  High-dimensional quantum information processing has emerged as a promising
avenue to transcend hardware limitations and advance the frontiers of quantum
technologies. Harnessing the untapped potential of the so-called qudits
necessitates the development of quantum protocols beyond the established qubit
methodologies. Here, we present a robust, hardware-efficient, and extensible
approach for operating multidimensional solid-state systems using
Raman-assisted two-photon interactions. To demonstrate its efficacy, we
construct a set of multi-qubit operations, realize highly entangled
multidimensional states including atomic squeezed states and Schr\"odinger cat
states, and implement programmable entanglement distribution along a qudit
array. Our work illuminates the quantum electrodynamics of strongly driven
multi-qudit systems and provides the experimental foundation for the future
development of high-dimensional quantum applications.
