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We introduce a way to express compact quantum electrodynamics with dynamicalmatter on two- and three-dimensional spatial lattices in a gaugeredundancy-free manner while preserving translational invariance. Bytransforming to a rotating frame, where the matter is decoupled from the gaugeconstraints, we can express the gauge field operators in terms of dualoperators. In two space dimensions, the dual representation is completely freeof any local constraints. In three space dimensions, local constraints amongthe dual operators remain but involve only the gauge field degrees of freedom(and not the matter degrees of freedom). These formulations, which reduce therequired Hilbert space dimension, could be useful for both numerical(classical) Hamiltonian computations and quantum simulation or computation.

A gauge redundancy-free formulation of compact QED with dynamical matter for quantum and classical computations