  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.
