We introduce tensor lattice field theory as a method to discretize the path-integral formulations of lattice models suitable for quantum computing. The individual tensors appear as the local building blocks of the reformulation. They contain all the information about the model and its symmetries. Using the transfer matrix formalism, we introduce the Hilbert space and truncations that respect the symmetries. We present a quantum Hamiltonian for scalar electrodynamics in one and two spatial dimensions where the electric field Hilbert space is approximated by a spin-1 triplet. We discuss quantum simulators for this model obtained by assembling arrays of Rydberg atoms with ladder structures and report on the recent experimental progress towards this implementation.