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We present a reformulation of an SU(2) Hamiltonian lattice gauge theory---a loop-string-hadron (LSH) formulation---that characterizes dynamics directly in terms of its loop, string, and hadronic degrees of freedom, while alleviating several apparent disadvantages of quantumly simulating the Kogut-Susskind formulation. This LSH formulation, derived from Schwinger bosons, extends the local loop formulation of (d+1)-dimensional lattice gauge theories by incorporating staggered quarks, furnishing the algebra of gauge-singlet operators, and succinctly encoding the dynamics among states having Gauss’s law built in to them. LSH operators are factored into explicit products of "normalized'' ladder operators and diagonal matrices, priming them for applications in quantum algorithms. Self-contained translations of the Hamiltonian are given and I comment on the next steps for this framework.