Moore's law continues to push the boundaries of capabilities with today's digital electronics, albeit with a much slower rate than decades prior. The end of Dennard scaling has similarly made digital electronics difficult to continue scaling with energy efficiency. The breakdown of these two observations first made in the early days of computing have lead to consequences in today's computing needs: Large-scale compute needed by artificial intelligence systems now require warehouses full of computers. Embedded smart-sensors for edge computing are limited by the energy efficiency of digital electronics. Analog computers have emerged as a platform for performing sensing and machine learning tasks owing to their energy efficiency, the ability to interface directly with the analog world, and the robustness of certain tasks like machine learning to hardware imperfections. In this thesis, we present two experiments that demonstrate two novel applications of analog computing with physical systems. In the first experiment, we construct a highly-multimode frequency domain fiber laser that is capable of simulating physics in two- and three-dimensional large-scale lattices. We leverage the programmability and scale of our simulator to study exotic condensed matter phenomena, such as time-reversal symmetry-breaking, non-Hermitian physics, and dynamics in non-euclidean geometries. In this work, we simulate lattices with up to 100,000 sites -- orders of magnitude greater than previously achieved in photonic simulators. In the second experiment, we describe and perform a proof-of-principle demonstration of a new form of application for quantum devices. In between the fields of quantum sensing and quantum computation, we perform microwave signal processing on ultra-low power signals, and propose a route towards achieving a quantum computational-sensing advantage: a quantum advantage in performing a computational task on analog signals that are inaccessible to any classical receiver. Our results provide the first step towards achieving such an advantage.