leads to frustration in quantum spin models. As a consequence, the ground state of such systems often displays a large degeneracy that can be lifted by thermal or quantum effects. One such example is the antiferromagnetic Ising model on the kagome lattice. It was shown that while the same model on the triangular lattice is ordered at zero temperature for small transverse field as a result of an order by disorder mechanism, the kagome lattice resists any such effects and exhibits only short range spin correlations and a trivial paramagnetic phase. We embed this model on the latest architecture of D-Wave's quantum annealer, the Advantage2 prototype, which uses the highly connected Zephyr graph. Using advanced embedding and calibration techniques, we are able to embed a kagome lattice with mixed open and periodic boundary conditions of 231 sites on the full graph of the currently available prototype. Through forward annealing experiments, we show that under a finite longitudinal field the system exhibits a one-third magnetization plateau, consistent with a classical spin liquid state of reduced entropy. An anneal-pause-quench protocol is then used to extract an experimental ensemble of states resulting from the equilibration of the model at finite transverse and longitudinal field. This allows us to construct a partial phase diagram and confirm that the system exits the constrained Hilbert space of the classical spin liquid when subjected to a transverse field. We connect our results to previous theoretical results and quantum Monte Carlo simulation, which helps us confirm the validity of the quantum simulation realized here. With these results, we are able to provide an understanding into the nature of the phase diagram of this model while extracting insight into the performance of the D-Wave quantum annealer to simulate nontrivial quantum systems in equilibrium.