The simulation of strongly correlated systems is one of the most exciting potential applications of quantum computers. There is hope that variational algorithms could enable the simulation of classically intractable problems on near-term devices, but this requires significant reductions in both variational circuit depths and measurement counts. I will discuss our recent efforts to lower these resource demands by eliminating quantum gates and circuits completely and instead optimizing control pulses directly. I will also describe a general approach to designing control pulses that suppress noise while implementing qubit rotations that is based on shaping geometric space curves.