Quantum simulation with two-dimensional ion crystal*

Quantum simulation can provide a solution of a complex problem that can be intractable in classical means. In particular, it is challenging to numerically simulate many-body quantum system in 2-dimension, which reveals geometric frustration and topological phase. A trapped-ion system has been used to realize quantum simulation of spin-models, but existing experiments were mostly limited to 1-dimensional ion-chain. Here, we present the quantum simulation with 2-dimensional ion-crystal that experimentally study quantum magnets on triangular lattice, and adiabatically prepare their ground-state for the first time. The 2D crystals are confined in a monolithic ion-trap, which eliminates disturbance of micromotions for quantum operations. Spin-dependent-force is applied to generate the Ising Hamiltonian, and ramp the strength of transverse field to adiabatically reach the ground state of the Ising Hamiltonian. We experimentally study the ferromagnetic and the frustrated ground states with ion numbers up to 10 ions. Our work paves the way to simulate 2-dimensional materials with ion-trap platform.