Qubits on programmable geometries with a trapped-ion quantum processor

Geometry and dimensionality have played crucial roles in our understanding of the fundamental laws of nature, with examples ranging from curved space time in general relativity to modern theories of quantum gravity. In quantum many-body systems, the entanglement structure can change if the constituents are connected differently, leading to altered bounds for correlation growth and difficulties for classical computers to simulate large systems. While a universal quantum computer can perform digital simulations, an analog-digital hybrid quantum processor offers advantages such as parallelism. Here, we engineer a class of high-dimensional Ising interactions using a linear one-dimensional ion chain with up to eight qubits through stroboscopic sequences of commuting Hamiltonians. In addition, we extend this method to noncommuting circuits and demonstrate the quantum XY and Heisenberg models using Floquet periodic drives with tunable symmetries. The realization of higher-dimensional spin models offers new opportunities ranging from studying topological phases of matter or quantum spin glasses to future fault-tolerant quantum computation.