The future of Space Exploration is entwined with the future of artificial intelligence (AI) and machine learning. Autonomous rovers, unmanned spacecraft, and remote space habitats must all make intelligent decisions with little or no human guidance. The decision-making required of such NASA assets stretches machine intelligence to its limits. Currently, AI problems are tackled using a variety of heuristic approaches, and practitioners are constantly trying to find new and better techniques. To achieve a radical breakthrough in AI, radical new approaches are needed. Quantum computing is one such approach.Many of the hard combinatorial problems in space exploration are instances of NP-complete or NP-hard problems. Neither traditional computers nor quantum computers are expected to be able to solve all instances of such problems efficiently. Many heuristic algorithms, such as simulated annealing, support vector machines, and SAT solvers, have been developed to solve or approximate solutions to practical instances of these problems. The efficacy of these approaches is generally determined by running them on benchmark sets of problem instances. Such empirical testing for quantum algorithms requires the availability of quantum hardware.Quantum annealing machines, analog quantum computational devices, are designed to solve discrete combinatorial optimization problems using properties of quantum adiabatic evolution. We are now on the cusp of being able to run small-scale examples of these problems on actual quantum annealing hardware which will enable us to test empirically the performance of quantum annealing on these problems. For example, D-Wave builds quantum annealing machines based on superconducting qubits. While at present noise and decoherence in quantum annealing devices cannot be easily controlled or corrected, these devices have been shown to display multi-spin tunneling, a distinct quantum phenomenon at the root of the quantum annealing process. In order to attack an optimization problem on these machines, the problem must be formulated in quadratic unconstrained binary optimization form in which the cost function is strictly quadratic in bit assignments (in physics applications this form is often referred to as an Ising model). The above limitation is not fundamental: all NP-complete problems can be mapped to this form. However, an optimal mapping involving small or no overhead in terms of additional bits is of significant practical interest because of the limited size of early quantum annealing machines.In this article, we discuss a sampling of the hardest artificial intelligence problems in space exploration in the context in which they emerge. We show how to map them onto equivalent Ising models