Tunable quantum simulation of spin models with a two-dimensional ion crystal

Quantum spin models have been extensively used to study the properties of strongly correlated systems and to find approximate solutions to combinatorial optimization problems. Trapped-ion systems have reliably demonstrated the quantum simulation of various quantum spin models in one-dimensional chains. The extension of trapped-ion simulators to two dimensions has been an enticing goal for decades. Here we present the quantum simulation of Ising models with two-dimensional ion crystals in a Paul trap. We benchmark the simulator by implementing various spin models with complex interaction networks and adiabatically prepare the corresponding ground states. Spin–spin interactions with different signs and sufficiently large strengths are generated by driving different vibrational modes. We probe the quantum coherence of the simulation by reversing the ramping profile of the transverse field to the initial value and then quantify the probability of returning to the initial state. Then, we test the scalability of the system for a large-scale quantum simulation. Our results show that major portions of the spin states are in the ground state even for highly frustrated spin models. Most quantum simulations of spin models with trapped ions have been restricted to one dimension. Now, tunable simulations of Ising models with single-site detection have been demonstrated in two-dimensional ion crystals.