Protecting gauge symmetries in the the dynamics of SU(3) lattice gauge theories

Quantum simulation of the dynamics of a lattice gauge theory demands imposing on-site constraints. Ideally, the dynamics remain confined within the physical Hilbert space, where all the states satisfy those constraints. For non-Abelian gauge theories, implementing local constraints is non-trivial, as is keeping the dynamics confined in the physical Hilbert space, considering the erroneous quantum devices. SU(3) gauge group, albeit crucial for describing the strong interaction of nature, is notorious for studying via Hamiltonian simulation. This work presents a couple of symmetry protection protocols for simulating the exact dynamics of SU(3) gauge theory in $1+1$ dimension. The first protocol doesn't require imposing any local symmetry but relies on protecting global symmetries, which are Abelian with a preferred choice of framework, namely the loop-string-hadron framework. Generalization to a higher dimension is possible, however, the protection scheme needs to be local for that case but is still Abelian and thus advantageous. The symmetry protection schemes presented here are important steps towards quantum simulating the full theory of quantum chromodynamics.