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A custom-built and precisely controlled quantum system may offer access to afundamental understanding of another, less accessible system of interest. Auniversal quantum computer is currently out of reach, but an analog quantumsimulator that makes the relevant observables, interactions, and states of aquantum model accessible could permit experimental insight into complex quantumdynamics that are intractable on conventional computers. Several platforms havebeen suggested and proof-of-principle experiments have been conducted. Here wecharacterise two-dimensional arrays of three ions trapped by radio-frequencyfields in individually controlled harmonic wells forming equilateral triangleswith side lengths 40 and 80 micrometer. In our approach, which is scalable toarbitrary two dimensional lattices, we demonstrate individual control of theelectronic and motional degrees of freedom, preparation of a fiducial initialstate with ion motion close to the ground state, as well as tuning of crucialcouplings between ions within experimental sequences. Our work paves the waytowards an analog quantum simulator of two-dimensional systems designed atwill.

Freely configurable quantum simulator based on a two-dimensional array of individually trapped ions