The question of how to efficiently formulate Hamiltonian gauge theories is experiencing renewed interest due to advances in building quantum simulation platforms. We introduce a reformulation of an SU (2) Hamiltonian lattice gauge theory---a loop-string-hadron (LSH) formulation---that describes dynamics directly in terms of its loop, string, and hadron degrees of freedom, while alleviating several disadvantages of quantum simulating the Kogut-Susskind formulation. This LSH formulation transcends the local loop formulation of d+1-dimensional lattice gauge theories by incorporating staggered quarks, furnishing the algebra of gauge-singlet operators, and being used to reconstruct dynamics between states that have Gauss's law built in to them. LSH operators are then factored into products of ``normalized'' ladder operators and diagonal matrices, priming them for classical or quantum information processing. Self-contained expressions of the Hamiltonian are given up to d=3. The LSH formalism makes little use of structures specific to SU (2), and its conceptual clarity makes it an attractive approach to apply to other non-Abelian groups like SU (3).
Raychowdhury et al. (Mon,) studied this question.