Simulating the real-time dynamics of non-abelian lattice gauge theories (LGTs) is an outstanding challenge, where quantum simulators can provide a practical advantage over classical methods. In this talk, I will present our recent results concerning co-designed hardware as well as new quantum algorithms towards achieving this goal. Specifically, I review a qudit architecture based on Rydberg atoms for implementing pure LGTs , and introduce an extension to a hybrid fermion-qudit processor, where the fermionic statistics of dynamical matter is accounted for at the hardware level . On the software level, I briefly discuss a q-deformed formulation of LGTs as an alternative truncation of the infinite-dimensional local Hilbert space of non-abelian gauge fields, which provides the basis for efficient classical and quantum spin network algorithms .
 González-Cuadra, Zache, Carrasco, Kraus & Zoller, Phys. Rev. Lett. 129, 160501 (2022)
 Zache, González-Cuadra & Zoller, arXiv:2303.08683 (2023)
 Zache, González-Cuadra & Zoller, arXiv:2304.02527 (2023)