  A custom-built and precisely controlled quantum system may offer access to a
fundamental understanding of another, less accessible system of interest. A
universal quantum computer is currently out of reach, but an analog quantum
simulator that makes the relevant observables, interactions, and states of a
quantum model accessible could permit experimental insight into complex quantum
dynamics that are intractable on conventional computers. Several platforms have
been suggested and proof-of-principle experiments have been conducted. Here we
characterise two-dimensional arrays of three ions trapped by radio-frequency
fields in individually controlled harmonic wells forming equilateral triangles
with side lengths 40 and 80 micrometer. In our approach, which is scalable to
arbitrary two dimensional lattices, we demonstrate individual control of the
electronic and motional degrees of freedom, preparation of a fiducial initial
state with ion motion close to the ground state, as well as tuning of crucial
couplings between ions within experimental sequences. Our work paves the way
towards an analog quantum simulator of two-dimensional systems designed at
will.
