Search for efficient formulations for Hamiltonian simulation of non-Abelian lattice gauge theories

Hamiltonian formulation of lattice gauge theories (LGTs) is the most natural framework for purpose quantum simulation, an area research that growing with advances in quantum-computing algorithms and hardware. It, therefore, remains important task to identify accurate, while computationally economic, formulation(s) such theories, considering necessary truncation imposed on Hilbert space bosons any finite computing resources. This paper a first step toward addressing this question case non-Abelian LGTs, which further require imposition Gauss's laws space, introducing additional computational complexity. Focusing SU(2) LGT 1+1 D coupled matter, number different formulations original Kogut-Susskind are analyzed regard dependence dimension physical boundary conditions, system's size, cutoff excitations bosons. The impact dependencies accuracy spectrum dynamics examined, (classical) computational-resource requirements given these considerations studied. Besides well-known angular-momentum theory, cases purely fermionic bosonic (with open conditions), Loop-String-Hadron analyzed, along brief discussion Quantum Link Model same theory. Clear advantages found working implements priori using complete set gauge-invariant operators. Although small lattices studied numerical analysis work, only simplest considered, range conclusions will be applicable larger systems potentially higher dimensions.