  Rydberg-atom quantum simulators are of keen interest because of their
possibilities towards high-dimensional qubit architectures. Here we report
three-dimensional conformation spectra of quantum-Ising Hamiltonian systems
with programmed qubit connections. With a Rydberg-atom quantum simulator,
various connected graphs, in which vertices and edges represent atoms and
blockaded couplings, respectively, are constructed in two or three-dimensional
space and their eigenenergies are probed during their topological
transformations. Star, complete, cyclic, and diamond graphs, and their
geometric intermediates, are tested for four atoms and antiprism structures for
six atoms. Spectroscopic resolution (dE/E) less than 10% is achieved and the
observed energy level shifts and merges through structural transformations are
in good agreement with the model few-body quantum-Ising Hamiltonian.
