Quantum computers have the potential to solve certain problems in lattice gauge theory that are thought to be exponentially hard for classical computers. The proposed starting point for such computations has been the Kogut-Susskind Hamiltonian supplemented by the Gauss law constraint, with a cutoff on electric field values. There are several disadvantages to this approach, including having to simulate the vast unphysical part of the Hilbert space. We consider pure U(1) gauge theory, and, motivated to restrict the calculation to purely physical states, are immediately led to a duality transformation. We highlight the potential advantages this formulation of lattice gauge theory could have for simulations on quantum computers.