The variational quantum eigensolver (VQE) is a promising technique for the near-term application of quantum coherent processors to the study of chemical and physical systems. However, the maximum accessible problem size is limited by the number of qubits in a processor that can be mutually entangled with high fidelity. For instance, swap operations needed to distribute entanglement across a device with limited connectivity can quickly consume the available error budget. Here we discuss how to soften this limitation by leveraging the structure of certain simulation problems to reduce the required circuit size. In the first half of our two-part presentation, we will discuss the theoretical formulation of our approach, and applicability to problems of interest. In the second half, we will present data from quantum hardware demonstrating the viability of the approach, and discuss technical details of the experimental realization.