  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 (1D) ion chain with up to 8 qubits through stroboscopic
sequences of commuting Hamiltonians. %with a thorough understanding of the
error sources and deviation from the target Hamiltonian. In addition, we extend
this method to non-commuting 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.
