Digital quantum simulation of a (1+1)D SU(2) lattice gauge theory with ion qudits

Abstract: We present a quantum simulation strategy for a (1+1)D SU(2) non-abelian lattice gauge theory with dynamical matter, a hardcore-gluon Hamiltonian Yang-Mills, tailored to a six-level trapped-ion qudit quantum processor, as recently experimentally realized. We employ a qudit encoding fulfilling gauge invariance, an SU(2) Gauss law. We discuss the experimental feasibility of generalized M\"olmer-S\"orensen gates used to efficiently simulate the dynamics. We illustrate how a shallow circuit with these resources is sufficient to implement scalable digital quantum simulation of the model. We also numerically show that this model, albeit simple, can dynamically manifest physically-relevant properties specific to non-abelian field theories, such as baryon excitations.