  Amorphous solids, i.e., systems which feature well-defined short-range
properties but lack long-range order, constitute an important research topic in
condensed matter. While their microscopic structure is known to differ from
their crystalline counterpart, there are still many open questions concerning
the emergent collective behavior in amorphous materials. This is particularly
the case in the quantum regime, where the numerical simulations are extremely
challenging. In this article, we instead propose to explore amorphous quantum
magnets with an analog quantum simulator. To this end, we first present an
algorithm to generate amorphous quantum magnets, suitable for Rydberg
simulators of the Ising model. Subsequently, we use semiclassical approaches to
get a preliminary insight of the physics of the model. In particular, for
ferromagnetic interactions, we calculate mean-field phase diagrams, and use the
linear-spin-wave theory to study localization properties and dynamical
structure factors of the excitations. For antiferromagnetic interactions, we
show that amorphous magnets exhibit a complex classical energy landscape by
means of simulated annealing. Finally, we outline an experimental proposal
based on Rydberg atoms in programmable tweezer arrays, thus opening the road
towards the study of amorphous quantum magnets in regimes difficult to simulate
classically.
