Quantum simulators are well-calibrated, highly controllable quantum many-body systems, being engineered to solve classically intractable computational problems. The key issues are scalability, control fidelities, and high-dimensional connectivities. Among many platforms, Rydberg-atom quantum simulators draw the latest attention because of their possible advantage in high-dimensional connection programming. They are mesoscopic-scale, deterministic arrangements of neutral atoms with controllable strong local interactions induced by Rydberg-atom excitations. In recent demonstrations, these systems are used to produce as many as 20-qubit GHZ entangled states and to observe quantum many-body phenomena involved with Ising-type or $XY$ quantum spin models across phase transitions. Of particular relevance in the context of the present work, three-dimensional qubit arrangements are possible in Rydberg-atom quantum simulators.

In this work, continuous tuning of three-dimensional arrangements of Rydberg atoms is realized and their coupled eigenenergies and eigenstates probed in particular during their structural deformations. We probe various connected-graph geometries of up to six qubits, in which the vertices and edges of the graphs respectively represent atoms and Rydberg-blockaded atom pairs. Conformation spectra of star, complete, cyclic, and diamond graphs are measured for four interacting atoms and antiprism structures for six atoms. The energy level shifts and merges of the tested structural transformations are clearly observed with Fourier-transform time-domain spectroscopy, and the results are all confirmed with the model few-body quantum Ising Hamiltonian. This work demonstrates the possibility of continuous tuning of three-dimensional qubit geometries and thus programming, in terms of qubit connections, of many-body spin-Hamiltonians in a broader range than before.