  Towards the goal of quantum computing for lattice quantum chromodynamics, we
present a loop-string-hadron (LSH) framework in 1+1 dimensions for describing
the dynamics of SU(3) gauge fields coupled to staggered fermions. This novel
framework was previously developed for an SU(2) lattice gauge theory in
$d\leq3$ spatial dimensions and its advantages for classical and quantum
algorithms have thus far been demonstrated in $d=1$. The LSH approach uses
gauge invariant degrees of freedoms such as loop segments, string ends, and
on-site hadrons, it is free of all nonabelian gauge redundancy, and it is
described by a Hamiltonian containing only local interactions. In this work,
the SU(3) LSH framework is systematically derived from the reformulation of
Hamiltonian lattice gauge theory in terms of irreducible Schwinger bosons,
including the addition of staggered quarks. Furthermore, the superselection
rules governing the LSH dynamics are identified directly from the form of the
Hamiltonian. The SU(3) LSH Hamiltonian with open boundary conditions has been
numerically confirmed to agree with the completely gauge-fixed Hamiltonian,
which contains long-range interactions and does not generalize to either
periodic boundary conditions or to $d>1$.
