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—in which the dynamical degrees of freedom are localized pieces of flux loops, meson strings, and hadrons. LSH operators are first derived from Schwinger bosons and used to construct a Hilbert space with the non-Abelian Gauss law built into it. They are subsequently factored into products of “normalized” ladder operators and diagonal matrices, priming them for classical or quantum information processing. The LSH formalism alleviates several disadvantages of quantum simulating the Kogut-Susskind formulation and makes little use of structures specific to SU(2). Its conceptual clarity makes it an attractive approach to apply to other non-Abelian groups like SU(3).