  The quest for experimental platforms that allow for the exploration, and even
control, of the interplay of low dimensionality and frustration is a
fundamental challenge in several fields of quantum many-body physics, such as
quantum magnetism. Here, we propose the use of cold crystals of trapped ions to
study a variety of frustrated quantum spin ladders. By optimizing the trap
geometry, we show how to tailor the low dimensionality of the models by
changing the number of legs of the ladders. Combined with a method for
selectively hiding of ions provided by laser addressing, it becomes possible to
synthesize stripes of both triangular and Kagome lattices. Besides, the degree
of frustration of the phonon-mediated spin interactions can be controlled by
shaping the trap frequencies. We support our theoretical considerations by
initial experiments with planar ion crystals, where a high and tunable
anisotropy of the radial trap frequencies is demonstrated. We take into account
an extensive list of possible error sources under typical experimental
conditions, and describe explicit regimes that guarantee the validity of our
scheme.
