Quantum-Ising Hamiltonian programming in trio, quartet, and sextet qubit systems

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.