From habitat automation to navigation and scheduling of tasks to networking, the challenges of modern space exploration are as much computational as they are aeronautical. Effective space exploration requires autonomous systems to maximize the utility of a mission that is subject to limited resources. Quantum computing holds great potential for helping NASA to advance the frontier of space exploration by solving larger problems more quickly, with higher quality solutions. Because quantum computing is such a young technology, exploiting that potential as soon as possible requires identifying the most promising applications and developing application-specific techniques that fully utilize small-scale hardware, as well as steering hardware development towards those applications. I propose an integrated, multi-faceted research program that pushes forward the state of the art in near-term quantum computing for applications by exploiting the synergy between three candidate quantum computing platforms: quantum annealing (QA), quantum approximate optimization algorithm, and networks of optical parametric oscillators (OPOs). First, I will map problems related to Air Traffic Management and planning the Stratospheric Observatory for Infrared Astronomy to the formalism used by quantum computers. Second, I will address the current challenge in implementing QA and QAOA due to hardware constraints by designing application-specific techniques for compiling higher level algorithms to low-level hardware. Third, I will utilize previous work on assessing the quantumness and performance of quantum annealers to answer analogous questions for OPOs. Lastly, I will design and implement error-correction schemes for quantum annealing based on continuous measurement and feedback. Addressing QA, QAOA, and OPOs together enables a more robust characterization of their relative strengths and weakness, as well as the extraction of general principles applicable to all near-term quantum computing efforts. This unification will accelerate progress towards near-term quantum computing for applications.